Finite Group Databasebeta

← #29689142

Subgroups — #29689142

Order 15616.

1622 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840274C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#21446261C214yesmaximal, complemented
5#21446120C214yesmaximal, complemented
6#21445918C211yesmaximal, characteristic, complemented
7#21445764C211yesmaximal, characteristic, complemented
8#21445762C211yesmaximal, characteristic, complemented
9C61×#1826C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11C23×C4×D61C2211yescharacteristic
12C2×M16×D61C2212yescomplemented
13#16840274—21no—
14#16840274—21no—
15#16840274—21no—
16#16840274—21no—
17#16840274C412yescomplemented
18#16840274C412yescomplemented
19#16840274C2212yes—
20#16840274C2212yes—
21C2×#14519761—21no—
22C2×#14519757C411yescharacteristic, complemented
23C2×#14519757C411yescharacteristic, complemented
24C2×#14519752C411yescharacteristic, complemented
25C2×#14519752C411yescharacteristic, complemented
26C2×#14519747—21no—
27C2×C4×D244—21no—
28C2×C4×D244—21no—
29C2×C22⋊C4×D61—21no—
30C2×C42×D61C2212yescomplemented
31C2×#14519705C2214yescomplemented
32C2×#14519703C2214yescomplemented
33#16839726C2211yescharacteristic
34#16839725C2212yescomplemented
35#16839724—21no—
36#16839724—21no—
37C22⋊C8×D61—21no—
38C22⋊C8×D61—21no—
39C22⋊C4×Dic61—21no—
40C4×#11758198C2212yescomplemented
41C4×C22⋊Dic61C2211yescharacteristic
42#16839609—21no—
43#95×D61—21no—
44#16839521C2214yescomplemented
45C2×#117×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#339C2214yescomplemented
49C24×D61D411yescharacteristic
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222—44no—
53C2×#11758222C2×C412yescomplemented
54C2×#11758222C2312yes—
55C22×Dic122C2×C411yescharacteristic, complemented
56C22×D244—21no—
57C22×D244—21no—
58C22×D244C2×C411yescharacteristic, complemented
59C22×C22⋊D61—21no—
60C23×Dic61D411yescharacteristic
61C22×C4×D61—22no—
62C22×C4×D61—21no—
63C22×C4×D61—44no—
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C2×#11758194C2312yes—
77C2×#11758189—22no—
78M16×D61—44no—
79C2×C8×D61—22no—
80#14519761—22no—
81#14519761—22no—
82#14519761—22no—
83#14519761—22no—
84#14519757—21no—
85#14519757—21no—
86#14519757—21no—
87#14519757—21no—
88#14519757C2×C412yes—
89#14519757C2×C412yes—
90#14519757C2×C412yescomplemented
91#14519757C2×C412yescomplemented
92#14519752—21no—
93#14519752—21no—
94#14519752—21no—
95#14519752—21no—
96#14519752C2×C412yes—
97#14519752C2×C412yes—
98#14519752C2×C412yescomplemented
99#14519752C2×C412yescomplemented
100#14519747—22no—
101#14519747—22no—
102#14519747—22no—
103#14519747—22no—
104C4×D244—22no—
105C4×D244—22no—
106C4×D244—22no—
107C4×D244—22no—
108C4×D244—22no—
109C4×D244—22no—
110C4×D244—22no—
111C4×D244—22no—
112C2×C4⋊Dic61—21no—
113C2×C4⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—22no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C22⋊C4×D61—28no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61C2312yes—
123C42×D61—44no—
124#14519705—44no—
125#14519703—44no—
126C22⋊#92418—21no—
127C22⋊#92418—21no—
128#14519689—22no—
129#14519689—22no—
130#14519684—21no—
131#14519684—22no—
132C23×C4×C61C2311yescharacteristic
133C2×M16×C61C2312yes—
134#117×C61—21no—
135#117×C61—21no—
136#117×C61C2×C412yescomplemented
137#117×C61C2312yes—
138C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
139C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C42×C61—21no—
143C2×C42×C61C2312yes—
144C22⋊C8×C61—21no—
145C22⋊C8×C61—21no—
146#95×C61—21no—
147C24×C61C2×D411yescharacteristic
148C23×D61—24no—
149C23×D61—21no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61C22⋊C411yescharacteristic
153C23×D61C22⋊C411yescharacteristic
154C23×D61C22⋊C411yescharacteristic
155C23×D61C22⋊C411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C23×D61C2×D411yescharacteristic
