Finite Group Databasebeta

← C2×#13082993 #15661470

Subgroups — C2×#13082993 #15661470

Order 2816.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082993C2132yesmaximal, direct product factor
2C2×#10623198C214yesmaximal, complemented
3C2×#10623094C211yesmaximal, characteristic, complemented
4C2×#10623147C212yesmaximal, complemented
5C2×#10623074C211yesmaximal, characteristic, complemented
6C2×#10623045C212yesmaximal, complemented
7C2×#10623173C212yesmaximal, complemented
8C2×#10623258C211yesmaximal, characteristic, complemented
9C2×#10623362C212yesmaximal, complemented
10C2×#10623031C212yesmaximal, complemented
11C2×#10623193C214yesmaximal, complemented
12C2×#10623150C212yesmaximal, complemented
13C2×#10623364C212yesmaximal, complemented
14C2×#10623159C212yesmaximal, complemented
15C2×#10623259C211yesmaximal, characteristic, complemented
16C2×#10623079C211yesmaximal, characteristic, complemented
17C2×#10623088C211yesmaximal, characteristic, complemented
18C2×C11×#547C211yesmaximal, characteristic, complemented
19C22×C11×#41C2212yes—
20C22×Q8×D11C2212yes—
21C22×#4339C2212yes—
22C11×#547C22116yescomplemented
23C2×C11×C4⋊Q8C2211yescharacteristic
24C2×C11×#123C2214yes—
25C2×C11×C22⋊Q8C2212yes—
26C2×C11×#121C2212yes—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C22×C11×C4⋊C4C2212yes—
30#10623364C22132yescomplemented
31#10623362C22132yescomplemented
32C2×#66999C2212yes—
33C2×#66999C2212yes—
34C2×Q8×Dic11C2212yes—
35C2×#66993C2211yescharacteristic
36C2×#66992C2214yes—
37C2×#66992C2214yes—
38C2×#66991C2211yescharacteristic
39C2×#66991C2211yescharacteristic
40C2×#66991C2212yes—
41C2×#66991C2214yes—
42C2×#66989C2211yescharacteristic
43C2×#66989C2214yes—
44C2×D4×Dic11C2212yes—
45C2×#66983C2212yes—
46C2×#66983C2214yes—
47C2×C4×C22⋊D11C2212yes—
48C2×C4×C22⋊D11C2212yes—
49C2×C4×C22⋊D11C2214yes—
50C2×#66979C2212yes—
51C2×#66979C2212yes—
52C22×C4⋊Dic11C2212yes—
53C2×#66977C2212yes—
54C2×#66977C2214yes—
55C2×#66977C2214yes—
56#10623259C22116yescomplemented
57#10623258C22116yescomplemented
58#10623198C22164yescomplemented
59#10623193C22164yescomplemented
60#10623173C22132yescomplemented
61#10623159C22132yescomplemented
62#10623150C22132yescomplemented
63#10623147C22132yescomplemented
64#10623094C22116yescomplemented
65#10623088C22116yescomplemented
66#10623079C22116yescomplemented
67#10623074C22116yescomplemented
68#10623045C22132yescomplemented
69C2×#66951C2214yes—
70C2×#66950C2211yescharacteristic
71C2×#66950C2212yes—
72C2×#66949C2214yes—
73C2×#66948C2211yescharacteristic
74C2×#66947C2214yes—
75C2×#66946C2212yes—
76C2×#66945C2212yes—
77C2×#66945C2212yes—
78#10623031C22132yescomplemented
79C2×#66943C2211yescharacteristic
80C2×#66943C2214yes—
81C2×#66943C2212yes—
82C2×#66943C2212yes—
83C2×#66941C2211yescharacteristic
84C2×#66941C2212yes—
85C2×#66941C2214yes—
86C2×#66940C2212yes—
87C2×#66939C2214yes—
88C2×#66938C2212yes—
89C2×#66938C2214yes—
90C2×#66938C2214yes—
