Finite Group Databasebeta

← C2×#13082754 #15660664

Subgroups — C2×#13082754 #15660664

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#13082754C2132yesmaximal, direct product factor
2C2×#10623182C211yesmaximal, characteristic, complemented
3C2×#10623177C212yesmaximal, complemented
4C2×#10623198C212yesmaximal, complemented
5C2×#10623178C212yesmaximal, complemented
6C2×#10623152C212yesmaximal, complemented
7C2×#10623125C211yesmaximal, characteristic, complemented
8C2×#10623197C211yesmaximal, characteristic, complemented
9C2×#10623126C212yesmaximal, complemented
10C2×#10623126C211yesmaximal, characteristic, complemented
11C2×#10623151C212yesmaximal, complemented
12C2×#10623079C212yesmaximal, complemented
13C2×#10623363C211yesmaximal, characteristic, complemented
14C2×#10623088C212yesmaximal, complemented
15C2×#10623069C212yesmaximal, complemented
16C2×#10623059C212yesmaximal, complemented
17C2×#10623322C212yesmaximal, complemented
18C2×#10623078C212yesmaximal, complemented
19C2×#10623359C211yesmaximal, characteristic, complemented
20C2×C11×#525C211yesmaximal, characteristic, complemented
21C22×C11×#41C2211yescharacteristic
22C24×C4×C11C2211yescharacteristic, complemented
23C22×#4339C2212yes—
24C22×#4339C2211yescharacteristic, complemented
25C23×C4×D11C2211yescharacteristic, complemented
26C11×#525C22116yescomplemented
27C2×C11×#123C2211yescharacteristic
28C2×C11×#123C2211yescharacteristic, complemented
29C2×C11×C22⋊Q8C2212yescomplemented
30C2×C11×#121C2212yes—
31C2×C11×#120C2211yescharacteristic
32C2×C11×#120C2211yescharacteristic, complemented
33C2×C4×D4×C11C2212yes—
34C2×C4×D4×C11C2212yescomplemented
35C2×C11×#117C2211yescharacteristic, complemented
36C2×#67006C2212yes—
37C2×#67006C2212yescomplemented
38#10623363C22116yescomplemented
39#10623359C22116yescomplemented
40C2×#67000C2211yescharacteristic, complemented
41C2×#66999C2212yescomplemented
42C2×#66997C2211yescharacteristic, complemented
43C2×#66993C2211yescharacteristic
44C2×#66993C2212yes—
45C2×#66992C2212yes—
46C2×#66992C2212yes—
47C2×#66992C2212yescomplemented
48C2×#66992C2212yescomplemented
49C2×#66991C2212yes—
50C2×#66991C2212yes—
51C2×#66991C2212yescomplemented
52C2×#66990C2212yes—
53C2×#66990C2211yescharacteristic
54C2×#66990C2211yescharacteristic, complemented
55C2×#66989C2212yes—
56C2×#66989C2211yescharacteristic
57C2×#66988C2211yescharacteristic
58C2×#66988C2212yescomplemented
59C2×#66988C2211yescharacteristic, complemented
60#10623322C22132yescomplemented
61C2×#66983C2212yes—
62C2×#66983C2212yes—
63C2×#66982C2212yes—
64C2×#66982C2212yescomplemented
65C2×C4×C22⋊D11C2212yes—
66C2×C4×C22⋊D11C2212yes—
67C2×C4×C22⋊D11C2212yescomplemented
68C2×C4×C22⋊D11C2212yescomplemented
69C2×C4×C22⋊D11C2212yescomplemented
70C2×C4×C22⋊D11C2212yescomplemented
71C2×#66979C2212yescomplemented
72C2×#66979C2211yescharacteristic, complemented
73C2×#66977C2212yescomplemented
74C2×#66977C2212yescomplemented
75C22×C4×Dic11C2211yescharacteristic, complemented
76#10623198C22132yescomplemented
77#10623197C22116yescomplemented
78#10623182C22116yescomplemented
79#10623178C22132yescomplemented
80#10623177C22132yescomplemented
81#10623152C22132yescomplemented
82#10623151C22132yescomplemented
83#10623126C22132yescomplemented
84#10623126C22116yescomplemented
85#10623125C22116yescomplemented
86#10623088C22132yescomplemented
87#10623079C22132yescomplemented
88#10623078C22132yescomplemented
89#10623069C22132yescomplemented
90#10623059C22132yescomplemented
91C2×#66951C2212yescomplemented
92C2×#66951C2212yescomplemented
93C2×#66950C2212yescomplemented
94C2×#66949C2212yescomplemented
95C2×#66949C2212yescomplemented
96C2×#66948C2212yescomplemented
97C2×#66947C2212yescomplemented
