Finite Group Databasebeta

← C2×#13082856 #15661018

Subgroups — C2×#13082856 #15661018

Order 2816.

7162 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082856C2132yesmaximal, direct product factor
2C2×#10623182C211yesmaximal, characteristic, complemented
3C2×#10623243C212yesmaximal, complemented
4C2×#10623203C211yesmaximal, characteristic, complemented
5C2×#10623181C212yesmaximal, complemented
6C2×#10623062C212yesmaximal, complemented
7C2×#10623118C211yesmaximal, characteristic, complemented
8C2×#10623026C212yesmaximal, complemented
9C2×D4×Dic22C212yesmaximal, complemented
10C2×#10623163C212yesmaximal, complemented
11C2×#10623154C212yesmaximal, complemented
12C2×#10623050C212yesmaximal, complemented
13C2×#10623232C212yesmaximal, complemented
14C2×#10623196C212yesmaximal, complemented
15C2×#10623095C212yesmaximal, complemented
16C2×#10623179C211yesmaximal, characteristic, complemented
17C2×#10623206C211yesmaximal, characteristic, complemented
18C2×#10623117C211yesmaximal, characteristic
19C22×#66931C212yesmaximal, complemented
20C2×C11×#551C211yesmaximal, characteristic, complemented
21C24×Dic11C2211yescharacteristic
22C22×Q8×D11C2211yescharacteristic, complemented
23C22×#4341C2211yescharacteristic
24C23×Dic22C2212yes—
25C23×Dic22C2211yescharacteristic, complemented
26C11×#551C22116yescomplemented
27C2×C11×#126C2212yes—
28C2×C11×#124C2211yescharacteristic
29C2×C11×#123C2212yes—
30C2×C11×#123C2211yescharacteristic
31C2×C11×C22⋊Q8C2212yes—
32C2×C11×#120C2211yescharacteristic
33C2×C4×D4×C11C2212yes—
34C2×C11×#117C2212yes—
35C22×C11×C22⋊C4C2212yes—
36C2×#67006C2211yescharacteristic
37C22×C22⋊Dic11C2212yes—
38C2×#66997C2211yescharacteristic, complemented
39C2×#66997C2212yescomplemented
40C2×#66992C2212yes—
41C2×#66989C2211yescharacteristic
42C2×#66988C2212yes—
43C2×#66988C2211yescharacteristic
44C2×#66988C2211yescharacteristic
45C2×D4×Dic11C2212yes—
46C2×D4×Dic11C2212yes—
47C2×#66982C2212yes—
48C2×#66982C2211yescharacteristic, complemented
49C2×C4×C22⋊D11C2212yes—
50C2×#66979C2212yes—
51C22×C4⋊Dic11C2212yes—
52C2×#66977C2212yes—
53C2×#66977C2212yescomplemented
54C22×Dic11⋊C4C2212yes—
55C22×Dic11⋊C4C2212yes—
56#10623243C22132yescomplemented
57#10623232C22132yescomplemented
58#10623206C22116yescomplemented
59#10623203C22116yescomplemented
60#10623196C22132yescomplemented
61#10623182C22116yescomplemented
62#10623181C22132yescomplemented
63#10623179C22116yescomplemented
64#10623163C22132yescomplemented
65#10623154C22132yescomplemented
66#10623118C22116yescomplemented
67#10623117C22116yes—
68#10623095C22132yescomplemented
69D4×Dic22C22132yescomplemented
70#10623062C22132yescomplemented
71#10623050C22132yescomplemented
72C2×#66951C2212yescomplemented
73C2×#66950C2212yescomplemented
74C2×#66949C2212yescomplemented
75C2×#66949C2212yescomplemented
76C2×#66943C2212yescomplemented
77C2×#66943C2212yescomplemented
78C2×#66942C2212yescomplemented
79C2×#66942C2212yescomplemented
80C2×#66942C2212yescomplemented
81C2×#66942C2212yescomplemented
82C2×#66942C2212yescomplemented
83C2×#66941C2212yescomplemented
84C2×#66941C2212yescomplemented
85C2×#66941C2212yescomplemented
86C2×#66941C2212yescomplemented
87C2×#66940C2212yescomplemented
88#10623026C22132yescomplemented
89C2×#66939C2212yes—
90C2×#66939C2211yescharacteristic
91C2×#66939C2211yescharacteristic, complemented
92C2×#66938C2212yes—
93C2×#66936C2212yes—
94C2×#66936C2212yescomplemented
95C2×(C22⋊D11)⋊C4C2212yes—
96C2×(C22⋊D11)⋊C4C2212yes—
97C2×#66932C2212yes—
98C2×#66932C2212yes—
