Finite Group Databasebeta

← #29699032

Subgroups — #29699032

Order 15616.

1052 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839812C211yesmaximal, characteristic, complemented
2C22×#14519706C211yesmaximal, characteristic, complemented
3C4×D4×Dic61C211yesmaximal, characteristic
4#21446428C211yesmaximal, characteristic, complemented
5#21446422C211yesmaximal, characteristic, complemented
6#21446377C211yesmaximal, characteristic, complemented
7#21446375C211yesmaximal, characteristic, complemented
8#21446112C211yesmaximal, characteristic
9#21445934C211yesmaximal, characteristic, complemented
10#21445797C211yesmaximal, characteristic, complemented
11#21445797C211yesmaximal, characteristic, complemented
12#21445667C211yesmaximal, characteristic, complemented
13#21445593C211yesmaximal, characteristic, complemented
14C8×C22⋊Dic61C211yesmaximal, characteristic, complemented
15C61×#1869C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×D4×Dic61C411yescharacteristic
18C2×D4×Dic61C411yescharacteristic
19C22×C4×Dic61C2211yescharacteristic
20C22×C4×Dic61C2211yescharacteristic
21#16839812—24no—
22C2×#14519706—24no—
23C2×#14519706C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic
36C4⋊C4×Dic61C411yescharacteristic
37C4⋊C4×Dic61C411yescharacteristic
38C4×C4⋊Dic61C2211yescharacteristic
39C22⋊C4×Dic61C411yescharacteristic
40C22⋊C4×Dic61C411yescharacteristic
41C22⋊C4×Dic61C411yescharacteristic
42C22⋊C4×Dic61C411yescharacteristic
43C4×C22⋊Dic61C2211yescharacteristic
44C4×C22⋊Dic61C2211yescharacteristic
45C42×Dic61C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C23×C8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C23×Dic61C2×C411yescharacteristic
62C23×Dic61C2×C411yescharacteristic
63C23×Dic61C2×C411yescharacteristic
64C23×Dic61C2×C411yescharacteristic
65C22×#92418—22no—
66C22×#92418—22no—
67C22×#92418—41no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72D4×Dic61—24no—
73D4×Dic61C818yescomplemented
74C2×C4⋊Dic61C2×C411yescharacteristic
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×C22⋊Dic61C2×C411yescharacteristic
77C2×C22⋊Dic61C2×C411yescharacteristic
78C2×C22⋊Dic61C2×C411yescharacteristic
79C2×C22⋊Dic61C2×C411yescharacteristic
80C2×C4×Dic61—22no—
81C2×C4×Dic61—22no—
82C2×C4×Dic61—22no—
83C2×C4×Dic61—22no—
84C2×C4×Dic61C2×C411yescharacteristic
85C2×C4×Dic61C2×C411yescharacteristic
86C2×C4×Dic61C2×C411yescharacteristic
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96#14519706—22no—
97#14519706—22no—
98#14519706—22no—
99#14519706—22no—
100#14519706—22no—
101#14519706D414yescomplemented
102C22⋊#92418—22no—
103C22⋊#92418—22no—
104C22⋊#92418—41no—
105C8×Dic61—22no—
106C8×Dic61—22no—
107C8×Dic61—41no—
108C8×Dic61—41no—
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115C22×D4×C61C2×C411yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C22×C8×C61—22no—
119C22×C8×C61—22no—
120C22×C8×C61—41no—
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C4×D4×C61—22no—
126C4×D4×C61—22no—
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61C2×C411yescharacteristic
129C2×C22⋊C4×C61C2×C411yescharacteristic
130C2×C42×C61C2311yescharacteristic
131C22⋊C8×C61—22no—
132C22⋊C8×C61—22no—
133C22⋊C8×C61—41no—
134C24×C61C22×C411yescharacteristic
