Finite Group Databasebeta

← C2×#13082231 #15660869

Subgroups — C2×#13082231 #15660869

Order 2816.

7706 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082231C2132yesmaximal, direct product factor
2C2×#10623098C211yesmaximal, characteristic, complemented
3C2×#10623115C211yesmaximal, characteristic, complemented
4C2×#10623064C212yesmaximal, complemented
5C2×#10623072C212yesmaximal, complemented
6C2×#10623062C214yesmaximal, complemented
7C2×D4×Dic22C211yesmaximal, characteristic, complemented
8C2×#10623083C212yesmaximal, complemented
9C2×#10623086C211yesmaximal, characteristic, complemented
10C2×#10623355C212yesmaximal, complemented
11C2×#10623001C211yesmaximal, characteristic, complemented
12C2×#10623109C212yesmaximal, complemented
13C2×#10623010C212yesmaximal, complemented
14C2×#10623069C214yesmaximal, complemented
15C2×C4×#4339C211yesmaximal, characteristic, complemented
16C2×C4×#4341C212yesmaximal, complemented
17C22×C4×Dic22C212yesmaximal, complemented
18C2×C4×C11×#41C211yesmaximal, characteristic, complemented
19C22×C11×#41C2211yescharacteristic
20C22×#4341C2212yes—
21C22×#4339C2211yescharacteristic
22C23×Dic22C2212yes—
23C4×C11×#41C22116yescomplemented
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11C2212yes—
27C2×C4×D4×C11C2212yes—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2212yes—
31C2×C11×#117C2211yescharacteristic
32C22×C42×C11C2212yes—
33C22×C42×C11C2211yescharacteristic
34#10623355C22132yescomplemented
35C2×#66999C2212yes—
36C2×#66997C2212yes—
37C2×#66992C2214yes—
38C2×#66988C2214yes—
39C2×D4×Dic11C2212yes—
40C2×#66983C2212yes—
41C2×#66982C2214yes—
42C2×C4×C22⋊D11C2212yes—
43C2×C4×C22⋊D11C2214yes—
44C2×C4×C22⋊D11C2212yes—
45C2×#66979C2211yescharacteristic
46C2×#66979C2212yes—
47C22×C4⋊Dic11C2212yes—
48C2×#66977C2212yes—
49C2×#66977C2212yes—
50C2×#66977C2212yes—
51C22×Dic11⋊C4C2214yes—
52C22×C4×Dic11C2214yes—
53#10623115C22116yescomplemented
54#10623109C22132yescomplemented
55#10623098C22116yescomplemented
56#10623086C22116yescomplemented
57#10623083C22132yescomplemented
58#10623072C22132yescomplemented
59#10623069C22164yescomplemented
60D4×Dic22C22116yescomplemented
61C4×#4341C22132yescomplemented
62#10623064C22132yescomplemented
63#10623062C22164yescomplemented
64C2×#66951C2214yes—
65C2×#66950C2212yes—
66C2×#66949C2214yes—
67C2×#66945C2212yes—
68C2×#66942C2214yes—
69C2×#66942C2214yes—
70C2×#66941C2212yes—
71C2×#66940C2212yes—
72C2×#66939C2214yes—
73C2×#66938C2214yes—
74C2×(C22⋊D11)⋊C4C2214yes—
75C2×#66932C2214yes—
76C2×#66931C2214yes—
77C2×#66930C2214yes—
78#10623010C22132yescomplemented
79C2×#66929C2214yes—
80C2×#66928C2212yes—
