Finite Group Databasebeta

← C2×#19148418 #26005077

Subgroups — C2×#19148418 #26005077

Order 11008.

6958 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148418C2132yesmaximal, direct product factor
2C2×#14583626C212yesmaximal, complemented
3C2×#14583624C212yesmaximal, complemented
4C2×#14583610C212yesmaximal, complemented
5C2×#14583607C214yesmaximal, complemented
6C2×#14583605C212yesmaximal, complemented
7C2×#14583603C214yesmaximal, complemented
8C2×#14583529C212yesmaximal, complemented
9C2×#14583527C211yesmaximal, characteristic, complemented
10C2×#14583526C212yesmaximal, complemented
11C2×#14583454C212yesmaximal, complemented
12C2×#14583452C211yesmaximal, characteristic, complemented
13C22×#13063316C211yesmaximal, characteristic, complemented
14C2×#125×D43C212yesmaximal, complemented
15C2×#14583380C211yesmaximal, characteristic
16C2×#14583379C211yesmaximal, characteristic
17C2×#14583367C211yesmaximal, characteristic
18C2×C43×#544C211yesmaximal, characteristic, complemented
19C22×#10621898C2211yescharacteristic
20#14583626C22132yescomplemented
21#14583624C22132yescomplemented
22#14583610C22132yescomplemented
23#14583607C22164yescomplemented
24#14583605C22132yescomplemented
25#14583603C22164yescomplemented
26#14583529C22132yescomplemented
27#14583527C22116yescomplemented
28#14583526C22132yescomplemented
29#14583454C22132yescomplemented
30#14583452C22116yescomplemented
31C2×#13063325C2212yes—
32C2×#13063324C2212yes—
33C2×#13063324C2214yes—
34C2×#13063324C2211yescharacteristic
35C2×#13063324C2211yescharacteristic
36C2×#13063323C2214yes—
37C2×#13063317C2212yes—
38C2×#13063316C2211yescharacteristic
39C2×#13063316C2212yes—
40C2×#13063316C2212yes—
41C2×#13063316C2212yes—
42C2×#13063316C2212yes—
43C2×#13063316C2212yes—
44C2×#13063316C2211yescharacteristic
45C2×#13063316C22116yescomplemented
46C2×#13063315C2214yes—
47C2×#13063315C2214yes—
48C2×#13063315C2214yes—
49C2×#13063315C2214yes—
50#125×D43C22132yescomplemented
51C2×#13063305C2214yes—
52C2×#13063305C2214yes—
53C2×#13063303C2214yes—
54C2×#13063303C2214yes—
55C2×#13063302C2212yes—
56C2×#13063302C2214yes—
57C2×#13063302C2212yes—
58C2×#13063301C2214yes—
59C2×#13063301C2214yes—
60#14583380C22116yes—
61#14583379C22116yes—
62#14583367C22116yes—
63C2×Q8×Dic43C2214yes—
64C2×C4×Dic86C2212yes—
65C2×C4×Dic86C2212yes—
66C2×C4×Dic86C2212yes—
67C2×#13063290C2212yes—
68C2×#13063290C2214yes—
69C2×#13063290C2211yescharacteristic
70C2×#13063290C2211yescharacteristic
71C2×C4×D172C2212yes—
72C2×#13063287C2212yes—
