Finite Group Databasebeta

← #30624847

Subgroups — #30624847

Order 15616.

2912 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840830C211yesmaximal, characteristic, complemented
2C22×Q8×#6923C211yesmaximal, characteristic, complemented
3#21462348C213yesmaximal, complemented
4#21462345C213yesmaximal, complemented
5#21462343C213yesmaximal, complemented
6#21462335C213yesmaximal
7#21462334C211yesmaximal, characteristic, complemented
8Q8×C22⋊#6923C211yesmaximal, characteristic, complemented
9Q8×C22⋊#6923C211yesmaximal, characteristic, complemented
10#21462310C213yesmaximal, complemented
11#21462306C213yesmaximal, complemented
12C22⋊Q8×#6923C213yesmaximal, complemented
13#21462273C213yesmaximal
14#21462259C211yesmaximal, characteristic, complemented
15D4×Q8×D61C211yesmaximal, characteristic
16#16840830—28no—
17C2×Q8×#6923—28no—
18C2×Q8×#6923C2213yes—
19C2×Q8×#6923C2211yescharacteristic
20C2×Q8×#6923C2213yes—
21C2×Q8×#6923C2213yes—
22C2×Q8×#6923C2211yescharacteristic
23C2×Q8×#6923C2213yes—
24C2×Q8×#6923C2211yescharacteristic
25C2×Q8×#6923C2211yescharacteristic
26C2×#14519856C2213yes—
27C2×#14519856C2213yes—
28C22×C4⋊#6923C2213yes—
29C22×C4×#6923C2213yes—
30(C2×#6923)⋊Q8C2213yes—
31(C2×#6923)⋊Q8C2213yes—
32(C2×#6923)⋊Q8C2213yes—
33(C2×#6923)⋊Q8C2213yes—
34#16840713C2213yes—
35#16840713C2213yes—
36#16840713C2216yes—
37#16840712C2213yes—
38#16840712C2213yes—
39#16840712C2216yes—
40#16840711C2213yes—
41#16840711C2213yes—
42#16840711C2216yes—
43#16840711C2216yes—
44#16840711C2216yes—
45#16840710C2211yescharacteristic
46#16840710C2213yes—
47#16840709C2213yes—
48#16840709C2213yes—
49#16840706C2213yes—
50#16840704C2213yes—
51#16840704C2213yes—
52C4⋊C4×#6923C2213yes—
53C4⋊C4×#6923C2216yes—
54C4⋊C4×#6923C2213yes—
55C4×C4⋊#6923C2213yes—
56C4×C4⋊#6923C2213yes—
57C22⋊C4×#6923C2216yes—
58C4×C22⋊#6923C2213yes—
59C4×C22⋊#6923C2213yes—
60#16840698C2213yes—
61C22×Q8×D61C2211yescharacteristic
62C22×Q8×D61C2211yescharacteristic
63Q8×D244C411yescharacteristic, complemented
64D4×Dic122C413yescomplemented
65#16840427C413yescomplemented
66Q8×C22⋊D61C411yescharacteristic, complemented
67Q8×C22⋊D61C411yescharacteristic, complemented
68#16840425C413yescomplemented
69#16840425C413yescomplemented
70C4⋊Q8×D61C2213yes—
71C22⋊Q8×D61C2213yes—
72C22⋊Q8×D61C2213yes—
73C4×Q8×D61C2211yescharacteristic
74C4×D4×D61C2213yes—
75D4×Q8×C61C411yescharacteristic, complemented
76C23×#6923C2311yescharacteristic
77C23×#6923C2313yes—
78Q8×#6923—24no—