81C4×#4339C22116yescomplemented
82C2×C4×D44C2211yescharacteristic
83C2×C4×D44C2211yescharacteristic
84C2×#66925C2212yes—
85C2×#66925C2214yes—
86C2×C42×D11C2212yes—
87#10623001C22116yescomplemented
88C2×#66923C2212yes—
89C2×#66923C2212yes—
90C2×#66922C2211yescharacteristic
91C2×#66922C2211yescharacteristic
92C2×C4×Dic22C2214yes—
93C2×C4×Dic22C2212yes—
94C2×C4×Dic22C2214yes—
95C2×C4×Dic22C2212yes—
96C2×C4×Dic22C2212yes—
97C2×C4×Dic22C2212yes—
98C2×C4×Dic22C2211yescharacteristic
99C2×C4×Dic22C2211yescharacteristic
100C2×C4×Dic22C22132yescomplemented
101C2×C11×#41—28no—
102C2×C11×#41C2318yes—
103C22×Q8×C11C2311yescharacteristic
104C22×D4×C11C2312yes—
105C22×D4×C11C2311yescharacteristic
106C23×C4×C11C2312yes—
107C23×C4×C11C2312yes—
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2312yes—
111C23×C4×C11C2311yescharacteristic
112C22×C22⋊D11C2314yes—
113C22×C22⋊D11C2312yes—
114C23×Dic11C2314yes—
115C23×Dic11C2314yes—
116C2×#4341—216no—
117C2×#4341C23116yes—
118C2×#4339—28no—
119C2×#4339C2318yes—
120C22×D44C2311yescharacteristic
121C22×C4×D11C2312yes—
122C22×C4×D11C2312yes—
123C22×C4×D11C2312yes—
124C22×Dic22—216no—
125C22×Dic22C2312yes—
126C22×Dic22C2314yes—
127C22×Dic22C2312yes—
128C22×Dic22C23116yes—
129C22×Dic22C2311yescharacteristic
130C4×Q8×C11C2318yes—
131C4×Q8×C11C2318yes—
132C4×D4×C11C2318yes—
133C4×D4×C11C2318yes—
134C4×D4×C11C23116yes—
135C4×D4×C11C23116yes—
136C11×#117C23116yes—
137C11×#117C2318yes—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2312yes—
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2312yes—
149C2×C42×C11C2312yes—
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C23116yes—
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2318yes—
154C2×C22⋊Dic11C2314yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2314yes—
157#66999C23116yes—
158#66997C23116yes—
159#66992C23132yes—
160#66988C23132yes—
161D4×Dic11C23116yes—
162#66983C23116yes—
163#66982C23132yes—
164C4×C22⋊D11C23116yes—
165C4×C22⋊D11C23116yes—
166C4×C22⋊D11C23132yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2314yes—
170C2×(C2×D11)⋊C4C2314yes—
171C2×(C2×D11)⋊C4C2314yes—
172#66979C23116yes—
173#66979C2318yes—
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2314yes—
177C2×C4⋊Dic11C2312yes—
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C23116yes—
180C2×C4⋊Dic11C2312yes—
181C2×C4⋊Dic11C2312yes—
182#66977C23116yes—
183#66977C23116yes—
184#66977C23116yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2314yes—
187C2×Dic11⋊C4C2314yes—
188C2×Dic11⋊C4C2314yes—
189C2×Dic11⋊C4C2314yes—
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C23132yes—
