Finite Group Databasebeta

← #29696327

Subgroups — #29696327

Order 15616.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840460C211yesmaximal, characteristic
2C2×#16839833C211yesmaximal, characteristic, complemented
3C4⋊C4×C22⋊D61C211yesmaximal, characteristic, complemented
4#21446786C211yesmaximal, characteristic, complemented
5#21446775C211yesmaximal, characteristic, complemented
6#21446256C211yesmaximal, characteristic, complemented
7#21446247C211yesmaximal, characteristic, complemented
8#21446136C211yesmaximal, characteristic, complemented
9#21446135C211yesmaximal, characteristic, complemented
10#21445912C211yesmaximal, characteristic, complemented
11#21445909C211yesmaximal, characteristic, complemented
12#21445818C211yesmaximal, characteristic, complemented
13#21445643C211yesmaximal, characteristic, complemented
14#21445537C211yesmaximal, characteristic, complemented
15C2×C61×#340C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17#16840460—24no—
18#16840460C418yescomplemented
19C2×#14519772—21no—
20C2×#14519768C2211yescharacteristic
21C2×#14519762—21no—
22C2×#14519752C2211yescharacteristic
23C2×#14519751—21no—
24C2×#14519751C2211yescharacteristic
25C2×#14519739C2211yescharacteristic
26C2×C4×C22⋊D61—21no—
27C2×C4×C22⋊D61—21no—
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31#16839833—24no—
32C2×#14519706C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519687C2211yescharacteristic
40#16839657—21no—
41#16839635—21no—
42#16839633—21no—
43#16839631C2211yescharacteristic
44#16839622C2211yescharacteristic
45#16839619C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C22×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×D244—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61D411yescharacteristic
66C22×C4×D61—21no—
67C22×C4×D61—21no—
68C22×C4×D61C2311yescharacteristic
69C2×#11758189—22no—
70C2×#11758189—22no—
71C2×#11758189—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519772—28no—
75#14519768—22no—
76#14519768C2×C414yescomplemented
77#14519762—28no—
78#14519752—22no—
79#14519752C2×C414yescomplemented
80#14519751—22no—
81#14519751—28no—
82#14519751C2×C414yescomplemented
83#14519739—22no—
84#14519739C2×C414yescomplemented
85C4×C22⋊D61—28no—
86C4×C22⋊D61—44no—
87C4×C22⋊D61C2×C414yes—
88C4×C22⋊D61D414yes—
89#14519735—22no—
90#14519735C2×C414yescomplemented
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196D411yescharacteristic
100C4⋊C4×D61—22no—
101C4⋊C4×D61—41no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61D411yescharacteristic
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198D411yescharacteristic
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113#14519706—22no—
114#14519699—22no—
115#14519699—41no—
116#14519697—22no—
117#14519697—41no—
118C22⋊#92418—22no—
119#14519689—22no—
120#14519687—22no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124C23×C4×C61—21no—
125C23×C4×C61—21no—
126C23×C4×C61C2311yescharacteristic
127C22×C8×C61—22no—
128C22×C8×C61—22no—
129C22×C8×C61—41no—
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—22no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—41no—
137C2×C4⋊C4×C61C2×C414yescomplemented
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C24×C61C2×D411yescharacteristic
143C23×D61—21no—
144C23×D61C2×D411yescharacteristic
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—24no—
153C22×C4×C61—21no—
154C22×C4×C61—42no—
155C22×C4×C61—42no—
156C22×C4×C61—81no—
157C22×C4×C61—81no—
158C22×C4×C61—81no—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2411yescharacteristic
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—24no—
166C2×C22⋊D61—42no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61C22⋊C414yes—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—24no—
181C2×D244—81no—
182C2×D244—81no—
183C2×D244C22×C412yes—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—24no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—81no—
192C2×C4×D61—81no—
193C2×C4×D61—81no—
194C2×C4×D61C22×C412yes—
195C2×C4×D61C2×D412yes—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—44no—
202C2×C8×C61#4112yes—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61C22×C412yes—
211C4⋊C4×C61C22×C412yes—
212C4⋊C4×C61#4112yes—
213C22⋊Dic61—42no—
214C22⋊Dic61C22⋊C414yes—
215#11758198—24no—
216#11758198—24no—
217#11758198—24no—
218#11758198—24no—
219#11758198—42no—
220#11758198C22⋊C414yes—
221C4⋊Dic61—21no—
222C4⋊Dic61—24no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61C22×C412yes—
