Finite Group Databasebeta

← #29695860

Subgroups — #29695860

Order 15616.

1478 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
1C22×#14519800C211yesmaximal, characteristic
2C2×C4×#11758201C211yesmaximal, characteristic, complemented
3C2×#16839847C211yesmaximal, characteristic, complemented
4#21448657C211yesmaximal, characteristic, complemented
5#21448648C211yesmaximal, characteristic, complemented
6#21446676C211yesmaximal, characteristic, complemented
7#21446670C211yesmaximal, characteristic, complemented
8#21446168C211yesmaximal, characteristic, complemented
9#21446166C211yesmaximal, characteristic, complemented
10#21446162C211yesmaximal, characteristic, complemented
11#21445843C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445758C211yesmaximal, characteristic, complemented
14#21445589C211yesmaximal, characteristic, complemented
15C61×#1878C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758226C2211yescharacteristic
18C2×#14519800—24no—
19C2×#14519800—24no—
20C2×#14519800C418yescomplemented
21C22×#11758201C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C22×D488C2211yescharacteristic
24C22×C8×D61C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×C4×D244C2211yescharacteristic
27C2×#14519739C2211yescharacteristic
28C4×#11758201—24no—
29#16839847—24no—
30C2×#14519708C2211yescharacteristic
31C2×#14519708C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×C4×#92418C2211yescharacteristic
40C2×C8×Dic61C2211yescharacteristic
41#16839669C2211yescharacteristic
42#16839664—21no—
43#16839664C2211yescharacteristic
44#16839663—21no—
45#16839663C2211yescharacteristic
46#16839640—21no—
47#16839640—21no—
48#16839624—21no—
49#16839619—21no—
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic
52C4×#11758198—21no—
53C4×#11758198C2211yescharacteristic
54#95×D61—21no—
55#16839525C2211yescharacteristic
56#16839516C2211yescharacteristic
57C22×Q16×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#391C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#336C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226—22no—
70C2×#11758226—41no—
71C2×#11758226—41no—
72C2×#11758226—41no—
73C2×#11758226—41no—
74C2×#11758226C2×C414yes—
75C2×#11758226C2×C414yescomplemented
76C22×D244—21no—
77C22×D244—21no—
78C22×D244C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C4×D61—21no—
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85#14519800—232no—
86C2×#11758201—22no—
87C2×#11758201—22no—
88C2×#11758201C2×C414yes—
89C2×#11758201C2×C414yescomplemented
90C2×#11758201D414yes—
91C2×#11758201D414yes—
92C2×D488—22no—
93C2×D488—22no—
94C2×D488C2×C414yes—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C2×C8×D61—22no—
98C2×C8×D61—22no—
99C2×C8×D61C2×C414yescomplemented
100Q8×Dic61—22no—
101Q8×Dic61—41no—
102C4×D244—22no—
103C4×D244—41no—
104#14519739—22no—
105#14519739—41no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198D411yescharacteristic
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61C2311yescharacteristic
121#14519708—22no—
122#14519708—22no—
123#14519701—22no—
124#14519701—41no—
125#14519699—22no—
126#14519699—41no—
127#14519697—22no—
128#14519697—41no—
129#14519689—22no—
130C4×#92418—22no—
131C8×Dic61—22no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684D411yescharacteristic
137#14519684D411yescharacteristic
138C22×Q8×C61C2311yescharacteristic
139C22×Q8×C61C2311yescharacteristic
140C2×Q16×C61—22no—
141C2×Q16×C61—22no—
142C2×Q16×C61C2×C414yescomplemented
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145C4×Q8×C61—22no—
146C4×Q8×C61—41no—
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C42×C61—21no—
151C2×C42×C61C2311yescharacteristic
152#103×C61—22no—
153#103×C61—41no—
154#95×C61—21no—
155#95×C61—21no—
156C23×D61—21no—
157C23×D61—21no—
158C23×D61C2×D411yescharacteristic
