Finite Group Databasebeta

← #29699652

Subgroups — #29699652

Order 15616.

960 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839816C211yesmaximal, characteristic, complemented
2C2×#16839812C211yesmaximal, characteristic, complemented
3C4×D4×Dic61C211yesmaximal, characteristic
4#21446618C211yesmaximal, characteristic
5#21446435C211yesmaximal, characteristic, complemented
6#21446429C211yesmaximal, characteristic, complemented
7#21446428C211yesmaximal, characteristic, complemented
8#21446422C211yesmaximal, characteristic, complemented
9#21445970C211yesmaximal, characteristic, complemented
10#21445797C211yesmaximal, characteristic, complemented
11#21445797C211yesmaximal, characteristic, complemented
12#21445696C211yesmaximal, characteristic, complemented
13#21445691C211yesmaximal, characteristic, complemented
14#21445673C211yesmaximal, characteristic, complemented
15C61×#1955C211yesmaximal, characteristic
16C2×D4×Dic61C411yescharacteristic
17C2×D4×Dic61C411yescharacteristic
18C22×C4×Dic61C2211yescharacteristic
19C22×C4×Dic61C2211yescharacteristic
20#16839816—24no—
21#16839812—24no—
22C2×C4⋊#92418C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×#14519688C2211yescharacteristic
34C2×#14519687C2211yescharacteristic
35C2×#14519687C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38C4⋊C4×Dic61C411yescharacteristic
39C4⋊C4×Dic61C411yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41C22⋊C4×Dic61C411yescharacteristic
42C22⋊C4×Dic61C411yescharacteristic
43C22⋊C4×Dic61C411yescharacteristic
44C22⋊C4×Dic61C411yescharacteristic
45C4×C22⋊Dic61C2211yescharacteristic
46C4×C22⋊Dic61C2211yescharacteristic
47C42×Dic61C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C23×Dic61C2×C411yescharacteristic
62C23×Dic61C2×C411yescharacteristic
63C23×Dic61C2×C411yescharacteristic
64C23×Dic61C2×C411yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69D4×Dic61—24no—
70D4×Dic61—24no—
71C2×C4⋊Dic61C2×C411yescharacteristic
72C2×C4⋊Dic61C2×C411yescharacteristic
73C2×C22⋊Dic61C2×C411yescharacteristic
74C2×C22⋊Dic61C2×C411yescharacteristic
75C2×C22⋊Dic61C2×C411yescharacteristic
76C2×C22⋊Dic61C2×C411yescharacteristic
77C2×C4×Dic61—22no—
78C2×C4×Dic61—22no—
79C2×C4×Dic61—22no—
80C2×C4×Dic61—22no—
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61C2×C411yescharacteristic
83C2×C4×Dic61C2×C411yescharacteristic
84C2×C4×Dic61C2×C411yescharacteristic
85C2×C4×Dic61C2×C411yescharacteristic
86C2×C4×Dic61C2×C411yescharacteristic
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2311yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93C4⋊#92418—22no—
94#14519706—22no—
95#14519706—22no—
96#14519706—22no—
97#14519706—41no—
98#14519706—41no—
99#14519706D414yescomplemented
100C22⋊#92418—22no—
101C22⋊#92418—22no—
102C22⋊#92418—41no—
103C22⋊#92418—41no—
104#14519688—22no—
105#14519687—22no—
106#14519687—22no—
107C8×Dic61—22no—
108C8×Dic61—22no—
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×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C2×C4⋊C4×C61C2×C411yescharacteristic
125C2×C22⋊C4×C61C2×C411yescharacteristic
126C2×C22⋊C4×C61C2×C411yescharacteristic
127C2×C42×C61C2311yescharacteristic
128C4⋊C8×C61—22no—
129C22⋊C8×C61—22no—
130C22⋊C8×C61—22no—
131C22⋊C8×C61—41no—
132C22⋊C8×C61—41no—
133#97×C61—22no—
134C24×C61C22×C411yescharacteristic
135C24×C61C22×C411yescharacteristic
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—22no—
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×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
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—22no—
165C22×Dic61—41no—
166C22×Dic61—41no—
167C22×Dic61M1614yes—
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×C61C2×D412yes—
188C4⋊C4×C61—22no—
189C22⋊C4×C61—22no—
190C22⋊C4×C61—22no—
191C42×C61#4112yes—
192C42×C61#4112yes—
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61M1614yes—
197C4⋊Dic61—22no—
198C4⋊Dic61—22no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