91C2×#66937C2212yes—
92C2×#66936C2212yes—
93C2×#66936C2214yes—
94C2×#66932C2212yes—
95C2×#66931C2214yes—
96C2×#66930C2214yes—
97C2×C4×D44C2211yescharacteristic
98C2×C42×D11C2211yescharacteristic
99C2×#66922C2211yescharacteristic
100C2×C4×Dic22C2211yescharacteristic
101C2×C11×#41—48no—
102C2×C11×#41C23116yes—
103C22×Q8×C11C2312yes—
104C22×D4×C11C2311yescharacteristic
105C22×D4×C11C2311yescharacteristic
106C22×D4×C11C2314yes—
107C23×C4×C11C2312yes—
108C23×C4×C11C2312yes—
109C23×C4×C11C2314yes—
110C22×C22⋊D11C2312yes—
111C22×C22⋊D11C2312yes—
112C22×C22⋊D11C2312yes—
113C22×C22⋊D11C2312yes—
114C22×C22⋊D11C2314yes—
115C23×Dic11C2314yes—
116C2×Q8×D11—48no—
117C2×Q8×D11C23116yes—
118C2×#4339—48no—
119C2×#4339C23116yes—
120C22×D44C2311yescharacteristic
121C22×D44C2312yes—
122C22×C4×D11C2311yescharacteristic
123C22×C4×D11C2311yescharacteristic
124C22×C4×D11C2312yes—
125C22×C4×D11C2311yescharacteristic
126C22×C4×D11C2314yes—
127C22×Dic22C2311yescharacteristic
128C22×Dic22C2312yes—
129C22×Dic22C2312yes—
130C22×Dic22C2314yes—
131C11×C4⋊Q8C2318yes—
132C11×#123C23132yes—
133C11×C22⋊Q8C23116yes—
134C11×#121C23116yes—
135C4×D4×C11C2318yes—
136C4×D4×C11C2318yes—
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2314yes—
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C23116yes—
143C2×C11×C22⋊C4C2314yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C42×C11C2311yescharacteristic
147C2×C22⋊Dic11C2312yes—
148C2×C22⋊Dic11C2314yes—
149C2×C22⋊Dic11C2312yes—
150C2×C22⋊Dic11C2312yes—
151C2×C22⋊Dic11C2312yes—
152C2×C22⋊Dic11C2314yes—
153#66999C23116yes—
154#66999C23116yes—
155Q8×Dic11C23116yes—
156#66993C2318yes—
157#66992C23132yes—
158#66992C23132yes—
159#66991C2318yes—
160#66991C2318yes—
161#66991C23116yes—
162#66991C23132yes—
163#66989C2318yes—
164#66989C23132yes—
165D4×Dic11C23116yes—
166#66983C23116yes—
167#66983C23132yes—
168C4×C22⋊D11C23116yes—
169C4×C22⋊D11C23132yes—
170C4×C22⋊D11C23116yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2314yes—
174C2×(C2×D11)⋊C4C2314yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2314yes—
177#66979C23116yes—
178#66979C23116yes—
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2312yes—
181C2×C4⋊Dic11C2312yes—
182C2×C4⋊Dic11C2311yescharacteristic
183C2×C4⋊Dic11C2314yes—
184C2×C4⋊Dic11C2312yes—
185C2×C4⋊Dic11C2312yes—
186C2×C4⋊Dic11C2314yes—
187C2×C4⋊Dic11C23116yes—
188#66977C23132yes—
189#66977C23132yes—
190#66977C23116yes—
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2314yes—
194C2×Dic11⋊C4C2314yes—
195C2×Dic11⋊C4C2314yes—
196C2×Dic11⋊C4C2312yes—
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2314yes—
202C2×C4×Dic11C2314yes—
203#66951C23132yes—
204#66950C23116yes—
205#66950C2318yes—
206#66949C23132yes—
207#66948C2318yes—
208#66947C23132yes—
209#66946C23116yes—
210#66945C23116yes—
211#66945C23116yes—
212#66943C23116yes—
213#66943C23116yes—
214#66943C23132yes—
215#66943C2318yes—
216#66941C23116yes—
