Finite Group Databasebeta

← #30624850

Subgroups — #30624850

Order 15616.

3112 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840831C211yesmaximal, characteristic, complemented
2C22×Q8×#6923C211yesmaximal, characteristic, complemented
3#21462350C213yesmaximal, complemented
4#21462344C213yesmaximal, complemented
5#21462343C213yesmaximal, complemented
6Q8×C4⋊#6923C211yesmaximal, characteristic, complemented
7D4×C4⋊#6923C213yesmaximal, complemented
8#21462324C211yesmaximal, characteristic, complemented
9Q8×C22⋊#6923C211yesmaximal, characteristic, complemented
10#21462309C213yesmaximal, complemented
11#21462306C213yesmaximal, complemented
12#121×#6923C213yesmaximal, complemented
13#21462273C213yesmaximal, complemented
14#21462259C211yesmaximal, characteristic, complemented
15#548×D61C211yesmaximal, characteristic
16#16840831—28no—
17C2×Q8×#6923—28no—
18C2×Q8×#6923C2213yes—
19C2×Q8×#6923C2211yescharacteristic
20C2×Q8×#6923C2213yes—
21C2×Q8×#6923C2211yescharacteristic
22C2×Q8×#6923C2211yescharacteristic
23C2×Q8×#6923C2211yescharacteristic
24C2×D4×#6923C2213yes—
25C2×D4×#6923C2213yes—
26C2×D4×#6923C2216yes—
27C2×#14519856C2213yes—
28C22×C4⋊#6923C2213yes—
29C22×C4⋊#6923C2213yes—
30C22×C4×#6923C2213yes—
31(C2×#6923)⋊Q8C2213yes—
32(C2×#6923)⋊Q8C2213yes—
33#16840714C2213yes—
34#16840714C2213yes—
35#16840713C2213yes—
36#16840713C2216yes—
37#16840713C2213yes—
38#16840712C2213yes—
39#16840712C2213yes—
40#16840712C2216yes—
41#16840712C2216yes—
42#16840711C2213yes—
43#16840711C2213yes—
44#16840710C2213yes—
45#16840710C2213yes—
46#16840709C2211yescharacteristic
47#16840709C2213yes—
48#16840709C2216yes—
49#16840709C2216yes—
50#16840708C2213yes—
51#16840704C2213yes—
52#16840704C2213yes—
53C4⋊C4×#6923C2213yes—
54C4⋊C4×#6923C2213yes—
55C4×C4⋊#6923C2213yes—
56C4×C4⋊#6923C2213yes—
57C22⋊C4×#6923C2216yes—
58C4×C22⋊#6923C2213yes—
59C4×C22⋊#6923C2213yes—
60#16840698C2213yes—
61C2×#41×D61C2211yescharacteristic
62C22×Q8×D61C2211yescharacteristic
63#16840424C411yescharacteristic, complemented
64#16840423C411yescharacteristic, complemented
65#16840422C413yescomplemented
66#16840421C413yescomplemented
67#16840420C413yescomplemented
68#16840419C411yescharacteristic, complemented
69#16840418C413yescomplemented
70#124×D61C2213yes—
71C22⋊Q8×D61C2213yes—
72#121×D61C2213yes—
73C4×Q8×D61C2211yescharacteristic
74C4×D4×D61C2213yes—
75C61×#548C411yescharacteristic, complemented
76C23×#6923C2311yescharacteristic
77C23×#6923C2313yes—
78C23×#6923C2316yes—
79Q8×#6923—24no—
80Q8×#6923—24no—
81Q8×#6923—24no—
82Q8×#6923—212no—
83Q8×#6923—212no—
84Q8×#6923D418yescomplemented
85D4×#6923—212no—
86D4×#6923—212no—
87D4×#6923—412no—
