Finite Group Databasebeta

← #29696333

Subgroups — #29696333

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×#16840458C211yesmaximal, characteristic
2D4×C4⋊Dic61C211yesmaximal, characteristic, complemented
3#21446788C211yesmaximal, characteristic, complemented
4#21446774C211yesmaximal, characteristic, complemented
5#21446257C211yesmaximal, characteristic, complemented
6#21446247C211yesmaximal, characteristic, complemented
7#21446134C211yesmaximal, characteristic, complemented
8#21446134C211yesmaximal, characteristic, complemented
9#21445915C211yesmaximal, characteristic, complemented
10#21445910C211yesmaximal, characteristic, complemented
11#21445820C211yesmaximal, characteristic, complemented
12#21445645C211yesmaximal, characteristic, complemented
13#21445539C211yesmaximal, characteristic, complemented
14C2×#16839525C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic, complemented
16#16840458—24no—
17#16840458C418yescomplemented
18C2×#14519772—21no—
19C2×#14519769C2211yescharacteristic
20C2×#14519759—21no—
21C2×#14519751C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×#14519749—21no—
24C2×C4×D244C2211yescharacteristic
25C2×D4×Dic61—21no—
26C2×#14519737—21no—
27C2×#14519736C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35#16839661—21no—
36#16839637—21no—
37#16839637—21no—
38#16839632C2211yescharacteristic
39#16839622C2211yescharacteristic
40#16839622C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C61×#435—24no—
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C23×Dic61—21no—
66C23×Dic61—21no—
67C23×Dic61—21no—
68C22×C4×D61—21no—
69#14519772—28no—
70#14519769—22no—
71#14519769C2×C414yescomplemented
72#14519759—28no—
73#14519751—22no—
74#14519751—22no—
75#14519751C2×C414yescomplemented
76#14519751C2×C414yescomplemented
77#14519749—28no—
78C4×D244—22no—
79C4×D244C2×C414yescomplemented
80D4×Dic61—44no—
81#14519737—28no—
82#14519736—22no—
83#14519736C2×C414yescomplemented
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—22no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—41no—
93C2×C4⋊Dic61—41no—
94C2×C4⋊Dic61C2×C414yescomplemented
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112#14519699—22no—
113#14519699—22no—
114#14519699—41no—
115#14519699—41no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×D4×C61D411yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C2×M16×C61—22no—
123C2×M16×C61—22no—
124C2×M16×C61—41no—
125C22×C8×C61—22no—
126C22×C8×C61—22no—
127C22×C8×C61—41no—
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C4×D4×C61C2×C414yes—
133C4×D4×C61D414yes—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—22no—
139C22⋊C8×C61—22no—
140C22⋊C8×C61—22no—
141#97×C61—22no—
142C24×C61C2×D411yescharacteristic
143C24×C61C2×D411yescharacteristic
144C23×D61—21no—
145C2×D4×C61—22no—
146C2×D4×C61—22no—
147C2×D4×C61C22⋊C414yes—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61C22×C412yes—
157C22×C4×C61C22×C412yes—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2411yescharacteristic
165C2×C22⋊D61—24no—
166C2×C22⋊D61—24no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61—42no—
169C2×C22⋊D61—81no—
170C2×C22⋊D61—81no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—24no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—42no—
180C22×Dic61—42no—
181C22×Dic61—42no—
182C22×Dic61—42no—
183C22×Dic61—81no—
184C22×Dic61—81no—
185C22×Dic61—81no—
186C22×Dic61—81no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244C22×C412yes—
193C2×C4×D61—24no—
194C2×C4×D61—81no—
195C2×C4×D61—81no—
196M16×C61—44no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—44no—
209C2×C8×C61#4112yes—
210C4⋊C4×C61C22⋊C414yes—
211C22⋊C4×C61C22⋊C414yes—
212C22⋊C4×C61C22⋊C414yes—
213C42×C61C22×C412yes—
214C42×C61C2×D412yes—
215C22⋊Dic61—24no—
216C22⋊Dic61—42no—
217C22⋊Dic61—42no—
218#11758198—24no—
219#11758198—24no—
220#11758198—24no—
221C4⋊Dic61—24no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—42no—
233C4⋊Dic61—42no—
234C4⋊Dic61—42no—
235C4⋊Dic61—81no—
236C4⋊Dic61C22×C412yes—
237C4⋊Dic61C22×C412yes—
238C4⋊Dic61C22×C412yes—
239C4⋊Dic61#4112yes—
240#11758196—24no—
241#11758196—24no—