192C2×Dic11⋊C4C2314yes—
193C2×Dic11⋊C4C2314yes—
194C2×Dic11⋊C4C2314yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2314yes—
197C2×C4×Dic11C2314yes—
198C2×C4×Dic11C2314yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C23132yes—
201C2×C4×Dic11C2312yes—
202#66951C23132yes—
203#66950C23116yes—
204#66949C23132yes—
205#66945C23116yes—
206#66942C23132yes—
207#66942C23132yes—
208#66941C23116yes—
209#66940C23116yes—
210#66939C23132yes—
211#66938C23132yes—
212(C22⋊D11)⋊C4C23132yes—
213#66932C23132yes—
214#66931C23132yes—
215#66930C23132yes—
216#66929C23132yes—
217#66928C23116yes—
218C4×D44C2318yes—
219C4×D44C2318yes—
220#66925C23116yes—
221#66925C23132yes—
222C42×D11C23116yes—
223#66923C23116yes—
224#66923C23116yes—
225#66922C2318yes—
226#66922C2318yes—
227C4×Dic22C2318yes—
228C4×Dic22C23116yes—
229C4×Dic22C23132yes—
230C4×Dic22C23132yes—
231C4×Dic22C23116yes—
232C4×Dic22C23116yes—
233C4×Dic22C23116yes—
234C4×Dic22C2318yes—
235C2×#3482—111nomaximal, Sylow
236C24×C11C2411yescharacteristic
237C24×C11C2412yes—
238C23×D11C2412yes—
239C11×#41—232no—
240C2×Q8×C11—24no—
241C2×Q8×C11C2414yes—
242C2×D4×C11—28no—
243C2×D4×C11#4118yescomplemented
244C2×D4×C11C2418yes—
245C2×D4×C11C2414yes—
246C22×C4×C11—28no—
247C22×C4×C11—28no—
248C22×C4×C11—24no—
249C22×C4×C11—24no—
250C22×C4×C11—28no—
251C22×C4×C11—24no—
252C22×C4×C11C2412yes—
253C22×C4×C11C2418yes—
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2412yes—
257C22×C4×C11C2418yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2412yes—
260C22×C4×C11C2414yes—
261C22×C4×C11C2414yes—
262C22×C4×C11C2418yes—
263C22×C4×C11C2414yes—
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2411yescharacteristic
267C2×C22⋊D11—28no—
268C2×C22⋊D11—216no—
269C2×C22⋊D11C24116yes—
270C2×C22⋊D11C2418yes—
271C22×Dic11—216no—
272C22×Dic11—216no—
273C22×Dic11C24116yes—
274C22×Dic11C24116yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2414yes—
278C22×Dic11C2414yes—
279C22×Dic11C2412yes—
280#4341—264no—
281#4339—232no—
282C2×D44—24no—
283C2×D44C2414yes—
284C2×C4×D11—28no—
285C2×C4×D11—28no—
286C2×C4×D11—28no—
287C2×C4×D11C2418yes—
288C2×C4×D11C2418yes—
289C2×C4×D11C2418yes—
290C2×Dic22—216no—
291C2×Dic22—264no—
292C2×Dic22—28no—
293C2×Dic22—28no—
294C2×Dic22#4118yescomplemented
295C2×Dic22C2418yes—
296C2×Dic22C24116yes—
297C2×Dic22C2418yes—
298C2×Dic22C2414yes—
299C11×C4⋊C4C2414yes—
300C11×C4⋊C4C2414yes—
301C11×C4⋊C4C2418yes—
302C11×C4⋊C4C2418yes—
303C11×C22⋊C4C2418yes—
304C11×C22⋊C4C2418yes—
305C11×C22⋊C4C2418yes—
306C42×C11C2414yes—
307C42×C11C2418yes—
308C42×C11C2414yes—
309C42×C11C2418yes—
310C42×C11C2418yes—
311C42×C11C2414yes—