99C2×#66932C2212yes—
100C2×#66932C2212yescomplemented
101C2×#66932C2212yescomplemented
102C2×#66931C2212yes—
103C2×#66931C2212yes—
104C2×#66931C2212yes—
105C2×#66931C2212yes—
106C2×#66931C2212yes—
107C2×#66931C2212yes—
108C2×#66931C2212yes—
109C2×#66931C2212yes—
110C2×#66931C2212yes—
111C2×#66931C2212yes—
112C2×#66931C2212yes—
113C2×#66931C22132yescomplemented
114C2×#66931C2212yescomplemented
115C2×#66931C2212yescomplemented
116C2×#66930C2212yes—
117C2×#66930C2212yes—
118C2×#66930C2211yescharacteristic
119C2×#66930C2211yescharacteristic, complemented
120C2×#66929C2212yescomplemented
121C2×#66925C2211yescharacteristic, complemented
122C2×#66923C2212yescomplemented
123C2×#66923C2212yescomplemented
124C2×#66922C2211yescharacteristic, complemented
125C2×#66922C2212yescomplemented
126C2×C4×Dic22C2212yescomplemented
127C25×C11C2311yescharacteristic
128C22×Q8×C11C2311yescharacteristic
129C22×D4×C11C2312yes—
130C22×D4×C11C2311yescharacteristic
131C23×C4×C11C2312yes—
132C23×C4×C11C2312yes—
133C23×C4×C11C2311yescharacteristic
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2311yescharacteristic
137C23×Dic11—44no—
138C23×Dic11C2312yes—
139C23×Dic11C2311yescharacteristic
140C23×Dic11C2311yescharacteristic
141C23×Dic11C2312yes—
142C23×Dic11C2311yescharacteristic
143C23×Dic11C2312yes—
144C23×Dic11C2312yes—
145C23×Dic11C2318yes—
146C23×Dic11C2311yescharacteristic
147C2×Q8×D11—44no—
148C2×Q8×D11C2318yescomplemented
149C2×#4341—44no—
150C2×#4341C2318yes—
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2312yes—
153C22×Dic22—48no—
154C22×Dic22—44no—
155C22×Dic22C2312yes—
156C22×Dic22C2312yes—
157C22×Dic22C2311yescharacteristic
158C22×Dic22C2311yescharacteristic
159C22×Dic22C2312yes—
160C22×Dic22C2312yes—
161C22×Dic22C2312yes—
162C22×Dic22C23116yes—
163C22×Dic22C2318yescomplemented
164C11×#126C23116yes—
165C11×#124C2318yes—
166C11×#123C2318yes—
167C11×#123C23116yes—
168C11×C22⋊Q8C23116yes—
169C11×#120C2318yes—
170C4×D4×C11C23116yes—
171C11×#117C23116yes—
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2312yes—
174C2×C11×C4⋊C4C2312yes—
175C2×C11×C4⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C11×C22⋊C4C2311yescharacteristic
180C2×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2312yes—
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C23116yes—
185C2×C42×C11C2312yes—
186C2×C42×C11C2311yescharacteristic
187#67006C2318yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190C2×C22⋊Dic11C2311yescharacteristic
191C2×C22⋊Dic11C2311yescharacteristic
192C2×C22⋊Dic11C2312yes—
193C2×C22⋊Dic11C2312yes—
194C2×C22⋊Dic11C2312yes—
195C2×C22⋊Dic11C23116yes—
196C2×C22⋊Dic11C2312yes—
197C2×C22⋊Dic11C2312yes—
198#66997C2318yescomplemented
199#66997C23116yescomplemented
200#66992C23116yes—
201#66989C2318yes—
202#66988C23116yes—
203#66988C2318yes—
204#66988C2318yes—
205D4×Dic11C23116yes—
206D4×Dic11C23116yes—
207#66982C23116yes—
208#66982C2318yescomplemented
209C4×C22⋊D11C23116yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2312yes—
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2312yes—
214#66979C23116yes—
215C2×C4⋊Dic11C2312yes—
216C2×C4⋊Dic11C2312yes—
217C2×C4⋊Dic11C2312yes—
218C2×C4⋊Dic11C2312yes—
219C2×C4⋊Dic11C2312yes—
220C2×C4⋊Dic11C2312yes—
221C2×C4⋊Dic11C2312yes—
222C2×C4⋊Dic11C2312yes—
223C2×C4⋊Dic11C2312yes—
224C2×C4⋊Dic11C23116yes—
225#66977C23116yes—
226#66977C23116yescomplemented
227C2×Dic11⋊C4C2312yes—
228C2×Dic11⋊C4C2312yes—
229C2×Dic11⋊C4C2312yes—
230C2×Dic11⋊C4C2312yes—
231C2×Dic11⋊C4C2312yes—