98C2×#66947C2212yescomplemented
99C2×#66943C2212yescomplemented
100C2×#66942C2212yescomplemented
101C2×#66942C2212yescomplemented
102C2×#66941C2212yescomplemented
103C2×#66939C2212yescomplemented
104C2×#66938C2212yes—
105C2×#66938C2212yes—
106C2×#66938C2212yes—
107C2×#66938C2212yescomplemented
108C2×#66937C2212yes—
109C2×#66937C2212yes—
110C2×#66937C2212yescomplemented
111C2×#66937C2212yescomplemented
112C2×#66936C2212yes—
113C2×#66936C2212yescomplemented
114C2×#66936C2212yescomplemented
115C2×#66936C2212yescomplemented
116C2×#66935C2212yescomplemented
117C2×#66932C2212yescomplemented
118C2×#66932C2212yescomplemented
119C2×#66932C2212yescomplemented
120C2×#66932C2212yescomplemented
121C2×#66931C2212yescomplemented
122C2×#66931C2212yescomplemented
123C2×C4×D44C2212yescomplemented
124C2×#66925C2212yescomplemented
125C2×C42×D11C2212yescomplemented
126C2×C4×Dic22C2212yescomplemented
127C25×C11C2311yescharacteristic
128C24×D11C2311yescharacteristic
129C2×C11×#41—44no—
130C2×C11×#41C2318yes—
131C22×Q8×C11C2311yescharacteristic
132C22×D4×C11C2311yescharacteristic
133C22×D4×C11C2311yescharacteristic
134C22×D4×C11C2312yes—
135C22×D4×C11C2312yes—
136C22×D4×C11C2311yescharacteristic
137C23×C4×C11—44no—
138C23×C4×C11C2311yescharacteristic
139C23×C4×C11C2312yes—
140C23×C4×C11C2311yescharacteristic
141C23×C4×C11C2311yescharacteristic
142C23×C4×C11C2311yescharacteristic
143C23×C4×C11C2312yes—
144C23×C4×C11C2318yescomplemented
145C22×C22⋊D11C2312yes—
146C22×C22⋊D11C2312yes—
147C22×C22⋊D11C2312yes—
148C22×C22⋊D11C2312yes—
149C22×C22⋊D11C2312yes—
150C22×C22⋊D11C2312yes—
151C22×C22⋊D11C2312yes—
152C22×C22⋊D11C2312yes—
153C22×C22⋊D11C2312yes—
154C23×Dic11C2311yescharacteristic
155C23×Dic11C2312yes—
156C2×#4339—48no—
157C2×#4339—44no—
158C2×#4339C23116yes—
159C2×#4339C2318yescomplemented
160C22×D44C2312yes—
161C22×D44C2312yes—
162C22×D44C2311yescharacteristic
163C22×C4×D11—44no—
164C22×C4×D11C2312yes—
165C22×C4×D11C2312yes—
166C22×C4×D11C2312yes—
167C22×C4×D11C2312yes—
168C22×C4×D11C2312yes—
169C22×C4×D11C2318yescomplemented
170C22×Dic22C2312yes—
171C22×Dic22C2312yes—
172C22×Dic22C2311yescharacteristic
173C11×#123C2318yes—
174C11×#123C2318yescomplemented
175C11×C22⋊Q8C23116yescomplemented
176C11×#121C23116yes—
177C11×#120C2318yes—
178C11×#120C2318yescomplemented
179C4×D4×C11C23116yes—
180C4×D4×C11C23116yescomplemented
181C11×#117C2318yescomplemented
182C2×C11×C4⋊C4C2312yes—
183C2×C11×C4⋊C4C2312yes—
184C2×C11×C4⋊C4C2312yes—
185C2×C11×C22⋊C4C2312yes—
186C2×C11×C22⋊C4C2312yes—
187C2×C11×C22⋊C4C2311yescharacteristic
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2311yescharacteristic
191C2×C42×C11C2312yes—
192#67006C23116yes—
193#67006C23116yescomplemented
194C2×C22⋊Dic11C2312yes—
195C2×C22⋊Dic11C2312yes—
196C2×C22⋊Dic11C2312yes—
197C2×C22⋊Dic11C2311yescharacteristic
198C2×C22⋊Dic11C2312yes—
199C2×C22⋊Dic11C2312yes—
200C2×C22⋊Dic11C2312yes—
201C2×C22⋊Dic11C2312yes—
202C2×C22⋊Dic11C2311yescharacteristic
203C2×C22⋊Dic11C2312yes—
204#67000C2318yescomplemented
205#66999C23116yescomplemented
206#66997C2318yescomplemented
207#66993C23116yes—
208#66993C2318yes—
209#66992C23116yes—
210#66992C23116yes—
211#66992C23116yescomplemented
212#66992C23116yescomplemented
213#66991C23116yes—
214#66991C23116yes—
215#66991C23116yescomplemented
216#66990C23116yes—
217#66990C2318yes—
218#66990C2318yescomplemented
219#66989C23116yes—
220#66989C2318yes—
221#66988C2318yes—
222#66988C23116yescomplemented
223#66988C2318yescomplemented
224#66983C23116yes—
225#66983C23116yes—
226#66982C23116yes—
227#66982C23116yescomplemented
228C4×C22⋊D11C23116yes—
229C4×C22⋊D11C23116yes—
230C4×C22⋊D11C23116yescomplemented
231C4×C22⋊D11C23116yescomplemented
