Finite Group Databasebeta

← #29699029

Subgroups — #29699029

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
2C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
3C4×#14519739C211yesmaximal, characteristic
4#21446426C211yesmaximal, characteristic, complemented
5#21446424C211yesmaximal, characteristic, complemented
6#21446378C211yesmaximal, characteristic, complemented
7#21446110C211yesmaximal, characteristic
8#21446110C211yesmaximal, characteristic
9#21445934C211yesmaximal, characteristic, complemented
10#21445798C211yesmaximal, characteristic, complemented
11#21445798C211yesmaximal, characteristic, complemented
12#21445667C211yesmaximal, characteristic, complemented
13C8×#11758198C211yesmaximal, characteristic, complemented
14#21445589C211yesmaximal, characteristic, complemented
15C61×#1916C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519739C411yescharacteristic
20C2×#14519739C411yescharacteristic
21C2×C42×D61C2211yescharacteristic
22C2×C42×D61C2211yescharacteristic
23#16839813—24no—
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C4⋊C8×D61—24no—
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38C2×C8×Dic61C2211yescharacteristic
39C4⋊C4×Dic61C411yescharacteristic
40C4⋊C4×Dic61C411yescharacteristic
41C4×#11758198C2211yescharacteristic
42C4×#11758198C2211yescharacteristic
43#16839609C411yescharacteristic
44#16839609C411yescharacteristic
45#16839609C411yescharacteristic
46#16839609C411yescharacteristic
47C42×Dic61C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×D244C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C2×C8×D61—22no—
73C2×C8×D61—22no—
74C2×C8×D61—22no—
75C2×C8×D61—22no—
76C2×C8×D61—41no—
77C2×C8×D61—41no—
78C4×D244—22no—
79C4×D244—22no—
80#14519739—24no—
81#14519739C818yescomplemented
82C2×C4⋊Dic61C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×#11758198C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×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×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2×C411yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C42×D61—22no—
100C42×D61—22no—
101C42×D61—22no—
102C42×D61—22no—
103C4⋊#92418—22no—
104#14519706—22no—
105#14519706—22no—
106#14519706—22no—
107#14519706D414yescomplemented
108#14519689—22no—
109#14519689—22no—
110#14519689—22no—
111#14519689—22no—
112#14519689—41no—
113#14519689—41no—
114C4×#92418—22no—
115C8×Dic61—41no—
116C8×Dic61—41no—
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2×C411yescharacteristic
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C42×C61C2311yescharacteristic
128C2×C42×C61C2311yescharacteristic
129C2×C42×C61C2311yescharacteristic
130C4⋊C8×C61—22no—
131C4×C8×C61—22no—
132#95×C61C2×C411yescharacteristic
133#95×C61C2×C411yescharacteristic
134C23×D61C22×C411yescharacteristic
135C23×D61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C2411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C2×D244—22no—
150C2×D244—22no—
151C2×D244C2×C814yes—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
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—41no—
171C2×C4×D61—41no—
172C2×C4×D61C2×C814yes—
173C2×C4×D61C2×C814yescomplemented
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—
188C4⋊C4×C61—22no—
189C4⋊C4×C61C2×C814yescomplemented
190C42×C61—21no—
191C42×C61—21no—
192C42×C61—21no—
193C42×C61—21no—
194C42×C61—21no—
195C42×C61—21no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198C2×C814yes—
200#11758198C2×C814yescomplemented
201#11758198M1614yes—
202C4⋊Dic61—22no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—22no—
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×C61C23×C411yescharacteristic
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61—21no—
235C22×D61—21no—
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61#11712yes—
241C22×D61C22×C812yes—
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—21no—
257C2×C4×C61—21no—
258C2×C4×C61C22×C812yes—
259C2×C4×C61C22×C812yes—
260C2×C4×C61C22×C812yes—
261C2×C4×C61C2×M1612yes—
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61H(5,𝔽2)11yescharacteristic
267C2×C4×C612−1+411yescharacteristic
268C2×Dic61—21no—
269C2×Dic61—21no—
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#11712yes—
280C2×Dic61C4×D412yes—
281C2×Dic61C4×D412yes—
282C2×Dic61C22×C812yes—
283C2×Dic61C22×C812yes—
284C2×Dic61C2×M1612yes—
285C2×Dic61#13112yes—
286D244—28no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—22no—
291C4×D61—28no—
292C4×D61—28no—
293C4×D61—44no—
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×C61C2×#11711yescharacteristic
309C22×C61C2×C4×D411yescharacteristic
310C22×C61#52011yescharacteristic
311C22×C61C23×C811yescharacteristic
312C22×C61C22×M1611yescharacteristic
313C22×C61C2×#13111yescharacteristic
314C22×C61#56811yescharacteristic
315C2×D61—22no—
316C2×D61—22no—
317C2×D61—22no—
318C2×D61—22no—
319C2×D61—22no—
320C2×D61—22no—
321C2×D61—22no—
322C2×D61—22no—
323C2×D61—22no—
324C2×D61—41no—
325C2×D61—41no—
326C2×D61—41no—
327C2×D61—41no—
328C2×D61#43114yescomplemented
329C4×C61—22no—
330C4×C61—22no—
331C4×C61—22no—
332C4×C61—22no—
333C4×C61—41no—
334C4×C61—41no—
335C4×C61#54611yescharacteristic
336C4×C61#54811yescharacteristic
337C4×C61#55211yescharacteristic
338C4×C61#55311yescharacteristic
