Finite Group Databasebeta

← C2×#13083234 #15661167

Subgroups — C2×#13083234 #15661167

Order 2816.

6598 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13083234C2132yesmaximal, direct product factor
2C2×#10623243C212yesmaximal, complemented
3C2×#10623243C212yesmaximal, complemented
4C2×#10623064C212yesmaximal, complemented
5C2×#10623070C212yesmaximal, complemented
6C2×#10623181C212yesmaximal, complemented
7C2×#10623062C212yesmaximal, complemented
8C2×#10623087C212yesmaximal, complemented
9C2×#10623189C212yesmaximal, complemented
10C2×#10623154C211yesmaximal, characteristic, complemented
11C2×#10623165C211yesmaximal, characteristic, complemented
12C2×#10623200C212yesmaximal, complemented
13C2×#10623227C212yesmaximal, complemented
14C2×#10623114C212yesmaximal, complemented
15C2×#10623133C211yesmaximal, characteristic, complemented
16C2×#10623095C212yesmaximal, complemented
17C2×#10623148C211yesmaximal, characteristic
18C2×#10623001C211yesmaximal, characteristic, complemented
19C22×#66929C211yesmaximal, characteristic, complemented
20C2×C11×#529C211yesmaximal, characteristic, complemented
21C11×#529C22116yescomplemented
22C2×C11×#126C2212yescomplemented
23C2×C11×#125C2211yescharacteristic, complemented
24C2×C11×#124C2211yescharacteristic, complemented
25C2×C11×#123C2212yes—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic, complemented
29C2×C4×D4×C11C2212yes—
30C2×C4×D4×C11C2211yescharacteristic, complemented
31C2×C11×#117C2212yescomplemented
32C22×C42×C11C2211yescharacteristic
33C2×#66999C2212yes—
34C2×#66997C2212yescomplemented
35C2×#66992C2212yes—
36C2×#66990C2212yes—
37C2×#66988C2212yes—
38C2×#66988C2212yescomplemented
39C2×D4×Dic11C2212yes—
40C2×D4×Dic11C2212yes—
41C2×#66982C2212yes—
42C2×C4×C22⋊D11C2212yes—
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C2×#66979C2212yes—
47C2×#66977C2212yes—
48C2×#66977C2211yescharacteristic
49C2×#66977C2211yescharacteristic
50C2×#66977C2212yescomplemented
51C22×Dic11⋊C4C2211yescharacteristic
52C22×Dic11⋊C4C2211yescharacteristic
53C22×Dic11⋊C4C2211yescharacteristic
54C22×Dic11⋊C4C2212yescomplemented
55#10623243C22132yescomplemented
56#10623243C22132yescomplemented
57#10623227C22132yescomplemented
58#10623200C22132yescomplemented
59#10623189C22132yescomplemented
60#10623181C22132yescomplemented
61#10623165C22116yescomplemented
62#10623154C22116yescomplemented
63#10623148C22116yes—
64#10623133C22116yescomplemented
65#10623114C22132yescomplemented
66#10623095C22132yescomplemented
67#10623087C22132yescomplemented
68#10623070C22132yescomplemented
69#10623064C22132yescomplemented
70#10623062C22132yescomplemented
71C2×#66951C2212yes—
72C2×#66951C2212yes—
73C2×#66951C2212yes—
74C2×#66951C2212yes—
75C2×#66950C2212yes—
76C2×#66950C2212yes—
77C2×#66949C2212yes—
78C2×#66949C2212yes—
79C2×#66949C2212yes—
80C2×#66945C2212yes—
81C2×#66943C2212yescomplemented
82C2×#66943C2212yescomplemented
83C2×#66942C2212yescomplemented
84C2×#66942C2212yescomplemented
85C2×#66942C2212yescomplemented
86C2×#66942C2212yescomplemented
87C2×#66942C2212yescomplemented
88C2×#66941C2212yescomplemented
89C2×#66941C2212yescomplemented
90C2×#66940C2212yescomplemented
91C2×#66939C2212yes—
92C2×#66939C2212yes—
93C2×#66938C2212yes—
94C2×#66938C2212yes—
95C2×#66938C2212yes—
96C2×#66936C2212yes—
97C2×#66936C2212yes—
98C2×(C22⋊D11)⋊C4C2212yes—