312C42×C11C2414yes—
313C22⋊Dic11C24116yes—
314C22⋊Dic11C2418yes—
315C22⋊Dic11C24116yes—
316(C2×D11)⋊C4C2418yes—
317(C2×D11)⋊C4C2418yes—
318(C2×D11)⋊C4C24116yes—
319(C2×D11)⋊C4C24116yes—
320(C2×D11)⋊C4C24116yes—
321C4⋊Dic11C2414yes—
322C4⋊Dic11C2418yes—
323C4⋊Dic11C24116yes—
324C4⋊Dic11C2418yes—
325C4⋊Dic11C2414yes—
326C4⋊Dic11C2418yes—
327C4⋊Dic11C2418yes—
328Dic11⋊C4C2418yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C24116yes—
331Dic11⋊C4C24116yes—
332Dic11⋊C4C24116yes—
333Dic11⋊C4C2418yes—
334Dic11⋊C4C24116yes—
335Dic11⋊C4C24116yes—
336Dic11⋊C4C24116yes—
337C4×Dic11C2418yes—
338C4×Dic11C24116yes—
339C4×Dic11C24116yes—
340C4×Dic11C24116yes—
341C4×Dic11C2418yes—
342C4×Dic11C2418yes—
343#3482—1132no—
344C2×#557—111no—
345C2×#556—111no—
346C2×#556—112no—
347C2×#552—112no—
348C2×#552—114no—
349C2×D4×Q8—111no—
350C2×#548—112no—
351C2×#547—112no—
352C2×#547—111no—
353C2×#533—111no—
354C2×#533—112no—
355C2×#529—112no—
356C2×#529—114no—
357C2×C4×#41—111no—
358C2×C4×#41—112no—
359C2×C4×#41D1111yescharacteristic, complemented
360C22×C4×Q8—112no—
361C23×C11—24no—
362C23×C11—24no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11C2×#4118yes—
367C23×C11C2512yes—
368C23×C11C2514yes—
369C23×C11C2511yescharacteristic
370C22×D11—24no—
371C22×D11—24no—
372C22×D11—24no—
373C22×D11C2514yes—
374Q8×C11—28no—
375D4×C11—216no—
376D4×C11C2×#41116yescomplemented
377C2×C4×C11—24no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—24no—
381C2×C4×C11—216no—
382C2×C4×C11—24no—
383C2×C4×C11—22no—
384C2×C4×C11—216no—
385C2×C4×C11—28no—
386C2×C4×C11—28no—
387C2×C4×C11—216no—
388C2×C4×C11—28no—
389C2×C4×C11C2×#4114yes—
390C2×C4×C11C2×#4114yes—
391C2×C4×C112−1+414yes—
392C2×C4×C11C2514yes—
393C2×C4×C11C2512yes—
394C2×C4×C11C2512yes—
395C2×C4×C11C2514yes—
396C2×C4×C11C2512yes—
397C2×C4×C11C2514yes—
398C2×C4×C11C2512yes—
399C2×C4×C11C2512yes—
400C2×C4×C11C2512yes—
401C22⋊D11—232no—
402C22⋊D11—216no—
403C2×Dic11—28no—
404C2×Dic11—28no—
405C2×Dic11—24no—
406C2×Dic11—232no—
407C2×Dic11—24no—
408C2×Dic11—232no—
409C2×Dic11C2×#4118yes—
410C2×Dic11C2514yes—
411C2×Dic11C2514yes—
412C2×Dic11C2518yes—
413C2×Dic11C2518yes—
414C2×Dic11C2514yes—
415D44—28no—
416C4×D11—216no—
417C4×D11—216no—
418C4×D11—216no—
419Dic22—216no—
420Dic22—216no—
421Dic22—232no—
422Dic22C2×#41116yescomplemented
423C22×#41—112no—
424C22×#41—111no—
425C22×#41C2×D1111yescharacteristic
426C23×Q8—112no—
427#557—1116no—
428#556—1116no—
429#556—1132no—
430#552—1132no—
431#552—1164no—
432D4×Q8—1116no—
433#548—1132no—
434#547—1132no—
435#547—1116no—
436#533—1132no—
437#533—1116no—
438C2×C4⋊Q8—112no—
439C2×C4⋊Q8—112no—
