Finite Group Databasebeta

← C2×#19148187 #26003659

Subgroups — C2×#19148187 #26003659

Order 11008.

7802 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148187C2132yesmaximal, direct product factor
2C2×#14583634C211yesmaximal, characteristic, complemented
3C2×#14583631C212yesmaximal, complemented
4C2×#14583624C211yesmaximal, characteristic, complemented
5C2×#14583621C212yesmaximal, complemented
6C2×#14583600C214yesmaximal, complemented
7C2×#14583593C212yesmaximal, complemented
8C2×#14583570C211yesmaximal, characteristic, complemented
9C2×#14583559C212yesmaximal, complemented
10C2×#14583450C211yesmaximal, characteristic, complemented
11C2×#14583448C212yesmaximal, complemented
12C2×#14583435C212yesmaximal, complemented
13C2×#14583432C214yesmaximal, complemented
14C2×C4×#10621902C212yesmaximal, complemented
15C2×#14583367C212yesmaximal, complemented
16C2×C4×#10621900C211yesmaximal, characteristic, complemented
17C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
18C2×C43×#556C211yesmaximal, characteristic, complemented
19C22×#10621902C2212yes—
20C22×#10621898C2212yes—
21C22×#10621900C2211yescharacteristic
22C22×Q8×D43C2211yescharacteristic
23#14583634C22116yescomplemented
24#14583631C22132yescomplemented
25#14583624C22116yescomplemented
26#14583621C22132yescomplemented
27#14583600C22164yescomplemented
28#14583593C22132yescomplemented
29#14583570C22116yescomplemented
30#14583559C22132yescomplemented
31#14583450C22116yescomplemented
32#14583448C22132yescomplemented
33C2×#13063323C2212yes—
34C2×#13063322C2211yescharacteristic
35C2×#13063321C2212yes—
36#14583435C22132yescomplemented
37#14583432C22164yescomplemented
38C2×#13063320C2214yes—
39C2×#13063319C2214yes—
40C2×#13063316C2212yes—
41C2×#13063315C2214yes—
42C2×#13063314C2212yes—
43C2×#13063314C2212yes—
44C2×#13063313C2212yes—
45C2×#13063311C2214yes—
46C2×#13063310C2214yes—
47C2×#13063309C2214yes—
48C2×#13063307C2214yes—
49C2×#13063303C2214yes—
50C2×#13063300C2212yes—
51C2×#13063300C2212yes—
52C2×#13063299C2212yes—
53C2×#13063298C2214yes—
54C2×#13063298C2214yes—
55C2×#13063298C2214yes—
56C4×#10621902C22132yescomplemented
57#14583367C22132yescomplemented
58C4×#10621900C22116yescomplemented
59C2×Q8×Dic43C2212yes—
60C2×Q8×Dic43C2211yescharacteristic
61C2×C4×Dic86C2211yescharacteristic
62C2×C4×Dic86C2212yes—
63C2×C4×Dic86C2211yescharacteristic
64C2×#13063290C2212yes—
65C2×#13063290C2212yes—
66C2×#13063290C2211yescharacteristic
67C2×#13063290C2211yescharacteristic
68C4×Q8×D43C22116yescomplemented
69C2×C4×D172C2214yes—
70C2×C4×D172C2212yes—
71C2×D4×Dic43C2211yescharacteristic
72C2×#13063287C2214yes—
73C2×#13063287C2212yes—
74C2×#13063287C2212yes—