88#14519856—212no—
89C2×C4⋊#6923—212no—
90C2×C4⋊#6923—212no—
91C2×C4⋊#6923C2313yes—
92C2×C4⋊#6923C2313yes—
93C2×C4⋊#6923C2313yes—
94C2×C4⋊#6923C2316yes—
95C2×C4⋊#6923C2311yescharacteristic
96C2×C4⋊#6923C2313yes—
97C2×C4⋊#6923C2311yescharacteristic
98C2×C4⋊#6923C2313yes—
99C2×C4⋊#6923C2316yes—
100C2×C4⋊#6923C2313yes—
101C2×C22⋊#6923C2313yes—
102C2×C22⋊#6923C2311yescharacteristic
103C2×C22⋊#6923C2313yes—
104C2×C22⋊#6923C2313yes—
105C2×C22⋊#6923C2313yes—
106C2×C22⋊#6923C2316yes—
107C2×C22⋊#6923C2313yes—
108C2×C4×#6923—212no—
109C2×C4×#6923C2313yes—
110C2×C4×#6923C2313yes—
111C2×C4×#6923C2313yes—
112C2×C4×#6923C2313yes—
113C2×C4×#6923C2313yes—
114C2×C4×#6923C2316yes—
115C2×C4×#6923C2313yes—
116(C2×#6923)⋊C4C2313yes—
117(C2×#6923)⋊C4C2316yes—
118(C2×#6923)⋊C4C2313yes—
119(C2×#6923)⋊C4C2313yes—
120(C2×#6923)⋊C4C2313yes—
121(C2×#6923)⋊C4C2311yescharacteristic
122(C2×#6923)⋊C4C2311yescharacteristic
123(C2×#6923)⋊C4C2313yes—
124(C2×#6923)⋊C4C2313yes—
125(C2×#6923)⋊C4C2313yes—
126(C2×#6923)⋊C4C2313yes—
127C2×#11758226C2×C411yescharacteristic, complemented
128C2×#11758222C2×C413yescomplemented
129C2×#11758224C2×C413yescomplemented
130#41×D61—24no—
131#41×D61—24no—
132C22×Dic122C2×C413yescomplemented
133C2×Q8×D61—24no—
134C2×Q8×D61—24no—
135C2×Q8×D61C2×C411yescharacteristic, complemented
136C2×Q8×D61C2×C413yescomplemented
137C2×Q8×D61C2313yes—
138C2×Q8×D61C2311yescharacteristic
139C2×D4×D61C2313yes—
140C2×D4×D61C2313yes—
141C22×C4×D61C2313yes—
142C22×C4×D61C2313yes—
143#14519766C2×C413yescomplemented
144#14519765C2×C413yescomplemented
145#14519764C2×C413yescomplemented
146#14519763C2×C416yescomplemented
147#14519763C2×C416yescomplemented
148#14519757C2×C413yescomplemented
149#14519756C2×C413yescomplemented
150#14519755C2×C416yescomplemented
151#14519754C2×C416yescomplemented
152#14519753C2×C413yescomplemented
153#14519752C2×C413yescomplemented
154#14519751C2×C413yescomplemented
155#14519750C2×C416yescomplemented
156#14519749C2×C416yescomplemented
157#14519748C2×C413yescomplemented
158Q8×Dic61C2×C411yescharacteristic, complemented
159C4×Dic122C2×C413yescomplemented
160#14519742C2×C413yescomplemented
161C4×D244C2×C413yescomplemented
162D4×Dic61C2×C413yescomplemented
163#14519739C2×C413yescomplemented
164C4×C22⋊D61C2×C413yescomplemented
165C4×C22⋊D61C2×C413yescomplemented
166#14519737C2×C413yescomplemented
167#14519737C2×C413yescomplemented
168C4⋊C4×D61C2313yes—
169C4⋊C4×D61C2313yes—
170C22⋊C4×D61C2311yescharacteristic
171C22⋊C4×D61C2313yes—
172C22⋊C4×D61C2316yes—
173C42×D61C2313yes—
174C2×#41×C61C2×C411yescharacteristic, complemented
175C22×Q8×C61C2×C411yescharacteristic, complemented
176#124×C61C2×C413yescomplemented