440C2×C4⋊Q8—111no—
441C2×C4⋊Q8—111no—
442#529—1164no—
443#529—1132no—
444C2×#126—114no—
445C2×#126—114no—
446C2×#126—114no—
447C2×#125—114no—
448C2×#125—114no—
449C2×#125—112no—
450C2×#125—112no—
451C2×#124—114no—
452C2×#124—112no—
453C2×#123—114no—
454C2×#123—114no—
455C2×#123—114no—
456C2×C22⋊Q8—112no—
457C2×C22⋊Q8—112no—
458C2×C22⋊Q8—112no—
459C2×C22⋊Q8—112no—
460C2×C22⋊Q8—114no—
461C2×C22⋊Q8—112no—
462C2×C22⋊Q8—114no—
463C2×#121—114no—
464C2×#121—112no—
465C4×#41—1132no—
466C4×#41—1116no—
467C4×#41C2×D11116yescomplemented
468C2×C4×Q8—112no—
469C2×C4×Q8—111no—
470C2×C4×Q8—112no—
471C2×C4×Q8—114no—
472C2×C4×Q8—112no—
473C2×C4×Q8—112no—
474C2×C4×Q8—114no—
475C2×C4×Q8—112no—
476C2×C4×Q8—111no—
477C2×C4×Q8—1132no—
478C2×C4×Q8C2×D1111yescharacteristic
479C2×C4×Q8C2×D1111yescharacteristic
480C2×C4×D4—112no—
481C2×C4×D4—114no—
482C2×C4×D4—112no—
483C2×C4×D4—112no—
484C2×C4×D4—114no—
485C2×C4×D4—111no—
486C2×C4×D4—111no—
487C2×C4×D4C2×D1111yescharacteristic
488C2×C4×D4C2×D1112yes—
489C2×C4×D4C2×D1111yescharacteristic
490C2×C4×D4C2×D1112yes—
491C2×#117—111no—
492C2×#117—112no—
493C2×#117—112no—
494C2×#117—114no—
495C2×#117—112no—
496C2×#117—114no—
497C2×#117C2×D1112yes—
498C2×#117C2×D1111yescharacteristic
499C22×C4⋊C4—114no—
500C22×C4⋊C4—112no—
501C22×C42—114no—
502C22×C42—112no—
503C22×C42C2×D1112yes—
504C22×C42C2×D1111yescharacteristic
505C22×C11—24no—
506C22×C11—24no—
507C22×C11—216no—
508C22×C11—22no—
509C22×C11—22no—
510C22×C11—22no—
511C22×C11—44no—
512C22×C11C22×#4118yes—
513C22×C11C22×#4112yes—
514C22×C11C22×#4112yes—
515C22×C11C2×2−1+412yes—
516C22×C11C2611yescharacteristic
517C2×D11—24no—
518C2×D11—24no—
519C2×D11—24no—
520C2×D11—48no—
521C4×C11—22no—
522C4×C11—24no—
523C4×C11—24no—
524C4×C11—22no—
525C4×C11—24no—
526C4×C11—22no—
527C4×C11C22×#4114yes—
528C4×C11C22×#4114yes—
529C4×C11C2×2−1+414yes—
530Dic11—28no—
531Dic11—28no—
532Dic11—24no—
533Dic11—24no—
534Dic11C22×#4118yes—
535C2×#41—28no—
536C2×#41—1116no—
537C2×#41—118no—
538C2×#41—228no—
539C2×#41—2216no—
540C2×#41C22×D1118yes—
541C22×Q8—111no—
542C22×Q8—114no—
543C22×Q8—112no—
544C22×Q8—112no—
545C22×Q8—1116no—
546C22×Q8—2216no—
547C22×Q8C22×D1111yescharacteristic
548C22×D4—114no—
549C22×D4—112no—
550C22×D4—111no—
551C22×D4C22×D1112yes—
552C22×D4C22×D1111yescharacteristic
553C23×C4—114no—
554C23×C4—114no—
555C23×C4—112no—
556C23×C4—112no—
557C23×C4—112no—
558C23×C4C22×D1112yes—
559C23×C4C22×D1112yes—
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563C23×C4C22×D1112yes—
564C4⋊Q8—1116no—
565C4⋊Q8—1116no—
566C4⋊Q8—118no—
567C4⋊Q8—118no—
568#126—1132no—
569#126—1132no—
570#126—1132no—
571#125—1132no—
