Finite Group Databasebeta

← #29842686

Subgroups — #29842686

Order 15616.

2106 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840298C211yesmaximal, characteristic
2#21449010C212yesmaximal, complemented
3#21449009C212yesmaximal, complemented
4#21449002C212yesmaximal, complemented
5#21448991C212yesmaximal, complemented
6#21448985C211yesmaximal, characteristic, complemented
7#21448978C211yesmaximal, characteristic
8#21448973C211yesmaximal, characteristic
9#21448965C212yesmaximal, complemented
10#21448965C212yesmaximal, complemented
11#21448311C212yesmaximal, complemented
12#21448300C212yesmaximal, complemented
13#21448294C212yesmaximal, complemented
14#21448279C212yesmaximal, complemented
15#21448261C212yesmaximal, complemented
16#21448257C212yesmaximal, complemented
17#21448221C211yesmaximal, characteristic, complemented
18#21448210C211yesmaximal, characteristic, complemented
19C61×#2378C211yesmaximal, characteristic, complemented
20#16840298C4116yescomplemented
21C2×#14519772C2212yes—
22C2×#14519768C2211yescharacteristic
23C2×#14519766C2211yescharacteristic
24C2×#14519761C2212yes—
25C2×#14519751C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×#14519739C2211yescharacteristic
28C2×#14519737C2212yes—
29C2×#14519735C2212yes—
30C2×#14519735C2212yes—
31C2×#14519733C2211yescharacteristic
32C2×#14519733C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C2×C42×D61C2212yes—
35#16839669C2212yes—
36#16839662C2212yes—
37#16839662C2212yes—
38#16839661C2212yes—
39#16839660C2212yes—
40#16839660C2212yes—
41#16839659C2212yes—
42#16839658C2212yes—
43#16839658C2212yes—
44#16839657C2212yes—
45#16839655C2212yes—
46#16839655C2212yes—
47#16839654C2212yes—
48#16839653C2212yes—
49#16839653C2212yes—
50#16839653C2212yes—
51#16839652C2212yes—
52#16839651C2212yes—
53#16839651C2212yes—
54#16839651C2212yes—
55#16839648C2212yes—
56#16839648C2212yes—
57#16839647C2212yes—
58#16839647C2212yes—
59#16839647C2212yes—
60#16839646C2212yes—
61#16839645C2212yes—
62#16839645C2212yes—
63#16839645C2212yes—
64#16839644C2212yes—
65#16839640C2212yes—
66#16839640C2212yes—
67#16839638C2212yes—
68#16839638C2212yes—
69#16839636C2212yes—
70#16839636C2212yes—
71#16839636C2212yes—
72#16839636C2212yes—
73#16839633C2212yes—
74#16839633C2212yes—
75#16839633C2212yes—
76#16839633C2212yes—
77#16839631C2212yes—
78#16839629C2211yescharacteristic
79#16839629C2211yescharacteristic
80#16839626C2212yes—
81#16839626C2212yes—
82#16839625C2211yescharacteristic
83#16839622C2211yescharacteristic
84#16839620C2212yes—
85#16839620C2211yescharacteristic
86#16839620C2211yescharacteristic
87C4⋊C4×Dic61C2212yes—
88C4⋊C4×Dic61C2212yes—
89#16839613C2211yescharacteristic
90#16839613C2211yescharacteristic
91#16839613C2212yes—
92#16839613C2212yes—
93C22⋊C4×Dic61C2212yes—
94#16839609C2212yes—
95#16839609C2212yes—
96#16839607C2212yes—
97#16839607C2212yes—
98C42×Dic61C2212yes—
99C2×C22⋊Q8×C61C2211yescharacteristic
100C61×#391C2212yes—
101C61×#389C2212yes—