177C22⋊Q8×C61C2×C413yescomplemented
178#121×C61C2×C413yescomplemented
179C4×Q8×C61C2×C411yescharacteristic, complemented
180C4×D4×C61C2×C413yescomplemented
181C23×D61C2413yes—
182C23×D61C2411yescharacteristic
183C22×#6923—22no—
184C22×#6923—22no—
185C22×#6923—22no—
186C22×#6923—26no—
187C22×#6923—26no—
188C22×#6923—212no—
189C22×#6923—43no—
190C22×#6923—46no—
191C22×#6923—46no—
192C22×#6923C2411yescharacteristic
193C22×#6923C2411yescharacteristic
194C22×#6923C2413yes—
195C22×#6923C2413yes—
196C22×#6923C2413yes—
197C22×#6923C2411yescharacteristic
198C22×#6923C2413yes—
199C22×#6923C2411yescharacteristic
200#41×C61—24no—
201C2×Q8×C61—24no—
202C2×Q8×C61C22×C413yes—
203C2×Q8×C61C22×C411yescharacteristic
204C2×D4×C61C22×C413yes—
205C2×D4×C61C22×C413yes—
206C22×C4×C61C22×C413yes—
207C22×C4×C61C22×C413yes—
208C2×C22⋊D61C22×C416yes—
209C2×C22⋊D61C22×C413yes—
210C2×C22⋊D61C22×C413yes—
211C22×Dic61C22×C413yes—
212C22×Dic61C22×C413yes—
213#11758226—24no—
214Q8×D61—24no—
215Q8×D61—26no—
216Q8×D61—26no—
217Q8×D61—212no—
218Q8×D61C2×D414yes—
219Q8×D61#4114yes—
220#11758224—212no—
221D4×D61—26no—
222D4×D61—26no—
223D4×D61—26no—
224D4×D61—26no—
225#11758222—212no—
226C2×D244C22×C413yes—
227C2×D244C22×C413yes—
228C2×C4×D61—26no—
229C2×C4×D61—26no—
230C2×C4×D61—26no—
231C2×C4×D61—26no—
232C2×C4×D61C22×C413yes—
233C2×C4×D61C22×C413yes—
234C2×C4×D61C22×C413yes—
235C2×C4×D61C22×C413yes—
236C2×C4×D61C2411yescharacteristic
237C2×C4×D61C2413yes—
238C2×C4×D61C2413yes—
239C2×C4×D61C2411yescharacteristic
240C2×C4×D61C2413yes—
241C2×Dic122—212no—
242C2×Dic122C22×C416yes—
243C2×Dic122C22×C413yes—
244C2×Dic122C22×C413yes—
245C22⋊#6923—26no—
246C22⋊#6923—22no—
247C22⋊#6923—26no—
248C22⋊#6923—26no—
249C22⋊#6923—26no—
250C22⋊#6923—43no—
251C22⋊#6923—46no—
252C4⋊#6923—26no—
253C4⋊#6923—212no—
254C4⋊#6923—22no—
255C4⋊#6923—22no—
256C4⋊#6923—26no—
257C4⋊#6923—26no—
258C4⋊#6923—26no—
259C4⋊#6923—43no—
260C4⋊#6923—46no—
261C4⋊#6923C2×D4112yes—
262C4×#6923—26no—
263C4×#6923—26no—
264C4×#6923—26no—
265C4×#6923—26no—
266C4×#6923—26no—
267C4×#6923—46no—
268C4×#6923C2×D4112yes—
269C4⋊C4×C61C22×C413yes—
270C4⋊C4×C61C22×C413yes—
271C22⋊C4×C61C22×C411yescharacteristic
272C22⋊C4×C61C22×C413yes—
273C22⋊C4×C61C22×C416yes—
274C42×C61C22×C413yes—
275C22⋊Dic61C22×C411yescharacteristic
276C22⋊Dic61C22×C413yes—
277C22⋊Dic61C22×C416yes—
278#11758198C22×C411yescharacteristic
279#11758198C22×C413yes—
280#11758198C22×C411yescharacteristic
281#11758198C22×C413yes—
282#11758198C22×C416yes—
283#11758198C22×C416yes—
284C4⋊Dic61C22×C413yes—
285C4⋊Dic61C22×C413yes—
286#11758196C22×C413yes—
287#11758196C22×C413yes—
288#11758196C22×C416yes—
289C4×Dic61C22×C413yes—