242C4×Dic61—24no—
243C4×Dic61—42no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61C2×C22⋊C412yes—
255C23×C61C2×C22⋊C412yes—
256C23×C61AGL(1,ℤ/8)12yes—
257C23×C61#13712yes—
258C23×C61C22×D411yescharacteristic
259C22×D61—22no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266D4×C61—28no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61C2×C22⋊C412yes—
284C2×C4×C61C2×C22⋊C412yes—
285C2×C4×C61C2×C22⋊C412yes—
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—48no—
294C22⋊D61—84no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
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×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—84no—
317C2×Dic61—84no—
318C2×Dic61—84no—
319D244—22no—
320D244—22no—
321D244—41no—
322D244—41no—
323C4×D61—84no—
324C8×C61—22no—
325C8×C61—41no—
326C8×C61—41no—
327C8×C61—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—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61#41714yes—
343C22×C61C22×C22⋊C411yescharacteristic
344C22×C61#54611yescharacteristic
345C22×C61#54711yescharacteristic
346C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C61C2×#13711yescharacteristic
348C22×C61#57611yescharacteristic
349C22×C61#57711yescharacteristic
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—22no—
359C4×C61—22no—
360C4×C61—22no—
361C4×C61C4×#4111yescharacteristic
362C4×C61#52011yescharacteristic
363C4×C61#54611yescharacteristic
364C4×C61#54711yescharacteristic
365Dic61—42no—
366Dic61—42no—
367Dic61—42no—
368Dic61—42no—
369Dic61—81no—
370Dic61—81no—
371Dic61—81no—
372C2×#553—611no—
373C2×#435D6111yescharacteristic, complemented
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×#340—611no—
387C2×C61—24no—
388C2×C61—42no—
389C2×C61#233911yescharacteristic
390C2×C61C2×#41711yescharacteristic
391C2×C61#289711yescharacteristic
392C2×C61#331811yescharacteristic
393C2×C61#332011yescharacteristic
394C2×C61#334511yescharacteristic
395C2×C61#334611yescharacteristic
396D61—82no—
397C22×M16C2×D6111yescharacteristic
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—1221no—
409C2×C4×D4—1221no—
410C2×C4×D4C2×D6111yescharacteristic
411C2×#117—611no—
412C22×C4⋊C4—611no—
413C22×C4⋊C4—611no—
414C22×C4⋊C4—611no—
415#435—24no—
416C2×C4⋊C8C2×D6111yescharacteristic
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×C22⋊C8C2×D6111yescharacteristic
422C2×C22⋊C8C2×D6111yescharacteristic
423C2×#97C2×D6111yescharacteristic
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#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443C61#2249311yescharacteristic, complemented, Sylow
444C22×D4—611no—
445C22×D4—1221no—
446C22×D4—1221no—
447C22×D4D24411yescharacteristic
448C23×C4—1221no—
449C23×C4—1221no—
450C23×C4—1221no—
451C23×C4—1221no—
452C23×C4C22×D6111yescharacteristic
453C23×C4C22×D6111yescharacteristic
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8—41no—
460C22×C8C22×D6111yescharacteristic
461C22×C8C22×D6111yescharacteristic
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—1228no—
471#121—1222no—
472#121—1222no—
473C4×D4—614no—
474C4×D4—1228no—
475C4×D4—1222no—
476C4×D4—2444no—
477C4×D4C4×D6114yes—
478C4×D4C22⋊D6114yes—
479#117—614no—
480#117—1222no—
481C2×C4⋊C4—614no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—1222no—
490C2×C4⋊C4—1222no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1222no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—2441no—
500C2×C4⋊C4—2441no—
501C2×C4⋊C4D24411yescharacteristic
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4D24411yescharacteristic
509C2×C22⋊C4D24411yescharacteristic
510C2×C42—1221no—
511C2×C42—1221no—
512C2×C42C22×D6111yescharacteristic
513C4⋊C8—22no—
514#102—1222no—
515#102—1222no—
516#102—2441no—
517#102—2441no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520#97—22no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524C24—1221no—
525C24C2×D24411yescharacteristic
526C24C2×D24411yescharacteristic
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—612no—
530C2×D4—1224no—
531C2×D4—1224no—
532C2×D4—1221no—
533C2×D4—1221no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—4881no—
538C2×D4—4881no—
539C2×D4—2442no—