99C2×C22⋊C4×D11C2212yes—
100C2×#66932C2212yescomplemented
101C2×#66932C2212yescomplemented
102C2×#66932C2212yescomplemented
103C2×#66931C2212yes—
104C2×#66931C2212yes—
105C2×#66931C2212yescomplemented
106C2×#66931C2212yescomplemented
107C2×#66931C2212yescomplemented
108C2×#66931C2212yescomplemented
109C2×#66930C2212yes—
110C2×#66930C2212yescomplemented
111C2×#66929C2212yes—
112C2×#66929C2212yes—
113C2×#66929C2212yes—
114C2×#66929C2212yes—
115C2×#66929C2212yes—
116C2×#66929C22116yescomplemented
117C2×#66925C2212yes—
118#10623001C22116yescomplemented
119C2×#66923C2212yescomplemented
120C2×#66923C2212yescomplemented
121C2×#66922C2211yescharacteristic, complemented
122C2×#66922C2211yescharacteristic, complemented
123C2×C4×Dic22C2211yescharacteristic, complemented
124C2×C4×Dic22C2212yescomplemented
125C2×C4×Dic22C2211yescharacteristic, complemented
126C2×C4×Dic22C2212yescomplemented
127C24×D11C2311yescharacteristic
128C22×Q8×C11C2311yescharacteristic
129C22×D4×C11C2312yes—
130C22×D4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C23×Dic11C2311yescharacteristic
138C23×Dic11C2312yes—
139C23×Dic11C2311yescharacteristic
140C23×Dic11C2311yescharacteristic
141C23×Dic11C2312yes—
142C22×C4×D11C2312yes—
143C22×C4×D11C2312yes—
144C22×Dic22C2311yescharacteristic
145C22×Dic22C2312yes—
146C22×Dic22C2311yescharacteristic
147C22×Dic22C2312yes—
148C22×Dic22C2312yes—
149C11×#126C23116yescomplemented
150C11×#125C2318yescomplemented
151C11×#124C2318yescomplemented
152C11×#123C23116yes—
153C11×C22⋊Q8C2318yes—
154C11×#121C2318yes—
155C4×Q8×C11C2318yescomplemented
156C4×D4×C11C23116yes—
157C4×D4×C11C2318yescomplemented
158C11×#117C23116yescomplemented
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2312yes—
173C2×C42×C11C2311yescharacteristic
174C2×C42×C11C2311yescharacteristic
175C2×C42×C11C2318yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182#66999C23116yes—
183#66997C23116yescomplemented
184#66992C23116yes—
185#66990C23116yes—
186#66988C23116yes—
187#66988C23116yescomplemented
188D4×Dic11C23116yes—
189D4×Dic11C23116yes—
190#66982C23116yes—
191C4×C22⋊D11C23116yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2318yes—
202C2×(C2×D11)⋊C4C2318yes—
203C2×(C2×D11)⋊C4C2318yes—
204C2×(C2×D11)⋊C4C2312yes—
205#66979C23116yes—
206C2×C4⋊Dic11C2312yes—
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2312yes—
210C2×C4⋊Dic11C2312yes—
211C2×C4⋊Dic11C2312yes—
212C2×C4⋊Dic11C2312yes—
213C2×C4⋊Dic11C2312yes—
214C2×C4⋊Dic11C2312yes—
215#66977C23116yes—
216#66977C2318yes—
217#66977C2318yes—
218#66977C23116yescomplemented
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×Dic11⋊C4C2312yes—
228C2×Dic11⋊C4C2312yes—
229C2×Dic11⋊C4C2312yes—
230C2×Dic11⋊C4C2312yes—
231C2×Dic11⋊C4C2312yes—
232C2×Dic11⋊C4C2312yes—
233C2×Dic11⋊C4C2312yes—
234C2×Dic11⋊C4C2318yes—
235C2×Dic11⋊C4C2318yes—
236C2×Dic11⋊C4C2318yes—
237C2×Dic11⋊C4C2312yes—
238C2×Dic11⋊C4C2312yes—
239C2×Dic11⋊C4C2312yes—
240C2×Dic11⋊C4C23116yescomplemented
241C2×C4×Dic11C2312yes—
242C2×C4×Dic11C2312yes—
243C2×C4×Dic11C2312yes—
244C2×C4×Dic11C2312yes—
245C2×C4×Dic11C2312yes—
246C2×C4×Dic11C2312yes—
247#66951C23116yes—
248#66951C23116yes—
249#66951C23116yes—
250#66951C23116yes—
251#66950C23116yes—
252#66950C23116yes—
253#66949C23116yes—
254#66949C23116yes—
255#66949C23116yes—
256#66945C23116yes—
257#66943C23116yescomplemented