232C4×C22⋊D11C23116yescomplemented
233C4×C22⋊D11C23116yescomplemented
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)⋊C4C2312yes—
244#66979C23116yescomplemented
245#66979C2318yescomplemented
246C2×C4⋊Dic11C2312yes—
247C2×C4⋊Dic11C2312yes—
248C2×C4⋊Dic11C2312yes—
249C2×C4⋊Dic11C2312yes—
250C2×C4⋊Dic11C2312yes—
251#66977C23116yescomplemented
252#66977C23116yescomplemented
253C2×Dic11⋊C4C2312yes—
254C2×Dic11⋊C4C2312yes—
255C2×Dic11⋊C4C2312yes—
256C2×Dic11⋊C4C2312yes—
257C2×Dic11⋊C4C2312yes—
258C2×Dic11⋊C4C2312yes—
259C2×Dic11⋊C4C2312yes—
260C2×Dic11⋊C4C2312yes—
261C2×Dic11⋊C4C2312yes—
262C2×Dic11⋊C4C2312yes—
263C2×C4×Dic11C2312yes—
264C2×C4×Dic11C2312yes—
265C2×C4×Dic11C2312yes—
266C2×C4×Dic11C2312yes—
267C2×C4×Dic11C2311yescharacteristic
268C2×C4×Dic11C2311yescharacteristic
269C2×C4×Dic11C2318yescomplemented
270#66951C23116yescomplemented
271#66951C23116yescomplemented
272#66950C23116yescomplemented
273#66949C23116yescomplemented
274#66949C23116yescomplemented
275#66948C23116yescomplemented
276#66947C23116yescomplemented
277#66947C23116yescomplemented
278#66943C23116yescomplemented
279#66942C23116yescomplemented
280#66942C23116yescomplemented
281#66941C23116yescomplemented
282#66939C23116yescomplemented
283#66938C23116yes—
284#66938C23116yes—
285#66938C23116yes—
286#66938C23116yescomplemented
287#66937C23116yes—
288#66937C23116yes—
289#66937C23116yescomplemented
290#66937C23116yescomplemented
291#66936C23116yes—
292#66936C23116yescomplemented
293#66936C23116yescomplemented
294#66936C23116yescomplemented
295#66935C23116yescomplemented
296#66932C23116yescomplemented
297#66932C23116yescomplemented
298#66932C23116yescomplemented
299#66932C23116yescomplemented
300#66931C23116yescomplemented
301#66931C23116yescomplemented
302C4×D44C23116yescomplemented
303#66925C23116yescomplemented
304C42×D11C23116yescomplemented
305C4×Dic22C23116yescomplemented
306C2×#3529—111nomaximal, Sylow
307C24×C11—42no—
308C24×C11—44no—
309C24×C11C2411yescharacteristic
310C24×C11C2412yes—
311C24×C11C2411yescharacteristic
312C24×C11C2411yescharacteristic
313C24×C11C2414yes—
314C23×D11—42no—
315C23×D11—44no—
316C23×D11C2412yes—
317C23×D11C2412yes—
318C23×D11C2414yes—
319C11×#41—416no—
320C2×Q8×C11—42no—
321C2×Q8×C11C2414yes—
322C2×D4×C11—44no—
323C2×D4×C11—44no—
324C2×D4×C11—42no—
325C2×D4×C11—42no—
326C2×D4×C11—42no—
327C2×D4×C11C2414yes—
328C2×D4×C11C2414yes—
329C2×D4×C11C2418yes—
330C2×D4×C11C2418yes—
331C2×D4×C11C2414yes—
332C22×C4×C11—24no—
333C22×C4×C11—28no—
334C22×C4×C11—24no—
335C22×C4×C11—24no—
336C22×C4×C11—416no—
337C22×C4×C11—42no—
338C22×C4×C11—44no—
339C22×C4×C11C2411yescharacteristic
340C22×C4×C11C2412yes—
341C22×C4×C11C2412yes—
342C22×C4×C11C2414yes—
343C22×C4×C11C2411yescharacteristic
344C22×C4×C11C2412yes—
345C22×C4×C11C2411yescharacteristic
346C22×C4×C11C2418yes—
347C22×C4×C11C2414yes—
348C22×C4×C11C2414yes—
349C22×C4×C11C2414yes—
350C22×C4×C11C2418yes—
351C22×C4×C11C2411yescharacteristic
352C2×C22⋊D11—44no—
353C2×C22⋊D11—44no—
354C2×C22⋊D11—44no—
355C2×C22⋊D11—44no—
356C2×C22⋊D11—44no—
357C2×C22⋊D11—44no—
358C2×C22⋊D11—44no—
359C2×C22⋊D11—44no—
360C2×C22⋊D11—44no—
361C2×C22⋊D11C2418yes—
362C2×C22⋊D11C2418yes—
363C2×C22⋊D11C2418yes—
364C2×C22⋊D11C2418yes—
365C2×C22⋊D11C2418yes—
366C2×C22⋊D11C2418yes—
367C2×C22⋊D11C2418yes—
368C2×C22⋊D11C2418yes—
369C2×C22⋊D11C2418yes—
370C22×Dic11—42no—
371C22×Dic11—44no—
372C22×Dic11C2412yes—
373C22×Dic11C2412yes—
374C22×Dic11C2412yes—
375C22×Dic11C2412yes—
376C22×Dic11C2412yes—
377C22×Dic11C2412yes—
378C22×Dic11C2414yes—
379C22×Dic11C2418yes—
380#4339—432no—
381#4339—416no—
382C2×D44—44no—
383C2×D44—44no—
384C2×D44—42no—
385C2×D44C2418yes—
386C2×D44C2418yes—
387C2×D44C2414yes—
388C2×C4×D11—28no—
