Finite Group Databasebeta

← #29685033

Subgroups — #29685033

Order 15616.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840292C211yesmaximal, characteristic
2C2×#16839820C211yesmaximal, characteristic, complemented
3C2×#16839720C211yesmaximal, characteristic, complemented
4#21446757C211yesmaximal, characteristic, complemented
5#21446753C211yesmaximal, characteristic, complemented
6#21446615C211yesmaximal, characteristic, complemented
7#21446611C211yesmaximal, characteristic, complemented
8#21446116C211yesmaximal, characteristic, complemented
9#21446112C211yesmaximal, characteristic, complemented
10#21446109C211yesmaximal, characteristic, complemented
11#21445584C211yesmaximal, characteristic, complemented
12#21445584C211yesmaximal, characteristic, complemented
13#21445583C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic61C211yesmaximal, characteristic, complemented
15C61×#1870C211yesmaximal, characteristic, complemented
16C23×#92418C2211yescharacteristic
17#16840292—24no—
18#16840292—24no—
19C2×#14519772C411yescharacteristic
20C2×#14519770C411yescharacteristic
21C2×#14519767C411yescharacteristic
22C2×#14519763C411yescharacteristic
23C2×#14519761C411yescharacteristic
24C2×#14519758C411yescharacteristic
25C2×#14519754C411yescharacteristic
26C2×#14519749C411yescharacteristic
27C2×C4×Dic122C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519736C2211yescharacteristic
31C2×#14519734C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839820—24no—
34C2×#14519706C2211yescharacteristic
35C2×#14519706C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43#16839720—24no—
44C2×#14519687C2211yescharacteristic
45C2×#14519687C2211yescharacteristic
46C2×#14519687C2211yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48C2×C8×Dic61C2211yescharacteristic
49C2×C8×Dic61C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic
66C23×Dic61C2×C411yescharacteristic
67C23×Dic61C2×C411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C22×#92418—22no—
70C22×#92418—22no—
71C22×#92418—22no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519772—24no—
77#14519770—24no—
78#14519767—24no—
79#14519763—24no—
80#14519761—24no—
81#14519758—24no—
82#14519754—24no—
83#14519749—24no—
84C4×Dic122—22no—
85C4×Dic122—22no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88C4×C22⋊D61—22no—
89C4×C22⋊D61—22no—
90#14519736D414yes—
91#14519736D414yes—
92#14519734—22no—
93#14519734—22no—
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×C22⋊Dic61C2×C411yescharacteristic
104C2×C22⋊Dic61C2×C411yescharacteristic
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×C4×Dic61—22no—
112C2×C4×Dic61—22no—
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2×C411yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118#14519706—22no—
119#14519706—22no—
120C22⋊#92418—22no—
121C22⋊#92418—22no—
122C22⋊#92418—22no—
123#14519689—22no—
124#14519689—22no—
125#14519689—22no—
126#14519689—22no—
127#14519687—22no—
128#14519687—22no—
129#14519687—22no—
130C8×Dic61—22no—
131C8×Dic61—22no—
132C8×Dic61—22no—
133C22×D4×C61C2×C411yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C2×M16×C61—22no—
137C2×M16×C61—22no—
138C2×M16×C61—22no—
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C4×D4×C61—22no—
144C4×D4×C61—22no—
145C2×C4⋊C4×C61C2×C411yescharacteristic
146C2×C22⋊C4×C61C2×C411yescharacteristic
147C2×C22⋊C4×C61C2×C411yescharacteristic
148C2×C42×C61C2311yescharacteristic
149C22⋊C8×C61—22no—
150C22⋊C8×C61—22no—
151C22⋊C8×C61—22no—
152C24×C61C22×C411yescharacteristic
153C24×C61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—41no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C2×D412yes—
173C22×C4×C61C2×D412yes—
174C22×C4×C61C2411yescharacteristic
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—41no—
180C2×C22⋊D61—41no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—41no—
186C22×Dic61—41no—
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C22×C411yescharacteristic
193C22×Dic61C22×C411yescharacteristic
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×Dic122—22no—
201C2×Dic122—22no—
202C2×Dic122—41no—
203M16×C61—28no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61#4112yes—
215C2×C8×C61#4112yes—
216C4⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—22no—
219C42×C61—21no—