572#125—1132no—
573#125—1116no—
574#125—1116no—
575#124—1132no—
576#124—1116no—
577#123—1132no—
578#123—1132no—
579#123—1132no—
580C22⋊Q8—1116no—
581C22⋊Q8—1116no—
582C22⋊Q8—1116no—
583C22⋊Q8—1116no—
584C22⋊Q8—1116no—
585C22⋊Q8—1132no—
586C22⋊Q8—1132no—
587#121—1132no—
588#121—1116no—
589C4×Q8—1116no—
590C4×Q8—118no—
591C4×Q8—1132no—
592C4×Q8—1116no—
593C4×Q8—1116no—
594C4×Q8—1116no—
595C4×Q8—1132no—
596C4×Q8—1116no—
597C4×Q8—118no—
598C4×Q8C22×D1118yes—
599C4×Q8C22×D1118yes—
600C4×D4—1116no—
601C4×D4—1116no—
602C4×D4—1132no—
603C4×D4—1116no—
604C4×D4—1132no—
605C4×D4—118no—
606C4×D4—118no—
607C4×D4C22×D1118yes—
608C4×D4C22×D11116yes—
609C4×D4C22×D1118yes—
610C4×D4C22×D11116yes—
611#117—118no—
612#117—1116no—
613#117—1116no—
614#117—1132no—
615#117—1116no—
616#117—1132no—
617#117C22×D11116yes—
618#117C22×D1118yes—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4—114no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—114no—
624C2×C4⋊C4—114no—
625C2×C4⋊C4—114no—
626C2×C4⋊C4—1132no—
627C2×C4⋊C4—1116no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—114no—
630C2×C4⋊C4—111no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—114no—
633C2×C4⋊C4—114no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—112no—
637C2×C4⋊C4C22×D1111yescharacteristic
638C2×C4⋊C4C22×D1112yes—
639C2×C4⋊C4C22×D1111yescharacteristic
640C2×C4⋊C4C22×D1112yes—
641C2×C22⋊C4—114no—
642C2×C22⋊C4—112no—
643C2×C22⋊C4—114no—
644C2×C22⋊C4—112no—
645C2×C22⋊C4—112no—
646C2×C22⋊C4—114no—
647C2×C22⋊C4—114no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4C22×D1112yes—
650C2×C22⋊C4C22×D1112yes—
651C2×C22⋊C4C22×D1112yes—
652C2×C42—112no—
653C2×C42—114no—
654C2×C42—112no—
655C2×C42—114no—
656C2×C42—1132no—
657C2×C42—114no—
658C2×C42—112no—
659C2×C42—1116no—
660C2×C42C22×D1111yescharacteristic
661C2×C42C22×D1112yes—
662C2×C42C22×D1111yescharacteristic
663C2×C42C22×D1112yes—
664C2×C42C22×D11116yes—
665C2×C42C22×D1118yes—
666C2×C42C22×D1112yes—
667C2×C42C22×D1111yescharacteristic
668C2×C42C22×D1111yescharacteristic
669C2×C11—28no—
670C2×C11—42no—
671C2×C11#348214yescomplemented
672C2×C11C23×#4111yescharacteristic
673C2×C11C23×#4111yescharacteristic
674C2×C11C22×2−1+411yescharacteristic
675D11—44no—
676C24—112no—
677C24C23×D1111yescharacteristic
678C24C23×D1112yes—
679#41—232no—
680#41—2232no—
681#41—2264no—
682C2×Q8—24no—
683C2×Q8—118no—
684C2×Q8—114no—
685C2×Q8—1116no—
686C2×Q8—118no—
687C2×Q8—118no—
688C2×Q8—2216no—
689C2×Q8—2264no—
690C2×Q8—228no—
691C2×Q8—228no—
692C2×Q8C23×D1114yes—
693C2×D4—28no—
694C2×D4—1116no—
695C2×D4—118no—
696C2×D4—114no—
697C2×D4—228no—
698C2×D4—2216no—