389C2×C4×D11—28no—
390C2×C4×D11—44no—
391C2×C4×D11—44no—
392C2×C4×D11—44no—
393C2×C4×D11—416no—
394C2×C4×D11C2418yes—
395C2×C4×D11C2418yes—
396C2×C4×D11C2418yes—
397C2×C4×D11C2418yes—
398C2×C4×D11C2418yes—
399C2×Dic22—44no—
400C2×Dic22—44no—
401C2×Dic22—42no—
402C2×Dic22C2418yes—
403C2×Dic22C2418yes—
404C2×Dic22C2414yes—
405C11×C4⋊C4C2418yes—
406C11×C4⋊C4C2418yes—
407C11×C4⋊C4C2418yes—
408C11×C22⋊C4C2418yes—
409C11×C22⋊C4C2418yes—
410C11×C22⋊C4C2414yes—
411C11×C22⋊C4C2418yes—
412C11×C22⋊C4C2418yes—
413C11×C22⋊C4C2414yes—
414C42×C11C2418yes—
415C22⋊Dic11C2418yes—
416C22⋊Dic11C2418yes—
417C22⋊Dic11C2418yes—
418C22⋊Dic11C2414yes—
419C22⋊Dic11C2418yes—
420C22⋊Dic11C2418yes—
421C22⋊Dic11C2418yes—
422C22⋊Dic11C2418yes—
423C22⋊Dic11C2414yes—
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—
435C4⋊Dic11C2418yes—
436C4⋊Dic11C2418yes—
437C4⋊Dic11C2418yes—
438C4⋊Dic11C2418yes—
439C4⋊Dic11C2418yes—
440Dic11⋊C4C2418yes—
441Dic11⋊C4C2418yes—
442Dic11⋊C4C2418yes—
443Dic11⋊C4C2418yes—
444Dic11⋊C4C2418yes—
445Dic11⋊C4C2418yes—
446Dic11⋊C4C2418yes—
447Dic11⋊C4C2418yes—
448Dic11⋊C4C2418yes—
449Dic11⋊C4C2418yes—
450C4×Dic11C2418yes—
451C4×Dic11C2418yes—
452C4×Dic11C2418yes—
453C4×Dic11C2418yes—
454C4×Dic11C2414yes—
455C4×Dic11C2414yes—
456#3529—1132no—
457C2×#563—111no—
458C2×#563—112no—
459C2×#562—112no—
460C2×#562—112no—
461C2×#562—112no—
462C2×H(3,𝔽4)—111no—
463C2×#560—111no—
464C2×#560—112no—
465C2×#560—111no—
466C2×#560—112no—
467C2×#532—111no—
468C2×#532—112no—
469C2×#529—112no—
470C2×#529—112no—
471C2×#529—112no—
472C2×#525—111no—
473C2×#525—112no—
474C2×#525—112no—
475C2×#525D1111yescharacteristic, complemented
476C23×C11—22no—
477C23×C11—24no—
478C23×C11—22no—
479C23×C11—22no—
480C23×C11—24no—
481C23×C11—24no—
482C23×C11—24no—
483C23×C11—24no—
484C23×C11—24no—
485C23×C11—44no—
486C23×C11—48no—
487C23×C11—416no—
488C23×C11C2512yes—
489C23×C11C2512yes—
490C23×C11C2514yes—
491C23×C11C2512yes—
492C23×C11C2511yescharacteristic
493C22×D11—24no—
494C22×D11—24no—
495C22×D11—24no—
496C22×D11—24no—
497C22×D11—24no—
498C22×D11—24no—
499C22×D11—44no—
500C22×D11—48no—
501C22×D11—416no—
502C22×D11C2514yes—
503C22×D11C2514yes—
504Q8×C11—44no—
505D4×C11—48no—
506D4×C11—48no—
507D4×C11—44no—
508D4×C11—44no—
509D4×C11—44no—
510C2×C4×C11—24no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—24no—
515C2×C4×C11—24no—
516C2×C4×C11—28no—
517C2×C4×C11—216no—
518C2×C4×C11—28no—
519C2×C4×C11—28no—
520C2×C4×C11—48no—
521C2×C4×C11—44no—
522C2×C4×C11H(5,𝔽2)14yes—
523C2×C4×C11C2512yes—
524C2×C4×C11C2514yes—
525C2×C4×C11C2514yes—
526C2×C4×C11C2512yes—
527C2×C4×C11C2514yes—
528C2×C4×C11C2512yes—
529C2×C4×C11C2512yes—
530C22⋊D11—48no—
531C22⋊D11—48no—
532C22⋊D11—48no—
533C22⋊D11—48no—
534C22⋊D11—48no—
535C22⋊D11—48no—
536C22⋊D11—48no—
537C22⋊D11—48no—
538C22⋊D11—48no—
539C2×Dic11—24no—
540C2×Dic11—24no—
541C2×Dic11—24no—
542C2×Dic11—24no—
543C2×Dic11—24no—
544C2×Dic11—24no—
545C2×Dic11—44no—
546C2×Dic11—48no—
547C2×Dic11C2514yes—
548C2×Dic11C2514yes—
549C2×Dic11C2514yes—
550C2×Dic11C2514yes—
551C2×Dic11C2514yes—
552C2×Dic11C2514yes—
553D44—48no—
554D44—48no—
555D44—44no—
556C4×D11—216no—
557C4×D11—216no—
558C4×D11—48no—
559C4×D11—48no—
560C4×D11—48no—
561Dic22—48no—
562Dic22—44no—
563Dic22—48no—
564C22×#41—112no—
565C22×#41—111no—
566C22×#41C2×D1111yescharacteristic
567C24×C4—111no—
568C24×C4C2×D1111yescharacteristic, complemented
569#563—1116no—
570#563—1132no—
571#562—1132no—
572#562—1132no—
573#562—1132no—
574H(3,𝔽4)—1116no—
575#560—1116no—
576#560—1132no—
577#560—1116no—
578#560—1132no—
579#532—1116no—
580#532—1132no—
581C2×C4⋊Q8—111no—
582C2×C4⋊Q8—112no—
583C2×#127—111no—
584C2×#127—112no—
585#529—1132no—
586#529—1132no—
587#529—1132no—