232C2×Dic11⋊C4C2312yes—
233C2×Dic11⋊C4C2312yes—
234C2×Dic11⋊C4C2312yes—
235C2×Dic11⋊C4C2312yes—
236C2×Dic11⋊C4C2312yes—
237C2×Dic11⋊C4C2312yes—
238C2×Dic11⋊C4C2312yes—
239C2×Dic11⋊C4C2312yes—
240C2×Dic11⋊C4C2312yes—
241C2×Dic11⋊C4C2312yes—
242C2×Dic11⋊C4C2312yes—
243C2×Dic11⋊C4C2312yes—
244C2×Dic11⋊C4C23116yes—
245C2×Dic11⋊C4C23116yes—
246C2×Dic11⋊C4C2312yes—
247C2×C4×Dic11C2312yes—
248C2×C4×Dic11C2312yes—
249C2×C4×Dic11C2311yescharacteristic
250C2×C4×Dic11C2312yes—
251C2×C4×Dic11C2312yes—
252C2×C4×Dic11C2312yes—
253#66951C23116yescomplemented
254#66950C23116yescomplemented
255#66949C23116yescomplemented
256#66949C23116yescomplemented
257#66943C23116yescomplemented
258#66943C23116yescomplemented
259#66942C23116yescomplemented
260#66942C23116yescomplemented
261#66942C23116yescomplemented
262#66942C23116yescomplemented
263#66942C23116yescomplemented
264#66941C23116yescomplemented
265#66941C23116yescomplemented
266#66941C23116yescomplemented
267#66941C23116yescomplemented
268#66940C23116yescomplemented
269#66939C2318yes—
270#66939C23116yes—
271#66939C2318yescomplemented
272#66938C23116yes—
273#66936C23116yes—
274#66936C23116yescomplemented
275(C22⋊D11)⋊C4C23116yes—
276(C22⋊D11)⋊C4C23116yes—
277#66932C23116yes—
278#66932C23116yes—
279#66932C23116yes—
280#66932C23116yescomplemented
281#66932C23116yescomplemented
282#66931C23116yes—
283#66931C23116yes—
284#66931C23116yes—
285#66931C23116yes—
286#66931C23116yes—
287#66931C23116yes—
288#66931C23116yes—
289#66931C23116yes—
290#66931C23116yes—
291#66931C23116yes—
292#66931C23116yes—
293#66931C23116yescomplemented
294#66931C23116yescomplemented
295#66930C2318yes—
296#66930C23116yes—
297#66930C23116yes—
298#66930C2318yescomplemented
299#66929C23116yescomplemented
300#66925C2318yescomplemented
301#66923C23116yescomplemented
302#66923C23116yescomplemented
303#66922C23116yescomplemented
304#66922C2318yescomplemented
305C4×Dic22C23116yescomplemented
306C2×#3538—111nomaximal, Sylow
307C24×C11—28no—
308C24×C11—42no—
309C24×C11C2411yescharacteristic
310C24×C11C2411yescharacteristic
311C24×C11C2414yes—
312C24×C11C2412yes—
313C23×D11C2411yescharacteristic
314C2×Q8×C11—42no—
315C2×Q8×C11C2414yes—
316C2×D4×C11—28no—
317C2×D4×C11—42no—
318C2×D4×C11C2418yes—
319C2×D4×C11C2414yes—
320C22×C4×C11—28no—
321C22×C4×C11—42no—
322C22×C4×C11—44no—
323C22×C4×C11C2412yes—
324C22×C4×C11C2412yes—
325C22×C4×C11C2411yescharacteristic
326C22×C4×C11C2412yes—
327C22×C4×C11C2412yes—
328C22×C4×C11C2412yes—
329C22×C4×C11C2418yes—
330C22×C4×C11C2418yes—
331C22×C4×C11C2414yes—
332C2×C22⋊D11—28no—
333C2×C22⋊D11—42no—
334C2×C22⋊D11—42no—
335C2×C22⋊D11C2418yes—
336C2×C22⋊D11C2414yes—
337C2×C22⋊D11C2414yes—
338C22×Dic11—24no—
339C22×Dic11—28no—
340C22×Dic11—24no—
341C22×Dic11—28no—
342C22×Dic11—44no—
343C22×Dic11—42no—
344C22×Dic11—44no—
345C22×Dic11—42no—
346C22×Dic11—416no—
347C22×Dic11C2418yes—
348C22×Dic11C2414yes—
349C22×Dic11C2414yes—
350C22×Dic11C2418yes—
351C22×Dic11C2412yes—
352C22×Dic11C2412yes—
353C22×Dic11C2412yes—
354C22×Dic11C2411yescharacteristic
355C22×Dic11C2412yes—
356C22×Dic11C2412yes—
357C22×Dic11C2411yescharacteristic
358C22×Dic11C2412yes—
359C22×Dic11C2414yes—
360C22×Dic11C2418yes—
361C22×Dic11C2418yes—
362C22×Dic11C2414yes—
363C22×Dic11C2411yescharacteristic
364Q8×D11—416no—
365#4341—416no—
366C2×C4×D11—24no—
367C2×C4×D11—44no—
368C2×C4×D11C2414yes—
369C2×C4×D11C2418yes—
370C2×Dic22—28no—
371C2×Dic22—28no—
372C2×Dic22—44no—
373C2×Dic22—44no—
374C2×Dic22—44no—
375C2×Dic22—42no—
376C2×Dic22—42no—
377C2×Dic22—432no—