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#1916D6111yescharacteristic, complemented
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#235211yescharacteristic
361C2×C61C2×#43111yescharacteristic
362C2×C61#292511yescharacteristic
363C2×C61C2×C8×D411yescharacteristic
364C2×C61D4×M1611yescharacteristic
365C2×C61#298811yescharacteristic
366C2×C61#299011yescharacteristic
367D61—24no—
368D61—42no—
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⋊C8—611no—
389C2×C22⋊C8—611no—
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⋊C4C2×D6111yescharacteristic
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#336C2×D6111yescharacteristic
411#336C2×D6111yescharacteristic
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×C4—611no—
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—1222no—
438C4×D4—1222no—
439C4×D4—1224no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4C4×D6111yescharacteristic
442C2×C4⋊C4C4×D6111yescharacteristic
443C2×C22⋊C4—611no—
444C2×C22⋊C4—611no—
445C2×C22⋊C4—611no—
446C2×C22⋊C4—611no—
447C2×C22⋊C4—611no—
448C2×C22⋊C4—611no—
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—1222no—
460C2×C42—1222no—
461C2×C42—1222no—
462C2×C42—1222no—
463C2×C42C22×D6111yescharacteristic
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—1222no—
473C22⋊C8—1222no—
474C22⋊C8—1222no—
475C22⋊C8—1222no—
476C22⋊C8—2441no—
477C22⋊C8—2441no—
478C4×C8—22no—
479C4×C8—1222no—
480C4×C8—2441no—
481C4×C8—2441no—
482#95—611no—
483#95—611no—
484#95—611no—
485#95—611no—
486#95C4×D6111yescharacteristic
487#95C4×D6111yescharacteristic
488C24—611no—
489C24—611no—
490C2×D4—614no—
491C2×D4—1222no—
492C2×D4—1222no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—612no—
499C22×C4—612no—
500C22×C4—614no—
501C22×C4—614no—
502C22×C4—611no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1221no—
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×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—22no—
557C4⋊C4—1222no—
558C4⋊C4C8×D6114yescomplemented
559C22⋊C4—614no—
560C22⋊C4—614no—
561C22⋊C4—614no—
562C22⋊C4—1222no—
563C22⋊C4—1222no—
564C22⋊C4—1222no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—612no—
572C42—612no—
573C42—614no—
574C42—1222no—
575C42—1222no—
576C42—1222no—
577C42—1222no—
578C42—1222no—
579C42—1222no—
580C42—1221no—
581C42—1221no—
582C42—2441no—
583C23—612no—
584C23—612no—
585C23—612no—
586C23—612no—
587C23—1221no—
588C23—1221no—
589C23—1221no—
590C23—1221no—
591C23—1221no—
592C23—1221no—
593C23—1221no—
594C23—1221no—
595C23—1221no—
596C23—1221no—
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—21no—
612C2×C4—21no—
613C2×C4—612no—
614C2×C4—612no—
615C2×C4—612no—
616C2×C4—612no—
617C2×C4—612no—
618C2×C4—612no—
619C2×C4—612no—
620C2×C4—1228no—
621C2×C4—1228no—
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—1222no—
631C2×C4—1222no—
632C2×C4—1222no—
633C2×C4—1222no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—1221no—
637C2×C4—2444no—
638C2×C4—2444no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4C2×C8×D6112yes—
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#1451982311yescharacteristic
652C2×C4#1451982511yescharacteristic
653C8—22no—
654C8—41no—
655C8—41no—
656C8—41no—
657C8—1222no—
658C8—2441no—
659C8—2441no—
660C8—2441no—
661C22—614no—
662C22—1222no—
663C22—1222no—
664C22—1222no—
665C22—1222no—
666C22—1222no—
667C22—1222no—
668C22—1222no—
669C22—1222no—
670C22—1222no—
671C22—2441no—
672C22—2441no—
673C22—2441no—
674C22—2441no—
675C22#117×D6111yescharacteristic
676C22C4×D4×D6111yescharacteristic
677C22#1684024411yescharacteristic
678C22C22×C8×D6111yescharacteristic
679C22C2×M16×D6111yescharacteristic
680C22#131×D6111yescharacteristic
681C22#1684052711yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—614no—
689C4—1222no—
690C4—1222no—
691C4—1222no—
692C4—1222no—
693C4—2441no—
694C4#1684040411yescharacteristic
695C4#1684042211yescharacteristic
696C4#1684044411yescharacteristic
697C4#1684046311yescharacteristic
698C2—1224no—
699C2—2442no—
700C2#2144874311yescharacteristic
701C2#431×D6111yescharacteristic
702C2#2145448211yescharacteristic
703C2C8×D4×D6111yescharacteristic
704C2#2145455211yescharacteristic
705C2#2145492911yescharacteristic
706C2#2145494311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutatorC22×C61C23×C8
FittingC61×#1916C2
socleC23×C61C23×C4
prime radicalC22×D244C2×C4
cosocleC22×C4×C61C24
hypercenter#1916D61
hypocenterC61#22748
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. C2×#16839813C2semidirect
2. C2×C4⋊C8×D61C2semidirect
4. #21446426C2semidirect
5. #21446424C2semidirect
6. #21446378C2semidirect
9. #21445934C2semidirect
10. #21445798C2semidirect
11. #21445798C2semidirect
12. #21445667C2semidirect
13. C8×#11758198C2semidirect
14. #21445589C2semidirect
15. C61×#1916C2semidirect
81. #14519739C8semidirect
107. #14519706D4semidirect
173. C2×C4×D61C2×C8semidirect
189. C4⋊C4×C61C2×C8semidirect
200. #11758198C2×C8semidirect
212. C4×Dic61C2×C8semidirect
328. C2×D61#431semidirect
351. #1916D61semidirect
414. C61#22748semidirect
558. C4⋊C4C8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398132
C2×C4⋊C8×D612
C4×#145197392
#214464262
#214464242
#214463782
#214461102
#214459342
#214457982
#214456672
C8×#117581982
#214455892
C61×#19162
#2274861