102C61×#388C2212yes—
103C61×#388C2212yes—
104C61×#387C2212yes—
105C61×#387C2212yes—
106C61×#381C2211yescharacteristic
107C61×#380C2211yescharacteristic
108C22×D244C2311yescharacteristic
109C22×C22⋊D61C2312yes—
110C23×Dic61C2311yescharacteristic
111C23×Dic61C2311yescharacteristic
112C22×C4×D61C2312yes—
113C22×C4×D61C2312yes—
114C22×C4×D61C2312yes—
115#14519772C2×C4116yescomplemented
116#14519768C2×C418yescomplemented
117#14519766C2×C418yes—
118#14519761C2×C4116yescomplemented
119#14519751C2×C418yes—
120Q8×Dic61C2×C418yescomplemented
121#14519739C2×C418yes—
122#14519737C2×C4116yescomplemented
123#14519735—44no—
124#14519735C2×C4116yescomplemented
125#14519733—42no—
126#14519733—42no—
127C2×C4⋊Dic61C2312yes—
128C2×C4⋊Dic61C2312yes—
129C2×C4⋊Dic61C2312yes—
130C2×C4⋊Dic61C2312yes—
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2312yes—
133C2×#11758196C2312yes—
134C2×#11758196C2312yes—
135C2×#11758196C2312yes—
136C2×#11758196C2312yes—
137C2×#11758196C2312yes—
138C2×#11758196C2312yes—
139C2×#11758196C2312yes—
140C2×#11758196C2312yes—
141C2×#11758196C2312yes—
142C2×C22⋊Dic61C2311yescharacteristic
143C2×C22⋊Dic61C2311yescharacteristic
144C2×C22⋊Dic61C2312yes—
145C2×#11758198C2312yes—
146C2×#11758198C2312yes—
147C2×#11758198C2312yes—
148C2×#11758198C2312yes—
149C2×#11758198C2312yes—
150C2×#11758198C2312yes—
151C2×#11758198C2312yes—
152C2×#11758198C2312yes—
153C2×#11758198C2312yes—
154C2×#11758198C2312yes—
155C2×C4×Dic61C2×C418yescomplemented
156C2×C4×Dic61C2312yes—
157C2×C4×Dic61C2312yes—
158C2×C4×Dic61C2312yes—
159C2×C4×Dic61C2312yes—
160C2×C4×Dic61C2312yes—
161C2×C4×Dic61C2312yes—
162C2×C4×Dic61C2312yes—
163C2×C4×Dic61C2312yes—
164C2×C4×Dic61C2311yescharacteristic
165C2×C4×Dic61C2311yescharacteristic
166C2×C4×Dic61C2311yescharacteristic
167C2×C4×Dic61C2311yescharacteristic
168C2×C4×Dic61C2312yes—
169C42×D61—44no—
170#14519684C2312yes—
171#14519684C2312yes—
172#14519684C2312yes—
173#14519684C2312yes—
174#14519684C2312yes—
175#14519684C2312yes—
176#14519684C2312yes—
177#14519684C2312yes—
178#14519684C2312yes—
179#14519684C2312yes—
180#14519684C2312yes—
181#14519684C2311yescharacteristic
182#14519684C2311yescharacteristic
183#14519684C2312yes—
184#14519684C2312yes—
185#14519684C2312yes—
186#14519684C2312yes—
187#14519684C2312yes—
188C22×Q8×C61C2311yescharacteristic
189C23×C4×C61C2311yescharacteristic
190C22⋊Q8×C61C2×C418yescomplemented
191C2×C4⋊C4×C61C2312yes—
192C2×C4⋊C4×C61C2312yes—
193C2×C4⋊C4×C61C2312yes—
194C2×C4⋊C4×C61C2312yes—
195C2×C4⋊C4×C61C2311yescharacteristic
196C2×C22⋊C4×C61C2311yescharacteristic
197C2×C22⋊C4×C61C2311yescharacteristic
198C2×C22⋊C4×C61C2312yes—
199C2×C22⋊C4×C61C2312yes—
200C2×C42×C61C2312yes—
201C2×C42×C61C2312yes—
202#95×C61C2312yes—
203#95×C61C2311yescharacteristic
204#95×C61C2312yes—
205#95×C61C2311yescharacteristic
206#95×C61C2312yes—
207#95×C61C2312yes—
208#95×C61C2312yes—
209#95×C61C2312yes—
210C24×C61C2411yescharacteristic
211C23×D61C2412yes—
