Finite Group Databasebeta

← #29828848

Subgroups — #29828848

Order 15616.

1468 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic61C211yesmaximal, characteristic
2C2×#16839970C211yesmaximal, characteristic, complemented
3C2×#16839965C211yesmaximal, characteristic, complemented
4C2×#16839924C211yesmaximal, characteristic
5#21454167C211yesmaximal, characteristic, complemented
6#21446162C211yesmaximal, characteristic, complemented
7#21446158C211yesmaximal, characteristic, complemented
8#21446155C211yesmaximal, characteristic, complemented
9#21446151C211yesmaximal, characteristic, complemented
10#21446132C211yesmaximal, characteristic, complemented
11#21446129C211yesmaximal, characteristic, complemented
12#21445822C211yesmaximal, characteristic, complemented
13#21445817C211yesmaximal, characteristic, complemented
14#21445797C211yesmaximal, characteristic, complemented
15C2×C61×#452C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519775C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20#41×Dic61—24no—
21#41×Dic61—24no—
22C2×Q8×Dic61C2211yescharacteristic
23C2×Q8×Dic61C2211yescharacteristic
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#16839970—24no—
33#16839965—24no—
34#16839924—24no—
35C2×#14519706C2211yescharacteristic
36C2×#14519706C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519701C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44#16839669C2211yescharacteristic
45#16839667C2211yescharacteristic
46#16839657—21no—
47#16839657—21no—
48#16839631C2211yescharacteristic
49#16839620—21no—
50#16839620—21no—
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839516C2211yescharacteristic
56#16839516C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58C22×Q16×C61C2211yescharacteristic
59C22×SD16×C61C2211yescharacteristic
60C2×C22⋊Q8×C61C2211yescharacteristic
61C61×#452—24no—
62C2×#103×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic
64C2×C22⋊C8×C61C2211yescharacteristic
65C22×Dic122C2311yescharacteristic
66C23×Dic61—21no—
67C23×Dic61—21no—
68C23×Dic61D411yescharacteristic
69C23×Dic61D411yescharacteristic
70C2×#11758202—22no—
71C2×#11758202—22no—
72C2×#11758202—22no—
73C2×#11758200—22no—
74C2×#11758200—22no—
75C2×#11758200—22no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78#14519775—22no—
79#14519775—22no—
80#14519756—22no—
81#14519756—22no—
82Q8×Dic61—22no—
83Q8×Dic61—22no—
84Q8×Dic61—22no—
85Q8×Dic61D414yes—
86D4×Dic61—28no—
87D4×Dic61—28no—
88D4×Dic61—22no—
89D4×Dic61—22no—
90D4×Dic61—22no—
91D4×Dic61D414yes—
92#14519736—28no—
93#14519736—22no—
94#14519736—22no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C4×Dic61—28no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61D411yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119#14519706—22no—
120#14519706—22no—
121#14519702—22no—
122#14519702—22no—
123#14519701—22no—
124#14519701—22no—
125#14519701—22no—
126#14519698—22no—
127C22⋊#92418—22no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131#14519684—21no—
132C2×#41×C61—22no—
133C2×#41×C61—22no—
134C2×#41×C61—22no—
135C2×#41×C61—22no—
136C2×#41×C61—22no—
137C2×#41×C61D414yes—
138C22×Q8×C61C2311yescharacteristic
139C22×Q8×C61C2311yescharacteristic
140C22×D4×C61—21no—
141C22×D4×C61C2311yescharacteristic
142C23×C4×C61—21no—
143C23×C4×C61C2311yescharacteristic
144C2×Q16×C61—22no—
145C2×Q16×C61—22no—
146C2×Q16×C61—22no—
147C2×SD16×C61—22no—
148C2×SD16×C61—22no—
149C2×SD16×C61—22no—
150C22×C8×C61C2311yescharacteristic
151C22×C8×C61C2311yescharacteristic
152C22⋊Q8×C61—22no—