378C2×Dic22—416no—
379C2×Dic22C2418yes—
380C2×Dic22C2418yes—
381C2×Dic22C2414yes—
382C2×Dic22C2414yes—
383C2×Dic22C2418yes—
384C2×Dic22C2418yes—
385C2×Dic22C2418yes—
386C11×C4⋊C4C2418yes—
387C11×C4⋊C4C2418yes—
388C11×C4⋊C4C2418yes—
389C11×C4⋊C4C2418yes—
390C11×C22⋊C4C2418yes—
391C11×C22⋊C4C2418yes—
392C11×C22⋊C4C2414yes—
393C11×C22⋊C4C2414yes—
394C11×C22⋊C4C2418yes—
395C11×C22⋊C4C2418yes—
396C11×C22⋊C4C2418yes—
397C11×C22⋊C4C2418yes—
398C42×C11C2418yes—
399C42×C11C2414yes—
400C22⋊Dic11C2418yes—
401C22⋊Dic11C2418yes—
402C22⋊Dic11C2414yes—
403C22⋊Dic11C2414yes—
404C22⋊Dic11C2418yes—
405C22⋊Dic11C2418yes—
406C22⋊Dic11C2418yes—
407C22⋊Dic11C2418yes—
408C22⋊Dic11C2418yes—
409(C2×D11)⋊C4C2418yes—
410(C2×D11)⋊C4C2418yes—
411(C2×D11)⋊C4C2418yes—
412(C2×D11)⋊C4C2418yes—
413C4⋊Dic11C2418yes—
414C4⋊Dic11C2418yes—
415C4⋊Dic11C2418yes—
416C4⋊Dic11C2418yes—
417C4⋊Dic11C2418yes—
418C4⋊Dic11C2418yes—
419C4⋊Dic11C2418yes—
420C4⋊Dic11C2418yes—
421C4⋊Dic11C2418yes—
422Dic11⋊C4C2418yes—
423Dic11⋊C4C2418yes—
424Dic11⋊C4C2418yes—
425Dic11⋊C4C2418yes—
426Dic11⋊C4C2418yes—
427Dic11⋊C4C2418yes—
428Dic11⋊C4C2418yes—
429Dic11⋊C4C2418yes—
430Dic11⋊C4C2418yes—
431Dic11⋊C4C2418yes—
432Dic11⋊C4C2418yes—
433Dic11⋊C4C2418yes—
434Dic11⋊C4C2418yes—
435Dic11⋊C4C2418yes—
436Dic11⋊C4C2418yes—
437Dic11⋊C4C2418yes—
438Dic11⋊C4C2418yes—
439Dic11⋊C4C2418yes—
440C4×Dic11C2418yes—
441C4×Dic11C2418yes—
442C4×Dic11C2414yes—
443C4×Dic11C2418yes—
444C4×Dic11C2418yes—
445C4×Dic11C2418yes—
446#3538—1132no—
447C2×#563—112no—
448C2×#563—111no—
449C2×#563—111no—
450C2×#552—112no—
451C2×#552—112no—
452C2×#551—111no—
453C2×#551—112no—
454C2×#551D1111yescharacteristic, complemented
455C2×D4×Q8—112no—
456C2×D4×Q8—112no—
457C2×#544—112no—
458C2×#544—112no—
459C2×#541—112no—
460C2×#539—112no—
461C2×#539—112no—
462C2×#536—111no—
463C2×#536—111no—
464C2×#525—111no—
465C22×C22⋊Q8—112no—
466C23×C11—24no—
467C23×C11—24no—
468C23×C11—22no—
469C23×C11—22no—
470C23×C11—24no—
471C23×C11—216no—
472C23×C11—24no—
473C23×C11—44no—
474C23×C11—416no—
475C23×C112−1+418yes—
476C23×C11C2512yes—
477C23×C11C2512yes—
478C23×C11C2514yes—
479C23×C11C2511yescharacteristic
480C22×D11—22no—
481C22×D11—24no—
482C22×D11C2512yes—
483Q8×C11—44no—
484D4×C11—216no—
485D4×C11—44no—
486C2×C4×C11—24no—
487C2×C4×C11—24no—
488C2×C4×C11—22no—
489C2×C4×C11—216no—
490C2×C4×C11—24no—
491C2×C4×C11—24no—
492C2×C4×C11—24no—
493C2×C4×C11—44no—
494C2×C4×C11—48no—
495C2×C4×C11C2514yes—
496C2×C4×C11C2514yes—
497C2×C4×C11C2512yes—
498C2×C4×C11C2514yes—
499C2×C4×C11C2514yes—
500C2×C4×C11C2514yes—
501C22⋊D11—216no—
502C22⋊D11—44no—
503C22⋊D11—44no—
504C2×Dic11—24no—
505C2×Dic11—24no—
506C2×Dic11—22no—
507C2×Dic11—24no—
508C2×Dic11—22no—
509C2×Dic11—216no—
510C2×Dic11—24no—
511C2×Dic11—24no—
512C2×Dic11—24no—
513C2×Dic11—28no—
514C2×Dic11—216no—
515C2×Dic11—28no—
516C2×Dic11—48no—
517C2×Dic11—44no—
518C2×Dic11—44no—
519C2×Dic11—48no—
520C2×Dic11H(5,𝔽2)14yes—
521C2×Dic11C2514yes—
522C2×Dic11C2514yes—
523C2×Dic11C2514yes—
524C2×Dic11C2512yes—
525C2×Dic11C2514yes—
526C2×Dic11C2514yes—
527C2×Dic11C2512yes—
528C2×Dic11C2514yes—
529C2×Dic11C2512yes—
530C4×D11—28no—
531C4×D11—48no—
532Dic22—216no—
533Dic22—216no—
534Dic22—48no—
535Dic22—48no—
536Dic22—48no—
537Dic22—44no—
538Dic22—44no—
539C22×#41—111no—
540C23×Q8—111no—
541C23×Q8—112no—
542C23×Q8—111no—
543C24×C4—111no—
544#563—1132no—
545#563—1116no—
546#563—1116no—
547#552—1132no—
548#552—1132no—
549#551—1116no—
550#551—1132no—
551#551C2×D11116yescomplemented
552D4×Q8—1132no—