699C2×D4—224no—
700C2×D4#433918yescomplemented
701C2×D4C23×D1118yes—
702C2×D4C23×D1114yes—
703C22×C4—28no—
704C22×C4—24no—
705C22×C4—28no—
706C22×C4—24no—
707C22×C4—28no—
708C22×C4—24no—
709C22×C4—112no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—114no—
713C22×C4—114no—
714C22×C4—1116no—
715C22×C4—1116no—
716C22×C4—118no—
717C22×C4—118no—
718C22×C4—118no—
719C22×C4—228no—
720C22×C4—2216no—
721C22×C4—2216no—
722C22×C4—228no—
723C22×C4—228no—
724C22×C4C23×D1112yes—
725C22×C4C23×D1118yes—
726C22×C4C23×D1111yescharacteristic
727C22×C4C23×D1111yescharacteristic
728C22×C4C23×D1111yescharacteristic
729C22×C4C23×D1112yes—
730C22×C4C23×D1112yes—
731C22×C4C23×D1118yes—
732C22×C4C23×D1118yes—
733C22×C4C23×D1114yes—
734C22×C4C23×D1114yes—
735C22×C4C23×D1114yes—
736C22×C4C23×D1111yescharacteristic
737C22×C4C23×D1111yescharacteristic
738C22×C4C23×D1111yescharacteristic
739C4⋊C4—118no—
740C4⋊C4—114no—
741C4⋊C4—1116no—
742C4⋊C4—118no—
743C4⋊C4—1116no—
744C4⋊C4—1116no—
745C4⋊C4—1116no—
746C4⋊C4—118no—
747C4⋊C4—1116no—
748C4⋊C4—114no—
749C4⋊C4—118no—
750C4⋊C4—1116no—
751C4⋊C4—1116no—
752C4⋊C4—118no—
753C4⋊C4—1116no—
754C4⋊C4—118no—
755C4⋊C4C23×D1114yes—
756C4⋊C4C23×D1118yes—
757C4⋊C4C23×D1114yes—
758C4⋊C4C23×D1118yes—
759C22⋊C4—1116no—
760C22⋊C4—118no—
761C22⋊C4—1116no—
762C22⋊C4—118no—
763C22⋊C4—118no—
764C22⋊C4—1116no—
765C22⋊C4—1116no—
766C22⋊C4—1116no—
767C22⋊C4C23×D1118yes—
768C22⋊C4C23×D1118yes—
769C22⋊C4C23×D1118yes—
770C42—118no—
771C42—118no—
772C42—1116no—
773C42—1116no—
774C42—118no—
775C42—1116no—
776C42C23×D1114yes—
777C42C23×D1114yes—
778C42C23×D1114yes—
779C42C23×D1118yes—
780C42C23×D1118yes—
781C42C23×D1114yes—
782C42C23×D1118yes—
783C11C2×#348211yescharacteristic, complemented, Sylow
784C23—24no—
785C23—24no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—114no—
790C23—224no—
791C23—224no—
792C23—224no—
793C23C2×#433918yes—
794C23C24×D1112yes—
795C23C24×D1114yes—
796C23C24×D1111yescharacteristic
797Q8—28no—
798Q8—1116no—
799Q8—2232no—
800Q8—2216no—
801Q8—2216no—
802D4—216no—
803D4—2216no—
804D4—2232no—
805D4—228no—
806D4C2×#4339116yescomplemented
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—216no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—28no—
815C2×C4—216no—
816C2×C4—28no—
817C2×C4—216no—
818C2×C4—28no—
819C2×C4—118no—
820C2×C4—114no—
821C2×C4—114no—
822C2×C4—114no—
823C2×C4—118no—
824C2×C4—118no—
825C2×C4—2216no—
826C2×C4—2232no—
827C2×C4—224no—
828C2×C4—228no—
829C2×C4—2232no—
830C2×C4—228no—
831C2×C4—224no—
832C2×C4—2216no—
833C2×C4—2216no—
834C2×C4C2×#433914yes—
835C2×C4#41×D1114yes—
836C2×C4#6704314yes—
837C2×C4C24×D1114yes—
