Finite Group Databasebeta

← #29700257

Subgroups — #29700257

Order 15616.

1164 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839838C211yesmaximal, characteristic, complemented
2C2×#16839837C211yesmaximal, characteristic, complemented
3C2×#16839729C211yesmaximal, characteristic, complemented
4#21449032C211yesmaximal, characteristic
5#21446611C211yesmaximal, characteristic, complemented
6#21446428C211yesmaximal, characteristic, complemented
7#21446422C211yesmaximal, characteristic, complemented
8#21446113C211yesmaximal, characteristic, complemented
9#21446111C211yesmaximal, characteristic, complemented
10#21446109C211yesmaximal, characteristic, complemented
11#21446002C211yesmaximal, characteristic, complemented
12#21446001C211yesmaximal, characteristic, complemented
13#21445593C211yesmaximal, characteristic, complemented
14C8×C22⋊Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#408C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22#16839838—24no—
23#16839837—24no—
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27#16839729—24no—
28C2×C22⋊#92418C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38#16839681C411yescharacteristic
39#16839676C411yescharacteristic
40#16839676C411yescharacteristic
41#16839676C411yescharacteristic
42#16839673C411yescharacteristic
43#16839670C411yescharacteristic
44#16839670C411yescharacteristic
45#16839670C411yescharacteristic
46C4×C22⋊Dic61C2211yescharacteristic
47C4×C22⋊Dic61C2211yescharacteristic
48C4×C22⋊Dic61C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×#41×C61C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic
58C61×#408—24no—
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758194—22no—
68C2×#11758194—22no—
69C2×#11758194—41no—
70C2×#11758189—22no—
71C2×#11758189—22no—
72C2×#11758189—41no—
73C22×#92418—22no—
74C22×#92418—22no—
75C22×#92418—41no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C4×C22⋊D61—22no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—41no—
85C4×C22⋊D61—41no—
86C2×#11758196C2×C411yescharacteristic
87C2×#11758196C2×C411yescharacteristic
88C2×#11758196C2×C411yescharacteristic
89C2×C22⋊Dic61C2×C411yescharacteristic
90C2×C22⋊Dic61C2×C411yescharacteristic
91C2×C22⋊Dic61C2×C411yescharacteristic
92C2×C22⋊Dic61C2×C411yescharacteristic
93C2×C22⋊Dic61C2×C411yescharacteristic
94C2×C22⋊Dic61C2×C411yescharacteristic
95C2×C22⋊Dic61C2×C411yescharacteristic
96C2×C22⋊Dic61C2×C411yescharacteristic
97C2×C22⋊Dic61C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104#14519706—22no—
105#14519706—22no—
106#14519706—41no—
107C22⋊#92418—22no—
108C22⋊#92418—22no—
109C22⋊#92418—22no—
110C22⋊#92418D414yescomplemented
111#14519689—22no—
112#14519689—22no—
113#14519689—41no—
114C8×Dic61—22no—
115C8×Dic61—22no—
116C8×Dic61—41no—
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123C2×#41×C61—22no—
124C2×#41×C61—22no—
125C2×#41×C61—22no—
126C2×#41×C61—22no—
127C2×#41×C61—41no—
128C2×#41×C61—41no—
129C22×Q8×C61C2×C411yescharacteristic
130C22×D4×C61C2×C411yescharacteristic
131C22×D4×C61C2×C411yescharacteristic
132C22×D4×C61C2×C411yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C2×M16×C61—22no—
137C2×M16×C61—22no—
138C2×M16×C61—41no—
139C22×C8×C61—22no—
140C22×C8×C61—22no—
141C22×C8×C61—41no—
142C22×C8×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146C22⋊C8×C61—22no—
147C22⋊C8×C61—22no—
148C22⋊C8×C61—22no—
149C22⋊C8×C61D414yescomplemented
150C24×C61C22×C411yescharacteristic
151C24×C61C22×C411yescharacteristic
152C24×C61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154#41×C61—44no—
155#41×C61—44no—
156#41×C61—44no—
157#41×C61—44no—
158C2×Q8×C61—22no—
159C2×Q8×C61—22no—
160C2×Q8×C61—41no—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—41no—
168C2×D4×C61—41no—
169C2×D4×C61—41no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C22×C411yescharacteristic
187C22×C4×C61C2×D412yes—
188C22×C4×C61C2×D412yes—
189C22×C4×C61#4112yes—
190C22×C4×C61#4112yes—
191C22×C4×C61C2411yescharacteristic
192C2×C22⋊D61—22no—
193C2×C22⋊D61—22no—
194C2×C22⋊D61—22no—
