Finite Group Databasebeta

← #29714073

Subgroups — #29714073

Order 15616.

1184 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840467C211yesmaximal, characteristic, complemented
2C2×#16840040C211yesmaximal, characteristic, complemented
3C2×#16839859C211yesmaximal, characteristic, complemented
4#21450718C211yesmaximal, characteristic
5#21447025C211yesmaximal, characteristic, complemented
6#21447023C211yesmaximal, characteristic, complemented
7#21446823C211yesmaximal, characteristic, complemented
8#21446822C211yesmaximal, characteristic, complemented
9#21446790C211yesmaximal, characteristic, complemented
10#21446615C211yesmaximal, characteristic, complemented
11#21446133C211yesmaximal, characteristic, complemented
12#21446008C211yesmaximal, characteristic, complemented
13#21446007C211yesmaximal, characteristic, complemented
14#21445833C211yesmaximal, characteristic, complemented
15C61×#1874C211yesmaximal, characteristic, complemented
16C22×#11758200C2211yescharacteristic
17#16840467—24no—
18#16840467—24no—
19C2×#14519776C2211yescharacteristic
20C2×#14519767—21no—
21C2×#14519757C2211yescharacteristic
22C2×#14519756—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519755—21no—
25C2×#14519748C2211yescharacteristic
26C2×#14519742C2211yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31#16840040—24no—
32#16839859—24no—
33C2×#14519711C2211yescharacteristic
34C2×#14519710C2211yescharacteristic
35C2×#14519710C2211yescharacteristic
36C2×#14519706C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519687C2211yescharacteristic
45#16839690—21no—
46#16839670—21no—
47#16839642—21no—
48#16839639—21no—
49#16839627C2211yescharacteristic
50#16839622C2211yescharacteristic
51#16839619C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C22×C4⋊C4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C22⋊D61D411yescharacteristic
67C23×Dic61—21no—
68C22×C4×D61—21no—
69C22×C4×D61C2311yescharacteristic
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—22no—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519776—22no—
76#14519776D414yescomplemented
77#14519767—28no—
78#14519757—22no—
79#14519757—22no—
80#14519756—28no—
81#14519756—22no—
82#14519756—22no—
83#14519755—28no—
84#14519748—22no—
85#14519748—41no—
86#14519742—22no—
87#14519742D414yescomplemented
88D4×Dic61—22no—
89D4×Dic61—22no—
90C4×C22⋊D61—28no—
91C4×C22⋊D61—22no—
92C4×C22⋊D61—22no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196D411yescharacteristic
102C4⋊C4×D61—22no—
103C4⋊C4×D61—22no—
104C2×C22⋊Dic61—21no—
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#14519711—22no—
115#14519710—22no—
116#14519710—22no—
117#14519706—22no—
118#14519702—22no—
119#14519702—41no—
120#14519700—41no—
121#14519698—22no—
122C22⋊#92418—22no—
123#14519689—22no—
124#14519689—41no—
125#14519687—22no—
126#14519684—21no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130C22×D4×C61—21no—
131C22×D4×C61C2311yescharacteristic
132C23×C4×C61—21no—
133C23×C4×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136#121×C61—22no—
137#121×C61—41no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61—22no—
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C22⋊C4×C61—21no—
145#102×C61—22no—
146#102×C61—22no—
147C22⋊C8×C61—41no—
148C24×C61—21no—
149C24×C61C2×D411yescharacteristic
150C23×D61C2×D411yescharacteristic
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—42no—
157C2×D4×C61—42no—
158C2×D4×C61—81no—
159C2×D4×C61#4112yes—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—24no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—81no—
171C22×C4×C61—81no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—81no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—42no—
185C22×Dic61—81no—
186C22×Dic61—81no—
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189C22×Dic61C2×D411yescharacteristic
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—24no—
197C2×C4×D61—81no—
198C2×C4×D61—81no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—24no—
205C2×Dic122—81no—
206C2×Dic122—81no—
207C2×Dic122C2×D412yes—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C4⋊C4×C61—24no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61C2×D412yes—
220C4⋊C4×C61C2×D412yes—
221C22⋊C4×C61—42no—
222C22⋊Dic61—24no—
223C22⋊Dic61—22no—
224C22⋊Dic61—42no—
225C22⋊Dic61—42no—
226C22⋊Dic61—81no—
227#11758200—28no—
228#11758198—24no—