838C2×C4C24×D1112yes—
839C2×C4C24×D1112yes—
840C2×C4C24×D1112yes—
841C2×C4C24×D1114yes—
842C2×C4C24×D1114yes—
843C2×C4C24×D1112yes—
844C2×C4C24×D1112yes—
845C2×C4C24×D1112yes—
846C22—24no—
847C22—24no—
848C22—216no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—224no—
854C22—224no—
855C22—224no—
856C22—448no—
857C22C22×#433918yes—
858C22C22×#433912yes—
859C22C2×#41×D1112yes—
860C22C2×#6704312yes—
861C22C25×D1111yescharacteristic
862C4—22no—
863C4—24no—
864C4—22no—
865C4—24no—
866C4—24no—
867C4—22no—
868C4—118no—
869C4—228no—
870C4—224no—
871C4—228no—
872C4—224no—
873C4C22×#433914yes—
874C4C2×#41×D1114yes—
875C4C2×#6704314yes—
876C2—28no—
877C2—42no—
878C2—444no—
879C2#1308223114yesdirect product factor
880C2C22×#41×D1111yescharacteristic
881C2C23×#433911yescharacteristic
882C2C22×#6704311yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C4×C11×#41C2
socleC23×C11C25
hypercenterC2×C4×#41D11
hypocenterC11C2×#3482
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13082231C2direct (N × H)
2. C2×#10623098C2semidirect
3. C2×#10623115C2semidirect
4. C2×#10623064C2semidirect
5. C2×#10623072C2semidirect
6. C2×#10623062C2semidirect
7. C2×D4×Dic22C2semidirect
8. C2×#10623083C2semidirect
9. C2×#10623086C2semidirect
10. C2×#10623355C2semidirect
11. C2×#10623001C2semidirect
12. C2×#10623109C2semidirect
13. C2×#10623010C2semidirect
14. C2×#10623069C2semidirect
15. C2×C4×#4339C2semidirect
16. C2×C4×#4341C2semidirect
17. C22×C4×Dic22C2semidirect
18. C2×C4×C11×#41C2semidirect
23. C4×C11×#41C22semidirect
34. #10623355C22semidirect
53. #10623115C22semidirect
54. #10623109C22semidirect
55. #10623098C22semidirect
56. #10623086C22semidirect
57. #10623083C22semidirect
58. #10623072C22semidirect
59. #10623069C22semidirect
60. D4×Dic22C22semidirect
61. C4×#4341C22semidirect
62. #10623064C22semidirect
63. #10623062C22semidirect
78. #10623010C22semidirect
81. C4×#4339C22semidirect
87. #10623001C22semidirect
100. C2×C4×Dic22C22semidirect
243. C2×D4×C11#41semidirect
294. C2×Dic22#41semidirect
359. C2×C4×#41D11semidirect
376. D4×C11C2×#41semidirect
422. Dic22C2×#41semidirect
467. C4×#41C2×D11semidirect
671. C2×C11#3482semidirect
700. C2×D4#4339semidirect
783. C11C2×#3482semidirect
806. D4C2×#4339semidirect
879. C2#13082231direct (N × H)

Maximal subgroups

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

subgroupindex
#130822312
C2×#106230982
C2×#106231152
C2×#106230642
C2×#106230722
C2×#106230622
C2×D4×Dic222
C2×#106230832
C2×#106230862
C2×#106233552
C2×#106230012
C2×#106231092
C2×#106230102
C2×#106230692
C2×C4×#43392
C2×C4×#43412
C22×C4×Dic222
C2×C4×C11×#412
C2×#348211