Finite Group Databasebeta

← C2×#13082879 #15661063

Subgroups — C2×#13082879 #15661063

Order 2816.

7418 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082879C2132yesmaximal, direct product factor
2C2×#10623214C212yesmaximal, complemented
3C2×#10623197C211yesmaximal, characteristic, complemented
4C2×#10623251C211yesmaximal, characteristic, complemented
5C2×#10623195C211yesmaximal, characteristic, complemented
6C2×#10623099C212yesmaximal, complemented
7C2×#10623201C212yesmaximal, complemented
8C2×#10623087C212yesmaximal, complemented
9C2×#10623083C212yesmaximal, complemented
10C2×#10623185C212yesmaximal, complemented
11C2×#10623113C212yesmaximal, complemented
12C2×#10623193C212yesmaximal, complemented
13C2×#10623200C212yesmaximal, complemented
14C2×#10623209C212yesmaximal, complemented
15C2×#10623091C212yesmaximal, complemented
16C2×#10623179C211yesmaximal, characteristic, complemented
17C2×#10623246C211yesmaximal, characteristic, complemented
18C2×#10623078C212yesmaximal, complemented
19C2×#10623187C211yesmaximal, characteristic, complemented
20C2×C11×#559C211yesmaximal, characteristic, complemented
21C22×#4341C2211yescharacteristic
22C22×D4×D11C2211yescharacteristic, complemented
23C22×#4339C2212yes—
24C23×C4×D11C2211yescharacteristic, complemented
25C23×Dic22C2211yescharacteristic, complemented
26C11×#559C22116yescomplemented
27C2×C11×#127C2211yescharacteristic
28C2×C11×#124C2212yescomplemented
29C2×C11×#124C2212yescomplemented
30C2×C11×#123C2211yescharacteristic, complemented
31C2×C11×#123C2211yescharacteristic, complemented
32C2×C11×#123C2212yescomplemented
33C2×C4×Q8×C11C2212yescomplemented
34C2×C4×D4×C11C2212yescomplemented
35C2×C4×D4×C11C2212yescomplemented
36C2×#67000C2212yes—
37C2×#67000C2212yescomplemented
38C2×#66999C2212yescomplemented
39C2×#66997C2212yescomplemented
40C2×#66993C2211yescharacteristic
41C2×#66992C2212yes—
42C2×#66992C2212yes—
43C2×#66992C2212yescomplemented
44C2×#66992C2212yescomplemented
45C2×#66992C2212yescomplemented
46C2×#66990C2212yes—
47C2×#66990C2212yescomplemented
48C2×#66990C2212yescomplemented
49C2×#66990C2211yescharacteristic, complemented
50C2×#66989C2211yescharacteristic, complemented
51C2×#66988C2212yescomplemented
52C2×#66988C2211yescharacteristic, complemented
53C2×#66983C2212yescomplemented
54C2×#66982C2211yescharacteristic
55C2×#66982C2211yescharacteristic, complemented
56C2×C4×C22⋊D11C2212yescomplemented
57C2×C4×C22⋊D11C2212yescomplemented
58C22×(C2×D11)⋊C4C2212yescomplemented
59C2×#66977C2212yescomplemented
60#10623251C22116yescomplemented
61#10623246C22116yescomplemented
62#10623214C22132yescomplemented
63#10623209C22132yescomplemented
64#10623201C22132yescomplemented
65#10623200C22132yescomplemented
66#10623197C22116yescomplemented
67#10623195C22116yescomplemented
68#10623193C22132yescomplemented
69#10623187C22116yescomplemented
70#10623185C22132yescomplemented
71#10623179C22116yescomplemented
72#10623113C22132yescomplemented
73#10623099C22132yescomplemented
74#10623091C22132yescomplemented
75#10623087C22132yescomplemented
76#10623083C22132yescomplemented
77#10623078C22132yescomplemented
78C2×#66951C2212yescomplemented
79C2×#66951C2212yescomplemented
80C2×#66949C2212yescomplemented
81C2×#66949C2212yescomplemented
82C2×#66949C2212yescomplemented
83C2×#66949C2212yescomplemented
84C2×#66948C2212yes—
85C2×#66947C2212yescomplemented
86C2×#66947C2212yescomplemented
87C2×#66946C2212yes—
88C2×#66941C2212yescomplemented
89C2×#66940C2212yescomplemented
90C2×#66939C2211yescharacteristic, complemented
91C2×#66938C2212yes—
92C2×#66938C2212yescomplemented
93C2×#66938C2212yescomplemented
94C2×#66938C2212yescomplemented
95C2×#66938C2212yescomplemented
96C2×#66938C2212yescomplemented
97C2×#66937C2212yes—
98C2×#66937C2212yes—
99C2×#66937C2212yescomplemented
100C2×#66936C2212yescomplemented
101C2×#66936C2212yescomplemented
102C2×#66935C2212yes—
103C2×#66935C2212yes—
104C2×#66935C2211yescharacteristic
105C2×#66935C2212yescomplemented
106C2×(C22⋊D11)⋊C4C2212yescomplemented