258#66943C23116yescomplemented
259#66942C23116yescomplemented
260#66942C23116yescomplemented
261#66942C23116yescomplemented
262#66942C23116yescomplemented
263#66942C23116yescomplemented
264#66941C23116yescomplemented
265#66941C23116yescomplemented
266#66940C23116yescomplemented
267#66939C23116yes—
268#66939C23116yes—
269#66938C23116yes—
270#66938C23116yes—
271#66938C23116yes—
272#66936C23116yes—
273#66936C23116yes—
274(C22⋊D11)⋊C4C23116yes—
275C22⋊C4×D11C23116yes—
276#66932C23116yescomplemented
277#66932C23116yescomplemented
278#66932C23116yescomplemented
279#66931C23116yes—
280#66931C23116yes—
281#66931C23116yescomplemented
282#66931C23116yescomplemented
283#66931C23116yescomplemented
284#66931C23116yescomplemented
285#66930C23116yes—
286#66930C23116yescomplemented
287#66929C23116yes—
288#66929C23116yes—
289#66929C23116yes—
290#66929C23116yes—
291#66929C23116yes—
292#66925C23116yes—
293#66923C23116yescomplemented
294#66923C23116yescomplemented
295#66922C2318yescomplemented
296#66922C2318yescomplemented
297C4×Dic22C2318yescomplemented
298C4×Dic22C2318yescomplemented
299C4×Dic22C23116yescomplemented
300C4×Dic22C23116yescomplemented
301C2×#3564—111nomaximal, Sylow
302C24×C11C2412yes—
303C24×C11C2411yescharacteristic
304C23×D11—24no—
305C23×D11—42no—
306C23×D11—42no—
307C23×D11C2412yes—
308C23×D11C2414yes—
309C2×Q8×C11—42no—
310C2×Q8×C11C2414yes—
311C2×D4×C11—28no—
312C2×D4×C11—42no—
313C2×D4×C11C2418yes—
314C2×D4×C11C2414yes—
315C22×C4×C11—24no—
316C22×C4×C11—42no—
317C22×C4×C11—42no—
318C22×C4×C11—44no—
319C22×C4×C11C2411yescharacteristic
320C22×C4×C11C2412yes—
321C22×C4×C11C2412yes—
322C22×C4×C11C2412yes—
323C22×C4×C11C2411yescharacteristic
324C22×C4×C11C2411yescharacteristic
325C22×C4×C11C2411yescharacteristic
326C22×C4×C11C2411yescharacteristic
327C22×C4×C11C2411yescharacteristic
328C22×C4×C11C2414yes—
329C22×C4×C11C2414yes—
330C22×C4×C11C2414yes—
331C22×C4×C11C2418yes—
332C2×C22⋊D11—44no—
333C2×C22⋊D11—44no—
334C2×C22⋊D11C2418yes—
335C2×C22⋊D11C2418yes—
336C22×Dic11—24no—
337C22×Dic11—42no—
338C22×Dic11—42no—
339C22×Dic11—44no—
340C22×Dic11—44no—
341C22×Dic11C2414yes—
342C22×Dic11C2412yes—
343C22×Dic11C2412yes—
344C22×Dic11C2412yes—
345C22×Dic11C2412yes—
346C22×Dic11C2412yes—
347C22×Dic11C2412yes—
348C22×Dic11C2412yes—
349C22×Dic11C2418yes—
350C22×Dic11C2414yes—
351C22×Dic11C2414yes—
352C22×Dic11C2418yes—
353C2×C4×D11—44no—
354C2×C4×D11—44no—
355C2×C4×D11C2418yes—
356C2×C4×D11C2418yes—
357C2×Dic22—44no—
358C2×Dic22—42no—
359C2×Dic22—42no—
360C2×Dic22—44no—
361C2×Dic22—44no—
362C2×Dic22C2414yes—
363C2×Dic22C2418yes—
364C2×Dic22C2414yes—
365C2×Dic22C2418yes—
366C2×Dic22C2418yes—
367C11×C4⋊C4C2418yes—
368C11×C4⋊C4C2418yes—
369C11×C4⋊C4C2418yes—
370C11×C4⋊C4C2414yes—
371C11×C4⋊C4C2414yes—
372C11×C4⋊C4C2418yes—
373C11×C22⋊C4C2418yes—
374C11×C22⋊C4C2418yes—
375C11×C22⋊C4C2418yes—
376C11×C22⋊C4C2418yes—
377C11×C22⋊C4C2418yes—
378C42×C11C2414yes—
379C42×C11C2414yes—
380C42×C11C2418yes—
381C42×C11C2414yes—
382C42×C11C2414yes—
383C22⋊Dic11C2418yes—
384C22⋊Dic11C2418yes—
385C22⋊Dic11C2418yes—
386C22⋊Dic11C2418yes—
387C22⋊Dic11C2418yes—
388C22⋊Dic11C2418yes—
389(C2×D11)⋊C4C2418yes—
390(C2×D11)⋊C4C2418yes—
391(C2×D11)⋊C4C2418yes—
392(C2×D11)⋊C4C2418yes—
393(C2×D11)⋊C4C2418yes—
394(C2×D11)⋊C4C2418yes—
395(C2×D11)⋊C4C2418yes—
396(C2×D11)⋊C4C2418yes—