217#66941C2318yes—
218#66941C23132yes—
219#66940C23116yes—
220#66939C23132yes—
221#66938C23116yes—
222#66938C23132yes—
223#66938C23132yes—
224#66937C23116yes—
225#66936C23116yes—
226#66936C23132yes—
227#66932C23116yes—
228#66931C23132yes—
229#66930C23132yes—
230C4×D44C2318yes—
231C42×D11C2318yes—
232#66922C2318yes—
233C4×Dic22C2318yes—
234C2×#3547—111nomaximal, Sylow
235C24×C11C2412yes—
236C24×C11C2412yes—
237C23×D11C2412yes—
238C23×D11C2411yescharacteristic
239C11×#41—432no—
240C2×Q8×C11—28no—
241C2×Q8×C11C2418yes—
242C2×D4×C11—24no—
243C2×D4×C11—24no—
244C2×D4×C11—48no—
245C2×D4×C11C2414yes—
246C2×D4×C11C2414yes—
247C2×D4×C11C24116yes—
248C22×C4×C11—28no—
249C22×C4×C11—28no—
250C22×C4×C11—48no—
251C22×C4×C11C2412yes—
252C22×C4×C11C2414yes—
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2412yes—
255C22×C4×C11C2418yes—
256C22×C4×C11C2418yes—
257C22×C4×C11C24116yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—44no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—48no—
265C2×C22⋊D11C2418yes—
266C2×C22⋊D11C2418yes—
267C2×C22⋊D11C2418yes—
268C2×C22⋊D11C2418yes—
269C2×C22⋊D11C24116yes—
270C22×Dic11—48no—
271C22×Dic11C2411yescharacteristic
272C22×Dic11C2411yescharacteristic
273C22×Dic11C2412yes—
274C22×Dic11C2411yescharacteristic
275C22×Dic11C2414yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C24116yes—
279Q8×D11—432no—
280#4339—432no—
281C2×D44—24no—
282C2×D44—44no—
283C2×D44C2414yes—
284C2×D44C2418yes—
285C2×C4×D11—24no—
286C2×C4×D11—28no—
287C2×C4×D11—24no—
288C2×C4×D11—42no—
289C2×C4×D11—48no—
290C2×C4×D11C2414yes—
291C2×C4×D11C2414yes—
292C2×C4×D11C2418yes—
293C2×C4×D11C2414yes—
294C2×C4×D11C24116yes—
295C2×Dic22—24no—
296C2×Dic22—44no—
297C2×Dic22—44no—
298C2×Dic22—48no—
299C2×Dic22C2414yes—
300C2×Dic22C2418yes—
301C2×Dic22C2418yes—
302C2×Dic22C24116yes—
303C11×C4⋊C4C2418yes—
304C11×C4⋊C4C2414yes—
305C11×C4⋊C4C2418yes—
306C11×C4⋊C4C24116yes—
307C11×C4⋊C4C2414yes—
308C11×C22⋊C4C24116yes—
309C11×C22⋊C4C2418yes—
310C11×C22⋊C4C2418yes—
311C42×C11C2414yes—
312C22⋊Dic11C2418yes—
313C22⋊Dic11C24116yes—
314C22⋊Dic11C2418yes—
315C22⋊Dic11C2418yes—
316C22⋊Dic11C2418yes—
317C22⋊Dic11C24116yes—
318(C2×D11)⋊C4C2418yes—
319(C2×D11)⋊C4C2418yes—
320(C2×D11)⋊C4C24116yes—
321(C2×D11)⋊C4C24116yes—
322(C2×D11)⋊C4C2418yes—
323(C2×D11)⋊C4C24116yes—
324C4⋊Dic11C2414yes—
325C4⋊Dic11C2418yes—
326C4⋊Dic11C2418yes—
327C4⋊Dic11C2414yes—
328C4⋊Dic11C24116yes—
329C4⋊Dic11C2418yes—
330C4⋊Dic11C2418yes—
331C4⋊Dic11C24116yes—
332Dic11⋊C4C2418yes—
333Dic11⋊C4C2418yes—
334Dic11⋊C4C24116yes—
335Dic11⋊C4C24116yes—
336Dic11⋊C4C24116yes—
337Dic11⋊C4C2418yes—
338C4×Dic11C2418yes—
339C4×Dic11C2414yes—
340C4×Dic11C2414yes—
341C4×Dic11C2414yes—
342C4×Dic11C24116yes—
343C4×Dic11C24116yes—
344#3547—1132no—
345C2×#562—114no—
346C2×#555—112no—
347C2×#555—111no—
348C2×#554—111no—
349C2×#553—112no—
350C2×#552—112no—
351C2×D4×Q8—111no—
352C2×#548—112no—
353C2×#547D1111yescharacteristic, complemented