107C2×(C22⋊D11)⋊C4C2212yescomplemented
108C2×(C22⋊D11)⋊C4C2212yescomplemented
109C2×C22⋊C4×D11C2212yescomplemented
110C2×#66932C2212yescomplemented
111C2×#66931C2212yescomplemented
112C2×#66931C2212yescomplemented
113C2×#66930C2212yescomplemented
114C2×#66930C2211yescharacteristic, complemented
115C2×#66930C2211yescharacteristic, complemented
116C2×#66929C2212yescomplemented
117C2×#66929C2212yescomplemented
118C2×#66929C2212yescomplemented
119C2×#66928C2212yes—
120C2×#66928C2211yescharacteristic, complemented
121C2×#66928C2212yescomplemented
122C2×C4×D44C2212yescomplemented
123C2×#66925C2212yescomplemented
124C2×#66925C2212yescomplemented
125C2×#66925C2211yescharacteristic, complemented
126C2×C4×Dic22C2212yescomplemented
127C24×D11C2312yes—
128C24×D11C2311yescharacteristic
129C22×Q8×C11C2312yes—
130C22×D4×C11C2312yes—
131C22×D4×C11C2311yescharacteristic
132C22×D4×C11C2311yescharacteristic
133C22×D4×C11C2312yes—
134C23×C4×C11C2312yes—
135C23×C4×C11C2311yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C22×C22⋊D11C2311yescharacteristic
143C22×C22⋊D11C2312yes—
144C22×C22⋊D11C2311yescharacteristic
145C23×Dic11C2311yescharacteristic
146C23×Dic11C2311yescharacteristic
147C23×Dic11C2312yes—
148C23×Dic11C2311yescharacteristic
149C2×#4341—44no—
150C2×#4341C2318yes—
151C2×D4×D11—44no—
152C2×D4×D11C2318yescomplemented
153C2×#4339—48no—
154C2×#4339C23116yes—
155C22×D44C2312yes—
156C22×D44C2312yes—
157C22×D44C2312yes—
158C22×D44C2311yescharacteristic
159C22×C4×D11—44no—
160C22×C4×D11C2312yes—
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2312yes—
163C22×C4×D11C2312yes—
164C22×C4×D11C2312yes—
165C22×C4×D11C2318yescomplemented
166C22×Dic22—44no—
167C22×Dic22C2312yes—
168C22×Dic22C2312yes—
169C22×Dic22C2312yes—
170C22×Dic22C2311yescharacteristic
171C22×Dic22C2318yescomplemented
172C11×#127C2318yes—
173C11×#124C23116yescomplemented
174C11×#124C23116yescomplemented
175C11×#123C2318yescomplemented
176C11×#123C23116yescomplemented
177C11×#123C2318yescomplemented
178C4×Q8×C11C23116yescomplemented
179C4×D4×C11C23116yescomplemented
180C4×D4×C11C23116yescomplemented
181C2×C11×C4⋊C4C2312yes—
182C2×C11×C4⋊C4C2312yes—
183C2×C11×C4⋊C4C2312yes—
184C2×C11×C22⋊C4C2312yes—
185C2×C11×C22⋊C4C2311yescharacteristic
186C2×C11×C22⋊C4C2311yescharacteristic
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C42×C11C2312yes—
192C2×C42×C11C2312yes—
193C2×C42×C11C2311yescharacteristic
194C2×C22⋊Dic11C2311yescharacteristic
195C2×C22⋊Dic11C2312yes—
196C2×C22⋊Dic11C2311yescharacteristic
197C2×C22⋊Dic11C2312yes—
198C2×C22⋊Dic11C2312yes—
199C2×C22⋊Dic11C2312yes—
200#67000C23116yes—
201#67000C23116yescomplemented
202#66999C23116yescomplemented
203#66997C23116yescomplemented
204#66993C2318yes—
205#66992C23116yes—
206#66992C23116yes—
207#66992C23116yescomplemented
208#66992C23116yescomplemented
209#66992C23116yescomplemented
210#66990C23116yes—
211#66990C23116yescomplemented
212#66990C23116yescomplemented
213#66990C2318yescomplemented
214#66989C2318yescomplemented
215#66988C23116yescomplemented
216#66988C2318yescomplemented
217#66983C23116yescomplemented
218#66982C2318yes—
219#66982C2318yescomplemented
220C4×C22⋊D11C23116yescomplemented
221C4×C22⋊D11C23116yescomplemented
222C2×(C2×D11)⋊C4C2312yes—
223C2×(C2×D11)⋊C4C2312yes—
224C2×(C2×D11)⋊C4C2312yes—
225C2×(C2×D11)⋊C4C2312yes—
226C2×(C2×D11)⋊C4C2312yes—
227C2×(C2×D11)⋊C4C2312yes—
228C2×(C2×D11)⋊C4C2312yes—
229C2×(C2×D11)⋊C4C2312yes—
230C2×(C2×D11)⋊C4C2312yes—
231C2×(C2×D11)⋊C4C2312yes—
232C2×(C2×D11)⋊C4C2312yes—
233C2×(C2×D11)⋊C4C2312yes—
234C2×(C2×D11)⋊C4C2312yes—
235C2×(C2×D11)⋊C4C2312yes—
236C2×(C2×D11)⋊C4C2312yes—
237C2×(C2×D11)⋊C4C2312yes—
238C2×(C2×D11)⋊C4C23116yescomplemented
239C2×C4⋊Dic11C2312yes—
240C2×C4⋊Dic11C2312yes—
241#66977C23116yescomplemented
242C2×Dic11⋊C4C2312yes—
243C2×Dic11⋊C4C2312yes—
244C2×Dic11⋊C4C2312yes—
245C2×Dic11⋊C4C2312yes—
246C2×Dic11⋊C4C2312yes—
247C2×Dic11⋊C4C2312yes—
248C2×Dic11⋊C4C2312yes—
249C2×Dic11⋊C4C2312yes—
250C2×Dic11⋊C4C2312yes—
251C2×Dic11⋊C4C2312yes—
252C2×C4×Dic11C2312yes—
253C2×C4×Dic11C2312yes—
