Finite Group Databasebeta

← C2×#13082885 #15661072

Subgroups — C2×#13082885 #15661072

Order 2816.

7418 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082885C2132yesmaximal, direct product factor
2C2×#10623125C211yesmaximal, characteristic, complemented
3C2×#10623214C211yesmaximal, characteristic, complemented
4C2×#10623197C212yesmaximal, complemented
5C2×#10623090C212yesmaximal, complemented
6C2×#10623233C212yesmaximal, complemented
7C2×#10623063C212yesmaximal, complemented
8C2×#10623190C211yesmaximal, characteristic, complemented
9C2×#10623164C212yesmaximal, complemented
10C2×#10623021C212yesmaximal, complemented
11C2×#10623065C212yesmaximal, complemented
12C2×#10623171C212yesmaximal, complemented
13C2×#10623193C212yesmaximal, complemented
14C2×#10623235C212yesmaximal, complemented
15C2×#10623025C212yesmaximal, complemented
16C2×#10623206C211yesmaximal, characteristic, complemented
17C2×#10623123C211yesmaximal, characteristic, complemented
18C2×#10623078C212yesmaximal, complemented
19C2×#10623187C211yesmaximal, characteristic, complemented
20C2×C11×#551C211yesmaximal, characteristic, complemented
21C23×C22⋊D11C2211yescharacteristic, complemented
22C22×Q8×D11C2211yescharacteristic, complemented
23C22×#4341C2211yescharacteristic
24C22×#4339C2212yes—
25C23×C4×D11C2211yescharacteristic, complemented
26C11×#551C22116yescomplemented
27C2×C11×#126C2212yescomplemented
28C2×C11×#124C2211yescharacteristic
29C2×C11×#123C2211yescharacteristic
30C2×C11×#123C2212yescomplemented
31C2×C11×C22⋊Q8C2212yescomplemented
32C2×C11×#120C2211yescharacteristic
33C2×C4×D4×C11C2212yescomplemented
34C2×C11×#117C2212yescomplemented
35C22×C11×C22⋊C4C2212yescomplemented
36C2×#67006C2212yes—
37C2×#67006C2211yescharacteristic, complemented
38C2×#67000C2212yescomplemented
39C2×#66997C2211yescharacteristic, complemented
40C2×#66993C2212yes—
41C2×#66992C2212yes—
42C2×#66990C2211yescharacteristic
43C2×#66990C2211yescharacteristic
44C2×#66990C2212yescomplemented
45C2×#66989C2211yescharacteristic
46C2×#66989C2212yescomplemented
47C2×#66983C2212yes—
48C2×#66983C2212yescomplemented
49C2×#66982C2211yescharacteristic, complemented
50C2×#66982C2212yescomplemented
51C2×C4×C22⋊D11C2212yescomplemented
52C2×C4×C22⋊D11C2212yescomplemented
53C2×C4×C22⋊D11C2212yescomplemented
54C2×C4×C22⋊D11C2212yescomplemented
55C2×#66977C2212yescomplemented
56#10623235C22132yescomplemented
57#10623233C22132yescomplemented
58#10623214C22116yescomplemented
59#10623206C22116yescomplemented
60#10623197C22132yescomplemented
61#10623193C22132yescomplemented
62#10623190C22116yescomplemented
63#10623187C22116yescomplemented
64#10623171C22132yescomplemented
65#10623164C22132yescomplemented
66#10623125C22116yescomplemented
67#10623123C22116yescomplemented
68#10623090C22132yescomplemented
69#10623078C22132yescomplemented
70#10623065C22132yescomplemented
71#10623063C22132yescomplemented
72C2×#66951C2212yescomplemented
73C2×#66951C2212yescomplemented
74C2×#66951C2212yescomplemented
75C2×#66949C2212yescomplemented
76C2×#66949C2212yescomplemented
77C2×#66949C2212yescomplemented
78C2×#66949C2212yescomplemented
79C2×#66948C2212yescomplemented
80C2×#66948C2212yescomplemented
81C2×#66947C2212yescomplemented
82C2×#66946C2212yescomplemented
83C2×#66946C2212yescomplemented
84C2×#66945C2212yescomplemented
85C2×#66941C2212yescomplemented
86C2×#66940C2212yescomplemented
87C2×#66940C2212yescomplemented
88#10623025C22132yescomplemented
89C2×#66938C2212yes—
90C2×#66938C2212yes—
91C2×#66938C2212yescomplemented
92C2×#66938C2212yescomplemented
93C2×#66938C2212yescomplemented
94C2×#66938C2212yescomplemented
95C2×#66938C2212yescomplemented
96C2×#66938C2212yescomplemented
