Finite Group Databasebeta

← C2×#13082883 #15661061

Subgroups — C2×#13082883 #15661061

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#13082883C2132yesmaximal, direct product factor
2C2×#10623125C212yesmaximal, complemented
3C2×#10623126C211yesmaximal, characteristic, complemented
4C2×#10623244C211yesmaximal, characteristic, complemented
5C2×#10623195C211yesmaximal, characteristic, complemented
6C2×#10623233C212yesmaximal, complemented
7C2×#10623147C212yesmaximal, complemented
8C2×#10623189C212yesmaximal, complemented
9C2×#10623129C212yesmaximal, complemented
10C2×#10623141C212yesmaximal, complemented
11C2×#10623193C212yesmaximal, complemented
12C2×#10623134C212yesmaximal, complemented
13C2×#10623241C212yesmaximal, complemented
14C2×#10623148C212yesmaximal, complemented
15C2×#10623144C212yesmaximal, complemented
16C2×#10623179C211yesmaximal, characteristic, complemented
17C2×#10623246C211yesmaximal, characteristic, complemented
18C2×#10623117C211yesmaximal, characteristic, complemented
19C2×#10623117C212yesmaximal, complemented
20C2×C11×#560C211yesmaximal, characteristic, complemented
21C24×Dic11C2211yescharacteristic, complemented
22C22×#4341C2211yescharacteristic
23C22×#4341C2212yes—
24C22×D4×D11C2211yescharacteristic, complemented
25C23×Dic22C2211yescharacteristic, complemented
26C11×#560C22116yescomplemented
27C2×C11×#127C2211yescharacteristic
28C2×C11×#126C2212yescomplemented
29C2×C11×#123C2211yescharacteristic, complemented
30C2×C11×#123C2212yescomplemented
31C2×C11×#121C2212yes—
32C2×C11×#121C2212yescomplemented
33C2×C11×#121C2212yescomplemented
34C2×C11×#120C2211yescharacteristic, complemented
35C2×C11×#120C2212yescomplemented
36C2×#67006C2211yescharacteristic
37C2×#67006C2212yescomplemented
38C2×#66993C2211yescharacteristic
39C2×#66992C2212yes—
40C2×#66992C2212yes—
41C2×#66992C2212yes—
42C2×#66992C2212yescomplemented
43C2×#66992C2212yescomplemented
44C2×#66991C2212yescomplemented
45C2×#66990C2212yes—
46C2×#66990C2212yes—
47C2×#66990C2212yes—
48C2×#66990C2212yescomplemented
49C2×#66989C2212yescomplemented
50C2×#66989C2212yescomplemented
51C2×#66989C2211yescharacteristic, complemented
52C2×#66989C2212yescomplemented
53C2×#66989C2212yescomplemented
54C2×#66988C2211yescharacteristic, complemented
55C2×#66988C2211yescharacteristic, complemented
56C2×#66988C2212yescomplemented
57C2×#66988C2212yescomplemented
58C2×D4×Dic11C2212yescomplemented
59C2×D4×Dic11C2212yescomplemented
60C2×D4×Dic11C2212yescomplemented
61C2×D4×Dic11C2212yescomplemented
62C2×#66982C2211yescharacteristic, complemented
63C2×C4×C22⋊D11C2212yescomplemented
64C2×C4×C22⋊D11C2212yescomplemented
65C22×(C2×D11)⋊C4C2212yescomplemented
66C2×#66979C2212yescomplemented
67C2×#66977C2212yescomplemented
68#10623246C22116yescomplemented
69#10623244C22116yescomplemented
70#10623241C22132yescomplemented
71#10623233C22132yescomplemented
72#10623195C22116yescomplemented
73#10623193C22132yescomplemented
74#10623189C22132yescomplemented
75#10623179C22116yescomplemented
76#10623148C22132yescomplemented
77#10623147C22132yescomplemented
78#10623144C22132yescomplemented
79#10623141C22132yescomplemented
80#10623134C22132yescomplemented
81#10623129C22132yescomplemented
82#10623126C22116yescomplemented
83#10623125C22132yescomplemented
84#10623117C22116yescomplemented
85#10623117C22132yescomplemented
86C2×#66951C2212yescomplemented
87C2×#66951C2212yescomplemented
88C2×#66951C2212yescomplemented
89C2×#66950C2212yescomplemented
90C2×#66949C2212yescomplemented
91C2×#66949C2212yescomplemented
92C2×#66947C2212yescomplemented
93C2×#66945C2212yescomplemented