79Q8×#6923—24no—
80Q8×#6923—24no—
81Q8×#6923—212no—
82Q8×#6923—212no—
83Q8×#6923—212no—
84Q8×#6923—212no—
85Q8×#6923D418yescomplemented
86#14519856—212no—
87#14519856—212no—
88C2×C4⋊#6923—212no—
89C2×C4⋊#6923C2313yes—
90C2×C4⋊#6923C2313yes—
91C2×C4⋊#6923C2313yes—
92C2×C4⋊#6923C2313yes—
93C2×C4⋊#6923C2313yes—
94C2×C4⋊#6923C2313yes—
95C2×C4⋊#6923C2316yes—
96C2×C4⋊#6923C2313yes—
97C2×C4⋊#6923C2313yes—
98C2×C22⋊#6923C2313yes—
99C2×C22⋊#6923C2311yescharacteristic
100C2×C22⋊#6923C2313yes—
101C2×C22⋊#6923C2311yescharacteristic
102C2×C22⋊#6923C2311yescharacteristic
103C2×C22⋊#6923C2313yes—
104C2×C4×#6923—212no—
105C2×C4×#6923C2313yes—
106C2×C4×#6923C2316yes—
107C2×C4×#6923C2313yes—
108C2×C4×#6923C2313yes—
109C2×C4×#6923C2313yes—
110C2×C4×#6923C2313yes—
111C2×C4×#6923C2316yes—
112C2×C4×#6923C2313yes—
113(C2×#6923)⋊C4C2316yes—
114(C2×#6923)⋊C4C2316yes—
115(C2×#6923)⋊C4C2313yes—
116(C2×#6923)⋊C4C2316yes—
117(C2×#6923)⋊C4C2313yes—
118(C2×#6923)⋊C4C2313yes—
119(C2×#6923)⋊C4C2313yes—
120(C2×#6923)⋊C4C2313yes—
121(C2×#6923)⋊C4C2311yescharacteristic
122(C2×#6923)⋊C4C2313yes—
123(C2×#6923)⋊C4C2311yescharacteristic
124(C2×#6923)⋊C4C2313yes—
125(C2×#6923)⋊C4C2313yes—
126C22×Dic122C2×C413yes—
127C22×Dic122C2×C413yescomplemented
128C2×Q8×D61—24no—
129C2×Q8×D61—24no—
130C2×Q8×D61—24no—
131C2×Q8×D61—24no—
132C2×Q8×D61C2×C413yes—
133C2×Q8×D61C2×C411yescharacteristic
134C2×Q8×D61C2×C413yescomplemented
135C2×Q8×D61C2×C411yescharacteristic, complemented
136C2×Q8×D61C2313yes—
137C2×Q8×D61C2313yes—
138C2×Q8×D61C2311yescharacteristic
139C2×D4×D61C2311yescharacteristic
140C22×C4×D61C2313yes—
141C22×C4×D61C2313yes—
142#14519777C2×C413yescomplemented
143#14519776C2×C416yescomplemented
144#14519776C2×C416yescomplemented
145#14519775C2×C413yescomplemented
146#14519775C2×C413yescomplemented
147#14519757C2×C413yes—
148#14519757C2×C413yescomplemented
149#14519756C2×C413yes—
150#14519756C2×C413yescomplemented
151#14519755C2×C416yes—
152#14519755C2×C416yescomplemented
153#14519754C2×C416yes—
154#14519754C2×C416yescomplemented
155#14519753C2×C413yes—
156#14519753C2×C413yescomplemented
157Q8×Dic61C2×C411yescharacteristic, complemented
158C4×Dic122C2×C413yescomplemented
159#14519742C2×C413yescomplemented
160C4×D244C2×C413yes—
161D4×Dic61C2×C413yes—
162#14519739C2×C413yes—
163C4×C22⋊D61C2×C413yes—
164C4×C22⋊D61C2×C413yes—
165#14519737C2×C413yes—
166#14519737C2×C413yes—
167C4⋊C4×D61C2313yes—
168C4⋊C4×D61C2316yes—
169C4⋊C4×D61C2313yes—
170C22⋊C4×D61C2313yes—