97#10623021C22132yescomplemented
98C2×#66937C2212yes—
99C2×#66937C2212yes—
100C2×#66937C2212yes—
101C2×#66937C2212yescomplemented
102C2×#66937C2212yescomplemented
103C2×#66936C2212yescomplemented
104C2×#66936C2212yescomplemented
105C2×#66936C2212yescomplemented
106C2×#66936C2212yescomplemented
107C2×#66936C2212yescomplemented
108C2×#66935C2212yes—
109C2×#66935C2212yescomplemented
110C2×#66935C2211yescharacteristic, complemented
111C2×#66935C2211yescharacteristic, complemented
112C2×(C22⋊D11)⋊C4C2212yes—
113C2×C22⋊C4×D11C2212yescomplemented
114C2×#66932C2212yescomplemented
115C2×#66932C2212yescomplemented
116C2×#66931C2212yescomplemented
117C2×#66931C2212yescomplemented
118C2×#66930C2211yescharacteristic, complemented
119C2×#66930C2211yescharacteristic, complemented
120C2×#66928C2212yescomplemented
121C2×#66928C2212yescomplemented
122C2×C4×D44C2212yescomplemented
123C2×#66925C2212yescomplemented
124C2×#66925C2211yescharacteristic, complemented
125C2×#66922C2211yescharacteristic, complemented
126C2×C4×Dic22C2212yescomplemented
127C25×C11C2311yescharacteristic
128C24×D11C2311yescharacteristic
129C24×D11C2311yescharacteristic
130C22×Q8×C11C2311yescharacteristic
131C22×D4×C11C2311yescharacteristic
132C22×D4×C11C2312yes—
133C23×C4×C11C2312yes—
134C23×C4×C11C2312yes—
135C23×C4×C11C2311yescharacteristic
136C22×C22⋊D11—44no—
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2311yescharacteristic
140C22×C22⋊D11C2311yescharacteristic
141C22×C22⋊D11C2312yes—
142C22×C22⋊D11C2312yes—
143C22×C22⋊D11C2312yes—
144C22×C22⋊D11C2312yes—
145C22×C22⋊D11C2312yes—
146C22×C22⋊D11C2318yescomplemented
147C23×Dic11C2311yescharacteristic
148C23×Dic11C2311yescharacteristic
149C2×Q8×D11—44no—
150C2×Q8×D11C2318yescomplemented
151C2×#4341—44no—
152C2×#4341C2318yes—
153C2×#4339—48no—
154C2×#4339C23116yes—
155C22×D44C2312yes—
156C22×D44C2312yes—
157C22×D44C2312yes—
158C22×D44C2312yes—
159C22×C4×D11—44no—
160C22×C4×D11C2312yes—
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2312yes—
163C22×C4×D11C2312yes—
164C22×C4×D11C2312yes—
165C22×C4×D11C2312yes—
166C22×C4×D11C2318yescomplemented
167C22×Dic22C2312yes—
168C22×Dic22C2312yes—
169C22×Dic22C2311yescharacteristic
170C22×Dic22C2311yescharacteristic
171C22×Dic22C2312yes—
172C11×#126C23116yescomplemented
173C11×#124C2318yes—
174C11×#123C2318yes—
175C11×#123C23116yescomplemented
176C11×C22⋊Q8C23116yescomplemented
177C11×#120C2318yes—
178C4×D4×C11C23116yescomplemented
179C11×#117C23116yescomplemented
180C2×C11×C4⋊C4C2312yes—
181C2×C11×C4⋊C4C2312yes—
182C2×C11×C4⋊C4C2312yes—
183C2×C11×C4⋊C4C2312yes—
184C2×C11×C22⋊C4C2311yescharacteristic
185C2×C11×C22⋊C4C2311yescharacteristic
186C2×C11×C22⋊C4C2312yes—
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2312yes—
192C2×C11×C22⋊C4C23116yescomplemented
193C2×C42×C11C2312yes—
194C2×C42×C11C2311yescharacteristic
195#67006C23116yes—
196#67006C2318yescomplemented
197C2×C22⋊Dic11C2311yescharacteristic
198C2×C22⋊Dic11C2311yescharacteristic
199C2×C22⋊Dic11C2312yes—
200C2×C22⋊Dic11C2312yes—
201C2×C22⋊Dic11C2312yes—
202C2×C22⋊Dic11C2312yes—
203C2×C22⋊Dic11C2312yes—
204#67000C23116yescomplemented
205#66997C2318yescomplemented
206#66993C23116yes—
207#66992C23116yes—
208#66990C2318yes—
209#66990C2318yes—
210#66990C23116yescomplemented
211#66989C2318yes—
212#66989C23116yescomplemented
213#66983C23116yes—
214#66983C23116yescomplemented
215#66982C23116yescomplemented
216#66982C2318yescomplemented
217C4×C22⋊D11C23116yescomplemented
218C4×C22⋊D11C23116yescomplemented
219C4×C22⋊D11C23116yescomplemented
220C4×C22⋊D11C23116yescomplemented
221C2×(C2×D11)⋊C4C2312yes—
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×C4⋊Dic11C2312yes—
236C2×C4⋊Dic11C2312yes—
