Finite Group Databasebeta

← #29699033

Subgroups — #29699033

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
2C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
3C4×#14519737C211yesmaximal, characteristic
4#21446427C211yesmaximal, characteristic, complemented
5#21446379C211yesmaximal, characteristic, complemented
6#21446373C211yesmaximal, characteristic, complemented
7#21446108C211yesmaximal, characteristic
8#21446108C211yesmaximal, characteristic
9#21445934C211yesmaximal, characteristic, complemented
10#21445798C211yesmaximal, characteristic, complemented
11#21445797C211yesmaximal, characteristic, complemented
12C4×#14519706C211yesmaximal, characteristic, complemented
13C8×#11758198C211yesmaximal, characteristic, complemented
14#21445589C211yesmaximal, characteristic, complemented
15C61×#1923C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×#14519737C411yescharacteristic
20C2×#14519737C411yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22C2×C42×D61C2211yescharacteristic
23#16839812—24no—
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C4⋊C8×D61—24no—
30C2×C22⋊#92418C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×C4×#92418C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
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
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊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×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C2×C8×D61—22no—
72C2×C8×D61—22no—
73C2×C8×D61—22no—
74C2×C8×D61—22no—
75C2×C8×D61—41no—
76C2×C8×D61—41no—
77C4×C22⋊D61—22no—
78C4×C22⋊D61—22no—
79#14519737—24no—
80#14519737C818yescomplemented
81C2×#11758196C2×C411yescharacteristic
82C2×#11758196C2×C411yescharacteristic
83C2×#11758196C2×C411yescharacteristic
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×#11758198C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×C4×Dic61—22no—
89C2×C4×Dic61—22no—
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2×C411yescharacteristic
97C2×C4×Dic61C2×C411yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101C42×D61—22no—
102C42×D61—22no—
103C4⋊#92418—22no—
104#14519706—22no—
105#14519706—22no—
106#14519706—22no—
107#14519706D414yescomplemented
108C22⋊#92418—22no—
109C22⋊#92418—41no—
110#14519689—22no—
111#14519689—22no—
112C4×#92418—41no—
113C8×Dic61—22no—
114C8×Dic61—22no—
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C2×C22⋊C4×C61C2×C411yescharacteristic
125C2×C22⋊C4×C61C2×C411yescharacteristic
126C2×C42×C61C2311yescharacteristic
127C2×C42×C61C2311yescharacteristic
128C4⋊C8×C61—22no—
129C22⋊C8×C61—22no—
130C22⋊C8×C61—41no—
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×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
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×C814yescomplemented
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—22no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—41no—
173C2×C4×D61C2×C814yes—
174C2×C4×D61#4112yes—
175C2×C4×D61#4112yes—
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×C61C2×D412yes—
188C22⋊C4×C61—22no—
189C22⋊C4×C61C2×C814yescomplemented
190C42×C61—21no—
191C42×C61—21no—
192C42×C61—21no—
193C42×C61—21no—
194C22⋊Dic61—22no—
195#11758198—22no—
196#11758198C2×C814yes—
197#11758198M1614yes—
198#11758196—22no—
199#11758196—22no—
200#11758196C2×C814yescomplemented
201C4×Dic61—22no—
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—41no—
212C4×Dic61C2×C814yescomplemented
213C4×Dic61C2×D412yes—
214C4×Dic61#4112yes—
215C2×#92418—21no—
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×#92418C2×D412yes—
227C8×D61—44no—
228C8×D61—44no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61C22×C812yes—
236C23×C61C23×C411yescharacteristic
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—21no—
241C22×D61#11712yes—
242C22×D61C22×C812yes—
243C22×D61C2×M1612yes—
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—21no—
255C2×C4×C61—21no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61C22×C812yes—
261C2×C4×C61C22×C812yes—
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—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—28no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—44no—
285C2×Dic61#11712yes—
286C2×Dic61C4×D412yes—
287C2×Dic61C4×D412yes—
288C2×Dic61C22×C812yes—
289C2×Dic61C22×C812yes—
290C2×Dic61C22×C812yes—
291C2×Dic61C2×M1612yes—
292C2×Dic61#13112yes—
293C4×D61—22no—
294C4×D61—22no—
295C4×D61—22no—
296C4×D61—22no—
297C4×D61—28no—
298C4×D61—44no—
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—41no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
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—22no—
326C2×D61—22no—
327C2×D61—22no—
328C2×D61#43114yescomplemented
329C4×C61—22no—
330C4×C61—22no—
331C4×C61—22no—
332C4×C61—41no—
333C4×C61—41no—
334C4×C61#54611yescharacteristic
335C4×C61#54811yescharacteristic
336C4×C61#55211yescharacteristic
337C4×C61#55311yescharacteristic
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#1923D6111yescharacteristic, complemented
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⋊C4—611no—
360C2×C61—42no—