171C22⋊C4×D61C2313yes—
172C42×D61C2313yes—
173C22×Q8×C61C2×C411yescharacteristic
174C22×Q8×C61C2×C411yescharacteristic, complemented
175C4⋊Q8×C61C2×C413yescomplemented
176C22⋊Q8×C61C2×C413yes—
177C22⋊Q8×C61C2×C413yescomplemented
178C4×Q8×C61C2×C411yescharacteristic, complemented
179C4×D4×C61C2×C413yes—
180C23×D61C2411yescharacteristic
181C23×D61C2411yescharacteristic
182C22×#6923—22no—
183C22×#6923—22no—
184C22×#6923—22no—
185C22×#6923—26no—
186C22×#6923—26no—
187C22×#6923—43no—
188C22×#6923C2411yescharacteristic
189C22×#6923C2413yes—
190C22×#6923C2413yes—
191C22×#6923C2413yes—
192C22×#6923C2411yescharacteristic
193C22×#6923C2411yescharacteristic
194C22×#6923C2413yes—
195C22×#6923C2411yescharacteristic
196C2×Q8×C61—24no—
197C2×Q8×C61—24no—
198C2×Q8×C61C22×C413yes—
199C2×Q8×C61C22×C413yes—
200C2×Q8×C61C22×C411yescharacteristic
201C2×D4×C61C22×C411yescharacteristic
202C22×C4×C61C22×C413yes—
203C22×C4×C61C22×C413yes—
204C2×C22⋊D61C22×C411yescharacteristic
205C2×C22⋊D61C22×C411yescharacteristic
206C22×Dic61C22×C413yes—
207C22×Dic61C22×C413yes—
208Q8×D61—24no—
209Q8×D61—24no—
210Q8×D61—26no—
211Q8×D61—26no—
212Q8×D61—26no—
213Q8×D61—26no—
214Q8×D61—212no—
215Q8×D61—212no—
216Q8×D61C2×D414yes—
217Q8×D61#4114yes—
218D4×D61—22no—
219D4×D61—22no—
220C2×D244C22×C411yescharacteristic
221C2×C4×D61—26no—
222C2×C4×D61—26no—
223C2×C4×D61—26no—
224C2×C4×D61—26no—
225C2×C4×D61C22×C413yes—
226C2×C4×D61C22×C413yes—
227C2×C4×D61C22×C413yes—
228C2×C4×D61C22×C413yes—
229C2×C4×D61C2413yes—
230C2×C4×D61C2413yes—
231C2×C4×D61C2411yescharacteristic
232C2×C4×D61C2413yes—
233C2×C4×D61C2413yes—
234C2×Dic122—212no—
235C2×Dic122—212no—
236C2×Dic122C22×C416yes—
237C2×Dic122C22×C413yes—
238C2×Dic122C22×C416yes—
239C2×Dic122C22×C413yes—
240C2×Dic122C22×C413yes—
241C22⋊#6923—26no—
242C22⋊#6923—22no—
243C22⋊#6923—22no—
244C22⋊#6923—26no—
245C22⋊#6923—22no—
246C22⋊#6923—43no—
247C4⋊#6923—212no—
248C4⋊#6923—26no—
249C4⋊#6923—26no—
250C4⋊#6923—26no—
251C4⋊#6923—26no—
252C4⋊#6923—26no—
253C4⋊#6923—26no—
254C4⋊#6923—43no—
255C4⋊#6923C2×D4112yes—
256C4×#6923—26no—
257C4×#6923—26no—
258C4×#6923—212no—
259C4×#6923—26no—
260C4×#6923—26no—
261C4×#6923—26no—
262C4×#6923—46no—
263C4×#6923C2×D4112yes—
264C4⋊C4×C61C22×C413yes—
265C4⋊C4×C61C22×C413yes—
266C4⋊C4×C61C22×C416yes—
267C22⋊C4×C61C22×C413yes—
268C22⋊C4×C61C22×C413yes—
269C42×C61C22×C413yes—
270C22⋊Dic61C22×C413yes—
271C22⋊Dic61C22×C413yes—
272#11758198C22×C413yes—
273#11758198C22×C413yes—
