Finite Group Databasebeta

← #29700739

Subgroups — #29700739

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic61C211yesmaximal, characteristic, complemented
2C2×#16839771C211yesmaximal, characteristic, complemented
3#21448861C211yesmaximal, characteristic
4Q8×C22⋊Dic61C211yesmaximal, characteristic, complemented
5#21446702C211yesmaximal, characteristic, complemented
6#21446497C211yesmaximal, characteristic, complemented
7#21446455C211yesmaximal, characteristic, complemented
8#21446258C211yesmaximal, characteristic
9#21446176C211yesmaximal, characteristic, complemented
10#21446155C211yesmaximal, characteristic, complemented
11#21446075C211yesmaximal, characteristic, complemented
12#21446020C211yesmaximal, characteristic, complemented
13#21445651C211yesmaximal, characteristic, complemented
14#21445605C211yesmaximal, characteristic, complemented
15C2×C61×#448C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C2×Q8×Dic61C2211yescharacteristic
18C2×Q8×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21SD16×Dic61—24no—
22C2×#14519711C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24#16839771—24no—
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839669—21no—
34#16839669—21no—
35#16839669C2211yescharacteristic
36#16839669C2211yescharacteristic
37#16839665—21no—
38#16839665C2211yescharacteristic
39#16839661C2211yescharacteristic
40#16839655—21no—
41#16839642—21no—
42#16839622—21no—
43#16839622C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C22⋊C4×Dic61—21no—
46C4×C22⋊Dic61—21no—
47C4×C22⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C23×Q8×C61C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C22×SD16×C61C2211yescharacteristic
57C2×#121×C61C2211yescharacteristic
58C61×#448C418yescomplemented
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C23×Dic61—21no—
63C2×#11758194—22no—
64C2×#11758194—22no—
65C2×#11758194—41no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68Q8×Dic61—22no—
69Q8×Dic61—22no—
70Q8×Dic61—41no—
71Q8×Dic61—41no—
72D4×Dic61—22no—
73D4×Dic61—41no—
74#14519736—22no—
75#14519736—41no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61D411yescharacteristic
89C2×C22⋊Dic61D411yescharacteristic
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61C2311yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96#14519711—41no—
97#14519709—22no—
98#14519701—22no—
99#14519701—22no—
100#14519701—22no—
101#14519701D414yescomplemented
102#14519698—22no—
103#14519698—41no—
104#14519687—41no—
105C8×Dic61—22no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684D411yescharacteristic
114#14519684D411yescharacteristic
115C22×Q8×C61—21no—
116C22×Q8×C61—22no—
117C22×Q8×C61—22no—
118C22×Q8×C61—22no—
119C22×Q8×C61—41no—
120C22×Q8×C61—41no—
121C22×Q8×C61C2×C414yescomplemented
122C22×Q8×C61C2311yescharacteristic
123C22×Q8×C61C2311yescharacteristic
124C22×D4×C61—21no—
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61C2311yescharacteristic
128C2×SD16×C61—22no—
129C2×SD16×C61—22no—
130C2×SD16×C61—41no—
131C2×SD16×C61—41no—
132C2×SD16×C61C2×C414yes—
133C2×SD16×C61C2×C414yes—
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136#121×C61—22no—
137#121×C61C2×C414yes—
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140#103×C61C2×C414yescomplemented
141#103×C61C2×C414yescomplemented
142C22⋊C8×C61C2×C414yescomplemented
143C24×C61—21no—
144C24×C61C2×D411yescharacteristic
145C2×Q8×C61—24no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—28no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—42no—
156C2×Q8×C61—42no—
157C2×Q8×C61—44no—
158C2×Q8×C61—44no—
159C2×Q8×C61—44no—
160C2×Q8×C61C22×C412yes—
161C2×Q8×C61C22×C412yes—
162C2×Q8×C61C2×D412yes—
163C2×Q8×C61#4112yes—
164C2×D4×C61—24no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—81no—
171C2×D4×C61—81no—
172C2×D4×C61C22×C412yes—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—24no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—42no—
182C22×C4×C61—42no—
183C22×C4×C61C22×C412yes—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61#4112yes—
186C22×C4×C61C2411yescharacteristic
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—42no—
192C22×Dic61—42no—
193C22×Dic61—81no—
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198SD16×C61—28no—
199SD16×C61—44no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61C22×C412yes—
205C2×C8×C61C22×C412yes—
206C4⋊C4×C61—21no—