290C4×Dic61C22×C413yes—
291C4×Dic61C22×C413yes—
292C23×C61C23×C413yes—
293C23×C61C23×C411yescharacteristic
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—23no—
299C22×D61—23no—
300C22×D61—23no—
301C22×D61—23no—
302C22×D61—23no—
303C22×D61—23no—
304C22×D61C23×C413yes—
305C22×D61C23×C411yescharacteristic
306C22×D61H(5,𝔽2)12yes—
307C22×D612−1+412yes—
308C22×D61C2511yescharacteristic
309C2×#6923—28no—
310C2×#6923—21no—
311C2×#6923—23no—
312C2×#6923—21no—
313C2×#6923—21no—
314C2×#6923—21no—
315C2×#6923—23no—
316C2×#6923—21no—
317C2×#6923—23no—
318C2×#6923—23no—
319C2×#6923—21no—
320C2×#6923—23no—
321C2×#6923—23no—
322C2×#6923—23no—
323C2×#6923—23no—
324C2×#6923—21no—
325C2×#6923—21no—
326C2×#6923—21no—
327C2×#6923—23no—
328C2×#6923—23no—
329C2×#6923—23no—
330C2×#6923—21no—
331C2×#6923—412no—
332C2×#6923—812no—
333C2×#6923C22×D412yes—
334C2×#6923C22×D416yes—
335C2×#69232−1+412yes—
336Q8×C61—26no—
337Q8×C61C4×D414yescomplemented
338D4×C61—26no—
339D4×C61—26no—
340C2×C4×C61—26no—
341C2×C4×C61—26no—
342C2×C4×C61C23×C411yescharacteristic
343C2×C4×C61C23×C413yes—
344C2×C4×C61C23×C411yescharacteristic
345C2×C4×C61C23×C413yes—
346C2×C4×C61C23×C413yes—
347C22⋊D61—26no—
348C22⋊D61—26no—
349C22⋊D61—212no—
350C2×Dic61—26no—
351C2×Dic61—26no—
352C2×Dic61C23×C411yescharacteristic
353C2×Dic61C23×C413yes—
354C2×Dic61C23×C411yescharacteristic
355C2×Dic61C23×C413yes—
356C2×Dic61C23×C413yes—
357D244—26no—
358D244—26no—
359C4×D61—23no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—23no—
363C4×D61—23no—
364C4×D61—21no—
365C4×D61—23no—
366C4×D61—21no—
367C4×D61—26no—
368C4×D61—26no—
369C4×D61—26no—
370C4×D61—26no—
371C4×D61C22×D416yes—
372C4×D61C2×#4116yes—
373Dic122—26no—
374Dic122—212no—
375Dic122C4×D4112yescomplemented
376#34294—611nomaximal, Sylow
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—23no—
380C22×C61—23no—
381C22×C61—23no—
382C22×C61#52012yescomplemented
383C22×C61C24×C411yescharacteristic
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—23no—
391C2×D61—23no—
392C2×D61—23no—
393C2×D61—43no—
394C2×D61—43no—
395C2×D61—43no—
396C2×D61—43no—
397C2×D61#52012yescomplemented
398C2×D61C23×D411yescharacteristic
399C2×D61C22×#4111yescharacteristic
400C2×D61C2×H(5,𝔽2)11yescharacteristic
401C2×D61C2×2−1+411yescharacteristic
402C2×D61C2×2−1+411yescharacteristic
403C2×D61#58511yescharacteristic
404#6923—22no—
405#6923—22no—
406#6923—26no—
407#6923—41no—
408#6923—43no—
409#6923—43no—
410#6923—41no—
411#6923—43no—
412C4×C61—23no—
413C4×C61—21no—
414C4×C61—23no—
415C4×C61—21no—
416C4×C61C2×C4×D416yes—
417Dic61—23no—
418Dic61—21no—
419Dic61—23no—
420Dic61—21no—
421Dic61C2×C4×D416yes—
422C2×#548—611no—