73C2×#13063287C2211yescharacteristic
74C2×#13063287C2211yescharacteristic
75C2×C4×C22⋊D43C2214yes—
76C2×(C22⋊D43)⋊C4C2214yes—
77C2×(C22⋊D43)⋊C4C2212yes—
78C2×(C22⋊D43)⋊C4C2212yes—
79C2×#13063284C2211yescharacteristic
80C2×#13063283C2212yes—
81C2×#13063283C2212yes—
82C2×#13063282C2212yes—
83C22×C4⋊Dic43C2211yescharacteristic
84C22×C4⋊Dic43C2212yes—
85C22×Dic43⋊C4C2212yes—
86C2×C4⋊C4×D43C2212yes—
87C2×C4⋊C4×D43C2212yes—
88C2×C4⋊C4×D43C2214yes—
89C2×C4⋊C4×D43C2214yes—
90C22×C4×Dic43C2211yescharacteristic
91C2×C42×D43C2212yes—
92C43×#544C22116yescomplemented
93C2×C4⋊Q8×C43C2212yes—
94C2×C4⋊Q8×C43C2212yes—
95C2×#125×C43C2212yes—
96C2×#125×C43C2212yes—
97C2×C22⋊Q8×C43C2214yes—
98C2×#117×C43C2211yescharacteristic
99C2×#117×C43C2211yescharacteristic
100C22×C4⋊C4×C43C2211yescharacteristic
101C2×#10621898Q8116yescomplemented
102C2×#10621898C2318yes—
103C22×Dic86C2314yes—
104C22×Dic86C2312yes—
105C22×Dic86C2312yes—
106C22×Dic86C2311yescharacteristic
107C22×D172C2311yescharacteristic
108C22×C22⋊D43C2312yes—
109C23×Dic43C2311yescharacteristic
110C23×Dic43C2311yescharacteristic
111C23×Dic43C2312yes—
112C22×C4×D43C2312yes—
113C22×C4×D43C2312yes—
114C22×C4×D43C2314yes—
115C22×C4×D43C2314yes—
116C22×C4×D43C2312yes—
117#13063325C23116yes—
118#13063324C23116yes—
119#13063324C23132yes—
120#13063324C2318yes—
121#13063324C2318yes—
122#13063323C23132yes—
123#13063317C23116yes—
124#13063316C23116yes—
125#13063316C23116yes—
126#13063316C23116yes—
127#13063316C2318yes—
128#13063316C23116yes—
129#13063316C23116yes—
130#13063316C2318yes—
131#13063315C23132yes—
132#13063315C23132yes—
133#13063315C23132yes—
134#13063315C23132yes—
135#13063305C23132yes—
136#13063305C23132yes—
137#13063303C23132yes—
138#13063303C23132yes—
139#13063302C23116yes—
140#13063302C23132yes—
141#13063302C23116yes—
142#13063301C23132yes—
143#13063301C23132yes—
144Q8×Dic43C23132yes—
145C4×Dic86C23116yes—
146C4×Dic86C23116yes—
147C4×Dic86C23116yes—
148#13063290C23132yes—
149#13063290C2318yes—
150#13063290C2318yes—
151#13063290C23116yes—
152C4×D172C23116yes—
153#13063287C2318yes—
154#13063287C23116yes—
155#13063287C2318yes—
156C4×C22⋊D43C23132yes—
157(C22⋊D43)⋊C4C23116yes—
158(C22⋊D43)⋊C4C23132yes—
159(C22⋊D43)⋊C4C23116yes—
160#13063284C2318yes—
161#13063283C23116yes—
162#13063283C23116yes—
163#13063282C23116yes—
164C2×C4⋊Dic43C2311yescharacteristic
165C2×C4⋊Dic43C2312yes—
166C2×C4⋊Dic43C2312yes—
167C2×C4⋊Dic43C2314yes—
168C2×C4⋊Dic43C23116yes—
169C2×C4⋊Dic43C2312yes—
170C2×C4⋊Dic43C2318yes—
171C2×C4⋊Dic43C2314yes—
172C2×C4⋊Dic43C2311yescharacteristic
