Finite Group Databasebeta

← #29713921

Subgroups — #29713921

Order 15616.

1218 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, characteristic, complemented
2C2×#16840050C211yesmaximal, characteristic, complemented
3C2×SD16×Dic61C211yesmaximal, characteristic, complemented
4#21450733C211yesmaximal, characteristic
5#21447014C211yesmaximal, characteristic, complemented
6#21447012C211yesmaximal, characteristic, complemented
7#21446819C211yesmaximal, characteristic, complemented
8#21446778C211yesmaximal, characteristic, complemented
9#21446611C211yesmaximal, characteristic, complemented
10#21446137C211yesmaximal, characteristic, complemented
11#21446133C211yesmaximal, characteristic, complemented
12#21446014C211yesmaximal, characteristic, complemented
13#21446013C211yesmaximal, characteristic, complemented
14#21445822C211yesmaximal, characteristic, complemented
15C61×#2000C211yesmaximal, characteristic, complemented
16#16840470—24no—
17#16840470—24no—
18C2×#14519776C2211yescharacteristic
19C2×#14519767—21no—
20C2×#14519757—21no—
21C2×#14519754—21no—
22C2×#14519753C2211yescharacteristic
23C2×#14519749—21no—
24C2×#14519748C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519737—21no—
29C22×C4⋊Dic61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31#16840050—24no—
32SD16×Dic61—24no—
33C2×#14519709C2211yescharacteristic
34C2×#14519709C2211yescharacteristic
35C2×#14519708C2211yescharacteristic
36C2×#14519706C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×C8×Dic61C2211yescharacteristic
45#16839677—21no—
46#16839676—21no—
47#16839631C2211yescharacteristic
48#16839622C2211yescharacteristic
49#16839620—21no—
50#16839619C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C22×SD16×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122—21no—
64C22×C22⋊D61—21no—
65C22×C22⋊D61D411yescharacteristic
66C23×Dic61—21no—
67C23×Dic61—21no—
68C22×C4×D61—21no—
69C22×C4×D61C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519776—22no—
73#14519776D414yescomplemented
74#14519767—28no—
75#14519757—28no—
76#14519754—28no—
77#14519753—22no—
78#14519753—22no—
79#14519749—44no—
80#14519748—22no—
81#14519748—41no—
82Q8×Dic61—22no—
83Q8×Dic61D414yescomplemented
84D4×Dic61—22no—
85D4×Dic61—22no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88#14519737—28no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61—22no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196D411yescharacteristic
103C4⋊C4×D61—22no—
104C4⋊C4×D61—22no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61D411yescharacteristic
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198D411yescharacteristic
112C2×C4×Dic61—21no—
113C2×C4×Dic61C2311yescharacteristic
114#14519709—22no—
115#14519709—22no—
116#14519708—22no—
117#14519706—22no—
118#14519701—22no—
119#14519701—41no—
120#14519698—22no—
121#14519698—22no—
122C22⋊#92418—41no—
123#14519689—22no—
124#14519689—41no—
125C8×Dic61—22no—
126#14519684—21no—
127#14519684—21no—
128C22×Q8×C61C2311yescharacteristic
129C22×D4×C61—21no—
130C22×D4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C2×SD16×C61—22no—
133C2×SD16×C61—22no—
134C2×SD16×C61—22no—
135C22×C8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C22⋊Q8×C61—22no—
138C22⋊Q8×C61—22no—
139#121×C61—22no—
140#121×C61—41no—
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146#103×C61—41no—
147#102×C61—22no—
148C22⋊C8×C61—22no—
149C24×C61—21no—
150C24×C61C2×D411yescharacteristic
151C23×D61C2×D411yescharacteristic
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61C2×D412yes—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61—81no—
166C2×D4×C61#4112yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2411yescharacteristic
178C2×C22⋊D61—22no—
179C2×C22⋊D61—22no—
180C2×C22⋊D61—42no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—81no—
183C2×C22⋊D61SD1614yescomplemented
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—24no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—42no—
190C22×Dic61—42no—
191C22×Dic61—42no—
192C22×Dic61—81no—
193C22×Dic61—81no—
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—24no—
204C2×C4×D61—81no—
205C2×C4×D61—81no—
206C2×Dic122—24no—
207C2×Dic122—81no—
208C2×Dic122—81no—
209SD16×C61—28no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61#4112yes—
216C4⋊C4×C61—24no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61C2×D412yes—
221C22⋊C4×C61—24no—
222C22⋊C4×C61—42no—
223C22⋊Dic61—22no—
224C22⋊Dic61—42no—
225C22⋊Dic61—42no—
226C22⋊Dic61—42no—
227#11758198—24no—
228#11758198—22no—
229#11758198—42no—