274#11758198C22×C413yes—
275#11758198C22×C413yes—
276C4⋊Dic61C22×C413yes—
277C4⋊Dic61C22×C413yes—
278C4⋊Dic61C22×C416yes—
279#11758196C22×C413yes—
280#11758196C22×C413yes—
281#11758196C22×C416yes—
282#11758196C22×C416yes—
283#11758196C22×C416yes—
284C4×Dic61C22×C413yes—
285C4×Dic61C22×C413yes—
286C4×Dic61C22×C413yes—
287C23×C61C23×C411yescharacteristic
288C23×C61C23×C411yescharacteristic
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61C23×C411yescharacteristic
300C22×D61C23×C411yescharacteristic
301C22×D612−1+412yes—
302C22×D612−1+412yes—
303C22×D61C2511yescharacteristic
304C2×#6923—28no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—21no—
309C2×#6923—23no—
310C2×#6923—23no—
311C2×#6923—23no—
312C2×#6923—21no—
313C2×#6923—23no—
314C2×#6923—21no—
315C2×#6923—23no—
316C2×#6923—23no—
317C2×#6923—23no—
318C2×#6923—21no—
319C2×#6923—23no—
320C2×#6923—21no—
321C2×#6923—21no—
322C2×#6923—23no—
323C2×#6923—23no—
324C2×#6923—21no—
325C2×#6923—23no—
326C2×#6923—412no—
327C2×#6923C22×D412yes—
328C2×#6923C22×D416yes—
329C2×#69232−1+412yes—
330Q8×C61—26no—
331Q8×C61—26no—
332Q8×C61C4×D414yes—
333D4×C61—22no—
334C2×C4×C61—26no—
335C2×C4×C61—26no—
336C2×C4×C61C23×C411yescharacteristic
337C2×C4×C61C23×C413yes—
338C2×C4×C61C23×C413yes—
339C2×C4×C61C23×C413yes—
340C2×C4×C61C23×C413yes—
341C22⋊D61—22no—
342C22⋊D61—22no—
343C2×Dic61—26no—
344C2×Dic61—26no—
345C2×Dic61C23×C411yescharacteristic
346C2×Dic61C23×C413yes—
347C2×Dic61C23×C413yes—
348C2×Dic61C23×C413yes—
349C2×Dic61C23×C413yes—
350D244—22no—
351C4×D61—23no—
352C4×D61—23no—
353C4×D61—23no—
354C4×D61—23no—
355C4×D61—23no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—23no—
359C4×D61—26no—
360C4×D61—26no—
361C4×D61—26no—
362C4×D61—26no—
363C4×D61C22×D416yes—
364C4×D61C2×#4116yes—
365Dic122—26no—
366Dic122—26no—
367Dic122—212no—
368Dic122—212no—
369Dic122C4×D4112yes—
370#34291—611nomaximal, Sylow
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61#51912yescomplemented
377C22×C61C24×C411yescharacteristic
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61#51912yescomplemented
392C2×D61C23×D411yescharacteristic
393C2×D61C22×#4111yescharacteristic
394C2×D61C2×2−1+411yescharacteristic
395C2×D61C2×2−1+411yescharacteristic
396C2×D61C2×2−1+411yescharacteristic
397C2×D61#58511yescharacteristic
398#6923—22no—
399#6923—22no—
400#6923—26no—
401#6923—43no—
402#6923—41no—
403#6923—43no—
404#6923—43no—
405#6923—41no—
406C4×C61—23no—
407C4×C61—23no—
408C4×C61—21no—