254C2×C4×Dic11C2312yes—
255C2×C4×Dic11C2312yes—
256C2×C4×Dic11C2311yescharacteristic
257#66951C23116yescomplemented
258#66951C23116yescomplemented
259#66949C23116yescomplemented
260#66949C23116yescomplemented
261#66949C23116yescomplemented
262#66949C23116yescomplemented
263#66948C23116yes—
264#66947C23116yescomplemented
265#66947C23116yescomplemented
266#66946C23116yes—
267#66941C23116yescomplemented
268#66940C23116yescomplemented
269#66939C2318yescomplemented
270#66938C23116yes—
271#66938C23116yescomplemented
272#66938C23116yescomplemented
273#66938C23116yescomplemented
274#66938C23116yescomplemented
275#66938C23116yescomplemented
276#66937C23116yes—
277#66937C23116yes—
278#66937C23116yescomplemented
279#66936C23116yescomplemented
280#66936C23116yescomplemented
281#66935C23116yes—
282#66935C23116yes—
283#66935C2318yes—
284#66935C23116yescomplemented
285(C22⋊D11)⋊C4C23116yescomplemented
286(C22⋊D11)⋊C4C23116yescomplemented
287(C22⋊D11)⋊C4C23116yescomplemented
288C22⋊C4×D11C23116yescomplemented
289#66932C23116yescomplemented
290#66931C23116yescomplemented
291#66931C23116yescomplemented
292#66930C23116yescomplemented
293#66930C2318yescomplemented
294#66930C2318yescomplemented
295#66929C23116yescomplemented
296#66929C23116yescomplemented
297#66929C23116yescomplemented
298#66928C23116yes—
299#66928C2318yescomplemented
300#66928C23116yescomplemented
301C4×D44C23116yescomplemented
302#66925C2318yescomplemented
303#66925C23116yescomplemented
304#66925C23116yescomplemented
305C4×Dic22C23116yescomplemented
306C2×#3540—111nomaximal, Sylow
307C24×C11C2411yescharacteristic
308C24×C11C2412yes—
309C24×C11C2411yescharacteristic
310C23×D11—42no—
311C23×D11—44no—
312C23×D11—44no—
313C23×D11—44no—
314C23×D11—44no—
315C23×D11C2411yescharacteristic
316C23×D11C2412yes—
317C23×D11C2412yes—
318C23×D11C2418yes—
319C23×D11C2414yes—
320C2×Q8×C11—44no—
321C2×Q8×C11C2418yes—
322C2×D4×C11—42no—
323C2×D4×C11—42no—
324C2×D4×C11—44no—
325C2×D4×C11—44no—
326C2×D4×C11C2418yes—
327C2×D4×C11C2414yes—
328C2×D4×C11C2414yes—
329C2×D4×C11C2418yes—
330C22×C4×C11—42no—
331C22×C4×C11—42no—
332C22×C4×C11—44no—
333C22×C4×C11C2412yes—
334C22×C4×C11C2412yes—
335C22×C4×C11C2412yes—
336C22×C4×C11C2411yescharacteristic
337C22×C4×C11C2412yes—
338C22×C4×C11C2412yes—
339C22×C4×C11C2418yes—
340C22×C4×C11C2414yes—
341C22×C4×C11C2414yes—
342C2×C22⋊D11—28no—
343C2×C22⋊D11—44no—
344C2×C22⋊D11—42no—
345C2×C22⋊D11—42no—
346C2×C22⋊D11—44no—
347C2×C22⋊D11—44no—
348C2×C22⋊D11—44no—
349C2×C22⋊D11—44no—
350C2×C22⋊D11C2418yes—
351C2×C22⋊D11C2418yes—
352C2×C22⋊D11C2418yes—
353C2×C22⋊D11C2418yes—
354C2×C22⋊D11C2418yes—
355C2×C22⋊D11C2414yes—
356C2×C22⋊D11C2418yes—
357C2×C22⋊D11C2414yes—
358C22×Dic11—24no—
359C22×Dic11—24no—
360C22×Dic11—42no—
361C22×Dic11—44no—
362C22×Dic11C2414yes—
363C22×Dic11C2414yes—
364C22×Dic11C2412yes—
365C22×Dic11C2412yes—
366C22×Dic11C2411yescharacteristic
367C22×Dic11C2412yes—
368C22×Dic11C2412yes—
369C22×Dic11C2411yescharacteristic
370C22×Dic11C2418yes—
371C22×Dic11C2414yes—
372C22×Dic11C2411yescharacteristic
373#4341—416no—
374D4×D11—416no—
375#4339—432no—
376C2×D44—44no—
377C2×D44—44no—
378C2×D44—44no—
379C2×D44—42no—
380C2×D44C2418yes—
381C2×D44C2418yes—
382C2×D44C2418yes—
383C2×D44C2414yes—
384C2×C4×D11—28no—
385C2×C4×D11—24no—
386C2×C4×D11—44no—
387C2×C4×D11—44no—
388C2×C4×D11—44no—
389C2×C4×D11—416no—
390C2×C4×D11C2418yes—
391C2×C4×D11C2414yes—
392C2×C4×D11C2418yes—
393C2×C4×D11C2418yes—
394C2×C4×D11C2418yes—
395C2×Dic22—28no—
396C2×Dic22—44no—
397C2×Dic22—44no—
398C2×Dic22—42no—
399C2×Dic22—416no—
400C2×Dic22C2418yes—
401C2×Dic22C2418yes—
402C2×Dic22C2418yes—
403C2×Dic22C2414yes—
404C11×C4⋊C4C2418yes—
405C11×C4⋊C4C2418yes—
406C11×C4⋊C4C2418yes—
407C11×C22⋊C4C2418yes—
408C11×C22⋊C4C2414yes—
409C11×C22⋊C4C2414yes—
410C11×C22⋊C4C2418yes—
411C11×C22⋊C4C2418yes—
412C11×C22⋊C4C2418yes—
413C11×C22⋊C4C2418yes—
414C42×C11C2418yes—
415C42×C11C2418yes—
416C42×C11C2414yes—
417C22⋊Dic11C2414yes—
418C22⋊Dic11C2418yes—
419C22⋊Dic11C2414yes—
420C22⋊Dic11C2418yes—