75C2×#13063287C2212yes—
76C2×#13063287C2212yes—
77C2×C4×C22⋊D43C2212yes—
78C2×(C22⋊D43)⋊C4C2214yes—
79C2×(C22⋊D43)⋊C4C2214yes—
80C2×(C22⋊D43)⋊C4C2212yes—
81C2×(C22⋊D43)⋊C4C2214yes—
82C2×#13063283C2211yescharacteristic
83C2×#13063283C2214yes—
84C2×#13063282C2214yes—
85C2×#13063281C2212yes—
86C2×C4⋊C4×D43C2211yescharacteristic
87C2×C4⋊C4×D43C2212yes—
88C22×C4×Dic43C2212yes—
89C2×C42×D43C2214yes—
90C2×C42×D43C2212yes—
91C2×C42×D43C2211yescharacteristic
92C43×#556C22116yescomplemented
93C2×C4⋊Q8×C43C2211yescharacteristic
94C2×#126×C43C2214yes—
95C2×#124×C43C2212yes—
96C2×C22⋊Q8×C43C2212yes—
97C2×C4×Q8×C43C2212yes—
98C2×C4×Q8×C43C2211yescharacteristic
99C2×C4×D4×C43C2211yescharacteristic
100C2×#117×C43C2212yes—
101C2×#10621902—216no—
102C2×#10621902C23116yes—
103C2×#10621898—216no—
104C2×#10621898C23116yes—
105C2×#10621900—28no—
106C2×#10621900C2318yes—
107C22×Dic86C2312yes—
108C22×Dic86C2311yescharacteristic
109C22×Dic86C2311yescharacteristic
110C2×Q8×D43—28no—
111C2×Q8×D43C2318yes—
112C22×D172C2312yes—
113C22×D172C2314yes—
114C22×D172C2312yes—
115C22×D172C2312yes—
116C22×C22⋊D43C2314yes—
117C22×C22⋊D43C2312yes—
118C22×C22⋊D43C2314yes—
119C23×Dic43C2312yes—
120C23×Dic43C2312yes—
121C22×C4×D43C2311yescharacteristic
122C22×C4×D43C2312yes—
123C22×C4×D43C2314yes—
124C22×C4×D43C2314yes—
125C22×C4×D43C2311yescharacteristic
126C22×C4×D43C2312yes—
127C22×C4×D43C2314yes—
128C22×C4×D43C2311yescharacteristic
129#13063323C23116yes—
130#13063322C2318yes—
131#13063321C23116yes—
132#13063320C23132yes—
133#13063319C23132yes—
134#13063316C23116yes—
135#13063315C23132yes—
136#13063314C23116yes—
137#13063314C23116yes—
138#13063313C23116yes—
139#13063311C23132yes—
140#13063310C23132yes—
141#13063309C23132yes—
142#13063307C23132yes—
143#13063303C23132yes—
144#13063300C23116yes—
145#13063300C23116yes—
146#13063299C23116yes—
147#13063298C23132yes—
148#13063298C23132yes—
149#13063298C23132yes—
150Q8×Dic43C2318yes—
151Q8×Dic43C23116yes—
152C4×Dic86C2318yes—
153C4×Dic86C23116yes—
154C4×Dic86C2318yes—
155#13063290C23116yes—
156#13063290C2318yes—
157#13063290C23116yes—
158#13063290C2318yes—
159C4×D172C23132yes—
160C4×D172C23116yes—
161D4×Dic43C2318yes—
162#13063287C23132yes—
163#13063287C23116yes—
164#13063287C23116yes—
165#13063287C23116yes—
166#13063287C23116yes—
167C4×C22⋊D43C23116yes—
168(C22⋊D43)⋊C4C23116yes—
169(C22⋊D43)⋊C4C23132yes—
170(C22⋊D43)⋊C4C23132yes—
171(C22⋊D43)⋊C4C23132yes—
172#13063283C2318yes—
173#13063283C23132yes—
174#13063282C23132yes—
175#13063281C23116yes—
176C2×C4⋊Dic43C2311yescharacteristic
177C2×C4⋊Dic43C2312yes—
178C2×C4⋊Dic43C2311yescharacteristic
179C2×C4⋊Dic43C2314yes—
180C2×Dic43⋊C4C2312yes—