409C4×C61—23no—
410C4×C61C2×C4×D416yes—
411Dic61—23no—
412Dic61—23no—
413Dic61—21no—
414Dic61—23no—
415Dic61C2×C4×D416yes—
416C2×D4×Q8—611no—
417C2×#519—611no—
418C22×C4×Q8—611no—
419#2365—613no—
420#2362—613no—
421#2360—613no—
422#2352—613no—
423#2351—611no—
424Q8×C22⋊C4—611no—
425Q8×C22⋊C4—611no—
426#2327—613no—
427#2323—613no—
428C4×C22⋊Q8—613no—
429#2290—613no—
430#2276—611no—
431C2×C61—22no—
432C2×C61—41no—
433C2×C61C22×C4×D411yescharacteristic
434C2×C61C2×#51911yescharacteristic
435C2×C61C4×2−1+411yescharacteristic
436D61—22no—
437D61—41no—
438D61#348611yescharacteristic
439D61#348911yescharacteristic
440D61#351611yescharacteristic
441D61#352311yescharacteristic
442C23×Q8—611no—
443C23×Q8—611no—
444D4×Q8—611no—
445D4×Q8—611no—
446D4×Q8—613no—
447D4×Q8—613no—
448D4×Q8—613no—
449D4×Q8—611no—
450D4×Q8—613no—
451D4×Q8#692311yescharacteristic, complemented
452C2×C4⋊Q8—613no—
453C2×C22⋊Q8—613no—
454C2×C22⋊Q8—613no—
455#519—1228no—
456C2×C4×Q8—611no—
457C2×C4×Q8—611no—
458C2×C4×Q8—613no—
459C2×C4×Q8—613no—
460C2×C4×Q8—611no—
461C2×C4×Q8—611no—
462C2×C4×Q8—611no—
463C2×C4×Q8—613no—
464C2×C4×Q8—613no—
465C2×C4×Q8—1228no—
466C2×C4×D4—613no—
467C2×#117—613no—
468C2×#117—613no—
469C22×C4⋊C4—613no—
470C22×C42—613no—
471#391—613no—
472#391—613no—
473#391—613no—
474#391—613no—
475#389—613no—
476#389—616no—
477#389—613no—
478#388—613no—
479#388—616no—
480#388—613no—
481#387—616no—
482#387—613no—
483#387—616no—
484#387—616no—
485#387—613no—
486#386—613no—
487#386—611no—
488#385—613no—
489#385—613no—
490#382—613no—
491#380—613no—
492#380—613no—
493C4×C4⋊C4—613no—
494C4×C4⋊C4—613no—
495C4×C4⋊C4—613no—
496C4×C4⋊C4—613no—
497C4×C4⋊C4—616no—
498C4×C22⋊C4—613no—
499C4×C22⋊C4—613no—
500C4×C22⋊C4—616no—
501#376—613no—
502C61#3429111yescharacteristic, complemented, Sylow
503C22×Q8—611no—
504C22×Q8—613no—
505C22×Q8—613no—
506C22×Q8—613no—
507C22×Q8—611no—
508C22×Q8—613no—
509C22×Q8—611no—
510C22×Q8—613no—
511C22×Q8—613no—
512C22×Q8—1224no—
513C22×Q8—1224no—
514C22×Q8—1224no—
515C22×Q8—1224no—
516C22×Q8C2×#692311yescharacteristic
517C22×Q8C2×#692311yescharacteristic, complemented
518C22×D4—611no—
519C23×C4—613no—
520C23×C4—613no—
521C23×C4—611no—
522C23×C4—613no—
523C4⋊Q8—613no—
524C4⋊Q8—613no—
525C4⋊Q8—616no—
526C4⋊Q8—616no—
527C4⋊Q8—613no—
528C4⋊Q8C2×#692313yescomplemented
529C22⋊Q8—613no—
530C22⋊Q8—613no—
531C22⋊Q8—613no—
532C22⋊Q8—613no—
533C22⋊Q8—616no—
534C22⋊Q8—616no—
535C22⋊Q8—613no—
536C22⋊Q8—613no—
537C22⋊Q8—616no—