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61C22×C412yes—
168C2×Q8×C61C22×C412yes—
169C2×Q8×C61C2×D412yes—
170C2×Q8×C61C2×D412yes—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2411yescharacteristic
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183#11758226—28no—
184#11758226—28no—
185#11758226—44no—
186#11758226—44no—
187#11758226—44no—
188#11758226—44no—
189#11758226—44no—
190#11758226—44no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—24no—
199C2×D244—24no—
200C2×D244—21no—
201C2×D244—42no—
202C2×D244—42no—
203C2×D244—42no—
204C2×D244—42no—
205C2×D244C22×C412yes—
206C2×D244C22×C412yes—
207C2×D244C2×D412yes—
208C2×D244C2×D412yes—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—42no—
216C2×C4×D61—42no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61—42no—
222C2×C4×D61—42no—
223C2×C4×D61—81no—
224C2×C4×D61—81no—
225C2×C4×D61C22×C412yes—
226C2×C4×D61#4112yes—
227Q16×C61—28no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61C22×C412yes—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—42no—
239C42×C61—21no—
240C42×C61—21no—
241C42×C61—42no—
242#11758201—28no—
243#11758201C22⋊C4116yescomplemented
244#11758198—22no—
245#11758198—22no—
246#11758198—42no—
247#11758198—42no—
248#11758198—42no—
249#11758198—42no—
250#11758198—81no—
251#11758198—81no—
252#11758198—81no—
253#11758198—81no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—42no—
259C4×Dic61—21no—
260C4×Dic61—21no—
261C4×Dic61—42no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418C22×C412yes—
266C2×#92418C2×D412yes—
267C2×#92418C2×D412yes—
268D488—28no—
269C8×D61—28no—
270C23×C61C22×D411yescharacteristic
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—22no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61C4×D412yes—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61—22no—
296Q8×C61—22no—
297Q8×C61—41no—
298Q8×C61—41no—
299Q8×C61C2×C22⋊C414yes—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—21no—
303C2×C4×C61—22no—
304C2×C4×C61—21no—
305C2×C4×C61—22no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61#13512yescomplemented
318C2×C4×C61C23×C411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C2×C4×C61H(5,𝔽2)11yescharacteristic
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61C4×D412yes—
338C2×Dic61#13512yescomplemented
339D244—22no—
340D244—22no—
341D244—22no—
342D244—22no—
343D244—22no—
344D244—48no—
345D244—48no—
346D244—41no—
347D244—41no—
348D244C2×C22⋊C414yes—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—48no—
354C4×D61—48no—
355C4×D61—84no—
356C4×D61—84no—
357C8×C61—22no—
358C8×C61—41no—
359#92418—41no—
360#92418C2×C22⋊C414yes—
361#22449—611nomaximal, Sylow
362C22×C61C2×C4×D411yescharacteristic
363C22×C61D4211yescharacteristic
364C22×C61D4211yescharacteristic
365C22×C61C2×#13511yescharacteristic
366C22×C61C2×#13511yescharacteristic
367C22×C61#57711yescharacteristic
368C22×C61#57711yescharacteristic
369C2×D61—22no—
370C2×D61—24no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C2×D61—81no—
390C4×C61—24no—
391C4×C61—22no—
392C4×C61—42no—
393C4×C61—41no—
394C4×C61—81no—
395C4×C61—81no—
396C4×C61C22×C22⋊C411yescharacteristic
397C4×C61#51811yescharacteristic
398C4×C61#54611yescharacteristic
399C4×C61#54611yescharacteristic
400Dic61—22no—
401Dic61—22no—
402Dic61—41no—
403Dic61—81no—
404Dic61—81no—
405C22×#135—611no—
406C2×C4×SD16—611no—
407C2×C4×SD16—611no—
408#2341—611no—
409#2339—611no—
410#1968—611no—
411#1968—611no—
412#1879—611no—
413#1879—611no—
414#1878—611no—
415#1878D6111yescharacteristic, complemented
416#1807—611no—
417#1788—611no—
418#1788—611no—
419C8×C22⋊C4—611no—
420C2×C61D4×C22⋊C411yescharacteristic
421C2×C61C4×#13511yescharacteristic
422C2×C61#295211yescharacteristic
423C2×C61#328211yescharacteristic
424C2×C61#328211yescharacteristic