94C2×#66941C2212yescomplemented
95C2×#66941C2212yescomplemented
96C2×#66940C2212yescomplemented
97C2×#66940C2212yescomplemented
98C2×#66939C2211yescharacteristic
99C2×#66939C2211yescharacteristic, complemented
100C2×#66939C2212yescomplemented
101C2×#66938C2212yes—
102C2×#66938C2212yes—
103C2×#66938C2212yes—
104C2×#66938C2212yescomplemented
105C2×#66938C2212yescomplemented
106C2×#66938C2212yescomplemented
107C2×#66938C2212yescomplemented
108C2×#66938C2212yescomplemented
109C2×#66937C2212yes—
110C2×#66936C2212yescomplemented
111C2×(C22⋊D11)⋊C4C2212yes—
112C2×(C22⋊D11)⋊C4C2212yescomplemented
113C2×(C22⋊D11)⋊C4C2212yescomplemented
114C2×C22⋊C4×D11C2212yescomplemented
115C2×#66932C2212yescomplemented
116C2×#66932C2212yescomplemented
117C2×#66931C2212yescomplemented
118C2×#66931C2212yescomplemented
119C2×#66931C2212yescomplemented
120C2×#66931C2212yescomplemented
121C2×#66930C2211yescharacteristic, complemented
122C2×#66930C2212yescomplemented
123C2×#66930C2211yescharacteristic, complemented
124C2×#66928C2211yescharacteristic, complemented
125C2×#66925C2211yescharacteristic, complemented
126C2×C4×Dic22C2212yescomplemented
127C25×C11C2311yescharacteristic
128C24×D11C2312yes—
129C22×D4×C11C2312yes—
130C22×D4×C11C2312yes—
131C22×D4×C11C2312yes—
132C22×D4×C11C2312yes—
133C22×D4×C11C2311yescharacteristic
134C22×D4×C11C2311yescharacteristic
135C22×D4×C11C2312yes—
136C23×C4×C11C2312yes—
137C23×C4×C11C2311yescharacteristic
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C22×C22⋊D11C2312yes—
143C22×C22⋊D11C2311yescharacteristic
144C22×C22⋊D11C2312yes—
145C22×C22⋊D11C2311yescharacteristic
146C23×Dic11—44no—
147C23×Dic11C2311yescharacteristic
148C23×Dic11C2312yes—
149C23×Dic11C2311yescharacteristic
150C23×Dic11C2312yes—
151C23×Dic11C2312yes—
152C23×Dic11C2311yescharacteristic
153C23×Dic11C2311yescharacteristic
154C23×Dic11C2318yescomplemented
155C2×#4341—48no—
156C2×#4341—44no—
157C2×#4341C2318yes—
158C2×#4341C23116yes—
159C2×D4×D11—44no—
160C2×D4×D11C2318yescomplemented
161C22×D44C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2312yes—
164C22×C4×D11C2312yes—
165C22×Dic22—44no—
166C22×Dic22C2312yes—
167C22×Dic22C2312yes—
168C22×Dic22C2311yescharacteristic
169C22×Dic22C2312yes—
170C22×Dic22C2312yes—
171C22×Dic22C2318yescomplemented
172C11×#127C2318yes—
173C11×#126C23116yescomplemented
174C11×#123C2318yescomplemented
175C11×#123C23116yescomplemented
176C11×#121C23116yes—
177C11×#121C23116yescomplemented
178C11×#121C23116yescomplemented
179C11×#120C23116yescomplemented
180C11×#120C2318yescomplemented
181C2×C11×C4⋊C4C2312yes—
182C2×C11×C4⋊C4C2312yes—
183C2×C11×C4⋊C4C2312yes—
184C2×C11×C22⋊C4C2311yescharacteristic
185C2×C11×C22⋊C4C2312yes—
186C2×C11×C22⋊C4C2311yescharacteristic
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C42×C11C2311yescharacteristic
192#67006C2318yes—
193#67006C23116yescomplemented
194C2×C22⋊Dic11C2312yes—
195C2×C22⋊Dic11C2311yescharacteristic
196C2×C22⋊Dic11C2311yescharacteristic
197C2×C22⋊Dic11C2312yes—
198C2×C22⋊Dic11C2312yes—
199C2×C22⋊Dic11C2312yes—
200C2×C22⋊Dic11C2312yes—
201C2×C22⋊Dic11C2312yes—
202C2×C22⋊Dic11C2312yes—
203C2×C22⋊Dic11C2312yes—
204C2×C22⋊Dic11C2312yes—
205C2×C22⋊Dic11C2312yes—
206#66993C2318yes—
207#66992C23116yes—
208#66992C23116yes—
209#66992C23116yes—
210#66992C23116yescomplemented
211#66992C23116yescomplemented
212#66991C23116yescomplemented
213#66990C23116yes—
214#66990C23116yes—
215#66990C23116yes—
216#66990C23116yescomplemented
217#66989C23116yescomplemented
218#66989C23116yescomplemented
219#66989C2318yescomplemented
220#66989C23116yescomplemented