220C42×C61—21no—
221C22⋊Dic61—22no—
222C22⋊Dic61—22no—
223C22⋊Dic61C22⋊C414yes—
224C22⋊Dic61C22⋊C414yes—
225#11758198—22no—
226#11758198—22no—
227#11758198—22no—
228#11758198—22no—
229C4⋊Dic61—22no—
230C4⋊Dic61C22⋊C414yes—
231C4⋊Dic61C22⋊C414yes—
232#11758196—22no—
233#11758196—22no—
234#11758196—22no—
235#11758196—22no—
236#11758196—22no—
237#11758196—22no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—22no—
241C4×Dic61—22no—
242C4×Dic61C2×D412yes—
243C4×Dic61C2×D412yes—
244C4×Dic61C2×D412yes—
245C4×Dic61C2×D412yes—
246C2×#92418—28no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418#4112yes—
258C2×#92418#4112yes—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61C2×C22⋊C412yes—
272C23×C61#13112yes—
273C23×C61C23×C411yescharacteristic
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281D4×C61—44no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61C2×C22⋊C412yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C22⋊D61—44no—
309C22⋊D61—44no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—44no—
327C2×Dic61—44no—
328C2×Dic61C2×C22⋊C412yes—
329C2×Dic61C2×C22⋊C412yes—
330C2×Dic61C2×C22⋊C412yes—
331C2×Dic61C2×C22⋊C412yes—
332C2×Dic61#13112yes—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337Dic122—44no—
338C8×C61—22no—
339C8×C61—22no—
340C8×C61—41no—
341C8×C61—41no—
342#92418—22no—
343#92418—22no—
344#92418—41no—
345#92418—41no—
346#21381—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61C22×C22⋊C411yescharacteristic
362C22×C61C4×#4111yescharacteristic
363C22×C61C4×#4111yescharacteristic
364C22×C61C2×#13111yescharacteristic
365C22×C61C2×#13111yescharacteristic
366C22×C61#56811yescharacteristic
367C22×C61#56811yescharacteristic
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C4×C61—22no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61#52511yescharacteristic
380C4×C61#52511yescharacteristic
381C4×C61#53211yescharacteristic
382C4×C61#53211yescharacteristic
383Dic61—22no—
384Dic61—22no—
385Dic61—22no—
386Dic61—22no—
387Dic61—22no—
388Dic61—41no—
389Dic61—41no—
390C2×#529—611no—
391C2×#433—611no—
392C2×#405—611no—
393#1985—611no—
394#1984—611no—
395#1955—611no—
396#1954—611no—
397#1870—611no—
398#1870D6111yescharacteristic, complemented
399#1869—611no—
400#1869—611no—
401#1750—611no—
402#1750—611no—
403#1749—611no—
404C4×C22⋊C8—611no—
405C2×C61—42no—
406C2×C61—42no—
407C2×C61#229711yescharacteristic
408C2×C61#288011yescharacteristic
409C2×C61#288011yescharacteristic
410C2×C61#296611yescharacteristic
411C2×C61#296711yescharacteristic
412C2×C61#296811yescharacteristic
413C2×C61#296911yescharacteristic
414D61—81no—
415C22×M16C2×D6111yescharacteristic
416C23×C8—611no—
417#529—1224no—
418#529—1224no—
419C2×#126—611no—
420C2×#126—611no—
421C2×#125—611no—
422C2×#124—611no—
423C2×#123—611no—
424C2×#123—611no—
425C2×C22⋊Q8—611no—
426C2×#121—611no—
427C2×C4×Q8—611no—
428C2×C4×D4—611no—
429C2×C4×D4—611no—
430C2×C4×D4C2×D6111yescharacteristic
431C2×#117—611no—
432C2×#117—611no—
433C22×C42—611no—
434#433—1224no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8—611no—
437C2×C22⋊C8—611no—
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8C2×D6111yescharacteristic
445C2×C22⋊C8C2×D6111yescharacteristic
446C2×C22⋊C8C2×D6111yescharacteristic
447#405—1224no—
448C2×#97—611no—
449C2×#97—611no—
450C2×#97—611no—
451C2×C4×C8—611no—
452C2×C4×C8—611no—
453C2×C4×C8—611no—
454#336—611no—
455#336—611no—
456#336—611no—
457#336—611no—
458#336—611no—
459#336—611no—
460#336C2×D6111yescharacteristic
461#336C2×D6111yescharacteristic
462C61#2138111yescharacteristic, complemented, Sylow
463C22×Q8—611no—
464C22×D4—611no—
465C22×D4—611no—
466C22×D4C4×D6111yescharacteristic
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4C22×D6111yescharacteristic
471C23×C4C22×D6111yescharacteristic
472C2×M16—22no—
473C2×M16—22no—
474C2×M16—22no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—1222no—
480C22×C8—1222no—
481C22×C8—1222no—
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486#126—1224no—
487#126—1224no—
488#125—1224no—
489#124—1224no—
490#123—1224no—
491#123—1224no—
492C22⋊Q8—1224no—
493#121—1224no—
494C4×Q8—1222no—
495C4×Q8—1222no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502#117—614no—
503#117—614no—
504#117—1222no—
