Finite Group Databasebeta

← #29699028

Subgroups — #29699028

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×#16839813C211yesmaximal, characteristic, complemented
2C22×#14519706C211yesmaximal, characteristic, complemented
3C4×#14519737C211yesmaximal, characteristic
4#21446425C211yesmaximal, characteristic, complemented
5#21446423C211yesmaximal, characteristic, complemented
6#21446376C211yesmaximal, characteristic, complemented
7#21446374C211yesmaximal, characteristic, complemented
8#21446111C211yesmaximal, characteristic
9#21446109C211yesmaximal, characteristic
10#21445934C211yesmaximal, characteristic, complemented
11#21445798C211yesmaximal, characteristic, complemented
12#21445797C211yesmaximal, characteristic, complemented
13C4×#14519706C211yesmaximal, characteristic, complemented
14C22⋊C4×#92418C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C23×#92418C2211yescharacteristic
17C2×C4×C22⋊D61C2211yescharacteristic
18C2×#14519737C411yescharacteristic
19C2×#14519737C411yescharacteristic
20C22×C4×Dic61C2211yescharacteristic
21C2×C42×D61C2211yescharacteristic
22#16839813—24no—
23C2×#14519706—24no—
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519706C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic
37C4×#11758196C2211yescharacteristic
38#16839613C411yescharacteristic
39#16839613C411yescharacteristic
40C22⋊C4×Dic61C411yescharacteristic
41C22⋊C4×Dic61C411yescharacteristic
42C4×#11758198C2211yescharacteristic
43#16839609C411yescharacteristic
44#16839609C411yescharacteristic
45C42×Dic61C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C23×C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C4×C8×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C23×Dic61C2×C411yescharacteristic
63C23×Dic61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C22×#92418—22no—
68C22×#92418—22no—
69C22×#92418—41no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C4×C22⋊D61—22no—
75C4×C22⋊D61—22no—
76#14519737—24no—
77#14519737C818yescomplemented
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×C22⋊Dic61C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×C4×Dic61—22no—
86C2×C4×Dic61—22no—
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C42×D61—22no—
99C42×D61—22no—
100#14519706—22no—
101#14519706—22no—
102#14519706—22no—
103#14519706—22no—
104#14519706—22no—
105#14519706D414yescomplemented
106C22⋊#92418—22no—
107#14519689—22no—
108#14519689—22no—
109#14519689—41no—
110#14519689—41no—
111C4×#92418—22no—
112C4×#92418—41no—
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
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
125C2×C22⋊C4×C61C2×C411yescharacteristic
126C2×C22⋊C4×C61C2×C411yescharacteristic
127C2×C42×C61C2311yescharacteristic
128C2×C42×C61C2311yescharacteristic
129C22⋊C8×C61—22no—
130C4×C8×C61—22no—
131C4×C8×C61—41no—
132#95×C61C2×C411yescharacteristic
133#95×C61C2×C411yescharacteristic
134C24×C61C22×C411yescharacteristic
135C23×D61C22×C411yescharacteristic
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61#4112yes—
146C22×C4×C61#4112yes—
147C22×C4×C61C2411yescharacteristic
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61C2×C814yes—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—41no—
156C22×Dic61C2×C814yes—
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—22no—
174C2×C4×D61—41no—
175C2×C4×D61C2×C814yescomplemented
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—
189C22⋊C4×C61C2×C814yes—
190C22⋊C4×C61M1614yes—
191C42×C61—21no—
192C42×C61—21no—
193C42×C61—21no—
194C42×C61—21no—
195C22⋊Dic61—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198C2×C814yescomplemented
199#11758196—22no—
200#11758196—22no—
201#11758196C2×C814yescomplemented
202C4×Dic61—22no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