421C22⋊Dic11C2418yes—
422C22⋊Dic11C2418yes—
423(C2×D11)⋊C4C2418yes—
424(C2×D11)⋊C4C2418yes—
425(C2×D11)⋊C4C2418yes—
426(C2×D11)⋊C4C2418yes—
427(C2×D11)⋊C4C2418yes—
428(C2×D11)⋊C4C2418yes—
429(C2×D11)⋊C4C2418yes—
430(C2×D11)⋊C4C2418yes—
431(C2×D11)⋊C4C2418yes—
432(C2×D11)⋊C4C2418yes—
433(C2×D11)⋊C4C2418yes—
434(C2×D11)⋊C4C2418yes—
435(C2×D11)⋊C4C2418yes—
436(C2×D11)⋊C4C2418yes—
437(C2×D11)⋊C4C2418yes—
438(C2×D11)⋊C4C2418yes—
439C4⋊Dic11C2418yes—
440C4⋊Dic11C2418yes—
441Dic11⋊C4C2418yes—
442Dic11⋊C4C2418yes—
443Dic11⋊C4C2418yes—
444Dic11⋊C4C2418yes—
445Dic11⋊C4C2418yes—
446Dic11⋊C4C2418yes—
447Dic11⋊C4C2418yes—
448Dic11⋊C4C2418yes—
449Dic11⋊C4C2418yes—
450Dic11⋊C4C2418yes—
451C4×Dic11C2418yes—
452C4×Dic11C2418yes—
453C4×Dic11C2418yes—
454C4×Dic11C2418yes—
455C4×Dic11C2414yes—
456#3540—1132no—
457C2×H(3,𝔽4)—112no—
458C2×#560—111no—
459C2×#560—111no—
460C2×#559—111no—
461C2×#559D1111yescharacteristic, complemented
462C2×#556—112no—
463C2×#555—112no—
464C2×#551—112no—
465C2×#548—112no—
466C2×#546—112no—
467C2×#542—112no—
468C2×#542—112no—
469C2×#542—112no—
470C2×#538—112no—
471C2×#538—112no—
472C2×#536—111no—
473C2×#535—111no—
474C2×#525—111no—
475C2×#525—112no—
476C23×C11—22no—
477C23×C11—22no—
478C23×C11—24no—
479C23×C11—24no—
480C23×C11—24no—
481C23×C11—24no—
482C23×C11—24no—
483C23×C11C2512yes—
484C23×C11C2514yes—
485C23×C11C2512yes—
486C23×C11C2511yescharacteristic
487C22×D11—24no—
488C22×D11—22no—
489C22×D11—24no—
490C22×D11—24no—
491C22×D11—24no—
492C22×D11—24no—
493C22×D11—24no—
494C22×D11—24no—
495C22×D11—44no—
496C22×D11—48no—
497C22×D11—48no—
498C22×D11—48no—
499C22×D11—48no—
500C22×D11—416no—
501C22×D11—816no—
502C22×D11C2512yes—
503C22×D11C2514yes—
504C22×D11C2514yes—
505Q8×C11—48no—
506D4×C11—44no—
507D4×C11—44no—
508D4×C11—48no—
509D4×C11—48no—
510C2×C4×C11—24no—
511C2×C4×C11—22no—
512C2×C4×C11—24no—
513C2×C4×C11—24no—
514C2×C4×C11—24no—
515C2×C4×C11—24no—
516C2×C4×C11—44no—
517C2×C4×C11—44no—
518C2×C4×C11—48no—
519C2×C4×C11C2514yes—
520C2×C4×C11C2514yes—
521C2×C4×C11C2514yes—
522C2×C4×C11C2512yes—
523C2×C4×C11C2514yes—
524C2×C4×C11C2514yes—
525C22⋊D11—216no—
526C22⋊D11—48no—
527C22⋊D11—44no—
528C22⋊D11—44no—
529C22⋊D11—48no—
530C22⋊D11—48no—
531C22⋊D11—48no—
532C22⋊D11—48no—
533C2×Dic11—24no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—24no—
537C2×Dic11—24no—
538C2×Dic11—24no—
539C2×Dic11—28no—
540C2×Dic11—28no—
541C2×Dic11—44no—
542C2×Dic11—48no—
543C2×Dic11H(5,𝔽2)14yes—
544C2×Dic11C2514yes—
545C2×Dic11C2514yes—
546C2×Dic11C2512yes—
547C2×Dic11C2514yes—
548C2×Dic11C2514yes—
549C2×Dic11C2512yes—
550C2×Dic11C2512yes—
551D44—48no—
552D44—48no—
553D44—48no—
554D44—44no—
555C4×D11—216no—
556C4×D11—28no—
557C4×D11—48no—
558C4×D11—48no—
559C4×D11—48no—
560Dic22—216no—
561Dic22—48no—
562Dic22—48no—
563Dic22—44no—
564C22×#41—111no—
565C22×#41—112no—
566C23×Q8—111no—
567C23×D4—111no—
568C24×C4—111no—
569H(3,𝔽4)—1132no—
570#560—1116no—
571#560—1116no—
572#559—1116no—
573#559C2×D11116yescomplemented
574#556—1132no—
575#555—1132no—
576#551—1132no—
577#548—1132no—
578#546—1132no—
579#542—1132no—
580#542—1132no—
581#542—1132no—
582#538—1132no—
583#538—1132no—
584#536—1116no—
585#535—1116no—
586C2×C4⋊Q8—112no—
587C2×C4⋊Q8—112no—
588C2×#127—111no—
589C2×#127C2×D1111yescharacteristic
590C2×#126—112no—
591C2×#126—112no—
592C2×#126—112no—
593C2×#126—112no—
594C2×#126—112no—
595C2×#126—112no—
596C2×#124—112no—
597C2×#124—112no—
598C2×#124—111no—
599C2×#124—112no—
600C2×#124—112no—
601C2×#124—112no—
602C2×#124—112no—
603C2×#124—112no—
604C2×#124—112no—
605C2×#124—112no—
606C2×#124—111no—
607C2×#124—112no—
608C2×#124C2×D1112yescomplemented
609C2×#124C2×D1112yescomplemented
610#525—1116no—
611#525—1132no—
612C2×#123—111no—
613C2×#123—112no—
614C2×#123—111no—
615C2×#123—111no—
616C2×#123—112no—
617C2×#123—112no—
618C2×#123—112no—
619C2×#123—112no—
620C2×#123—111no—
621C2×#123C2×D1111yescharacteristic, complemented
622C2×#123C2×D1111yescharacteristic, complemented
623C2×#123C2×D1112yescomplemented
624C2×C22⋊Q8—112no—
625C2×C22⋊Q8—112no—