173C2×C4⋊Dic43C2312yes—
174C2×C4⋊Dic43C2314yes—
175C2×Dic43⋊C4C23116yes—
176C2×Dic43⋊C4C2312yes—
177C2×Dic43⋊C4C2314yes—
178C2×Dic43⋊C4C2314yes—
179C2×Dic43⋊C4C2314yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2314yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2312yes—
188C4⋊C4×D43C23132yes—
189C4⋊C4×D43C23132yes—
190C4⋊C4×D43C23116yes—
191C4⋊C4×D43C23116yes—
192C2×C22⋊Dic43C2312yes—
193C2×(C2×D43)⋊C4C2312yes—
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2314yes—
196C2×(C2×D43)⋊C4C2314yes—
197C2×C4×Dic43C2311yescharacteristic
198C2×C4×Dic43C2312yes—
199C2×C4×Dic43C2312yes—
200C2×C4×Dic43C2311yescharacteristic
201C2×C4×Dic43C2311yescharacteristic
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C2318yes—
204C2×C4×Dic43C2314yes—
205C2×C4×Dic43C2314yes—
206C2×C4×Dic43C2312yes—
207C42×D43C23116yes—
208C22×Q8×C43C2314yes—
209C23×C4×C43C2312yes—
210C23×C4×C43C2311yescharacteristic
211C4⋊Q8×C43C23116yes—
212C4⋊Q8×C43C23116yes—
213#125×C43C23116yes—
214#125×C43C23116yes—
215C22⋊Q8×C43C23132yes—
216#117×C43C2318yes—
217#117×C43C2318yes—
218C2×C4⋊C4×C43C2312yes—
219C2×C4⋊C4×C43C2312yes—
220C2×C4⋊C4×C43C2318yes—
221C2×C4⋊C4×C43C2311yescharacteristic
222C2×C4⋊C4×C43C2311yescharacteristic
223C2×C4⋊C4×C43C2311yescharacteristic
224C2×C4⋊C4×C43C2311yescharacteristic
225C2×C4⋊C4×C43C2314yes—
226C2×C4⋊C4×C43C2314yes—
227C2×C4⋊C4×C43C2314yes—
228C2×C22⋊C4×C43C2312yes—
229C2×C22⋊C4×C43C2312yes—
230C2×C42×C43C2312yes—
231C2×C42×C43C2312yes—
232C24×C43C2411yescharacteristic
233C23×D43C2412yes—
234C2×Q8×C43—48no—
235C2×Q8×C43C24116yes—
236C22×C4×C43—44no—
237C22×C4×C43C2×Q818yes—
238C22×C4×C43C2412yes—
239C22×C4×C43C2412yes—
240C22×C4×C43C2412yes—
241C22×C4×C43C2412yes—
242C22×C4×C43C2414yes—
243C22×C4×C43C2418yes—
244C22×C4×C43C2411yescharacteristic
245C22×C4×C43C2411yescharacteristic
246C22×C4×C43C2414yes—
247C2×C22⋊D43C2×Q8116yes—
248C2×C22⋊D43C2418yes—
249C22×Dic43—42no—
250C22×Dic43—44no—
251C22×Dic43—42no—
252C22×Dic43C2411yescharacteristic
253C22×Dic43C2411yescharacteristic
254C22×Dic43C2412yes—
255C22×Dic43C2411yescharacteristic
256C22×Dic43C2411yescharacteristic
257C22×Dic43C2414yes—
258C22×Dic43C2412yes—
259C22×Dic43C2414yes—
260C22×Dic43C2414yes—
261C22×Dic43C2418yes—
262C22×Dic43C2412yes—
263#10621898C2×Q8164yescomplemented
264C2×D172C2×Q818yes—
265C2×D172C2414yes—
266C2×C4×D43—48no—
267C2×C4×D43—48no—
268C2×C4×D43—44no—
269C2×C4×D43—44no—
270C2×C4×D43C2×Q8116yes—
271C2×C4×D43C2418yes—
272C2×C4×D43C2418yes—
273C2×C4×D43C24116yes—