212C2×Q8×C61—42no—
213C2×Q8×C61C22×C414yes—
214C22×C4×C61—42no—
215C22×C4×C61C22×C414yes—
216C22×C4×C61C2412yes—
217C22×C4×C61C2412yes—
218C22×C4×C61C2412yes—
219C22×C4×C61C2412yes—
220C22×C4×C61C2412yes—
221C22×C4×C61C2411yescharacteristic
222C22×C4×C61C2412yes—
223C22×C4×C61C2411yescharacteristic
224C2×C22⋊D61—42no—
225C2×C22⋊D61—42no—
226C2×C22⋊D61C22×C418yes—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61—42no—
230C22×Dic61C22×C414yes—
231C22×Dic61C22×C414yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C22×Dic61C2412yes—
236C22×Dic61C2411yescharacteristic
237C22×Dic61C2411yescharacteristic
238C22×Dic61C2411yescharacteristic
239C22×Dic61C2412yes—
240C22×Dic61C2411yescharacteristic
241C2×D244—42no—
242C2×D244C22×C414yes—
243C2×C4×D61—24no—
244C2×C4×D61—24no—
245C2×C4×D61—42no—
246C2×C4×D61—42no—
247C2×C4×D61—42no—
248C2×C4×D61—42no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61C22×C418yes—
252C4⋊C4×C61—42no—
253C4⋊C4×C61—42no—
254C4⋊C4×C61—42no—
255C4⋊C4×C61C22×C418yes—
256C4⋊C4×C61C22×C414yes—
257C22⋊C4×C61—42no—
258C22⋊C4×C61—41no—
259C22⋊C4×C61—41no—
260C22⋊C4×C61C22×C418yes—
261C42×C61—42no—
262C42×C61—42no—
263C22⋊Dic61—42no—
264C22⋊Dic61—41no—
265C22⋊Dic61—41no—
266#11758198—42no—
267#11758198—42no—
268#11758198—42no—
269#11758198—42no—
270#11758198—42no—
271#11758198—42no—
272#11758198C22×C418yes—
273#11758198C22×C418yes—
274#11758198C22×C418yes—
275#11758198C22×C418yes—
276C4⋊Dic61—42no—
277C4⋊Dic61—42no—
278C4⋊Dic61—42no—
279C4⋊Dic61C22×C418yes—
280C4⋊Dic61C22×C414yes—
281C4⋊Dic61C22×C418yes—
282#11758196—42no—
283#11758196—42no—
284#11758196—42no—
285#11758196—42no—
286#11758196—42no—
287#11758196—42no—
288#11758196—42no—
289#11758196—42no—
290#11758196C22×C418yes—
291C4×Dic61—24no—
292C4×Dic61—24no—
293C4×Dic61—24no—
294C4×Dic61—24no—
295C4×Dic61—42no—
296C4×Dic61—42no—
297C4×Dic61—42no—
298C4×Dic61—42no—
299C4×Dic61C22×C414yes—
300C4×Dic61C22×C414yes—
301C4×Dic61C22×C414yes—
302C4×Dic61C22×C414yes—
303C4×Dic61C22×C418yes—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61C23×C412yes—
309C23×C61C2511yescharacteristic
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61C23×C414yes—
317Q8×C61—44no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—44no—
337C2×C4×C61C23×C412yes—
338C2×C4×C61C23×C412yes—
339C2×C4×C61C23×C414yes—
340C2×C4×C61C23×C414yes—
341C22⋊D61—48no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—28no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—44no—
362C2×Dic61C23×C412yes—
363C2×Dic61C23×C412yes—
364C2×Dic61C23×C412yes—
365C2×Dic61C23×C414yes—
366C2×Dic61C23×C412yes—
367C2×Dic61H(5,𝔽2)12yes—
368C2×Dic612−1+412yes—
369D244—44no—
370C4×D61—216no—
371C4×D61—48no—
372C4×D61—48no—
373#34350—611nomaximal, Sylow
374C22×C61—22no—
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61C24×C411yescharacteristic
380C22×C61C2×H(5,𝔽2)11yescharacteristic
381C22×C61C2×2−1+411yescharacteristic
382C22×C61#58512yes—