237C2×C4⋊Dic11C2312yes—
238#66977C23116yescomplemented
239C2×Dic11⋊C4C2312yes—
240C2×Dic11⋊C4C2312yes—
241C2×Dic11⋊C4C2312yes—
242C2×Dic11⋊C4C2312yes—
243C2×Dic11⋊C4C2312yes—
244C2×Dic11⋊C4C2312yes—
245C2×Dic11⋊C4C2312yes—
246C2×Dic11⋊C4C2312yes—
247C2×C4×Dic11C2312yes—
248C2×C4×Dic11C2312yes—
249C2×C4×Dic11C2312yes—
250C2×C4×Dic11C2311yescharacteristic
251C2×C4×Dic11C2312yes—
252C2×C4×Dic11C2312yes—
253#66951C23116yescomplemented
254#66951C23116yescomplemented
255#66951C23116yescomplemented
256#66949C23116yescomplemented
257#66949C23116yescomplemented
258#66949C23116yescomplemented
259#66949C23116yescomplemented
260#66948C23116yescomplemented
261#66948C23116yescomplemented
262#66947C23116yescomplemented
263#66946C23116yescomplemented
264#66946C23116yescomplemented
265#66945C23116yescomplemented
266#66941C23116yescomplemented
267#66940C23116yescomplemented
268#66940C23116yescomplemented
269#66938C23116yes—
270#66938C23116yes—
271#66938C23116yescomplemented
272#66938C23116yescomplemented
273#66938C23116yescomplemented
274#66938C23116yescomplemented
275#66938C23116yescomplemented
276#66938C23116yescomplemented
277#66937C23116yes—
278#66937C23116yes—
279#66937C23116yes—
280#66937C23116yescomplemented
281#66937C23116yescomplemented
282#66936C23116yescomplemented
283#66936C23116yescomplemented
284#66936C23116yescomplemented
285#66936C23116yescomplemented
286#66936C23116yescomplemented
287#66935C23116yes—
288#66935C2318yescomplemented
289#66935C23116yescomplemented
290#66935C2318yescomplemented
291(C22⋊D11)⋊C4C23116yes—
292C22⋊C4×D11C23116yescomplemented
293#66932C23116yescomplemented
294#66932C23116yescomplemented
295#66931C23116yescomplemented
296#66931C23116yescomplemented
297#66930C2318yescomplemented
298#66930C2318yescomplemented
299#66928C23116yescomplemented
300#66928C23116yescomplemented
301C4×D44C23116yescomplemented
302#66925C23116yescomplemented
303#66925C2318yescomplemented
304#66922C2318yescomplemented
305C4×Dic22C23116yescomplemented
306C2×#3540—111nomaximal, Sylow
307C24×C11—42no—
308C24×C11—44no—
309C24×C11C2411yescharacteristic
310C24×C11C2411yescharacteristic
311C24×C11C2412yes—
312C24×C11C2414yes—
313C23×D11—42no—
314C23×D11—44no—
315C23×D11—42no—
316C23×D11—44no—
317C23×D11C2412yes—
318C23×D11C2412yes—
319C23×D11C2411yescharacteristic
320C23×D11C2414yes—
321C23×D11C2414yes—
322C2×Q8×C11—42no—
323C2×Q8×C11C2414yes—
324C2×D4×C11—42no—
325C2×D4×C11—44no—
326C2×D4×C11C2414yes—
327C2×D4×C11C2418yes—
328C22×C4×C11—42no—
329C22×C4×C11—44no—
330C22×C4×C11—44no—
331C22×C4×C11C2412yes—
332C22×C4×C11C2412yes—
333C22×C4×C11C2412yes—
334C22×C4×C11C2412yes—
335C22×C4×C11C2411yescharacteristic
336C22×C4×C11C2412yes—
337C22×C4×C11C2418yes—
338C22×C4×C11C2418yes—
339C22×C4×C11C2414yes—
340C2×C22⋊D11—28no—
341C2×C22⋊D11—44no—
342C2×C22⋊D11—42no—
343C2×C22⋊D11—42no—
344C2×C22⋊D11—44no—
345C2×C22⋊D11—44no—
346C2×C22⋊D11—44no—
347C2×C22⋊D11—44no—
348C2×C22⋊D11—44no—
349C2×C22⋊D11—416no—
350C2×C22⋊D11C2418yes—
351C2×C22⋊D11C2418yes—
352C2×C22⋊D11C2414yes—
353C2×C22⋊D11C2414yes—
354C2×C22⋊D11C2418yes—
355C2×C22⋊D11C2418yes—
356C2×C22⋊D11C2418yes—
357C2×C22⋊D11C2418yes—
358C2×C22⋊D11C2418yes—
359C22×Dic11—24no—
360C22×Dic11—24no—
361C22×Dic11C2414yes—
362C22×Dic11C2414yes—
363C22×Dic11C2412yes—
364C22×Dic11C2412yes—
365C22×Dic11C2411yescharacteristic
366C22×Dic11C2412yes—
367C22×Dic11C2412yes—
368C22×Dic11C2411yescharacteristic
369C22×Dic11C2411yescharacteristic
370Q8×D11—416no—
371#4341—416no—
372#4339—432no—
373C2×D44—44no—
374C2×D44—44no—
375C2×D44—44no—
376C2×D44—44no—
377C2×D44C2418yes—
378C2×D44C2418yes—
379C2×D44C2418yes—
380C2×D44C2418yes—
381C2×C4×D11—28no—
382C2×C4×D11—24no—
383C2×C4×D11—44no—