153C22⋊Q8×C61—22no—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C22⋊C4×C61—21no—
157#103×C61—22no—
158#102×C61—22no—
159C22⋊C8×C61—22no—
160C24×C61—21no—
161C24×C61C2×D411yescharacteristic
162#41×C61—28no—
163#41×C61—28no—
164#41×C61—28no—
165#41×C61—28no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61C2×D412yes—
176C2×Q8×C61C2×D412yes—
177C2×Q8×C61#4112yes—
178C2×D4×C61—24no—
179C2×D4×C61—24no—
180C2×D4×C61—24no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61C2×D412yes—
185C2×D4×C61C2×D412yes—
186C2×D4×C61#4112yes—
187C22×C4×C61—24no—
188C22×C4×C61—24no—
189C22×C4×C61—21no—
190C22×C4×C61—24no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D412yes—
199C22×C4×C61#4112yes—
200C22×C4×C61C2411yescharacteristic
201C22×Dic61—24no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—24no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—41no—
213C22×Dic61—42no—
214C22×Dic61—42no—
215C22×Dic61—42no—
216C22×Dic61—42no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227Q16×C61—44no—
228SD16×C61—44no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—42no—
238C22⋊C4×C61—42no—
239C22⋊Dic61—24no—
240C22⋊Dic61—24no—
241C22⋊Dic61—24no—
242C22⋊Dic61—42no—
243#11758202—44no—
244#11758200—44no—
245C4⋊Dic61—24no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—24no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61C2×D412yes—
252C4⋊Dic61C2×D412yes—
253#11758196—42no—
254#11758196—42no—
255#11758196—42no—
256#11758196—42no—
257#11758196—42no—
258C4×Dic61—24no—
259C4×Dic61—24no—
260C4×Dic61—21no—
261C4×Dic61—21no—
262C4×Dic61—22no—
263C4×Dic61—24no—
264C4×Dic61—22no—
265C4×Dic61C2×D412yes—
266C4×Dic61C2×D412yes—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C23×C61—21no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—21no—
277C23×C61—22no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61#12112yes—
287C23×C61C22×D411yescharacteristic
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61—41no—
292Q8×C61—41no—
293Q8×C61—41no—
294Q8×C61—41no—
295Q8×C61#12114yes—
296D4×C61—216no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—22no—
300D4×C61#12114yes—
301C2×C4×C61—216no—
302C2×C4×C61—21no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
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#12112yes—
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C2×C4×C61C2×#4111yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—44no—
334C2×Dic61—48no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—44no—
340C2×Dic61—48no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61#12012yes—
348C2×Dic61#12012yes—
349C2×Dic61#13512yes—
350C2×Dic61#13712yes—
351C2×Dic61#13712yes—
352Dic122—41no—
353Dic122—41no—
354Dic122—41no—
355Dic122—41no—
356C8×C61—41no—
357C8×C61—41no—
358#92418—41no—
359#92418—41no—
360#32907—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—24no—
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—41no—
366C22×C61—42no—
367C22×C61—41no—
368C22×C61—42no—
369C22×C61—41no—
370C22×C61—42no—
371C22×C61—41no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61C2×#12011yescharacteristic
376C22×C61C2×#12111yescharacteristic
377C22×C61#52511yescharacteristic
378C22×C61C2×#13511yescharacteristic
379C22×C61C2×#13711yescharacteristic
380C22×C61C2×#13711yescharacteristic
381C22×C61#57511yescharacteristic
382C4×C61—22no—
383C4×C61—24no—
384C4×C61—81no—
385C4×C61—81no—
386C4×C61C2×#12111yescharacteristic
387C4×C61C2×#12111yescharacteristic
388C4×C61#52511yescharacteristic
389C4×C61#52511yescharacteristic