135C24×C61C22×C411yescharacteristic
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61C2×C814yes—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61#4112yes—
154C22×C4×C61#4112yes—
155C22×C4×C61C2411yescharacteristic
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—41no—
165C22×Dic61—41no—
166C22×Dic61C2×C814yes—
167C22×Dic61C2×C814yescomplemented
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—44no—
188C2×C8×C61C2×D412yes—
189C4⋊C4×C61—22no—
190C22⋊C4×C61—22no—
191C22⋊C4×C61—22no—
192C42×C61—21no—
193C42×C61—21no—
194C22⋊Dic61—22no—
195C22⋊Dic61C2×C814yes—
196C22⋊Dic61C2×C814yescomplemented
197C22⋊Dic61M1614yes—
198C4⋊Dic61—22no—
199C4⋊Dic61C2×C814yescomplemented
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61—41no—
213C4×Dic61C2×C814yescomplemented
214C4×Dic61C2×D412yes—
215C4×Dic61#4112yes—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—44no—
228C2×#92418C2×D412yes—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61#11712yes—
240C23×C61C22×C812yes—
241C23×C61C22×C812yes—
242C23×C61C2×M1612yes—
243C23×C61C23×C411yescharacteristic
244D4×C61—28no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61#11712yes—
264C2×C4×C61C22×C812yes—
265C2×C4×C61C22×D411yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61C2×#4111yescharacteristic
268C2×C4×C61C2×#4111yescharacteristic
269C2×C4×C61H(5,𝔽2)11yescharacteristic
270C2×C4×C612−1+411yescharacteristic
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—28no—
284C2×Dic61—28no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—44no—
289C2×Dic61—44no—
290C2×Dic61C4×D412yes—
291C2×Dic61C4×D412yes—
292C2×Dic61C22×C812yes—
293C2×Dic61C22×C812yes—
294C2×Dic61C22×C812yes—
295C2×Dic61C22×C812yes—
296C2×Dic61C2×M1612yes—
297C2×Dic61C2×M1612yes—
298C2×Dic61#13112yes—
299C8×C61—22no—
300C8×C61—41no—
301C8×C61—41no—
302C8×C61—41no—
303#92418—22no—
304#92418—41no—
305#92418—41no—
306#92418—41no—
307#22748—611nomaximal, Sylow
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—22no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61#43114yescomplemented
322C22×C61C2×#11711yescharacteristic
323C22×C61C2×C4×D411yescharacteristic
324C22×C61#52011yescharacteristic
325C22×C61C23×C811yescharacteristic
326C22×C61C22×M1611yescharacteristic
327C22×C61C2×#13111yescharacteristic
328C22×C61#56811yescharacteristic
329C4×C61—22no—
330C4×C61—22no—
331C4×C61—41no—
332C4×C61—41no—
333C4×C61#54611yescharacteristic
334C4×C61#54811yescharacteristic
335C4×C61#55211yescharacteristic
336C4×C61#55311yescharacteristic
337Dic61—22no—
338Dic61—22no—
339Dic61—22no—
340Dic61—22no—
341Dic61—22no—
342Dic61—22no—
343Dic61—41no—
344Dic61C8×D414yes—
345C2×#431—611no—
346C22×C4⋊C8—611no—
347C42×D4—611no—
348#1923—611no—
349#1923—611no—
350#1916—611no—
351#1916—611no—
352#1869—611no—
353#1869D6111yescharacteristic
354#1831—611no—
355#1797—611no—
356#1797—611no—
357C4×C4⋊C8—611no—
358C8×C22⋊C4—611no—
359C8×C22⋊C4—611no—
360C2×C61—24no—
361C2×C61—42no—
362C2×C61#235211yescharacteristic
363C2×C61C2×#43111yescharacteristic
364C2×C61#292511yescharacteristic
365C2×C61C2×C8×D411yescharacteristic
366C2×C61D4×M1611yescharacteristic
367C2×C61#298811yescharacteristic
368C2×C61#299011yescharacteristic
369C23×C8—611no—
370C23×C8C2×D6111yescharacteristic