384C2×C4×D11—44no—
385C2×C4×D11—44no—
386C2×C4×D11—44no—
387C2×C4×D11—416no—
388C2×C4×D11C2418yes—
389C2×C4×D11C2414yes—
390C2×C4×D11C2418yes—
391C2×C4×D11C2418yes—
392C2×C4×D11C2418yes—
393C2×C4×D11C2418yes—
394C2×Dic22—28no—
395C2×Dic22—44no—
396C2×Dic22—44no—
397C2×Dic22—42no—
398C2×Dic22—42no—
399C2×Dic22C2418yes—
400C2×Dic22C2418yes—
401C2×Dic22C2414yes—
402C2×Dic22C2414yes—
403C2×Dic22C2418yes—
404C11×C4⋊C4C2418yes—
405C11×C4⋊C4C2418yes—
406C11×C4⋊C4C2418yes—
407C11×C4⋊C4C2418yes—
408C11×C22⋊C4C2414yes—
409C11×C22⋊C4C2414yes—
410C11×C22⋊C4C2418yes—
411C11×C22⋊C4C2418yes—
412C11×C22⋊C4C2418yes—
413C11×C22⋊C4C2418yes—
414C11×C22⋊C4C2418yes—
415C11×C22⋊C4C2418yes—
416C42×C11C2418yes—
417C42×C11C2414yes—
418C22⋊Dic11C2414yes—
419C22⋊Dic11C2414yes—
420C22⋊Dic11C2418yes—
421C22⋊Dic11C2418yes—
422C22⋊Dic11C2418yes—
423C22⋊Dic11C2418yes—
424C22⋊Dic11C2418yes—
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—
441C4⋊Dic11C2418yes—
442Dic11⋊C4C2418yes—
443Dic11⋊C4C2418yes—
444Dic11⋊C4C2418yes—
445Dic11⋊C4C2418yes—
446Dic11⋊C4C2418yes—
447Dic11⋊C4C2418yes—
448Dic11⋊C4C2418yes—
449Dic11⋊C4C2418yes—
450C4×Dic11C2418yes—
451C4×Dic11C2418yes—
452C4×Dic11C2418yes—
453C4×Dic11C2414yes—
454C4×Dic11C2418yes—
455C4×Dic11C2418yes—
456#3540—1132no—
457C2×H(3,𝔽4)—111no—
458C2×H(3,𝔽4)—111no—
459C2×#560—112no—
460C2×#559—112no—
461C2×#556—112no—
462C2×#555—112no—
463C2×#551—111no—
464C2×#551D1111yescharacteristic, complemented
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×C11—44no—
484C23×C11—48no—
485C23×C11—88no—
486C23×C11C2512yes—
487C23×C11C2512yes—
488C23×C11C2514yes—
489C23×C11C2511yescharacteristic
490C22×D11—22no—
491C22×D11—24no—
492C22×D11—24no—
493C22×D11—24no—
494C22×D11—24no—
495C22×D11—24no—
496C22×D11—24no—
497C22×D11—24no—
498C22×D11—44no—
499C22×D11—48no—
500C22×D11—44no—
501C22×D11—48no—
502C22×D11—416no—
503C22×D11—88no—
504C22×D11C2514yes—
505C22×D11C2514yes—
506C22×D11C2512yes—
507Q8×C11—44no—
508D4×C11—44no—
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—48no—
518C2×C4×C11—48no—
519C2×C4×C11C2514yes—
520C2×C4×C11C2514yes—
521C2×C4×C11C2514yes—
522C2×C4×C11C2514yes—
523C2×C4×C11C2512yes—
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—
533C22⋊D11—48no—
534C2×Dic11—24no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—24no—
538C2×Dic11—24no—
539C2×Dic11—24no—
540C2×Dic11—28no—
541C2×Dic11—28no—
542C2×Dic11H(5,𝔽2)14yes—
543C2×Dic11C2514yes—
544C2×Dic11C2514yes—
545C2×Dic11C2512yes—
546C2×Dic11C2514yes—
547C2×Dic11C2514yes—
548C2×Dic11C2512yes—
549C2×Dic11C2512yes—
550D44—48no—
551D44—48no—
552D44—48no—
553D44—48no—
554C4×D11—216no—
555C4×D11—28no—
556C4×D11—48no—
557C4×D11—48no—
558C4×D11—48no—
559C4×D11—48no—
560Dic22—216no—
561Dic22—48no—
562Dic22—48no—
563Dic22—44no—
564Dic22—44no—
565C22×#41—111no—
566C22×#41—112no—
567C23×Q8—111no—
568C23×D4—111no—
569C24×C4—111no—
570H(3,𝔽4)—1116no—
571H(3,𝔽4)—1116no—
572#560—1132no—
573#559—1132no—
574#556—1132no—
575#555—1132no—
576#551—1116no—
577#551C2×D11116yescomplemented
578#548—1132no—
579#546—1132no—
580#542—1132no—
581#542—1132no—
582#542—1132no—
583#538—1132no—
584#538—1132no—
585#536—1116no—
586#535—1116no—
587C2×C4⋊Q8—111no—
588C2×C4⋊Q8—112no—
589C2×C4⋊Q8—111no—
590C2×#127—112no—
591C2×#126—112no—
592C2×#126—112no—
593C2×#126—112no—
594C2×#126—112no—
595C2×#126—112no—
596C2×#126C2×D1112yescomplemented
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—112no—
607C2×#124—112no—
608C2×#124—112no—
609C2×#124—112no—
610C2×#124C2×D1111yescharacteristic
611#525—1116no—
612#525—1132no—
613C2×#123—111no—
614C2×#123—112no—
615C2×#123—112no—
616C2×#123—112no—
617C2×#123—112no—
618C2×#123—112no—
619C2×#123—112no—
620C2×#123—112no—