397(C2×D11)⋊C4C2418yes—
398(C2×D11)⋊C4C2418yes—
399C4⋊Dic11C2418yes—
400C4⋊Dic11C2414yes—
401C4⋊Dic11C2414yes—
402C4⋊Dic11C2418yes—
403C4⋊Dic11C2418yes—
404C4⋊Dic11C2418yes—
405C4⋊Dic11C2418yes—
406C4⋊Dic11C2418yes—
407C4⋊Dic11C2418yes—
408Dic11⋊C4C2418yes—
409Dic11⋊C4C2418yes—
410Dic11⋊C4C2418yes—
411Dic11⋊C4C2418yes—
412Dic11⋊C4C2418yes—
413Dic11⋊C4C2418yes—
414Dic11⋊C4C2418yes—
415Dic11⋊C4C2418yes—
416Dic11⋊C4C2418yes—
417Dic11⋊C4C2418yes—
418Dic11⋊C4C2418yes—
419Dic11⋊C4C2418yes—
420Dic11⋊C4C2418yes—
421Dic11⋊C4C2418yes—
422Dic11⋊C4C2418yes—
423Dic11⋊C4C2418yes—
424Dic11⋊C4C2418yes—
425Dic11⋊C4C2418yes—
426C4×Dic11C2418yes—
427C4×Dic11C2418yes—
428C4×Dic11C2418yes—
429C4×Dic11C2418yes—
430C4×Dic11C2418yes—
431C4×Dic11C2418yes—
432#3564—1132no—
433C2×#563—112no—
434C2×#563—112no—
435C2×#556—112no—
436C2×#554—112no—
437C2×#552—112no—
438C2×#552—112no—
439C2×#551—112no—
440C2×#551—112no—
441C2×#544—111no—
442C2×#543—111no—
443C2×#542—112no—
444C2×#541—112no—
445C2×#541—112no—
446C2×#539—111no—
447C2×#539—112no—
448C2×#538—111no—
449C2×#533—111no—
450C2×#529D1111yescharacteristic, complemented
451C22×#126—111no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—24no—
455C23×C11—24no—
456C23×C11—24no—
457C23×C112−1+414yes—
458C23×C11C2514yes—
459C23×C11C2512yes—
460C23×C11C2511yescharacteristic
461C22×D11—24no—
462C22×D11—24no—
463C22×D11—24no—
464C22×D11—28no—
465C22×D11—44no—
466C22×D11—44no—
467C22×D11—88no—
468C22×D11C2514yes—
469Q8×C11—44no—
470D4×C11—216no—
471D4×C11—44no—
472C2×C4×C11—28no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—24no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—24no—
479C2×C4×C11—24no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—44no—
483C2×C4×C11—48no—
484C2×C4×C11—44no—
485C2×C4×C11C2512yes—
486C2×C4×C11C2514yes—
487C2×C4×C11C2514yes—
488C2×C4×C11C2514yes—
489C2×C4×C11C2512yes—
490C2×C4×C11C2512yes—
491C2×C4×C11C2512yes—
492C2×C4×C11C2512yes—
493C2×C4×C11C2512yes—
494C22⋊D11—48no—
495C22⋊D11—48no—
496C2×Dic11—28no—
497C2×Dic11—24no—
498C2×Dic11—24no—
499C2×Dic11—24no—
500C2×Dic11—24no—
501C2×Dic11—24no—
502C2×Dic11—24no—
503C2×Dic11—24no—
504C2×Dic11—48no—
505C2×Dic11—44no—
506C2×Dic11—44no—
507C2×Dic11—48no—
508C2×Dic11C2514yes—
509C2×Dic11C2514yes—
510C2×Dic11C2514yes—
511C2×Dic11C2514yes—
512C2×Dic11C2514yes—
513C2×Dic11C2514yes—
514C2×Dic11C2514yes—
515C4×D11—48no—
516C4×D11—48no—
517Dic22—48no—
518Dic22—48no—
519Dic22—44no—
520Dic22—48no—
521Dic22—44no—
522#563—1132no—
523#563—1132no—
524#556—1132no—
525#554—1132no—
526#552—1132no—
527#552—1132no—
528#551—1132no—
529#551—1132no—
530#544—1116no—
531#543—1116no—
532#542—1132no—
533#541—1132no—
534#541—1132no—
535#539—1116no—
536#539—1132no—
537#538—1116no—
538#533—1116no—
539C2×C4⋊Q8—112no—
540C2×C4⋊Q8—112no—
541C2×C4⋊Q8—112no—
542C2×C4⋊Q8—111no—
543C2×C4⋊Q8—111no—
544#529C2×D11116yescomplemented
545C2×#126—112no—
546C2×#126—112no—
547C2×#126—112no—
548C2×#126—112no—
549C2×#126—112no—
550C2×#126—112no—
551C2×#126—112no—
552C2×#126—112no—
553C2×#126—112no—
554C2×#126—112no—
555C2×#126—112no—
556C2×#126—112no—
557C2×#126—1116no—
558C2×#126C2×D1112yescomplemented
559C2×#125—112no—
560C2×#125—112no—
561C2×#125—112no—
562C2×#125—112no—
563C2×#125—112no—
564C2×#125—112no—
565C2×#125—112no—
566C2×#125—112no—
567C2×#125—112no—
568C2×#125C2×D1111yescharacteristic, complemented
