Finite Group Databasebeta

← #29695652

Subgroups — #29695652

Order 15616.

1426 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840425C211yesmaximal, characteristic
2C2×#16839837C211yesmaximal, characteristic
3C2×#16839770C211yesmaximal, characteristic, complemented
4C2×#16839769C211yesmaximal, characteristic, complemented
5#21448769C211yesmaximal, characteristic
6#21446740C211yesmaximal, characteristic, complemented
7#21446619C211yesmaximal, characteristic, complemented
8#21446253C211yesmaximal, characteristic, complemented
9#21446251C211yesmaximal, characteristic, complemented
10#21446130C211yesmaximal, characteristic, complemented
11#21445823C211yesmaximal, characteristic, complemented
12#21445755C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445638C211yesmaximal, characteristic, complemented
15C61×#1873C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20#16840425—24no—
21#16840425C418yescomplemented
22C2×#14519776—21no—
23C2×#14519775C2211yescharacteristic
24C2×#14519757C2211yescharacteristic
25C2×#14519755—21no—
26C2×#14519754—21no—
27C2×#14519742C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519737—21no—
30C2×#14519735C2211yescharacteristic
31#16839837—24no—
32C2×#14519706C2211yescharacteristic
33#16839770—24no—
34#16839769—24no—
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×#14519700C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×C8×Dic61C2211yescharacteristic
47#16839662—21no—
48#16839653—21no—
49#16839650—21no—
50#16839631C2211yescharacteristic
51#16839622C2211yescharacteristic
52#16839619C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54C4×#11758196—21no—
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×#117×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C22×Dic122—22no—
65C22×Dic122—22no—
66C22×Dic122—21no—
67C22×Dic122—22no—
68C22×Dic122—21no—
69C22×Dic122—41no—
70C22×Dic122—41no—
71C22×Dic122C2×C414yes—
72C22×Dic122C2311yescharacteristic
73C22×Dic122C2311yescharacteristic
74C2×Q8×D61—22no—
75C2×Q8×D61—22no—
76C2×Q8×D61—22no—
77C2×Q8×D61—41no—
78C2×Q8×D61—41no—
79C2×Q8×D61C2×C414yes—
80C22×C22⋊D61D411yescharacteristic
81C23×Dic61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C2×#11758194—22no—
85C2×#11758194—22no—
86C2×#11758194—41no—
87C2×#11758189—22no—
88C2×#11758189—22no—
89C2×#11758189—41no—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92#14519776—28no—
93#14519775—22no—
94#14519775C2×C414yes—
95#14519757—22no—
96#14519757C2×C414yes—
97#14519755—28no—
98#14519754—28no—
99#14519742—22no—
100#14519742C2×C414yes—
101C4×C22⋊D61C2×C414yes—
102C4×C22⋊D61D414yes—
103#14519737—28no—
104#14519735—22no—
105#14519735—41no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196—21no—
114C2×#11758196D411yescharacteristic
115C2×C22⋊Dic61—21no—
116C2×C22⋊Dic61D411yescharacteristic
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198D411yescharacteristic
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61—21no—
124C2×C4×Dic61C2311yescharacteristic
125#14519706—22no—
126#14519702—22no—
127#14519702—22no—
128#14519702—41no—
129#14519702—41no—
130#14519701—22no—
131#14519701—41no—
132#14519700—22no—
133#14519700—22no—
134#14519700—22no—
135#14519700D414yescomplemented
136#14519689—22no—
137C8×Dic61—22no—
138#14519684—21no—
139#14519684—21no—
140#14519684—21no—
141C22×Q8×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145C22⋊Q8×C61—22no—
146C22⋊Q8×C61C2×C414yes—
147#117×C61—22no—
148#117×C61—41no—
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61—21no—
155C2×C42×C61—21no—
156#103×C61—22no—
157#103×C61—41no—
158C22⋊C8×C61—22no—
159C24×C61C2×D411yescharacteristic