621C2×#123C2×D1111yescharacteristic
622C2×#123C2×D1112yescomplemented
623C2×C22⋊Q8—112no—
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⋊Q8C2×D1112yescomplemented
631C2×#121—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×#120—111no—
642C2×#120—112no—
643C2×#120—111no—
644C2×#120—111no—
645C2×#120—112no—
646C2×#120—112no—
647C2×#120—111no—
648C2×#120—112no—
649C2×#120—111no—
650C2×#120C2×D1111yescharacteristic
651C2×C4×Q8—112no—
652C2×C4×Q8—112no—
653C2×C4×Q8—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×D4—112no—
661C2×C4×D4—112no—
662C2×C4×D4C2×D1112yescomplemented
663C2×#117—112no—
664C2×#117—111no—
665C2×#117—111no—
666C2×#117—112no—
667C2×#117—111no—
668C2×#117C2×D1112yescomplemented
669C22×C22⋊C4—112no—
670C22×C22⋊C4C2×D1112yescomplemented
671C22×C11—22no—
672C22×C11—24no—
673C22×C11—22no—
674C22×C11—24no—
675C22×C11—24no—
676C22×C11—24no—
677C22×C11—24no—
678C22×C11—44no—
679C22×C11—44no—
680C22×C11—48no—
681C22×C11—88no—
682C22×C11C2×H(5,𝔽2)12yes—
683C22×C11#58514yes—
684C22×C11C2611yescharacteristic
685C2×D11—24no—
686C2×D11—24no—
687C2×D11—22no—
688C2×D11—24no—
689C2×D11—24no—
690C2×D11—24no—
691C2×D11—24no—
692C2×D11—24no—
693C2×D11—416no—
694C2×D11—44no—
695C2×D11—48no—
696C2×D11—48no—
697C2×D11—88no—
698C4×C11—24no—
699C4×C11—24no—
700C4×C11—22no—
701C4×C11—24no—
702C4×C11—24no—
703C4×C11—24no—
704Dic11—24no—
705Dic11—22no—
706Dic11—22no—
707Dic11—24no—
708Dic11—24no—
709Dic11—24no—
710Dic11C2×H(5,𝔽2)14yes—
711C25—111no—
712C25—111no—
713C25C22×D1111yescharacteristic
714C2×#41—118no—
715C2×#41—1116no—
716C2×#41—448no—
717C2×#41—444no—
718C22×Q8—118no—
719C22×Q8—112no—
720C22×Q8—112no—
721C22×Q8—112no—
722C22×Q8—111no—
723C22×Q8—111no—
724C22×Q8—444no—
725C22×Q8C22×D1111yescharacteristic
726C22×D4—112no—
727C22×D4—112no—
728C22×D4—112no—
729C22×D4—112no—
730C22×D4—112no—
731C22×D4—111no—
732C22×D4—112no—
733C22×D4—111no—
734C22×D4—112no—
735C22×D4—118no—
736C22×D4—112no—
737C22×D4—112no—
738C22×D4—112no—
739C22×D4—112no—
740C22×D4—444no—
741C22×D4C22×D1112yes—
742C22×D4C22×D1111yescharacteristic
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—112no—
747C23×C4—112no—
748C23×C4—112no—
749C23×C4—112no—
750C23×C4—112no—
751C23×C4—118no—
752C23×C4—444no—
753C23×C4C22×D1112yes—
754C23×C4C22×D1112yes—
755C23×C4C22×D1111yescharacteristic
756C4⋊Q8—118no—
757C4⋊Q8—1116no—
758C4⋊Q8—118no—
759#127—1116no—
760#126—1116no—
761#126—1116no—
762#126—1116no—
763#126—1116no—
764#126—1116no—
765#126C22×D11116yescomplemented
766#124—1116no—
767#124—118no—
768#124—1116no—
769#124—1116no—
770#124—1116no—
771#124—1116no—
772#124—1116no—
773#124—1116no—
774#124—1116no—
775#124—1116no—
776#124—1116no—
777#124—1116no—
778#124—1116no—
779#124C22×D1118yes—
780#123—118no—
781#123—1116no—
782#123—1116no—
783#123—1116no—
784#123—1116no—
785#123—1116no—
786#123—1116no—
787#123—1116no—
788#123C22×D1118yes—
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⋊Q8C22×D11116yescomplemented
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—118no—
812#120—118no—
813#120—118no—
814#120—1116no—
815#120—118no—
816#120—1116no—
817#120C22×D1118yes—
818C4×Q8—1116no—
819C4×Q8—1116no—
820C4×Q8—1116no—
821C4×D4—1116no—
822C4×D4—1116no—
823C4×D4—1116no—
824C4×D4—1116no—
825C4×D4—1116no—
826C4×D4—1116no—
827C4×D4—1116no—
828C4×D4—1116no—
829C4×D4C22×D11116yescomplemented
830#117—1116no—
831#117—118no—
832#117—118no—
833#117—1116no—
834#117—118no—
835#117C22×D11116yescomplemented
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⋊C4—112no—
847C2×C4⋊C4C22×D1112yes—
848C2×C4⋊C4C22×D1112yes—
849C2×C4⋊C4C22×D1112yes—
850C2×C4⋊C4C22×D1112yes—
851C2×C22⋊C4—112no—
852C2×C22⋊C4—111no—
853C2×C22⋊C4—111no—