274C2×C4×D43C24116yes—
275C2×C4×D43C2418yes—
276C2×Dic86—44no—
277C2×Dic86—48no—
278C2×Dic86—44no—
279C2×Dic86C2×Q818yes—
280C2×Dic86C24116yes—
281C2×Dic86C2418yes—
282C2×Dic86C2418yes—
283C2×Dic86C2414yes—
284C4⋊C4×C43C2418yes—
285C4⋊C4×C43C2418yes—
286C4⋊C4×C43C2414yes—
287C4⋊C4×C43C2414yes—
288C4⋊C4×C43C2414yes—
289C4⋊C4×C43C2414yes—
290C4⋊C4×C43C24116yes—
291C4⋊C4×C43C24116yes—
292C4⋊C4×C43C24116yes—
293C22⋊C4×C43C2418yes—
294C22⋊C4×C43C2418yes—
295C42×C43C2418yes—
296C42×C43C2418yes—
297C22⋊Dic43C2418yes—
298(C2×D43)⋊C4C2418yes—
299(C2×D43)⋊C4C2418yes—
300(C2×D43)⋊C4C24116yes—
301(C2×D43)⋊C4C24116yes—
302C4⋊Dic43C2414yes—
303C4⋊Dic43C2418yes—
304C4⋊Dic43C2418yes—
305C4⋊Dic43C24116yes—
306C4⋊Dic43C2418yes—
307C4⋊Dic43C24116yes—
308C4⋊Dic43C2414yes—
309C4⋊Dic43C2418yes—
310C4⋊Dic43C24116yes—
311Dic43⋊C4C2418yes—
312Dic43⋊C4C24116yes—
313Dic43⋊C4C24116yes—
314Dic43⋊C4C24116yes—
315Dic43⋊C4C24116yes—
316Dic43⋊C4C24116yes—
317Dic43⋊C4C24116yes—
318Dic43⋊C4C2418yes—
319Dic43⋊C4C2418yes—
320Dic43⋊C4C2418yes—
321Dic43⋊C4C2418yes—
322Dic43⋊C4C2418yes—
323C4×Dic43C2414yes—
324C4×Dic43C2418yes—
325C4×Dic43C2418yes—
326C4×Dic43C2414yes—
327C4×Dic43C2414yes—
328C4×Dic43C2414yes—
329C4×Dic43C24116yes—
330C4×Dic43C24116yes—
331C4×Dic43C2418yes—
332C23×C43—22no—
333C23×C43—22no—
334C23×C43C22×Q814yes—
335C23×C43C2512yes—
336C23×C43C2511yescharacteristic
337C22×D43—24no—
338C22×D43—24no—
339C22×D43C22×Q818yes—
340C22×D43C2514yes—
341Q8×C43—416no—
342C2×C4×C43—24no—
343C2×C4×C43—24no—
344C2×C4×C43—24no—
345C2×C4×C43—28no—
346C2×C4×C43—24no—
347C2×C4×C43—48no—
348C2×C4×C43C22×Q814yes—
349C2×C4×C43C22×Q814yes—
350C2×C4×C43C22×Q8116yes—
351C2×C4×C43C2514yes—
352C2×C4×C43C2514yes—
353C2×C4×C43C2518yes—
354C2×C4×C43C2514yes—
355C2×C4×C43C2514yes—
356C2×C4×C43C2512yes—
357C2×C4×C43C2512yes—
358C22⋊D43C22×Q8132yes—
359C2×Dic43—24no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—24no—
363C2×Dic43—28no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—44no—
367C2×Dic43—44no—
368C2×Dic43—48no—
369C2×Dic43C22×Q818yes—
370C2×Dic43C2512yes—
371C2×Dic43C2512yes—
372C2×Dic43C2514yes—
373C2×Dic43C2512yes—
374C2×Dic43C2512yes—
375C2×Dic43C2514yes—
376C2×Dic43C2518yes—
377C2×Dic43C2514yes—
378D172C22×Q8116yes—
379C4×D43—416no—
380C4×D43—416no—
381C4×D43—48no—
382C4×D43—48no—
383C4×D43C22×Q8132yes—
384Dic86—48no—
385Dic86—416no—
386Dic86—48no—
387Dic86C22×Q8116yes—
388C2×#3504—431nomaximal, Sylow
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—28no—
392C22×C43C23×Q814yes—