361C2×C61#235211yescharacteristic
362C2×C61C2×#43111yescharacteristic
363C2×C61#292511yescharacteristic
364C2×C61C2×C8×D411yescharacteristic
365C2×C61D4×M1611yescharacteristic
366C2×C61#298811yescharacteristic
367C2×C61#299011yescharacteristic
368D61—24no—
369C23×C8—611no—
370C23×C8—611no—
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—1224no—
383C2×C4⋊C8C2×D6111yescharacteristic
384C2×C22⋊C8—611no—
385C2×C22⋊C8—611no—
386C2×C22⋊C8—611no—
387C2×C22⋊C8—611no—
388C2×C22⋊C8C2×D6111yescharacteristic
389C2×C22⋊C8C2×D6111yescharacteristic
390C2×C4×C8—611no—
391C2×C4×C8—611no—
392C2×C4×C8—611no—
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—611no—
423C22×C8—611no—
424C22×C8—611no—
425C22×C8—611no—
426C22×C8—1222no—
427C22×C8—1222no—
428C22×C8—1222no—
429C22×C8—1222no—
430C22×C8—2441no—
431C22×C8—2441no—
432C22×C8C22×D6111yescharacteristic
433C22×C8C22×D6111yescharacteristic
434C22×C8C22×D6111yescharacteristic
435C22×C8C22×D6111yescharacteristic
436C4×D4—618no—
437C4×D4—1224no—
438C4×D4—1222no—
439C4×D4—1222no—
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—22no—
467C4⋊C8—614no—
468C4⋊C8—1222no—
469C4⋊C8—1222no—
470C4⋊C8—1222no—
471C4⋊C8—1222no—
472C22⋊C8—22no—
473C22⋊C8—41no—
474C22⋊C8—1222no—
475C22⋊C8—1222no—
476C22⋊C8—1222no—
477C22⋊C8—2441no—
478C4×C8—41no—
479C4×C8—1222no—
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—21no—
498C22×C4—21no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—614no—
506C22×C4—612no—
507C22×C4—612no—
508C22×C4—614no—
509C22×C4—611no—
510C22×C4—1222no—
511C22×C4—1222no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—2441no—
523C22×C4—2441no—
524C22×C4C2×C4×D6111yescharacteristic
525C22×C4C2×C4×D6111yescharacteristic
526C22×C4C2×C4×D6111yescharacteristic
527C22×C4C2×C4×D6111yescharacteristic
528C22×C4C2×C4×D6111yescharacteristic
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—612no—
542C2×C8—1221no—
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—2444no—
554C2×C8—2444no—
555C2×C8D4×D6112yes—
556C4⋊C4—614no—
557C4⋊C4—1222no—
558C4⋊C4—1222no—
559C22⋊C4—22no—
560C22⋊C4—614no—
561C22⋊C4—614no—
562C22⋊C4—1222no—
563C22⋊C4—1222no—
564C22⋊C4C8×D6114yescomplemented
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—21no—
588C23—21no—
589C23—612no—
590C23—612no—
591C23—612no—
592C23—1221no—
593C23—1221no—
594C23—1221no—
595C23—1221no—
596C23C2×C8×D6112yes—
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—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—612no—
616C2×C4—612no—
617C2×C4—612no—
618C2×C4—612no—
619C2×C4—612no—
620C2×C4—612no—
621C2×C4—612no—
622C2×C4—612no—
623C2×C4—1228no—
624C2×C4—1228no—
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—1222no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—1222no—
639C2×C4—1221no—
640C2×C4—1221no—
641C2×C4—1221no—
642C2×C4—2444no—
643C2×C4—2444no—
644C2×C4C2×C8×D6112yes—
645C2×C4C2×C8×D6112yes—
646C2×C4M16×D6112yes—
647C2×C4C2×D4×D6111yescharacteristic
648C2×C4#41×D6111yescharacteristic
649C2×C4#41×D6111yescharacteristic
650C2×C4#41×D6111yescharacteristic
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—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—614no—
669C22—1222no—
670C22—1222no—
671C22—1222no—
672C22—1222no—
673C22—1222no—
674C22—1222no—
675C22#117×D6111yescharacteristic
676C22C4×D4×D6111yescharacteristic
677C22#1684024111yescharacteristic
678C22C22×C8×D6111yescharacteristic
679C22C2×M16×D6111yescharacteristic
680C22#131×D6111yescharacteristic
681C22#1684052711yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—41no—
686C4—41no—
687C4—614no—
688C4—1222no—
689C4—1222no—
690C4—1222no—
691C4—1222no—
692C4—1222no—
693C4—2441no—
694C4#1684040111yescharacteristic
695C4#1684042011yescharacteristic
696C4#1684044811yescharacteristic
697C4#1684045711yescharacteristic
698C2—42no—
699C2—1224no—
700C2#2144874711yescharacteristic
701C2#431×D6111yescharacteristic
702C2#2145448211yescharacteristic
703C2C8×D4×D6111yescharacteristic
704C2#2145455511yescharacteristic
705C2#2145492611yescharacteristic
706C2#2145493911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutatorC22×C61C23×C8
FittingC61×#1923C2
socleC23×C61C23×C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1923D61
hypocenterC61#22748
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#16839812C2semidirect
2. C2×C4⋊C8×D61C2semidirect
4. #21446427C2semidirect
5. #21446379C2semidirect
6. #21446373C2semidirect
9. #21445934C2semidirect
10. #21445798C2semidirect
11. #21445797C2semidirect
12. C4×#14519706C2semidirect
13. C8×#11758198C2semidirect
14. #21445589C2semidirect
15. C61×#1923C2semidirect
80. #14519737C8semidirect
107. #14519706D4semidirect
156. C22×Dic61C2×C8semidirect
189. C22⋊C4×C61C2×C8semidirect
200. #11758196C2×C8semidirect
212. C4×Dic61C2×C8semidirect
328. C2×D61#431semidirect
349. #1923D61semidirect
414. C61#22748semidirect
564. C22⋊C4C8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398122
C2×C4⋊C8×D612
C4×#145197372
#214464272
#214463792
#214463732
#214461082
#214459342
#214457982
#214457972
C4×#145197062
C8×#117581982
#214455892
C61×#19232
#2274861