371C2×C4×D4—611no—
372C2×C4×D4—611no—
373C2×C4×D4C2×D6111yescharacteristic
374C22×C42—611no—
375C22×C42—611no—
376#431—1224no—
377C2×C4⋊C8—611no—
378C2×C4⋊C8—611no—
379C2×C4⋊C8—611no—
380C2×C4⋊C8—611no—
381C2×C4⋊C8—611no—
382C2×C4⋊C8—611no—
383C2×C4⋊C8—1224no—
384C2×C22⋊C8—611no—
385C2×C22⋊C8—611no—
386C2×C22⋊C8—611no—
387C2×C22⋊C8C2×D6111yescharacteristic
388C2×C22⋊C8C2×D6111yescharacteristic
389C2×C22⋊C8C2×D6111yescharacteristic
390C2×C4×C8—611no—
391C2×C4×C8—611no—
392C2×C4×C8—611no—
393C2×C4×C8—611no—
394C4×C4⋊C4—611no—
395C4×C4⋊C4—611no—
396C4×C4⋊C4—611no—
397C4×C22⋊C4—611no—
398C4×C22⋊C4—611no—
399C4×C22⋊C4—611no—
400C4×C22⋊C4—611no—
401C4×C22⋊C4—611no—
402C4×C22⋊C4—611no—
403C43—611no—
404#336—611no—
405#336—611no—
406#336—611no—
407#336—611no—
408#336—611no—
409#336—611no—
410#336—611no—
411#336—611no—
412#336C2×D6111yescharacteristic
413#336C2×D6111yescharacteristic
414C61#2274811yescharacteristic, complemented, Sylow
415C22×D4C4×D6111yescharacteristic
416C23×C4—611no—
417C23×C4—611no—
418C23×C4—611no—
419C23×C4—611no—
420C23×C4C22×D6111yescharacteristic
421C23×C4C22×D6111yescharacteristic
422C22×C8—22no—
423C22×C8—22no—
424C22×C8—41no—
425C22×C8—611no—
426C22×C8—611no—
427C22×C8—611no—
428C22×C8—611no—
429C22×C8—1222no—
430C22×C8—1222no—
431C22×C8—2441no—
432C22×C8C22×D6111yescharacteristic
433C22×C8C22×D6111yescharacteristic
434C22×C8C22×D6111yescharacteristic
435C22×C8C22×D6111yescharacteristic
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—618no—
439C4×D4—1224no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4C4×D6111yescharacteristic
443C2×C22⋊C4—611no—
444C2×C22⋊C4—611no—
445C2×C22⋊C4—611no—
446C2×C22⋊C4—611no—
447C2×C22⋊C4C4×D6111yescharacteristic
448C2×C22⋊C4C4×D6111yescharacteristic
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—611no—
457C2×C42—611no—
458C2×C42—611no—
459C2×C42—611no—
460C2×C42—611no—
461C2×C42—1222no—
462C2×C42—1222no—
463C2×C42—1222no—
464C2×C42—1222no—
465C2×C42C22×D6111yescharacteristic
466C4⋊C8—614no—
467C4⋊C8—1222no—
468C4⋊C8—1222no—
469C4⋊C8—1222no—
470C4⋊C8—1222no—
471C4⋊C8—1222no—
472C22⋊C8—22no—
473C22⋊C8—22no—
474C22⋊C8—41no—
475C22⋊C8—1222no—
476C22⋊C8—1222no—
477C22⋊C8—2441no—
478C4×C8—1222no—
479C4×C8—1222no—
480C4×C8—2441no—
481C4×C8—2441no—
482#95—611no—
483#95—611no—
484#95—611no—
485#95—611no—
486#95—611no—
487#95—611no—
488C24C2×C4×D6111yescharacteristic
489C24C2×C4×D6111yescharacteristic
490C2×D4—22no—
491C2×D4—22no—
492C2×D4C8×D6114yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—614no—
511C22×C4—614no—
512C22×C4—611no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1222no—
519C22×C4—1222no—
520C22×C4—1222no—
521C22×C4—2441no—
522C22×C4—2441no—
523C22×C4C2×C4×D6111yescharacteristic
524C22×C4C2×C4×D6111yescharacteristic
525C22×C4C2×C4×D6111yescharacteristic
526C22×C4C2×C4×D6111yescharacteristic
527C22×C4#1175822412yes—
528C22×C4#1175822412yes—
529C22×C4C23×D6111yescharacteristic
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—44no—
542C2×C8—612no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—2444no—
555C2×C8D4×D6112yes—
556C4⋊C4—22no—
557C4⋊C4—614no—
558C4⋊C4—1222no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—614no—
562C22⋊C4—614no—
563C22⋊C4—614no—
564C22⋊C4—1222no—
565C42—21no—