390Dic61—22no—
391Dic61—22no—
392Dic61—41no—
393Dic61—42no—
394Dic61—42no—
395Dic61—81no—
396Dic61—81no—
397Dic61#45214yescomplemented
398C2×C4×#41—611no—
399C2×#462—611no—
400C2×#461—611no—
401C2×#452—611no—
402C2×#452D6111yescharacteristic
403#2857—611no—
404#1878—611no—
405#1878—611no—
406#1877—611no—
407#1877—611no—
408#1873—611no—
409#1873—611no—
410#1803—611no—
411#1802—611no—
412#1797—611no—
413C2×C61—42no—
414C2×C61—44no—
415C2×C61#284711yescharacteristic
416C2×C61C2×#45211yescharacteristic
417C2×C61#300711yescharacteristic
418C2×C61#303511yescharacteristic
419C2×C61#303911yescharacteristic
420C2×C61#310711yescharacteristic
421C2×C61#311611yescharacteristic
422C22×#41C2×D6111yescharacteristic
423C22×Q16—611no—
424C22×Q16C2×D6111yescharacteristic
425C22×SD16—611no—
426C22×SD16C2×D6111yescharacteristic
427C2×C4⋊Q8—611no—
428C2×C22⋊Q8—611no—
429C2×C22⋊Q8C2×D6111yescharacteristic
430C4×#41—1224no—
431C4×#41—1224no—
432C2×C4×Q8—611no—
433C2×C4×Q8—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—1221no—
437C2×C4×D4—1221no—
438C2×#117—611no—
439C2×#117—1221no—
440C22×C42—611no—
441C22×C42—1221no—
442#462—1224no—
443#461—1224no—
444#452—24no—
445#452—1224no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103C2×D6111yescharacteristic
454C2×#102—611no—
455C2×#102C2×D6111yescharacteristic
456C2×C22⋊C8—611no—
457C2×C22⋊C8C2×D6111yescharacteristic
458#391—611no—
459#391—611no—
460#389—1221no—
461#389—1221no—
462#384—611no—
463#380—1221no—
464#380—1221no—
465#340—611no—
466#340—611no—
467#340—611no—
468#340—611no—
469#336—611no—
470#336—611no—
471C61#3290711yescharacteristic, complemented, Sylow
472C2×#41—22no—
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41C22⋊D6114yes—
478C22×Q8—611no—
479C22×Q8C22×D6111yescharacteristic
480C22×Q8C22×D6111yescharacteristic
481C22×D4—21no—
482C22×D4C22×D6111yescharacteristic
483C23×C4—21no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—1221no—
487C23×C4—1221no—
488C23×C4C22×D6111yescharacteristic
489C2×Q16—22no—
490C2×Q16—22no—
491C2×Q16—22no—
492C2×Q16—1222no—
493C2×Q16—1222no—
494C2×Q16—1222no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—1222no—
499C2×SD16—1222no—
500C2×SD16—1222no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505C4⋊Q8—1222no—
506C4⋊Q8—1222no—
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—1222no—
510C22⋊Q8—1222no—
511C4×Q8—614no—
512C4×Q8—1222no—
513C4×Q8—1222no—
514C4×Q8—1222no—
515C4×D4—614no—
516C4×D4—1222no—
517C4×D4—1222no—
518C4×D4—1228no—
519C4×D4—1228no—
520C4×D4—1222no—
521#117—1222no—
522#117—1222no—
523#117—1228no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4C22×D6111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C42—611no—
542C2×C42—611no—
543C2×C42—611no—
544C2×C42—611no—
545C2×C42—1222no—
546C2×C42—1222no—
547C2×C42—1221no—
548C2×C42—1221no—
549C2×C42—1228no—
550C2×C42—1221no—
551C4⋊C8—1222no—
552C4⋊C8—1222no—
553#103—22no—
554#103—1222no—
555#103—1222no—
556#103—1222no—
557#103—1222no—
558#103—1222no—
559#102—22no—
560#102—1222no—
561C22⋊C8—22no—
562C22⋊C8—1222no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566#95—1221no—
567C24—21no—
568C24D4×D6111yescharacteristic
569#41—28no—
570#41—28no—
571#41—28no—
572#41—28no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—1221no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8D4×D6112yes—
589C2×Q8#1175822412yes—
590C2×Q8C2×C22⋊D6112yes—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—24no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4D4×D6112yes—