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—22no—
212C4×Dic61—41no—
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—
227C23×C61—21no—
228C23×C61—21no—
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×C61C2×M1612yes—
240C23×C61C2×M1612yes—
241C23×C61C23×C411yescharacteristic
242D4×C61—28no—
243C2×C4×C61—21no—
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—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61#11712yes—
262C2×C4×C61#11712yes—
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
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—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—44no—
288C2×Dic61—44no—
289C2×Dic61—44no—
290C2×Dic61C4×D412yes—
291C2×Dic61C4×D412yes—
292C2×Dic61C2×M1612yes—
293C2×Dic61C2×M1612yes—
294C2×Dic61C2×M1612yes—
295C2×Dic61C2×M1612yes—
296C2×Dic61#13112yes—
297C8×C61—22no—
298C8×C61—41no—
299C8×C61—41no—
300C8×C61—41no—
301#92418—22no—
302#92418—41no—
303#92418—41no—
304#92418—41no—
305#22797—611nomaximal, Sylow
306C22×C61—22no—
307C22×C61—22no—
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61C2×#11711yescharacteristic
321C22×C61C2×C4×D411yescharacteristic
322C22×C61#52011yescharacteristic
323C22×C61C22×M1611yescharacteristic
324C22×C61C22×M1611yescharacteristic
325C22×C61C2×#13111yescharacteristic
326C22×C61#56811yescharacteristic
327C4×C61—22no—
328C4×C61—22no—
329C4×C61—41no—
330C4×C61—41no—
331C4×C61#54711yescharacteristic
332C4×C61#55011yescharacteristic
333C4×C61#55511yescharacteristic
334C4×C61#55611yescharacteristic
335Dic61—22no—
336Dic61—22no—
337Dic61—22no—
338Dic61—22no—
339Dic61—41no—
340Dic61—41no—
341Dic61—41no—
342Dic61#43514yes—
343C2×#432—611no—
344C2×#431—611no—
345C42×D4—611no—
346#1955—611no—
347#1955D6111yescharacteristic
348#1924—611no—
349#1924—611no—
350#1923—611no—
351#1923—611no—
352#1842—611no—
353#1797—611no—
354#1797—611no—
355#1771—611no—
356#1771—611no—
357#1767—611no—
358C2×C61—42no—
359C2×C61—42no—
360C2×C61#235411yescharacteristic
361C2×C61#292011yescharacteristic
362C2×C61#292511yescharacteristic
363C2×C61C2×#43511yescharacteristic
364C2×C61D4×M1611yescharacteristic
365C2×C61#298911yescharacteristic
366C2×C61#299011yescharacteristic
367C2×C4×D4—611no—
368C2×C4×D4—611no—
369C2×C4×D4C2×D6111yescharacteristic
370C22×C42—611no—
371C22×C42—611no—
372#432—1224no—
373#431—1224no—
374C2×C4⋊C8—611no—
375C2×C4⋊C8—611no—
376C2×C4⋊C8—611no—
377C2×C4⋊C8—611no—
378C2×C4⋊C8—611no—
379C2×C4⋊C8—611no—
380C2×C4⋊C8—611no—
381C2×C4⋊C8C2×D6111yescharacteristic
382C2×C22⋊C8—611no—
383C2×C22⋊C8—611no—
384C2×C22⋊C8—611no—
385C2×C22⋊C8—611no—
386C2×C22⋊C8C2×D6111yescharacteristic
387C2×C22⋊C8C2×D6111yescharacteristic
388C2×C22⋊C8C2×D6111yescharacteristic
389C2×C22⋊C8C2×D6111yescharacteristic
390C2×#97—611no—
391C2×#97—611no—
392C2×#97—611no—
393C2×#97C2×D6111yescharacteristic
394C2×C4×C8—611no—
395C2×C4×C8—611no—
396C4×C4⋊C4—611no—
397C4×C4⋊C4—611no—
398C4×C4⋊C4—611no—
399C4×C22⋊C4—611no—
400C4×C22⋊C4—611no—
401C4×C22⋊C4—611no—
402C4×C22⋊C4—611no—
403C4×C22⋊C4—611no—
404C4×C22⋊C4—611no—
405C43—611no—
406#336—611no—
407#336—611no—
408#336—611no—
409#336—611no—
410#336—611no—
411#336—611no—
412C61#2279711yescharacteristic, complemented, Sylow
413C22×D4C4×D6111yescharacteristic
414C23×C4—611no—
415C23×C4—611no—
416C23×C4—611no—
417C23×C4—611no—
418C23×C4C22×D6111yescharacteristic
419C23×C4C22×D6111yescharacteristic
420C22×C8—611no—
421C22×C8—611no—
422C22×C8—611no—
423C22×C8—611no—
424C22×C8C22×D6111yescharacteristic
425C22×C8C22×D6111yescharacteristic
426C22×C8C22×D6111yescharacteristic
427C22×C8C22×D6111yescharacteristic
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—1224no—
431C4×D4—1224no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4C4×D6111yescharacteristic
435C2×C22⋊C4—611no—
436C2×C22⋊C4—611no—
437C2×C22⋊C4—611no—
438C2×C22⋊C4—611no—
439C2×C22⋊C4C4×D6111yescharacteristic
440C2×C22⋊C4C4×D6111yescharacteristic
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—1222no—
