Finite Group Databasebeta

← #29689593

Subgroups — #29689593

Order 15616.

1434 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758222C211yesmaximal, characteristic
2C2×#16839814C211yesmaximal, characteristic, complemented
3C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
4#21446753C212yesmaximal, complemented
5#21446611C212yesmaximal, complemented
6#21446110C212yesmaximal, complemented
7#21446108C212yesmaximal, complemented
8#21445799C211yesmaximal, characteristic, complemented
9#21445796C211yesmaximal, characteristic, complemented
10#21445796C211yesmaximal, characteristic, complemented
11C61×#1797C211yesmaximal, characteristic, complemented
12C22×#11758222C411yescharacteristic
13C22×C8×D61C2212yes—
14C4×#11758222—24no—
15C4×#11758222—24no—
16C2×C4×Dic122C411yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×C4×D244C411yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×C22⋊D61C411yescharacteristic
21C2×C4×C22⋊D61C411yescharacteristic
22C2×C4×C22⋊D61C2211yescharacteristic
23C2×C4×C22⋊D61C2211yescharacteristic
24C2×#14519736C411yescharacteristic
25C2×#14519734C411yescharacteristic
26C2×#14519734C411yescharacteristic
27C2×C42×D61C2211yescharacteristic
28C2×C42×D61C2211yescharacteristic
29#16839814—24no—
30C2×C4⋊#92418C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519706C2212yes—
33C4⋊C8×D61—24no—
34C2×C22⋊#92418C2212yes—
35C2×#14519689C2212yes—
36C2×#14519689C2212yes—
37C2×#14519689C2212yes—
38C2×C8×Dic61C2212yes—
39#16839517C2212yes—
40#16839516C2212yes—
41#16839516C2212yes—
42C22×C42×C61C2211yescharacteristic
43C2×C4⋊C8×C61C2211yescharacteristic
44C2×C4⋊C8×C61C2211yescharacteristic
45C2×C22⋊C8×C61C2212yes—
46C61×#336C2212yes—
47C2×#11758222—24no—
48C2×#11758222—24no—
49C2×#11758222C818yescomplemented
50C22×Dic122C2×C411yescharacteristic
51C22×D244C2×C411yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C22⋊D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C22×#92418C2312yes—
61C22×#92418C2312yes—
62C2×C8×D61—24no—
63C2×C8×D61—42no—
64C2×C8×D61—42no—
65C4×Dic122—24no—
66C4×Dic122—22no—
67C4×Dic122—22no—
68C4×D244—24no—
69C4×D244—22no—
70C4×D244—22no—
71C4×C22⋊D61—24no—
72C4×C22⋊D61—22no—
73C4×C22⋊D61—22no—
74C4×C22⋊D61—24no—
75C4×C22⋊D61—22no—
76C4×C22⋊D61—22no—
77#14519736—24no—
78#14519734—24no—
79#14519734—24no—
80C2×C4⋊Dic61C2×C411yescharacteristic
81C2×C4⋊Dic61C2×C411yescharacteristic
82C2×#11758196C2×C411yescharacteristic
83C2×#11758196C2×C411yescharacteristic
84C2×#11758196C2×C411yescharacteristic
85C2×#11758196C2×C411yescharacteristic
86C2×C22⋊Dic61C2×C411yescharacteristic
87C2×C22⋊Dic61C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C42×D61—22no—
99C42×D61—22no—
100C42×D61D414yes—
101C42×D61D414yes—
102C4⋊#92418—22no—
103C4⋊#92418—22no—
104#14519706—24no—
105C22⋊#92418—42no—
106#14519689—24no—
107#14519689—42no—
108#14519689—42no—
109C8×Dic61—24no—
110C23×C4×C61C2×C411yescharacteristic
111C23×C4×C61C2×C411yescharacteristic
112C23×C4×C61C2311yescharacteristic
113C22×C8×C61C2312yes—
114C22×C8×C61C2312yes—
115C2×C42×C61—22no—
116C2×C42×C61—22no—
117C2×C42×C61C2×C411yescharacteristic
118C2×C42×C61C2×C411yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121C4⋊C8×C61—22no—
122C4⋊C8×C61—22no—
123C22⋊C8×C61—42no—
124C24×C61C22×C411yescharacteristic
125C23×D61C22×C411yescharacteristic
126C23×D61C22×C411yescharacteristic
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—41no—
137C22×C4×C61—41no—
138C22×C4×C61C2×C814yescomplemented
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2411yescharacteristic
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61C2×C814yes—
150C2×C22⋊D61C2×C814yescomplemented
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157#11758222—232no—