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—112no—
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×D1112yes—
875C2×C22⋊C4C22×D1112yes—
876C2×C22⋊C4C22×D1112yes—
877C2×C22⋊C4C22×D1111yescharacteristic
878C2×C22⋊C4C22×D1111yescharacteristic
879C2×C22⋊C4C22×D1112yes—
880C2×C22⋊C4C22×D1112yes—
881C2×C22⋊C4C22×D11116yescomplemented
882C2×C42—111no—
883C2×C42—112no—
884C2×C42—112no—
885C2×C42—112no—
886C2×C42—112no—
887C2×C42—112no—
888C2×C42C22×D1111yescharacteristic
889C2×C42C22×D1112yes—
890C2×C11—42no—
891C2×C11—42no—
892C2×C11—44no—
893C2×C11#354014yescomplemented
894C2×C11C22×H(5,𝔽2)11yescharacteristic
895C2×C11C2×#58512yes—
896D11—42no—
897D11—44no—
898D11—44no—
899C24—42no—
900C24—44no—
901C24—112no—
902C24—112no—
903C24—111no—
904C24—114no—
905C24—114no—
906C24—442no—
907C24—444no—
908C24—442no—
909C24—444no—
910C24C23×D1111yescharacteristic
911C24C23×D1111yescharacteristic
912C24C23×D1112yes—
913C24C23×D1114yes—
914#41—4432no—
915#41—4416no—
916C2×Q8—42no—
917C2×Q8—118no—
918C2×Q8—118no—
919C2×Q8—118no—
920C2×Q8—114no—
921C2×Q8—114no—
922C2×Q8—228no—
923C2×Q8—442no—
924C2×Q8—442no—
925C2×Q8—444no—
926C2×Q8—444no—
927C2×Q8—4416no—
928C2×Q8C23×D1114yes—
929C2×D4—42no—
930C2×D4—44no—
931C2×D4—118no—
932C2×D4—118no—
933C2×D4—118no—
934C2×D4—118no—
935C2×D4—118no—
936C2×D4—114no—
937C2×D4—118no—
938C2×D4—114no—
939C2×D4—118no—
940C2×D4—118no—
941C2×D4—118no—
942C2×D4—118no—
943C2×D4—118no—
944C2×D4—228no—
945C2×D4—444no—
946C2×D4—444no—
947C2×D4—444no—
948C2×D4—444no—
949C2×D4—4416no—
950C2×D4—444no—
951C2×D4—442no—
952C2×D4—442no—
953C2×D4—444no—
954C2×D4—444no—
955C2×D4—444no—
956C2×D4—444no—
957C2×D4—444no—
958C2×D4C23×D1118yes—
959C2×D4C23×D1114yes—
960C22×C4—42no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—111no—
964C22×C4—114no—
965C22×C4—114no—
966C22×C4—112no—
967C22×C4—112no—
968C22×C4—112no—
969C22×C4—111no—
970C22×C4—112no—
971C22×C4—111no—
972C22×C4—114no—
973C22×C4—118no—
974C22×C4—118no—
975C22×C4—118no—
976C22×C4—118no—
977C22×C4—118no—
978C22×C4—228no—
979C22×C4—224no—
980C22×C4—224no—
981C22×C4—224no—
982C22×C4—444no—
983C22×C4—444no—
984C22×C4—444no—
985C22×C4—444no—
986C22×C4—4416no—
987C22×C4C23×D1112yes—
988C22×C4C23×D1111yescharacteristic
989C22×C4C23×D1112yes—
990C22×C4C23×D1112yes—
991C22×C4C23×D1112yes—
992C22×C4C23×D1112yes—
993C22×C4C23×D1118yes—
994C22×C4C23×D1118yes—
995C22×C4C23×D1114yes—
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⋊C4—118no—
1007C4⋊C4C23×D1118yes—
1008C4⋊C4C23×D1118yes—
1009C4⋊C4C23×D1118yes—
1010C4⋊C4C23×D1118yes—
1011C22⋊C4—118no—
1012C22⋊C4—114no—
1013C22⋊C4—114no—
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⋊C4—118no—
1032C22⋊C4C23×D1118yes—
1033C22⋊C4C23×D1118yes—
1034C22⋊C4C23×D1118yes—
1035C22⋊C4C23×D1118yes—
1036C22⋊C4C23×D1114yes—
1037C22⋊C4C23×D1114yes—
1038C22⋊C4C23×D1118yes—
1039C22⋊C4C23×D1118yes—
1040C42—114no—
1041C42—118no—
1042C42—118no—
1043C42—118no—
1044C42—118no—
1045C42—118no—
1046C42C23×D1114yes—
1047C42C23×D1118yes—
1048C11C2×#354011yescharacteristic, complemented, Sylow
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—22no—
1054C23—24no—
1055C23—22no—
1056C23—44no—
1057C23—48no—
1058C23—88no—
1059C23—114no—
1060C23—114no—
1061C23—112no—
1062C23—224no—
1063C23—224no—
1064C23—224no—
1065C23—224no—
1066C23—224no—
1067C23—222no—
1068C23—224no—
1069C23—224no—
1070C23—444no—
1071C23—448no—
1072C23—444no—
1073C23—448no—
1074C23—4416no—
1075C23—888no—
1076C23C24×D1112yes—
1077C23C24×D1112yes—
1078C23C24×D1114yes—
1079C23C24×D1111yescharacteristic
1080Q8—44no—
1081Q8—2216no—
1082Q8—444no—
1083Q8—444no—
1084Q8—448no—
1085Q8—448no—
1086D4—48no—
1087D4—44no—
1088D4—2216no—
1089D4—448no—
