Finite Group Databasebeta

← #29685770

Subgroups — #29685770

Order 15616.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840245C211yesmaximal, characteristic
2C2×#16839924C211yesmaximal, characteristic
3C2×#16839866C211yesmaximal, characteristic, complemented
4C2×#16839853C211yesmaximal, characteristic, complemented
5#21448497C211yesmaximal, characteristic, complemented
6#21446158C211yesmaximal, characteristic, complemented
7#21446151C211yesmaximal, characteristic, complemented
8#21446124C211yesmaximal, characteristic, complemented
9#21446085C211yesmaximal, characteristic, complemented
10#21446078C211yesmaximal, characteristic, complemented
11#21446011C211yesmaximal, characteristic, complemented
12#21445646C211yesmaximal, characteristic, complemented
13#103×Dic61C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19#16840245—24no—
20#16840245—24no—
21C2×Q8×Dic61C2211yescharacteristic
22C2×Q8×Dic61C2211yescharacteristic
23C2×#14519742C2211yescharacteristic
24C2×D4×Dic61—21no—
25C2×D4×Dic61—21no—
26C2×D4×Dic61C2211yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28C2×#14519736—21no—
29C2×#14519736C2211yescharacteristic
30C22×C4⋊Dic61—21no—
31C22×C4⋊Dic61C2211yescharacteristic
32#16839924C418yescomplemented
33#16839866—24no—
34#16839853—24no—
35C2×#14519708C2211yescharacteristic
36C2×#14519708C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519687C2211yescharacteristic
43C2×C8×Dic61C2211yescharacteristic
44#16839667C2211yescharacteristic
45#16839659—21no—
46#16839658C2211yescharacteristic
47#16839656—21no—
48#16839650—21no—
49#16839649—21no—
50C4⋊C4×Dic61C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839516C2211yescharacteristic
56#16839516C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C22×Dic122C2311yescharacteristic
65C23×Dic61—21no—
66C23×Dic61—21no—
67C23×Dic61—21no—
68C2×#11758202—22no—
69C2×#11758202—22no—
70C2×#11758202C2×C414yescomplemented
71C2×#11758200—22no—
72C2×#11758200—22no—
73C2×#11758200C2×C414yescomplemented
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519756—22no—
77#14519756C2×C414yescomplemented
78Q8×Dic61—22no—
79Q8×Dic61—22no—
80Q8×Dic61—22no—
81Q8×Dic61D414yes—
82#14519742—22no—
83#14519742—22no—
84D4×Dic61—28no—
85D4×Dic61—28no—
86D4×Dic61—22no—
87D4×Dic61—22no—
88D4×Dic61—22no—
89D4×Dic61D414yes—
90#14519736—28no—
91#14519736—22no—
92#14519736—22no—
93C2×C4⋊Dic61—28no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61—22no—
99C2×C4⋊Dic61D411yescharacteristic
100C2×C4⋊Dic61D411yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61D411yescharacteristic
111C2×C22⋊Dic61D411yescharacteristic
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118#14519708—22no—
119#14519708—22no—
120#14519702—22no—
121#14519702—22no—
122#14519701C2×C414yescomplemented
123#14519698C2×C414yescomplemented
124C22⋊#92418C2×C414yescomplemented
125#14519687—22no—
126C8×Dic61—22no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131C2×#41×C61—22no—
132C2×#41×C61—22no—
133C2×#41×C61—22no—
134C2×#41×C61—22no—
135C2×#41×C61—22no—
136C2×#41×C61C2×C414yes—
137C22×Q8×C61C2311yescharacteristic
138C22×D4×C61—21no—
139C22×D4×C61C2311yescharacteristic
140C23×C4×C61—21no—
141C23×C4×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147#103×C61—22no—
148#103×C61—22no—
149#102×C61—22no—
150#102×C61—22no—
151C22⋊C8×C61—22no—
152#95×C61—21no—
153C24×C61—21no—
154C24×C61C2×D411yescharacteristic