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#11712yes—
234C23×C61C22×C812yes—
235C23×C61C2×M1612yes—
236C23×C61C23×C411yescharacteristic
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—21no—
241C22×D61—21no—
242C22×D61—21no—
243C22×D61C22×C812yes—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61#11712yes—
259C2×C4×C61C22×C812yes—
260C2×C4×C61C22×C812yes—
261C2×C4×C61C2×M1612yes—
262C2×C4×C61C2×M1612yes—
263C2×C4×C61C22×D411yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61H(5,𝔽2)11yescharacteristic
268C2×C4×C612−1+411yescharacteristic
269C22⋊D61—28no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—28no—
277C2×Dic61—21no—
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—44no—
287C2×Dic61C4×D412yes—
288C2×Dic61C4×D412yes—
289C2×Dic61C22×C812yes—
290C2×Dic61C22×C812yes—
291C2×Dic61C22×C812yes—
292C2×Dic61#13112yes—
293C4×D61—28no—
294C4×D61—44no—
295C4×D61—41no—
296C4×D61—41no—
297C4×D61—41no—
298C4×D61—41no—
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#43114yescomplemented
315C22×C61C2×#11711yescharacteristic
316C22×C61C2×C4×D411yescharacteristic
317C22×C61#52011yescharacteristic
318C22×C61C23×C811yescharacteristic
319C22×C61C22×M1611yescharacteristic
320C22×C61C2×#13111yescharacteristic
321C22×C61#56811yescharacteristic
322C2×D61—22no—
323C2×D61—22no—
324C2×D61—22no—
325C2×D61—41no—
326C2×D61—41no—
327C2×D61—41no—
328C2×D61—41no—
329C4×C61—22no—
330C4×C61—22no—
331C4×C61—22no—
332C4×C61—22no—
333C4×C61—22no—
334C4×C61#54611yescharacteristic
335C4×C61#54811yescharacteristic
336C4×C61#55211yescharacteristic
337C4×C61#55311yescharacteristic
338Dic61—22no—
339Dic61—22no—
340Dic61—22no—
341Dic61—41no—
342Dic61—41no—
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#1869—611no—
354#1831—611no—
355#1797—611no—
356#1797—611no—
357C4×C4⋊C8—611no—
358C8×C22⋊C4—611no—
359C8×C22⋊C4D6111yescharacteristic, complemented
360C2×C61—24no—
361C2×C61#235211yescharacteristic
362C2×C61C2×#43111yescharacteristic
363C2×C61#292511yescharacteristic
364C2×C61C2×C8×D411yescharacteristic
365C2×C61D4×M1611yescharacteristic
366C2×C61#298811yescharacteristic
367C2×C61#299011yescharacteristic
368D61—42no—
369C23×C8—611no—
370C23×C8C2×D6111yescharacteristic
371C2×C4×D4—611no—
372C2×C4×D4—611no—
373C2×C4×D4—611no—
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⋊C8—611no—
388C2×C22⋊C8—611no—
389C2×C22⋊C8C2×D6111yescharacteristic
390C2×C4×C8—611no—
391C2×C4×C8—611no—
392C2×C4×C8C2×D6111yescharacteristic
393C2×C4×C8C2×D6111yescharacteristic
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⋊C4C2×D6111yescharacteristic
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×D4—611no—
416C23×C4—611no—
417C23×C4—611no—
418C23×C4—611no—
419C23×C4—611no—
420C23×C4—611no—
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—618no—
437C4×D4—1222no—
438C4×D4—1222no—
439C4×D4—1224no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—611no—
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—1222no—
461C2×C42—1222no—
462C2×C42—1222no—
463C2×C42—1222no—
464C2×C42C22×D6111yescharacteristic
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—1222no—
474C22⋊C8—1222no—
475C22⋊C8—1222no—
476C22⋊C8—2441no—
477C22⋊C8—2441no—
478C4×C8—22no—
479C4×C8—41no—
480C4×C8—1222no—
481C4×C8—2441no—
482#95—611no—
483#95—611no—
484#95—611no—
485#95—611no—
486#95C4×D6111yescharacteristic
487#95C4×D6111yescharacteristic
488C24—611no—
489C24C2×C4×D6111yescharacteristic
490C2×D4—614no—
491C2×D4—1222no—
492C2×D4—1222no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—614no—
502C22×C4—614no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1222no—
511C22×C4—1222no—
512C22×C4—1222no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1222no—
520C22×C4—2441no—