229#11758198—22no—
230#11758198—81no—
231C4⋊Dic61—24no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61C2×D412yes—
238#11758196—24no—
239#11758196—24no—
240#11758196—24no—
241#11758196—24no—
242#11758196—22no—
243C4×Dic61—24no—
244C4×Dic61C2×D412yes—
245C4×Dic61C2×D412yes—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418#4112yes—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—22no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61#13712yes—
266C23×C61C22×D411yescharacteristic
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61#13712yes—
274D4×C61—22no—
275D4×C61—22no—
276D4×C61—41no—
277D4×C61—41no—
278D4×C61—84no—
279C2×C4×C61—22no—
280C2×C4×C61—21no—
281C2×C4×C61—22no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—84no—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61H(5,𝔽2)11yescharacteristic
301C2×C4×C612−1+411yescharacteristic
302C22⋊D61—28no—
303C22⋊D61—84no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—22no—
309C2×Dic61—21no—
310C2×Dic61—22no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—84no—
324C2×Dic61#12012yes—
325C2×Dic61#12012yes—
326C4×D61—41no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—84no—
331Dic122—22no—
332Dic122—22no—
333Dic122—41no—
334Dic122—41no—
335Dic122—84no—
336C8×C61—41no—
337C8×C61—41no—
338#92418—22no—
339#92418—41no—
340#24130—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61C2×#12011yescharacteristic
356C22×C61#54611yescharacteristic
357C22×C61#54711yescharacteristic
358C22×C61C2×#13711yescharacteristic
359C22×C61C2×#13711yescharacteristic
360C22×C61#57611yescharacteristic
361C22×C61#57611yescharacteristic
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C4×C61—41no—
370C4×C61—42no—
371C4×C61—42no—
372C4×C61—81no—
373C4×C61#52511yescharacteristic
374C4×C61#53711yescharacteristic
375C4×C61#54811yescharacteristic
376C4×C61#55011yescharacteristic
377Dic61—22no—
378Dic61—22no—
379Dic61—42no—
380Dic61—41no—
381Dic61—42no—
382Dic61—81no—
383Dic61—81no—
384C2×#554—611no—
385C2×#474—611no—
386C2×#440—611no—
387#2535—611no—
388#2036—611no—
389#2036—611no—
390#2000—611no—
391#2000—611no—
392#1993—611no—
393#1955—611no—
394#1874—611no—
395#1874D6111yescharacteristic, complemented
396#1852—611no—
397#1852—611no—
398#1805—611no—
399C2×C61—42no—
400C2×C61—82no—
401C2×C61#240711yescharacteristic
402C2×C61#300411yescharacteristic
403C2×C61#300811yescharacteristic
404C2×C61#331411yescharacteristic
405C2×C61#331411yescharacteristic
406C2×C61#334611yescharacteristic
407C2×C61#334611yescharacteristic
408D61—42no—
409C22×SD16—611no—
410#554—1224no—
411#554—1224no—
412C2×C4⋊Q8—611no—
413C2×#125—1221no—
414C2×C22⋊Q8—611no—
415C2×C22⋊Q8—611no—
416C2×C22⋊Q8—1221no—
417C2×C22⋊Q8—1221no—
418C2×#121—611no—
419C2×#121C2×D6111yescharacteristic
420C2×C4×Q8—611no—
421C2×C4×D4—611no—
422C2×C4×D4—611no—
423C2×C4×D4—1221no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4C2×D6111yescharacteristic
426#474—1224no—
427#440—1224no—
428C2×#107—611no—
429C2×#107—611no—
430C2×#107—611no—
431C2×C4⋊C8—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#102—611no—
436C2×#102C2×D6111yescharacteristic
437C2×#102C2×D6111yescharacteristic
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8C2×D6111yescharacteristic
442C2×#97—611no—
443#397—1221no—
444#392—1221no—
445#386—1221no—
446#386—1221no—
447#382—611no—
448#380—611no—
449#380—611no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#340C2×D6111yescharacteristic
455#340C2×D6111yescharacteristic
456C61#2413011yescharacteristic, complemented, Sylow
457C22×Q8—611no—
458C22×Q8—1221no—
459C22×D4—21no—
460C22×D4—611no—
461C22×D4—1221no—
462C22×D4C22×D6111yescharacteristic
463C23×C4—21no—
464C23×C4—611no—
465C23×C4—1221no—
466C23×C4—1221no—
467C23×C4C22×D6111yescharacteristic
468C2×SD16—1222no—
469C2×SD16—1222no—
470C2×SD16—1222no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C4⋊Q8—614no—
476C4⋊Q8—1222no—
477#125—1228no—
478C22⋊Q8—1222no—
479C22⋊Q8—1228no—
480C22⋊Q8—1222no—
481C22⋊Q8—1222no—
482C22⋊Q8—1228no—
483C22⋊Q8—1222no—
484#121—22no—
485#121—41no—
486#121—1222no—
487#121—2441no—
488C4×Q8—614no—
489C4×Q8—1222no—
490C4×D4—1222no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494C4×D4—1228no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—1222no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1222no—