228#11758196—24no—
229#11758196—42no—
230#11758196—42no—
231#11758196—81no—
232#11758196C22⋊C414yes—
233C4×Dic61—24no—
234C4×Dic61—42no—
235C4×Dic61C22×C412yes—
236C4×Dic61C2×D412yes—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243#11758189—44no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61C2×C22⋊C412yes—
249C23×C61AGL(1,ℤ/8)12yes—
250C23×C61#13712yes—
251C23×C61C22×D411yescharacteristic
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—22no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61C2×C22⋊C412yes—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—84no—
285C2×C4×C61—84no—
286C2×C4×C61C2×C22⋊C412yes—
287C2×C4×C61C23×C411yescharacteristic
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C2×C4×C612−1+411yescharacteristic
293C22⋊D61—28no—
294C22⋊D61—48no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—22no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61C2×C22⋊C412yes—
311C2×Dic61C2×C22⋊C412yes—
312C2×Dic61C2×C22⋊C412yes—
313D244—22no—
314D244—22no—
315D244—41no—
316D244—41no—
317D244—84no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—84no—
323C4×D61—84no—
324C8×C61—22no—
325C8×C61—41no—
326#92418—41no—
327#92418—41no—
328#22493—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61#41714yes—
336C22×C61C22×C22⋊C411yescharacteristic
337C22×C61#54611yescharacteristic
338C22×C61#54711yescharacteristic
339C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C61C2×#13711yescharacteristic
341C22×C61#57611yescharacteristic
342C22×C61#57711yescharacteristic
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C4×C61—22no—
358C4×C61—42no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61—81no—
362C4×C61C4×#4111yescharacteristic
363C4×C61#52011yescharacteristic
364C4×C61#54611yescharacteristic
365C4×C61#54711yescharacteristic
366Dic61—22no—
367Dic61—22no—
368Dic61—22no—
369Dic61—42no—
370Dic61—81no—
371Dic61—81no—
372C2×#553—611no—
373C2×#435—611no—
374D4×C4⋊C4—611no—
375#1992—611no—
376#1989—611no—
377#1895—611no—
378#1893—611no—
379#1874—611no—
380#1874—611no—
381#1825—611no—
382#1824—611no—
383#1802—611no—
384#1762—611no—
385#1736—611no—
386C2×#340D6111yescharacteristic, complemented
387C2×C61—24no—
388C2×C61#233911yescharacteristic
389C2×C61C2×#41711yescharacteristic
390C2×C61#289711yescharacteristic
391C2×C61#331811yescharacteristic
392C2×C61#332011yescharacteristic
393C2×C61#334511yescharacteristic
394C2×C61#334611yescharacteristic
395D61—42no—
396D61—82no—
397C22×M16—611no—
398C23×C8C2×D6111yescharacteristic
399#553—618no—
400#553—1224no—
401C2×#126—1221no—
402C2×#125—611no—
403C2×#123—1221no—
404C2×#121—611no—
405C2×#121—611no—
406C2×#121—1221no—
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C2×C4×D4—1221no—
410C2×C4×D4—1221no—
411C2×#117—611no—
412C22×C4⋊C4—611no—
413C22×C4⋊C4C2×D6111yescharacteristic
414C22×C4⋊C4C2×D6111yescharacteristic
415#435—1224no—
416C2×C4⋊C8—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—611no—
423C2×#97—611no—
424#389—1221no—
425#385—1221no—
426#385—1221no—
427#384—611no—
428#380—611no—
429#380—611no—
430C4×C4⋊C4—611no—
431#340—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340C2×D6111yescharacteristic
440#340C2×D6111yescharacteristic
441#340C2×D6111yescharacteristic
442#340C2×D6111yescharacteristic
443C61#2249311yescharacteristic, complemented, Sylow
444C22×D4—611no—
445C22×D4—611no—
446C22×D4—1221no—
447C22×D4—1221no—
448C23×C4—21no—
449C23×C4—21no—
450C23×C4—611no—
451C23×C4—1221no—
452C23×C4—1221no—
453C23×C4C22×D6111yescharacteristic
454C2×M16—1222no—
455C2×M16—1222no—
456C2×M16—2441no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8—41no—
460C22×C8—611no—
461C22×C8—611no—
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6111yescharacteristic
464#126—1228no—
465#125—614no—
466#125—1222no—
467#123—1228no—
468#121—614no—
469#121—614no—
470#121—1222no—
471#121—1228no—
472#121—1222no—
473C4×D4—614no—
474C4×D4—614no—
475C4×D4—614no—
476C4×D4—1222no—
477C4×D4—1228no—
478C4×D4—2444no—
479#117—614no—
480#117—1222no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1222no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—2441no—
497C2×C4⋊C4C4×D6114yescomplemented
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C4⋊C4C22×D6111yescharacteristic
500C2×C4⋊C4C22×D6111yescharacteristic
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C22⋊C4—611no—
503C2×C22⋊C4—611no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C42—611no—
511C2×C42—1221no—