221#66989C23116yescomplemented
222#66988C2318yescomplemented
223#66988C2318yescomplemented
224#66988C23116yescomplemented
225#66988C23116yescomplemented
226D4×Dic11C23116yescomplemented
227D4×Dic11C23116yescomplemented
228D4×Dic11C23116yescomplemented
229D4×Dic11C23116yescomplemented
230#66982C2318yescomplemented
231C4×C22⋊D11C23116yescomplemented
232C4×C22⋊D11C23116yescomplemented
233C2×(C2×D11)⋊C4C2312yes—
234C2×(C2×D11)⋊C4C2312yes—
235C2×(C2×D11)⋊C4C2312yes—
236C2×(C2×D11)⋊C4C2312yes—
237C2×(C2×D11)⋊C4C2312yes—
238C2×(C2×D11)⋊C4C2312yes—
239C2×(C2×D11)⋊C4C2312yes—
240C2×(C2×D11)⋊C4C2312yes—
241C2×(C2×D11)⋊C4C2312yes—
242C2×(C2×D11)⋊C4C2312yes—
243C2×(C2×D11)⋊C4C23116yescomplemented
244#66979C23116yescomplemented
245C2×C4⋊Dic11C2312yes—
246C2×C4⋊Dic11C2312yes—
247C2×C4⋊Dic11C2312yes—
248C2×C4⋊Dic11C2312yes—
249#66977C23116yescomplemented
250C2×Dic11⋊C4C2312yes—
251C2×Dic11⋊C4C2312yes—
252C2×Dic11⋊C4C2312yes—
253C2×Dic11⋊C4C2312yes—
254C2×Dic11⋊C4C2312yes—
255C2×Dic11⋊C4C2312yes—
256C2×Dic11⋊C4C2312yes—
257C2×Dic11⋊C4C2312yes—
258C2×C4×Dic11C2312yes—
259C2×C4×Dic11C2312yes—
260C2×C4×Dic11C2311yescharacteristic
261C2×C4×Dic11C2312yes—
262C2×C4×Dic11C2312yes—
263C2×C4×Dic11C2312yes—
264C2×C4×Dic11C2312yes—
265#66951C23116yescomplemented
266#66951C23116yescomplemented
267#66951C23116yescomplemented
268#66950C23116yescomplemented
269#66949C23116yescomplemented
270#66949C23116yescomplemented
271#66947C23116yescomplemented
272#66945C23116yescomplemented
273#66941C23116yescomplemented
274#66941C23116yescomplemented
275#66940C23116yescomplemented
276#66940C23116yescomplemented
277#66939C2318yes—
278#66939C23116yescomplemented
279#66939C2318yescomplemented
280#66938C23116yes—
281#66938C23116yes—
282#66938C23116yes—
283#66938C23116yescomplemented
284#66938C23116yescomplemented
285#66938C23116yescomplemented
286#66938C23116yescomplemented
287#66938C23116yescomplemented
288#66937C23116yes—
289#66936C23116yescomplemented
290(C22⋊D11)⋊C4C23116yes—
291(C22⋊D11)⋊C4C23116yescomplemented
292(C22⋊D11)⋊C4C23116yescomplemented
293C22⋊C4×D11C23116yescomplemented
294#66932C23116yescomplemented
295#66932C23116yescomplemented
296#66931C23116yescomplemented
297#66931C23116yescomplemented
298#66931C23116yescomplemented
299#66931C23116yescomplemented
300#66930C23116yescomplemented
301#66930C2318yescomplemented
302#66930C2318yescomplemented
303#66928C2318yescomplemented
304#66925C2318yescomplemented
305C4×Dic22C23116yescomplemented
306C2×#3540—111nomaximal, Sylow
307C24×C11—42no—
308C24×C11—44no—
309C24×C11C2412yes—
310C24×C11C2412yes—
311C24×C11C2411yescharacteristic
312C24×C11C2411yescharacteristic
313C24×C11C2414yes—
314C23×D11—44no—
315C23×D11—44no—
316C23×D11—44no—
317C23×D11C2411yescharacteristic
318C23×D11C2412yes—
319C23×D11C2418yes—
320C2×D4×C11—42no—
321C2×D4×C11—44no—
322C2×D4×C11—42no—
323C2×D4×C11—44no—
324C2×D4×C11—44no—
325C2×D4×C11—44no—
326C2×D4×C11—44no—
327C2×D4×C11C2418yes—
328C2×D4×C11C2418yes—
329C2×D4×C11C2418yes—
330C2×D4×C11C2418yes—
331C2×D4×C11C2414yes—
332C2×D4×C11C2414yes—
333C2×D4×C11C2418yes—
334C22×C4×C11—42no—
335C22×C4×C11—44no—
336C22×C4×C11C2412yes—
337C22×C4×C11C2412yes—
338C22×C4×C11C2411yescharacteristic
339C22×C4×C11C2412yes—
340C22×C4×C11C2412yes—
341C22×C4×C11C2418yes—
342C22×C4×C11C2414yes—
343C2×C22⋊D11—28no—
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⋊D11—44no—
351C2×C22⋊D11C2418yes—
352C2×C22⋊D11C2418yes—
353C2×C22⋊D11C2418yes—
354C2×C22⋊D11C2418yes—
355C2×C22⋊D11C2418yes—
356C2×C22⋊D11C2414yes—
357C2×C22⋊D11C2418yes—
358C2×C22⋊D11C2414yes—
359C22×Dic11—24no—