181C2×Dic43⋊C4C2312yes—
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2314yes—
186C2×Dic43⋊C4C2314yes—
187C4⋊C4×D43C2318yes—
188C4⋊C4×D43C23116yes—
189C2×C22⋊Dic43C2312yes—
190C2×(C2×D43)⋊C4C2314yes—
191C2×(C2×D43)⋊C4C2314yes—
192C2×(C2×D43)⋊C4C2312yes—
193C2×(C2×D43)⋊C4C2314yes—
194C2×(C2×D43)⋊C4C2314yes—
195C2×(C2×D43)⋊C4C2314yes—
196C2×(C2×D43)⋊C4C2314yes—
197C2×C4×Dic43C2312yes—
198C2×C4×Dic43C2312yes—
199C2×C4×Dic43C2311yescharacteristic
200C2×C4×Dic43C2311yescharacteristic
201C2×C4×Dic43C2312yes—
202C2×C4×Dic43C2314yes—
203C2×C4×Dic43C2312yes—
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2312yes—
206C2×C4×Dic43C2312yes—
207C2×C4×Dic43C23116yes—
208C42×D43C2318yes—
209C42×D43C23116yes—
210C42×D43C23132yes—
211C22×Q8×C43C2311yescharacteristic
212C22×Q8×C43C2312yes—
213C22×D4×C43C2311yescharacteristic
214C23×C4×C43C2312yes—
215C4⋊Q8×C43C2318yes—
216#126×C43C23132yes—
217#124×C43C23116yes—
218C22⋊Q8×C43C23116yes—
219C4×Q8×C43C2318yes—
220C4×Q8×C43C23116yes—
221C4×D4×C43C2318yes—
222#117×C43C23116yes—
223C2×C4⋊C4×C43C2311yescharacteristic
224C2×C4⋊C4×C43C2312yes—
225C2×C4⋊C4×C43C2311yescharacteristic
226C2×C4⋊C4×C43C2314yes—
227C2×C4⋊C4×C43C2312yes—
228C2×C4⋊C4×C43C2312yes—
229C2×C22⋊C4×C43C2314yes—
230C2×C22⋊C4×C43C2312yes—
231C2×C22⋊C4×C43C2314yes—
232C2×C42×C43C2314yes—
233C2×C42×C43C2311yescharacteristic
234C2×C42×C43C2312yes—
235C24×C43C2412yes—
236C23×D43C2414yes—
237C23×D43C2411yescharacteristic
238C2×Q8×C43—24no—
239C2×Q8×C43—28no—
240C2×Q8×C43C2414yes—
241C2×Q8×C43C2418yes—
242C2×D4×C43—24no—
243C2×D4×C43C2414yes—
244C22×C4×C43—28no—
245C22×C4×C43C2412yes—
246C22×C4×C43C2412yes—
247C22×C4×C43C2411yescharacteristic
248C22×C4×C43C2412yes—
249C22×C4×C43C2414yes—
250C22×C4×C43C2418yes—
251C22×C4×C43C2411yescharacteristic
252C22×C4×C43C2411yescharacteristic
253C2×C22⋊D43—216no—
254C2×C22⋊D43—28no—
255C2×C22⋊D43—48no—
256C2×C22⋊D43C24116yes—
257C2×C22⋊D43C2418yes—
258C2×C22⋊D43C24116yes—
259C22×Dic43—28no—
260C22×Dic43—44no—
261C22×Dic43C2411yescharacteristic
262C22×Dic43C2412yes—
263C22×Dic43C2411yescharacteristic
264C22×Dic43C2412yes—
265C22×Dic43C2412yes—
266C22×Dic43C2418yes—
267C22×Dic43C2418yes—
268C22×Dic43C2411yescharacteristic
269C22×Dic43C2412yes—
270#10621902—264no—
271Q8×D43—232no—
272#10621900—232no—
273#10621898—264no—
274C2×D172—28no—
275C2×D172—28no—
276C2×D172—216no—
277C2×D172—44no—
278C2×D172C2418yes—
279C2×D172C24116yes—
280C2×D172C2418yes—
281C2×D172C2418yes—
282C2×C4×D43—24no—
283C2×C4×D43—28no—
284C2×C4×D43—216no—
285C2×C4×D43—216no—
286C2×C4×D43—42no—
287C2×C4×D43—44no—
288C2×C4×D43—48no—
289C2×C4×D43#4118yescomplemented
290C2×C4×D43C2414yes—