588C2×#126—112no—
589C2×#126—112no—
590C2×#126—112no—
591C2×#126—112no—
592C2×#126—112no—
593C2×#126—112no—
594C2×#125—112no—
595C2×#125—112no—
596C2×#125—112no—
597C2×#124—111no—
598C2×#124—112no—
599C2×#124—111no—
600C2×#124—112no—
601C2×#124—112no—
602C2×#124—112no—
603C2×#124—112no—
604#525—1116no—
605#525—1132no—
606#525—1132no—
607#525C2×D11116yescomplemented
608C2×#123—111no—
609C2×#123—111no—
610C2×#123—112no—
611C2×#123—112no—
612C2×#123—112no—
613C2×#123—112no—
614C2×#123—112no—
615C2×#123—112no—
616C2×#123—112no—
617C2×#123—112no—
618C2×#123—112no—
619C2×#123—112no—
620C2×#123C2×D1111yescharacteristic
621C2×#123C2×D1111yescharacteristic, complemented
622C2×C22⋊Q8—112no—
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×#121—112no—
642C2×#121—112no—
643C2×#121—112no—
644C2×#121—112no—
645C2×#121C2×D1112yes—
646C2×#120—112no—
647C2×#120—112no—
648C2×#120—111no—
649C2×#120—112no—
650C2×#120—111no—
651C2×#120—112no—
652C2×#120C2×D1111yescharacteristic
653C2×#120C2×D1111yescharacteristic, complemented
654C2×C4×Q8—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×D1112yes—
663C2×C4×D4C2×D1112yescomplemented
664C2×#117—111no—
665C2×#117—112no—
666C2×#117—112no—
667C2×#117C2×D1111yescharacteristic, complemented
668C22×C42—111no—
669C22×C42—112no—
670C22×C11—22no—
671C22×C11—24no—
672C22×C11—22no—
673C22×C11—22no—
674C22×C11—24no—
675C22×C11—24no—
676C22×C11—24no—
677C22×C11—24no—
678C22×C11—24no—
679C22×C11—416no—
680C22×C11—44no—
681C22×C11—44no—
682C22×C11—48no—
683C22×C11—44no—
684C22×C11C2×H(5,𝔽2)12yes—
685C22×C11#58514yes—
686C22×C11C2611yescharacteristic
687C2×D11—24no—
688C2×D11—24no—
689C2×D11—24no—
690C2×D11—24no—
691C2×D11—24no—
692C2×D11—24no—
693C2×D11—416no—
694C2×D11—48no—
695C2×D11—48no—
696C4×C11—22no—
697C4×C11—24no—
698C4×C11—22no—
699C4×C11—22no—
700C4×C11—24no—
701C4×C11—24no—
702C4×C11C2×H(5,𝔽2)14yes—
703Dic11—24no—
704Dic11—24no—
705Dic11—24no—
706Dic11—24no—
707Dic11—24no—
708Dic11—24no—
709C25—111no—
710C25C22×D1111yescharacteristic
711C2×#41—44no—
712C2×#41—1116no—
713C2×#41—118no—
714C2×#41—448no—
715C2×#41—444no—
716C2×#41C22×D1118yes—
717C22×Q8—112no—
718C22×Q8—112no—
719C22×Q8—111no—
720C22×Q8C22×D1111yescharacteristic
721C22×D4—112no—
722C22×D4—112no—
723C22×D4—112no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—112no—
728C22×D4—112no—
729C22×D4—112no—
730C22×D4—112no—
731C22×D4—112no—
732C22×D4—111no—
733C22×D4C22×D1112yes—
734C22×D4C22×D1112yes—
735C22×D4C22×D1111yescharacteristic
736C22×D4C22×D1111yescharacteristic
737C22×D4C22×D1111yescharacteristic
738C23×C4—44no—
739C23×C4—112no—
740C23×C4—111no—
741C23×C4—112no—
742C23×C4—112no—
743C23×C4—112no—
744C23×C4—112no—
745C23×C4—112no—
746C23×C4—118no—
747C23×C4—444no—
748C23×C4C22×D1111yescharacteristic
749C23×C4C22×D1112yes—
750C23×C4C22×D1111yescharacteristic
751C23×C4C22×D1111yescharacteristic
752C23×C4C22×D1111yescharacteristic
753C23×C4C22×D1112yes—
754C23×C4C22×D1118yescomplemented
755C4⋊Q8—118no—
756C4⋊Q8—1116no—
757#127—118no—
758#127—1116no—
759#126—1116no—
760#126—1116no—
761#126—1116no—
762#126—1116no—
763#126—1116no—
764#126—1116no—
765#125—1116no—
766#125—1116no—
767#125—1116no—
768#124—118no—
769#124—1116no—
770#124—118no—
771#124—1116no—
772#124—1116no—
773#124—1116no—
774#124—1116no—
775#123—118no—
776#123—118no—
777#123—1116no—
778#123—1116no—
779#123—1116no—
780#123—1116no—
781#123—1116no—
782#123—1116no—
783#123—1116no—
784#123—1116no—
785#123—1116no—
786#123—1116no—
787#123C22×D1118yes—
788#123C22×D1118yescomplemented
789C22⋊Q8—1116no—
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#121—1116no—
809#121—1116no—
810#121—1116no—
811#121—1116no—
812#121C22×D11116yes—
813#120—1116no—