383C22×C61#58512yes—
384C2×D61—24no—
385C2×D61—24no—
386C2×D61—24no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C4×C61—24no—
392C4×C61—22no—
393C4×C61—22no—
394C4×C61—24no—
395C4×C61—42no—
396C4×C61—42no—
397C4×C61—42no—
398C4×C61—42no—
399Dic61—22no—
400Dic61—22no—
401Dic61—22no—
402Dic61—24no—
403Dic61—42no—
404Dic61—42no—
405Dic61—42no—
406Dic61—42no—
407Dic61#52014yes—
408C2×#529—611no—
409#2383—612no—
410#2383—612no—
411#2382—612no—
412#2379—612no—
413#2378—611no—
414#2378D6111yescharacteristic, complemented
415#2377—611no—
416#2377—611no—
417#2376—612no—
418#2376—612no—
419#2298—612no—
420#2296—612no—
421#2295—612no—
422#2293—612no—
423#2290—612no—
424#2290—612no—
425#2285—611no—
426#2283—611no—
427C2×C61—42no—
428C2×C61C2×#52011yescharacteristic
429C2×C61#342811yescharacteristic
430C2×C61#342811yescharacteristic
431C2×C61#352912yes—
432C2×C61#353112yes—
433D61—44no—
434#529—6116no—
435C2×#126—612no—
436C2×#125—611no—
437C2×#124—611no—
438C2×#123—612no—
439C2×C22⋊Q8C2×D6111yescharacteristic
440C2×#121—611no—
441C2×C4×Q8—611no—
442C2×C4×D4—611no—
443C2×C4×D4—612no—
444C2×#117—612no—
445C2×#117—612no—
446C2×#117—611no—
447C2×#117—611no—
448C22×C42—611no—
449C22×C42—612no—
450#391—612no—
451#391C2×D6112yes—
452#390—612no—
453#390—612no—
454#389—612no—
455#389—612no—
456#389—612no—
457#389—612no—
458#389—612no—
459#389—612no—
460#389—612no—
461#389C2×D6112yes—
462#388—612no—
463#388—612no—
464#388—612no—
465#388—612no—
466#388—612no—
467#388—612no—
468#388—612no—
469#388—612no—
470#388—612no—
471#388—612no—
472#388C2×D6112yes—
473#388C2×D6112yes—
474#387—612no—
475#387—612no—
476#387—612no—
477#387—612no—
478#387—612no—
479#387—612no—
480#387—612no—
481#387—612no—
482#387—612no—
483#387—612no—
484#387C2×D6112yes—
485#387C2×D6112yes—
486#386—612no—
487#386—612no—
488#386—612no—
489#386—612no—
490#385—612no—
491#385—612no—
492#385—612no—
493#385—612no—
494#385—612no—
495#385—612no—
496#385—612no—
497#385—612no—
498#384—612no—
499#383—611no—
500#383—611no—
501#382—612no—
502#382—612no—
503#381—611no—
504#381C2×D6111yescharacteristic
505#380—611no—
506#380—612no—
507#380—611no—
508#380—611no—
509#380C2×D6111yescharacteristic
510C4×C4⋊C4—612no—
511C4×C4⋊C4—612no—
512C4×C4⋊C4—611no—
513C4×C4⋊C4—611no—
514C4×C4⋊C4—612no—
515C4×C4⋊C4—612no—
516C4×C22⋊C4—612no—
517C4×C22⋊C4—612no—
518C4×C22⋊C4—612no—
519#376—612no—
520#376—612no—
521C43—612no—
522C61#3435011yescharacteristic, complemented, Sylow
523C22×Q8C22×D6111yescharacteristic
524C22×D4—612no—
525C22×D4—611no—
526C23×C4—611no—
527C23×C4—611no—
528C23×C4—612no—
529C23×C4—612no—
530C23×C4—612no—
531C23×C4C22×D6111yescharacteristic
532#126—6116no—
533#125—618no—
534#124—618no—
535#123—6116no—
536C22⋊Q8C4×D6118yescomplemented
537#121—618no—
538C4×Q8—618no—
539C4×D4—618no—
540C4×D4—6116no—
541#117—6116no—
542#117—2442no—
543#117—2442no—
544#117—2444no—
545C2×C4⋊C4—612no—
546C2×C4⋊C4—612no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—612no—
