Finite Group Databasebeta

← #29685636

Subgroups — #29685636

Order 15616.

1480 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic61C211yesmaximal, characteristic
2C2×#16839924C211yesmaximal, characteristic
3C2×#16839854C211yesmaximal, characteristic, complemented
4C2×#16839853C211yesmaximal, characteristic, complemented
5#21448347C211yesmaximal, characteristic, complemented
6#21446158C211yesmaximal, characteristic, complemented
7#21446151C211yesmaximal, characteristic, complemented
8#21446129C211yesmaximal, characteristic, complemented
9#21446085C211yesmaximal, characteristic, complemented
10#21446064C211yesmaximal, characteristic, complemented
11#21446016C211yesmaximal, characteristic, complemented
12#103×Dic61C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic61C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19#41×Dic61—24no—
20#41×Dic61—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#16839854—24no—
34#16839853—24no—
35C2×#14519710C2211yescharacteristic
36C2×#14519708C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C8×Dic61C2211yescharacteristic
43C2×C8×Dic61C2211yescharacteristic
44#16839667C2211yescharacteristic
45#16839658C2211yescharacteristic
46#16839644—21no—
47#16839634—21no—
48C4⋊C4×Dic61C2211yescharacteristic
49#16839613—21no—
50C22⋊C4×Dic61—21no—
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×Dic61D411yescharacteristic
68C23×Dic61D411yescharacteristic
69C2×#11758202—22no—
70C2×#11758202—22no—
71C2×#11758202C2×C414yescomplemented
72C2×#11758200—22no—
73C2×#11758200—22no—
74C2×#11758200C2×C414yescomplemented
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519756—22no—
78#14519756C2×C414yescomplemented
79Q8×Dic61—22no—
80Q8×Dic61—22no—
81Q8×Dic61—22no—
82Q8×Dic61D414yes—
83#14519742—22no—
84#14519742—22no—
85D4×Dic61—28no—
86D4×Dic61—28no—
87D4×Dic61—22no—
88D4×Dic61—22no—
89D4×Dic61—22no—
90D4×Dic61D414yes—
91#14519736—28no—
92#14519736—22no—
93#14519736—22no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C4×Dic61—28no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61—22no—
111C2×C4×Dic61—22no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118#14519710—22no—
119#14519708—22no—
120#14519702—22no—
121#14519702—22no—
122#14519701C2×C414yescomplemented
123#14519698C2×C414yescomplemented
124C22⋊#92418C2×C414yescomplemented
125C8×Dic61—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—24no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—24no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—41no—
200C22×Dic61—42no—
201C22×Dic61—42no—
202C22×Dic61—42no—
203C22×Dic61—42no—
204C22×Dic61C2×D411yescharacteristic
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122C22×C412yes—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C22⋊C4×C61—42no—
225C22⋊Dic61—24no—
226C22⋊Dic61—24no—
227C22⋊Dic61—24no—
228C22⋊Dic61—24no—
229#11758202—28no—
230#11758200—28no—
231C4⋊Dic61—24no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—24no—
236C4⋊Dic61C22×C412yes—
237C4⋊Dic61C2×D412yes—
238C4⋊Dic61C2×D412yes—
239#11758196—24no—
240#11758196—42no—
241#11758196—42no—
242C4×Dic61—24no—
243C4×Dic61—24no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—22no—
247C4×Dic61—24no—
248C4×Dic61—22no—
249C4×Dic61—42no—
250C4×Dic61—42no—
251C4×Dic61C2×D412yes—
252C4×Dic61C2×D412yes—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418C22×C412yes—
258C2×#92418C22×C412yes—
259C23×C61—22no—
260C23×C61—21no—
261C23×C61—22no—
262C23×C61—21no—
263C23×C61—22no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61C4×D412yes—
273C23×C61C22×D411yescharacteristic
274Q8×C61—22no—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61C4×D414yes—
278D4×C61—216no—
279D4×C61—22no—
280D4×C61—22no—
281D4×C61—22no—
282D4×C61C4×D414yes—
283C2×C4×C61—216no—
284C2×C4×C61—22no—
285C2×C4×C61—21no—
286C2×C4×C61—22no—
287C2×C4×C61—21no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61C4×D412yes—
300C2×C4×C61C23×C411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—21no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—44no—
318C2×Dic61—48no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—44no—