160C23×D61C2×D411yescharacteristic
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61C22×C412yes—
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×C61C22×C412yes—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D412yes—
178C22×C4×C61C2411yescharacteristic
179C2×C22⋊D61—22no—
180C2×C22⋊D61—22no—
181C2×C22⋊D61C22⋊C414yes—
182C22×Dic61—21no—
183C22×Dic61—24no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C22×Dic61C2×D411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192Q8×D61—28no—
193Q8×D61—44no—
194Q8×D61—44no—
195Q8×D61—44no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—24no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61C22×C412yes—
204C2×C4×D61C2×D412yes—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—28no—
213C2×Dic122—24no—
214C2×Dic122—21no—
215C2×Dic122—24no—
216C2×Dic122—44no—
217C2×Dic122—44no—
218C2×Dic122—44no—
219C2×Dic122—42no—
220C2×Dic122—42no—
221C2×Dic122—42no—
222C2×Dic122—42no—
223C2×Dic122C22×C412yes—
224C2×Dic122C22×C412yes—
225C2×Dic122C2×D412yes—
226C2×Dic122#4112yes—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61C22×C412yes—
239C4⋊C4×C61C2×D412yes—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—42no—
242C42×C61—42no—
243C22⋊Dic61—81no—
244C22⋊Dic61C22⋊C414yes—
245#11758198—24no—
246#11758198—42no—
247#11758198—81no—
248#11758198C22⋊C414yes—
249C4⋊Dic61—24no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257#11758196—42no—
258#11758196—81no—
259#11758196C22⋊C414yes—
260C4×Dic61—24no—
261C4×Dic61—42no—
262C4×Dic61—42no—
263C4×Dic61C22×C412yes—
264C4×Dic61C2×D412yes—
265#11758194—44no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418C2×D412yes—
272#11758189—44no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61C2×C22⋊C412yes—
280C23×C61C22×D411yescharacteristic
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61C2×C22⋊C412yes—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—41no—
291Q8×C61—41no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61C2×C22⋊C412yes—
311C2×C4×C61C23×C411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C2×C4×C61H(5,𝔽2)11yescharacteristic
317C22⋊D61—28no—
318C2×Dic61—22no—
319C2×Dic61—21no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—22no—
326C2×Dic61—48no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61C2×C22⋊C412yes—
336C2×Dic61C2×C22⋊C412yes—
337C2×Dic61C2×C22⋊C412yes—
338C2×Dic61#13712yes—
339C2×Dic61#13712yes—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—48no—
345Dic122—22no—
346Dic122—22no—
347Dic122—22no—
348Dic122—22no—
349Dic122—22no—
350Dic122—48no—
351Dic122—48no—
352Dic122—41no—
353Dic122—41no—
354Dic122C4×D414yes—
355C8×C61—41no—
356C8×C61—41no—
357#92418—22no—
358#92418—41no—
359#22430—611nomaximal, Sylow
360C22×C61—22no—
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61C22×C22⋊C411yescharacteristic
368C22×C61D4211yescharacteristic
369C22×C61#54611yescharacteristic
370C22×C61C2×#13711yescharacteristic
371C22×C61C2×#13711yescharacteristic
372C22×C61#57711yescharacteristic
373C22×C61#57811yescharacteristic
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C4×C61—22no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—42no—
385C4×C61—81no—
386C4×C61C2×C4×D411yescharacteristic
387C4×C61#51811yescharacteristic
388C4×C61D4211yescharacteristic
389C4×C61#54611yescharacteristic
390Dic61—24no—
391Dic61—22no—
392Dic61—22no—
393Dic61—42no—
394Dic61—81no—
395Dic61—81no—
396Dic61#41914yescomplemented
397C2×D4×Q8—611no—
398C2×#436—611no—
399C2×#419—611no—
400C2×#419—611no—
401#2354—611no—
402#1981—611no—
403#1956—611no—
404#1894—611no—
405#1894—611no—