360C22×Dic11—24no—
361C22×Dic11—28no—
362C22×Dic11—42no—
363C22×Dic11—44no—
364C22×Dic11—44no—
365C22×Dic11—42no—
366C22×Dic11—416no—
367C22×Dic11C2414yes—
368C22×Dic11C2418yes—
369C22×Dic11C2414yes—
370C22×Dic11C2412yes—
371C22×Dic11C2412yes—
372C22×Dic11C2412yes—
373C22×Dic11C2412yes—
374C22×Dic11C2411yescharacteristic
375C22×Dic11C2412yes—
376C22×Dic11C2411yescharacteristic
377C22×Dic11C2418yes—
378C22×Dic11C2418yes—
379C22×Dic11C2414yes—
380C22×Dic11C2414yes—
381C22×Dic11C2411yescharacteristic
382#4341—432no—
383#4341—416no—
384D4×D11—416no—
385C2×D44—42no—
386C2×D44C2414yes—
387C2×C4×D11—24no—
388C2×C4×D11—44no—
389C2×C4×D11—44no—
390C2×C4×D11C2414yes—
391C2×C4×D11C2418yes—
392C2×C4×D11C2418yes—
393C2×Dic22—28no—
394C2×Dic22—44no—
395C2×Dic22—44no—
396C2×Dic22—44no—
397C2×Dic22—42no—
398C2×Dic22—416no—
399C2×Dic22C2418yes—
400C2×Dic22C2418yes—
401C2×Dic22C2414yes—
402C2×Dic22C2418yes—
403C2×Dic22C2418yes—
404C11×C4⋊C4C2418yes—
405C11×C4⋊C4C2418yes—
406C11×C4⋊C4C2418yes—
407C11×C22⋊C4C2414yes—
408C11×C22⋊C4C2418yes—
409C11×C22⋊C4C2414yes—
410C11×C22⋊C4C2418yes—
411C11×C22⋊C4C2418yes—
412C11×C22⋊C4C2418yes—
413C11×C22⋊C4C2418yes—
414C42×C11C2414yes—
415C22⋊Dic11C2418yes—
416C22⋊Dic11C2414yes—
417C22⋊Dic11C2414yes—
418C22⋊Dic11C2418yes—
419C22⋊Dic11C2418yes—
420C22⋊Dic11C2418yes—
421C22⋊Dic11C2418yes—
422C22⋊Dic11C2418yes—
423C22⋊Dic11C2418yes—
424C22⋊Dic11C2418yes—
425C22⋊Dic11C2418yes—
426C22⋊Dic11C2418yes—
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—
437C4⋊Dic11C2418yes—
438C4⋊Dic11C2418yes—
439C4⋊Dic11C2418yes—
440C4⋊Dic11C2418yes—
441Dic11⋊C4C2418yes—
442Dic11⋊C4C2418yes—
443Dic11⋊C4C2418yes—
444Dic11⋊C4C2418yes—
445Dic11⋊C4C2418yes—
446Dic11⋊C4C2418yes—
447Dic11⋊C4C2418yes—
448Dic11⋊C4C2418yes—
449C4×Dic11C2418yes—
450C4×Dic11C2418yes—
451C4×Dic11C2414yes—
452C4×Dic11C2418yes—
453C4×Dic11C2418yes—
454C4×Dic11C2418yes—
455C4×Dic11C2418yes—
456#3540—1132no—
457C2×H(3,𝔽4)—112no—
458C2×#560—111no—
459C2×#560D1111yescharacteristic, complemented
460C2×#559—111no—
461C2×#559—111no—
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×C11—24no—
484C23×C11—24no—
485C23×C11—24no—
486C23×C11—44no—
487C23×C11—48no—
488C23×C11—416no—
489C23×C11C2514yes—
490C23×C11C2514yes—
491C23×C11C2512yes—
492C23×C11C2512yes—
493C23×C11C2511yescharacteristic
494C22×D11—22no—
495C22×D11—24no—
496C22×D11—24no—
497C22×D11—24no—
498C22×D11—24no—
499C22×D11—48no—
500C22×D11—48no—
501C22×D11—48no—
502C22×D11—816no—
503C22×D11C2512yes—
504C22×D11C2514yes—
505D4×C11—44no—
506D4×C11—48no—
507D4×C11—44no—
508D4×C11—48no—
509D4×C11—48no—
510D4×C11—48no—
511D4×C11—48no—
512C2×C4×C11—24no—
513C2×C4×C11—22no—
514C2×C4×C11—24no—
515C2×C4×C11—24no—
516C2×C4×C11—24no—
517C2×C4×C11—44no—
518C2×C4×C11—48no—
519C2×C4×C11C2514yes—
520C2×C4×C11C2514yes—
521C2×C4×C11C2512yes—
522C2×C4×C11C2514yes—
523C2×C4×C11C2514yes—
524C22⋊D11—216no—
525C22⋊D11—48no—
526C22⋊D11—44no—
527C22⋊D11—44no—
528C22⋊D11—48no—
529C22⋊D11—48no—
530C22⋊D11—48no—
531C22⋊D11—48no—
532C2×Dic11—24no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—24no—
536C2×Dic11—24no—
537C2×Dic11—24no—
538C2×Dic11—24no—
539C2×Dic11—28no—
540C2×Dic11—28no—
541C2×Dic11—216no—
542C2×Dic11—44no—
543C2×Dic11—48no—
544C2×Dic11—48no—
545C2×Dic11—44no—
546C2×Dic11H(5,𝔽2)14yes—
547C2×Dic11C2514yes—
548C2×Dic11C2514yes—
549C2×Dic11C2514yes—
550C2×Dic11C2514yes—
551C2×Dic11C2512yes—
552C2×Dic11C2514yes—
553C2×Dic11C2512yes—
554C2×Dic11C2512yes—
555D44—44no—
556C4×D11—28no—
557C4×D11—48no—
558C4×D11—48no—
559Dic22—216no—
560Dic22—48no—