158C2×D244—22no—
159C2×D244—22no—
160C2×D244C2×C814yes—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—22no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—41no—
175C2×C4×D61—41no—
176C2×C4×D61—41no—
177C2×C4×D61—41no—
178C2×C4×D61C22⋊C414yes—
179C2×C4×D61C22⋊C414yes—
180C2×C4×D61C2×C814yes—
181C2×C4×D61C2×C814yescomplemented
182C2×C4×D61M1614yes—
183C2×C4×D61C2×D412yes—
184C2×C4×D61C2×D412yes—
185C2×Dic122—22no—
186C2×Dic122—22no—
187C2×Dic122C2×C814yescomplemented
188C2×C8×C61—22no—
189C2×C8×C61—22no—
190C2×C8×C61—22no—
191C2×C8×C61—22no—
192C2×C8×C61—22no—
193C2×C8×C61—22no—
194C42×C61—22no—
195C42×C61—22no—
196C42×C61—21no—
197C42×C61—21no—
198C42×C61C2×D412yes—
199C42×C61C2×D412yes—
200C22⋊Dic61—22no—
201C22⋊Dic61—22no—
202#11758198—22no—
203#11758198—22no—
204#11758198—22no—
205#11758198—22no—
206C4⋊Dic61—22no—
207C4⋊Dic61—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212C4×Dic61—22no—
213C4×Dic61—22no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61C22⋊C414yes—
217C4×Dic61C22⋊C414yes—
218C4×Dic61C2×D412yes—
219C4×Dic61C2×D412yes—
220C2×#92418—22no—
221C2×#92418—22no—
222C2×#92418—22no—
223C2×#92418—22no—
224C2×#92418—22no—
225C2×#92418—22no—
226C8×D61—48no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61C22×C812yes—
234C23×C61C23×C411yescharacteristic
235C22×D61—21no—
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—21no—
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61C2×C22⋊C412yes—
246C22×D61C22×C812yes—
247C22×D61C22×C812yes—
248C22×D61C2×M1612yes—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—28no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—44no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61C2×C22⋊C412yes—
266C2×C4×C61C2×C22⋊C412yes—
267C2×C4×C61C22×C812yes—
268C2×C4×C61C22×C812yes—
269C2×C4×C61C2×M1612yes—
270C2×C4×C61C22×D411yescharacteristic
271C2×C4×C61C22×D411yescharacteristic
272C2×C4×C61H(5,𝔽2)11yescharacteristic
273C2×C4×C61H(5,𝔽2)11yescharacteristic
274C2×C4×C612−1+411yescharacteristic
275C2×C4×C612−1+411yescharacteristic
276C22⋊D61—28no—
277C22⋊D61—28no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61C2×C22⋊C412yes—
291C2×Dic61C2×C22⋊C412yes—
292C2×Dic61C2×C22⋊C412yes—
293C2×Dic61C22×C812yes—
294C2×Dic61C22×C812yes—
295C2×Dic61C2×M1612yes—
296D244—28no—
297C4×D61—22no—
298C4×D61—22no—
299C4×D61—22no—
300C4×D61—22no—
301C4×D61—28no—
302C4×D61—44no—
303C4×D61—44no—
304C4×D61—41no—
305C4×D61—41no—
306C4×D61—41no—
307C4×D61—41no—
308C4×D61C22⋊C8116yescomplemented
309Dic122—28no—
310C8×C61—42no—
311C8×C61—42no—
312#92418—42no—
313#92418—42no—
314#21847—611nomaximal, Sylow
315C22×C61—22no—
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61C22×C22⋊C411yescharacteristic
323C22×C61#52011yescharacteristic
324C22×C61#52011yescharacteristic
325C22×C61C23×C811yescharacteristic
326C22×C61C22×M1611yescharacteristic
327C22×C61#56811yescharacteristic
328C22×C61#56811yescharacteristic
329C2×D61—22no—
330C2×D61—22no—
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—22no—
334C2×D61—22no—
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—41no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61C2×C22⋊C814yes—
343C4×C61—22no—
344C4×C61—22no—
345C4×C61—41no—
346C4×C61—41no—
347C4×C61C2×C22⋊C814yes—
348C4×C61#53511yescharacteristic
349C4×C61#53611yescharacteristic
350C4×C61#53711yescharacteristic
351C4×C61#53711yescharacteristic
352Dic61—22no—
353Dic61—22no—
354Dic61—22no—
355Dic61—41no—
356Dic61—41no—
357Dic61C2×C22⋊C814yes—
358C2×C4×#41—611no—
359C2×#431—611no—
360C22×C4⋊C8—611no—
361#1984—612no—
362#1954—612no—
363#1869—612no—
364#1869—612no—
365#1797—611no—
366#1797—611no—