553D4×Q8—1132no—
554#544—1132no—
555#544—1132no—
556#541—1132no—
557#539—1132no—
558#539—1132no—
559#536—1116no—
560#536—1116no—
561C2×C4⋊Q8—111no—
562C2×C4⋊Q8—112no—
563C2×C4⋊Q8—112no—
564C2×C4⋊Q8—112no—
565C2×C4⋊Q8—112no—
566C2×C4⋊Q8—112no—
567C2×C4⋊Q8—111no—
568C2×C4⋊Q8—112no—
569C2×#126—112no—
570C2×#126—112no—
571C2×#126—112no—
572C2×#126—112no—
573C2×#126—112no—
574C2×#126—112no—
575C2×#126—112no—
576C2×#126C2×D1112yes—
577C2×#125—112no—
578C2×#125—112no—
579C2×#125—112no—
580C2×#125—112no—
581C2×#125—112no—
582C2×#125—112no—
583C2×#125—112no—
584C2×#125—112no—
585C2×#125—112no—
586C2×#124—111no—
587C2×#124—112no—
588C2×#124C2×D1111yescharacteristic
589#525—1116no—
590C2×#123—111no—
591C2×#123—111no—
592C2×#123—112no—
593C2×#123—112no—
594C2×#123—111no—
595C2×#123—112no—
596C2×#123—112no—
597C2×#123—111no—
598C2×#123—112no—
599C2×#123—111no—
600C2×#123C2×D1111yescharacteristic
601C2×#123C2×D1112yes—
602C2×C22⋊Q8—112no—
603C2×C22⋊Q8—112no—
604C2×C22⋊Q8—112no—
605C2×C22⋊Q8—112no—
606C2×C22⋊Q8—112no—
607C2×C22⋊Q8—112no—
608C2×C22⋊Q8—112no—
609C2×C22⋊Q8—112no—
610C2×C22⋊Q8—112no—
611C2×C22⋊Q8—112no—
612C2×C22⋊Q8—112no—
613C2×C22⋊Q8—112no—
614C2×C22⋊Q8—112no—
615C2×C22⋊Q8—112no—
616C2×C22⋊Q8—112no—
617C2×C22⋊Q8—112no—
618C2×C22⋊Q8—1132no—
619C2×C22⋊Q8—112no—
620C2×C22⋊Q8—112no—
621C2×C22⋊Q8C2×D1112yes—
622C2×#121—112no—
623C2×#120—111no—
624C2×#120C2×D1111yescharacteristic
625C2×C4×Q8—112no—
626C2×C4×Q8—112no—
627C2×C4×D4—112no—
628C2×C4×D4—112no—
629C2×C4×D4—112no—
630C2×C4×D4—112no—
631C2×C4×D4—112no—
632C2×C4×D4C2×D1112yes—
633C2×#117—112no—
634C2×#117—111no—
635C2×#117—112no—
636C2×#117—112no—
637C2×#117—111no—
638C2×#117—111no—
639C2×#117C2×D1112yes—
640C22×C4⋊C4—112no—
641C22×C4⋊C4—112no—
642C22×C4⋊C4—112no—
643C22×C22⋊C4—112no—
644C22×C22⋊C4C2×D1112yes—
645C22×C11—24no—
646C22×C11—24no—
647C22×C11—216no—
648C22×C11—22no—
649C22×C11—22no—
650C22×C11—24no—
651C22×C11—24no—
652C22×C11—416no—
653C22×C11—44no—
654C22×C11—44no—
655C22×C11C2×H(5,𝔽2)12yes—
656C22×C11C2×2−1+418yes—
657C22×C11C2×2−1+414yes—
658C22×C11C2611yescharacteristic
659C2×D11—22no—
660C2×D11—24no—
661C2×D11—44no—
662C4×C11—24no—
663C4×C11—24no—
664C4×C11—22no—
665C4×C11—24no—
666C4×C11—24no—
667C4×C11—24no—
668Dic11—24no—
669Dic11—24no—
670Dic11—22no—
671Dic11—24no—
672Dic11—22no—
673Dic11—24no—
674Dic11—24no—
675Dic11—24no—
676Dic11C2×H(5,𝔽2)14yes—
677C25C22×D1111yescharacteristic
678C2×#41—118no—
679C2×#41—444no—
680C22×Q8—118no—
681C22×Q8—112no—
682C22×Q8—112no—
683C22×Q8—112no—
684C22×Q8—112no—
685C22×Q8—112no—
686C22×Q8—111no—
687C22×Q8—111no—
688C22×Q8—1116no—
689C22×Q8—118no—
690C22×Q8—448no—
691C22×Q8—444no—
692C22×Q8—444no—
693C22×Q8C22×D1111yescharacteristic
694C22×D4—112no—
695C22×D4—111no—
696C22×D4—111no—
697C22×D4C22×D1112yes—
698C22×D4C22×D1111yescharacteristic
699C23×C4—112no—
700C23×C4—112no—
701C23×C4—111no—
702C23×C4—111no—
703C23×C4—112no—
704C23×C4—112no—
705C23×C4—111no—
706C23×C4—111no—
707C23×C4—118no—
708C23×C4—111no—
709C23×C4—112no—
710C23×C4—444no—
711C23×C4C22×D1112yes—
712C23×C4C22×D1112yes—
713C23×C4C22×D1111yescharacteristic
714C4⋊Q8—118no—
715C4⋊Q8—1116no—
716C4⋊Q8—1116no—
717C4⋊Q8—1116no—
718C4⋊Q8—1116no—
719C4⋊Q8—1116no—
720C4⋊Q8—118no—
721C4⋊Q8—1116no—
722#126—1116no—
723#126—1116no—
724#126—1116no—
725#126—1116no—
726#126—1116no—
727#126—1116no—
728#126—1116no—
729#126C22×D11116yes—
730#125—1116no—
731#125—1116no—
732#125—1116no—
733#125—1116no—
734#125—1116no—
735#125—1116no—
736#125—1116no—
737#125—1116no—