569C2×#124—112no—
570C2×#124—112no—
571C2×#124—112no—
572C2×#124C2×D1111yescharacteristic, complemented
573C2×#123—112no—
574C2×#123—112no—
575C2×#123—112no—
576C2×#123—112no—
577C2×#123—112no—
578C2×#123—112no—
579C2×#123—112no—
580C2×#123C2×D1112yes—
581C2×C22⋊Q8—112no—
582C2×C22⋊Q8—111no—
583C2×C22⋊Q8—111no—
584C2×C22⋊Q8—112no—
585C2×C22⋊Q8—112no—
586C2×C22⋊Q8—112no—
587C2×C22⋊Q8—112no—
588C2×C22⋊Q8—112no—
589C2×C22⋊Q8—112no—
590C2×C22⋊Q8—112no—
591C2×C22⋊Q8—112no—
592C2×C22⋊Q8—112no—
593C2×C22⋊Q8—112no—
594C2×C22⋊Q8—112no—
595C2×C22⋊Q8—112no—
596C2×C22⋊Q8—112no—
597C2×C22⋊Q8C2×D1111yescharacteristic
598C2×#121—112no—
599C2×#121C2×D1111yescharacteristic
600C2×#120—112no—
601C2×C4×Q8—112no—
602C2×C4×Q8—112no—
603C2×C4×Q8—111no—
604C2×C4×Q8—111no—
605C2×C4×Q8—112no—
606C2×C4×Q8C2×D1111yescharacteristic, complemented
607C2×C4×D4—112no—
608C2×C4×D4—112no—
609C2×C4×D4—112no—
610C2×C4×D4—112no—
611C2×C4×D4C2×D1112yes—
612C2×C4×D4C2×D1111yescharacteristic, complemented
613C2×#117—112no—
614C2×#117—112no—
615C2×#117—112no—
616C2×#117—112no—
617C2×#117—112no—
618C2×#117C2×D1112yescomplemented
619C22×C4⋊C4—111no—
620C22×C4⋊C4—111no—
621C22×C4⋊C4—111no—
622C22×C4⋊C4—112no—
623C22×C22⋊C4—111no—
624C22×C22⋊C4—111no—
625C22×C22⋊C4—111no—
626C22×C22⋊C4—112no—
627C22×C42C2×D1111yescharacteristic
628C22×C11—22no—
629C22×C11—22no—
630C22×C11—28no—
631C22×C11—24no—
632C22×C11—24no—
633C22×C11—24no—
634C22×C11—48no—
635C22×C11C2×2−1+414yes—
636C22×C11C2×2−1+412yes—
637C22×C11#58512yes—
638C22×C11#58512yes—
639C22×C11C2611yescharacteristic
640C2×D11—24no—
641C2×D11—24no—
642C2×D11—24no—
643C2×D11—48no—
644C2×D11—88no—
645C4×C11—22no—
646C4×C11—22no—
647C4×C11—24no—
648C4×C11—22no—
649C4×C11—22no—
650C4×C11—22no—
651C4×C11—22no—
652C4×C11—24no—
653C4×C11—24no—
654Dic11—24no—
655Dic11—24no—
656Dic11—24no—
657Dic11—24no—
658Dic11—24no—
659Dic11—24no—
660Dic11—24no—
661C25—111no—
662C22×Q8—112no—
663C22×Q8—111no—
664C22×Q8—112no—
665C22×Q8—112no—
666C22×Q8—111no—
667C22×Q8C22×D1111yescharacteristic
668C22×D4—112no—
669C22×D4—112no—
670C22×D4C22×D1112yes—
671C22×D4C22×D1111yescharacteristic
672C23×C4—111no—
673C23×C4—111no—
674C23×C4—111no—
675C23×C4—112no—
676C23×C4—112no—
677C23×C4—112no—
678C23×C4—112no—
679C23×C4C22×D1111yescharacteristic
680C23×C4C22×D1111yescharacteristic
681C23×C4C22×D1111yescharacteristic
682C23×C4C22×D1112yes—
683C4⋊Q8—1116no—
684C4⋊Q8—1116no—
685C4⋊Q8—1116no—
686C4⋊Q8—118no—
687C4⋊Q8—118no—
688#126—1116no—
689#126—1116no—
690#126—1116no—
691#126—1116no—
692#126—1116no—
693#126—1116no—
694#126—1116no—
695#126—1116no—
696#126—1116no—
697#126—1116no—
698#126—1116no—
699#126—1116no—
700#126C22×D11116yescomplemented
701#125—1116no—
702#125—1116no—
703#125—1116no—
704#125—1116no—
705#125—1116no—
706#125—1116no—
707#125—1116no—
708#125—1116no—
709#125—1116no—
710#125C22×D1118yescomplemented
711#124—1116no—
712#124—1116no—
713#124—1116no—
714#124C22×D1118yescomplemented
715#123—1116no—
716#123—1116no—
717#123—1116no—
718#123—1116no—
719#123—1116no—
720#123—1116no—
721#123—1116no—
722#123C22×D11116yes—
723C22⋊Q8—1116no—
724C22⋊Q8—118no—
725C22⋊Q8—118no—
726C22⋊Q8—1116no—
727C22⋊Q8—1116no—
728C22⋊Q8—1116no—
729C22⋊Q8—1116no—
730C22⋊Q8—1116no—
731C22⋊Q8—1116no—
732C22⋊Q8—1116no—
733C22⋊Q8—1116no—
734C22⋊Q8—1116no—
735C22⋊Q8—1116no—
736C22⋊Q8—1116no—