393C22×C43C23×Q812yes—
394C22×C43#58512yes—
395C22×C43#58512yes—
396C22×C43C2611yescharacteristic
397C2×D43—24no—
398C2×D43—24no—
399C2×D43—216no—
400C2×D43C23×Q818yes—
401C4×C43—24no—
402C4×C43—24no—
403C4×C43—24no—
404C4×C43—28no—
405C4×C43—24no—
406C4×C43C23×Q814yes—
407C4×C43C23×Q814yes—
408Dic43—24no—
409Dic43—22no—
410Dic43—22no—
411Dic43—24no—
412Dic43—28no—
413Dic43—22no—
414Dic43—22no—
415Dic43C23×Q818yes—
416#3504—4332no—
417C2×#557—432no—
418C2×#557—432no—
419C2×#554—432no—
420C2×#554—432no—
421C2×#554—434no—
422C2×#554—434no—
423C2×#544—432no—
424C2×#544—432no—
425C2×#544—431no—
426C2×#544D4311yescharacteristic, complemented
427C2×#533—432no—
428C2×#533—431no—
429C22×#125—432no—
430C22×#125—431no—
431C2×#520—431no—
432C2×#520—431no—
433C2×C4×#41—431no—
434C2×C43—24no—
435C2×C43#350414yescomplemented
436C2×C43C24×Q811yescharacteristic
437C2×C43C2×#58511yescharacteristic
438C2×C43C2×#58511yescharacteristic
439D43—28no—
440C22×#41—431no—
441#557—4332no—
442#557—4332no—
443#554—4332no—
444#554—4332no—
445#554—4364no—
446#554—4364no—
447#544—4332no—
448#544—4332no—
449#544—4316no—
450#544C2×D43116yescomplemented
451#533—4332no—
452#533—4316no—
453C2×C4⋊Q8—434no—
454C2×C4⋊Q8—431no—
455C2×C4⋊Q8—431no—
456C2×C4⋊Q8—434no—
457C2×C4⋊Q8—432no—
458C2×C4⋊Q8—432no—
459C2×C4⋊Q8C2×D4312yes—
460C2×C4⋊Q8C2×D4312yes—
461C2×#125—4332no—
462C2×#125—431no—
463C2×#125—432no—
464C2×#125—434no—
465C2×#125—434no—
466C2×#125—432no—
467C2×#125—432no—
468C2×#125—432no—
469C2×#125—4316no—
470C2×#125—431no—
471C2×#125—434no—
472C2×#125—434no—
473C2×#125—432no—
474C2×#125—432no—
475C2×#125C2×D4312yes—
476C2×#125C2×D4312yes—
477C2×C22⋊Q8—434no—
478C2×C22⋊Q8—434no—
479C2×C22⋊Q8—434no—
480C2×C22⋊Q8—434no—
481C2×C22⋊Q8—434no—
482C2×C22⋊Q8—434no—
483C2×C22⋊Q8—432no—
484C2×C22⋊Q8—432no—
485C2×C22⋊Q8—434no—
486C2×C22⋊Q8C2×D4314yes—
487#520—4316no—
488#520—4316no—
489C4×#41—4316no—
490C2×C4×Q8—434no—
491C2×C4×Q8—431no—
492C2×C4×Q8—431no—
493C2×C4×Q8—432no—
494C2×C4×Q8—434no—
495C2×C4×Q8—432no—
496C2×C4×Q8—432no—
497C2×C4×Q8—432no—
498C2×C4×D4—434no—
499C2×C4×D4—431no—
500C2×C4×D4—431no—
501C2×C4×D4—432no—
502C2×C4×D4—432no—
503C2×C4×D4—432no—
504C2×C4×D4—434no—
505C2×C4×D4—432no—
506C2×#117—431no—
507C2×#117—432no—
508C2×#117—432no—
509C2×#117—432no—
510C2×#117C2×D4311yescharacteristic
511C2×#117C2×D4311yescharacteristic
512C22×C4⋊C4—432no—
513C22×C4⋊C4—431no—
514C22×C4⋊C4—432no—
515C22×C4⋊C4—432no—
516C22×C4⋊C4—432no—
517C22×C4⋊C4—434no—
518C22×C4⋊C4—434no—
519C22×C4⋊C4C2×D4311yescharacteristic