738#125—1116no—
739#124—118no—
740#124—1116no—
741#124C22×D1118yes—
742#123—118no—
743#123—118no—
744#123—1116no—
745#123—118no—
746#123—1116no—
747#123—118no—
748#123—1116no—
749#123—118no—
750#123—1116no—
751#123—1116no—
752#123C22×D1118yes—
753#123C22×D11116yes—
754C22⋊Q8—1116no—
755C22⋊Q8—1116no—
756C22⋊Q8—1116no—
757C22⋊Q8—1116no—
758C22⋊Q8—1116no—
759C22⋊Q8—1116no—
760C22⋊Q8—1116no—
761C22⋊Q8—1116no—
762C22⋊Q8—1116no—
763C22⋊Q8—1116no—
764C22⋊Q8—1116no—
765C22⋊Q8—1116no—
766C22⋊Q8—1116no—
767C22⋊Q8—1116no—
768C22⋊Q8—1116no—
769C22⋊Q8—1116no—
770C22⋊Q8—1116no—
771C22⋊Q8—1116no—
772C22⋊Q8C22×D11116yes—
773#121—1116no—
774#120—118no—
775#120C22×D1118yes—
776C4×Q8—1116no—
777C4×Q8—1116no—
778C4×D4—1116no—
779C4×D4—1116no—
780C4×D4—1116no—
781C4×D4—1116no—
782C4×D4—1116no—
783C4×D4C22×D11116yes—
784#117—1116no—
785#117—118no—
786#117—118no—
787#117—1116no—
788#117—1116no—
789#117—118no—
790#117C22×D11116yes—
791C2×C4⋊C4—112no—
792C2×C4⋊C4—112no—
793C2×C4⋊C4—112no—
794C2×C4⋊C4—112no—
795C2×C4⋊C4—112no—
796C2×C4⋊C4—112no—
797C2×C4⋊C4—112no—
798C2×C4⋊C4—112no—
799C2×C4⋊C4—112no—
800C2×C4⋊C4—112no—
801C2×C4⋊C4—112no—
802C2×C4⋊C4—112no—
803C2×C4⋊C4—1116no—
804C2×C4⋊C4—1116no—
805C2×C4⋊C4—1116no—
806C2×C4⋊C4—112no—
807C2×C4⋊C4—112no—
808C2×C4⋊C4—112no—
809C2×C4⋊C4—112no—
810C2×C4⋊C4—112no—
811C2×C4⋊C4—112no—
812C2×C4⋊C4—112no—
813C2×C4⋊C4—112no—
814C2×C4⋊C4—112no—
815C2×C4⋊C4—112no—
816C2×C4⋊C4—112no—
817C2×C4⋊C4—112no—
818C2×C4⋊C4—112no—
819C2×C4⋊C4—112no—
820C2×C4⋊C4—112no—
821C2×C4⋊C4C22×D1112yes—
822C2×C4⋊C4C22×D1112yes—
823C2×C4⋊C4C22×D1112yes—
824C2×C4⋊C4C22×D1112yes—
825C2×C22⋊C4—112no—
826C2×C22⋊C4—112no—
827C2×C22⋊C4—112no—
828C2×C22⋊C4—112no—
829C2×C22⋊C4—1116no—
830C2×C22⋊C4—112no—
831C2×C22⋊C4—111no—
832C2×C22⋊C4—111no—
833C2×C22⋊C4—112no—
834C2×C22⋊C4—112no—
835C2×C22⋊C4—112no—
836C2×C22⋊C4—112no—
837C2×C22⋊C4—112no—
838C2×C22⋊C4—112no—
839C2×C22⋊C4C22×D1112yes—
840C2×C22⋊C4C22×D1112yes—
841C2×C22⋊C4C22×D1112yes—
842C2×C22⋊C4C22×D1112yes—
843C2×C22⋊C4C22×D11116yes—
844C2×C22⋊C4C22×D1112yes—
845C2×C22⋊C4C22×D1111yescharacteristic
846C2×C22⋊C4C22×D1111yescharacteristic
847C2×C22⋊C4C22×D1112yes—
848C2×C42—111no—
849C2×C42—112no—
850C2×C42—112no—
851C2×C42—112no—
852C2×C42—112no—
853C2×C42—112no—
854C2×C42C22×D1111yescharacteristic
855C2×C42C22×D1112yes—
856C2×C11—28no—
857C2×C11—42no—
858C2×C11—42no—
859C2×C11#353814yescomplemented
860C2×C11C22×H(5,𝔽2)11yescharacteristic
861C2×C11C22×2−1+412yes—
862D11—42no—
863C24—28no—
864C24—42no—
865C24—111no—
866C24C23×D1111yescharacteristic
867C24C23×D1111yescharacteristic
868C24C23×D1114yes—
869C24C23×D1112yes—
870#41—4416no—
871C2×Q8—42no—
872C2×Q8—118no—
873C2×Q8—118no—
874C2×Q8—118no—
875C2×Q8—118no—
876C2×Q8—118no—
877C2×Q8—114no—
878C2×Q8—114no—
879C2×Q8—228no—
880C2×Q8—228no—
881C2×Q8—444no—
882C2×Q8—444no—
883C2×Q8—444no—
884C2×Q8—442no—
885C2×Q8—442no—
886C2×Q8—4432no—
887C2×Q8—4416no—
888C2×Q8—4416no—
889C2×Q8C23×D1114yes—
890C2×D4—28no—
891C2×D4—42no—
892C2×D4—118no—
893C2×D4—114no—
894C2×D4—114no—
895C2×D4—228no—
896C2×D4—442no—
897C2×D4—442no—
898C2×D4C23×D1118yes—
899C2×D4C23×D1114yes—
900C22×C4—28no—
901C22×C4—42no—
902C22×C4—44no—
903C22×C4—111no—
904C22×C4—118no—
905C22×C4—118no—
906C22×C4—114no—
907C22×C4—114no—
908C22×C4—112no—
909C22×C4—112no—
910C22×C4—112no—
911C22×C4—111no—
912C22×C4—112no—
913C22×C4—112no—
914C22×C4—112no—
915C22×C4—111no—
916C22×C4—118no—
917C22×C4—118no—
918C22×C4—114no—
919C22×C4—114no—
920C22×C4—114no—
921C22×C4—118no—
922C22×C4—224no—