230C4⋊Dic61—24no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—24no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61C2×D412yes—
239C4⋊Dic61C2×D412yes—
240#11758196—24no—
241#11758196—24no—
242#11758196—24no—
243#11758196—22no—
244#11758196—42no—
245#11758196—81no—
246C4×Dic61—24no—
247C4×Dic61C2×D412yes—
248C4×Dic61C2×D412yes—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—22no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61C2×SD1612yes—
269C23×C61C22×D411yescharacteristic
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61C2×SD1612yes—
277Q8×C61—22no—
278Q8×C61—22no—
279Q8×C61—41no—
280Q8×C61—41no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—41no—
284D4×C61—41no—
285D4×C61—84no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
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×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C612−1+411yescharacteristic
308C22⋊D61—28no—
309C22⋊D61—84no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—22no—
313C2×Dic61—21no—
314C2×Dic61—22no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—41no—
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—41no—
327C2×Dic61—84no—
328C2×Dic61—84no—
329C2×Dic61#12012yes—
330C2×Dic61#12012yes—
331C2×Dic61C2×SD1612yes—
332C2×Dic61#13712yes—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—84no—
338Dic122—84no—
339C8×C61—22no—
340C8×C61—41no—
341#92418—41no—
342#92418—41no—
343#24118—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—81no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61C2×#12011yescharacteristic
359C22×C61#54611yescharacteristic
360C22×C61#54711yescharacteristic
361C22×C61C22×SD1611yescharacteristic
362C22×C61C2×#13711yescharacteristic
363C22×C61#57611yescharacteristic
364C22×C61#57711yescharacteristic
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C4×C61—41no—
373C4×C61—42no—
374C4×C61—42no—
375C4×C61—81no—
376C4×C61#52511yescharacteristic
377C4×C61#53711yescharacteristic
378C4×C61#54811yescharacteristic
379C4×C61#55011yescharacteristic
380Dic61—22no—
381Dic61—41no—
382Dic61—42no—
383Dic61—42no—
384Dic61—81no—
385Dic61—81no—
386Dic61#44814yes—
387C2×#554—611no—
388C2×#476—611no—
389C2×C4×SD16—611no—
390#2537—611no—
391#2035—611no—
392#2035—611no—
393#2000—611no—
394#2000D6111yescharacteristic, complemented
395#1990—611no—
396#1954—611no—
397#1874—611no—
398#1874—611no—
399#1853—611no—
400#1853—611no—
401#1803—611no—
402C2×C61—42no—
403C2×C61—82no—
404C2×C61#240711yescharacteristic
405C2×C61C2×#44811yescharacteristic
406C2×C61#301211yescharacteristic
407C2×C61#329511yescharacteristic
408C2×C61#333111yescharacteristic
409C2×C61#333511yescharacteristic
410C2×C61#335711yescharacteristic
411D61—42no—
412C22×SD16C2×D6111yescharacteristic
413#554—1224no—
414#554—1224no—
415C2×C4⋊Q8—611no—
416C2×#125—1221no—
417C2×C22⋊Q8—611no—
418C2×C22⋊Q8—1221no—
419C2×C22⋊Q8—1221no—
420C2×C22⋊Q8C2×D6111yescharacteristic
421C2×#121—611no—
422C2×#121—1221no—
423C2×#121C2×D6111yescharacteristic
424C2×C4×Q8—611no—
425C2×C4×D4—611no—
426C2×C4×D4—611no—
427C2×C4×D4—1221no—
428C22×C4⋊C4—611no—
429C22×C4⋊C4—611no—
430#476—1224no—
431C4×SD16—1224no—
432C2×#106—611no—
433C2×#106—611no—
434C2×#106—611no—
435C2×C4⋊C8—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103C2×D6111yescharacteristic
439C2×#102—611no—
440C2×#102—611no—
441C2×#102C2×D6111yescharacteristic
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8C2×D6111yescharacteristic
446C2×C4×C8—611no—
447#394—1221no—
448#394—1221no—
449#384—611no—
450#380—611no—
451#380—611no—
452#380—1221no—
453#340—611no—
454#340—611no—
455#340—611no—
456#340—611no—
457#340—611no—
458#340C2×D6111yescharacteristic
459C61#2411811yescharacteristic, complemented, Sylow
460C22×Q8—1221no—
461C22×Q8C22×D6111yescharacteristic
462C22×D4—21no—
463C22×D4—611no—
464C22×D4—1221no—
465C22×D4C22×D6111yescharacteristic
466C23×C4—611no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4—1221no—
470C23×C4C22×D6111yescharacteristic
471C2×SD16—22no—
472C2×SD16—22no—
473C2×SD16—22no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8C22×D6111yescharacteristic
477C22×C8C22×D6111yescharacteristic
478C4⋊Q8—614no—
479C4⋊Q8—1222no—
480#125—1228no—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8—1228no—
484C22⋊Q8—1228no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487#121—22no—
488#121—41no—
489#121—1222no—
490#121—2441no—
491#121—2444no—
492C4×Q8—614no—
493C4×Q8—1222no—
