Finite Group Databasebeta

← #29585243

Subgroups — #29585243

Order 15616.

1414 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D61C211yesmaximal, characteristic
2C2×#16839725C211yesmaximal, characteristic
3#21448198C211yesmaximal, characteristic
4C2×#16839519C211yesmaximal, characteristic, complemented
5C2×#16839518C211yesmaximal, characteristic, complemented
6C2×#16839518C211yesmaximal, characteristic, complemented
7C2×C61×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C2×#14519736C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12C2×#14519735—21no—
13C2×#14519734C412yescomplemented
14C2×#14519733—21no—
15#117×D61—22no—
16#117×D61—22no—
17#117×D61—22no—
18#117×D61—22no—
19C2×C4⋊C4×D61—21no—
20C2×C22⋊C4×D61—21no—
21C2×C42×D61C412yescomplemented
22#16839725—21no—
23#16839725—21no—
24#16839725—22no—
25C2×#14519689C414yescomplemented
26#16839623—21no—
27#16839619—22no—
28#16839617—21no—
29C4×#11758198C414yescomplemented
30#16839519—22no—
31#16839518—22no—
32#16839518—22no—
33C22×M16×C61C2211yescharacteristic
34C2×#117×C61C2211yescharacteristic
35C2×#117×C61C2211yescharacteristic
36C61×H(3,ℤ/4)—22no—
37C24×D61D411yescharacteristic
38C23×Dic61D411yescharacteristic
39C22×C4×D61—21no—
40C22×C4×D61—21no—
41C22×C4×D61—21no—
42C22×C4×D61—21no—
43C22×C4×D61—21no—
44C22×C4×D61—21no—
45C22×C4×D61—21no—
46C22×C4×D61—21no—
47C22×C4×D61—22no—
48C22×C4×D61C2×C412yes—
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C412yes—
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D412yes—
55C22×C4×D61Q812yes—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194—21no—
62C22×#92418C2×C412yescomplemented
63#14519736—21no—
64#14519736—21no—
65#14519736—21no—
66#14519736—21no—
67#14519736—21no—
68#14519736—21no—
69#14519736D412yes—
70#14519736D412yes—
71#14519735—24no—
72#14519735—24no—
73#14519734—24no—
74#14519734—24no—
75#14519733—24no—
76#14519733—24no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×#11758196—22no—
80C4⋊C4×D61—24no—
81C4⋊C4×D61—24no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×#11758198—22no—
85C2×#11758198—24no—
86C22⋊C4×D61—24no—
87C22⋊C4×D61—24no—
88C2×C4×Dic61—22no—
89C2×C4×Dic61C2×C412yes—
90C2×C4×Dic61C2×C412yescomplemented
91C42×D61—24no—
92C42×D61—24no—
93#14519689—24no—
94#14519689—24no—
95#14519684—24no—
96C23×C4×C61C2311yescharacteristic
97C2×M16×C61—21no—
98C2×M16×C61—21no—
99C2×M16×C61—21no—
100C2×M16×C61—21no—
101C2×M16×C61—21no—
102C2×M16×C61—21no—
103C22×C8×C61C2×C412yescomplemented
104#117×C61—21no—
105#117×C61—21no—
106#117×C61—21no—
107#117×C61—21no—
108#117×C61—21no—
109#117×C61—21no—
110#117×C61D412yes—
111#117×C61D412yes—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C42×C61C2×C412yes—
117C2×C42×C61C2×C412yescomplemented
118C24×C61C2×D411yescharacteristic
119C23×D61—21no—
120C23×D61—21no—
121C23×D61—21no—
122C23×D61—21no—
123C23×D61—44no—
124C23×D61C22⋊C411yescharacteristic
125C23×D61C22⋊C412yes—
126C23×D61C22⋊C411yescharacteristic
127C23×D61C4⋊C412yes—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×Q811yescharacteristic
140C22×C4×C61#4111yescharacteristic