425C2×C61#328411yescharacteristic
426C2×C61#328411yescharacteristic
427D61—42no—
428D61—44no—
429D61—82no—
430C22×#41—611no—
431C22×#41—611no—
432C2×#135—618no—
433C2×#135—1224no—
434C2×#135—1224no—
435C22×Q16C2×D6111yescharacteristic
436C22×SD16—611no—
437C22×SD16—611no—
438C22×D8—611no—
439C23×C8—611no—
440C2×C4×Q8—611no—
441C2×C4×Q8C2×D6111yescharacteristic
442C2×C4×D4—611no—
443C2×C4×D4—611no—
444C4×SD16—1224no—
445C4×SD16—1224no—
446C2×#106—611no—
447C2×#106—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103C2×D6111yescharacteristic
451C2×#103C2×D6111yescharacteristic
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×C22⋊C8—611no—
457C2×C4×C8—611no—
458C2×C4×C8—611no—
459#391—611no—
460#391C2×D6111yescharacteristic
461#390—611no—
462#390—611no—
463#390—1221no—
464#390—1221no—
465#386—1221no—
466#386—1221no—
467#381—1221no—
468#380—611no—
469#380—611no—
470#380—1221no—
471C4×C22⋊C4—611no—
472C4×C22⋊C4—1221no—
473C2×#95—1221no—
474#340—611no—
475#340C2×D6111yescharacteristic
476#336—611no—
477#336C2×D6111yescharacteristic
478C61#2244911yescharacteristic, complemented, Sylow
479C2×#41—614no—
480C2×#41—614no—
481C2×#41—1222no—
482C2×#41—1222no—
483C2×#41—1222no—
484C2×#41—1222no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—2441no—
488C2×#41—2441no—
489C2×#41—2441no—
490C2×#41—2441no—
491C22×Q8C22×D6111yescharacteristic
492C22×Q8C22×D6111yescharacteristic
493C22×D4—611no—
494C22×D4—611no—
495C22×D4—1221no—
496C22×D4—1221no—
497C23×C4—611no—
498C23×C4—1221no—
499C23×C4—1221no—
500C23×C4—1221no—
501C23×C4—1221no—
502#135—12232no—
503C2×Q16—22no—
504C2×Q16—22no—
505C2×Q16C4×D6114yescomplemented
506C2×SD16—614no—
507C2×SD16—614no—
508C2×SD16—614no—
509C2×SD16—614no—
510C2×SD16—1222no—
511C2×SD16—1222no—
512C2×D8—614no—
513C2×D8—1222no—
514C2×D8—1222no—
515C22×C8—611no—
516C22×C8—614no—
517C22×C8—611no—
518C22×C8—1222no—
519C22×C8—1222no—
520C22×C8C22×D6111yescharacteristic
521C22×C8C22×D6111yescharacteristic
522C4×Q8—22no—
523C4×Q8—41no—
524C4×Q8—1222no—
525C4×Q8—2441no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—2441no—
529C4×D4—2441no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4C22×D6111yescharacteristic
535C2×C4⋊C4C22×D6111yescharacteristic
536C2×C22⋊C4—611no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C42—21no—
547C2×C42—611no—
548C2×C42—1221no—
549C2×C42C22×D6111yescharacteristic
550#106—1222no—
551#106—1222no—
552#103—22no—
553#103—41no—
554#103—1222no—
555#103—2441no—
556#102—1222no—
557#102—1222no—
558#102—2441no—
559#102—2441no—
560C22⋊C8—1222no—
561C4×C8—1222no—
562C4×C8—1222no—
563#95—21no—
564#95—21no—
565#95—611no—
566#95—611no—
567#95—1221no—
568#95—1221no—
569#95—1221no—
570#95—1221no—
571C24—611no—
572C24—1221no—
573C24—1221no—
574#41—1228no—
575#41—1228no—
576#41—2444no—
577#41—2444no—
578#41—2444no—
579#41—2444no—
580#41—2444no—
581#41—2444no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8C2×C4×D6112yes—
591C2×Q8C2×C4×D6112yes—
592C2×Q8D4×D6112yes—
593C2×Q8D4×D6112yes—
594C2×D4—612no—
595C2×D4—612no—
596C2×D4—612no—
597C2×D4—612no—
598C2×D4—1224no—
599C2×D4—1224no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—2442no—
609C2×D4—2442no—
610C2×D4—2442no—
611C2×D4—2442no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—612no—
619C22×C4—612no—
620C22×C4—611no—
621C22×C4—1224no—
622C22×C4—1224no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—4881no—
630C22×C4—4881no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4—2442no—
634C22×C4—2442no—
635C22×C4—2442no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4D4×D6111yescharacteristic
640C22×C4D4×D6111yescharacteristic
641C22×C4C23×D6111yescharacteristic
642Q16—28no—
643SD16—6116no—
644SD16—1228no—
645D8—1228no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—612no—
