Finite Group Databasebeta

← #29713943

Subgroups — #29713943

Order 15616.

1350 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840412C211yesmaximal, characteristic
2C2×#16840045C211yesmaximal, characteristic, complemented
3C2×SD16×Dic61C211yesmaximal, characteristic, complemented
4#21450738C211yesmaximal, characteristic, complemented
5#21447007C211yesmaximal, characteristic, complemented
6#21447005C211yesmaximal, characteristic, complemented
7#21446819C211yesmaximal, characteristic, complemented
8#21446778C211yesmaximal, characteristic, complemented
9#21446611C211yesmaximal, characteristic, complemented
10#21446127C211yesmaximal, characteristic, complemented
11#21446123C211yesmaximal, characteristic, complemented
12#21446014C211yesmaximal, characteristic, complemented
13#21446013C211yesmaximal, characteristic, complemented
14#21445817C211yesmaximal, characteristic, complemented
15C61×#2000C211yesmaximal, characteristic, complemented
16C22×#11758224—21no—
17#16840412—24no—
18#16840412—24no—
19C2×#14519776C2211yescharacteristic
20C2×#14519759—21no—
21C2×#14519758—21no—
22C2×#14519754—21no—
23C2×#14519753C2211yescharacteristic
24C2×#14519748C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30#16840045—24no—
31SD16×Dic61—24no—
32C2×#14519709C2211yescharacteristic
33C2×#14519709C2211yescharacteristic
34C2×#14519708C2211yescharacteristic
35C2×#14519706C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×C8×Dic61C2211yescharacteristic
44#16839685—21no—
45#16839684—21no—
46#16839662—21no—
47#16839657—21no—
48#16839631C2211yescharacteristic
49#16839622C2211yescharacteristic
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
63C2×#11758224—28no—
64C2×#11758224—44no—
65C2×#11758224—44no—
66C22×Dic122—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61D411yescharacteristic
69C23×Dic61—21no—
70C23×Dic61—21no—
71C22×C4×D61—21no—
72C22×C4×D61C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519776—22no—
76#14519776D414yes—
77#14519759—28no—
78#14519758—28no—
79#14519754—28no—
80#14519753—22no—
81#14519753—41no—
82#14519748—22no—
83#14519748—22no—
84Q8×Dic61—22no—
85Q8×Dic61—22no—
86D4×Dic61—22no—
87D4×Dic61D414yes—
88C4×C22⋊D61—22no—
89C4×C22⋊D61—22no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61—22no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196D411yescharacteristic
104C4⋊C4×D61—22no—
105C4⋊C4×D61—22no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61D411yescharacteristic
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198D411yescharacteristic
113C2×C4×Dic61—21no—
114C2×C4×Dic61C2311yescharacteristic
115#14519709—22no—
116#14519709—22no—
117#14519708—22no—
118#14519706—22no—
119#14519701—22no—
120#14519701—22no—
121#14519698—22no—
122#14519698—41no—
123C22⋊#92418—41no—
124#14519689—22no—
125#14519689—41no—
126C8×Dic61—22no—
127#14519684—21no—
128#14519684—21no—
129C22×Q8×C61C2311yescharacteristic
130C22×D4×C61—21no—
131C22×D4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C2×SD16×C61—22no—
134C2×SD16×C61—22no—
135C2×SD16×C61—22no—
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22⋊Q8×C61—22no—
139C22⋊Q8×C61—41no—
140#121×C61—22no—
141#121×C61—22no—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147#103×C61—22no—
148#102×C61—41no—
149C22⋊C8×C61—22no—
150C24×C61—21no—
151C24×C61C2×D411yescharacteristic
152C23×D61C2×D411yescharacteristic
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61#4112yescomplemented
159C2×D4×C61—24no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—42no—
166C2×D4×C61—42no—
167C2×D4×C61C2×D412yes—
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×C61—21no—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2411yescharacteristic
179C2×C22⋊D61—24no—
180C2×C22⋊D61—22no—
181C2×C22⋊D61—22no—
182C2×C22⋊D61—42no—
183C2×C22⋊D61—42no—
184C2×C22⋊D61SD1614yescomplemented
185C22×Dic61—24no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—24no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—42no—
192C22×Dic61—42no—
193C22×Dic61—42no—
194C22×Dic61—42no—
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198#11758224—432no—
199C2×C4×D61—24no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×Dic122—24no—
209C2×Dic122—42no—
210C2×Dic122—42no—
211SD16×C61—28no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61#4112yescomplemented
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—42no—
222C4⋊C4×C61C2×D412yes—
223C22⋊C4×C61—24no—
224C22⋊C4×C61—42no—
225C22⋊Dic61—24no—
226C22⋊Dic61—24no—
227C22⋊Dic61—22no—