509C2×C4⋊C4C22×D6111yescharacteristic
510C2×C4⋊C4C22×D6111yescharacteristic
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C42—611no—
522C2×C42—1221no—
523#107—1222no—
524#107—1222no—
525#107—1222no—
526C4⋊C8—1222no—
527#103—1222no—
528#103—2441no—
529#103—2441no—
530#102—22no—
531#102—22no—
532#102—1222no—
533C22⋊C8—41no—
534C22⋊C8—1222no—
535C22⋊C8—1222no—
536C22⋊C8—2441no—
537#97—1222no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542C24—21no—
543C24—611no—
544C24D4×D6111yescharacteristic
545C2×Q8—612no—
546C2×Q8—1224no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—4881no—
553C2×Q8—4881no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—81no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—4881no—
566C2×D4—2442no—
567C2×D4—2442no—
568C2×D4#1175822212yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—1224no—
585C22×C4—1221no—
586C22×C4—1221no—
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—4881no—
596C22×C4—4881no—
597C22×C4—4881no—
598C22×C4—4881no—
599C22×C4—2442no—
600C22×C4D4×D6111yescharacteristic
601C22×C4C23×D6111yescharacteristic
602SD16—1228no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—612no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—612no—
621C4⋊C4—1222no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4D4×D6112yes—
633C4⋊C4D4×D6112yes—
634C22⋊C4—42no—
635C22⋊C4—1222no—
636C22⋊C4—1224no—
637C22⋊C4—1222no—
638C22⋊C4—1224no—
639C22⋊C4—4881no—
640C22⋊C4—4881no—
641C22⋊C4—2442no—
642C22⋊C4—2442no—
643C42—612no—
644C42—612no—
645C42—1224no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—612no—
660C23—1221no—
661C23—1221no—
662C23—1221no—
663C23—1221no—
664C23—1221no—
665C23—1221no—
666C23#1451980612yes—
667C23C2×D4×D6111yescharacteristic
668Q8—1222no—
669Q8—1222no—
670Q8—4884no—
671Q8—2441no—
672Q8—2441no—
673D4—22no—
674D4—22no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—1228no—
679D4—4884no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—84no—
697C2×C4—612no—
698C2×C4—612no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—4884no—
709C2×C4—4884no—
710C2×C4—2441no—
711C2×C4—2441no—
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—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4C2×D4×D6111yescharacteristic
725C2×C4C2×D4×D6111yescharacteristic
726C2×C4#41×D6111yescharacteristic
727C2×C4C2×#1175822211yescharacteristic
728C2×C4#1451982211yescharacteristic
729C2×C4#1451982411yescharacteristic
730C8—41no—
731C8—41no—
732C8—1222no—
733C8—2441no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—1222no—
749C22—1222no—
750C22—1222no—
751C22—2441no—
752C22—2441no—
753C22—2441no—
754C22—2441no—
755C22#120×D6111yescharacteristic
756C22#1684040211yescharacteristic
757C22#1684041011yescharacteristic
758C22#137×D6111yescharacteristic
759C22C2×#1451980611yescharacteristic
760C22#1684056311yescharacteristic
761C22#1684056611yescharacteristic
762C4—41no—
763C4—42no—
764C4—42no—
765C4—81no—
766C4—1222no—
767C4—1222no—
768C4—4881no—
769C4—4881no—
770C4—2441no—
771C4—2442no—
772C4—2442no—
773C4#1684027111yescharacteristic
774C4#1684034111yescharacteristic
775C4#1684042111yescharacteristic
776C4#1684043011yescharacteristic
777C2—42no—
778C2—82no—
779C2—2442no—
780C2#2144916111yescharacteristic
781C2#2145505011yescharacteristic
782C2#2145508211yescharacteristic
783C2#2145789611yescharacteristic
784C2#2145790111yescharacteristic
785C2#2145830211yescharacteristic
786C2#2145830711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1874C2
socleC23×C61C22×D4
prime radical#21450718C2
hypercenter#1874D61
hypocenterC61#24130
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C2×#16840467C2semidirect
2. C2×#16840040C2semidirect
3. C2×#16839859C2semidirect
5. #21447025C2semidirect
6. #21447023C2semidirect
7. #21446823C2semidirect
8. #21446822C2semidirect
9. #21446790C2semidirect
10. #21446615C2semidirect
11. #21446133C2semidirect
12. #21446008C2semidirect
13. #21446007C2semidirect
14. #21445833C2semidirect
15. C61×#1874C2semidirect
76. #14519776D4semidirect
87. #14519742D4semidirect
395. #1874D61semidirect
456. C61#24130semidirect

Maximal subgroups

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

subgroupindex
C2×#168404672
C2×#168400402
C2×#168398592
#214507182
#214470252
#214470232
#214468232
#214468222
#214467902
#214466152
#214461332
#214460082
#214460072
#214458332
C61×#18742
#2413061