141C22×C4×C61#4111yescharacteristic
142C22×C4×C61#4111yescharacteristic
143C22×C4×C61#4111yescharacteristic
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61C22⋊C412yes—
151C22×Dic61C22⋊C411yescharacteristic
152C22×Dic61C22⋊C411yescharacteristic
153C22×Dic61C4⋊C412yes—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—22no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—28no—
187C2×C4×D61—48no—
188C2×C4×D61C4212yes—
189C2×C4×D61C4212yes—
190C2×C4×D61C22⋊C412yes—
191C2×C4×D61C22⋊C412yes—
192C2×C4×D61C4⋊C412yes—
193C2×C4×D61C4⋊C412yes—
194C2×C4×D61C4⋊C412yes—
195C2×C4×D61C4⋊C412yes—
196M16×C61—41no—
197M16×C61—41no—
198M16×C61—41no—
199M16×C61—41no—
200C2×C8×C61—22no—
201C2×C8×C61—22no—
202C2×C8×C61—22no—
203C4⋊C4×C61—22no—
204C4⋊C4×C61—22no—
205C4⋊C4×C61—41no—
206C4⋊C4×C61—41no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—41no—
210C22⋊C4×C61—41no—
211C42×C61—22no—
212C42×C61—22no—
213C42×C61—22no—
214C42×C61C22⋊C414yescomplemented
215C22⋊Dic61—22no—
216C22⋊Dic61—22no—
217C22⋊Dic61—41no—
218C22⋊Dic61—41no—
219#11758198—28no—
220#11758198—48no—
221C4⋊Dic61—22no—
222C4⋊Dic61—22no—
223C4⋊Dic61—41no—
224C4⋊Dic61—41no—
225#11758196—28no—
226C4×Dic61—28no—
227C4×Dic61—22no—
228C4×Dic61—22no—
229C4×Dic61—22no—
230C4×Dic61C22⋊C414yescomplemented
231#11758194—41no—
232#11758194—41no—
233#11758194—41no—
234#11758194—41no—
235C2×#92418—22no—
236C2×#92418—22no—
237C2×#92418—22no—
238C23×C61—42no—
239C23×C61C2×C22⋊C411yescharacteristic
240C23×C61C2×C22⋊C411yescharacteristic
241C23×C61C2×C4⋊C411yescharacteristic
242C23×C61#12011yescharacteristic
243C23×C61#12011yescharacteristic
244C23×C61#12311yescharacteristic
245C23×C61#12311yescharacteristic
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—24no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—24no—
256C22×D61—24no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—42no—
260C22×D61—44no—
261C22×D61—44no—
262C22×D61—44no—
263C22×D61—44no—
264C22×D61#9512yes—
265C22×D61#9512yes—
266C2×C4×C61—24no—
267C2×C4×C61—44no—
268C2×C4×C61—44no—
269C2×C4×C61—42no—
270C2×C4×C61C2×C4211yescharacteristic
271C2×C4×C61C2×C22⋊C411yescharacteristic
272C2×C4×C61C2×C22⋊C411yescharacteristic
273C2×C4×C61C2×C22⋊C411yescharacteristic
274C2×C4×C61C2×C4⋊C411yescharacteristic
275C2×C4×C61C2×C4⋊C411yescharacteristic
276C2×C4×C61#11711yescharacteristic
277C2×C4×C61#11711yescharacteristic
278C2×C4×C61C4×D411yescharacteristic
279C2×C4×C61C4×D411yescharacteristic
280C2×C4×C61C4×D411yescharacteristic
281C2×C4×C61C4×D411yescharacteristic
282C2×C4×C61C4×D411yescharacteristic
283C2×C4×C61C4×D411yescharacteristic
284C2×C4×C61C4×D411yescharacteristic
285C2×C4×C61C4×D411yescharacteristic
286C2×C4×C61#12011yescharacteristic
287C2×C4×C61#12011yescharacteristic
288C2×C4×C61#12111yescharacteristic
289C2×C4×C61#12111yescharacteristic
290C2×C4×C61#12111yescharacteristic
291C2×C4×C61#12111yescharacteristic
292C2×C4×C61C22⋊Q811yescharacteristic
293C2×C4×C61C22⋊Q811yescharacteristic
294C2×C4×C61C22⋊Q811yescharacteristic
295C2×C4×C61C22⋊Q811yescharacteristic
296C2×C4×C61#12311yescharacteristic
297C2×C4×C61#12311yescharacteristic