540C2×D4—2442no—
541C2×D4#1175819814yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—1224no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1224no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—4881no—
560C22×C4—4881no—
561C22×C4—4881no—
562C22×C4—4881no—
563C22×C4—4881no—
564C22×C4—4881no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4—2442no—
568C22×C4—2442no—
569C22×C4C2×C4×D6112yes—
570C22×C4C2×C4×D6112yes—
571C22×C4C2×D24411yescharacteristic
572C22×C4C2×D24411yescharacteristic
573C22×C4C2×D24411yescharacteristic
574C22×C4C2×D24411yescharacteristic
575C22×C4C2×C22⋊D6112yes—
576C22×C4C2×C22⋊D6112yes—
577C22×C4C23×D6111yescharacteristic
578M16—44no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—44no—
591C2×C8#1175822412yes—
592C4⋊C4—612no—
593C4⋊C4—612no—
594C4⋊C4—612no—
595C4⋊C4—612no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1224no—
601C4⋊C4—1224no—
602C4⋊C4—1224no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—4881no—
610C4⋊C4—2442no—
611C4⋊C4—2442no—
612C4⋊C4—2442no—
613C4⋊C4#1175819814yes—
614C22⋊C4—1224no—
615C22⋊C4—1224no—
616C22⋊C4—1224no—
617C22⋊C4—1224no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4#1175819814yes—
621C22⋊C4#1175819814yes—
622C42—1224no—
623C42—2442no—
624C42C2×C4×D6112yes—
625C42C2×C22⋊D6112yes—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—1222no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23C2×#1175819812yes—
644C23C2×#1175819812yes—
645C23#1451980512yes—
646C23#1451981012yes—
647C23C22×D24411yescharacteristic
648D4—28no—
649D4—1222no—
650D4—1222no—
651D4—4884no—
652D4—2448no—
653D4—2441no—
654D4—2441no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—4884no—
676C2×C4—4884no—
677C2×C4—4884no—
678C2×C4—4884no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4C2×#1175819812yes—
697C2×C4C2×#1175819812yes—
698C2×C4C2×#1175819812yes—
699C2×C4C2×#1175819812yes—
700C2×C4C22×C4×D6111yescharacteristic
701C2×C4C22×C22⋊D6111yescharacteristic
702C2×C4#41×D6111yescharacteristic
703C2×C4C2×#1175822411yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982411yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—4881no—
724C22—4881no—
725C22—4881no—
726C22—4881no—
727C22—2442no—
728C22—2442no—
729C22—2442no—
730C22#1683976414yes—
731C22C22×#1175819811yescharacteristic
732C22#1684040711yescharacteristic
733C22#1684041611yescharacteristic
734C22C2×#1451980511yescharacteristic
735C22C2×#1451981011yescharacteristic
736C22#1684056711yescharacteristic
737C22#1684057411yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—4881no—
743C4—4881no—
744C4—4881no—
745C4—2442no—
746C4—2442no—
747C4—2442no—
748C4—2442no—
749C4C4×#1175822411yescharacteristic
750C4#1684024111yescharacteristic
751C4#1684040611yescharacteristic
752C4#1684041111yescharacteristic
753C2—24no—
754C2—42no—
755C2—4882no—
756C2#2144864411yescharacteristic
757C2C2×#1683976411yescharacteristic
758C2#2145434611yescharacteristic
759C2#2145796211yescharacteristic
760C2#2145799211yescharacteristic
761C2#2145829111yescharacteristic
762C2#2145830611yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC2×#16840458C2
cosocleC22×C4×C61C24
hypercenterC2×#435D61
hypocenterC61#22493
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. D4×C4⋊Dic61C2semidirect
3. #21446788C2semidirect
4. #21446774C2semidirect
5. #21446257C2semidirect
6. #21446247C2semidirect
7. #21446134C2semidirect
8. #21446134C2semidirect
9. #21445915C2semidirect
10. #21445910C2semidirect
11. #21445820C2semidirect
12. #21445645C2semidirect
13. #21445539C2semidirect
14. C2×#16839525C2semidirect
15. C2×C61×#435C2semidirect
17. #16840458C4semidirect
71. #14519769C2×C4semidirect
75. #14519751C2×C4semidirect
76. #14519751C2×C4semidirect
79. C4×D244C2×C4semidirect
83. #14519736C2×C4semidirect
94. C2×C4⋊Dic61C2×C4semidirect
373. C2×#435D61semidirect
443. C61#22493semidirect

Maximal subgroups

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

subgroupindex
C2×#168404582
D4×C4⋊Dic612
#214467882
#214467742
#214462572
#214462472
#214461342
#214459152
#214459102
#214458202
#214456452
#214455392
C2×#168395252
C2×C61×#4352
#2249361