423C2×#520—611no—
424C22×C4×Q8—611no—
425#2367—613no—
426#2361—613no—
427#2360—613no—
428Q8×C4⋊C4—611no—
429D4×C4⋊C4—613no—
430#2341—611no—
431Q8×C22⋊C4—611no—
432#2326—613no—
433#2323—613no—
434C4×#121—613no—
435#2290—613no—
436#2276—611no—
437C2×C61—22no—
438C2×C61—43no—
439C2×C61C22×C4×D411yescharacteristic
440C2×C61C2×#52011yescharacteristic
441C2×C61C4×2−1+411yescharacteristic
442D61—22no—
443D61—43no—
444D61#348611yescharacteristic
445D61#348811yescharacteristic
446D61#351611yescharacteristic
447D61#352211yescharacteristic
448C22×#41—611no—
449C23×Q8—611no—
450#548—611no—
451#548—611no—
452#548—613no—
453#548—613no—
454#548—613no—
455#548—611no—
456#548—613no—
457#548#692311yescharacteristic, complemented
458C2×#124—613no—
459C2×C22⋊Q8—613no—
460C2×#121—613no—
461#520—1228no—
462C2×C4×Q8—611no—
463C2×C4×Q8—611no—
464C2×C4×Q8—613no—
465C2×C4×Q8—611no—
466C2×C4×Q8—611no—
467C2×C4×Q8—611no—
468C2×C4×Q8—613no—
469C2×C4×Q8—1228no—
470C2×C4×D4—613no—
471C2×C4×D4—613no—
472C2×C4×D4—613no—
473C2×C4×D4—616no—
474C2×#117—613no—
475C22×C4⋊C4—613no—
476C22×C4⋊C4—613no—
477C22×C42—613no—
478#391—613no—
479#391—613no—
480#390—613no—
481#390—613no—
482#389—616no—
483#389—613no—
484#389—613no—
485#388—616no—
486#388—616no—
487#388—613no—
488#388—613no—
489#387—613no—
490#387—613no—
491#386—613no—
492#386—613no—
493#385—616no—
494#385—616no—
495#385—613no—
496#385—611no—
497#384—613no—
498#380—613no—
499#380—613no—
500C4×C4⋊C4—613no—
501C4×C4⋊C4—613no—
502C4×C4⋊C4—613no—
503C4×C4⋊C4—613no—
504C4×C22⋊C4—613no—
505C4×C22⋊C4—613no—
506C4×C22⋊C4—616no—
507#376—613no—
508C61#3429411yescharacteristic, complemented, Sylow
509C2×#41—611no—
510C2×#41—613no—
511C2×#41—613no—
512C2×#41—1224no—
513C2×#41—1224no—
514C2×#41C2×#692311yescharacteristic, complemented
515C22×Q8—611no—
516C22×Q8—613no—
517C22×Q8—613no—
518C22×Q8—611no—
519C22×Q8—613no—
520C22×Q8—1224no—
521C22×Q8—1224no—
522C22×Q8C2×#692311yescharacteristic, complemented
523C22×D4—613no—
524C22×D4—613no—
525C23×C4—613no—
526C23×C4—613no—
527C23×C4—611no—
528C23×C4—613no—
529C23×C4—616no—
530#124—613no—
531#124—613no—
532#124—616no—
533#124—616no—
534#124—613no—
535#124C2×#692313yescomplemented
536C22⋊Q8—613no—
537C22⋊Q8—613no—
538C22⋊Q8—616no—
539C22⋊Q8—613no—
540C22⋊Q8—616no—
541C22⋊Q8C2×#692313yescomplemented
542#121—613no—
543#121—616no—
544#121—613no—
545#121—613no—
546#121—616no—
547#121C2×#692313yescomplemented
548C4×Q8—618no—
549C4×Q8—611no—
550C4×Q8—613no—
551C4×Q8—613no—
552C4×Q8—12212no—
553C4×Q8—12212no—
554C4×Q8—1224no—
555C4×Q8—1224no—
556C4×Q8—1224no—
557C4×Q8C2×#692311yescharacteristic, complemented
558C4×D4—613no—
559C4×D4—613no—
560C4×D4—613no—