354C2×#544—112no—
355C2×#542—114no—
356C2×#540—112no—
357C2×#537—112no—
358C2×#536—112no—
359C2×#533—111no—
360C2×#532—111no—
361C2×#529—111no—
362C23×C11—24no—
363C23×C11—24no—
364C23×C11—24no—
365C23×C11—24no—
366C23×C11—24no—
367C23×C11—24no—
368C23×C11C2514yes—
369C23×C11C2514yes—
370C23×C11C2511yescharacteristic
371C22×D11—24no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—24no—
375C22×D11—22no—
376C22×D11—24no—
377C22×D11C2514yes—
378C22×D11C2512yes—
379Q8×C11—216no—
380D4×C11—28no—
381D4×C11—28no—
382D4×C11—416no—
383C2×C4×C11—28no—
384C2×C4×C11—24no—
385C2×C4×C11—24no—
386C2×C4×C11—22no—
387C2×C4×C11—216no—
388C2×C4×C11—216no—
389C2×C4×C11—416no—
390C2×C4×C11H(5,𝔽2)14yes—
391C2×C4×C112−1+414yes—
392C2×C4×C11C2514yes—
393C2×C4×C11C2518yes—
394C2×C4×C11C2512yes—
395C2×C4×C11C2514yes—
396C2×C4×C11C2512yes—
397C2×C4×C11C2512yes—
398C22⋊D11—48no—
399C22⋊D11—48no—
400C22⋊D11—416no—
401C22⋊D11—48no—
402C22⋊D11—48no—
403C2×Dic11—24no—
404C2×Dic11—24no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—28no—
408C2×Dic11—22no—
409C2×Dic11—24no—
410C2×Dic11—416no—
411C2×Dic11C2512yes—
412C2×Dic11C2512yes—
413C2×Dic11C2514yes—
414C2×Dic11C2512yes—
415C2×Dic11C2518yes—
416C2×Dic11C2514yes—
417C2×Dic11C2514yes—
418D44—28no—
419D44—48no—
420C4×D11—28no—
421C4×D11—216no—
422C4×D11—28no—
423C4×D11—44no—
424C4×D11—416no—
425Dic22—28no—
426Dic22—48no—
427Dic22—48no—
428Dic22—416no—
429C22×#41—112no—
430C22×#41C2×D1112yes—
431C23×Q8—112no—
432#562—1164no—
433#555—1132no—
434#555—1116no—
435#554—1116no—
436#553—1132no—
437#552—1132no—
438D4×Q8—1116no—
439#548—1132no—
440#547C2×D11116yescomplemented
441#544—1132no—
442#542—1164no—
443#540—1132no—
444#537—1132no—
445#536—1132no—
446#533—1116no—
447#532—1116no—
448C2×C4⋊Q8—111no—
449C2×C4⋊Q8—114no—
450C2×C4⋊Q8—112no—
451C2×C4⋊Q8—111no—
452C2×C4⋊Q8C2×D1111yescharacteristic
453C2×#127—111no—
454#529—1116no—
455C2×#126—114no—
456C2×#126—112no—
457C2×#125—111no—
458C2×#125—112no—
459C2×#125—114no—
460C2×#125—112no—
461C2×#124—111no—
462C2×#124—114no—
463C2×#124—112no—
464C2×#124—114no—
465C2×#124—114no—
466C2×#123—114no—
467C2×#123—112no—
468C2×#123—114no—
469C2×#123—114no—
470C2×#123C2×D1114yes—
471C2×C22⋊Q8—112no—
472C2×C22⋊Q8—112no—
473C2×C22⋊Q8—112no—
474C2×C22⋊Q8—114no—
475C2×C22⋊Q8—114no—
476C2×C22⋊Q8—114no—
477C2×C22⋊Q8—111no—
478C2×C22⋊Q8—112no—
479C2×C22⋊Q8—114no—
480C2×C22⋊Q8C2×D1112yes—
481C2×#121—111no—
482C2×#121—111no—
483C2×#121—112no—
484C2×#121—114no—
485C2×#121—114no—
486C2×#121—114no—
487C2×#121—114no—
488C2×#121—112no—
489C2×#121—111no—
490C2×#121—112no—
491C2×#121C2×D1112yes—
492C2×C4×Q8—112no—
493C2×C4×Q8—112no—
494C2×C4×Q8—111no—
495C2×C4×D4—112no—
496C2×C4×D4—112no—
497C2×C4×D4—112no—
498C2×C4×D4—114no—
499C2×C4×D4—112no—
500C2×C4×D4—111no—
501C2×C4×D4C2×D1111yescharacteristic
502C2×C4×D4C2×D1111yescharacteristic
503C2×#117—112no—
504C2×#117—112no—
505C2×#117—112no—
506C2×#117—112no—