505#117—1222no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4C4×D6111yescharacteristic
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—611no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4C4×D6111yescharacteristic
525C2×C22⋊C4C4×D6111yescharacteristic
526C2×C42—611no—
527C2×C42—611no—
528C2×C42—611no—
529C2×C42—611no—
530C2×C42—611no—
531C2×C42—1222no—
532C2×C42—1222no—
533C2×C42C22×D6111yescharacteristic
534C4⋊C8—1222no—
535C4⋊C8—1222no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—1222no—
540C22⋊C8—1222no—
541C22⋊C8—1222no—
542C22⋊C8—1222no—
543C22⋊C8—1222no—
544C22⋊C8—1222no—
545C22⋊C8—1222no—
546#97—1222no—
547#97—1222no—
548#97—1222no—
549C4×C8—1222no—
550C4×C8—1222no—
551C4×C8—1222no—
552C24—611no—
553C24C2×C4×D6111yescharacteristic
554C24C2×C4×D6111yescharacteristic
555C2×Q8—1222no—
556C2×Q8—1222no—
557C2×Q8—2441no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—41no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—2441no—
566C2×D4—2441no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—2441no—
595C22×C4—2441no—
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4D4×D6112yes—
601C22×C4D4×D6112yes—
602C22×C4C23×D6111yescharacteristic
603M16—28no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—612no—
615C2×C8—612no—
616C2×C8—1228no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8#1175822412yes—
628C2×C8#1175822412yes—
629C4⋊C4—22no—
630C4⋊C4—614no—
631C4⋊C4—614no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4—1222no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C4⋊C4—1222no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—614no—
642C22⋊C4—614no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C42—21no—
650C42—21no—
651C42—612no—
652C42—612no—
653C42—612no—
654C42—612no—
655C42—1222no—
656C42—1222no—
657C42—1221no—
658C42—1221no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23C22⋊C4×D6112yes—
679C23#1451978512yes—
680C23C22×C4×D6111yescharacteristic
681Q8—2444no—
682D4—44no—
683D4—2444no—
684D4—2444no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—612no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—2444no—
726C2×C4—2444no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4C22⋊C4×D6112yes—
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4C2×D4×D6111yescharacteristic
734C2×C4#41×D6111yescharacteristic
735C2×C4#41×D6111yescharacteristic
736C2×C4C2×#1175822411yescharacteristic
737C2×C4C2×#1175822411yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C8—1222no—
743C8—1222no—
744C8—2441no—
745C8—2441no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—2441no—
761C22—2441no—
762C22—2441no—
763C22—2441no—
764C22—2441no—
765C22—2441no—
766C22—2441no—
767C22C2×C22⋊C4×D6111yescharacteristic
768C22C4×#1175822411yescharacteristic
769C22C4×#1175822411yescharacteristic
770C22#131×D6111yescharacteristic
771C22C2×#1451978511yescharacteristic
772C22#1684052711yescharacteristic
773C22#1684052811yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—1222no—
779C4—1222no—
780C4—1222no—
781C4—1222no—
782C4—1222no—
783C4—2441no—
784C4—2441no—
785C4#1684026811yescharacteristic
786C4#1684027011yescharacteristic
787C4#1684030711yescharacteristic
788C4#1684030711yescharacteristic
789C2—42no—
790C2—42no—
791C2—4881no—
792C2#2144830411yescharacteristic
793C2#2145426711yescharacteristic
794C2#2145426911yescharacteristic
795C2#2145478911yescharacteristic
796C2#2145480511yescharacteristic
797C2#2145481411yescharacteristic
798C2#2145481811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1870C2
prime radicalC2×#14519749C4
cosocleC22×C4×C61C24
hypercenter#1870D61
hypocenterC61#21381
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#16839820C2semidirect
3. C2×#16839720C2semidirect
4. #21446757C2semidirect
5. #21446753C2semidirect
6. #21446615C2semidirect
7. #21446611C2semidirect
8. #21446116C2semidirect
9. #21446112C2semidirect
10. #21446109C2semidirect
11. #21445584C2semidirect
12. #21445584C2semidirect
13. #21445583C2semidirect
14. C22⋊C8×Dic61C2semidirect
15. C61×#1870C2semidirect
398. #1870D61semidirect
462. C61#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#168402922
C2×#168398202
C2×#168397202
#214467572
#214467532
#214466152
#214466112
#214461162
#214461122
#214461092
#214455842
#214455832
C22⋊C8×Dic612
C61×#18702
#2138161