538C22⋊Q8—616no—
539C22⋊Q8C2×#692313yes—
540C22⋊Q8C2×#692313yescomplemented
541C4×Q8—618no—
542C4×Q8—611no—
543C4×Q8—613no—
544C4×Q8—613no—
545C4×Q8—12212no—
546C4×Q8—12212no—
547C4×Q8—12212no—
548C4×Q8—12212no—
549C4×Q8—1224no—
550C4×Q8—1224no—
551C4×Q8—1224no—
552C4×Q8C2×#692311yescharacteristic, complemented
553C4×D4—613no—
554C4×D4—613no—
555C4×D4—613no—
556C4×D4—613no—
557C4×D4—613no—
558C4×D4—613no—
559C4×D4—613no—
560C4×D4C2×#692313yes—
561#117—12212no—
562#117—12212no—
563C2×C4⋊C4—613no—
564C2×C4⋊C4—613no—
565C2×C4⋊C4—613no—
566C2×C4⋊C4—616no—
567C2×C4⋊C4—613no—
568C2×C4⋊C4—616no—
569C2×C4⋊C4—613no—
570C2×C4⋊C4—613no—
571C2×C4⋊C4—613no—
572C2×C4⋊C4—613no—
573C2×C4⋊C4—613no—
574C2×C4⋊C4—613no—
575C2×C4⋊C4—12212no—
576C2×C22⋊C4—613no—
577C2×C22⋊C4—613no—
578C2×C22⋊C4—611no—
579C2×C22⋊C4—613no—
580C2×C22⋊C4—613no—
581C2×C22⋊C4—611no—
582C2×C22⋊C4—611no—
583C2×C22⋊C4—613no—
584C2×C42—613no—
585C2×C42—613no—
586C2×C42—616no—
587C2×C42—613no—
588C2×C42—613no—
589C2×C42—613no—
590C2×C42—613no—
591C2×C42—613no—
592C2×C42—616no—
593C2×C42—12212no—
594#95—611no—
595#95—613no—
596#95—613no—
597#95—613no—
598#95—613no—
599#95—616no—
600#95—616no—
601#95—613no—
602#95—613no—
603#95—613no—
604#95—611no—
605#95—616no—
606#95—613no—
607C24—611no—
608C24—611no—
609C2×Q8—24no—
610C2×Q8—24no—
611C2×Q8—614no—
612C2×Q8—614no—
613C2×Q8—613no—
614C2×Q8—616no—
615C2×Q8—616no—
616C2×Q8—613no—
617C2×Q8—613no—
618C2×Q8—12212no—
619C2×Q8—12212no—
620C2×Q8—1226no—
621C2×Q8—1226no—
622C2×Q8—1226no—
623C2×Q8—1226no—
624C2×Q8—12212no—
625C2×Q8—12212no—
626C2×Q8—1224no—
627C2×Q8—1224no—
628C2×Q8C22×#692313yes—
629C2×Q8C22×#692313yes—
630C2×Q8C22×#692311yescharacteristic
631C2×D4—611no—
632C2×D4—611no—
633C2×D4—611no—
634C2×D4—1222no—
635C2×D4—1222no—
636C2×D4C22×#692311yescharacteristic
637C22×C4—613no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—613no—
641C22×C4—613no—
642C22×C4—613no—
643C22×C4—611no—
644C22×C4—613no—
645C22×C4—613no—
646C22×C4—613no—
647C22×C4—613no—
648C22×C4—613no—
649C22×C4—613no—
650C22×C4—613no—
651C22×C4—611no—
652C22×C4—613no—
653C22×C4—613no—
654C22×C4—613no—
655C22×C4—611no—
656C22×C4—1226no—
657C22×C4—1226no—
658C22×C4—1226no—
659C22×C4—1226no—
660C22×C4—1222no—
661C22×C4—1222no—
662C22×C4—1226no—
663C22×C4—1222no—
664C22×C4—1226no—
665C22×C4—2443no—
666C22×C4C22×#692313yes—
667C22×C4C22×#692313yes—
668C4⋊C4—6112no—
669C4⋊C4—613no—
670C4⋊C4—613no—
671C4⋊C4—616no—
672C4⋊C4—616no—
673C4⋊C4—616no—