814#120—1116no—
815#120—118no—
816#120—118no—
817#120—1116no—
818#120—1116no—
819#120C22×D1118yes—
820#120C22×D1118yescomplemented
821C4×Q8—1116no—
822C4×D4—1116no—
823C4×D4—1116no—
824C4×D4—1116no—
825C4×D4—1116no—
826C4×D4—1116no—
827C4×D4—1116no—
828C4×D4—1116no—
829C4×D4C22×D11116yes—
830C4×D4C22×D11116yescomplemented
831#117—118no—
832#117—1116no—
833#117—1116no—
834#117C22×D1118yescomplemented
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⋊C4—112no—
847C2×C4⋊C4—112no—
848C2×C4⋊C4—112no—
849C2×C4⋊C4—112no—
850C2×C4⋊C4C22×D1112yes—
851C2×C4⋊C4C22×D1112yes—
852C2×C4⋊C4C22×D1112yes—
853C2×C22⋊C4—111no—
854C2×C22⋊C4—112no—
855C2×C22⋊C4—111no—
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—112no—
873C2×C22⋊C4C22×D1111yescharacteristic
874C2×C22⋊C4C22×D1111yescharacteristic
875C2×C22⋊C4C22×D1112yes—
876C2×C22⋊C4C22×D1112yes—
877C2×C22⋊C4C22×D1112yes—
878C2×C22⋊C4C22×D1112yes—
879C2×C42—111no—
880C2×C42—112no—
881C2×C42—111no—
882C2×C42—112no—
883C2×C42—118no—
884C2×C42—112no—
885C2×C42—112no—
886C2×C42—1116no—
887C2×C42C22×D1112yes—
888C2×C11—42no—
889C2×C11—42no—
890C2×C11—42no—
891C2×C11—44no—
892C2×C11#352914yescomplemented
893C2×C11C22×H(5,𝔽2)11yescharacteristic
894C2×C11C2×#58512yes—
895D11—44no—
896D11—44no—
897C24—42no—
898C24—44no—
899C24—112no—
900C24—112no—
901C24—114no—
902C24—442no—
903C24—444no—
904C24C23×D1111yescharacteristic
905C24C23×D1111yescharacteristic
906C24C23×D1112yes—
907C24C23×D1111yescharacteristic
908C24C23×D1114yes—
909#41—416no—
910#41—4432no—
911#41—4416no—
912C2×Q8—42no—
913C2×Q8—118no—
914C2×Q8—118no—
915C2×Q8—114no—
916C2×Q8—444no—
917C2×Q8—442no—
918C2×Q8—444no—
919C2×Q8C23×D1114yes—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—118no—
926C2×D4—118no—
927C2×D4—118no—
928C2×D4—118no—
929C2×D4—118no—
930C2×D4—118no—
931C2×D4—118no—
932C2×D4—118no—
933C2×D4—118no—
934C2×D4—118no—
935C2×D4—118no—
936C2×D4—114no—
937C2×D4—444no—
938C2×D4—442no—
939C2×D4—444no—
940C2×D4—444no—
941C2×D4—444no—
942C2×D4—444no—
943C2×D4—444no—
944C2×D4—444no—
945C2×D4—444no—
946C2×D4—444no—
947C2×D4—444no—
948C2×D4—444no—
949C2×D4C23×D1118yes—
950C2×D4C23×D1118yes—
951C2×D4C23×D1114yes—
952C2×D4C23×D1114yes—
953C2×D4C23×D1114yes—
954C22×C4—24no—
955C22×C4—28no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—416no—
959C22×C4—44no—
960C22×C4—42no—
961C22×C4—112no—
962C22×C4—112no—
963C22×C4—112no—
964C22×C4—112no—
965C22×C4—112no—
966C22×C4—112no—
967C22×C4—118no—
968C22×C4—114no—
969C22×C4—118no—
970C22×C4—118no—
971C22×C4—118no—
972C22×C4—118no—
973C22×C4—118no—
974C22×C4—228no—
975C22×C4—228no—
976C22×C4—4416no—
977C22×C4—444no—
978C22×C4—444no—
979C22×C4—444no—
980C22×C4—442no—
981C22×C4—444no—
982C22×C4C23×D1111yescharacteristic
983C22×C4C23×D1114yes—
984C22×C4C23×D1112yes—
985C22×C4C23×D1112yes—
986C22×C4C23×D1111yescharacteristic
987C22×C4C23×D1111yescharacteristic
988C22×C4C23×D1112yes—
989C22×C4C23×D1114yes—
990C22×C4C23×D1118yes—
991C22×C4C23×D1114yes—
992C22×C4C23×D1114yes—
993C22×C4C23×D1118yes—
994C22×C4C23×D1111yescharacteristic
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⋊C4—118no—
1007C4⋊C4—118no—
1008C4⋊C4—118no—
1009C4⋊C4—118no—
1010C4⋊C4C23×D1118yes—
1011C4⋊C4C23×D1118yes—
1012C4⋊C4C23×D1118yes—
1013C22⋊C4—114no—
1014C22⋊C4—118no—
1015C22⋊C4—114no—
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⋊C4—118no—
1033C22⋊C4C23×D1114yes—
1034C22⋊C4C23×D1114yes—
1035C22⋊C4C23×D1118yes—
1036C22⋊C4C23×D1118yes—
1037C22⋊C4C23×D1118yes—
1038C22⋊C4C23×D1118yes—
1039C42—118no—
1040C42—118no—
1041C42—114no—
1042C42—118no—
1043C42—114no—
1044C42—118no—
1045C42C23×D1118yes—
1046C11C2×#352911yescharacteristic, complemented, Sylow
1047C23—22no—
1048C23—24no—