367#1797—611no—
368#1797D6111yescharacteristic, complemented
369C2×C61—42no—
370C2×C61#231111yescharacteristic
371C2×C61C22×C22⋊C811yescharacteristic
372C2×C61#287911yescharacteristic
373C2×C61#298811yescharacteristic
374C2×C61#298811yescharacteristic
375C2×C61#298911yescharacteristic
376C2×C61#298911yescharacteristic
377D61—24no—
378D61—42no—
379C22×#41—611no—
380C23×C8—612no—
381C4×#41—1224no—
382C4×#41—1224no—
383C2×C4×Q8—611no—
384C2×C4×Q8—611no—
385C2×C4×D4—611no—
386C2×C4×D4—611no—
387C2×C4×D4—611no—
388C2×C4×D4—611no—
389C2×C4×D4—611no—
390C2×C4×D4—611no—
391C2×#117—611no—
392C2×#117—611no—
393C2×#117—611no—
394C22×C42—611no—
395C22×C42—611no—
396C22×C42C2×D6111yescharacteristic
397#431—1224no—
398C2×C4⋊C8—612no—
399C2×C4⋊C8—611no—
400C2×C4⋊C8—611no—
401C2×C4⋊C8—1224no—
402C2×C4⋊C8C2×D6111yescharacteristic
403C2×C4⋊C8C2×D6111yescharacteristic
404C2×C22⋊C8—612no—
405C2×C22⋊C8—612no—
406C2×C22⋊C8—612no—
407C2×C22⋊C8—612no—
408C2×C22⋊C8C2×D6112yes—
409C2×C4×C8—612no—
410#336—612no—
411#336—612no—
412#336—612no—
413#336C2×D6112yes—
414C61#2184711yescharacteristic, complemented, Sylow
415C2×#41—618no—
416C2×#41—1224no—
417C2×#41—1224no—
418C22×Q8—611no—
419C22×D4—611no—
420C22×D4—611no—
421C22×D4—611no—
422C23×C4—611no—
423C23×C4—611no—
424C23×C4—611no—
425C23×C4—611no—
426C23×C4—611no—
427C23×C4—611no—
428C23×C4C4×D6111yescharacteristic
429C23×C4C4×D6111yescharacteristic
430C23×C4C22×D6111yescharacteristic
431C22×C8—612no—
432C22×C8—612no—
433C22×C8—1224no—
434C22×C8—2442no—
435C22×C8—2442no—
436C22×C8C22×D6112yes—
437C22×C8C22×D6112yes—
438C4×Q8—1222no—
439C4×Q8—1222no—
440C4×Q8—1224no—
441C4×D4—1222no—
442C4×D4—1222no—
443C4×D4—1224no—
444C4×D4—1222no—
445C4×D4—1222no—
446C4×D4—1224no—
447C4×D4—1222no—
448C4×D4—1222no—
449C4×D4—1224no—
450#117—1224no—
451#117—1224no—
452#117—1224no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—611no—
459C2×C22⋊C4—611no—
460C2×C22⋊C4—611no—
461C2×C22⋊C4—611no—
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—611no—
468C2×C42—611no—
469C2×C42—611no—
470C2×C42—614no—
471C2×C42—614no—
472C2×C42—611no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—1222no—
476C2×C42—1222no—
477C2×C42C4×D6111yescharacteristic
478C2×C42C4×D6111yescharacteristic
479C2×C42C22×D6111yescharacteristic
480C2×C42C22×D6111yescharacteristic
481C4⋊C8—22no—
482C4⋊C8—22no—
483C4⋊C8—1224no—
484C4⋊C8—1222no—
485C4⋊C8—1222no—
486C22⋊C8—42no—
487C22⋊C8—1224no—
488C22⋊C8—2442no—
489C22⋊C8—2442no—
490C22⋊C8—2442no—
491C4×C8—1224no—
492C24—611no—
493C24—611no—
494C24C2×C4×D6111yescharacteristic
495#41—12232no—
496C2×Q8—614no—
497C2×Q8—1222no—
498C2×Q8—1222no—
499C2×D4—614no—
500C2×D4—614no—
501C2×D4—614no—
502C2×D4—1222no—
503C2×D4—1222no—
504C2×D4—1222no—
505C2×D4—1222no—
506C2×D4—1222no—
507C2×D4—1222no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—611no—
520C22×C4—614no—
521C22×C4—614no—
522C22×C4—614no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—612no—
527C22×C4—612no—
528C22×C4—614no—
529C22×C4—614no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1222no—
537C22×C4—1222no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1222no—
545C22×C4—2441no—
546C22×C4—2441no—
547C22×C4—2441no—
548C22×C4—2441no—
549C22×C4C8×D6114yescomplemented
550C22×C4C2×C4×D6111yescharacteristic
551C22×C4C2×C4×D6111yescharacteristic
552C22×C4C2×C4×D6111yescharacteristic
553C22×C4C2×C4×D6111yescharacteristic
554C22×C4C2×C4×D6111yescharacteristic
555C22×C4C23×D6111yescharacteristic
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—1222no—
563C2×C8—1222no—
564C2×C8—1222no—
565C2×C8—1222no—
566C2×C8—1222no—
567C2×C8—1222no—
568C2×C8—2448no—
569C4⋊C4—1222no—
570C4⋊C4—1222no—