561C4×D4—613no—
562C4×D4—613no—
563C4×D4—613no—
564C4×D4—613no—
565C4×D4—12212no—
566C4×D4—12212no—
567C4×D4—24412no—
568C4×D4C2×#692313yescomplemented
569#117—12212no—
570C2×C4⋊C4—613no—
571C2×C4⋊C4—613no—
572C2×C4⋊C4—613no—
573C2×C4⋊C4—613no—
574C2×C4⋊C4—613no—
575C2×C4⋊C4—613no—
576C2×C4⋊C4—616no—
577C2×C4⋊C4—611no—
578C2×C4⋊C4—613no—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—616no—
581C2×C4⋊C4—613no—
582C2×C4⋊C4—12212no—
583C2×C4⋊C4—12212no—
584C2×C22⋊C4—611no—
585C2×C22⋊C4—613no—
586C2×C22⋊C4—616no—
587C2×C22⋊C4—613no—
588C2×C22⋊C4—613no—
589C2×C22⋊C4—613no—
590C2×C22⋊C4—611no—
591C2×C22⋊C4—613no—
592C2×C22⋊C4—616no—
593C2×C22⋊C4—613no—
594C2×C42—613no—
595C2×C42—613no—
596C2×C42—613no—
597C2×C42—613no—
598C2×C42—613no—
599C2×C42—613no—
600C2×C42—613no—
601C2×C42—616no—
602C2×C42—12212no—
603#95—611no—
604#95—613no—
605#95—613no—
606#95—613no—
607#95—611no—
608#95—613no—
609#95—613no—
610#95—616no—
611#95—613no—
612#95—613no—
613#95—613no—
614C24—611no—
615C24—613no—
616#41—24no—
617#41—12212no—
618#41—12212no—
619#41—1224no—
620C2×Q8—24no—
621C2×Q8—614no—
622C2×Q8—614no—
623C2×Q8—613no—
624C2×Q8—616no—
625C2×Q8—613no—
626C2×Q8—12212no—
627C2×Q8—1226no—
628C2×Q8—1226no—
629C2×Q8—12212no—
630C2×Q8—1224no—
631C2×Q8C22×#692313yes—
632C2×Q8C22×#692311yescharacteristic
633C2×D4—613no—
634C2×D4—613no—
635C2×D4—616no—
636C2×D4—613no—
637C2×D4—613no—
638C2×D4—1226no—
639C2×D4—1226no—
640C2×D4—1226no—
641C2×D4—1226no—
642C2×D4C22×#692313yes—
643C2×D4C22×#692313yes—
644C22×C4—613no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—613no—
648C22×C4—613no—
649C22×C4—613no—
650C22×C4—611no—
651C22×C4—613no—
652C22×C4—613no—
653C22×C4—611no—
654C22×C4—613no—
655C22×C4—613no—
656C22×C4—613no—
657C22×C4—613no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—613no—
661C22×C4—613no—
662C22×C4—613no—
663C22×C4—1226no—
664C22×C4—1226no—
665C22×C4—1226no—
666C22×C4—1226no—
667C22×C4—1222no—
668C22×C4—1222no—
669C22×C4—12212no—
670C22×C4—1226no—
671C22×C4—1222no—
672C22×C4—1226no—
673C22×C4—2446no—
674C22×C4—2446no—
675C22×C4—2443no—
676C22×C4C22×#692313yes—
677C22×C4C22×#692313yes—
678C4⋊C4—6112no—
679C4⋊C4—613no—
680C4⋊C4—613no—
681C4⋊C4—616no—
682C4⋊C4—613no—
683C4⋊C4—613no—
684C4⋊C4—1226no—
685C4⋊C4—1226no—
686C4⋊C4—1226no—
687C4⋊C4—12212no—
688C4⋊C4—1222no—
689C4⋊C4—1226no—
690C4⋊C4—1222no—
691C4⋊C4—2446no—
692C4⋊C4—2443no—
693C4⋊C4C22×#692313yes—
694C4⋊C4C22×#692313yes—
695C22⋊C4—611no—
696C22⋊C4—613no—
697C22⋊C4—616no—
698C22⋊C4—611no—
699C22⋊C4—611no—
700C22⋊C4—613no—
701C22⋊C4—613no—
702C22⋊C4—616no—
703C22⋊C4—616no—
704C22⋊C4—1226no—
705C22⋊C4—1226no—
706C22⋊C4—1226no—
707C22⋊C4—1226no—