328C2×Dic61—48no—
329C2×Dic61#12012yes—
330C2×Dic61#12012yes—
331C2×Dic61#13512yes—
332C2×Dic61#13512yes—
333C2×Dic61#13712yes—
334Dic122—22no—
335Dic122—22no—
336Dic122—41no—
337Dic122—41no—
338C8×C61—41no—
339C8×C61—41no—
340#92418—22no—
341#92418—22no—
342C4×#452—611nomaximal, Sylow
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—24no—
347C22×C61—41no—
348C22×C61—42no—
349C22×C61—41no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—41no—
354C22×C61—42no—
355C22×C61—41no—
356C22×C61—42no—
357C22×C61C2×C4×D411yescharacteristic
358C22×C61C2×#12011yescharacteristic
359C22×C61#52511yescharacteristic
360C22×C61C2×#13511yescharacteristic
361C22×C61C2×#13511yescharacteristic
362C22×C61C2×#13711yescharacteristic
363C22×C61#57511yescharacteristic
364C4×C61—22no—
365C4×C61—24no—
366C4×C61—81no—
367C4×C61—81no—
368C4×C61C2×C4×D411yescharacteristic
369C4×C61C2×C4×D411yescharacteristic
370C4×C61#52511yescharacteristic
371C4×C61#52511yescharacteristic
372Dic61—22no—
373Dic61—22no—
374Dic61—42no—
375Dic61—41no—
376Dic61—42no—
377Dic61—42no—
378Dic61—42no—
379Dic61#45214yescomplemented
380C2×C4×#41—611no—
381C2×#452—611no—
382C2×C4×Q16—611no—
383C2×C4×SD16—611no—
384C4×C22⋊Q8—611no—
385#1878—611no—
386#1877—611no—
387#1873—611no—
388#1865—611no—
389#1862—611no—
390#1854—611no—
391#1788D6111yescharacteristic
392C4×#103—611no—
393C4×#102—611no—
394C4×C22⋊C8—611no—
395C2×C61—42no—
396C2×C61—44no—
397C2×C61C4×#12011yescharacteristic
398C2×C61C4×#13511yescharacteristic
399C2×C61C4×#13711yescharacteristic
400C2×C61C2×#45211yescharacteristic
401C2×C61#300211yescharacteristic
402C2×C61#310211yescharacteristic
403C2×C61#310711yescharacteristic
404C22×#41C2×D6111yescharacteristic
405C22×Q16—611no—
406C22×SD16—611no—
407C2×C22⋊Q8—611no—
408C4×#41—1224no—
409C4×#41—1224no—
410C2×C4×Q8—611no—
411C2×C4×Q8—611no—
412C2×C4×Q8—611no—
413C2×C4×D4—611no—
414C2×C4×D4—611no—
415C2×C4×D4—1221no—
416C2×C4×D4—1221no—
417C2×#117—611no—
418C2×#117—1221no—
419C22×C42—611no—
420C22×C42—1221no—
421#452—618no—
422C4×Q16—1224no—
423C4×SD16—1224no—
424C2×#107—611no—
425C2×#106—611no—
426C2×#103—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#103C2×D6111yescharacteristic
430C2×#103C2×D6111yescharacteristic
431C2×#102—611no—
432C2×#102C2×D6111yescharacteristic
433C2×#102C2×D6111yescharacteristic
434C2×C22⋊C8—611no—
435C2×C22⋊C8C2×D6111yescharacteristic
436C2×C4×C8—611no—
437C2×C4×C8—611no—
438#391—611no—
439#389—611no—
440#387—1221no—
441#385—1221no—
442#380C2×D6111yescharacteristic
443C4×C4⋊C4—611no—
444C4×C4⋊C4—1221no—
445C4×C22⋊C4—1221no—
446#340—611no—
447#340—611no—
448#340—611no—
449#340—611no—
450#336—611no—
451#336—611no—
452C61C4×#45211yescharacteristic, complemented, Sylow
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41C4×D6114yes—
459C22×Q8—611no—
460C22×Q8C22×D6111yescharacteristic
461C22×D4—21no—
462C22×D4C22×D6111yescharacteristic
463C23×C4—21no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4C22×D6111yescharacteristic
469C2×Q16—614no—
470C2×Q16—1222no—
471C2×Q16—1222no—
472C2×SD16—614no—
473C2×SD16—1222no—
474C2×SD16—1222no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8C22×D6111yescharacteristic
478C22×C8C22×D6111yescharacteristic
479C22⋊Q8—614no—
480C22⋊Q8—1222no—
481C4×Q8—614no—
482C4×Q8—1222no—
483C4×Q8—1222no—
484C4×Q8—1222no—
485C4×Q8—1222no—
486C4×Q8—1222no—
487C4×D4—614no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—1228no—
491C4×D4—1228no—
492C4×D4—1222no—
493#117—1222no—
494#117—1222no—
495#117—1228no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C42—611no—
512C2×C42—611no—
513C2×C42—611no—
514C2×C42—611no—
515C2×C42—1222no—
516C2×C42—1222no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42—1228no—
520C2×C42—1221no—
521C2×C42—1221no—
522C2×C42—1221no—
523#107—1222no—
524#106—1222no—
525#103—22no—
526#103—22no—
527#103—614no—
528#103—1222no—
529#103—1222no—
530#102—22no—
531#102—22no—
532#102—614no—
533C22⋊C8—22no—
534C22⋊C8—614no—
535C4×C8—1222no—
536C4×C8—1222no—
537#95—21no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542C24—21no—