571C4⋊C4—1222no—
572C4⋊C4—1222no—
573C4⋊C4—1222no—
574C4⋊C4—1222no—
575C22⋊C4—1222no—
576C22⋊C4—1222no—
577C22⋊C4—1222no—
578C22⋊C4—1222no—
579C22⋊C4—1222no—
580C22⋊C4—1222no—
581C42—21no—
582C42—21no—
583C42—22no—
584C42—22no—
585C42—612no—
586C42—612no—
587C42—614no—
588C42—614no—
589C42—1221no—
590C42—1221no—
591C42—1222no—
592C42—1222no—
593C42D4×D6112yes—
594C42D4×D6112yes—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—612no—
602C23—612no—
603C23—612no—
604C23—612no—
605C23—1221no—
606C23—1221no—
607C23—1221no—
608C23—1221no—
609C23—1221no—
610C23—1221no—
611C23—1221no—
612C23—1221no—
613C23—1221no—
614C23—1221no—
615C23C2×C8×D6112yes—
616C23C22×C4×D6111yescharacteristic
617Q8—1228no—
618D4—1228no—
619D4—1228no—
620D4—1228no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—28no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—44no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—612no—
638C2×C4—612no—
639C2×C4—612no—
640C2×C4—6116no—
641C2×C4—612no—
642C2×C4—612no—
643C2×C4—612no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1221no—
649C2×C4—1221no—
650C2×C4—1228no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1222no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—2444no—
662C2×C4—2444no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4C22⋊C4×D6112yes—
668C2×C4C22⋊C4×D6112yes—
669C2×C4C2×C8×D6112yes—
670C2×C4C2×C8×D6112yes—
671C2×C4M16×D6112yes—
672C2×C4C2×D4×D6111yescharacteristic
673C2×C4C2×D4×D6111yescharacteristic
674C2×C4#1451982211yescharacteristic
675C2×C4#1451982311yescharacteristic
676C2×C4#1451982411yescharacteristic
677C2×C4#1451982511yescharacteristic
678C8—42no—
679C8—42no—
680C8—2442no—
681C8—2442no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—614no—
690C22—1222no—
691C22—1222no—
692C22—1222no—
693C22—1222no—
694C22—1222no—
695C22—1222no—
696C22—1222no—
697C22—1222no—
698C22—1222no—
699C22—2441no—
700C22—2441no—
701C22—2441no—
702C22—2441no—
703C22C2×C22⋊C4×D6111yescharacteristic
704C22#1684024211yescharacteristic
705C22#1684024311yescharacteristic
706C22C22×C8×D6111yescharacteristic
707C22C2×M16×D6111yescharacteristic
708C22#1684052811yescharacteristic
709C22#1684052811yescharacteristic
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—614no—
715C4—1222no—
716C4—1222no—
717C4—1222no—
718C4—2441no—
719C4—2441no—
720C4C22⋊C8×D6114yes—
721C4#1684032811yescharacteristic
722C4#1684033511yescharacteristic
723C4#1684034111yescharacteristic
724C4#1684034211yescharacteristic
725C2—42no—
726C2—1224no—
727C2—2442no—
728C2#2144840811yescharacteristic
729C2C2×C22⋊C8×D6111yescharacteristic
730C2#2145426211yescharacteristic
731C2#2145492711yescharacteristic
732C2#2145492811yescharacteristic
733C2#2145493311yescharacteristic
734C2#2145493811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutatorC22×C61C23×C8
FittingC61×#1797C2
socleC23×C61C23×C4
prime radicalC22×#11758222C4
cosocleC22×C4×C61C24
hypercenter#1797D61
hypocenterC61#21847
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#16839814C2semidirect
3. C2×C4⋊C8×D61C2semidirect
4. #21446753C2semidirect
5. #21446611C2semidirect
6. #21446110C2semidirect
7. #21446108C2semidirect
8. #21445799C2semidirect
9. #21445796C2semidirect
10. #21445796C2semidirect
11. C61×#1797C2semidirect
49. C2×#11758222C8semidirect
138. C22×C4×C61C2×C8semidirect
150. C2×C22⋊D61C2×C8semidirect
181. C2×C4×D61C2×C8semidirect
187. C2×Dic122C2×C8semidirect
308. C4×D61C22⋊C8semidirect
368. #1797D61semidirect
414. C61#21847semidirect
549. C22×C4C8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582222
C2×#168398142
C2×C4⋊C8×D612
#214467532
#214466112
#214461102
#214461082
#214457992
#214457962
C61×#17972
#2184761