520C22×C42—431no—
521C22×C42—432no—
522C43C2×#350411yescharacteristic, complemented, Sylow
523C2×#41—4316no—
524C2×#41—438no—
525C22×Q8—431no—
526C22×Q8—432no—
527C22×Q8—434no—
528C22×Q8—432no—
529C22×Q8C22×D4314yes—
530C22×D4—432no—
531C22×D4—431no—
532C23×C4—432no—
533C23×C4—432no—
534C23×C4—431no—
535C23×C4—431no—
536C23×C4—434no—
537C23×C4—434no—
538C23×C4—432no—
539C23×C4—432no—
540C23×C4C22×D4312yes—
541C23×C4C22×D4311yescharacteristic
542C4⋊Q8—4332no—
543C4⋊Q8—438no—
544C4⋊Q8—438no—
545C4⋊Q8—4332no—
546C4⋊Q8—4316no—
547C4⋊Q8—4316no—
548C4⋊Q8C22×D43116yes—
549C4⋊Q8C22×D43116yes—
550#125—438no—
551#125—4316no—
552#125—4316no—
553#125—4332no—
554#125—4332no—
555#125—4316no—
556#125—4316no—
557#125—438no—
558#125—4332no—
559#125—4332no—
560#125—4316no—
561#125—4316no—
562#125C22×D43116yes—
563#125C22×D43116yes—
564C22⋊Q8—4332no—
565C22⋊Q8—4332no—
566C22⋊Q8—4332no—
567C22⋊Q8—4332no—
568C22⋊Q8—4332no—
569C22⋊Q8—4332no—
570C22⋊Q8—4316no—
571C22⋊Q8—4316no—
572C22⋊Q8—4332no—
573C22⋊Q8C22×D43132yes—
574C4×Q8—4332no—
575C4×Q8—438no—
576C4×Q8—438no—
577C4×Q8—4316no—
578C4×Q8—4332no—
579C4×Q8—4316no—
580C4×Q8—4316no—
581C4×Q8—4316no—
582C4×D4—4332no—
583C4×D4—438no—
584C4×D4—438no—
585C4×D4—4316no—
586C4×D4—4316no—
587C4×D4—4316no—
588C4×D4—4332no—
589C4×D4—4316no—
590#117—438no—
591#117—4316no—
592#117—4316no—
593#117—4316no—
594#117C22×D4318yes—
595#117C22×D4318yes—
596C2×C4⋊C4—432no—
597C2×C4⋊C4—431no—
598C2×C4⋊C4—434no—
599C2×C4⋊C4—432no—
600C2×C4⋊C4—434no—
601C2×C4⋊C4—432no—
602C2×C4⋊C4—434no—
603C2×C4⋊C4—434no—
604C2×C4⋊C4—432no—
605C2×C4⋊C4—438no—
606C2×C4⋊C4—434no—
607C2×C4⋊C4—434no—
608C2×C4⋊C4—434no—
609C2×C4⋊C4—434no—
610C2×C4⋊C4—4316no—
611C2×C4⋊C4—4316no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—432no—
614C2×C4⋊C4—432no—
615C2×C4⋊C4—432no—
616C2×C4⋊C4—432no—
617C2×C4⋊C4—432no—
618C2×C4⋊C4—432no—
619C2×C4⋊C4—434no—
620C2×C4⋊C4—4316no—
621C2×C4⋊C4—4316no—
622C2×C4⋊C4—4332no—
623C2×C4⋊C4—4332no—
624C2×C4⋊C4C22×D4311yescharacteristic
625C2×C4⋊C4C22×D4312yes—
626C2×C4⋊C4C22×D4314yes—
627C2×C4⋊C4C22×D4314yes—
628C2×C4⋊C4C22×D4312yes—
629C2×C4⋊C4C22×D4318yes—
630C2×C4⋊C4C22×D4311yescharacteristic
631C2×C4⋊C4C22×D4311yescharacteristic
632C2×C4⋊C4C22×D4311yescharacteristic
633C2×C4⋊C4C22×D4314yes—
634C2×C22⋊C4—432no—
635C2×C22⋊C4—434no—
636C2×C22⋊C4—432no—
637C2×C22⋊C4—432no—
638C2×C22⋊C4—434no—
639C2×C22⋊C4C22×D4312yes—
640C2×C22⋊C4C22×D4312yes—
641C2×C42—431no—
642C2×C42—434no—
643C2×C42—434no—
644C2×C42—432no—
645C2×C42—432no—
646C2×C42—432no—