626C2×C22⋊Q8—112no—
627C2×C22⋊Q8—112no—
628C2×C22⋊Q8—112no—
629C2×C22⋊Q8—112no—
630C2×C22⋊Q8—112no—
631C2×C22⋊Q8—112no—
632C2×#121—112no—
633C2×#121—112no—
634C2×#121—112no—
635C2×#121—112no—
636C2×#121—112no—
637C2×#121—112no—
638C2×#121—112no—
639C2×#121—112no—
640C2×#121—112no—
641C2×#121—112no—
642C2×#120—112no—
643C2×#120—111no—
644C2×#120—112no—
645C2×#120—112no—
646C2×#120—111no—
647C2×#120—112no—
648C2×#120—112no—
649C2×#120—112no—
650C2×C4×Q8—112no—
651C2×C4×Q8—112no—
652C2×C4×Q8C2×D1112yescomplemented
653C2×C4×D4—112no—
654C2×C4×D4—112no—
655C2×C4×D4—112no—
656C2×C4×D4—112no—
657C2×C4×D4—112no—
658C2×C4×D4—112no—
659C2×C4×D4—112no—
660C2×C4×D4C2×D1112yescomplemented
661C2×C4×D4C2×D1112yescomplemented
662C2×#117—111no—
663C2×#117—111no—
664C2×#117—112no—
665C2×#117—112no—
666C2×#117—111no—
667C2×#117—112no—
668C22×C22⋊C4—112no—
669C22×C22⋊C4—112no—
670C22×C11—22no—
671C22×C11—24no—
672C22×C11—22no—
673C22×C11—24no—
674C22×C11—24no—
675C22×C11—24no—
676C22×C11—24no—
677C22×C11—44no—
678C22×C11—48no—
679C22×C11—44no—
680C22×C11C2×H(5,𝔽2)12yes—
681C22×C11#58514yes—
682C22×C11C2611yescharacteristic
683C2×D11—22no—
684C2×D11—24no—
685C2×D11—24no—
686C2×D11—24no—
687C2×D11—24no—
688C2×D11—24no—
689C2×D11—24no—
690C2×D11—24no—
691C2×D11—416no—
692C2×D11—48no—
693C2×D11—48no—
694C2×D11—44no—
695C2×D11—816no—
696C4×C11—24no—
697C4×C11—24no—
698C4×C11—22no—
699C4×C11—24no—
700C4×C11—24no—
701C4×C11—24no—
702Dic11—24no—
703Dic11—22no—
704Dic11—22no—
705Dic11—24no—
706Dic11—24no—
707Dic11—24no—
708Dic11C2×H(5,𝔽2)14yes—
709C25—112no—
710C25—111no—
711C2×#41—118no—
712C2×#41—1116no—
713C2×#41—448no—
714C2×#41—444no—
715C22×Q8—112no—
716C22×Q8—112no—
717C22×Q8—112no—
718C22×Q8—111no—
719C22×Q8—118no—
720C22×Q8—444no—
721C22×Q8C22×D1112yes—
722C22×D4—112no—
723C22×D4—112no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—111no—
728C22×D4—111no—
729C22×D4—112no—
730C22×D4—118no—
731C22×D4—112no—
732C22×D4—112no—
733C22×D4—112no—
734C22×D4—111no—
735C22×D4—444no—
736C22×D4C22×D1112yes—
737C22×D4C22×D1112yes—
738C22×D4C22×D1111yescharacteristic
739C22×D4C22×D1111yescharacteristic
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—112no—
743C23×C4—111no—
744C23×C4—112no—
745C23×C4—111no—
746C23×C4—112no—
747C23×C4—112no—
748C23×C4—112no—
749C23×C4—118no—
750C23×C4—444no—
751C23×C4C22×D1112yes—
752C23×C4C22×D1111yescharacteristic
753C23×C4C22×D1111yescharacteristic
754C4⋊Q8—1116no—
755C4⋊Q8—1116no—
756#127—118no—
757#127C22×D1118yes—
758#126—1116no—
759#126—1116no—
760#126—1116no—
761#126—1116no—
762#126—1116no—
763#126—1116no—
764#124—1116no—
765#124—1116no—
766#124—118no—
767#124—1116no—
768#124—1116no—
769#124—1116no—
770#124—1116no—
771#124—1116no—
772#124—1116no—
773#124—118no—
774#124—1116no—
775#124—1116no—
776#124C22×D11116yescomplemented
777#124C22×D11116yescomplemented
778#123—118no—
779#123—1116no—
780#123—118no—
781#123—118no—
782#123—1116no—
783#123—1116no—
784#123—1116no—
785#123—118no—
786#123—1116no—
787#123C22×D1118yescomplemented
788#123C22×D1118yescomplemented
789#123C22×D11116yescomplemented
790C22⋊Q8—1116no—
791C22⋊Q8—1116no—
792C22⋊Q8—1116no—
793C22⋊Q8—1116no—
794C22⋊Q8—1116no—
795C22⋊Q8—1116no—
796C22⋊Q8—1116no—
797C22⋊Q8—1116no—
798#121—1116no—
799#121—1116no—
800#121—1116no—
801#121—1116no—
802#121—1116no—
803#121—1116no—
804#121—1116no—
805#121—1116no—
806#121—1116no—
807#121—1116no—
808#120—118no—
809#120—1116no—
810#120—1116no—
811#120—1116no—
812#120—1116no—
813#120—118no—
814#120—1116no—
815#120—1116no—
816C4×Q8—1116no—
817C4×Q8—1116no—
818C4×Q8C22×D11116yescomplemented
819C4×D4—1116no—
820C4×D4—1116no—
821C4×D4—1116no—
822C4×D4—1116no—
823C4×D4—1116no—
824C4×D4—1116no—
825C4×D4—1116no—
826C4×D4C22×D11116yescomplemented
827C4×D4C22×D11116yescomplemented
828#117—118no—
829#117—118no—
830#117—1116no—
831#117—1116no—
832#117—118no—
833#117—1116no—
834C2×C4⋊C4—112no—
835C2×C4⋊C4—112no—
836C2×C4⋊C4—112no—
837C2×C4⋊C4—112no—
838C2×C4⋊C4—112no—
839C2×C4⋊C4—112no—
840C2×C4⋊C4—112no—
841C2×C4⋊C4—112no—