674C4⋊C4—613no—
675C4⋊C4—613no—
676C4⋊C4—616no—
677C4⋊C4—1226no—
678C4⋊C4—12212no—
679C4⋊C4—1226no—
680C4⋊C4—1226no—
681C4⋊C4—1226no—
682C4⋊C4—1226no—
683C4⋊C4—1226no—
684C4⋊C4—2443no—
685C4⋊C4C22×#692313yes—
686C4⋊C4C22×#692313yes—
687C4⋊C4C22×#692316yes—
688C22⋊C4—613no—
689C22⋊C4—613no—
690C22⋊C4—613no—
691C22⋊C4—613no—
692C22⋊C4—613no—
693C22⋊C4—613no—
694C22⋊C4—1222no—
695C22⋊C4—1226no—
696C22⋊C4—1222no—
697C22⋊C4—1226no—
698C22⋊C4—1222no—
699C22⋊C4—2443no—
700C22⋊C4C22×#692313yes—
701C22⋊C4C22×#692313yes—
702C42—6112no—
703C42—613no—
704C42—613no—
705C42—613no—
706C42—1226no—
707C42—1226no—
708C42—1226no—
709C42—1226no—
710C42—12212no—
711C42—1226no—
712C42—2446no—
713C42C22×#692313yes—
714C23—611no—
715C23—612no—
716C23—612no—
717C23—611no—
718C23—611no—
719C23—1221no—
720C23—1221no—
721C23—1221no—
722C23—1221no—
723C23—1221no—
724C23—1221no—
725C23—1221no—
726C23—1221no—
727C23—1221no—
728C23—1221no—
729C23C23×#692311yescharacteristic
730C23C23×#692311yescharacteristic
731Q8—26no—
732Q8—26no—
733Q8—6112no—
734Q8—12212no—
735Q8—12212no—
736Q8—1226no—
737Q8—1226no—
738Q8D4×#692314yes—
739D4—22no—
740D4—1222no—
741D4—1222no—
742D4—1222no—
743C2×C4—26no—
744C2×C4—26no—
745C2×C4—613no—
746C2×C4—616no—
747C2×C4—616no—
748C2×C4—612no—
749C2×C4—616no—
750C2×C4—612no—
751C2×C4—611no—
752C2×C4—613no—
753C2×C4—613no—
754C2×C4—613no—
755C2×C4—1226no—
756C2×C4—1226no—
757C2×C4—1223no—
758C2×C4—1223no—
759C2×C4—1223no—
760C2×C4—1223no—
761C2×C4—1223no—
762C2×C4—1223no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1226no—
766C2×C4—1226no—
767C2×C4—1221no—
768C2×C4—1223no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1223no—
773C2×C4—1228no—
774C2×C4—1226no—
775C2×C4—1226no—
776C2×C4—1223no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1223no—
780C2×C4—1223no—
781C2×C4—1223no—
782C2×C4—1221no—
783C2×C4—1223no—
784C2×C4—1223no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1223no—
788C2×C4—1223no—
789C2×C4—1221no—
790C2×C4—1223no—
791C2×C4—24412no—
792C2×C4C23×#692311yescharacteristic
793C2×C4C23×#692313yes—
794C2×C4C23×#692313yes—
795C2×C4C23×#692313yes—
796C2×C4C23×#692313yes—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—611no—
803C22—611no—
804C22—611no—
805C22—611no—
806C22—611no—
807C22—611no—
808C22—612no—
809C22—1222no—
810C22—1222no—
811C22—1222no—
812C22—1222no—
813C22—1221no—
814C22—1221no—
815C22—1221no—
816C22—1221no—
817C22—1221no—
818C22—2441no—
819C22—2441no—