1049C23—22no—
1050C23—22no—
1051C23—24no—
1052C23—24no—
1053C23—24no—
1054C23—24no—
1055C23—24no—
1056C23—44no—
1057C23—48no—
1058C23—416no—
1059C23—114no—
1060C23—114no—
1061C23—224no—
1062C23—224no—
1063C23—224no—
1064C23—224no—
1065C23—224no—
1066C23—224no—
1067C23—444no—
1068C23—448no—
1069C23—4416no—
1070C23C24×D1112yes—
1071C23C24×D1112yes—
1072C23C24×D1114yes—
1073C23C24×D1112yes—
1074C23C24×D1111yescharacteristic
1075Q8—44no—
1076Q8—448no—
1077Q8—444no—
1078Q8—448no—
1079D4—48no—
1080D4—48no—
1081D4—44no—
1082D4—44no—
1083D4—44no—
1084D4—448no—
1085D4—444no—
1086D4—448no—
1087D4—448no—
1088D4—448no—
1089D4—448no—
1090D4—448no—
1091D4—448no—
1092D4—448no—
1093D4—448no—
1094D4—448no—
1095D4—448no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—28no—
1103C2×C4—216no—
1104C2×C4—28no—
1105C2×C4—28no—
1106C2×C4—48no—
1107C2×C4—44no—
1108C2×C4—114no—
1109C2×C4—114no—
1110C2×C4—114no—
1111C2×C4—114no—
1112C2×C4—114no—
1113C2×C4—114no—
1114C2×C4—224no—
1115C2×C4—224no—
1116C2×C4—224no—
1117C2×C4—224no—
1118C2×C4—224no—
1119C2×C4—224no—
1120C2×C4—2216no—
1121C2×C4—2216no—
1122C2×C4—448no—
1123C2×C4—448no—
1124C2×C4—448no—
1125C2×C4—444no—
1126C2×C4—448no—
1127C2×C4#6703714yes—
1128C2×C4C24×D1112yes—
1129C2×C4C24×D1114yes—
1130C2×C4C24×D1114yes—
1131C2×C4C24×D1112yes—
1132C2×C4C24×D1112yes—
1133C2×C4C24×D1114yes—
1134C2×C4C24×D1112yes—
1135C22—22no—
1136C22—24no—
1137C22—22no—
1138C22—22no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—416no—
1145C22—44no—
1146C22—48no—
1147C22—44no—
1148C22—44no—
1149C22—224no—
1150C22—224no—
1151C22—224no—
1152C22—224no—
1153C22—224no—
1154C22—224no—
1155C22—4416no—
1156C22—448no—
1157C22—448no—
1158C22C2×#6703712yes—
1159C22#1062345314yes—
1160C22C25×D1111yescharacteristic
1161C4—22no—
1162C4—24no—
1163C4—22no—
1164C4—22no—
1165C4—24no—
1166C4—24no—
1167C4—224no—
1168C4—224no—
1169C4—224no—
1170C4—224no—
1171C4—224no—
1172C4—224no—
1173C4C2×#6703714yes—
1174C2—42no—
1175C2—44no—
1176C2—42no—
1177C2—42no—
1178C2—444no—
1179C2—444no—
1180C2#1308275414yesdirect product factor
1181C2C22×#6703711yescharacteristic
1182C2C2×#1062345312yes—
subgroupG/H
centerC22×C4C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#525C2
socleC23×C11C25
hypercenterC2×#525D11
hypocenterC11C2×#3529
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #13082754C2direct (N × H)
2. C2×#10623182C2semidirect
3. C2×#10623177C2semidirect
4. C2×#10623198C2semidirect
5. C2×#10623178C2semidirect
6. C2×#10623152C2semidirect
7. C2×#10623125C2semidirect
8. C2×#10623197C2semidirect
9. C2×#10623126C2semidirect
10. C2×#10623126C2semidirect
11. C2×#10623151C2semidirect
12. C2×#10623079C2semidirect
13. C2×#10623363C2semidirect
14. C2×#10623088C2semidirect
15. C2×#10623069C2semidirect
16. C2×#10623059C2semidirect
17. C2×#10623322C2semidirect
18. C2×#10623078C2semidirect
19. C2×#10623359C2semidirect
20. C2×C11×#525C2semidirect
22. C24×C4×C11C22semidirect
24. C22×#4339C22semidirect
25. C23×C4×D11C22semidirect
26. C11×#525C22semidirect
28. C2×C11×#123C22semidirect
29. C2×C11×C22⋊Q8C22semidirect
32. C2×C11×#120C22semidirect
34. C2×C4×D4×C11C22semidirect
35. C2×C11×#117C22semidirect
37. C2×#67006C22semidirect
38. #10623363C22semidirect
39. #10623359C22semidirect
40. C2×#67000C22semidirect
41. C2×#66999C22semidirect
42. C2×#66997C22semidirect
47. C2×#66992C22semidirect
48. C2×#66992C22semidirect
51. C2×#66991C22semidirect
54. C2×#66990C22semidirect
58. C2×#66988C22semidirect
59. C2×#66988C22semidirect
60. #10623322C22semidirect
64. C2×#66982C22semidirect
67. C2×C4×C22⋊D11C22semidirect
68. C2×C4×C22⋊D11C22semidirect
69. C2×C4×C22⋊D11C22semidirect
70. C2×C4×C22⋊D11C22semidirect
71. C2×#66979C22semidirect
72. C2×#66979C22semidirect