158C22×C4×C61—24no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—22no—
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—44no—
171C22×Dic61—21no—
172C22×Dic61—22no—
173C22×Dic61—42no—
174C22×Dic61C22⋊C411yescharacteristic
175C22×Dic61C22⋊C411yescharacteristic
176C22×Dic61C22⋊C411yescharacteristic
177C22×Dic61C22⋊C411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180#11758222—24no—
181#11758222—24no—
182#11758222—42no—
183#11758222—42no—
184#11758222—44no—
185#11758222—44no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—21no—
191C2×D244—42no—
192C2×D244—44no—
193C2×D244—44no—
194C2×D244C22×C412yes—
195C2×C4×D61—24no—
196C2×C4×D61—24no—
197C2×C4×D61—28no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—44no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22⋊C411yescharacteristic
221C2×C4×D61C22×C411yescharacteristic
222C2×C4×D61C22×C411yescharacteristic
223C2×C4×D61C22×C411yescharacteristic
224C2×C4×D61C22×C411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×Dic122—21no—
230C2×Dic122—42no—
231C2×Dic122C22×C412yes—
232M16×C61—24no—
233C2×C8×C61—22no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61C22×C412yes—
237C4⋊C4×C61C22×C412yes—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C42×C61—22no—
242C42×C61—22no—
243C42×C61—24no—
244C22⋊Dic61—24no—
245#11758198—28no—
246#11758198—22no—
247#11758198—22no—
248#11758198—22no—
249#11758198—22no—
250#11758198—22no—
251#11758198—22no—
252#11758198—22no—
253#11758198—22no—
254C4⋊Dic61—22no—
255C4⋊Dic61—22no—
256C4⋊Dic61—22no—
257C4⋊Dic61—22no—
258C4×Dic61—24no—
259C4×Dic61—44no—
260#11758194—24no—
261C2×#92418—22no—
262#11758189—44no—
263C8×D61—44no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—41no—
267C23×C61C2×C22⋊C411yescharacteristic
268C23×C61C2×C22⋊C411yescharacteristic
269C23×C61C22×D411yescharacteristic
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
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—416no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61#10414yescomplemented
293C22×D61C2×C22⋊C411yescharacteristic
294C22×D61C2×C22⋊C411yescharacteristic
295C22×D61C2×C22⋊C411yescharacteristic
296C22×D61C2×C22⋊C411yescharacteristic
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—24no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C2×C22⋊C411yescharacteristic
311C2×C4×C61C23×C411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61H(5,𝔽2)14yes—
314C22⋊D61—44no—
315C22⋊D61—44no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—24no—
319C2×Dic61—22no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61C2×C22⋊C411yescharacteristic
328C2×Dic61C2×C22⋊C411yescharacteristic
329C2×Dic61C2×C22⋊C411yescharacteristic
330C2×Dic61C2×C22⋊C411yescharacteristic
331D244—22no—
332D244—22no—
333D244—42no—
334D244—44no—
335D244—44no—
336D244—44no—
337D244—44no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—44no—
355C4×D61—416no—
356C4×D61—44no—
357Dic122—22no—
358Dic122—22no—
359Dic122—42no—
360C8×C61—42no—
361#92418—42no—
362#21773—611nomaximal, Sylow
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—44no—
371C22×C61C2×#10412yes—
372C22×C61C22×C22⋊C411yescharacteristic
373C22×C61#53412yes—
374C2×D61—28no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—44no—
385C2×D61—44no—
386C2×D61—44no—
387C2×D61—44no—
388C2×D61—44no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—84no—
393C2×D61C2×#10412yes—
394C2×D61C2×#10412yes—
395C2×D61#42112yes—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—44no—
399C4×C61—42no—
400C4×C61—42no—
401C4×C61#51812yes—
402C4×C61#53412yes—
403Dic61—21no—
404Dic61—21no—
405Dic61—21no—
406Dic61—21no—
407Dic61—44no—
408Dic61—42no—
409C2×#525—611no—
410C2×#407—611no—
411C2×C4×C22⋊C4—611no—
412#1896—614no—
413#1871—614no—
414#1826—611no—
415#1826D6111yescharacteristic, complemented
416#1789—611no—
417#1789—611no—