842C2×C4⋊C4—112no—
843C2×C4⋊C4—112no—
844C2×C4⋊C4—112no—
845C2×C4⋊C4—112no—
846C2×C4⋊C4C22×D1112yes—
847C2×C4⋊C4C22×D1112yes—
848C2×C4⋊C4C22×D1112yes—
849C2×C22⋊C4—112no—
850C2×C22⋊C4—112no—
851C2×C22⋊C4—111no—
852C2×C22⋊C4—111no—
853C2×C22⋊C4—112no—
854C2×C22⋊C4—112no—
855C2×C22⋊C4—112no—
856C2×C22⋊C4—112no—
857C2×C22⋊C4—112no—
858C2×C22⋊C4—112no—
859C2×C22⋊C4—112no—
860C2×C22⋊C4—1116no—
861C2×C22⋊C4—112no—
862C2×C22⋊C4—112no—
863C2×C22⋊C4—112no—
864C2×C22⋊C4—112no—
865C2×C22⋊C4—112no—
866C2×C22⋊C4—112no—
867C2×C22⋊C4—112no—
868C2×C22⋊C4—112no—
869C2×C22⋊C4—112no—
870C2×C22⋊C4—112no—
871C2×C22⋊C4—112no—
872C2×C22⋊C4—1116no—
873C2×C22⋊C4C22×D1112yes—
874C2×C22⋊C4C22×D1111yescharacteristic
875C2×C22⋊C4C22×D1111yescharacteristic
876C2×C22⋊C4C22×D1112yes—
877C2×C22⋊C4C22×D1112yes—
878C2×C22⋊C4C22×D1112yes—
879C2×C22⋊C4C22×D1112yes—
880C2×C42—112no—
881C2×C42—112no—
882C2×C42—112no—
883C2×C42—111no—
884C2×C42—112no—
885C2×C42C22×D1112yes—
886C2×C42C22×D1111yescharacteristic
887C2×C42C22×D1112yes—
888C2×C11—42no—
889C2×C11—44no—
890C2×C11—42no—
891C2×C11#354014yescomplemented
892C2×C11C22×H(5,𝔽2)11yescharacteristic
893C2×C11C2×#58512yes—
894D11—44no—
895D11—44no—
896D11—42no—
897C24—111no—
898C24—112no—
899C24—112no—
900C24—118no—
901C24—114no—
902C24—442no—
903C24—444no—
904C24—444no—
905C24—444no—
906C24—444no—
907C24C23×D1112yes—
908C24C23×D1111yescharacteristic
909C24C23×D1111yescharacteristic
910#41—4432no—
911#41—4416no—
912C2×Q8—44no—
913C2×Q8—118no—
914C2×Q8—118no—
915C2×Q8—118no—
916C2×Q8—114no—
917C2×Q8—228no—
918C2×Q8—444no—
919C2×Q8—442no—
920C2×Q8—444no—
921C2×Q8—4416no—
922C2×Q8C23×D1118yes—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—118no—
928C2×D4—118no—
929C2×D4—118no—
930C2×D4—118no—
931C2×D4—118no—
932C2×D4—114no—
933C2×D4—114no—
934C2×D4—118no—
935C2×D4—118no—
936C2×D4—118no—
937C2×D4—118no—
938C2×D4—114no—
939C2×D4—228no—
940C2×D4—442no—
941C2×D4—444no—
942C2×D4—444no—
943C2×D4—444no—
944C2×D4—4416no—
945C2×D4—442no—
946C2×D4—442no—
947C2×D4—444no—
948C2×D4—444no—
949C2×D4—444no—
950C2×D4—444no—
951C2×D4—444no—
952C2×D4C23×D1118yes—
953C2×D4C23×D1118yes—
954C2×D4C23×D1114yes—
955C2×D4C23×D1114yes—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—44no—
959C22×C4—111no—
960C22×C4—114no—
961C22×C4—114no—
962C22×C4—112no—
963C22×C4—112no—
964C22×C4—111no—
965C22×C4—112no—
966C22×C4—112no—
967C22×C4—111no—
968C22×C4—118no—
969C22×C4—114no—
970C22×C4—118no—
971C22×C4—114no—
972C22×C4—118no—
973C22×C4—118no—
974C22×C4—118no—
975C22×C4—228no—
976C22×C4—224no—
977C22×C4—224no—
978C22×C4—224no—
979C22×C4—444no—
980C22×C4—444no—
981C22×C4—444no—
982C22×C4—4416no—
983C22×C4—442no—
984C22×C4—444no—
985C22×C4C23×D1112yes—
986C22×C4C23×D1112yes—
987C22×C4C23×D1112yes—
988C22×C4C23×D1111yescharacteristic
989C22×C4C23×D1112yes—
990C22×C4C23×D1112yes—
991C22×C4C23×D1118yes—
992C22×C4C23×D1114yes—
993C22×C4C23×D1114yes—
994C4⋊C4—118no—
995C4⋊C4—118no—
996C4⋊C4—118no—
997C4⋊C4—118no—
998C4⋊C4—118no—
999C4⋊C4—118no—
1000C4⋊C4—118no—
1001C4⋊C4—118no—
1002C4⋊C4—118no—
1003C4⋊C4—118no—
1004C4⋊C4—118no—
1005C4⋊C4—118no—
1006C4⋊C4C23×D1118yes—
1007C4⋊C4C23×D1118yes—
1008C4⋊C4C23×D1118yes—
1009C22⋊C4—118no—
1010C22⋊C4—118no—
1011C22⋊C4—114no—
1012C22⋊C4—114no—
1013C22⋊C4—118no—
1014C22⋊C4—118no—
1015C22⋊C4—118no—
1016C22⋊C4—118no—
1017C22⋊C4—118no—
1018C22⋊C4—118no—
1019C22⋊C4—118no—
1020C22⋊C4—118no—
1021C22⋊C4—118no—
1022C22⋊C4—118no—
1023C22⋊C4—118no—
1024C22⋊C4—118no—
1025C22⋊C4—118no—
1026C22⋊C4—118no—
1027C22⋊C4—118no—
1028C22⋊C4—118no—
1029C22⋊C4—118no—
1030C22⋊C4—118no—
1031C22⋊C4C23×D1118yes—
1032C22⋊C4C23×D1114yes—
1033C22⋊C4C23×D1114yes—
1034C22⋊C4C23×D1118yes—
1035C22⋊C4C23×D1118yes—
1036C22⋊C4C23×D1118yes—
1037C22⋊C4C23×D1118yes—
1038C42—118no—
1039C42—118no—
1040C42—118no—
1041C42—114no—
1042C42—118no—
1043C42C23×D1118yes—
1044C42C23×D1114yes—
1045C42C23×D1118yes—
1046C11C2×#354011yescharacteristic, complemented, Sylow
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—22no—
1052C23—22no—
1053C23—24no—
1054C23—112no—