737C22⋊Q8—1116no—
738C22⋊Q8—1116no—
739C22⋊Q8C22×D1118yes—
740#121—1116no—
741#121C22×D1118yes—
742#120—1116no—
743C4×Q8—1116no—
744C4×Q8—1116no—
745C4×Q8—118no—
746C4×Q8—118no—
747C4×Q8—1116no—
748C4×Q8C22×D1118yescomplemented
749C4×D4—1116no—
750C4×D4—1116no—
751C4×D4—1116no—
752C4×D4—1116no—
753C4×D4C22×D11116yes—
754C4×D4C22×D1118yescomplemented
755#117—1116no—
756#117—1116no—
757#117—1116no—
758#117—1116no—
759#117—1116no—
760#117C22×D11116yescomplemented
761C2×C4⋊C4—112no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—112no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—118no—
771C2×C4⋊C4—118no—
772C2×C4⋊C4—118no—
773C2×C4⋊C4—1116no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—111no—
789C2×C4⋊C4—112no—
790C2×C4⋊C4—111no—
791C2×C4⋊C4—112no—
792C2×C4⋊C4C22×D1112yes—
793C2×C4⋊C4C22×D1112yes—
794C2×C4⋊C4C22×D1112yes—
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C4⋊C4C22×D1111yescharacteristic
797C2×C4⋊C4C22×D1112yes—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—118no—
813C2×C22⋊C4—118no—
814C2×C22⋊C4—118no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—1116no—
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1112yes—
820C2×C22⋊C4C22×D1112yes—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C42—112no—
824C2×C42—112no—
825C2×C42—112no—
826C2×C42—112no—
827C2×C42—112no—
828C2×C42—112no—
829C2×C42C22×D1112yes—
830C2×C42C22×D1111yescharacteristic
831C2×C42C22×D1111yescharacteristic
832C2×C42C22×D1111yescharacteristic
833C2×C42C22×D1111yescharacteristic
834C2×C42C22×D1118yes—
835C2×C11—24no—
836C2×C11—44no—
837C2×C11#356414yescomplemented
838C2×C11C22×2−1+411yescharacteristic
839C2×C11C2×#58511yescharacteristic
840C2×C11C2×#58511yescharacteristic
841D11—44no—
842C24—112no—
843C24—114no—
844C24—224no—
845C24—442no—
846C24—442no—
847C24C23×D1112yes—
848C24C23×D1111yescharacteristic
849C2×Q8—42no—
850C2×Q8—118no—
851C2×Q8—114no—
852C2×Q8—118no—
853C2×Q8—118no—
854C2×Q8—114no—
855C2×Q8—444no—
856C2×Q8—442no—
857C2×Q8—444no—
858C2×Q8—442no—
859C2×Q8—444no—
860C2×Q8C23×D1114yes—
861C2×D4—28no—
862C2×D4—42no—
863C2×D4—118no—
864C2×D4—118no—
865C2×D4—444no—
866C2×D4—444no—
867C2×D4C23×D1118yes—
868C2×D4C23×D1114yes—
869C22×C4—24no—
870C22×C4—44no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—114no—
874C22×C4—112no—
875C22×C4—112no—
876C22×C4—112no—
877C22×C4—112no—
878C22×C4—112no—
879C22×C4—112no—
880C22×C4—112no—
881C22×C4—114no—
882C22×C4—114no—
883C22×C4—118no—
884C22×C4—118no—
885C22×C4—118no—
886C22×C4—118no—
887C22×C4—224no—
888C22×C4—444no—
889C22×C4—444no—
890C22×C4—442no—
891C22×C4—442no—
892C22×C4—444no—
893C22×C4—444no—
894C22×C4C23×D1114yes—
895C22×C4C23×D1111yescharacteristic
896C22×C4C23×D1112yes—
897C22×C4C23×D1112yes—
898C22×C4C23×D1112yes—
899C22×C4C23×D1111yescharacteristic
900C22×C4C23×D1111yescharacteristic
901C22×C4C23×D1111yescharacteristic
902C22×C4C23×D1111yescharacteristic
903C22×C4C23×D1111yescharacteristic
904C22×C4C23×D1114yes—
905C22×C4C23×D1114yes—
906C22×C4C23×D1118yes—
907C4⋊C4—118no—
908C4⋊C4—118no—
909C4⋊C4—118no—
910C4⋊C4—118no—
911C4⋊C4—118no—
912C4⋊C4—118no—
913C4⋊C4—118no—
914C4⋊C4—118no—
915C4⋊C4—118no—
916C4⋊C4—118no—
917C4⋊C4—118no—
918C4⋊C4—118no—
919C4⋊C4—118no—
920C4⋊C4—118no—
921C4⋊C4—118no—
922C4⋊C4—118no—
923C4⋊C4—118no—
924C4⋊C4—118no—
925C4⋊C4—118no—