454C2×C42—1222no—
455C2×C42—1222no—
456C2×C42—1222no—
457C2×C42C22×D6111yescharacteristic
458C4⋊C8—22no—
459C4⋊C8—614no—
460C4⋊C8—1222no—
461C4⋊C8—1222no—
462C4⋊C8—1222no—
463C4⋊C8—1222no—
464C4⋊C8—2441no—
465C4⋊C8—2441no—
466C22⋊C8—22no—
467C22⋊C8—22no—
468C22⋊C8—41no—
469C22⋊C8—41no—
470C22⋊C8—1222no—
471C22⋊C8—1222no—
472C22⋊C8—2441no—
473C22⋊C8—2441no—
474#97—22no—
475#97—1222no—
476#97—1222no—
477#97—1222no—
478C4×C8—1222no—
479C4×C8—1222no—
480#95—611no—
481#95—611no—
482#95—611no—
483#95—611no—
484#95—611no—
485#95—611no—
486C24C2×C4×D6111yescharacteristic
487C24C2×C4×D6111yescharacteristic
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C22×C4—21no—
492C22×C4—21no—
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—614no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—1222no—
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×C4C23×D6111yescharacteristic
528C2×C8—21no—
529C2×C8—21no—
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—612no—
540C2×C8—1221no—
541C2×C8—1221no—
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×C8D4×D6112yes—
552C4⋊C4—22no—
553C4⋊C4—1222no—
554C4⋊C4—1222no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—614no—
558C22⋊C4—1222no—
559C22⋊C4—1222no—
560C22⋊C4—1222no—
561C42—612no—
562C42—612no—
563C42—1222no—
564C42—1222no—
565C42—1222no—
566C42—1222no—
567C42—1222no—
568C42—1222no—
569C42—1222no—
570C42—1221no—
571C42—1221no—
572C42—1221no—
573C42—1221no—
574C42—1221no—
575C42—1221no—
576C42—2441no—
577C42#1175822412yes—
578C42#1175822412yes—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23M16×D6112yes—
592C23M16×D6112yes—
593C23C22×C4×D6111yescharacteristic
594D4—28no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
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—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—1221no—
637C2×C4—1221no—
638C2×C4—2444no—
639C2×C4—2444no—
640C2×C4—2444no—
641C2×C4#1451973312yes—
642C2×C4#1451973312yes—
643C2×C4C2×D4×D6111yescharacteristic
644C2×C4#41×D6111yescharacteristic
645C2×C4C2×#1175822411yescharacteristic
646C2×C4C2×#1175822411yescharacteristic
647C2×C4#1451982211yescharacteristic
648C2×C4#1451982411yescharacteristic
649C8—22no—
650C8—41no—
651C8—41no—
652C8—41no—
653C8—1222no—
654C8—2441no—
655C8—2441no—
656C8—2441no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22C2×#1451973311yescharacteristic
672C22C4×D4×D6111yescharacteristic
673C22#1684024111yescharacteristic
674C22C2×M16×D6111yescharacteristic
675C22C2×M16×D6111yescharacteristic
676C22#131×D6111yescharacteristic
677C22#1684052711yescharacteristic
678C4—22no—
679C4—22no—
680C4—41no—
681C4—41no—
682C4—614no—
683C4—1222no—
684C4—1222no—
685C4—1222no—
686C4—1222no—
687C4—2441no—
688C4—2441no—
689C4—2441no—
690C4#1684041211yescharacteristic
691C4#1684043211yescharacteristic
692C4#1684047611yescharacteristic
693C4#1684048111yescharacteristic
694C2—42no—
695C2—42no—
696C2#2144876711yescharacteristic
697C2#2145444811yescharacteristic
698C2#2145448111yescharacteristic
699C2#435×D6111yescharacteristic
700C2#2145455211yescharacteristic
701C2#2145493111yescharacteristic
702C2#2145493911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1955C2
prime radicalC22×D4×C61C2×C4
cosocleC22×C4×C61C24
hypercenter#1955D61
hypocenterC61#22797
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. C2×#16839816C2semidirect
2. C2×#16839812C2semidirect
5. #21446435C2semidirect
6. #21446429C2semidirect
7. #21446428C2semidirect
8. #21446422C2semidirect
9. #21445970C2semidirect
10. #21445797C2semidirect
11. #21445797C2semidirect
12. #21445696C2semidirect
13. #21445691C2semidirect
14. #21445673C2semidirect
99. #14519706D4semidirect
412. C61#22797semidirect

Maximal subgroups

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

subgroupindex
C2×#168398162
C2×#168398122
C4×D4×Dic612
#214466182
#214464352
#214464292
#214464282
#214464222
#214459702
#214457972
#214456962
#214456912
#214456732
C61×#19552
#2279761