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#560C2×D11116yescomplemented
572#559—1116no—
573#559—1116no—
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×#126C2×D1112yescomplemented
596C2×#124—111no—
597C2×#124—112no—
598C2×#124—112no—
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—111no—
610#525—1116no—
611#525—1132no—
612C2×#123—112no—
613C2×#123—111no—
614C2×#123—111no—
615C2×#123—112no—
616C2×#123—111no—
617C2×#123—112no—
618C2×#123—112no—
619C2×#123—111no—
620C2×#123—112no—
621C2×#123—111no—
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×#121C2×D1112yes—
640C2×#121C2×D1112yescomplemented
641C2×#121C2×D1112yescomplemented
642C2×#120—111no—
643C2×#120—112no—
644C2×#120—112no—
645C2×#120—112no—
646C2×#120—112no—
647C2×#120—112no—
648C2×#120C2×D1111yescharacteristic, complemented
649C2×#120C2×D1112yescomplemented
650C2×C4×Q8—112no—
651C2×C4×Q8—112no—
652C2×C4×Q8—112no—
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×D4—112no—
661C2×C4×D4—112no—
662C2×#117—112no—
663C2×#117—112no—
664C2×#117—111no—
665C2×#117—112no—
666C2×#117—111no—
667C2×#117—111no—
668C22×C22⋊C4—112no—
669C22×C22⋊C4—112no—
670C22×C11—22no—
671C22×C11—24no—
672C22×C11—24no—
673C22×C11—22no—
674C22×C11—24no—
675C22×C11—24no—
676C22×C11—24no—
677C22×C11—24no—
678C22×C11—24no—
679C22×C11—24no—
680C22×C11—416no—
681C22×C11—48no—
682C22×C11—44no—
683C22×C11—44no—
684C22×C11—48no—
685C22×C11C2×H(5,𝔽2)12yes—
686C22×C11#58514yes—
687C22×C11C2611yescharacteristic
688C2×D11—22no—
689C2×D11—24no—
690C2×D11—24no—
691C2×D11—24no—
692C2×D11—24no—
693C2×D11—48no—
694C2×D11—44no—
695C2×D11—816no—
696C4×C11—24no—
697C4×C11—22no—
698C4×C11—24no—
699C4×C11—24no—
700C4×C11—24no—
701Dic11—24no—
702Dic11—22no—
703Dic11—22no—
704Dic11—24no—
705Dic11—24no—
706Dic11—24no—
707Dic11—24no—
708Dic11C2×H(5,𝔽2)14yes—
709C25—112no—
710C25C22×D1111yescharacteristic
711C2×#41—118no—
712C2×#41—1116no—
713C2×#41—444no—
714C2×#41—448no—
715C22×Q8—112no—
716C22×Q8—112no—
717C22×Q8—112no—
718C22×Q8—112no—
719C22×Q8—111no—
720C22×Q8—118no—
721C22×Q8—444no—
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—111no—
732C22×D4—444no—
733C22×D4C22×D1112yes—
734C22×D4C22×D1112yes—
735C22×D4C22×D1112yes—
736C22×D4C22×D1112yes—
737C22×D4C22×D1112yes—
738C22×D4C22×D1111yescharacteristic
739C22×D4C22×D1111yescharacteristic
740C23×C4—111no—
741C23×C4—112no—
742C23×C4—111no—
743C23×C4—112no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—112no—
747C23×C4—118no—
748C23×C4—111no—
749C23×C4—112no—
750C23×C4—112no—
751C23×C4—444no—
752C23×C4C22×D1112yes—
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#126C22×D11116yescomplemented
764#124—118no—
765#124—1116no—
766#124—1116no—
767#124—1116no—
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—118no—
778#123—1116no—
779#123—118no—
780#123—118no—
781#123—1116no—
782#123—118no—
783#123—1116no—
784#123—1116no—
785#123—118no—
786#123—118no—
787#123—1116no—
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#121C22×D11116yes—
806#121C22×D11116yescomplemented
807#121C22×D11116yescomplemented
808#120—1116no—
809#120—118no—
810#120—1116no—
811#120—1116no—
812#120—1116no—
813#120—1116no—
814#120C22×D1118yescomplemented
815#120C22×D11116yescomplemented
816C4×Q8—1116no—
817C4×Q8—1116no—
818C4×Q8—1116no—
819C4×D4—1116no—
820C4×D4—1116no—
821C4×D4—1116no—
822C4×D4—1116no—
823C4×D4—1116no—
824C4×D4—1116no—
825C4×D4—1116no—
826C4×D4—1116no—
827C4×D4—1116no—
828#117—1116no—
829#117—1116no—
830#117—118no—
831#117—1116no—
832#117—118no—
833#117—118no—
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—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—1116no—