926C4⋊C4—118no—
927C4⋊C4—118no—
928C4⋊C4—118no—
929C4⋊C4—118no—
930C4⋊C4—114no—
931C4⋊C4—118no—
932C4⋊C4—114no—
933C4⋊C4—118no—
934C4⋊C4C23×D1118yes—
935C4⋊C4C23×D1118yes—
936C4⋊C4C23×D1118yes—
937C4⋊C4C23×D1114yes—
938C4⋊C4C23×D1114yes—
939C4⋊C4C23×D1118yes—
940C22⋊C4—118no—
941C22⋊C4—118no—
942C22⋊C4—118no—
943C22⋊C4—118no—
944C22⋊C4—118no—
945C22⋊C4—118no—
946C22⋊C4—118no—
947C22⋊C4—118no—
948C22⋊C4—118no—
949C22⋊C4—118no—
950C22⋊C4—118no—
951C22⋊C4—118no—
952C22⋊C4—118no—
953C22⋊C4—118no—
954C22⋊C4—118no—
955C22⋊C4—118no—
956C22⋊C4C23×D1118yes—
957C22⋊C4C23×D1118yes—
958C22⋊C4C23×D1118yes—
959C22⋊C4C23×D1118yes—
960C22⋊C4C23×D1118yes—
961C42—118no—
962C42—118no—
963C42—118no—
964C42—118no—
965C42—118no—
966C42—118no—
967C42C23×D1114yes—
968C42C23×D1114yes—
969C42C23×D1114yes—
970C42C23×D1114yes—
971C42C23×D1118yes—
972C11C2×#356411yescharacteristic, complemented, Sylow
973C23—22no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—114no—
979C23—224no—
980C23—224no—
981C23—224no—
982C23—228no—
983C23—444no—
984C23—444no—
985C23—888no—
986C23#6704314yes—
987C23C24×D1114yes—
988C23C24×D1112yes—
989C23C24×D1111yescharacteristic
990Q8—44no—
991Q8—448no—
992Q8—444no—
993Q8—448no—
994Q8—444no—
995Q8—448no—
996D4—216no—
997D4—44no—
998D4—448no—
999D4—448no—
1000C2×C4—28no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—48no—
1011C2×C4—44no—
1012C2×C4—44no—
1013C2×C4—114no—
1014C2×C4—114no—
1015C2×C4—114no—
1016C2×C4—114no—
1017C2×C4—114no—
1018C2×C4—114no—
1019C2×C4—114no—
1020C2×C4—228no—
1021C2×C4—224no—
1022C2×C4—224no—
1023C2×C4—224no—
1024C2×C4—224no—
1025C2×C4—224no—
1026C2×C4—224no—
1027C2×C4—224no—
1028C2×C4—448no—
1029C2×C4—448no—
1030C2×C4—444no—
1031C2×C4—444no—
1032C2×C4—448no—
1033C2×C4—448no—
1034C2×C4C24×D1112yes—
1035C2×C4C24×D1114yes—
1036C2×C4C24×D1114yes—
1037C2×C4C24×D1114yes—
1038C2×C4C24×D1112yes—
1039C2×C4C24×D1112yes—
1040C2×C4C24×D1112yes—
1041C2×C4C24×D1112yes—
1042C2×C4C24×D1112yes—
1043C22—22no—
1044C22—22no—
1045C22—28no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—48no—
1050C22—224no—
1051C22—224no—
1052C22—224no—
1053C22—448no—
1054C22—888no—
1055C22C2×#6704314yes—
1056C22C2×#6704312yes—
1057C22#1062345312yes—
1058C22#1062345312yes—
1059C22C25×D1111yescharacteristic
1060C4—22no—
1061C4—22no—
1062C4—24no—
1063C4—22no—
1064C4—24no—
1065C4—22no—
1066C4—22no—
1067C4—22no—
1068C4—24no—
1069C4—224no—
1070C4—224no—
1071C4—224no—
1072C4—224no—
1073C4—224no—
1074C4—224no—
1075C4—224no—
1076C2—24no—
1077C2—44no—
1078C2—444no—
1079C2#1308323414yesdirect product factor
1080C2C22×#6704311yescharacteristic
1081C2C2×#1062345311yescharacteristic
1082C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#529C2
socleC23×C11C25
prime radicalC2×#10623148C2
hypercenterC2×#529D11
hypocenterC11C2×#3564
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #13083234C2direct (N × H)
2. C2×#10623243C2semidirect
3. C2×#10623243C2semidirect
4. C2×#10623064C2semidirect
5. C2×#10623070C2semidirect
6. C2×#10623181C2semidirect
7. C2×#10623062C2semidirect
8. C2×#10623087C2semidirect
9. C2×#10623189C2semidirect
10. C2×#10623154C2semidirect
11. C2×#10623165C2semidirect
12. C2×#10623200C2semidirect
13. C2×#10623227C2semidirect
14. C2×#10623114C2semidirect
15. C2×#10623133C2semidirect
16. C2×#10623095C2semidirect
18. C2×#10623001C2semidirect