543C24D4×D6111yescharacteristic
544#41—28no—
545#41—28no—
546#41—28no—
547#41—28no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—612no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8C2×C4×D6112yes—
558C2×Q8D4×D6112yes—
559C2×Q8#1175822412yes—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4C2×C4×D6112yes—
567C2×D4D4×D6112yes—
568C2×D4#1175822412yes—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—1224no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1224no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—2442no—
595C22×C4—2442no—
596C22×C4—2442no—
597C22×C4—2441no—
598C22×C4—2442no—
599C22×C4C2×C4×D6112yes—
600C22×C4D4×D6111yescharacteristic
601C22×C4#1175822412yes—
602C22×C4C23×D6111yescharacteristic
603Q16—1228no—
604SD16—1228no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—612no—
612C2×C8—612no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—612no—
622C4⋊C4—612no—
623C4⋊C4—612no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1224no—
630C4⋊C4—2442no—
631C4⋊C4—2442no—
632C22⋊C4—42no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C42—612no—
638C42—612no—
639C42—1222no—
640C42—1222no—
641C42—1224no—
642C42—1224no—
643C42—1224no—
644C42—1221no—
645C42—1221no—
646C42—2442no—
647C42—2442no—
648C23—22no—
649C23—21no—
650C23—22no—
651C23—21no—
652C23—22no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23#1451973712yes—
662C23C2×D4×D6111yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—22no—
666Q8—1222no—
667Q8—1222no—
668Q8—2441no—
669Q8—2441no—
670Q8#1451973714yes—
671D4—216no—
672D4—22no—
673D4—22no—
674D4—22no—
675D4#1451973714yes—
676C2×C4—216no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—612no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—612no—
696C2×C4—612no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—2444no—
709C2×C4—2448no—
710C2×C4—2444no—
711C2×C4—2448no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4#1451973712yes—
721C2×C4C22×C4×D6111yescharacteristic
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C2×D4×D6111yescharacteristic
724C2×C4C2×#1175822411yescharacteristic
725C2×C4C2×#1175822411yescharacteristic
726C2×C4C2×#1175822411yescharacteristic
727C8—41no—
728C8—41no—
729C8—1222no—
730C8—1222no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—22no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—42no—
745C22C2×#1451973711yescharacteristic
746C22#120×D6111yescharacteristic
747C22#1684026811yescharacteristic
748C22#135×D6111yescharacteristic
749C22#135×D6111yescharacteristic
750C22#137×D6111yescharacteristic
751C22#1684055811yescharacteristic
752C4—22no—
753C4—24no—
754C4—81no—
755C4—81no—
756C4—614no—
757C4—1222no—
758C4—1222no—
759C4—2442no—
760C4—2441no—
761C4—2442no—
762C4—2442no—
763C4—2442no—
764C4C2×#1451973711yescharacteristic
765C4C2×#1451973711yescharacteristic
766C4#1684026811yescharacteristic
767C4#1684026811yescharacteristic
768C2—42no—
769C2—44no—
770C2#2144831811yescharacteristic
771C2#2145458711yescharacteristic
772C2#2145464311yescharacteristic
773C2#452×D6111yescharacteristic
774C2#2145503411yescharacteristic
775C2#2145583011yescharacteristic
776C2#2145588311yescharacteristic
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
hypocenterC61C4×#452
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×#16839854C2semidirect
4. C2×#16839853C2semidirect
5. #21448347C2semidirect
6. #21446158C2semidirect
7. #21446151C2semidirect
8. #21446129C2semidirect
9. #21446085C2semidirect
10. #21446064C2semidirect
11. #21446016C2semidirect
12. #103×Dic61C2semidirect
13. #102×Dic61C2semidirect
14. C22⋊C8×Dic61C2semidirect
32. #16839924C4semidirect
71. C2×#11758202C2×C4semidirect
74. C2×#11758200C2×C4semidirect
78. #14519756C2×C4semidirect
122. #14519701C2×C4semidirect
123. #14519698C2×C4semidirect
124. C22⋊#92418C2×C4semidirect
379. Dic61#452semidirect
452. C61C4×#452semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic612
C2×#168399242
C2×#168398542
C2×#168398532
#214483472
#214461582
#214461512
#214461292
#214460852
#214460642
#214460162
#103×Dic612
#102×Dic612
C22⋊C8×Dic612
C61×#17882
C4×#45261