1090D4—448no—
1091D4—448no—
1092D4—448no—
1093D4—448no—
1094D4—444no—
1095D4—444no—
1096D4—448no—
1097D4—448no—
1098D4—448no—
1099D4—448no—
1100D4—448no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—44no—
1108C2×C4—48no—
1109C2×C4—48no—
1110C2×C4—114no—
1111C2×C4—112no—
1112C2×C4—114no—
1113C2×C4—114no—
1114C2×C4—114no—
1115C2×C4—112no—
1116C2×C4—114no—
1117C2×C4—112no—
1118C2×C4—2216no—
1119C2×C4—228no—
1120C2×C4—228no—
1121C2×C4—228no—
1122C2×C4—224no—
1123C2×C4—224no—
1124C2×C4—224no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—224no—
1128C2×C4—448no—
1129C2×C4—448no—
1130C2×C4—448no—
1131C2×C4—448no—
1132C2×C4C24×D1114yes—
1133C2×C4C24×D1112yes—
1134C2×C4C24×D1114yes—
1135C2×C4C24×D1114yes—
1136C2×C4C24×D1114yes—
1137C2×C4C24×D1114yes—
1138C22—22no—
1139C22—24no—
1140C22—22no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—44no—
1146C22—48no—
1147C22—44no—
1148C22—88no—
1149C22—222no—
1150C22—224no—
1151C22—224no—
1152C22—224no—
1153C22—224no—
1154C22—224no—
1155C22—224no—
1156C22—224no—
1157C22—4416no—
1158C22—448no—
1159C22—448no—
1160C22—444no—
1161C22—888no—
1162C22#1062345314yes—
1163C22D11×H(5,𝔽2)12yes—
1164C22C25×D1111yescharacteristic
1165C4—24no—
1166C4—24no—
1167C4—22no—
1168C4—24no—
1169C4—24no—
1170C4—24no—
1171C4—114no—
1172C4—222no—
1173C4—222no—
1174C4—224no—
1175C4—224no—
1176C4—224no—
1177C4—224no—
1178C2—42no—
1179C2—44no—
1180C2—42no—
1181C2—444no—
1182C2—444no—
1183C2—442no—
1184C2#1308288514yesdirect product factor
1185C2C2×D11×H(5,𝔽2)11yescharacteristic
1186C2C2×#1062345312yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#551C2
socleC23×C11C25
hypercenterC2×#551D11
hypocenterC11C2×#3540
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. #13082885C2direct (N × H)
2. C2×#10623125C2semidirect
3. C2×#10623214C2semidirect
4. C2×#10623197C2semidirect
5. C2×#10623090C2semidirect
6. C2×#10623233C2semidirect
7. C2×#10623063C2semidirect
8. C2×#10623190C2semidirect
9. C2×#10623164C2semidirect
10. C2×#10623021C2semidirect
11. C2×#10623065C2semidirect
12. C2×#10623171C2semidirect
13. C2×#10623193C2semidirect
14. C2×#10623235C2semidirect
15. C2×#10623025C2semidirect
16. C2×#10623206C2semidirect
17. C2×#10623123C2semidirect
18. C2×#10623078C2semidirect
19. C2×#10623187C2semidirect
20. C2×C11×#551C2semidirect
21. C23×C22⋊D11C22semidirect
22. C22×Q8×D11C22semidirect
25. C23×C4×D11C22semidirect
26. C11×#551C22semidirect
27. C2×C11×#126C22semidirect
30. C2×C11×#123C22semidirect
31. C2×C11×C22⋊Q8C22semidirect
33. C2×C4×D4×C11C22semidirect
34. C2×C11×#117C22semidirect
35. C22×C11×C22⋊C4C22semidirect
37. C2×#67006C22semidirect
38. C2×#67000C22semidirect
39. C2×#66997C22semidirect
44. C2×#66990C22semidirect
46. C2×#66989C22semidirect
48. C2×#66983C22semidirect
49. C2×#66982C22semidirect
50. C2×#66982C22semidirect
51. C2×C4×C22⋊D11C22semidirect
52. C2×C4×C22⋊D11C22semidirect
53. C2×C4×C22⋊D11C22semidirect
54. C2×C4×C22⋊D11C22semidirect
55. C2×#66977C22semidirect
56. #10623235C22semidirect
57. #10623233C22semidirect
58. #10623214C22semidirect
59. #10623206C22semidirect
60. #10623197C22semidirect
61. #10623193C22semidirect
62. #10623190C22semidirect
63. #10623187C22semidirect
64. #10623171C22semidirect
65. #10623164C22semidirect
66. #10623125C22semidirect
67. #10623123C22semidirect
68. #10623090C22semidirect
69. #10623078C22semidirect
70. #10623065C22semidirect
71. #10623063C22semidirect
72. C2×#66951C22semidirect
73. C2×#66951C22semidirect
74. C2×#66951C22semidirect
75. C2×#66949C22semidirect
76. C2×#66949C22semidirect
77. C2×#66949C22semidirect
78. C2×#66949C22semidirect
79. C2×#66948C22semidirect
80. C2×#66948C22semidirect
81. C2×#66947C22semidirect