512C2×C42—1221no—
513C4⋊C8—1222no—
514#102—1222no—
515#102—1222no—
516#102—2441no—
517#102—2441no—
518C22⋊C8—1222no—
519C22⋊C8—1222no—
520#97—1222no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524C24—611no—
525C24—1221no—
526C24D4×D6111yescharacteristic
527C2×D4—614no—
528C2×D4—612no—
529C2×D4—1224no—
530C2×D4—1222no—
531C2×D4—1222no—
532C2×D4—1224no—
533C2×D4—1221no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—4881no—
539C2×D4—4881no—
540C2×D4—2442no—
541C2×D4—2442no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—21no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—1224no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—4881no—
570C22×C4—4881no—
571C22×C4—4881no—
572C22×C4—2442no—
573C22×C4—2442no—
574C22×C4C2×C4×D6112yes—
575C22×C4D4×D6112yes—
576C22×C4D4×D6111yescharacteristic
577C22×C4C23×D6111yescharacteristic
578M16—2444no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—44no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8#1175822212yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—614no—
600C4⋊C4—612no—
601C4⋊C4—1224no—
602C4⋊C4—1224no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—4881no—
609C4⋊C4—2442no—
610C4⋊C4—2442no—
611C4⋊C4C2×C4×D6112yes—
612C4⋊C4C2×C4×D6112yes—
613C4⋊C4#1175822212yes—
614C22⋊C4—614no—
615C22⋊C4—614no—
616C22⋊C4—1224no—
617C22⋊C4—1224no—
618C22⋊C4—1224no—
619C22⋊C4—1224no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C42—612no—
623C42—612no—
624C42—1224no—
625C42—2442no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—612no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1222no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23C22⋊C4×D6112yes—
645C23#1451980412yes—
646C23#1451980912yes—
647C23C2×D4×D6111yescharacteristic
648D4—1228no—
649D4—1222no—
650D4—1222no—
651D4—4884no—
652D4—2448no—
653D4—2441no—
654D4—2441no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—84no—
674C2×C4—84no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—4884no—
690C2×C4—4884no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4C22⋊C4×D6112yes—
700C2×C4C22×C4×D6111yescharacteristic
701C2×C4C2×D4×D6111yescharacteristic
702C2×C4C2×#1175822211yescharacteristic
703C2×C4C2×#1175822211yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982511yescharacteristic
706C8—22no—
707C8—41no—
708C8—2441no—
709C8—2441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—1222no—
717C22—1222no—
718C22—1222no—
719C22—4881no—
720C22—4881no—
721C22—4881no—
722C22—4881no—
723C22—2442no—
724C22—2442no—
725C22—2442no—
726C22—2441no—
727C22—2441no—
728C22—2441no—
729C22—2441no—
730C22#1683976214yes—
731C22C2×C22⋊C4×D6111yescharacteristic
732C22#1684040211yescharacteristic
733C22#1684041311yescharacteristic
734C22C2×#1451980411yescharacteristic
735C22C2×#1451980911yescharacteristic
736C22#1684056311yescharacteristic
737C22#1684056811yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—81no—
743C4—1222no—
744C4—1222no—
745C4—1222no—
746C4—4881no—
747C4—4881no—
748C4—2442no—
749C4C4×#1175822211yescharacteristic
750C4#1684024311yescharacteristic
751C4#1684040211yescharacteristic
752C4#1684041311yescharacteristic
753C2—24no—
754C2—4882no—
755C2—2442no—
756C2#2144864611yescharacteristic
757C2C2×#1683976211yescharacteristic
758C2#2145434011yescharacteristic
759C2#2145795611yescharacteristic
760C2#2145798611yescharacteristic
761C2#2145828511yescharacteristic
762C2#2145830011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#340C2
socleC23×C61C22×D4
prime radicalC2×#16840460C2
cosocleC22×C4×C61C24
hypercenterC2×#340D61
hypocenterC61#22493
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C2×#16839833C2semidirect
3. C4⋊C4×C22⋊D61C2semidirect
4. #21446786C2semidirect
5. #21446775C2semidirect
6. #21446256C2semidirect
7. #21446247C2semidirect
8. #21446136C2semidirect
9. #21446135C2semidirect
10. #21445912C2semidirect
11. #21445909C2semidirect
12. #21445818C2semidirect
13. #21445643C2semidirect
14. #21445537C2semidirect
15. C2×C61×#340C2semidirect
18. #16840460C4semidirect
76. #14519768C2×C4semidirect
79. #14519752C2×C4semidirect
82. #14519751C2×C4semidirect
84. #14519739C2×C4semidirect
90. #14519735C2×C4semidirect
137. C2×C4⋊C4×C61C2×C4semidirect
386. C2×#340D61semidirect
443. C61#22493semidirect
497. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404602
C2×#168398332
C4⋊C4×C22⋊D612
#214467862
#214467752
#214462562
#214462472
#214461362
#214461352
#214459122
#214459092
#214458182
#214456432
#214455372
C2×C61×#3402
#2249361