228C22⋊Dic61—81no—
229#11758198—22no—
230#11758198—42no—
231#11758198—81no—
232C4⋊Dic61—24no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—42no—
240C4⋊Dic61C2×D412yes—
241C4⋊Dic61C2×D412yes—
242#11758196—24no—
243#11758196—24no—
244#11758196—22no—
245#11758196—42no—
246#11758196—42no—
247#11758196—81no—
248C4×Dic61—42no—
249C4×Dic61C2×D412yes—
250C4×Dic61C2×D412yes—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—22no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61C2×SD1612yes—
271C23×C61C22×D411yescharacteristic
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61C2×SD1612yes—
279Q8×C61—22no—
280Q8×C61—22no—
281Q8×C61—41no—
282Q8×C61—41no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—48no—
286D4×C61—41no—
287D4×C61—41no—
288C2×C4×C61—22no—
289C2×C4×C61—21no—
290C2×C4×C61—22no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
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×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C612−1+411yescharacteristic
310C22⋊D61—28no—
311C22⋊D61—48no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—48no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—48no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61#12012yes—
332C2×Dic61#12012yes—
333C2×Dic61C2×SD1612yes—
334C2×Dic61AGL(1,ℤ/8)12yes—
335C4×D61—48no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340Dic122—48no—
341C8×C61—22no—
342C8×C61—41no—
343#92418—41no—
344#92418—41no—
345#24120—611nomaximal, Sylow
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61C2×#12011yescharacteristic
361C22×C61#54611yescharacteristic
362C22×C61#54711yescharacteristic
363C22×C61C22×SD1611yescharacteristic
364C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C61#57711yescharacteristic
366C22×C61#57811yescharacteristic
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C4×C61—41no—
375C4×C61—42no—
376C4×C61—42no—
377C4×C61—81no—
378C4×C61#52511yescharacteristic
379C4×C61#53711yescharacteristic
380C4×C61#54811yescharacteristic
381C4×C61#55011yescharacteristic
382Dic61—22no—
383Dic61—41no—
384Dic61—42no—
385Dic61—42no—
386Dic61—81no—
387Dic61—81no—
388Dic61#45014yes—
389C2×#547—611no—
390C2×#475—611no—
391C2×C4×SD16—611no—
392#2538—611no—
393#2034—611no—
394#2034—611no—
395#2000—611no—
396#2000D6111yescharacteristic, complemented
397#1990—611no—
398#1954—611no—
399#1872—611no—
400#1872—611no—
401#1853—611no—
402#1853—611no—
403#1802—611no—
404C2×C61—42no—
405C2×C61—82no—
406C2×C61#240711yescharacteristic
407C2×C61C2×#45011yescharacteristic
408C2×C61#301311yescharacteristic
409C2×C61#329811yescharacteristic
410C2×C61#333211yescharacteristic
411C2×C61#333511yescharacteristic
412C2×C61#335311yescharacteristic
413D61—42no—
414C22×#41—1221no—
415C22×SD16C2×D6111yescharacteristic
416#547—1224no—
417#547—1224no—
418C2×C4⋊Q8—611no—
419C2×#123—1221no—
420C2×#123—1221no—
421C2×C22⋊Q8—611no—
422C2×C22⋊Q8—1221no—
423C2×C22⋊Q8C2×D6111yescharacteristic
424C2×#121—611no—
425C2×#121C2×D6111yescharacteristic
426C2×C4×Q8—611no—
427C2×C4×D4—611no—
428C2×C4×D4—611no—
429C22×C4⋊C4—611no—
430C22×C4⋊C4—611no—
431#475—1224no—
432C4×SD16—1224no—
433C2×#106—611no—
434C2×#106—611no—
435C2×#106—611no—
436C2×C4⋊C8—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103C2×D6111yescharacteristic
440C2×#102—611no—
441C2×#102—611no—
442C2×#102C2×D6111yescharacteristic
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8C2×D6111yescharacteristic
447C2×C4×C8—611no—
448#396—1221no—
449#396—1221no—
450#390—1221no—
451#389—1221no—
452#384—611no—
453#380—611no—
454#380—611no—
455#340—611no—
456#340—611no—
457#340—611no—
458#340—611no—
459#340—611no—
460#340C2×D6111yescharacteristic
461C61#2412011yescharacteristic, complemented, Sylow
462C2×#41—1228no—
463C2×#41—2444no—
464C2×#41—2444no—
465C22×Q8—1221no—
466C22×Q8C22×D6111yescharacteristic
467C22×D4—21no—
468C22×D4—611no—
469C22×D4—1221no—
470C22×D4C22×D6111yescharacteristic
471C23×C4—611no—
472C23×C4—1221no—
473C23×C4—1221no—
474C23×C4—1221no—
475C23×C4C22×D6111yescharacteristic
476C2×SD16—22no—
477C2×SD16—22no—
478C2×SD16—22no—
479C22×C8—611no—
480C22×C8—611no—
481C22×C8C22×D6111yescharacteristic
482C22×C8C22×D6111yescharacteristic
483C4⋊Q8—614no—
484C4⋊Q8—1222no—
485#123—1228no—
486#123—1228no—
487C22⋊Q8—22no—
488C22⋊Q8—41no—
489C22⋊Q8—1228no—
490C22⋊Q8—1222no—
491C22⋊Q8—2441no—
492#121—22no—
493#121—22no—
494#121—1222no—
495#121—1222no—
496C4×Q8—1222no—
497C4×Q8—1222no—