155#41×C61—28no—
156#41×C61—28no—
157#41×C61—28no—
158#41×C61—28no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61C22×C412yes—
163C2×Q8×C61C2×D412yes—
164C2×Q8×C61#4112yes—
165C2×D4×C61—24no—
166C2×D4×C61—24no—
167C2×D4×C61—24no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61C22×C412yes—
172C2×D4×C61C2×D412yes—
173C2×D4×C61#4112yes—
174C22×C4×C61—24no—
175C22×C4×C61—24no—
176C22×C4×C61—21no—
177C22×C4×C61—24no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61C22×C412yes—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61#4112yes—
187C22×C4×C61C2411yescharacteristic
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—24no—
193C22×Dic61—24no—
194C22×Dic61—24no—
195C22×Dic61—81no—
196C22×Dic61—81no—
197C22×Dic61—81no—
198C22×Dic61—81no—
199C22×Dic61—81no—
200C22×Dic61—81no—
201C22×Dic61C2×D411yescharacteristic
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122C22×C412yes—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C22⋊C4×C61—81no—
222C22⋊Dic61—24no—
223C22⋊Dic61—24no—
224C22⋊Dic61—24no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227#11758202—28no—
228#11758200—28no—
229C4⋊Dic61—24no—
230C4⋊Dic61—24no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—22no—
235C4⋊Dic61—24no—
236C4⋊Dic61—22no—
237C4⋊Dic61C22×C412yes—
238C4⋊Dic61C2×D412yes—
239C4⋊Dic61C2×D412yes—
240#11758196—24no—
241#11758196—42no—
242#11758196—81no—
243C4×Dic61—24no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—24no—
247C4×Dic61—42no—
248C4×Dic61—81no—
249C4×Dic61C2×D412yes—
250C4×Dic61C2×D412yes—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418C22×C412yes—
256C2×#92418C22×C412yes—
257C23×C61—22no—
258C23×C61—21no—
259C23×C61—22no—
260C23×C61—21no—
261C23×C61—22no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61C4×D412yes—
271C23×C61C22×D411yescharacteristic
272Q8×C61—22no—
273Q8×C61—22no—
274Q8×C61—22no—
275Q8×C61C4×D414yes—
276D4×C61—216no—
277D4×C61—22no—
278D4×C61—22no—
279D4×C61—22no—
280D4×C61C4×D414yes—
281C2×C4×C61—216no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61C4×D412yes—
298C2×C4×C61C23×C411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—84no—
327C2×Dic61—84no—
328C2×Dic61—84no—
329C2×Dic61#12012yes—
330C2×Dic61#12012yes—
331Dic122—22no—
332Dic122—22no—
333Dic122—41no—
334Dic122—41no—
335C8×C61—41no—
336C8×C61—41no—
337#92418—22no—
338#92418—22no—
339#21461—611nomaximal, Sylow
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—24no—
344C22×C61—41no—
345C22×C61—42no—
346C22×C61—41no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—41no—
351C22×C61—42no—
352C22×C61—41no—
353C22×C61—42no—
354C22×C61C2×C4×D411yescharacteristic
355C22×C61C2×#12011yescharacteristic
356C22×C61#52511yescharacteristic
357C22×C61#57711yescharacteristic
358C22×C61#57711yescharacteristic
359C22×C61#57711yescharacteristic
360C22×C61#57811yescharacteristic
361C4×C61—22no—
362C4×C61—24no—
363C4×C61—81no—
364C4×C61—81no—
365C4×C61C2×C4×D411yescharacteristic
366C4×C61C2×C4×D411yescharacteristic
367C4×C61#52511yescharacteristic
368C4×C61#52511yescharacteristic
369Dic61—22no—
370Dic61—22no—
371Dic61—42no—
372Dic61—41no—
373Dic61—42no—
374Dic61—42no—
375Dic61—41no—
376Dic61—42no—
377C2×#520—611no—
378C2×#452—611no—
379C2×#441—611no—
380C2×C4×SD16—611no—
381#2323—611no—
382#1878—611no—
383#1877—611no—
384#1872—611no—
385#1865—611no—
386#1864—611no—
387#1853—611no—