291C2×C4×D43C2418yes—
292C2×C4×D43C24116yes—
293C2×C4×D43C24116yes—
294C2×C4×D43C2414yes—
295C2×C4×D43C2418yes—
296C2×C4×D43C24116yes—
297C2×C4×D43C2414yes—
298C2×Dic86—24no—
299C2×Dic86—28no—
300C2×Dic86#4118yescomplemented
301C2×Dic86C2418yes—
302C2×Dic86C2414yes—
303C2×Dic86C2414yes—
304C4⋊C4×C43C2414yes—
305C4⋊C4×C43C2418yes—
306C4⋊C4×C43C2414yes—
307C4⋊C4×C43C24116yes—
308C4⋊C4×C43C2418yes—
309C4⋊C4×C43C2418yes—
310C22⋊C4×C43C24116yes—
311C22⋊C4×C43C2418yes—
312C22⋊C4×C43C24116yes—
313C42×C43C24116yes—
314C42×C43C2414yes—
315C42×C43C2418yes—
316C22⋊Dic43C2418yes—
317(C2×D43)⋊C4C24116yes—
318(C2×D43)⋊C4C24116yes—
319(C2×D43)⋊C4C2418yes—
320(C2×D43)⋊C4C24116yes—
321(C2×D43)⋊C4C24116yes—
322(C2×D43)⋊C4C24116yes—
323(C2×D43)⋊C4C24116yes—
324C4⋊Dic43C2414yes—
325C4⋊Dic43C2418yes—
326C4⋊Dic43C2414yes—
327C4⋊Dic43C24116yes—
328Dic43⋊C4C2418yes—
329Dic43⋊C4C2418yes—
330Dic43⋊C4C2418yes—
331Dic43⋊C4C2418yes—
332Dic43⋊C4C2418yes—
333Dic43⋊C4C24116yes—
334Dic43⋊C4C24116yes—
335C4×Dic43C2418yes—
336C4×Dic43C2418yes—
337C4×Dic43C2414yes—
338C4×Dic43C2414yes—
339C4×Dic43C2418yes—
340C4×Dic43C24116yes—
341C4×Dic43C2418yes—
342C4×Dic43C2414yes—
343C4×Dic43C2418yes—
344C4×Dic43C2418yes—
345C23×C43—24no—
346C23×C43—24no—
347C23×C43—24no—
348C23×C43C2514yes—
349C23×C43C2511yescharacteristic
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—28no—
353C22×D43—28no—
354C22×D43—28no—
355C22×D43C2×#4114yes—
356C22×D43C2518yes—
357C22×D43C2512yes—
358Q8×C43—28no—
359Q8×C43—216no—
360D4×C43—28no—
361C2×C4×C43—24no—
362C2×C4×C43—24no—
363C2×C4×C43—28no—
364C2×C4×C43—24no—
365C2×C4×C43—22no—
366C2×C4×C43—216no—
367C2×C4×C43C2×#4114yes—
368C2×C4×C43C2×#4114yes—
369C2×C4×C43C2514yes—
370C2×C4×C43C2512yes—
371C2×C4×C43C2518yes—
372C2×C4×C43C2514yes—
373C2×C4×C43C2514yes—
374C2×C4×C43C2512yes—
375C2×C4×C43C2512yes—
376C22⋊D43—216no—
377C22⋊D43—232no—
378C22⋊D43—416no—
379C2×Dic43—22no—
380C2×Dic43—24no—
381C2×Dic43—24no—
382C2×Dic43—22no—
383C2×Dic43—24no—
384C2×Dic43—216no—
385C2×Dic43—48no—
386C2×Dic43C2×#4118yes—
387C2×Dic43C2×#4114yes—
388C2×Dic43C2512yes—
389C2×Dic43C2514yes—
390C2×Dic43C2514yes—
391C2×Dic43C2514yes—
392C2×Dic43C2512yes—
393C2×Dic43C2512yes—
394C2×Dic43C2514yes—
395D172—232no—
396D172—216no—
397D172—216no—
398D172—48no—
399C4×D43—28no—
400C4×D43—232no—
401C4×D43—216no—
402C4×D43—232no—
403C4×D43—416no—
404C4×D43—44no—
405C4×D43—48no—
406C4×D43C2×#41116yescomplemented
407Dic86—28no—
408Dic86—216no—
409Dic86C2×#41116yescomplemented
410C2×#3480—431nomaximal, Sylow
411C22×C43—24no—
412C22×C43—24no—
413C22×C43—24no—
414C22×C43—48no—
415C22×C43C22×#4112yes—
416C22×C43C22×#4112yes—
417C22×C43#58512yes—