923C22×C4—228no—
924C22×C4—224no—
925C22×C4—224no—
926C22×C4—228no—
927C22×C4—444no—
928C22×C4—4416no—
929C22×C4—444no—
930C22×C4—442no—
931C22×C4—444no—
932C22×C4—442no—
933C22×C4C23×D1118yes—
934C22×C4C23×D1112yes—
935C22×C4C23×D1112yes—
936C22×C4C23×D1111yescharacteristic
937C22×C4C23×D1112yes—
938C22×C4C23×D1112yes—
939C22×C4C23×D1112yes—
940C22×C4C23×D1118yes—
941C22×C4C23×D1114yes—
942C4⋊C4—118no—
943C4⋊C4—118no—
944C4⋊C4—118no—
945C4⋊C4—118no—
946C4⋊C4—118no—
947C4⋊C4—118no—
948C4⋊C4—118no—
949C4⋊C4—118no—
950C4⋊C4—118no—
951C4⋊C4—118no—
952C4⋊C4—118no—
953C4⋊C4—118no—
954C4⋊C4—118no—
955C4⋊C4—118no—
956C4⋊C4—118no—
957C4⋊C4—118no—
958C4⋊C4—118no—
959C4⋊C4—118no—
960C4⋊C4—118no—
961C4⋊C4—118no—
962C4⋊C4—118no—
963C4⋊C4—118no—
964C4⋊C4—118no—
965C4⋊C4—118no—
966C4⋊C4—118no—
967C4⋊C4—118no—
968C4⋊C4—118no—
969C4⋊C4C23×D1118yes—
970C4⋊C4C23×D1118yes—
971C4⋊C4C23×D1118yes—
972C4⋊C4C23×D1118yes—
973C22⋊C4—118no—
974C22⋊C4—118no—
975C22⋊C4—118no—
976C22⋊C4—118no—
977C22⋊C4—118no—
978C22⋊C4—114no—
979C22⋊C4—114no—
980C22⋊C4—118no—
981C22⋊C4—118no—
982C22⋊C4—118no—
983C22⋊C4—118no—
984C22⋊C4—118no—
985C22⋊C4—118no—
986C22⋊C4C23×D1118yes—
987C22⋊C4C23×D1118yes—
988C22⋊C4C23×D1118yes—
989C22⋊C4C23×D1118yes—
990C22⋊C4C23×D1118yes—
991C22⋊C4C23×D1114yes—
992C22⋊C4C23×D1114yes—
993C22⋊C4C23×D1118yes—
994C42—114no—
995C42—118no—
996C42—118no—
997C42—118no—
998C42—118no—
999C42—118no—
1000C42C23×D1114yes—
1001C42C23×D1118yes—
1002C11C2×#353811yescharacteristic, complemented, Sylow
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—216no—
1007C23—24no—
1008C23—22no—
1009C23—22no—
1010C23—44no—
1011C23—416no—
1012C23—112no—
1013C23—224no—
1014C23—222no—
1015C23#6704318yes—
1016C23C24×D1112yes—
1017C23C24×D1112yes—
1018C23C24×D1114yes—
1019C23C24×D1111yescharacteristic
1020Q8—44no—
1021Q8—2216no—
1022Q8—2216no—
1023Q8—448no—
1024Q8—448no—
1025Q8—448no—
1026Q8—444no—
1027Q8—444no—
1028D4—216no—
1029D4—44no—
1030D4—2216no—
1031D4—444no—
1032D4—444no—
1033C2×C4—216no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—44no—
1041C2×C4—48no—
1042C2×C4—114no—
1043C2×C4—112no—
1044C2×C4—114no—
1045C2×C4—114no—
1046C2×C4—114no—
1047C2×C4—112no—
1048C2×C4—114no—
1049C2×C4—114no—
1050C2×C4—114no—
1051C2×C4—112no—
1052C2×C4—228no—
1053C2×C4—2216no—
1054C2×C4—228no—
1055C2×C4—228no—
1056C2×C4—2216no—
1057C2×C4—224no—
1058C2×C4—224no—
1059C2×C4—224no—
1060C2×C4—222no—
1061C2×C4—224no—
1062C2×C4—222no—
1063C2×C4—224no—
1064C2×C4—224no—
1065C2×C4—448no—
1066C2×C4—448no—
1067C2×C4—444no—
1068C2×C4—448no—
1069C2×C4—444no—
1070C2×C4C24×D1114yes—
1071C2×C4C24×D1114yes—
1072C2×C4C24×D1112yes—
1073C2×C4C24×D1114yes—
1074C2×C4C24×D1114yes—
1075C2×C4C24×D1114yes—
1076C22—24no—
1077C22—24no—
1078C22—216no—
1079C22—22no—
1080C22—22no—
1081C22—24no—
1082C22—24no—
1083C22—416no—
1084C22—44no—
1085C22—44no—
1086C22—222no—
1087C22—224no—
1088C22—444no—
1089C22C2×#6704318yes—
1090C22C2×#6704314yes—
1091C22D11×H(5,𝔽2)12yes—
1092C22C25×D1111yescharacteristic
1093C4—24no—
1094C4—24no—
1095C4—22no—
1096C4—24no—
1097C4—24no—
1098C4—24no—
1099C4—114no—
1100C4—222no—
1101C4—224no—
1102C4—222no—
1103C4—224no—
1104C4—224no—
1105C4—224no—
1106C4—224no—
1107C4—224no—
1108C2—28no—
1109C2—42no—
1110C2—42no—
1111C2—442no—
1112C2#1308285614yesdirect product factor
1113C2C2×D11×H(5,𝔽2)11yescharacteristic
1114C2C22×#6704312yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#551C2
socleC23×C11C25
prime radicalC2×#10623117C2
hypercenterC2×#551D11
hypocenterC11C2×#3538