708C22⋊C4—1222no—
709C22⋊C4—2446no—
710C22⋊C4—2443no—
711C22⋊C4C22×#692311yescharacteristic
712C22⋊C4C22×#692313yes—
713C22⋊C4C22×#692316yes—
714C42—6112no—
715C42—613no—
716C42—613no—
717C42—613no—
718C42—1226no—
719C42—1226no—
720C42—1226no—
721C42—1226no—
722C42—1226no—
723C42—2446no—
724C42C22×#692313yes—
725C23—611no—
726C23—612no—
727C23—612no—
728C23—611no—
729C23—613no—
730C23—1221no—
731C23—1221no—
732C23—1221no—
733C23—1221no—
734C23—1223no—
735C23—1223no—
736C23—1223no—
737C23—1223no—
738C23—1223no—
739C23—1223no—
740C23C23×#692313yes—
741C23C23×#692311yescharacteristic
742Q8—26no—
743Q8—6112no—
744Q8—12212no—
745Q8—1226no—
746Q8D4×#692314yescomplemented
747D4—26no—
748D4—26no—
749D4—1226no—
750D4—12212no—
751D4—1226no—
752D4—1226no—
753D4—1226no—
754C2×C4—26no—
755C2×C4—26no—
756C2×C4—613no—
757C2×C4—616no—
758C2×C4—616no—
759C2×C4—612no—
760C2×C4—616no—
761C2×C4—612no—
762C2×C4—611no—
763C2×C4—613no—
764C2×C4—613no—
765C2×C4—611no—
766C2×C4—1226no—
767C2×C4—1226no—
768C2×C4—1223no—
769C2×C4—1223no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1223no—
775C2×C4—1223no—
776C2×C4—1226no—
777C2×C4—1226no—
778C2×C4—1221no—
779C2×C4—1223no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1223no—
784C2×C4—1228no—
785C2×C4—1226no—
786C2×C4—1226no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1223no—
790C2×C4—1223no—
791C2×C4—1223no—
792C2×C4—1223no—
793C2×C4—1223no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1223no—
797C2×C4—1221no—
798C2×C4—1223no—
799C2×C4—1223no—
800C2×C4—1221no—
801C2×C4—1223no—
802C2×C4—48812no—
803C2×C4—24412no—
804C2×C4C23×#692311yescharacteristic
805C2×C4C23×#692313yes—
806C2×C4C23×#692313yes—
807C2×C4C23×#692311yescharacteristic
808C2×C4C23×#692313yes—
809C22—21no—
810C22—21no—
811C22—23no—
812C22—23no—
813C22—23no—
814C22—611no—
815C22—611no—
816C22—611no—
817C22—611no—
818C22—611no—
819C22—611no—
820C22—612no—
821C22—1222no—
822C22—1222no—
823C22—1222no—
824C22—1222no—
825C22—1221no—
826C22—1221no—
827C22—1223no—
828C22—1223no—
829C22—1223no—
830C22—2443no—
831C22—2443no—
832C22—2443no—
833C22—2443no—
834C22#1684083112yescomplemented
835C22C24×#692311yescharacteristic
836C4—21no—
837C4—23no—
838C4—23no—
839C4—21no—
840C4—616no—
841C4—1222no—
842C4—1222no—
843C4—1226no—
844C4—1221no—
845C4—1223no—
846C4—1223no—
847C4—1221no—
848C4—2443no—
849C4—2443no—
850C4—2441no—
851C4—2443no—
852C4—2441no—
853C4C2×D4×#692316yes—
854C2—22no—
855C2—43no—
856C2—611no—
857C2—611no—
858C2—611no—
859C2—611no—
860C2—1222no—
861C2—2443no—
862C2C22×D4×#692311yescharacteristic
863C2C2×#1684083111yescharacteristic
864C22−1+4×#692311yescharacteristic
subgroupG/H