406#1873—611no—
407#1873D6111yescharacteristic, complemented
408#1803—611no—
409#1787—611no—
410#1787—611no—
411C4×#103—611no—
412C2×C61—42no—
413C2×C61D4×C22⋊C411yescharacteristic
414C2×C61C2×#41911yescharacteristic
415C2×C61#289811yescharacteristic
416C2×C61#327611yescharacteristic
417C2×C61#327811yescharacteristic
418C2×C61#332811yescharacteristic
419C2×C61#332911yescharacteristic
420D61—42no—
421C23×Q8—611no—
422C23×Q8—611no—
423C22×M16—611no—
424C22×M16—611no—
425D4×Q8—618no—
426D4×Q8—1224no—
427C2×C4⋊Q8—611no—
428C2×C4⋊Q8—1221no—
429C2×C22⋊Q8—611no—
430C2×C22⋊Q8—1221no—
431C2×C22⋊Q8—1221no—
432C2×C22⋊Q8C2×D6111yescharacteristic
433C2×C4×Q8—611no—
434C2×C4×D4—611no—
435C2×C4×D4—1221no—
436C2×#117—611no—
437C2×#117C2×D6111yescharacteristic
438#436—1224no—
439C2×C4⋊C8—611no—
440#419—1224no—
441#419—1224no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#103—611no—
446C2×#103—611no—
447C2×#103—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103C2×D6111yescharacteristic
453C2×#103C2×D6111yescharacteristic
454C2×C22⋊C8—611no—
455C2×C22⋊C8C2×D6111yescharacteristic
456C2×C4×C8—611no—
457#390—1221no—
458#388—1221no—
459#388—1221no—
460#384—611no—
461#380—611no—
462#380—611no—
463C4×C4⋊C4—611no—
464C4×C4⋊C4—1221no—
465#340—611no—
466#340—611no—
467#340C2×D6111yescharacteristic
468#340C2×D6111yescharacteristic
469C61#2243011yescharacteristic, complemented, Sylow
470C22×Q8—614no—
471C22×Q8—614no—
472C22×Q8—611no—
473C22×Q8—611no—
474C22×Q8—1221no—
475C22×Q8—1222no—
476C22×Q8—1222no—
477C22×Q8—1222no—
478C22×Q8—1221no—
479C22×Q8—1222no—
480C22×Q8—1222no—
481C22×Q8—1222no—
482C22×Q8—2441no—
483C22×Q8—2441no—
484C22×Q8—2441no—
485C22×Q8—2441no—
486C22×Q8C22×D6111yescharacteristic
487C22×D4—611no—
488C23×C4—611no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4C22×D6111yescharacteristic
492C2×M16—1222no—
493C2×M16—1222no—
494C2×M16—1222no—
495C2×M16—1222no—
496C2×M16—2441no—
497C2×M16—2441no—
498C22×C8—611no—
499C22×C8—611no—
500C22×C8C22×D6111yescharacteristic
501C22×C8C22×D6111yescharacteristic
502C4⋊Q8—614no—
503C4⋊Q8—1222no—
504C4⋊Q8—1228no—
505C22⋊Q8—22no—
506C22⋊Q8—614no—
507C22⋊Q8—1228no—
508C22⋊Q8—1228no—
509C22⋊Q8—1222no—
510C22⋊Q8C4×D6114yes—
511C4×Q8—614no—
512C4×Q8—1222no—
513C4×D4—614no—
514C4×D4—614no—
515C4×D4—1228no—
516#117—22no—
517#117—41no—
518#117—1222no—
519#117—2441no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4C22×D6111yescharacteristic
531C2×C4⋊C4C22×D6111yescharacteristic
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C42—21no—
542C2×C42—611no—
543C2×C42—1221no—
544C2×C42—1221no—
545C2×C42—1221no—
546C4⋊C8—1222no—
547#103—22no—
548#103—41no—
549#103—614no—
550#103—1222no—
551#103—1222no—
552#103—1222no—
553#103—1222no—
554#103—1222no—
555#103—1222no—
556#103—2441no—
557#103—2441no—
558#103—2441no—
559C22⋊C8—22no—
560C22⋊C8—1222no—
561C4×C8—1222no—
562#95—1221no—
563#95—1221no—
564#95—1221no—
565C24—611no—
566C24D4×D6111yescharacteristic
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—612no—
573C2×Q8—612no—
574C2×Q8—612no—
575C2×Q8—612no—
576C2×Q8—1224no—
577C2×Q8—1228no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8—1221no—
582C2×Q8—1224no—
583C2×Q8—1228no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8—2442no—
589C2×Q8—2442no—
590C2×Q8—2444no—
591C2×Q8—2444no—
592C2×Q8—2444no—
593C2×Q8—2442no—
594C2×Q8—2442no—
595C2×Q8—2444no—
596C2×Q8—2444no—
597C2×Q8—2444no—
598C2×Q8C2×C4×D6112yes—
599C2×D4—614no—
600C2×D4—1222no—
601C2×D4—1222no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—612no—
614C22×C4—612no—