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—24no—
307C2×Dic61—44no—
308C2×Dic61—44no—
309C2×Dic61—42no—
310C2×Dic61#9512yes—
311C2×Dic61#9512yes—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—416no—
329C8×C61—42no—
330#92418—42no—
331#10716—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61C2×#9511yescharacteristic
340C22×C61#37911yescharacteristic
341C22×C61#38111yescharacteristic
342C22×C61#38511yescharacteristic
343C22×C61#38511yescharacteristic
344C22×C61#38611yescharacteristic
345C22×C61#38611yescharacteristic
346C2×D61—24no—
347C2×D61—24no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—44no—
354C2×D61—44no—
355C2×D61—44no—
356C2×D61—44no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61H(3,ℤ/4)14yescomplemented
360C4×C61—44no—
361C4×C61—82no—
362C4×C61C4×C22⋊C411yescharacteristic
363C4×C61C4×C22⋊C411yescharacteristic
364C4×C61#38011yescharacteristic
365C4×C61#38011yescharacteristic
366C4×C61#38511yescharacteristic
367C4×C61#38511yescharacteristic
368C4×C61#38611yescharacteristic
369C4×C61#38611yescharacteristic
370Dic61—22no—
371Dic61—22no—
372Dic61—44no—
373Dic61—82no—
374C22×#117—611no—
375C2×#407—611no—
376#2280—611no—
377C2×H(3,ℤ/4)—611no—
378C2×H(3,ℤ/4)—611no—
379C2×H(3,ℤ/4)—611no—
380C2×H(3,ℤ/4)D6111yescharacteristic, complemented
381C2×C61—21no—
382C2×C61—21no—
383C2×C61—21no—
384C2×C61—21no—
385C2×C61—21no—
386C2×C61—21no—
387C2×C61C22⋊#9511yescharacteristic
388C2×C61C2×H(3,ℤ/4)12yes—
389D61—24no—
390D61—42no—
391C24×C4—611no—
392C22×M16—611no—
393C22×M16C2×D6111yescharacteristic
394C2×#117—611no—
395C2×#117—611no—
396C2×#117—612no—
397C2×#117—1221no—
398C2×#117—1221no—
399C2×#117—1222no—
400C2×#117—1222no—
401C2×#117—1222no—
402C2×#117—1222no—
403C2×#117C2×D6111yescharacteristic
404C2×#117C2×D6111yescharacteristic
405C22×C4⋊C4—1221no—
406C22×C22⋊C4—1221no—
407C22×C42—612no—
408#407—1221no—
409#407—1221no—
410#407—1222no—
411C2×C22⋊C8—614no—
412#381—1221no—
413#380—1222no—
414#379—1221no—
415C4×C22⋊C4—614no—
416H(3,ℤ/4)—22no—
417H(3,ℤ/4)—1222no—
418H(3,ℤ/4)—1222no—
419H(3,ℤ/4)—1222no—
420C61#1071611yescharacteristic, complemented, Sylow
421C25—611no—
422C23×C4—611no—
423C23×C4—611no—
424C23×C4—612no—
425C23×C4—612no—
426C23×C4—611no—
427C23×C4—611no—
428C23×C4—611no—
429C23×C4—612no—
430C23×C4—612no—
431C23×C4—1222no—
432C23×C4—1221no—
433C23×C4—1221no—
434C23×C4—1221no—
435C23×C4—1221no—
436C23×C4—1221no—
437C23×C4—1221no—
438C23×C4—1221no—
439C23×C4—1221no—
440C23×C4C22×D6111yescharacteristic
441C2×M16—21no—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16—21no—
446C2×M16—21no—
447C2×M16—1221no—
448C2×M16—1221no—
449C2×M16—1221no—
450C2×M16—1221no—
451C2×M16—1221no—
452C2×M16—1221no—
453C22×C8—612no—
454C22×C8C4×D6112yescomplemented
455#117—21no—
456#117—21no—
457#117—21no—
458#117—21no—
459#117—21no—
460#117—21no—
461#117—612no—
462#117—612no—
463#117—1224no—
464#117—1224no—
465#117—1224no—
466#117—1224no—
467#117—1224no—
468#117—1221no—
469#117—1221no—
470#117—1221no—
471#117—1221no—
472#117—1221no—
473#117—1221no—
474#117—1224no—
475#117D24412yes—