507C2×#117—114no—
508C22×C4⋊C4—112no—
509C22×C4⋊C4C2×D1112yes—
510C22×C42—111no—
511C22×C11—24no—
512C22×C11—24no—
513C22×C11—24no—
514C22×C11—24no—
515C22×C11—24no—
516C22×C11—24no—
517C22×C11—48no—
518C22×C11—48no—
519C22×C11C2×H(5,𝔽2)12yes—
520C22×C11C2×2−1+412yes—
521C22×C11#58512yes—
522C22×C11C2611yescharacteristic
523C2×D11—24no—
524C2×D11—22no—
525C2×D11—22no—
526C2×D11—24no—
527C2×D11—22no—
528C2×D11—24no—
529C2×D11—48no—
530C2×D11—44no—
531C4×C11—24no—
532C4×C11—28no—
533C4×C11—24no—
534C4×C11—22no—
535C4×C11C2×H(5,𝔽2)14yes—
536C4×C11C2×2−1+414yes—
537Dic11—24no—
538Dic11—24no—
539Dic11—22no—
540Dic11—22no—
541Dic11—28no—
542Dic11—22no—
543Dic11—24no—
544C2×#41—48no—
545C2×#41—1116no—
546C2×#41—448no—
547C2×#41C22×D11116yes—
548C22×Q8—1116no—
549C22×Q8—111no—
550C22×Q8—112no—
551C22×Q8—114no—
552C22×Q8—112no—
553C22×Q8—448no—
554C22×Q8C22×D1112yes—
555C22×D4—112no—
556C22×D4—114no—
557C22×D4—112no—
558C22×D4—112no—
559C22×D4—112no—
560C22×D4—111no—
561C22×D4—112no—
562C22×D4C22×D1111yescharacteristic
563C22×D4C22×D1111yescharacteristic
564C22×D4C22×D1114yes—
565C23×C4—114no—
566C23×C4—111no—
567C23×C4—112no—
568C23×C4—111no—
569C23×C4—114no—
570C23×C4—111no—
571C23×C4C22×D1112yes—
572C23×C4C22×D1112yes—
573C23×C4C22×D1114yes—
574C4⋊Q8—118no—
575C4⋊Q8—1132no—
576C4⋊Q8—1116no—
577C4⋊Q8—118no—
578C4⋊Q8C22×D1118yes—
579#127—118no—
580#126—1132no—
581#126—1116no—
582#125—118no—
583#125—1116no—
584#125—1132no—
585#125—1116no—
586#124—118no—
587#124—1132no—
588#124—1116no—
589#124—1132no—
590#124—1132no—
591#123—1132no—
592#123—1116no—
593#123—1132no—
594#123—1132no—
595#123C22×D11132yes—
596C22⋊Q8—1116no—
597C22⋊Q8—1116no—
598C22⋊Q8—1116no—
599C22⋊Q8—1132no—
600C22⋊Q8—1132no—
601C22⋊Q8—118no—
602C22⋊Q8—1116no—
603C22⋊Q8—1132no—
604C22⋊Q8—1132no—
605C22⋊Q8C22×D11116yes—
606#121—118no—
607#121—118no—
608#121—1132no—
609#121—1116no—
610#121—1132no—
611#121—1132no—
612#121—1132no—
613#121—1116no—
614#121—118no—
615#121—1116no—
616#121C22×D11116yes—
617C4×Q8—1116no—
618C4×Q8—1116no—
619C4×Q8—118no—
620C4×D4—1116no—
621C4×D4—1116no—
622C4×D4—1116no—
623C4×D4—1132no—
624C4×D4—1116no—
625C4×D4—118no—
626C4×D4C22×D1118yes—
627C4×D4C22×D1118yes—
628#117—1116no—
629#117—1116no—
630#117—1116no—
631#117—1116no—
632#117—1132no—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—1116no—
637C2×C4⋊C4—112no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—114no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—114no—
645C2×C4⋊C4—114no—
646C2×C4⋊C4—114no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4C22×D1111yescharacteristic
649C2×C4⋊C4C22×D1112yes—
650C2×C4⋊C4C22×D1114yes—
651C2×C4⋊C4C22×D11116yes—
652C2×C4⋊C4C22×D1111yescharacteristic
653C2×C4⋊C4C22×D1112yes—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—114no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—114no—
662C2×C22⋊C4—112no—
663C2×C22⋊C4—114no—
664C2×C22⋊C4—112no—