207C4⋊C4×C61C22×C412yes—
208C22⋊C4×C61—24no—
209C22⋊Dic61—22no—
210C22⋊Dic61—41no—
211C22⋊Dic61—42no—
212C22⋊Dic61—42no—
213C22⋊Dic61—42no—
214C22⋊Dic61—42no—
215C22⋊Dic61—81no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—42no—
224C4⋊Dic61—42no—
225C4⋊Dic61—81no—
226C4⋊Dic61C2×D412yes—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—42no—
232C4×Dic61—42no—
233C4×Dic61—42no—
234C4×Dic61—81no—
235#11758194—44no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418C2×D412yes—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—22no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61C4×D412yes—
256C23×C61C22×D411yescharacteristic
257Q8×C61—22no—
258Q8×C61—22no—
259Q8×C61—22no—
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—48no—
263Q8×C61—41no—
264Q8×C61—41no—
265Q8×C61C4×D414yes—
266D4×C61—22no—
267D4×C61—22no—
268D4×C61—41no—
269D4×C61—41no—
270D4×C61—84no—
271C2×C4×C61—22no—
272C2×C4×C61—21no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—21no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—48no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61C4×D412yes—
288C2×C4×C61C23×C411yescharacteristic
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—22no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—84no—
318C2×Dic61#13712yes—
319C8×C61—22no—
320C8×C61—22no—
321#92418—22no—
322#92418—41no—
323#22885—611nomaximal, Sylow
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61C2×C4×D411yescharacteristic
339C22×C61D4211yescharacteristic
340C22×C61#54611yescharacteristic
341C22×C61C2×#13711yescharacteristic
342C22×C61#57511yescharacteristic
343C22×C61#57711yescharacteristic
344C22×C61#57711yescharacteristic
345C4×C61—22no—
346C4×C61—24no—
347C4×C61—42no—
348C4×C61—42no—
349C4×C61C2×C4×D411yescharacteristic
350C4×C61#51811yescharacteristic
351C4×C61#54611yescharacteristic
352C4×C61#55111yescharacteristic
353Dic61—22no—
354Dic61—41no—
355Dic61—42no—
356Dic61—41no—
357Dic61—41no—
358Dic61—81no—
359Dic61—81no—
360Dic61—81no—
361C2×#448D6111yescharacteristic
362C2×C4×SD16—611no—
363C2×#419—611no—
364#2363—611no—
365Q8×C22⋊C4—611no—
366#1973—611no—
367#1933—611no—
368#1927—611no—
369#1895—611no—
370#1880—611no—
371#1877—611no—
372#1863—611no—
373#1854—611no—
374#1763—611no—
375#1753—611no—
376C2×C61—42no—
377C2×C61—82no—
378C2×C61#235811yescharacteristic
379C2×C61C4×#13711yescharacteristic
380C2×C61#294911yescharacteristic
381C2×C61#326611yescharacteristic
382C2×C61#327111yescharacteristic
383C2×C61#332611yescharacteristic
384C2×C61#332911yescharacteristic
385C23×Q8C2×D6111yescharacteristic
386C22×SD16C2×D6111yescharacteristic
387C22×SD16C2×D6111yescharacteristic
388C22×M16—611no—
389C2×#121C2×D6111yescharacteristic
390C2×C4×Q8—611no—
391C2×C4×Q8—611no—
392C2×C4×D4—611no—
393C2×#117—611no—
394#448Dic6118yescomplemented
395C4×SD16—1224no—
396C2×#107—611no—
397C2×#106—611no—
398#419—1224no—
399C2×#103—611no—
400C2×#103—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103C2×D6111yescharacteristic
404C2×#103C2×D6111yescharacteristic
405C2×#102—611no—
406C2×#102—611no—
407C2×C22⋊C8C2×D6111yescharacteristic
408C2×#97—611no—
409C2×C4×C8—611no—
410#391—611no—
411#391—611no—
412#391—1221no—
413#391—1221no—
414#390—611no—
415#390—1221no—
416#389—611no—
417#388—1221no—
418#386—1221no—
419#380—611no—
420#380—1221no—
421C4×C4⋊C4—611no—
422C4×C22⋊C4—611no—
423C4×C22⋊C4—1221no—
424C4×C22⋊C4—1221no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#336—611no—
430#336—611no—
431C61#2288511yescharacteristic, complemented, Sylow
432C22×Q8—21no—
433C22×Q8—22no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—41no—
437C22×Q8—41no—
438C22×Q8C2×Dic6114yescomplemented
439C22×Q8C22×D6111yescharacteristic
440C22×Q8C22×D6111yescharacteristic
441C22×D4—21no—
442C22×D4C22×D6111yescharacteristic
443C23×C4—21no—
444C23×C4—1221no—
445C23×C4C22×D6111yescharacteristic
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—41no—
449C2×SD16—41no—
450C2×SD16C2×Dic6114yes—
451C2×SD16C2×Dic6114yes—
452C2×M16—1222no—
453C2×M16—1222no—
454C2×M16—2441no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8C22×D6111yescharacteristic
458C22×C8C22×D6111yescharacteristic
459#121—22no—
460#121C2×Dic6114yes—
461C4×Q8—1222no—
462C4×Q8—1222no—
463C4×Q8—2441no—
464C4×Q8—2441no—
465C4×D4—1222no—
466C4×D4—2441no—
467#117—1222no—