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×D1111yescharacteristic
876C2×C22⋊C4C22×D1111yescharacteristic
877C2×C22⋊C4C22×D1112yes—
878C2×C22⋊C4C22×D1112yes—
879C2×C22⋊C4C22×D1112yes—
880C2×C42—112no—
881C2×C42—112no—
882C2×C42—112no—
883C2×C42—112no—
884C2×C42—111no—
885C2×C42—112no—
886C2×C42—112no—
887C2×C42C22×D1111yescharacteristic
888C2×C11—44no—
889C2×C11—42no—
890C2×C11—44no—
891C2×C11—42no—
892C2×C11#354014yescomplemented
893C2×C11C22×H(5,𝔽2)11yescharacteristic
894C2×C11C2×#58512yes—
895D11—44no—
896D11—42no—
897C24—42no—
898C24—44no—
899C24—111no—
900C24—112no—
901C24—118no—
902C24—444no—
903C24—444no—
904C24—444no—
905C24C23×D1112yes—
906C24C23×D1112yes—
907C24C23×D1111yescharacteristic
908C24C23×D1111yescharacteristic
909C24C23×D1114yes—
910#41—4416no—
911#41—4432no—
912C2×Q8—118no—
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—444no—
922C2×Q8—4416no—
923C2×D4—42no—
924C2×D4—44no—
925C2×D4—42no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—118no—
931C2×D4—118no—
932C2×D4—118no—
933C2×D4—118no—
934C2×D4—118no—
935C2×D4—114no—
936C2×D4—114no—
937C2×D4—118no—
938C2×D4—114no—
939C2×D4—228no—
940C2×D4—442no—
941C2×D4—4416no—
942C2×D4—442no—
943C2×D4—442no—
944C2×D4—444no—
945C2×D4—444no—
946C2×D4—444no—
947C2×D4—444no—
948C2×D4—444no—
949C2×D4C23×D1118yes—
950C2×D4C23×D1118yes—
951C2×D4C23×D1118yes—
952C2×D4C23×D1118yes—
953C2×D4C23×D1118yes—
954C2×D4C23×D1114yes—
955C2×D4C23×D1114yes—
956C22×C4—42no—
957C22×C4—44no—
958C22×C4—111no—
959C22×C4—114no—
960C22×C4—118no—
961C22×C4—114no—
962C22×C4—112no—
963C22×C4—112no—
964C22×C4—112no—
965C22×C4—111no—
966C22×C4—112no—
967C22×C4—112no—
968C22×C4—111no—
969C22×C4—118no—
970C22×C4—114no—
971C22×C4—114no—
972C22×C4—118no—
973C22×C4—114no—
974C22×C4—118no—
975C22×C4—118no—
976C22×C4—224no—
977C22×C4—228no—
978C22×C4—224no—
979C22×C4—224no—
980C22×C4—444no—
981C22×C4—444no—
982C22×C4—4416no—
983C22×C4—442no—
984C22×C4—444no—
985C22×C4—442no—
986C22×C4—444no—
987C22×C4C23×D1112yes—
988C22×C4C23×D1112yes—
989C22×C4C23×D1111yescharacteristic
990C22×C4C23×D1112yes—
991C22×C4C23×D1112yes—
992C22×C4C23×D1118yes—
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—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⋊C4C23×D1118yes—
1032C22⋊C4C23×D1118yes—
1033C22⋊C4C23×D1114yes—
1034C22⋊C4C23×D1114yes—
1035C22⋊C4C23×D1118yes—
1036C22⋊C4C23×D1118yes—
1037C22⋊C4C23×D1118yes—
1038C42—118no—
1039C42—118no—
1040C42—118no—
1041C42—118no—
1042C42—114no—
1043C42—118no—
1044C42—118no—
1045C42C23×D1114yes—
1046C11C2×#354011yescharacteristic, complemented, Sylow
1047C23—22no—
1048C23—24no—
1049C23—22no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—24no—
1054C23—24no—
1055C23—24no—
1056C23—24no—
1057C23—44no—
1058C23—48no—
1059C23—416no—
1060C23—112no—
1061C23—114no—
1062C23—222no—
1063C23—224no—
1064C23—224no—
1065C23—224no—
1066C23—224no—
1067C23—448no—
1068C23—448no—
1069C23—448no—
1070C23—8816no—
1071C23C24×D1114yes—
1072C23C24×D1114yes—
1073C23C24×D1112yes—
1074C23C24×D1112yes—
1075C23C24×D1111yescharacteristic
1076Q8—2216no—
1077Q8—448no—
1078Q8—444no—
1079Q8—448no—
1080Q8—448no—
1081D4—44no—
1082D4—48no—
1083D4—48no—
1084D4—48no—
1085D4—48no—
1086D4—48no—
1087D4—44no—
1088D4—2216no—
1089D4—444no—
1090D4—444no—
1091D4—444no—
1092D4—448no—
1093D4—448no—
1094D4—448no—
1095D4—448no—
1096D4—448no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—48no—
1103C2×C4—44no—
1104C2×C4—114no—
1105C2×C4—112no—
1106C2×C4—114no—
1107C2×C4—114no—
1108C2×C4—114no—
1109C2×C4—112no—
1110C2×C4—114no—