665C2×C22⋊C4—112no—
666C2×C22⋊C4C22×D1114yes—
667C2×C22⋊C4C22×D1112yes—
668C2×C22⋊C4C22×D1112yes—
669C2×C42—114no—
670C2×C42—114no—
671C2×C42—111no—
672C2×C42—112no—
673C2×C42—111no—
674C2×C42—111no—
675C2×C42—118no—
676C2×C42C22×D1111yescharacteristic
677C2×C11—44no—
678C2×C11—44no—
679C2×C11#354714yescomplemented
680C2×C11C22×H(5,𝔽2)11yescharacteristic
681C2×C11C22×2−1+411yescharacteristic
682C2×C11C2×#58511yescharacteristic
683D11—44no—
684D11—42no—
685C24—112no—
686C24—111no—
687C24C23×D1112yes—
688C24C23×D1112yes—
689#41—432no—
690#41—4432no—
691C2×Q8—28no—
692C2×Q8—114no—
693C2×Q8—118no—
694C2×Q8—1116no—
695C2×Q8—118no—
696C2×Q8—224no—
697C2×Q8—448no—
698C2×Q8—444no—
699C2×Q8—444no—
700C2×Q8—4432no—
701C2×Q8C23×D1118yes—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—48no—
705C2×D4—118no—
706C2×D4—1116no—
707C2×D4—118no—
708C2×D4—118no—
709C2×D4—118no—
710C2×D4—114no—
711C2×D4—118no—
712C2×D4—224no—
713C2×D4—444no—
714C2×D4—444no—
715C2×D4—444no—
716C2×D4—444no—
717C2×D4—444no—
718C2×D4—448no—
719C2×D4C23×D1114yes—
720C2×D4C23×D1114yes—
721C2×D4C23×D11116yes—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—48no—
725C22×C4—111no—
726C22×C4—114no—
727C22×C4—112no—
728C22×C4—111no—
729C22×C4—111no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—1116no—
733C22×C4—114no—
734C22×C4—114no—
735C22×C4—118no—
736C22×C4—114no—
737C22×C4—1116no—
738C22×C4—228no—
739C22×C4—224no—
740C22×C4—224no—
741C22×C4—448no—
742C22×C4—442no—
743C22×C4—448no—
744C22×C4C23×D1118yes—
745C22×C4C23×D1118yes—
746C22×C4C23×D1112yes—
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1114yes—
749C22×C4C23×D1112yes—
750C22×C4C23×D11116yes—
751C22×C4C23×D1111yescharacteristic
752C22×C4C23×D1111yescharacteristic
753C4⋊C4—114no—
754C4⋊C4—118no—
755C4⋊C4—1116no—
756C4⋊C4—118no—
757C4⋊C4—114no—
758C4⋊C4—118no—
759C4⋊C4—1116no—
760C4⋊C4—118no—
761C4⋊C4—118no—
762C4⋊C4—118no—
763C4⋊C4—1116no—
764C4⋊C4—1116no—
765C4⋊C4—1116no—
766C4⋊C4—118no—
767C4⋊C4C23×D1114yes—
768C4⋊C4C23×D1118yes—
769C4⋊C4C23×D11116yes—
770C4⋊C4C23×D1114yes—
771C4⋊C4C23×D1118yes—
772C22⋊C4—118no—
773C22⋊C4—118no—
774C22⋊C4—118no—
775C22⋊C4—1116no—
776C22⋊C4—118no—
777C22⋊C4—1116no—
778C22⋊C4—1116no—
779C22⋊C4—1116no—
780C22⋊C4—118no—
781C22⋊C4—1116no—
782C22⋊C4—118no—
783C22⋊C4—118no—
784C22⋊C4C23×D11116yes—
785C22⋊C4C23×D1118yes—
786C22⋊C4C23×D1118yes—
787C42—114no—
788C42—114no—
789C42—114no—
790C42—1116no—
791C42—1116no—
792C42—118no—
793C42C23×D1114yes—
794C11C2×#354711yescharacteristic, complemented, Sylow
795C23—24no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—114no—
802C23—112no—
803C23—224no—
804C23—222no—
805C23—222no—
806C23—224no—
807C23—222no—
808C23—224no—
809C23C24×D1114yes—
810C23C24×D1114yes—
811C23C24×D1111yescharacteristic
812Q8—216no—
813Q8—228no—
814Q8—4416no—
815Q8—448no—
816Q8—448no—
817D4—28no—
818D4—28no—
819D4—416no—
820D4—228no—
821D4—448no—
822D4—448no—
823D4—448no—