418C22×C43C2611yescharacteristic
419C2×D43—22no—
420C2×D43—22no—
421C2×D43—28no—
422C2×D43—28no—
423C2×D43—28no—
424C2×D43—28no—
425C2×D43—416no—
426C2×D43C22×#4114yes—
427C4×C43—24no—
428C4×C43—24no—
429C4×C43—28no—
430C4×C43—24no—
431C4×C43—22no—
432C4×C43C22×#4114yes—
433C4×C43C22×#4114yes—
434Dic43—22no—
435Dic43—24no—
436Dic43—24no—
437Dic43—22no—
438Dic43—24no—
439Dic43C22×#4118yes—
440Dic43C22×#4114yes—
441#3480—4332no—
442C2×#559—432no—
443C2×#559—431no—
444C2×#557—431no—
445C2×#556—432no—
446C2×#556D4311yescharacteristic, complemented
447C2×#553—434no—
448C2×#553—432no—
449C2×#550—431no—
450C2×#548—432no—
451C2×#532—431no—
452C2×#532—432no—
453C2×#529—434no—
454C2×#529—432no—
455C2×C4×#41—432no—
456C2×C4×#41—431no—
457C2×C4×#41—432no—
458C22×C4×Q8—431no—
459C2×C43—44no—
460C2×C43#348014yescomplemented
461C2×C43C23×#4111yescharacteristic
462C2×C43C23×#4111yescharacteristic
463C2×C43C2×#58511yescharacteristic
464D43—24no—
465D43—48no—
466C22×#41—432no—
467C22×#41—431no—
468C22×#41—432no—
469C23×Q8—431no—
470#559—4332no—
471#559—4316no—
472#557—4316no—
473#556—4332no—
474#556C2×D43116yescomplemented
475#553—4364no—
476#553—4332no—
477#550—4316no—
478#548—4332no—
479#532—4316no—
480#532—4332no—
481C2×C4⋊Q8—432no—
482C2×C4⋊Q8C2×D4311yescharacteristic
483C2×#127—432no—
484C2×#127—431no—
485#529—4364no—
486#529—4332no—
487C2×#126—434no—
488C2×#126—434no—
489C2×#126C2×D4314yes—
490C2×#125—434no—
491C2×#125—432no—
492C2×#124—432no—
493C2×#124—432no—
494C2×#124—434no—
495C2×#124—432no—
496C2×#124C2×D4312yes—
497C2×#123—434no—
498C2×#123—434no—
499C2×#123—434no—
500C2×C22⋊Q8—434no—
501C2×C22⋊Q8C2×D4312yes—
502C2×#121—432no—
503C2×#121—432no—
504C2×#121—432no—
505C2×#121—434no—
506C2×#121—434no—
507C2×#121—434no—
508C4×#41—4332no—
509C4×#41—4316no—
510C4×#41—4332no—
511C2×C4×Q8—431no—
512C2×C4×Q8—432no—
513C2×C4×Q8—4316no—
514C2×C4×Q8—431no—
515C2×C4×Q8—432no—
516C2×C4×Q8—432no—
517C2×C4×Q8—431no—
518C2×C4×Q8—431no—
519C2×C4×Q8—432no—
520C2×C4×Q8—431no—
521C2×C4×Q8C2×D4311yescharacteristic
522C2×C4×Q8C2×D4312yes—
523C2×C4×D4—431no—
524C2×C4×D4—432no—
525C2×C4×D4—432no—
526C2×C4×D4—434no—
527C2×C4×D4—432no—
528C2×C4×D4—432no—
529C2×C4×D4—432no—
530C2×C4×D4—434no—
531C2×C4×D4—432no—
532C2×C4×D4—434no—
533C2×C4×D4—434no—
534C2×C4×D4—434no—
535C2×C4×D4—432no—
536C2×C4×D4C2×D4311yescharacteristic
537C2×#117—431no—
538C2×#117—434no—
539C2×#117—432no—
540C2×#117—434no—
541C2×#117C2×D4312yes—
542C22×C4⋊C4—432no—
543C22×C4⋊C4—431no—
544C22×C42—432no—
545C22×C42—431no—
546C22×C42—432no—
547C22×C42—434no—
548C43C2×#348011yescharacteristic, complemented, Sylow
549C2×#41—4316no—
550C2×#41—438no—