820C22—2441no—
821C22—2441no—
822C22#1684083012yescomplemented
823C22C24×#692311yescharacteristic
824C4—23no—
825C4—23no—
826C4—21no—
827C4—23no—
828C4—616no—
829C4—1222no—
830C4—1222no—
831C4—1226no—
832C4—1223no—
833C4—1223no—
834C4—1221no—
835C4—1223no—
836C4—2443no—
837C4—2441no—
838C4—2443no—
839C4—2443no—
840C4—2441no—
841C4C2×D4×#692316yes—
842C2—22no—
843C2—41no—
844C2—611no—
845C2—611no—
846C2—611no—
847C2—611no—
848C2—1222no—
849C2—2441no—
850C2C22×D4×#692311yescharacteristic
851C2C2×#1684083011yescharacteristic
852C22−1+4×#692311yescharacteristic
subgroupG/H
center, FrattiniC22C24×#6923
commutator, socleC22×C61C24×C4
FittingD4×Q8×C61C4
prime radicalC2×D4×D61C23
cosocleC22×D61C25
hypercenterD4×Q8#6923
hypocenterC61#34291
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16840830C2semidirect
2. C22×Q8×#6923C2semidirect
3. #21462348C2semidirect
4. #21462345C2semidirect
5. #21462343C2semidirect
7. #21462334C2semidirect
8. Q8×C22⋊#6923C2semidirect
9. Q8×C22⋊#6923C2semidirect
10. #21462310C2semidirect
11. #21462306C2semidirect
12. C22⋊Q8×#6923C2semidirect
14. #21462259C2semidirect
63. Q8×D244C4semidirect
64. D4×Dic122C4semidirect
65. #16840427C4semidirect
66. Q8×C22⋊D61C4semidirect
67. Q8×C22⋊D61C4semidirect
68. #16840425C4semidirect
69. #16840425C4semidirect
75. D4×Q8×C61C4semidirect
85. Q8×#6923D4semidirect
127. C22×Dic122C2×C4semidirect
134. C2×Q8×D61C2×C4semidirect
135. C2×Q8×D61C2×C4semidirect
142. #14519777C2×C4semidirect
143. #14519776C2×C4semidirect
144. #14519776C2×C4semidirect
145. #14519775C2×C4semidirect
146. #14519775C2×C4semidirect
148. #14519757C2×C4semidirect
150. #14519756C2×C4semidirect
152. #14519755C2×C4semidirect
154. #14519754C2×C4semidirect
156. #14519753C2×C4semidirect
157. Q8×Dic61C2×C4semidirect
158. C4×Dic122C2×C4semidirect
159. #14519742C2×C4semidirect
174. C22×Q8×C61C2×C4semidirect
175. C4⋊Q8×C61C2×C4semidirect
177. C22⋊Q8×C61C2×C4semidirect
178. C4×Q8×C61C2×C4semidirect
376. C22×C61#519semidirect
391. C2×D61#519semidirect
451. D4×Q8#6923semidirect
502. C61#34291semidirect
517. C22×Q8C2×#6923semidirect
528. C4⋊Q8C2×#6923semidirect
540. C22⋊Q8C2×#6923semidirect
552. C4×Q8C2×#6923semidirect
822. C22#16840830semidirect

Maximal subgroups

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

subgroupindex
C2×#168408302
C22×Q8×#69232
#214623482
#214623452
#214623432
#214623352
#214623342
Q8×C22⋊#69232
#214623102
#214623062
C22⋊Q8×#69232
#214622732
#214622592
D4×Q8×D612
#3429161