388#1788D6111yescharacteristic
389#1762—611no—
390C4×#103—611no—
391#1750—611no—
392C2×C61—42no—
393C2×C61—44no—
394C2×C61C4×#12011yescharacteristic
395C2×C61#294711yescharacteristic
396C2×C61#295211yescharacteristic
397C2×C61#300911yescharacteristic
398C2×C61#301311yescharacteristic
399C2×C61#312011yescharacteristic
400C2×C61#312511yescharacteristic
401C22×#41C2×D6111yescharacteristic
402C22×Q16—611no—
403C22×SD16—611no—
404C2×C22⋊Q8—611no—
405#520—1224no—
406#520—1224no—
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—611no—
410C2×C4×D4—611no—
411C2×C4×D4—611no—
412C2×C4×D4—1221no—
413C2×C4×D4—1221no—
414C2×#117—611no—
415C2×#117—1221no—
416C22×C4⋊C4—611no—
417C22×C4⋊C4—1221no—
418#452—618no—
419#441—1224no—
420C4×SD16—1224no—
421C2×#106—611no—
422C2×#106—611no—
423C2×#103—611no—
424C2×#103—611no—
425C2×#103—611no—
426C2×#103C2×D6111yescharacteristic
427C2×#103C2×D6111yescharacteristic
428C2×#102—611no—
429C2×#102C2×D6111yescharacteristic
430C2×#102C2×D6111yescharacteristic
431C2×C22⋊C8—611no—
432C2×C22⋊C8C2×D6111yescharacteristic
433C2×#97—611no—
434C2×C4×C8—611no—
435#391—611no—
436#389—611no—
437#389—1221no—
438#388—1221no—
439#388—1221no—
440#387—1221no—
441#380C2×D6111yescharacteristic
442C4×C4⋊C4—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#336—611no—
448#336—611no—
449C61#2146111yescharacteristic, complemented, Sylow
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41C4×D6114yes—
456C22×Q8—611no—
457C22×Q8C22×D6111yescharacteristic
458C22×D4—21no—
459C22×D4C22×D6111yescharacteristic
460C23×C4—21no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4C22×D6111yescharacteristic
465C2×Q16—614no—
466C2×Q16—1222no—
467C2×Q16—1222no—
468C2×SD16—614no—
469C2×SD16—1222no—
470C2×SD16—1222no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C22⋊Q8—614no—
476C22⋊Q8—1222no—
477C4×Q8—614no—
478C4×Q8—1222no—
479C4×Q8—1222no—
480C4×Q8—1222no—
481C4×Q8—1222no—
482C4×Q8—1222no—
483C4×D4—614no—
484C4×D4—1222no—
485C4×D4—1222no—
486C4×D4—1228no—
487C4×D4—1228no—
488C4×D4—1222no—
489#117—1222no—
490#117—1222no—
491#117—1228no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1222no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1228no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—611no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C42—611no—
515C2×C42—611no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42—1221no—
520#106—1222no—
521#106—1222no—
522#103—22no—
523#103—22no—
524#103—614no—
525#103—1222no—
526#103—1222no—
527#102—22no—
528#102—22no—
529#102—614no—
530C22⋊C8—22no—
531C22⋊C8—614no—
532#97—1222no—
533C4×C8—1222no—
534#95—21no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—21no—
540C24D4×D6111yescharacteristic
541#41—28no—
542#41—28no—
543#41—28no—
544#41—28no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—612no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8C2×C4×D6112yes—
555C2×Q8D4×D6112yes—
556C2×Q8#1175822412yes—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C2×C4×D6112yes—
564C2×D4D4×D6112yes—
565C2×D4#1175822412yes—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—1224no—
581C22×C4—1224no—
582C22×C4—1224no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—4881no—
588C22×C4—4881no—
589C22×C4—4881no—
590C22×C4—4881no—
591C22×C4—4881no—
592C22×C4—4881no—
593C22×C4C2×C4×D6112yes—
594C22×C4D4×D6111yescharacteristic
595C22×C4#1175822412yes—