549C2×C4⋊C4—612no—
550C2×C4⋊C4—612no—
551C2×C4⋊C4—612no—
552C2×C4⋊C4—612no—
553C2×C4⋊C4—612no—
554C2×C4⋊C4—612no—
555C2×C4⋊C4—612no—
556C2×C4⋊C4—612no—
557C2×C4⋊C4—612no—
558C2×C4⋊C4—612no—
559C2×C4⋊C4—612no—
560C2×C4⋊C4C22×D6112yes—
561C2×C4⋊C4C22×D6112yes—
562C2×C4⋊C4C22×D6112yes—
563C2×C4⋊C4C22×D6112yes—
564C2×C4⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4—612no—
566C2×C22⋊C4—612no—
567C2×C22⋊C4—612no—
568C2×C22⋊C4—612no—
569C2×C22⋊C4—611no—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—612no—
572C2×C22⋊C4—612no—
573C2×C22⋊C4—612no—
574C2×C22⋊C4—612no—
575C2×C22⋊C4—612no—
576C2×C22⋊C4—612no—
577C2×C22⋊C4—612no—
578C2×C22⋊C4C22×D6111yescharacteristic
579C2×C22⋊C4C22×D6111yescharacteristic
580C2×C22⋊C4C22×D6112yes—
581C2×C22⋊C4C22×D6112yes—
582C2×C42—618no—
583C2×C42—611no—
584C2×C42—612no—
585C2×C42—611no—
586C2×C42—611no—
587C2×C42—611no—
588C2×C42—612no—
589C2×C42—612no—
590C2×C42—612no—
591C2×C42—612no—
592C2×C42—612no—
593C2×C42—612no—
594C2×C42—612no—
595C2×C42—612no—
596C2×C42—2444no—
597C2×C42C22×D6112yes—
598C2×C42C22×D6112yes—
599#95—612no—
600#95—612no—
601#95—612no—
602#95—612no—
603#95—612no—
604#95—612no—
605#95—612no—
606#95—612no—
607#95—612no—
608#95—612no—
609#95—612no—
610#95—612no—
611#95—612no—
612#95—611no—
613#95—611no—
614#95—612no—
615#95—612no—
616#95—612no—
617#95C22×D6112yes—
618#95C22×D6112yes—
619#95C22×D6112yes—
620#95C22×D6112yes—
621#95C22×D6112yes—
622#95C22×D6111yescharacteristic
623#95C22×D6111yescharacteristic
624#95C22×D6112yes—
625C24—612no—
626C24C23×D6111yescharacteristic
627C2×Q8—42no—
628C2×Q8C2×C4×D6114yes—
629C2×D4—618no—
630C2×D4—614no—
631C2×D4—2442no—
632C2×D4—2442no—
633C2×D4—2442no—
634C22×C4—42no—
635C22×C4—611no—
636C22×C4—614no—
637C22×C4—612no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—614no—
642C22×C4—618no—
643C22×C4—612no—
644C22×C4—612no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—1224no—
648C22×C4—1224no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—2442no—
652C22×C4—2442no—
653C22×C4—2442no—
654C22×C4—2442no—
655C22×C4—2442no—
656C22×C4—2442no—
657C22×C4—2442no—
658C22×C4C2×C4×D6114yes—
659C22×C4C23×D6112yes—
660C22×C4C23×D6112yes—
661C22×C4C23×D6112yes—
662C22×C4C23×D6112yes—
663C22×C4C23×D6111yescharacteristic
664C22×C4C23×D6112yes—
665C22×C4C23×D6111yescharacteristic
666C22×C4C23×D6112yes—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—618no—
671C4⋊C4—618no—
672C4⋊C4—614no—
673C4⋊C4—618no—
674C4⋊C4—2442no—
675C4⋊C4—2442no—
676C4⋊C4—2442no—
677C4⋊C4—2442no—
678C4⋊C4—2442no—
679C4⋊C4—2442no—
680C4⋊C4—2442no—
681C4⋊C4—2442no—
682C4⋊C4—2442no—
683C4⋊C4—2442no—
684C4⋊C4—2442no—
685C4⋊C4C2×C4×D6118yes—
686C4⋊C4C2×C4×D6114yes—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—42no—
690C22⋊C4—618no—
691C22⋊C4—618no—
692C22⋊C4—618no—
693C22⋊C4—618no—
694C22⋊C4—2442no—
695C22⋊C4—2442no—
696C22⋊C4—2442no—
697C22⋊C4—2442no—
698C22⋊C4—2442no—
699C22⋊C4—2442no—