476#117C22⋊D6112yes—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—1224no—
480C2×C4⋊C4—1224no—
481C2×C4⋊C4—1222no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—1224no—
487C2×C22⋊C4—1224no—
488C2×C22⋊C4—1222no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1224no—
491C2×C22⋊C4—1221no—
492C2×C42—612no—
493C2×C42—612no—
494C2×C42—1224no—
495C2×C42—1222no—
496C2×C42—1224no—
497C2×C42C4×D6112yes—
498C2×C42C4×D6112yescomplemented
499C22⋊C8—1224no—
500C22⋊C8—1224no—
501#95—1224no—
502C24—611no—
503C24—612no—
504C24—612no—
505C24—611no—
506C24—1221no—
507C24—1221no—
508C24—1221no—
509C24—1221no—
510C24—2444no—
511C24D4×D6111yescharacteristic
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—612no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—612no—
518C22×C4—612no—
519C22×C4—612no—
520C22×C4—612no—
521C22×C4—612no—
522C22×C4—612no—
523C22×C4—612no—
524C22×C4—612no—
525C22×C4—612no—
526C22×C4—1228no—
527C22×C4—1221no—
528C22×C4—1221no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—1221no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1222no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—1222no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—1222no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—2448no—
566C22×C4C2×C4×D6111yescharacteristic
567C22×C4C2×C4×D6111yescharacteristic
568C22×C4C2×C4×D6111yescharacteristic
569C22×C4C2×D24411yescharacteristic
570C22×C4#1175822211yescharacteristic
571C22×C4#1175822211yescharacteristic
572C22×C4D4×D6111yescharacteristic
573C22×C4D4×D6111yescharacteristic
574C22×C4D4×D6111yescharacteristic
575C22×C4D4×D6111yescharacteristic
576C22×C4#1175822411yescharacteristic
577C22×C4Q8×D6111yescharacteristic
578C22×C4#1175822611yescharacteristic
579C22×C4C2×C22⋊D6111yescharacteristic
580M16—41no—
581M16—41no—
582M16—41no—
583M16—41no—
584M16—2441no—
585M16—2441no—
586M16—2441no—
587M16—2441no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—1222no—
592C2×C8—1222no—
593C2×C8—1222no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—1228no—
599C4⋊C4—1222no—
600C4⋊C4—1222no—
601C4⋊C4—2441no—
602C4⋊C4—2441no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—1228no—
608C22⋊C4—1222no—
609C22⋊C4—1222no—
610C22⋊C4—2448no—
611C22⋊C4—2441no—
612C22⋊C4—2441no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—614no—
617C42—1228no—
618C42—1222no—
619C42—1222no—
620C42—1222no—
621C42#1175819814yescomplemented
622C23—42no—
623C23—612no—
624C23—612no—
625C23—1224no—
626C23—1224no—
627C23—1224no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1222no—
633C23—1222no—
634C23—1222no—
635C23—1222no—
636C23—2442no—
637C23—2442no—
638C23—2442no—
639C23—2444no—
640C23—2444no—
641C23—2444no—
642C23—2444no—
643C23C22⋊C4×D6111yescharacteristic
644C23C22⋊C4×D6111yescharacteristic
645C23C4⋊C4×D6111yescharacteristic
646C23#1451974511yescharacteristic
647C23#1451974711yescharacteristic
648C23#1451975911yescharacteristic
649C23#1451976211yescharacteristic
650C2×C4—24no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—42no—
654C2×C4—612no—
655C2×C4—612no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1224no—