1111C2×C4—114no—
1112C2×C4—112no—
1113C2×C4—228no—
1114C2×C4—2216no—
1115C2×C4—228no—
1116C2×C4—228no—
1117C2×C4—224no—
1118C2×C4—222no—
1119C2×C4—222no—
1120C2×C4—224no—
1121C2×C4—224no—
1122C2×C4—224no—
1123C2×C4—224no—
1124C2×C4—448no—
1125C2×C4—448no—
1126C2×C4—444no—
1127C2×C4—448no—
1128C2×C4—444no—
1129C2×C4—448no—
1130C2×C4C24×D1114yes—
1131C2×C4C24×D1114yes—
1132C2×C4C24×D1112yes—
1133C2×C4C24×D1114yes—
1134C2×C4C24×D1114yes—
1135C22—22no—
1136C22—24no—
1137C22—22no—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—416no—
1146C22—48no—
1147C22—44no—
1148C22—48no—
1149C22—44no—
1150C22—222no—
1151C22—224no—
1152C22—224no—
1153C22—224no—
1154C22—224no—
1155C22—444no—
1156C22—448no—
1157C22—8816no—
1158C22D11×H(5,𝔽2)12yes—
1159C22#1062345514yes—
1160C22C25×D1111yescharacteristic
1161C4—24no—
1162C4—22no—
1163C4—24no—
1164C4—24no—
1165C4—24no—
1166C4—114no—
1167C4—224no—
1168C4—222no—
1169C4—222no—
1170C4—224no—
1171C4—224no—
1172C4—224no—
1173C4—224no—
1174C2—44no—
1175C2—42no—
1176C2—44no—
1177C2—42no—
1178C2—442no—
1179C2—444no—
1180C2#1308288314yesdirect product factor
1181C2C2×D11×H(5,𝔽2)11yescharacteristic
1182C2C2×#1062345512yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#560C2
socleC23×C11C25
hypercenterC2×#560D11
hypocenterC11C2×#3540
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#560

Complements

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

NH ≅ G/Ntype
1. #13082883C2direct (N × H)
2. C2×#10623125C2semidirect
3. C2×#10623126C2semidirect
4. C2×#10623244C2semidirect
5. C2×#10623195C2semidirect
6. C2×#10623233C2semidirect
7. C2×#10623147C2semidirect
8. C2×#10623189C2semidirect
9. C2×#10623129C2semidirect
10. C2×#10623141C2semidirect
11. C2×#10623193C2semidirect
12. C2×#10623134C2semidirect
13. C2×#10623241C2semidirect
14. C2×#10623148C2semidirect
15. C2×#10623144C2semidirect
16. C2×#10623179C2semidirect
17. C2×#10623246C2semidirect
18. C2×#10623117C2semidirect
19. C2×#10623117C2semidirect
20. C2×C11×#560C2semidirect
21. C24×Dic11C22semidirect
24. C22×D4×D11C22semidirect
25. C23×Dic22C22semidirect
26. C11×#560C22semidirect
28. C2×C11×#126C22semidirect
29. C2×C11×#123C22semidirect
30. C2×C11×#123C22semidirect
32. C2×C11×#121C22semidirect
33. C2×C11×#121C22semidirect
34. C2×C11×#120C22semidirect
35. C2×C11×#120C22semidirect
37. C2×#67006C22semidirect
42. C2×#66992C22semidirect
43. C2×#66992C22semidirect
44. C2×#66991C22semidirect
48. C2×#66990C22semidirect
49. C2×#66989C22semidirect
50. C2×#66989C22semidirect
51. C2×#66989C22semidirect
52. C2×#66989C22semidirect
53. C2×#66989C22semidirect
54. C2×#66988C22semidirect
55. C2×#66988C22semidirect
56. C2×#66988C22semidirect
57. C2×#66988C22semidirect
58. C2×D4×Dic11C22semidirect
59. C2×D4×Dic11C22semidirect
60. C2×D4×Dic11C22semidirect
61. C2×D4×Dic11C22semidirect
62. C2×#66982C22semidirect
63. C2×C4×C22⋊D11C22semidirect
64. C2×C4×C22⋊D11C22semidirect
65. C22×(C2×D11)⋊C4C22semidirect
66. C2×#66979C22semidirect
67. C2×#66977C22semidirect
68. #10623246C22semidirect
69. #10623244C22semidirect
70. #10623241C22semidirect
71. #10623233C22semidirect
72. #10623195C22semidirect
73. #10623193C22semidirect
74. #10623189C22semidirect
75. #10623179C22semidirect
76. #10623148C22semidirect
77. #10623147C22semidirect
78. #10623144C22semidirect
79. #10623141C22semidirect
80. #10623134C22semidirect
81. #10623129C22semidirect
82. #10623126C22semidirect
83. #10623125C22semidirect
84. #10623117C22semidirect
85. #10623117C22semidirect
86. C2×#66951C22semidirect
87. C2×#66951C22semidirect
88. C2×#66951C22semidirect
89. C2×#66950C22semidirect