494C4×D4—1222no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1228no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4—1222no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1222no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4C22×D6111yescharacteristic
517C2×C4⋊C4C22×D6111yescharacteristic
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C42—611no—
528C2×C42—1221no—
529#106—1222no—
530#106—1222no—
531#106—1222no—
532C4⋊C8—1222no—
533#103—41no—
534#103—1222no—
535#103—2441no—
536#102—22no—
537#102—1222no—
538#102—1222no—
539C22⋊C8—22no—
540C22⋊C8—1222no—
541C22⋊C8—2441no—
542C22⋊C8—2441no—
543C4×C8—1222no—
544#95—1221no—
545#95—1221no—
546C24—21no—
547C24—611no—
548C24D4×D6111yescharacteristic
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—1224no—
555C2×Q8—4881no—
556C2×Q8—4881no—
557C2×Q8D4×D6112yes—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—81no—
566C2×D4—614no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—4881no—
570C2×D4—2442no—
571C2×D4—2442no—
572C2×D4#1175822412yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—1224no—
586C22×C4—1224no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—4881no—
598C22×C4—4881no—
599C22×C4—4881no—
600C22×C4—4881no—
601C22×C4—2442no—
602C22×C4—2442no—
603C22×C4—2442no—
604C22×C4D4×D6111yescharacteristic
605C22×C4C23×D6111yescharacteristic
606SD16—28no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8#1175822412yes—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—612no—
624C4⋊C4—612no—
625C4⋊C4—1222no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—4881no—
638C4⋊C4—2442no—
639C4⋊C4D4×D6112yes—
640C22⋊C4—24no—
641C22⋊C4—42no—
642C22⋊C4—1222no—
643C22⋊C4—1224no—
644C22⋊C4—1222no—
645C22⋊C4—2442no—
646C22⋊C4—2442no—
647C22⋊C4—2442no—
648C22⋊C4—2442no—
649C42—612no—
650C42—612no—
651C42—1224no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—612no—
666C23—1221no—
667C23—1221no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23SD16×D6112yes—
673C23C2×D4×D6111yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—41no—
677Q8—41no—
678Q8—4884no—
679D4—22no—
680D4—22no—
681D4—41no—
682D4—41no—
683D4—84no—
684D4—1228no—
685D4—4884no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—612no—
703C2×C4—612no—
704C2×C4—612no—
705C2×C4—612no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—4884no—
714C2×C4—4884no—
715C2×C4—4884no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4C2×D4×D6111yescharacteristic
731C2×C4C2×D4×D6111yescharacteristic
732C2×C4C2×#1175822411yescharacteristic
733C2×C4C2×#1175822411yescharacteristic
734C2×C4#1451982211yescharacteristic
735C2×C4#1451982411yescharacteristic
736C8—22no—
737C8—41no—
738C8—2441no—
739C8—2441no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—1222no—
755C22—1222no—
756C22—1222no—
757C22—2441no—
758C22—2441no—
759C22—2441no—
760C22—2441no—
761C22#120×D6111yescharacteristic
762C22#1684039911yescharacteristic
763C22#1684041211yescharacteristic
764C22C2×SD16×D6111yescharacteristic
765C22#137×D6111yescharacteristic
766C22#1684056611yescharacteristic
767C22#1684056911yescharacteristic
768C4—42no—
769C4—41no—
770C4—42no—
771C4—81no—
772C4—614no—
773C4—1222no—
774C4—4881no—
775C4—4881no—
776C4—2442no—
777C4—2442no—
778C4—2441no—
779C4#1684026811yescharacteristic
780C4#1684033911yescharacteristic
781C4#1684041811yescharacteristic
782C4#1684043211yescharacteristic
783C2—42no—
784C2—82no—
785C2—2442no—
786C2#2144915711yescharacteristic
787C2#448×D6111yescharacteristic
788C2#2145512111yescharacteristic
789C2#2145763611yescharacteristic
790C2#2145812811yescharacteristic
791C2#2145817111yescharacteristic
792C2#2145844011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2000C2
socleC23×C61C22×D4
prime radical#21450733C2
hypercenter#2000D61
hypocenterC61#24118
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#16840470C2semidirect
2. C2×#16840050C2semidirect
3. C2×SD16×Dic61C2semidirect
5. #21447014C2semidirect
6. #21447012C2semidirect
7. #21446819C2semidirect
8. #21446778C2semidirect
9. #21446611C2semidirect
10. #21446137C2semidirect
11. #21446133C2semidirect
12. #21446014C2semidirect
13. #21446013C2semidirect
14. #21445822C2semidirect
15. C61×#2000C2semidirect
73. #14519776D4semidirect
83. Q8×Dic61D4semidirect
183. C2×C22⋊D61SD16semidirect
394. #2000D61semidirect
459. C61#24118semidirect

Maximal subgroups

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

subgroupindex
C2×#168404702
C2×#168400502
C2×SD16×Dic612
#214507332
#214470142
#214470122
#214468192
#214467782
#214466112
#214461372
#214461332
#214460142
#214460132
#214458222
C61×#20002
#2411861