598C2×D4#1175822412yes—
599C2×D4C2×C22⋊D6112yes—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—1224no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1224no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4—2441no—
629C22×C4—2442no—
630C22×C4D4×D6111yescharacteristic
631C22×C4#1175822412yes—
632C22×C4C2×C22⋊D6112yes—
633C22×C4C23×D6111yescharacteristic
634Q16—44no—
635Q16—2444no—
636SD16—44no—
637SD16—2444no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—612no—
654C4⋊C4—612no—
655C4⋊C4—1224no—
656C4⋊C4—1224no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—2442no—
662C4⋊C4—2442no—
663C4⋊C4—2442no—
664C4⋊C4—2442no—
665C4⋊C4—2442no—
666C22⋊C4—42no—
667C22⋊C4—1224no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—2442no—
671C42—612no—
672C42—612no—
673C42—1222no—
674C42—1222no—
675C42—1224no—
676C42—1224no—
677C42—1224no—
678C42—1221no—
679C42—1221no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—21no—
684C23—22no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23#1451974912yes—
694C23C2×D4×D6111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—41no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702Q8—2441no—
703Q8—2441no—
704Q8—2441no—
705Q8—2441no—
706Q8#1451974914yes—
707D4—216no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4#1451974914yes—
712C2×C4—216no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—612no—
729C2×C4—612no—
730C2×C4—612no—
731C2×C4—612no—
732C2×C4—612no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—2444no—
743C2×C4—2448no—
744C2×C4—2444no—
745C2×C4—2448no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4#1451974912yes—
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C2×C4C22×C22⋊D6111yescharacteristic
760C2×C4C2×#1175822411yescharacteristic
761C2×C4C2×#1175822411yescharacteristic
762C2×C4C2×#1175822411yescharacteristic
763C8—41no—
764C8—41no—
765C8—2441no—
766C8—2441no—
767C22—22no—
768C22—24no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22#120×D6111yescharacteristic
782C22C2×#1451974911yescharacteristic
783C22#1684026811yescharacteristic
784C22#135×D6111yescharacteristic
785C22#137×D6111yescharacteristic
786C22#137×D6111yescharacteristic
787C22#1684055911yescharacteristic
788C4—22no—
789C4—24no—
790C4—81no—
791C4—81no—
792C4—614no—
793C4—1222no—
794C4—1222no—
795C4—4881no—
796C4—4881no—
797C4—2441no—
798C4—2442no—
799C4—2442no—
800C4C2×#1451974911yescharacteristic
801C4C2×#1451974911yescharacteristic
802C4#1684026811yescharacteristic
803C4#1684026811yescharacteristic
804C2—42no—
805C2—44no—
806C2#2145409911yescharacteristic
807C2#452×D6111yescharacteristic
808C2#2145507611yescharacteristic
809C2#2145527011yescharacteristic
810C2#2145530411yescharacteristic
811C2#2145588311yescharacteristic
812C2#2145597411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
hypercenterC2×#452D61
hypocenterC61#32907
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#16839970C2semidirect
3. C2×#16839965C2semidirect
5. #21454167C2semidirect
6. #21446162C2semidirect
7. #21446158C2semidirect
8. #21446155C2semidirect
9. #21446151C2semidirect
10. #21446132C2semidirect
11. #21446129C2semidirect
12. #21445822C2semidirect
13. #21445817C2semidirect
14. #21445797C2semidirect
397. Dic61#452semidirect
471. C61#32907semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic612
C2×#168399702
C2×#168399652
C2×#168399242
#214541672
#214461622
#214461582
#214461552
#214461512
#214461322
#214461292
#214458222
#214458172
#214457972
C2×C61×#4522
#3290761