824D4—448no—
825D4—448no—
826D4—4416no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—24no—
830C2×C4—22no—
831C2×C4—216no—
832C2×C4—216no—
833C2×C4—416no—
834C2×C4—112no—
835C2×C4—118no—
836C2×C4—114no—
837C2×C4—112no—
838C2×C4—112no—
839C2×C4—114no—
840C2×C4—114no—
841C2×C4—222no—
842C2×C4—224no—
843C2×C4—224no—
844C2×C4—222no—
845C2×C4—224no—
846C2×C4—222no—
847C2×C4—228no—
848C2×C4—2216no—
849C2×C4—228no—
850C2×C4—228no—
851C2×C4—4416no—
852C2×C4—444no—
853C2×C4—4416no—
854C2×C4#6703714yes—
855C2×C4#6704314yes—
856C2×C4C24×D1114yes—
857C2×C4C24×D1112yes—
858C2×C4C24×D1118yes—
859C2×C4C24×D1114yes—
860C2×C4C24×D1112yes—
861C2×C4C24×D1112yes—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—48no—
869C22—48no—
870C22—224no—
871C22—222no—
872C22—222no—
873C22—224no—
874C22—222no—
875C22—224no—
876C22—448no—
877C22—444no—
878C22C2×#6703712yes—
879C22C2×#6704312yes—
880C22#1062345712yes—
881C22C25×D1111yescharacteristic
882C4—24no—
883C4—28no—
884C4—24no—
885C4—22no—
886C4—222no—
887C4—224no—
888C4—224no—
889C4—222no—
890C4—224no—
891C4—222no—
892C4—228no—
893C4C2×#6703714yes—
894C4C2×#6704314yes—
895C2—44no—
896C2—44no—
897C2—444no—
898C2—442no—
899C2#1308299314yesdirect product factor
900C2C22×#6703711yescharacteristic
901C2C22×#6704311yescharacteristic
902C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#547C2
socleC23×C11C25
hypercenterC2×#547D11
hypocenterC11C2×#3547
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13082993C2direct (N × H)
2. C2×#10623198C2semidirect
3. C2×#10623094C2semidirect
4. C2×#10623147C2semidirect
5. C2×#10623074C2semidirect
6. C2×#10623045C2semidirect
7. C2×#10623173C2semidirect
8. C2×#10623258C2semidirect
9. C2×#10623362C2semidirect
10. C2×#10623031C2semidirect
11. C2×#10623193C2semidirect
12. C2×#10623150C2semidirect
13. C2×#10623364C2semidirect
14. C2×#10623159C2semidirect
15. C2×#10623259C2semidirect
16. C2×#10623079C2semidirect
17. C2×#10623088C2semidirect
18. C2×C11×#547C2semidirect
22. C11×#547C22semidirect
30. #10623364C22semidirect
31. #10623362C22semidirect
56. #10623259C22semidirect
57. #10623258C22semidirect
58. #10623198C22semidirect
59. #10623193C22semidirect
60. #10623173C22semidirect
61. #10623159C22semidirect
62. #10623150C22semidirect
63. #10623147C22semidirect
64. #10623094C22semidirect
65. #10623088C22semidirect
66. #10623079C22semidirect
67. #10623074C22semidirect
68. #10623045C22semidirect
78. #10623031C22semidirect
353. C2×#547D11semidirect
440. #547C2×D11semidirect
679. C2×C11#3547semidirect
794. C11C2×#3547semidirect
899. C2#13082993direct (N × H)

Maximal subgroups

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

subgroupindex
#130829932
C2×#106231982
C2×#106230942
C2×#106231472
C2×#106230742
C2×#106230452
C2×#106231732
C2×#106232582
C2×#106233622
C2×#106230312
C2×#106231932
C2×#106231502
C2×#106233642
C2×#106231592
C2×#106232592
C2×#106230792
C2×#106230882
C2×C11×#5472
C2×#354711