1055C23—114no—
1056C23—114no—
1057C23—224no—
1058C23—224no—
1059C23—224no—
1060C23—224no—
1061C23—224no—
1062C23—224no—
1063C23—222no—
1064C23—224no—
1065C23—444no—
1066C23—448no—
1067C23—448no—
1068C23—448no—
1069C23—448no—
1070C23—4416no—
1071C23—8816no—
1072C23C24×D1112yes—
1073C23C24×D1114yes—
1074C23C24×D1112yes—
1075C23C24×D1111yescharacteristic
1076Q8—48no—
1077Q8—2216no—
1078Q8—448no—
1079Q8—444no—
1080Q8—448no—
1081D4—44no—
1082D4—48no—
1083D4—48no—
1084D4—44no—
1085D4—2216no—
1086D4—444no—
1087D4—448no—
1088D4—448no—
1089D4—448no—
1090D4—444no—
1091D4—444no—
1092D4—448no—
1093D4—448no—
1094D4—448no—
1095D4—448no—
1096D4—448no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—44no—
1104C2×C4—44no—
1105C2×C4—48no—
1106C2×C4—114no—
1107C2×C4—112no—
1108C2×C4—114no—
1109C2×C4—114no—
1110C2×C4—112no—
1111C2×C4—114no—
1112C2×C4—114no—
1113C2×C4—112no—
1114C2×C4—2216no—
1115C2×C4—228no—
1116C2×C4—228no—
1117C2×C4—228no—
1118C2×C4—224no—
1119C2×C4—224no—
1120C2×C4—224no—
1121C2×C4—222no—
1122C2×C4—222no—
1123C2×C4—224no—
1124C2×C4—448no—
1125C2×C4—448no—
1126C2×C4—448no—
1127C2×C4—444no—
1128C2×C4—448no—
1129C2×C4C24×D1114yes—
1130C2×C4C24×D1114yes—
1131C2×C4C24×D1114yes—
1132C2×C4C24×D1112yes—
1133C2×C4C24×D1114yes—
1134C2×C4C24×D1114yes—
1135C22—22no—
1136C22—22no—
1137C22—24no—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—44no—
1143C22—48no—
1144C22—44no—
1145C22—224no—
1146C22—222no—
1147C22—224no—
1148C22—224no—
1149C22—224no—
1150C22—224no—
1151C22—224no—
1152C22—224no—
1153C22—4416no—
1154C22—448no—
1155C22—444no—
1156C22—448no—
1157C22—8816no—
1158C22#1062345314yes—
1159C22D11×H(5,𝔽2)12yes—
1160C22C25×D1111yescharacteristic
1161C4—24no—
1162C4—24no—
1163C4—22no—
1164C4—24no—
1165C4—24no—
1166C4—24no—
1167C4—114no—
1168C4—222no—
1169C4—222no—
1170C4—224no—
1171C4—224no—
1172C4—224no—
1173C4—224no—
1174C2—42no—
1175C2—44no—
1176C2—42no—
1177C2—444no—
1178C2—442no—
1179C2—444no—
1180C2#1308287914yesdirect product factor
1181C2C2×D11×H(5,𝔽2)11yescharacteristic
1182C2C2×#1062345312yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#559C2
socleC23×C11C25
hypercenterC2×#559D11
hypocenterC11C2×#3540
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#559

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13082879C2direct (N × H)
2. C2×#10623214C2semidirect
3. C2×#10623197C2semidirect
4. C2×#10623251C2semidirect
5. C2×#10623195C2semidirect
6. C2×#10623099C2semidirect
7. C2×#10623201C2semidirect
8. C2×#10623087C2semidirect
9. C2×#10623083C2semidirect
10. C2×#10623185C2semidirect
11. C2×#10623113C2semidirect
12. C2×#10623193C2semidirect
13. C2×#10623200C2semidirect
14. C2×#10623209C2semidirect
15. C2×#10623091C2semidirect
16. C2×#10623179C2semidirect
17. C2×#10623246C2semidirect
18. C2×#10623078C2semidirect
19. C2×#10623187C2semidirect
20. C2×C11×#559C2semidirect
22. C22×D4×D11C22semidirect
24. C23×C4×D11C22semidirect
25. C23×Dic22C22semidirect
26. C11×#559C22semidirect
28. C2×C11×#124C22semidirect
29. C2×C11×#124C22semidirect
30. C2×C11×#123C22semidirect
31. C2×C11×#123C22semidirect
32. C2×C11×#123C22semidirect
33. C2×C4×Q8×C11C22semidirect
34. C2×C4×D4×C11C22semidirect
35. C2×C4×D4×C11C22semidirect
37. C2×#67000C22semidirect
38. C2×#66999C22semidirect
39. C2×#66997C22semidirect
43. C2×#66992C22semidirect
44. C2×#66992C22semidirect
45. C2×#66992C22semidirect
47. C2×#66990C22semidirect
48. C2×#66990C22semidirect
49. C2×#66990C22semidirect
50. C2×#66989C22semidirect
51. C2×#66988C22semidirect
52. C2×#66988C22semidirect
53. C2×#66983C22semidirect
55. C2×#66982C22semidirect
56. C2×C4×C22⋊D11C22semidirect
57. C2×C4×C22⋊D11C22semidirect
58. C22×(C2×D11)⋊C4C22semidirect
59. C2×#66977C22semidirect
60. #10623251C22semidirect
61. #10623246C22semidirect
62. #10623214C22semidirect
63. #10623209C22semidirect
64. #10623201C22semidirect
65. #10623200C22semidirect
66. #10623197C22semidirect
67. #10623195C22semidirect
68. #10623193C22semidirect
69. #10623187C22semidirect
70. #10623185C22semidirect
71. #10623179C22semidirect