551C2×#41—4316no—
552C2×#41—8616no—
553C2×#41—868no—
554C2×#41—8616no—
555C22×Q8—438no—
556C22×Q8—431no—
557C22×Q8—432no—
558C22×Q8—431no—
559C22×Q8—868no—
560C22×Q8C22×D4311yescharacteristic
561C22×Q8C22×D4312yes—
562C22×D4—432no—
563C22×D4—434no—
564C22×D4—434no—
565C22×D4—434no—
566C22×D4—432no—
567C22×D4—432no—
568C22×D4—432no—
569C22×D4C22×D4311yescharacteristic
570C23×C4—431no—
571C23×C4—432no—
572C23×C4—432no—
573C23×C4—432no—
574C23×C4—431no—
575C23×C4—434no—
576C23×C4—434no—
577C23×C4—431no—
578C23×C4—432no—
579C23×C4—434no—
580C23×C4C22×D4312yes—
581C4⋊Q8—4316no—
582C4⋊Q8C22×D4318yes—
583#127—4316no—
584#127—438no—
585#126—4332no—
586#126—4332no—
587#126C22×D43132yes—
588#125—4332no—
589#125—4316no—
590#124—4316no—
591#124—4316no—
592#124—4332no—
593#124—4316no—
594#124C22×D43116yes—
595#123—4332no—
596#123—4332no—
597#123—4332no—
598C22⋊Q8—4332no—
599C22⋊Q8C22×D43116yes—
600#121—4316no—
601#121—4316no—
602#121—4316no—
603#121—4332no—
604#121—4332no—
605#121—4332no—
606C4×Q8—438no—
607C4×Q8—4316no—
608C4×Q8—438no—
609C4×Q8—4316no—
610C4×Q8—4316no—
611C4×Q8—438no—
612C4×Q8—438no—
613C4×Q8—4316no—
614C4×Q8—438no—
615C4×Q8C22×D4318yes—
616C4×Q8C22×D43116yes—
617C4×D4—438no—
618C4×D4—4316no—
619C4×D4—4316no—
620C4×D4—4332no—
621C4×D4—4316no—
622C4×D4—4316no—
623C4×D4—4316no—
624C4×D4—4332no—
625C4×D4—4316no—
626C4×D4—4332no—
627C4×D4—4332no—
628C4×D4—4332no—
629C4×D4—4316no—
630C4×D4C22×D4318yes—
631#117—438no—
632#117—4332no—
633#117—4316no—
634#117—4332no—
635#117C22×D43116yes—
636C2×C4⋊C4—432no—
637C2×C4⋊C4—432no—
638C2×C4⋊C4—431no—
639C2×C4⋊C4—432no—
640C2×C4⋊C4—432no—
641C2×C4⋊C4—431no—
642C2×C4⋊C4—434no—
643C2×C4⋊C4—432no—
644C2×C4⋊C4—432no—
645C2×C4⋊C4—434no—
646C2×C4⋊C4—434no—
647C2×C4⋊C4—4316no—
648C2×C4⋊C4—438no—
649C2×C4⋊C4C22×D4311yescharacteristic
650C2×C4⋊C4C22×D4312yes—
651C2×C4⋊C4C22×D4311yescharacteristic
652C2×C4⋊C4C22×D4314yes—
653C2×C4⋊C4C22×D4312yes—
654C2×C4⋊C4C22×D4312yes—
655C2×C22⋊C4—432no—
656C2×C22⋊C4—432no—
657C2×C22⋊C4—434no—
658C2×C22⋊C4—434no—
659C2×C22⋊C4—434no—
660C2×C22⋊C4—434no—
661C2×C22⋊C4—434no—
662C2×C22⋊C4—434no—
663C2×C22⋊C4C22×D4312yes—
664C2×C22⋊C4C22×D4314yes—
665C2×C22⋊C4C22×D4314yes—
666C2×C42—432no—
667C2×C42—431no—
668C2×C42—432no—
669C2×C42—432no—
670C2×C42—434no—
671C2×C42—432no—
672C2×C42—432no—
673C2×C42—431no—
674C2×C42—431no—
675C2×C42—432no—
676C2×C42—4316no—
677C2×C42—438no—
678C2×C42—4316no—
679C2×C42—4332no—
680C2×C42C22×D4314yes—
681C2×C42C22×D4312yes—
682C2×C42C22×D4311yescharacteristic
683C24—431no—
684C24—434no—
685C24C23×D4312yes—
686#41—8664no—
687#41—8632no—
688#41—8664no—
689C2×Q8—24no—
690C2×Q8—28no—
691C2×Q8—438no—
692C2×Q8—434no—