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. #13082856C2direct (N × H)
2. C2×#10623182C2semidirect
3. C2×#10623243C2semidirect
4. C2×#10623203C2semidirect
5. C2×#10623181C2semidirect
6. C2×#10623062C2semidirect
7. C2×#10623118C2semidirect
8. C2×#10623026C2semidirect
9. C2×D4×Dic22C2semidirect
10. C2×#10623163C2semidirect
11. C2×#10623154C2semidirect
12. C2×#10623050C2semidirect
13. C2×#10623232C2semidirect
14. C2×#10623196C2semidirect
15. C2×#10623095C2semidirect
16. C2×#10623179C2semidirect
17. C2×#10623206C2semidirect
19. C22×#66931C2semidirect
20. C2×C11×#551C2semidirect
22. C22×Q8×D11C22semidirect
25. C23×Dic22C22semidirect
26. C11×#551C22semidirect
38. C2×#66997C22semidirect
39. C2×#66997C22semidirect
48. C2×#66982C22semidirect
53. C2×#66977C22semidirect
56. #10623243C22semidirect
57. #10623232C22semidirect
58. #10623206C22semidirect
59. #10623203C22semidirect
60. #10623196C22semidirect
61. #10623182C22semidirect
62. #10623181C22semidirect
63. #10623179C22semidirect
64. #10623163C22semidirect
65. #10623154C22semidirect
66. #10623118C22semidirect
68. #10623095C22semidirect
69. D4×Dic22C22semidirect
70. #10623062C22semidirect
71. #10623050C22semidirect
72. C2×#66951C22semidirect
73. C2×#66950C22semidirect
74. C2×#66949C22semidirect
75. C2×#66949C22semidirect
76. C2×#66943C22semidirect
77. C2×#66943C22semidirect
78. C2×#66942C22semidirect
79. C2×#66942C22semidirect
80. C2×#66942C22semidirect
81. C2×#66942C22semidirect
82. C2×#66942C22semidirect
83. C2×#66941C22semidirect
84. C2×#66941C22semidirect
85. C2×#66941C22semidirect
86. C2×#66941C22semidirect
87. C2×#66940C22semidirect
88. #10623026C22semidirect
91. C2×#66939C22semidirect
94. C2×#66936C22semidirect
100. C2×#66932C22semidirect
101. C2×#66932C22semidirect
113. C2×#66931C22semidirect
114. C2×#66931C22semidirect
115. C2×#66931C22semidirect
119. C2×#66930C22semidirect
120. C2×#66929C22semidirect
121. C2×#66925C22semidirect
122. C2×#66923C22semidirect
123. C2×#66923C22semidirect
124. C2×#66922C22semidirect
125. C2×#66922C22semidirect
126. C2×C4×Dic22C22semidirect
148. C2×Q8×D11C23semidirect
163. C22×Dic22C23semidirect
198. #66997C23semidirect
199. #66997C23semidirect
208. #66982C23semidirect
226. #66977C23semidirect
253. #66951C23semidirect
254. #66950C23semidirect
255. #66949C23semidirect
256. #66949C23semidirect
257. #66943C23semidirect
258. #66943C23semidirect
259. #66942C23semidirect
260. #66942C23semidirect
261. #66942C23semidirect
262. #66942C23semidirect
263. #66942C23semidirect
264. #66941C23semidirect
265. #66941C23semidirect
266. #66941C23semidirect
267. #66941C23semidirect
268. #66940C23semidirect
271. #66939C23semidirect
274. #66936C23semidirect
280. #66932C23semidirect
281. #66932C23semidirect
293. #66931C23semidirect
294. #66931C23semidirect
298. #66930C23semidirect
299. #66929C23semidirect
300. #66925C23semidirect
301. #66923C23semidirect
302. #66923C23semidirect
303. #66922C23semidirect
304. #66922C23semidirect
305. C4×Dic22C23semidirect
454. C2×#551D11semidirect
551. #551C2×D11semidirect
859. C2×C11#3538semidirect
1002. C11C2×#3538semidirect
1112. C2#13082856direct (N × H)

Maximal subgroups

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

subgroupindex
#130828562
C2×#106231822
C2×#106232432
C2×#106232032
C2×#106231812
C2×#106230622
C2×#106231182
C2×#106230262
C2×D4×Dic222
C2×#106231632
C2×#106231542
C2×#106230502
C2×#106232322
C2×#106231962
C2×#106230952
C2×#106231792
C2×#106232062
C2×#106231172
C22×#669312
C2×C11×#5512
C2×#353811