498C4×D4—614no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—1222no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1222no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C42—611no—
531C2×C42—1221no—
532#106—1222no—
533#106—1222no—
534#106—1222no—
535C4⋊C8—1222no—
536#103—22no—
537#103—1222no—
538#103—1222no—
539#102—41no—
540#102—1222no—
541#102—2441no—
542C22⋊C8—22no—
543C22⋊C8—1222no—
544C22⋊C8—2441no—
545C22⋊C8—2441no—
546C4×C8—1222no—
547#95—1221no—
548#95—1221no—
549C24—21no—
550C24—611no—
551C24D4×D6111yescharacteristic
552#41—24432no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—1224no—
559C2×Q8—2442no—
560C2×Q8—2442no—
561C2×Q8#1175822412yescomplemented
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—614no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1224no—
574C2×D4—2442no—
575C2×D4—2442no—
576C2×D4D4×D6112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—1224no—
590C22×C4—1224no—
591C22×C4—1224no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—2442no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4—2442no—
608C22×C4D4×D6111yescharacteristic
609C22×C4C23×D6111yescharacteristic
610SD16—28no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8#1175822412yescomplemented
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—42no—
627C4⋊C4—612no—
628C4⋊C4—612no—
629C4⋊C4—1222no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1224no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—4881no—
640C4⋊C4—2442no—
641C4⋊C4—2442no—
642C4⋊C4—2442no—
643C4⋊C4D4×D6112yes—
644C22⋊C4—24no—
645C22⋊C4—42no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1224no—
649C22⋊C4—1224no—
650C22⋊C4—4881no—
651C22⋊C4—4881no—
652C22⋊C4—2442no—
653C42—612no—
654C42—612no—
655C42—2442no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—612no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23SD16×D6112yes—
677C23C2×D4×D6111yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682Q8—2448no—
683D4—22no—
684D4—22no—
685D4—48no—
686D4—41no—
687D4—41no—
688D4—1228no—
689D4—2448no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—612no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—2448no—
718C2×C4—2448no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2448no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4C2×D4×D6111yescharacteristic
735C2×C4C2×D4×D6111yescharacteristic
736C2×C4C2×#1175822411yescharacteristic
737C2×C4C2×#1175822411yescharacteristic
738C2×C4#1451982211yescharacteristic
739C2×C4#1451982411yescharacteristic
740C8—22no—
741C8—41no—
742C8—2441no—
743C8—2441no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—1222no—
759C22—1222no—
760C22—1222no—
761C22—2441no—
762C22—2441no—
763C22—2441no—
764C22—2441no—
765C22#120×D6111yescharacteristic
766C22#1684039911yescharacteristic
767C22#1684041211yescharacteristic
768C22C2×SD16×D6111yescharacteristic
769C22AGL(1,ℤ/8)×D6111yescharacteristic
770C22#1684056911yescharacteristic
771C22#1684057811yescharacteristic
772C4—42no—
773C4—41no—
774C4—42no—
775C4—81no—
776C4—614no—
777C4—1222no—
778C4—4881no—
779C4—4881no—
780C4—2442no—
781C4—2442no—
782C4—2441no—
783C4#1684026811yescharacteristic
784C4#1684033911yescharacteristic
785C4#1684041811yescharacteristic
786C4#1684043211yescharacteristic
787C2—42no—
788C2—82no—
789C2—2442no—
790C2#2144915711yescharacteristic
791C2#450×D6111yescharacteristic
792C2#2145513811yescharacteristic
793C2#2145767711yescharacteristic
794C2#2145813911yescharacteristic
795C2#2145817111yescharacteristic
796C2#2145839811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2000C2
socleC23×C61C22×D4
prime radicalC2×#16840412C2
hypercenter#2000D61
hypocenterC61#24120
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
2. C2×#16840045C2semidirect
3. C2×SD16×Dic61C2semidirect
4. #21450738C2semidirect
5. #21447007C2semidirect
6. #21447005C2semidirect
7. #21446819C2semidirect
8. #21446778C2semidirect
9. #21446611C2semidirect
10. #21446127C2semidirect
11. #21446123C2semidirect
12. #21446014C2semidirect
13. #21446013C2semidirect
14. #21445817C2semidirect
15. C61×#2000C2semidirect
158. C2×Q8×C61#41semidirect
184. C2×C22⋊D61SD16semidirect
217. C2×C8×C61#41semidirect
396. #2000D61semidirect
461. C61#24120semidirect
561. C2×Q8#11758224semidirect
622. C2×C8#11758224semidirect

Maximal subgroups

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

subgroupindex
C2×#168404122
C2×#168400452
C2×SD16×Dic612
#214507382
#214470072
#214470052
#214468192
#214467782
#214466112
#214461272
#214461232
#214460142
#214460132
#214458172
C61×#20002
#2412061