652C2×C8—612no—
653C2×C8—612no—
654C2×C8—1228no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8C2×C4×D6112yes—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—42no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—2442no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—4881no—
672C22⋊C4—4881no—
673C22⋊C4—4881no—
674C22⋊C4—4881no—
675C22⋊C4—2442no—
676C22⋊C4—2442no—
677C22⋊C4—2442no—
678C22⋊C4—2442no—
679C42—21no—
680C42—21no—
681C42—42no—
682C42—1221no—
683C42—1221no—
684C42—2442no—
685C23—612no—
686C23—1222no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23—1222no—
692C23—1221no—
693C23—1222no—
694C23—1221no—
695C23—1222no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23C2×D4×D6111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—22no—
712Q8—41no—
713Q8—41no—
714Q8C22⋊C4×D6114yes—
715D4—614no—
716D4—1222no—
717D4—1222no—
718D4—1222no—
719D4—1222no—
720D4—1222no—
721D4—2448no—
722D4—2448no—
723D4—2441no—
724D4—2441no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—612no—
743C2×C4—612no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—4884no—
756C2×C4—4884no—
757C2×C4—2448no—
758C2×C4—2448no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4#1451980012yescomplemented
766C2×C4C22×C4×D6111yescharacteristic
767C2×C4C2×D4×D6111yescharacteristic
768C2×C4C2×D4×D6111yescharacteristic
769C2×C4#41×D6111yescharacteristic
770C2×C4#1451982211yescharacteristic
771C2×C4#1451982311yescharacteristic
772C8—22no—
773C8—41no—
774C8—614no—
775C8—2441no—
776C22—1222no—
777C22—1222no—
778C22—1224no—
779C22—1222no—
780C22—4881no—
781C22—4881no—
782C22—4881no—
783C22—4881no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2441no—
790C22—2442no—
791C22—2441no—
792C22—2441no—
793C22—2442no—
794C22—2441no—
795C22—2442no—
796C22—2442no—
797C22C4×D4×D6111yescharacteristic
798C22#1684039411yescharacteristic
799C22#1684039611yescharacteristic
800C22#135×D6111yescharacteristic
801C22C2×#1451980011yescharacteristic
802C22#1684057111yescharacteristic
803C22#1684057111yescharacteristic
804C4—22no—
805C4—24no—
806C4—41no—
807C4—42no—
808C4—81no—
809C4—81no—
810C4—1222no—
811C4—1222no—
812C4—4881no—
813C4—4881no—
814C4—2441no—
815C4C2×C22⋊C4×D6111yescharacteristic
816C4#1684023411yescharacteristic
817C4#1684040111yescharacteristic
818C4#1684040411yescharacteristic
819C2—4882no—
820C2—2442no—
821C2—2444no—
822C2#2144863711yescharacteristic
823C2C4×#1451980011yescharacteristic
824C2#2145469911yescharacteristic
825C2#2145751911yescharacteristic
826C2#2145752111yescharacteristic
827C2#2145754211yescharacteristic
828C2#2145754411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1878C2
socleC23×C61C22×D4
prime radicalC22×#14519800C2
cosocleC22×C4×C61C24
hypercenter#1878D61
hypocenterC61#22449
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758201C2semidirect
3. C2×#16839847C2semidirect
4. #21448657C2semidirect
5. #21448648C2semidirect
6. #21446676C2semidirect
7. #21446670C2semidirect
8. #21446168C2semidirect
9. #21446166C2semidirect
10. #21446162C2semidirect
11. #21445843C2semidirect
12. #21445758C2semidirect
13. #21445758C2semidirect
14. #21445589C2semidirect
15. C61×#1878C2semidirect
20. C2×#14519800C4semidirect
75. C2×#11758226C2×C4semidirect
89. C2×#11758201C2×C4semidirect
99. C2×C8×D61C2×C4semidirect
142. C2×Q16×C61C2×C4semidirect
243. #11758201C22⋊C4semidirect
317. C2×C4×C61#135semidirect
338. C2×Dic61#135semidirect
415. #1878D61semidirect
478. C61#22449semidirect
505. C2×Q16C4×D61semidirect
765. C2×C4#14519800semidirect

Maximal subgroups

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

subgroupindex
C22×#145198002
C2×C4×#117582012
C2×#168398472
#214486572
#214486482
#214466762
#214466702
#214461682
#214461662
#214461622
#214458432
#214457582
#214455892
C61×#18782
#2244961