566C42—21no—
567C42—612no—
568C42—612no—
569C42—614no—
570C42—1222no—
571C42—1222no—
572C42—1222no—
573C42—1222no—
574C42—1222no—
575C42—1222no—
576C42—1221no—
577C42—1221no—
578C42—1221no—
579C42—1221no—
580C42—1221no—
581C42—1221no—
582C42—2441no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23#1451973312yes—
594C23C2×C8×D6112yes—
595C23C2×C8×D6112yes—
596C23M16×D6112yes—
597C23C22×C4×D6111yescharacteristic
598D4—28no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—612no—
618C2×C4—612no—
619C2×C4—612no—
620C2×C4—612no—
621C2×C4—612no—
622C2×C4—612no—
623C2×C4—612no—
624C2×C4—612no—
625C2×C4—612no—
626C2×C4—1228no—
627C2×C4—1228no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1221no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—1221no—
637C2×C4—1221no—
638C2×C4—1221no—
639C2×C4—1221no—
640C2×C4—1221no—
641C2×C4—1221no—
642C2×C4—1221no—
643C2×C4—2444no—
644C2×C4—2444no—
645C2×C4#1451973312yes—
646C2×C4C2×C8×D6112yes—
647C2×C4C2×D4×D6111yescharacteristic
648C2×C4#41×D6111yescharacteristic
649C2×C4C2×#1175822411yescharacteristic
650C2×C4C2×#1175822411yescharacteristic
651C2×C4#1451982211yescharacteristic
652C2×C4#1451982411yescharacteristic
653C8—22no—
654C8—41no—
655C8—41no—
656C8—41no—
657C8—1222no—
658C8—2441no—
659C8—2441no—
660C8—2441no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22#1683981214yescomplemented
675C22C2×#1451973311yescharacteristic
676C22C4×D4×D6111yescharacteristic
677C22#1684024111yescharacteristic
678C22C22×C8×D6111yescharacteristic
679C22C2×M16×D6111yescharacteristic
680C22#131×D6111yescharacteristic
681C22#1684052711yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—41no—
686C4—614no—
687C4—1222no—
688C4—1222no—
689C4—1222no—
690C4—1222no—
691C4—1222no—
692C4—1222no—
693C4—2441no—
694C4#1684039911yescharacteristic
695C4#1684041811yescharacteristic
696C4#1684044911yescharacteristic
697C4#1684045511yescharacteristic
698C2—24no—
699C2—42no—
700C2#2144874611yescharacteristic
701C2C2×#1683981211yescharacteristic
702C2#2145448111yescharacteristic
703C2C8×D4×D6111yescharacteristic
704C2#2145455211yescharacteristic
705C2#2145492611yescharacteristic
706C2#2145493911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutatorC22×C61C23×C8
FittingC61×#1869C2
socleC23×C61C23×C4
prime radicalC22×D4×C61C2×C4
cosocleC22×C4×C61C24
hypercenter#1869D61
hypocenterC61#22748
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#16839812C2semidirect
2. C22×#14519706C2semidirect
4. #21446428C2semidirect
5. #21446422C2semidirect
6. #21446377C2semidirect
7. #21446375C2semidirect
9. #21445934C2semidirect
10. #21445797C2semidirect
11. #21445797C2semidirect
12. #21445667C2semidirect
13. #21445593C2semidirect
14. C8×C22⋊Dic61C2semidirect
73. D4×Dic61C8semidirect
101. #14519706D4semidirect
167. C22×Dic61C2×C8semidirect
196. C22⋊Dic61C2×C8semidirect
199. C4⋊Dic61C2×C8semidirect
213. C4×Dic61C2×C8semidirect
321. C22×C61#431semidirect
414. C61#22748semidirect
674. C22#16839812semidirect

Maximal subgroups

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

subgroupindex
C2×#168398122
C22×#145197062
C4×D4×Dic612
#214464282
#214464222
#214463772
#214463752
#214461122
#214459342
#214457972
#214456672
#214455932
C8×C22⋊Dic612
C61×#18692
#2274861