73. C2×#66977C22semidirect
74. C2×#66977C22semidirect
75. C22×C4×Dic11C22semidirect
76. #10623198C22semidirect
77. #10623197C22semidirect
78. #10623182C22semidirect
79. #10623178C22semidirect
80. #10623177C22semidirect
81. #10623152C22semidirect
82. #10623151C22semidirect
83. #10623126C22semidirect
84. #10623126C22semidirect
85. #10623125C22semidirect
86. #10623088C22semidirect
87. #10623079C22semidirect
88. #10623078C22semidirect
89. #10623069C22semidirect
90. #10623059C22semidirect
91. C2×#66951C22semidirect
92. C2×#66951C22semidirect
93. C2×#66950C22semidirect
94. C2×#66949C22semidirect
95. C2×#66949C22semidirect
96. C2×#66948C22semidirect
97. C2×#66947C22semidirect
98. C2×#66947C22semidirect
99. C2×#66943C22semidirect
100. C2×#66942C22semidirect
101. C2×#66942C22semidirect
102. C2×#66941C22semidirect
103. C2×#66939C22semidirect
107. C2×#66938C22semidirect
110. C2×#66937C22semidirect
111. C2×#66937C22semidirect
113. C2×#66936C22semidirect
114. C2×#66936C22semidirect
115. C2×#66936C22semidirect
116. C2×#66935C22semidirect
117. C2×#66932C22semidirect
118. C2×#66932C22semidirect
119. C2×#66932C22semidirect
120. C2×#66932C22semidirect
121. C2×#66931C22semidirect
122. C2×#66931C22semidirect
123. C2×C4×D44C22semidirect
124. C2×#66925C22semidirect
125. C2×C42×D11C22semidirect
126. C2×C4×Dic22C22semidirect
144. C23×C4×C11C23semidirect
159. C2×#4339C23semidirect
169. C22×C4×D11C23semidirect
174. C11×#123C23semidirect
175. C11×C22⋊Q8C23semidirect
178. C11×#120C23semidirect
180. C4×D4×C11C23semidirect
181. C11×#117C23semidirect
193. #67006C23semidirect
204. #67000C23semidirect
205. #66999C23semidirect
206. #66997C23semidirect
211. #66992C23semidirect
212. #66992C23semidirect
215. #66991C23semidirect
218. #66990C23semidirect
222. #66988C23semidirect
223. #66988C23semidirect
227. #66982C23semidirect
230. C4×C22⋊D11C23semidirect
231. C4×C22⋊D11C23semidirect
232. C4×C22⋊D11C23semidirect
233. C4×C22⋊D11C23semidirect
244. #66979C23semidirect
245. #66979C23semidirect
251. #66977C23semidirect
252. #66977C23semidirect
269. C2×C4×Dic11C23semidirect
270. #66951C23semidirect
271. #66951C23semidirect
272. #66950C23semidirect
273. #66949C23semidirect
274. #66949C23semidirect
275. #66948C23semidirect
276. #66947C23semidirect
277. #66947C23semidirect
278. #66943C23semidirect
279. #66942C23semidirect
280. #66942C23semidirect
281. #66941C23semidirect
282. #66939C23semidirect
286. #66938C23semidirect
289. #66937C23semidirect
290. #66937C23semidirect
292. #66936C23semidirect
293. #66936C23semidirect
294. #66936C23semidirect
295. #66935C23semidirect
296. #66932C23semidirect
297. #66932C23semidirect
298. #66932C23semidirect
299. #66932C23semidirect
300. #66931C23semidirect
301. #66931C23semidirect
302. C4×D44C23semidirect
303. #66925C23semidirect
304. C42×D11C23semidirect
305. C4×Dic22C23semidirect
475. C2×#525D11semidirect
568. C24×C4C2×D11semidirect
607. #525C2×D11semidirect
621. C2×#123C2×D11semidirect
630. C2×C22⋊Q8C2×D11semidirect
653. C2×#120C2×D11semidirect
663. C2×C4×D4C2×D11semidirect
667. C2×#117C2×D11semidirect
754. C23×C4C22×D11semidirect
788. #123C22×D11semidirect
797. C22⋊Q8C22×D11semidirect
820. #120C22×D11semidirect
830. C4×D4C22×D11semidirect
834. #117C22×D11semidirect
892. C2×C11#3529semidirect
1046. C11C2×#3529semidirect
1180. C2#13082754direct (N × H)

Maximal subgroups

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

subgroupindex
#130827542
C2×#106231822
C2×#106231772
C2×#106231982
C2×#106231782
C2×#106231522
C2×#106231252
C2×#106231972
C2×#106231262
C2×#106231512
C2×#106230792
C2×#106233632
C2×#106230882
C2×#106230692
C2×#106230592
C2×#106233222
C2×#106230782
C2×#106233592
C2×C11×#5252
C2×#352911