521C22×C4—2441no—
522C22×C4C2×C4×D6111yescharacteristic
523C22×C4C2×C4×D6111yescharacteristic
524C22×C4C2×C4×D6111yescharacteristic
525C22×C4C2×C4×D6111yescharacteristic
526C22×C4C2×C4×D6111yescharacteristic
527C22×C4#1175822212yes—
528C22×C4#1175822212yes—
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—614no—
557C4⋊C4—1222no—
558C4⋊C4—1222no—
559C22⋊C4—614no—
560C22⋊C4—1222no—
561C22⋊C4—1222no—
562C22⋊C4—1222no—
563C22⋊C4C8×D6114yes—
564C22⋊C4#1175818914yes—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—612no—
570C42—612no—
571C42—614no—
572C42—1222no—
573C42—1222no—
574C42—1222no—
575C42—1222no—
576C42—1222no—
577C42—1221no—
578C42—1221no—
579C42—1221no—
580C42—1221no—
581C42—1222no—
582C42—2441no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—612no—
588C23—1221no—
589C23—1221no—
590C23—1221no—
591C23—1221no—
592C23—1221no—
593C23—1221no—
594C23#1451973412yes—
595C23C2×C8×D6112yes—
596C23C2×#1175818912yes—
597C23C22×C4×D6111yescharacteristic
598D4—1228no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—612no—
614C2×C4—612no—
615C2×C4—612no—
616C2×C4—612no—
617C2×C4—612no—
618C2×C4—612no—
619C2×C4—1228no—
620C2×C4—1228no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—1221no—
627C2×C4—1221no—
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—2444no—
637C2×C4—2444no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4#1451973412yes—
643C2×C4C2×C8×D6112yes—
644C2×C4C2×C8×D6112yes—
645C2×C4C2×#1175818912yes—
646C2×C4C2×#1175818912yes—
647C2×C4C2×D4×D6111yescharacteristic
648C2×C4#41×D6111yescharacteristic
649C2×C4C2×#1175822211yescharacteristic
650C2×C4C2×#1175822211yescharacteristic
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—1222no—
668C22—1222no—
669C22—1222no—
670C22—2441no—
671C22—2441no—
672C22—2441no—
673C22—2441no—
674C22#1683981314yescomplemented
675C22C2×#1451973411yescharacteristic
676C22C4×D4×D6111yescharacteristic
677C22#1684024111yescharacteristic
678C22C22×C8×D6111yescharacteristic
679C22C22×#1175818911yescharacteristic
680C22#131×D6111yescharacteristic
681C22#1684052711yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—22no—
687C4—614no—
688C4—1222no—
689C4—1222no—
690C4—1222no—
691C4—2441no—
692C4—2441no—
693C4—2441no—
694C4#1684040211yescharacteristic
695C4#1684042111yescharacteristic
696C4#1684044511yescharacteristic
697C4#1684046111yescharacteristic
698C2—24no—
699C2—2442no—
700C2#2144874211yescharacteristic
701C2C2×#1683981311yescharacteristic
702C2#2145448311yescharacteristic
703C2C8×D4×D6111yescharacteristic
704C2D4×#1175818911yescharacteristic
705C2#2145492611yescharacteristic
706C2#2145494211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutatorC22×C61C23×C8
FittingC8×C22⋊C4×C61C2
socleC23×C61C23×C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenterC8×C22⋊C4D61
hypocenterC61#22748
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16839813C2semidirect
2. C22×#14519706C2semidirect
4. #21446425C2semidirect
5. #21446423C2semidirect
6. #21446376C2semidirect
7. #21446374C2semidirect
10. #21445934C2semidirect
11. #21445798C2semidirect
12. #21445797C2semidirect
13. C4×#14519706C2semidirect
14. C22⋊C4×#92418C2semidirect
15. C8×C22⋊C4×C61C2semidirect
77. #14519737C8semidirect
105. #14519706D4semidirect
175. C2×C4×D61C2×C8semidirect
198. #11758198C2×C8semidirect
201. #11758196C2×C8semidirect
213. C4×Dic61C2×C8semidirect
314. C22×C61#431semidirect
359. C8×C22⋊C4D61semidirect
414. C61#22748semidirect
674. C22#16839813semidirect

Maximal subgroups

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

subgroupindex
C2×#168398132
C22×#145197062
C4×#145197372
#214464252
#214464232
#214463762
#214463742
#214461112
#214461092
#214459342
#214457982
#214457972
C4×#145197062
C22⋊C4×#924182
C8×C22⋊C4×C612
#2274861