647C2×C42—431no—
648C2×C42—431no—
649C2×C42—438no—
650C2×C42—431no—
651C2×C42—4316no—
652C2×C42C22×D4312yes—
653C2×C42C22×D4312yes—
654C24—432no—
655C24C23×D4311yescharacteristic
656#41—4364no—
657C2×Q8—48no—
658C2×Q8—438no—
659C2×Q8—434no—
660C2×Q8—438no—
661C2×Q8—4316no—
662C2×Q8—438no—
663C2×Q8—1724no—
664C2×Q8—1724no—
665C2×Q8—1728no—
666C2×Q8C23×D43116yes—
667C2×D4—4316no—
668C2×D4—438no—
669C2×D4—438no—
670C2×D4—434no—
671C22×C4—44no—
672C22×C4—432no—
673C22×C4—4316no—
674C22×C4—438no—
675C22×C4—431no—
676C22×C4—431no—
677C22×C4—432no—
678C22×C4—431no—
679C22×C4—431no—
680C22×C4—432no—
681C22×C4—434no—
682C22×C4—434no—
683C22×C4—434no—
684C22×C4—438no—
685C22×C4—438no—
686C22×C4—438no—
687C22×C4—4316no—
688C22×C4—4316no—
689C22×C4—1728no—
690C22×C4—1724no—
691C22×C4—1728no—
692C22×C4—1724no—
693C22×C4—1722no—
694C22×C4—1722no—
695C22×C4—1724no—
696C22×C4Q8×D4318yes—
697C22×C4C23×D4312yes—
698C22×C4C23×D4312yes—
699C22×C4C23×D4312yes—
700C22×C4C23×D4314yes—
701C22×C4C23×D4312yes—
702C22×C4C23×D4318yes—
703C22×C4C23×D4314yes—
704C22×C4C23×D4311yescharacteristic
705C22×C4C23×D4311yescharacteristic
706C4⋊C4—438no—
707C4⋊C4—434no—
708C4⋊C4—4316no—
709C4⋊C4—438no—
710C4⋊C4—4316no—
711C4⋊C4—438no—
712C4⋊C4—4316no—
713C4⋊C4—4316no—
714C4⋊C4—438no—
715C4⋊C4—4316no—
716C4⋊C4—4316no—
717C4⋊C4—4316no—
718C4⋊C4—4316no—
719C4⋊C4—434no—
720C4⋊C4—438no—
721C4⋊C4—438no—
722C4⋊C4—438no—
723C4⋊C4—438no—
724C4⋊C4—438no—
725C4⋊C4—438no—
726C4⋊C4—4316no—
727C4⋊C4C23×D4314yes—
728C4⋊C4C23×D4318yes—
729C4⋊C4C23×D43116yes—
730C4⋊C4C23×D43116yes—
731C4⋊C4C23×D4318yes—
732C4⋊C4C23×D4314yes—
733C4⋊C4C23×D4314yes—
734C4⋊C4C23×D4314yes—
735C4⋊C4C23×D43116yes—
736C22⋊C4—438no—
737C22⋊C4—4316no—
738C22⋊C4—438no—
739C22⋊C4—438no—
740C22⋊C4—4316no—
741C22⋊C4C23×D4318yes—
742C22⋊C4C23×D4318yes—
743C42—434no—
744C42—434no—
745C42—438no—
746C42—438no—
747C42—434no—
748C42—434no—
749C42—4316no—
750C42—4316no—
751C42—438no—
752C42C23×D4318yes—
753C42C23×D4318yes—
754C23—22no—
755C23—22no—
756C23—438no—
757C23—434no—
758C23—864no—
759C23—864no—
760C23C2×Q8×D4314yes—
761C23C24×D4312yes—
762C23C24×D4311yescharacteristic
763Q8—416no—
764Q8—4316no—
765Q8—1728no—
766Q8—1728no—
767Q8—17216no—
768D4—4332no—
769D4—4316no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—48no—
776C2×C4—438no—
777C2×C4—434no—
778C2×C4—4332no—
779C2×C4—432no—
780C2×C4—432no—
781C2×C4—434no—
782C2×C4—432no—
783C2×C4—432no—
784C2×C4—434no—
785C2×C4—438no—
786C2×C4—862no—
787C2×C4—864no—
788C2×C4—862no—
789C2×C4—862no—