418C2×C61—22no—
419C2×C61—22no—
420C2×C61—41no—
421C2×C61#230811yescharacteristic
422C2×C61C22×#10411yescharacteristic
423C2×C61C2×#42111yescharacteristic
424D61—22no—
425D61—22no—
426D61—22no—
427D61—41no—
428D61—82no—
429C22×#41—611no—
430C24×C4—611no—
431C22×M16—612no—
432#525—612no—
433#525—612no—
434#525—612no—
435#525—612no—
436#525—1221no—
437#525—1221no—
438#525—1221no—
439#525—1221no—
440C2×#123—1221no—
441C2×C22⋊Q8—611no—
442C2×C22⋊Q8—611no—
443C2×#121—611no—
444C2×#121—611no—
445C2×#120—1221no—
446C2×C4×D4—1221no—
447C2×C4×D4—1221no—
448C2×#117C2×D6111yescharacteristic
449C22×C22⋊C4—1221no—
450C22×C42—612no—
451C2×#104—614no—
452C2×#104—614no—
453#407—611no—
454#407—612no—
455#407—1221no—
456#407—1221no—
457#407C2×D6111yescharacteristic
458C2×C22⋊C8—1221no—
459C2×C22⋊C8—1221no—
460C4×C22⋊C4—611no—
461C4×C22⋊C4—612no—
462C4×C22⋊C4—1221no—
463C4×C22⋊C4—1221no—
464C4×C22⋊C4C2×D6111yescharacteristic
465C2×#95—1221no—
466#339—614no—
467#339C2×D6114yescomplemented
468C61#2177311yescharacteristic, complemented, Sylow
469C25—611no—
470C2×#41—612no—
471C2×#41—612no—
472C2×#41—1221no—
473C2×#41—1221no—
474C2×#41—2444no—
475C22×Q8—611no—
476C22×D4—611no—
477C22×D4—1221no—
478C22×D4—1221no—
479C22×D4—1221no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—1222no—
494C23×C4—1221no—
495C23×C4—2444no—
496C23×C4C22×D6111yescharacteristic
497C2×M16—612no—
498C2×M16—1222no—
499C2×M16—2444no—
500C2×M16C22×D6112yes—
501C22×C8—1222no—
502#123—1222no—
503#123—1222no—
504#123—1222no—
505#123—1222no—
506C22⋊Q8—612no—
507C22⋊Q8—612no—
508C22⋊Q8—612no—
509C22⋊Q8—612no—
510C22⋊Q8—1221no—
511C22⋊Q8—1221no—
512C22⋊Q8—1221no—
513C22⋊Q8—1221no—
514#121—612no—
515#121—612no—
516#121—612no—
517#121—612no—
518#121—1221no—
519#121—1221no—
520#121—1221no—
521#121—1221no—
522#120—1222no—
523#120—1222no—
524#120—1222no—
525#120—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4—1222no—
531C4×D4—1222no—
532C4×D4—1222no—
533C4×D4—1222no—
534#117—21no—
535#117—21no—
536#117C4×D6112yescomplemented
537#117C22×D6112yes—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4C4×D6111yescharacteristic, complemented
541C2×C4⋊C4C4×D6111yescharacteristic, complemented
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—1228no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1222no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C42—21no—
552C2×C42—612no—
553C2×C42—1222no—
554C2×C42—2444no—
555C2×C42C22×D6112yes—
556#104—2444no—
557#104—2444no—
558C22⋊C8—21no—
559C22⋊C8—21no—
560C22⋊C8—1222no—
561C22⋊C8—1222no—
562C22⋊C8—1221no—
563C22⋊C8—1221no—
564#95—21no—
565#95—1222no—
566#95—1221no—
567C24—611no—
568C24—611no—
569C24—611no—
570C24—611no—
571C24—611no—
572C24—611no—
573C24—1224no—
574C24—1221no—
575C24—2442no—
576C24—2442no—
577C24D4×D6111yescharacteristic
578#41—1224no—
579#41—1224no—
580#41—2442no—
581#41—2442no—
582#41—2444no—
583#41—2444no—
584C2×Q8—612no—
585C2×Q8—1221no—
586C2×Q8—2442no—
587C2×D4—612no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—1222no—
594C2×D4—1221no—
595C2×D4—2442no—
596C2×D4—2444no—
597C2×D4—2444no—
598C2×D4—2444no—
599C22×C4—24no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—1228no—
626C22×C4—1224no—
627C22×C4—1224no—
628C22×C4—1222no—
629C22×C4—1221no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—2442no—
633C22×C4—2442no—
634C22×C4—2442no—
635C22×C4—2442no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4—2442no—
642C22×C4—2444no—
643C22×C4—2444no—
644C22×C4—2444no—
645C22×C4—2442no—
646C22×C4C2×C4×D6111yescharacteristic
647C22×C4C2×C4×D6111yescharacteristic
648C22×C4D4×D6111yescharacteristic
649C22×C4D4×D6111yescharacteristic
650C22×C4D4×D6111yescharacteristic
651C22×C4C23×D6111yescharacteristic
652M16—24no—
653M16—1224no—
654M16—2444no—
655C2×C8—22no—
656C2×C8—1222no—