90. C2×#66949C22semidirect
91. C2×#66949C22semidirect
92. C2×#66947C22semidirect
93. C2×#66945C22semidirect
94. C2×#66941C22semidirect
95. C2×#66941C22semidirect
96. C2×#66940C22semidirect
97. C2×#66940C22semidirect
99. C2×#66939C22semidirect
100. C2×#66939C22semidirect
104. C2×#66938C22semidirect
105. C2×#66938C22semidirect
106. C2×#66938C22semidirect
107. C2×#66938C22semidirect
108. C2×#66938C22semidirect
110. C2×#66936C22semidirect
112. C2×(C22⋊D11)⋊C4C22semidirect
113. C2×(C22⋊D11)⋊C4C22semidirect
114. C2×C22⋊C4×D11C22semidirect
115. C2×#66932C22semidirect
116. C2×#66932C22semidirect
117. C2×#66931C22semidirect
118. C2×#66931C22semidirect
119. C2×#66931C22semidirect
120. C2×#66931C22semidirect
121. C2×#66930C22semidirect
122. C2×#66930C22semidirect
123. C2×#66930C22semidirect
124. C2×#66928C22semidirect
125. C2×#66925C22semidirect
126. C2×C4×Dic22C22semidirect
154. C23×Dic11C23semidirect
160. C2×D4×D11C23semidirect
171. C22×Dic22C23semidirect
173. C11×#126C23semidirect
174. C11×#123C23semidirect
175. C11×#123C23semidirect
177. C11×#121C23semidirect
178. C11×#121C23semidirect
179. C11×#120C23semidirect
180. C11×#120C23semidirect
193. #67006C23semidirect
210. #66992C23semidirect
211. #66992C23semidirect
212. #66991C23semidirect
216. #66990C23semidirect
217. #66989C23semidirect
218. #66989C23semidirect
219. #66989C23semidirect
220. #66989C23semidirect
221. #66989C23semidirect
222. #66988C23semidirect
223. #66988C23semidirect
224. #66988C23semidirect
225. #66988C23semidirect
226. D4×Dic11C23semidirect
227. D4×Dic11C23semidirect
228. D4×Dic11C23semidirect
229. D4×Dic11C23semidirect
230. #66982C23semidirect
231. C4×C22⋊D11C23semidirect
232. C4×C22⋊D11C23semidirect
243. C2×(C2×D11)⋊C4C23semidirect
244. #66979C23semidirect
249. #66977C23semidirect
265. #66951C23semidirect
266. #66951C23semidirect
267. #66951C23semidirect
268. #66950C23semidirect
269. #66949C23semidirect
270. #66949C23semidirect
271. #66947C23semidirect
272. #66945C23semidirect
273. #66941C23semidirect
274. #66941C23semidirect
275. #66940C23semidirect
276. #66940C23semidirect
278. #66939C23semidirect
279. #66939C23semidirect
283. #66938C23semidirect
284. #66938C23semidirect
285. #66938C23semidirect
286. #66938C23semidirect
287. #66938C23semidirect
289. #66936C23semidirect
291. (C22⋊D11)⋊C4C23semidirect
292. (C22⋊D11)⋊C4C23semidirect
293. C22⋊C4×D11C23semidirect
294. #66932C23semidirect
295. #66932C23semidirect
296. #66931C23semidirect
297. #66931C23semidirect
298. #66931C23semidirect
299. #66931C23semidirect
300. #66930C23semidirect
301. #66930C23semidirect
302. #66930C23semidirect
303. #66928C23semidirect
304. #66925C23semidirect
305. C4×Dic22C23semidirect
459. C2×#560D11semidirect
571. #560C2×D11semidirect
595. C2×#126C2×D11semidirect
622. C2×#123C2×D11semidirect
623. C2×#123C2×D11semidirect
640. C2×#121C2×D11semidirect
641. C2×#121C2×D11semidirect
648. C2×#120C2×D11semidirect
649. C2×#120C2×D11semidirect
763. #126C22×D11semidirect
788. #123C22×D11semidirect
789. #123C22×D11semidirect
806. #121C22×D11semidirect
807. #121C22×D11semidirect
814. #120C22×D11semidirect
815. #120C22×D11semidirect
892. C2×C11#3540semidirect
1046. C11C2×#3540semidirect
1180. C2#13082883direct (N × H)

Maximal subgroups

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

subgroupindex
#130828832
C2×#106231252
C2×#106231262
C2×#106232442
C2×#106231952
C2×#106232332
C2×#106231472
C2×#106231892
C2×#106231292
C2×#106231412
C2×#106231932
C2×#106231342
C2×#106232412
C2×#106231482
C2×#106231442
C2×#106231792
C2×#106232462
C2×#106231172
C2×C11×#5602
C2×#354011