596C22×C4C23×D6111yescharacteristic
597Q16—1228no—
598SD16—1228no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—612no—
606C2×C8—612no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—612no—
616C4⋊C4—612no—
617C4⋊C4—612no—
618C4⋊C4—1222no—
619C4⋊C4—1222no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1224no—
627C4⋊C4—4881no—
628C4⋊C4—2442no—
629C22⋊C4—81no—
630C22⋊C4—1222no—
631C22⋊C4—1222no—
632C22⋊C4—1224no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C42—612no—
636C42—612no—
637C42—1224no—
638C42—1224no—
639C42—1221no—
640C42—1221no—
641C42—4881no—
642C42—2442no—
643C23—22no—
644C23—21no—
645C23—22no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23#1451973712yes—
657C23C2×D4×D6111yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—1222no—
662Q8—1222no—
663Q8—2441no—
664Q8—2441no—
665Q8#1451973714yes—
666D4—216no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4#1451973714yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—612no—
688C2×C4—612no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1221no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—4884no—
704C2×C4—4884no—
705C2×C4—4884no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4#1451973712yes—
715C2×C4C22×C4×D6111yescharacteristic
716C2×C4C2×D4×D6111yescharacteristic
717C2×C4C2×D4×D6111yescharacteristic
718C2×C4C2×#1175822411yescharacteristic
719C2×C4C2×#1175822411yescharacteristic
720C2×C4C2×#1175822411yescharacteristic
721C8—41no—
722C8—41no—
723C8—1222no—
724C8—1222no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—24no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22C2×#1451973711yescharacteristic
740C22#120×D6111yescharacteristic
741C22#1684026811yescharacteristic
742C22#1684056911yescharacteristic
743C22#1684057111yescharacteristic
744C22#1684057211yescharacteristic
745C22#1684057611yescharacteristic
746C4—22no—
747C4—24no—
748C4—81no—
749C4—81no—
750C4—1222no—
751C4—1222no—
752C4—2441no—
753C4—2442no—
754C4—2442no—
755C4—2441no—
756C4—2442no—
757C4—2442no—
758C4C2×#1451973711yescharacteristic
759C4C2×#1451973711yescharacteristic
760C4#1684026811yescharacteristic
761C4#1684026811yescharacteristic
762C2—42no—
763C2—44no—
764C2#2144831811yescharacteristic
765C2#2145466511yescharacteristic
766C2#2145469811yescharacteristic
767C2#2145509311yescharacteristic
768C2#2145513211yescharacteristic
769C2#2145603411yescharacteristic
770C2#2145609711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenter#1788D61
hypocenterC61#21461
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
3. C2×#16839866C2semidirect
4. C2×#16839853C2semidirect
5. #21448497C2semidirect
6. #21446158C2semidirect
7. #21446151C2semidirect
8. #21446124C2semidirect
9. #21446085C2semidirect
10. #21446078C2semidirect
11. #21446011C2semidirect
12. #21445646C2semidirect
13. #103×Dic61C2semidirect
14. #21445587C2semidirect
32. #16839924C4semidirect
70. C2×#11758202C2×C4semidirect
73. C2×#11758200C2×C4semidirect
77. #14519756C2×C4semidirect
122. #14519701C2×C4semidirect
123. #14519698C2×C4semidirect
124. C22⋊#92418C2×C4semidirect
449. C61#21461semidirect

Maximal subgroups

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

subgroupindex
C2×#168402452
C2×#168399242
C2×#168398662
C2×#168398532
#214484972
#214461582
#214461512
#214461242
#214460852
#214460782
#214460112
#214456462
#103×Dic612
#214455872
C61×#17882
#2146161