657C2×C8—2444no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—1222no—
661C4⋊C4—1222no—
662C4⋊C4—1222no—
663C4⋊C4—1222no—
664C4⋊C4C2×C4×D6112yes—
665C4⋊C4C2×C4×D6112yes—
666C22⋊C4—24no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—1222no—
672C22⋊C4—1222no—
673C22⋊C4—1222no—
674C22⋊C4—1222no—
675C22⋊C4—1222no—
676C22⋊C4—1222no—
677C22⋊C4—1228no—
678C22⋊C4—1224no—
679C42—22no—
680C42—22no—
681C42—24no—
682C42—1224no—
683C42—2444no—
684C23—22no—
685C23—22no—
686C23—41no—
687C23—611no—
688C23—611no—
689C23—611no—
690C23—614no—
691C23—611no—
692C23—1222no—
693C23—1222no—
694C23—1222no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—1222no—
701C23—1222no—
702C23—1222no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23—2441no—
709C23—2441no—
710C23—2442no—
711C23—2442no—
712C23—24416no—
713C23—2442no—
714C23C22⋊C4×D6111yescharacteristic
715C23C22⋊C4×D6111yescharacteristic
716C23C2×D4×D6111yescharacteristic
717Q8—1222no—
718Q8—1222no—
719Q8—2442no—
720D4—1222no—
721D4—1222no—
722D4—2442no—
723D4—2444no—
724D4—2444no—
725D4—2444no—
726D4—2444no—
727D4—2444no—
728D4—2444no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—611no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1224no—
756C2×C4—1222no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2444no—
766C2×C4—24416no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4—2442no—
774C2×C4—2444no—
775C2×C4C22⋊C4×D6111yescharacteristic
776C2×C4C22⋊C4×D6111yescharacteristic
777C2×C4C22×C4×D6111yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C2×C4#1451982314yes—
780C8—42no—
781C8—2442no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—44no—
790C22—612no—
791C22—612no—
792C22—612no—
793C22—1228no—
794C22—1221no—
795C22—1221no—
796C22—1221no—
797C22—1221no—
798C22—1221no—
799C22—1221no—
800C22—1221no—
801C22—1221no—
802C22—1221no—
803C22—4884no—
804C22—2444no—
805C22—2444no—
806C22—2444no—
807C22—2444no—
808C22—2444no—
809C22—2442no—
810C22—2442no—
811C22—2442no—
812C22#104×D6112yes—
813C22C2×C22⋊C4×D6111yescharacteristic
814C22#1684032312yes—
815C4—21no—
816C4—21no—
817C4—44no—
818C4—42no—
819C4—42no—
820C4—1221no—
821C4—1221no—
822C4—1221no—
823C4—1221no—
824C4—2444no—
825C4—2442no—
826C4#1684023612yes—
827C4#1684032312yes—
828C2—22no—
829C2—22no—
830C2—41no—
831C2—1222no—
832C2—1222no—
833C2—1222no—
834C2—4882no—
835C2—2441no—
836C2#2144839611yescharacteristic
837C2C2×#104×D6111yescharacteristic
838C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1826C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840274C2
cosocleC22×C4×C61C24
hypercenter#1826D61
hypocenterC61#21773
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. C4×C22⋊C4×D61C2semidirect
4. #21446261C2semidirect
5. #21446120C2semidirect
6. #21445918C2semidirect
7. #21445764C2semidirect
8. #21445762C2semidirect
9. C61×#1826C2semidirect
12. C2×M16×D61C22semidirect
17. #16840274C4semidirect
18. #16840274C4semidirect
22. C2×#14519757C4semidirect
23. C2×#14519757C4semidirect
24. C2×#14519752C4semidirect
25. C2×#14519752C4semidirect
30. C2×C42×D61C22semidirect
31. C2×#14519705C22semidirect
32. C2×#14519703C22semidirect
34. #16839725C22semidirect
40. C4×#11758198C22semidirect
44. #16839521C22semidirect
48. C61×#339C22semidirect
53. C2×#11758222C2×C4semidirect
55. C22×Dic122C2×C4semidirect
58. C22×D244C2×C4semidirect
90. #14519757C2×C4semidirect
91. #14519757C2×C4semidirect
98. #14519752C2×C4semidirect
99. #14519752C2×C4semidirect
136. #117×C61C2×C4semidirect
138. C2×C4⋊C4×C61C2×C4semidirect
139. C2×C4⋊C4×C61C2×C4semidirect
292. C22×D61#104semidirect
415. #1826D61semidirect
467. #339C2×D61semidirect
468. C61#21773semidirect
536. #117C4×D61semidirect
540. C2×C4⋊C4C4×D61semidirect
541. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402742
#407×D612
C4×C22⋊C4×D612
#214462612
#214461202
#214459182
#214457642
#214457622
C61×#18262
#2177361