82. C2×#66946C22semidirect
83. C2×#66946C22semidirect
84. C2×#66945C22semidirect
85. C2×#66941C22semidirect
86. C2×#66940C22semidirect
87. C2×#66940C22semidirect
88. #10623025C22semidirect
91. C2×#66938C22semidirect
92. C2×#66938C22semidirect
93. C2×#66938C22semidirect
94. C2×#66938C22semidirect
95. C2×#66938C22semidirect
96. C2×#66938C22semidirect
97. #10623021C22semidirect
101. C2×#66937C22semidirect
102. C2×#66937C22semidirect
103. C2×#66936C22semidirect
104. C2×#66936C22semidirect
105. C2×#66936C22semidirect
106. C2×#66936C22semidirect
107. C2×#66936C22semidirect
109. C2×#66935C22semidirect
110. C2×#66935C22semidirect
111. C2×#66935C22semidirect
113. C2×C22⋊C4×D11C22semidirect
114. C2×#66932C22semidirect
115. C2×#66932C22semidirect
116. C2×#66931C22semidirect
117. C2×#66931C22semidirect
118. C2×#66930C22semidirect
119. C2×#66930C22semidirect
120. C2×#66928C22semidirect
121. C2×#66928C22semidirect
122. C2×C4×D44C22semidirect
123. C2×#66925C22semidirect
124. C2×#66925C22semidirect
125. C2×#66922C22semidirect
126. C2×C4×Dic22C22semidirect
146. C22×C22⋊D11C23semidirect
150. C2×Q8×D11C23semidirect
166. C22×C4×D11C23semidirect
172. C11×#126C23semidirect
175. C11×#123C23semidirect
176. C11×C22⋊Q8C23semidirect
178. C4×D4×C11C23semidirect
179. C11×#117C23semidirect
192. C2×C11×C22⋊C4C23semidirect
196. #67006C23semidirect
204. #67000C23semidirect
205. #66997C23semidirect
210. #66990C23semidirect
212. #66989C23semidirect
214. #66983C23semidirect
215. #66982C23semidirect
216. #66982C23semidirect
217. C4×C22⋊D11C23semidirect
218. C4×C22⋊D11C23semidirect
219. C4×C22⋊D11C23semidirect
220. C4×C22⋊D11C23semidirect
238. #66977C23semidirect
253. #66951C23semidirect
254. #66951C23semidirect
255. #66951C23semidirect
256. #66949C23semidirect
257. #66949C23semidirect
258. #66949C23semidirect
259. #66949C23semidirect
260. #66948C23semidirect
261. #66948C23semidirect
262. #66947C23semidirect
263. #66946C23semidirect
264. #66946C23semidirect
265. #66945C23semidirect
266. #66941C23semidirect
267. #66940C23semidirect
268. #66940C23semidirect
271. #66938C23semidirect
272. #66938C23semidirect
273. #66938C23semidirect
274. #66938C23semidirect
275. #66938C23semidirect
276. #66938C23semidirect
280. #66937C23semidirect
281. #66937C23semidirect
282. #66936C23semidirect
283. #66936C23semidirect
284. #66936C23semidirect
285. #66936C23semidirect
286. #66936C23semidirect
288. #66935C23semidirect
289. #66935C23semidirect
290. #66935C23semidirect
292. C22⋊C4×D11C23semidirect
293. #66932C23semidirect
294. #66932C23semidirect
295. #66931C23semidirect
296. #66931C23semidirect
297. #66930C23semidirect
298. #66930C23semidirect
299. #66928C23semidirect
300. #66928C23semidirect
301. C4×D44C23semidirect
302. #66925C23semidirect
303. #66925C23semidirect
304. #66922C23semidirect
305. C4×Dic22C23semidirect
464. C2×#551D11semidirect
577. #551C2×D11semidirect
596. C2×#126C2×D11semidirect
622. C2×#123C2×D11semidirect
630. C2×C22⋊Q8C2×D11semidirect
662. C2×C4×D4C2×D11semidirect
668. C2×#117C2×D11semidirect
670. C22×C22⋊C4C2×D11semidirect
765. #126C22×D11semidirect
789. #123C22×D11semidirect
797. C22⋊Q8C22×D11semidirect
829. C4×D4C22×D11semidirect
835. #117C22×D11semidirect
881. C2×C22⋊C4C22×D11semidirect
893. C2×C11#3540semidirect
1048. C11C2×#3540semidirect
1184. C2#13082885direct (N × H)

Maximal subgroups

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

subgroupindex
#130828852
C2×#106231252
C2×#106232142
C2×#106231972
C2×#106230902
C2×#106232332
C2×#106230632
C2×#106231902
C2×#106231642
C2×#106230212
C2×#106230652
C2×#106231712
C2×#106231932
C2×#106232352
C2×#106230252
C2×#106232062
C2×#106231232
C2×#106230782
C2×#106231872
C2×C11×#5512
C2×#354011