center, FrattiniC22C24×#6923
commutator, socleC22×C61C24×C4
FittingC61×#548C4
prime radical#548×D61C2
cosocleC22×D61C25
hypercenter#548#6923
hypocenterC61#34294
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#16840831C2semidirect
2. C22×Q8×#6923C2semidirect
3. #21462350C2semidirect
4. #21462344C2semidirect
5. #21462343C2semidirect
6. Q8×C4⋊#6923C2semidirect
7. D4×C4⋊#6923C2semidirect
8. #21462324C2semidirect
9. Q8×C22⋊#6923C2semidirect
10. #21462309C2semidirect
11. #21462306C2semidirect
12. #121×#6923C2semidirect
13. #21462273C2semidirect
14. #21462259C2semidirect
63. #16840424C4semidirect
64. #16840423C4semidirect
65. #16840422C4semidirect
66. #16840421C4semidirect
67. #16840420C4semidirect
68. #16840419C4semidirect
69. #16840418C4semidirect
75. C61×#548C4semidirect
84. Q8×#6923D4semidirect
127. C2×#11758226C2×C4semidirect
128. C2×#11758222C2×C4semidirect
129. C2×#11758224C2×C4semidirect
132. C22×Dic122C2×C4semidirect
135. C2×Q8×D61C2×C4semidirect
136. C2×Q8×D61C2×C4semidirect
143. #14519766C2×C4semidirect
144. #14519765C2×C4semidirect
145. #14519764C2×C4semidirect
146. #14519763C2×C4semidirect
147. #14519763C2×C4semidirect
148. #14519757C2×C4semidirect
149. #14519756C2×C4semidirect
150. #14519755C2×C4semidirect
151. #14519754C2×C4semidirect
152. #14519753C2×C4semidirect
153. #14519752C2×C4semidirect
154. #14519751C2×C4semidirect
155. #14519750C2×C4semidirect
156. #14519749C2×C4semidirect
157. #14519748C2×C4semidirect
158. Q8×Dic61C2×C4semidirect
159. C4×Dic122C2×C4semidirect
160. #14519742C2×C4semidirect
161. C4×D244C2×C4semidirect
162. D4×Dic61C2×C4semidirect
163. #14519739C2×C4semidirect
164. C4×C22⋊D61C2×C4semidirect
165. C4×C22⋊D61C2×C4semidirect
166. #14519737C2×C4semidirect
167. #14519737C2×C4semidirect
174. C2×#41×C61C2×C4semidirect
175. C22×Q8×C61C2×C4semidirect
176. #124×C61C2×C4semidirect
177. C22⋊Q8×C61C2×C4semidirect
178. #121×C61C2×C4semidirect
179. C4×Q8×C61C2×C4semidirect
180. C4×D4×C61C2×C4semidirect
337. Q8×C61C4×D4semidirect
375. Dic122C4×D4semidirect
382. C22×C61#520semidirect
397. C2×D61#520semidirect
457. #548#6923semidirect
508. C61#34294semidirect
514. C2×#41C2×#6923semidirect
522. C22×Q8C2×#6923semidirect
535. #124C2×#6923semidirect
541. C22⋊Q8C2×#6923semidirect
547. #121C2×#6923semidirect
557. C4×Q8C2×#6923semidirect
568. C4×D4C2×#6923semidirect
746. Q8D4×#6923semidirect
834. C22#16840831semidirect

Maximal subgroups

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

subgroupindex
C2×#168408312
C22×Q8×#69232
#214623502
#214623442
#214623432
Q8×C4⋊#69232
D4×C4⋊#69232
#214623242
Q8×C22⋊#69232
#214623092
#214623062
#121×#69232
#214622732
#214622592
#548×D612
#3429461