681C2×C4—24416no—
682C2×C4—2444no—
683C2×C4—2442no—
684C2×C4—2444no—
685C2×C4C42×D6111yescharacteristic
686C2×C4C22⋊C4×D6111yescharacteristic
687C2×C4C22⋊C4×D6111yescharacteristic
688C2×C4C2×#1175819811yescharacteristic
689C2×C4C4⋊C4×D6111yescharacteristic
690C2×C4C4⋊C4×D6111yescharacteristic
691C2×C4#1451973411yescharacteristic
692C2×C4#1451973511yescharacteristic
693C2×C4#1451973711yescharacteristic
694C2×C4#1451973711yescharacteristic
695C2×C4C4×C22⋊D6111yescharacteristic
696C2×C4C4×C22⋊D6111yescharacteristic
697C2×C4#1451973911yescharacteristic
698C2×C4#1451973911yescharacteristic
699C2×C4C4×D24411yescharacteristic
700C2×C4C4×D24411yescharacteristic
701C2×C4#1451974511yescharacteristic
702C2×C4#1451974711yescharacteristic
703C2×C4#1451974811yescharacteristic
704C2×C4#1451975011yescharacteristic
705C2×C4#1451975011yescharacteristic
706C2×C4#1451975211yescharacteristic
707C2×C4#1451975311yescharacteristic
708C2×C4#1451975511yescharacteristic
709C2×C4#1451975511yescharacteristic
710C2×C4#1451975711yescharacteristic
711C2×C4#1451975911yescharacteristic
712C2×C4#1451976211yescharacteristic
713C8—42no—
714C8—2442no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—614no—
723C22—1224no—
724C22—1224no—
725C22—1222no—
726C22—1222no—
727C22—1222no—
728C22—1222no—
729C22—1222no—
730C22—2444no—
731C22—2444no—
732C22—2444no—
733C22—2444no—
734C22—2442no—
735C22—2442no—
736C22#95×D6111yescharacteristic
737C22#1683961711yescharacteristic
738C22#1683962411yescharacteristic
739C22#1683963311yescharacteristic
740C22#1683963611yescharacteristic
741C22#1683963811yescharacteristic
742C22#1683964011yescharacteristic
743C4—44no—
744C4—82no—
745C4—1222no—
746C4—1222no—
747C4—4882no—
748C4—2444no—
749C4#1683960911yescharacteristic
750C4C4×#1175819811yescharacteristic
751C4#1683961911yescharacteristic
752C4#1683962111yescharacteristic
753C4#1683963311yescharacteristic
754C4#1683963611yescharacteristic
755C4#1683963811yescharacteristic
756C4#1683964011yescharacteristic
757C2—21no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—1224no—
764C2—2442no—
765C2#2144404011yescharacteristic
766C2H(3,ℤ/4)×D6112yes—
subgroupG/H
centerC2×C4C42×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×H(3,ℤ/4)C2
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenterC2×H(3,ℤ/4)D61
hypocenterC61#10716
LCSG ▷ C2×C4×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. C2×#16839519C2semidirect
5. C2×#16839518C2semidirect
6. C2×#16839518C2semidirect
7. C2×C61×H(3,ℤ/4)C2semidirect
13. C2×#14519734C4semidirect
21. C2×C42×D61C4semidirect
25. C2×#14519689C4semidirect
29. C4×#11758198C4semidirect
62. C22×#92418C2×C4semidirect
90. C2×C4×Dic61C2×C4semidirect
103. C22×C8×C61C2×C4semidirect
117. C2×C42×C61C2×C4semidirect
214. C42×C61C22⋊C4semidirect
230. C4×Dic61C22⋊C4semidirect
359. C2×D61H(3,ℤ/4)semidirect
380. C2×H(3,ℤ/4)D61semidirect
420. C61#10716semidirect
454. C22×C8C4×D61semidirect
498. C2×C42C4×D61semidirect
621. C42#11758198semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D612
C2×#168397252
#214481982
C2×#168395192
C2×#168395182
C2×C61×H(3,ℤ/4)2
#1071661