615C22×C4—1224no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1224no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4C2×C4×D6112yes—
630C22×C4D4×D6112yes—
631C22×C4D4×D6111yescharacteristic
632C22×C4C23×D6111yescharacteristic
633M16—2444no—
634M16—2444no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—612no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—24no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—614no—
653C4⋊C4—1224no—
654C4⋊C4—1224no—
655C4⋊C4—1224no—
656C4⋊C4—1224no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—4881no—
662C4⋊C4—2442no—
663C4⋊C4C2×C4×D6112yes—
664C4⋊C4D4×D6112yes—
665C22⋊C4—24no—
666C22⋊C4—42no—
667C22⋊C4—614no—
668C22⋊C4—614no—
669C22⋊C4—1224no—
670C22⋊C4—4881no—
671C22⋊C4—4881no—
672C22⋊C4—2442no—
673C42—42no—
674C42—612no—
675C42—612no—
676C42—1224no—
677C42—2442no—
678C42—2442no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—612no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23C22⋊C4×D6112yes—
693C23C2×D4×D6111yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—41no—
697Q8—41no—
698Q8—614no—
699Q8—1222no—
700Q8—1222no—
701Q8—1222no—
702Q8—1222no—
703Q8—1222no—
704Q8—2448no—
705Q8—2448no—
706Q8—2441no—
707Q8—2441no—
708D4—1228no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—612no—
730C2×C4—612no—
731C2×C4—612no—
732C2×C4—1222no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1222no—
737C2×C4—1221no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—2448no—
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×C4C22⋊C4×D6112yes—
755C2×C4C22×C4×D6111yescharacteristic
756C2×C4C2×D4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C2×C4#1451982211yescharacteristic
760C2×C4#1451982311yescharacteristic
761C8—41no—
762C8—41no—
763C8—1222no—
764C8—2441no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—1222no—
773C22—1222no—
774C22—1222no—
775C22—2441no—
776C22—2441no—
777C22—2441no—
778C22—2441no—
779C22C2×C22⋊C4×D6111yescharacteristic
780C22#1684039411yescharacteristic
781C22#1684040411yescharacteristic
782C22#137×D6111yescharacteristic
783C22#137×D6111yescharacteristic
784C22#1684056911yescharacteristic
785C22#1684057611yescharacteristic
786C4—22no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—81no—
791C4—614no—
792C4—1222no—
793C4—1222no—
794C4—1224no—
795C4—4881no—
796C4—4881no—
797C4—2442no—
798C4C4×D4×D6111yescharacteristic
799C4#1684023411yescharacteristic
800C4#1684039611yescharacteristic
801C4#1684040111yescharacteristic
802C2—42no—
803C2—2442no—
804C2#2144863711yescharacteristic
805C2#419×D6111yescharacteristic
806C2#2145434811yescharacteristic
807C2#2145746311yescharacteristic
808C2#2145747811yescharacteristic
809C2#2145810011yescharacteristic
810C2#2145811111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1873C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
cosocleC22×C4×C61C24
hypercenter#1873D61
hypocenterC61#22430
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
3. C2×#16839770C2semidirect
4. C2×#16839769C2semidirect
6. #21446740C2semidirect
7. #21446619C2semidirect
8. #21446253C2semidirect
9. #21446251C2semidirect
10. #21446130C2semidirect
11. #21445823C2semidirect
12. #21445755C2semidirect
13. #21445752C2semidirect
14. #21445638C2semidirect
15. C61×#1873C2semidirect
21. #16840425C4semidirect
135. #14519700D4semidirect
396. Dic61#419semidirect
407. #1873D61semidirect
469. C61#22430semidirect

Maximal subgroups

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

subgroupindex
C2×#168404252
C2×#168398372
C2×#168397702
C2×#168397692
#214487692
#214467402
#214466192
#214462532
#214462512
#214461302
#214458232
#214457552
#214457522
#214456382
C61×#18732
#2243061