700C22⋊C4—2441no—
701C22⋊C4—2441no—
702C22⋊C4—2442no—
703C22⋊C4C2×C4×D6118yes—
704C42—42no—
705C42—42no—
706C42—614no—
707C42—614no—
708C42—614no—
709C42—614no—
710C42—618no—
711C42—1224no—
712C42—1224no—
713C42—1224no—
714C42—1224no—
715C42—2442no—
716C42—2442no—
717C42—2442no—
718C42—2442no—
719C23—21no—
720C23—21no—
721C23—22no—
722C23—22no—
723C23—614no—
724C23—1222no—
725C23—1222no—
726C23—1222no—
727C23—1222no—
728C23—1222no—
729C23—1222no—
730C23C22×C4×D6112yes—
731C23C24×D6111yescharacteristic
732Q8—44no—
733D4—2444no—
734D4—2448no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—44no—
754C2×C4—612no—
755C2×C4—612no—
756C2×C4—612no—
757C2×C4—612no—
758C2×C4—612no—
759C2×C4—612no—
760C2×C4—614no—
761C2×C4—12216no—
762C2×C4—1228no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—2448no—
782C2×C4—2448no—
783C2×C4—2444no—
784C2×C4C22×C4×D6112yes—
785C2×C4C22×C4×D6112yes—
786C2×C4C22×C4×D6114yes—
787C2×C4C22×C4×D6114yes—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—42no—
792C22—42no—
793C22—1224no—
794C22—1224no—
795C22—1224no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22C23×C4×D6111yescharacteristic
801C22H(5,𝔽2)×D6111yescharacteristic
802C222−1+4×D6111yescharacteristic
803C22#1684059712yes—
804C22#1684059912yes—
805C4—24no—
806C4—22no—
807C4—22no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—614no—
814C4—1222no—
815C4—1222no—
816C4—1222no—
817C4—1224no—
818C4—2442no—
819C4—2442no—
820C4—2442no—
821C4—2442no—
822C2—42no—
823C2—2444no—
824C2#520×D6111yescharacteristic
825C2#2145901711yescharacteristic
826C2#2145902111yescharacteristic
827C2#2145995612yes—
828C2#2145996512yes—
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2378C2
socle, cosocleC23×C61C25
prime radicalC2×#14519751C22
hypercenter#2378D61
hypocenterC61#34350
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2378

Complements

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

NH ≅ G/Ntype
2. #21449010C2semidirect
3. #21449009C2semidirect
4. #21449002C2semidirect
5. #21448991C2semidirect
6. #21448985C2semidirect
9. #21448965C2semidirect
10. #21448965C2semidirect
11. #21448311C2semidirect
12. #21448300C2semidirect
13. #21448294C2semidirect
14. #21448279C2semidirect
15. #21448261C2semidirect
16. #21448257C2semidirect
17. #21448221C2semidirect
18. #21448210C2semidirect
19. C61×#2378C2semidirect
20. #16840298C4semidirect
115. #14519772C2×C4semidirect
116. #14519768C2×C4semidirect
118. #14519761C2×C4semidirect
120. Q8×Dic61C2×C4semidirect
122. #14519737C2×C4semidirect
124. #14519735C2×C4semidirect
155. C2×C4×Dic61C2×C4semidirect
190. C22⋊Q8×C61C2×C4semidirect
414. #2378D61semidirect
522. C61#34350semidirect
536. C22⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402982
#214490102
#214490092
#214490022
#214489912
#214489852
#214489782
#214489732
#214489652
#214483112
#214483002
#214482942
#214482792
#214482612
#214482572
#214482212
#214482102
C61×#23782
#3435061