693C2×Q8—438no—
694C2×Q8—434no—
695C2×Q8—868no—
696C2×Q8—8632no—
697C2×Q8—864no—
698C2×Q8C23×D4314yes—
699C2×Q8C23×D4318yes—
700C2×D4—24no—
701C2×D4—438no—
702C2×D4—4316no—
703C2×D4—4316no—
704C2×D4—4316no—
705C2×D4—438no—
706C2×D4—438no—
707C2×D4—438no—
708C2×D4—8616no—
709C2×D4—8616no—
710C2×D4—868no—
711C2×D4—868no—
712C2×D4—868no—
713C2×D4—1724no—
714C2×D4—1728no—
715C2×D4C23×D4314yes—
716C22×C4—28no—
717C22×C4—431no—
718C22×C4—432no—
719C22×C4—438no—
720C22×C4—434no—
721C22×C4—438no—
722C22×C4—432no—
723C22×C4—431no—
724C22×C4—431no—
725C22×C4—432no—
726C22×C4—432no—
727C22×C4—438no—
728C22×C4—438no—
729C22×C4—434no—
730C22×C4—4316no—
731C22×C4—4316no—
732C22×C4—434no—
733C22×C4—438no—
734C22×C4—4316no—
735C22×C4—868no—
736C22×C4—8616no—
737C22×C4—8616no—
738C22×C4—868no—
739C22×C4—864no—
740C22×C4—1728no—
741C22×C4—1724no—
742C22×C4—1722no—
743C22×C4—1724no—
744C22×C4C23×D4318yes—
745C22×C4C23×D4312yes—
746C22×C4C23×D4312yes—
747C22×C4C23×D4312yes—
748C22×C4C23×D4314yes—
749C22×C4C23×D4311yescharacteristic
750C22×C4C23×D4311yescharacteristic
751C22×C4C23×D4311yescharacteristic
752C4⋊C4—438no—
753C4⋊C4—438no—
754C4⋊C4—434no—
755C4⋊C4—438no—
756C4⋊C4—438no—
757C4⋊C4—434no—
758C4⋊C4—4316no—
759C4⋊C4—438no—
760C4⋊C4—438no—
761C4⋊C4—4316no—
762C4⋊C4—4316no—
763C4⋊C4C23×D4314yes—
764C4⋊C4C23×D4318yes—
765C4⋊C4C23×D4314yes—
766C4⋊C4C23×D43116yes—
767C4⋊C4C23×D4318yes—
768C4⋊C4C23×D4318yes—
769C22⋊C4—438no—
770C22⋊C4—438no—
771C22⋊C4—4316no—
772C22⋊C4—4316no—
773C22⋊C4—4316no—
774C22⋊C4—4316no—
775C22⋊C4—4316no—
776C22⋊C4—4316no—
777C22⋊C4C23×D4318yes—
778C22⋊C4C23×D43116yes—
779C22⋊C4C23×D43116yes—
780C42—438no—
781C42—438no—
782C42—434no—
783C42—434no—
784C42—438no—
785C42—438no—
786C42—4316no—
787C42—438no—
788C42—434no—
789C42—438no—
790C42C23×D43116yes—
791C42C23×D4318yes—
792C42C23×D4314yes—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—434no—
797C23—432no—
798C23—438no—
799C23—862no—
800C23—862no—
801C23—868no—
802C23—868no—
803C23—868no—
804C23C24×D4314yes—
805C23C24×D4311yescharacteristic
806Q8—28no—
807Q8—216no—
808Q8—4316no—
809Q8—8616no—
810Q8—868no—
811D4—28no—
812D4—8632no—
813D4—8632no—
814D4—8616no—
815D4—8616no—
816D4—8616no—
817D4—1728no—
818D4—17216no—
819C2×C4—24no—
820C2×C4—28no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—216no—
825C2×C4—434no—
826C2×C4—438no—
827C2×C4—432no—
828C2×C4—434no—
829C2×C4—4316no—
830C2×C4—434no—
831C2×C4—432no—
832C2×C4—432no—
833C2×C4—434no—
834C2×C4—434no—
835C2×C4—8616no—
836C2×C4—8632no—
837C2×C4—8632no—
838C2×C4—8616no—
839C2×C4—864no—
840C2×C4—862no—
841C2×C4—864no—
842C2×C4—862no—
843C2×C4—864no—
844C2×C4—868no—