468#117—2441no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—1221no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42—1221no—
491#107—2441no—
492#106—1222no—
493#103—614no—
494#103—1222no—
495#103—1222no—
496#103—1222no—
497#103C2×Dic6114yescomplemented
498#103C2×Dic6114yescomplemented
499#102—1222no—
500#102—2441no—
501C22⋊C8C2×Dic6114yescomplemented
502#97—2441no—
503C4×C8—1222no—
504#95—611no—
505#95—611no—
506#95—1221no—
507#95—1221no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513C24—21no—
514C24D4×D6111yescharacteristic
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—24no—
520C2×Q8—28no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8D4×D6112yes—
531C2×Q8#1175822412yes—
532C2×Q8C22×Dic6112yes—
533C2×Q8C22×Dic6112yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—81no—
541C2×D4—81no—
542C2×D4C22×Dic6112yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—4881no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4D4×D6111yescharacteristic
565C22×C4#1175822412yes—
566C22×C4C22×Dic6112yes—
567C22×C4C23×D6111yescharacteristic
568SD16—28no—
569SD16—44no—
570M16—2444no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—612no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8C22×Dic6112yes—
582C2×C8C22×Dic6112yes—
583C4⋊C4—21no—
584C4⋊C4—612no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—4881no—
593C4⋊C4—2442no—
594C4⋊C4—2442no—
595C4⋊C4C22×Dic6112yes—
596C22⋊C4—24no—
597C22⋊C4—1222no—
598C22⋊C4—4881no—
599C22⋊C4—2441no—
600C22⋊C4—2442no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C22⋊C4—2442no—
604C42—1221no—
605C42—1221no—
606C42—1221no—
607C42—1221no—
608C42—4881no—
609C42—2442no—
610C42—2442no—
611C42—2442no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—22no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23D4×Dic6112yes—
626C23C2×D4×D6111yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—48no—
633Q8—41no—
634Q8—41no—
635Q8D4×Dic6114yes—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—84no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—612no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1222no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—4884no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4D4×Dic6112yes—
683C2×C4C23×Dic6111yescharacteristic
684C2×C4C2×D4×D6111yescharacteristic
685C2×C4C2×#1175822411yescharacteristic
686C2×C4C2×#1175822411yescharacteristic
687C2×C4#1451982211yescharacteristic
688C2×C4#1451982211yescharacteristic
689C8—22no—
690C8—22no—
691C8—1222no—
692C8—2441no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22C2×D4×Dic6111yescharacteristic
708C22#1684039411yescharacteristic
709C22#1684039911yescharacteristic
710C22#137×D6111yescharacteristic
711C22#1684056111yescharacteristic
712C22#1684056811yescharacteristic
713C22#1684056811yescharacteristic
714C4—22no—
715C4—24no—
716C4—42no—
717C4—42no—
718C4—1222no—
719C4—4881no—
720C4—4881no—
721C4—4881no—
722C4—2441no—
723C4—2442no—
724C4—2441no—
725C4—2441no—
726C4C2×D4×Dic6111yescharacteristic
727C4#1684023711yescharacteristic
728C4#1684039911yescharacteristic
729C4#1684044311yescharacteristic
730C2—42no—
731C2—82no—
732C2#2144880311yescharacteristic
733C2#137×Dic6111yescharacteristic
734C2#2145467911yescharacteristic
735C2#2145733211yescharacteristic
736C2#2145740711yescharacteristic
737C2#2145807611yescharacteristic
738C2#2145810611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#448C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#448D61
hypocenterC61#22885
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic61C2semidirect
2. C2×#16839771C2semidirect
4. Q8×C22⋊Dic61C2semidirect
5. #21446702C2semidirect
6. #21446497C2semidirect
7. #21446455C2semidirect
9. #21446176C2semidirect
10. #21446155C2semidirect
11. #21446075C2semidirect
12. #21446020C2semidirect
13. #21445651C2semidirect
14. #21445605C2semidirect
58. C61×#448C4semidirect
101. #14519701D4semidirect
121. C22×Q8×C61C2×C4semidirect
140. #103×C61C2×C4semidirect
141. #103×C61C2×C4semidirect
142. C22⋊C8×C61C2×C4semidirect
394. #448Dic61semidirect
431. C61#22885semidirect
438. C22×Q8C2×Dic61semidirect
497. #103C2×Dic61semidirect
498. #103C2×Dic61semidirect
501. C22⋊C8C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic612
C2×#168397712
#214488612
Q8×C22⋊Dic612
#214467022
#214464972
#214464552
#214462582
#214461762
#214461552
#214460752
#214460202
#214456512
#214456052
C2×C61×#4482
#2288561