790C2×C4—868no—
791C2×C4—862no—
792C2×C4—864no—
793C2×C4—17216no—
794C2×C4—1728no—
795C2×C4—17216no—
796C2×C4—1728no—
797C2×C4—1724no—
798C2×C4—1724no—
799C2×C4—1728no—
800C2×C4C2×Q8×D4314yes—
801C2×C4C2×Q8×D4314yes—
802C2×C4C2×Q8×D43116yes—
803C2×C4C24×D4314yes—
804C2×C4C24×D4314yes—
805C2×C4C24×D4314yes—
806C2×C4C24×D4318yes—
807C2×C4C24×D4314yes—
808C2×C4C24×D4312yes—
809C2×C4C24×D4312yes—
810C22—22no—
811C22—22no—
812C22—28no—
813C22—438no—
814C22—864no—
815C22—864no—
816C22—8616no—
817C22C22×Q8×D4314yes—
818C22C22×Q8×D4312yes—
819C22#1458373412yes—
820C22#1458373612yes—
821C22C25×D4311yescharacteristic
822C4—28no—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—438no—
828C4—862no—
829C4—864no—
830C4—862no—
831C4—862no—
832C4—868no—
833C4—862no—
834C4—864no—
835C4C22×Q8×D4314yes—
836C4C22×Q8×D4314yes—
837C2—24no—
838C2—868no—
839C2#1914841814yesdirect product factor
840C2C23×Q8×D4311yescharacteristic
841C2C2×#1458373411yescharacteristic
842C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#544C2
socleC23×C43C25
prime radicalC22×#10621898C22
hypercenterC2×#544D43
hypocenterC43C2×#3504
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #19148418C2direct (N × H)
2. C2×#14583626C2semidirect
3. C2×#14583624C2semidirect
4. C2×#14583610C2semidirect
5. C2×#14583607C2semidirect
6. C2×#14583605C2semidirect
7. C2×#14583603C2semidirect
8. C2×#14583529C2semidirect
9. C2×#14583527C2semidirect
10. C2×#14583526C2semidirect
11. C2×#14583454C2semidirect
12. C2×#14583452C2semidirect
13. C22×#13063316C2semidirect
14. C2×#125×D43C2semidirect
18. C2×C43×#544C2semidirect
20. #14583626C22semidirect
21. #14583624C22semidirect
22. #14583610C22semidirect
23. #14583607C22semidirect
24. #14583605C22semidirect
25. #14583603C22semidirect
26. #14583529C22semidirect
27. #14583527C22semidirect
28. #14583526C22semidirect
29. #14583454C22semidirect
30. #14583452C22semidirect
45. C2×#13063316C22semidirect
50. #125×D43C22semidirect
92. C43×#544C22semidirect
101. C2×#10621898Q8semidirect
263. #10621898C2×Q8semidirect
426. C2×#544D43semidirect
435. C2×C43#3504semidirect
450. #544C2×D43semidirect
522. C43C2×#3504semidirect
839. C2#19148418direct (N × H)

Maximal subgroups

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

subgroupindex
#191484182
C2×#145836262
C2×#145836242
C2×#145836102
C2×#145836072
C2×#145836052
C2×#145836032
C2×#145835292
C2×#145835272
C2×#145835262
C2×#145834542
C2×#145834522
C22×#130633162
C2×#125×D432
C2×#145833802
C2×#145833792
C2×#145833672
C2×C43×#5442
C2×#350443