845C2×C4—17216no—
846C2×C4—1728no—
847C2×C4—1724no—
848C2×C4—1728no—
849C2×C4#41×D4314yes—
850C2×C4#41×D4314yes—
851C2×C4C24×D4314yes—
852C2×C4C24×D4314yes—
853C2×C4C24×D4314yes—
854C2×C4C24×D4318yes—
855C2×C4C24×D4312yes—
856C2×C4C24×D4312yes—
857C2×C4C24×D4312yes—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—48no—
862C22—434no—
863C22—862no—
864C22—862no—
865C22—868no—
866C22—868no—
867C22—868no—
868C22—868no—
869C22—17216no—
870C22C2×#41×D4312yes—
871C22C2×#41×D4312yes—
872C22#1458373612yes—
873C22C25×D4311yescharacteristic
874C4—24no—
875C4—28no—
876C4—24no—
877C4—24no—
878C4—22no—
879C4—434no—
880C4—438no—
881C4—864no—
882C4—862no—
883C4—864no—
884C4—862no—
885C4—864no—
886C4C2×#41×D4314yes—
887C4C2×#41×D4314yes—
888C2—44no—
889C2—864no—
890C2—1728no—
891C2#1914818714yesdirect product factor
892C2C22×#41×D4311yescharacteristic
893C2C22×#41×D4311yescharacteristic
894C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#556C2
socleC23×C43C25
hypercenterC2×#556D43
hypocenterC43C2×#3480
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #19148187C2direct (N × H)
2. C2×#14583634C2semidirect
3. C2×#14583631C2semidirect
4. C2×#14583624C2semidirect
5. C2×#14583621C2semidirect
6. C2×#14583600C2semidirect
7. C2×#14583593C2semidirect
8. C2×#14583570C2semidirect
9. C2×#14583559C2semidirect
10. C2×#14583450C2semidirect
11. C2×#14583448C2semidirect
12. C2×#14583435C2semidirect
13. C2×#14583432C2semidirect
14. C2×C4×#10621902C2semidirect
15. C2×#14583367C2semidirect
16. C2×C4×#10621900C2semidirect
17. C2×C4×Q8×D43C2semidirect
18. C2×C43×#556C2semidirect
23. #14583634C22semidirect
24. #14583631C22semidirect
25. #14583624C22semidirect
26. #14583621C22semidirect
27. #14583600C22semidirect
28. #14583593C22semidirect
29. #14583570C22semidirect
30. #14583559C22semidirect
31. #14583450C22semidirect
32. #14583448C22semidirect
36. #14583435C22semidirect
37. #14583432C22semidirect
56. C4×#10621902C22semidirect
57. #14583367C22semidirect
58. C4×#10621900C22semidirect
68. C4×Q8×D43C22semidirect
92. C43×#556C22semidirect
289. C2×C4×D43#41semidirect
300. C2×Dic86#41semidirect
406. C4×D43C2×#41semidirect
409. Dic86C2×#41semidirect
446. C2×#556D43semidirect
460. C2×C43#3480semidirect
474. #556C2×D43semidirect
548. C43C2×#3480semidirect
891. C2#19148187direct (N × H)

Maximal subgroups

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

subgroupindex
#191481872
C2×#145836342
C2×#145836312
C2×#145836242
C2×#145836212
C2×#145836002
C2×#145835932
C2×#145835702
C2×#145835592
C2×#145834502
C2×#145834482
C2×#145834352
C2×#145834322
C2×C4×#106219022
C2×#145833672
C2×C4×#106219002
C2×C4×Q8×D432
C2×C43×#5562
C2×#348043