72. #10623113C22semidirect
73. #10623099C22semidirect
74. #10623091C22semidirect
75. #10623087C22semidirect
76. #10623083C22semidirect
77. #10623078C22semidirect
78. C2×#66951C22semidirect
79. C2×#66951C22semidirect
80. C2×#66949C22semidirect
81. C2×#66949C22semidirect
82. C2×#66949C22semidirect
83. C2×#66949C22semidirect
85. C2×#66947C22semidirect
86. C2×#66947C22semidirect
88. C2×#66941C22semidirect
89. C2×#66940C22semidirect
90. C2×#66939C22semidirect
92. C2×#66938C22semidirect
93. C2×#66938C22semidirect
94. C2×#66938C22semidirect
95. C2×#66938C22semidirect
96. C2×#66938C22semidirect
99. C2×#66937C22semidirect
100. C2×#66936C22semidirect
101. C2×#66936C22semidirect
105. C2×#66935C22semidirect
106. C2×(C22⋊D11)⋊C4C22semidirect
107. C2×(C22⋊D11)⋊C4C22semidirect
108. C2×(C22⋊D11)⋊C4C22semidirect
109. C2×C22⋊C4×D11C22semidirect
110. C2×#66932C22semidirect
111. C2×#66931C22semidirect
112. C2×#66931C22semidirect
113. C2×#66930C22semidirect
114. C2×#66930C22semidirect
115. C2×#66930C22semidirect
116. C2×#66929C22semidirect
117. C2×#66929C22semidirect
118. C2×#66929C22semidirect
120. C2×#66928C22semidirect
121. C2×#66928C22semidirect
122. C2×C4×D44C22semidirect
123. C2×#66925C22semidirect
124. C2×#66925C22semidirect
125. C2×#66925C22semidirect
126. C2×C4×Dic22C22semidirect
152. C2×D4×D11C23semidirect
165. C22×C4×D11C23semidirect
171. C22×Dic22C23semidirect
173. C11×#124C23semidirect
174. C11×#124C23semidirect
175. C11×#123C23semidirect
176. C11×#123C23semidirect
177. C11×#123C23semidirect
178. C4×Q8×C11C23semidirect
179. C4×D4×C11C23semidirect
180. C4×D4×C11C23semidirect
201. #67000C23semidirect
202. #66999C23semidirect
203. #66997C23semidirect
207. #66992C23semidirect
208. #66992C23semidirect
209. #66992C23semidirect
211. #66990C23semidirect
212. #66990C23semidirect
213. #66990C23semidirect
214. #66989C23semidirect
215. #66988C23semidirect
216. #66988C23semidirect
217. #66983C23semidirect
219. #66982C23semidirect
220. C4×C22⋊D11C23semidirect
221. C4×C22⋊D11C23semidirect
238. C2×(C2×D11)⋊C4C23semidirect
241. #66977C23semidirect
257. #66951C23semidirect
258. #66951C23semidirect
259. #66949C23semidirect
260. #66949C23semidirect
261. #66949C23semidirect
262. #66949C23semidirect
264. #66947C23semidirect
265. #66947C23semidirect
267. #66941C23semidirect
268. #66940C23semidirect
269. #66939C23semidirect
271. #66938C23semidirect
272. #66938C23semidirect
273. #66938C23semidirect
274. #66938C23semidirect
275. #66938C23semidirect
278. #66937C23semidirect
279. #66936C23semidirect
280. #66936C23semidirect
284. #66935C23semidirect
285. (C22⋊D11)⋊C4C23semidirect
286. (C22⋊D11)⋊C4C23semidirect
287. (C22⋊D11)⋊C4C23semidirect
288. C22⋊C4×D11C23semidirect
289. #66932C23semidirect
290. #66931C23semidirect
291. #66931C23semidirect
292. #66930C23semidirect
293. #66930C23semidirect
294. #66930C23semidirect
295. #66929C23semidirect
296. #66929C23semidirect
297. #66929C23semidirect
299. #66928C23semidirect
300. #66928C23semidirect
301. C4×D44C23semidirect
302. #66925C23semidirect
303. #66925C23semidirect
304. #66925C23semidirect
305. C4×Dic22C23semidirect
461. C2×#559D11semidirect
573. #559C2×D11semidirect
608. C2×#124C2×D11semidirect
609. C2×#124C2×D11semidirect
621. C2×#123C2×D11semidirect
622. C2×#123C2×D11semidirect
623. C2×#123C2×D11semidirect
652. C2×C4×Q8C2×D11semidirect
660. C2×C4×D4C2×D11semidirect
661. C2×C4×D4C2×D11semidirect
776. #124C22×D11semidirect
777. #124C22×D11semidirect
787. #123C22×D11semidirect
788. #123C22×D11semidirect
789. #123C22×D11semidirect
818. C4×Q8C22×D11semidirect
826. C4×D4C22×D11semidirect
827. C4×D4C22×D11semidirect
891. C2×C11#3540semidirect
1046. C11C2×#3540semidirect
1180. C2#13082879direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130828792
C2×#106232142
C2×#106231972
C2×#106232512
C2×#106231952
C2×#106230992
C2×#106232012
C2×#106230872
C2×#106230832
C2×#106231852
C2×#106231132
C2×#106231932
C2×#106232002
C2×#106232092
C2×#106230912
C2×#106231792
C2×#106232462
C2×#106230782
C2×#106231872
C2×C11×#5592
C2×#354011