19. C22×#66929C2semidirect
20. C2×C11×#529C2semidirect
21. C11×#529C22semidirect
22. C2×C11×#126C22semidirect
23. C2×C11×#125C22semidirect
24. C2×C11×#124C22semidirect
28. C2×C4×Q8×C11C22semidirect
30. C2×C4×D4×C11C22semidirect
31. C2×C11×#117C22semidirect
34. C2×#66997C22semidirect
38. C2×#66988C22semidirect
50. C2×#66977C22semidirect
54. C22×Dic11⋊C4C22semidirect
55. #10623243C22semidirect
56. #10623243C22semidirect
57. #10623227C22semidirect
58. #10623200C22semidirect
59. #10623189C22semidirect
60. #10623181C22semidirect
61. #10623165C22semidirect
62. #10623154C22semidirect
64. #10623133C22semidirect
65. #10623114C22semidirect
66. #10623095C22semidirect
67. #10623087C22semidirect
68. #10623070C22semidirect
69. #10623064C22semidirect
70. #10623062C22semidirect
81. C2×#66943C22semidirect
82. C2×#66943C22semidirect
83. C2×#66942C22semidirect
84. C2×#66942C22semidirect
85. C2×#66942C22semidirect
86. C2×#66942C22semidirect
87. C2×#66942C22semidirect
88. C2×#66941C22semidirect
89. C2×#66941C22semidirect
90. C2×#66940C22semidirect
100. C2×#66932C22semidirect
101. C2×#66932C22semidirect
102. C2×#66932C22semidirect
105. C2×#66931C22semidirect
106. C2×#66931C22semidirect
107. C2×#66931C22semidirect
108. C2×#66931C22semidirect
110. C2×#66930C22semidirect
116. C2×#66929C22semidirect
118. #10623001C22semidirect
119. C2×#66923C22semidirect
120. C2×#66923C22semidirect
121. C2×#66922C22semidirect
122. C2×#66922C22semidirect
123. C2×C4×Dic22C22semidirect
124. C2×C4×Dic22C22semidirect
125. C2×C4×Dic22C22semidirect
126. C2×C4×Dic22C22semidirect
149. C11×#126C23semidirect
150. C11×#125C23semidirect
151. C11×#124C23semidirect
155. C4×Q8×C11C23semidirect
157. C4×D4×C11C23semidirect
158. C11×#117C23semidirect
183. #66997C23semidirect
187. #66988C23semidirect
218. #66977C23semidirect
240. C2×Dic11⋊C4C23semidirect
257. #66943C23semidirect
258. #66943C23semidirect
259. #66942C23semidirect
260. #66942C23semidirect
261. #66942C23semidirect
262. #66942C23semidirect
263. #66942C23semidirect
264. #66941C23semidirect
265. #66941C23semidirect
266. #66940C23semidirect
276. #66932C23semidirect
277. #66932C23semidirect
278. #66932C23semidirect
281. #66931C23semidirect
282. #66931C23semidirect
283. #66931C23semidirect
284. #66931C23semidirect
286. #66930C23semidirect
293. #66923C23semidirect
294. #66923C23semidirect
295. #66922C23semidirect
296. #66922C23semidirect
297. C4×Dic22C23semidirect
298. C4×Dic22C23semidirect
299. C4×Dic22C23semidirect
300. C4×Dic22C23semidirect
450. C2×#529D11semidirect
544. #529C2×D11semidirect
558. C2×#126C2×D11semidirect
568. C2×#125C2×D11semidirect
572. C2×#124C2×D11semidirect
606. C2×C4×Q8C2×D11semidirect
612. C2×C4×D4C2×D11semidirect
618. C2×#117C2×D11semidirect
700. #126C22×D11semidirect
710. #125C22×D11semidirect
714. #124C22×D11semidirect
748. C4×Q8C22×D11semidirect
754. C4×D4C22×D11semidirect
760. #117C22×D11semidirect
837. C2×C11#3564semidirect
972. C11C2×#3564semidirect
1079. C2#13083234direct (N × H)

Maximal subgroups

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

subgroupindex
#130832342
C2×#106232432
C2×#106230642
C2×#106230702
C2×#106231812
C2×#106230622
C2×#106230872
C2×#106231892
C2×#106231542
C2×#106231652
C2×#106232002
C2×#106232272
C2×#106231142
C2×#106231332
C2×#106230952
C2×#106231482
C2×#106230012
C22×#669292
C2×C11×#5292
C2×#356411