195C2×C22⋊D61—22no—
196C2×C22⋊D61—22no—
197C2×C22⋊D61—41no—
198C2×C22⋊D61—41no—
199C2×C22⋊D61—41no—
200C2×C22⋊D61—41no—
201C22×Dic61C22×C411yescharacteristic
202C22×Dic61C22×C411yescharacteristic
203C22×Dic61C22×C411yescharacteristic
204C22×Dic61C22×C411yescharacteristic
205C22×Dic61C22×C411yescharacteristic
206C22×Dic61C22×C411yescharacteristic
207C22×Dic61C22×C411yescharacteristic
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214M16×C61—44no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—44no—
226C2×C8×C61C2×D412yes—
227C2×C8×C61C2×D412yes—
228C22⋊Dic61—22no—
229C22⋊Dic61—22no—
230C22⋊Dic61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235C22⋊Dic61—22no—
236C22⋊Dic61—41no—
237#11758198—22no—
238#11758198—22no—
239#11758198—41no—
240#11758196—22no—
241#11758196—22no—
242#11758196—41no—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249#11758194—44no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—44no—
261C2×#92418C2×D412yes—
262C2×#92418C2×D412yes—
263#11758189—44no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61C4×D412yes—
284C23×C61C4×D412yes—
285C23×C61C23×C411yescharacteristic
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293Q8×C61—44no—
294D4×C61—44no—
295D4×C61—44no—
296D4×C61—44no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61C4×D412yes—
317C2×C4×C61C4×D412yes—
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C2×C4×C61H(5,𝔽2)11yescharacteristic
324C22⋊D61—44no—
325C22⋊D61—44no—
326C22⋊D61—44no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61#13112yes—
346C2×Dic61#13112yes—
347C2×Dic61#13112yes—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—41no—
352C8×C61—22no—
353C8×C61—22no—
354C8×C61—41no—
355C8×C61—41no—
356#92418—22no—
357#92418—22no—
358#92418—41no—
359#92418—41no—
360#22853—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61C2×C4×D411yescharacteristic
383C22×C61C2×C4×D411yescharacteristic
384C22×C61#51811yescharacteristic
385C22×C61C2×#13111yescharacteristic
386C22×C61C2×#13111yescharacteristic
387C22×C61C2×#13111yescharacteristic
388C22×C61#56811yescharacteristic
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—41no—
399C4×C61D4211yescharacteristic
400C4×C61#54611yescharacteristic
401C4×C61#54611yescharacteristic
402C4×C61#55111yescharacteristic
403Dic61—22no—
404Dic61—22no—
405Dic61—22no—
406Dic61—41no—
407Dic61—41no—
408Dic61—41no—
409Dic61—41no—
410C2×#436—611no—
411C2×#436—611no—
412C2×#408—611no—
413C2×#408D6111yescharacteristic, complemented
414#2388—611no—
415#1954—611no—
416#1923—611no—
417#1923—611no—
418#1870—611no—
419#1869—611no—
420#1869—611no—
421#1851—611no—
422#1851—611no—
423C8×C22⋊C4—611no—
424C8×C22⋊C4—611no—
425C2×C61—42no—
426C2×C61—42no—
427C2×C61—81no—
428C2×C61#235811yescharacteristic
429C2×C61#293111yescharacteristic
430C2×C61#293111yescharacteristic
431C2×C61#293311yescharacteristic
432C2×C61#293311yescharacteristic
433C2×C61#297611yescharacteristic
434C2×C61#297911yescharacteristic
435D61—81no—
436C22×#41C2×D6111yescharacteristic
437C22×M16—611no—
438C22×M16—611no—
439C22×M16C2×D6111yescharacteristic
440C23×C8—611no—
441C23×C8C2×D6111yescharacteristic
442C2×C4×D4—611no—
443C2×C4×D4—611no—
444C2×C4×D4—611no—
445#436—1224no—
446#436—1224no—
447C2×C4⋊C8—611no—
448C2×C4⋊C8—611no—
449C2×C4⋊C8—611no—
450#408—24no—
451#408—1224no—
452C2×C22⋊C8—611no—
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×C22⋊C8—611no—
459C2×C22⋊C8C2×D6111yescharacteristic
460C2×C22⋊C8C2×D6111yescharacteristic
461C2×C22⋊C8C2×D6111yescharacteristic
462C2×C22⋊C8C2×D6111yescharacteristic
463C2×C4×C8—611no—
464C2×C4×C8—611no—
465C2×C4×C8—611no—
466#395—611no—
467#394—611no—
468#394—611no—
469#394—611no—
470#393—611no—
471#392—611no—
472#392—611no—
473#392—611no—
474C4×C22⋊C4—611no—
475C4×C22⋊C4—611no—
476C4×C22⋊C4—611no—
477#336—611no—
478#336—611no—
479#336—611no—
480#336—611no—
481#336—611no—
482#336—611no—
483C61#2285311yescharacteristic, complemented, Sylow
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C22×Q8C4×D6111yescharacteristic
491C22×D4—611no—
492C22×D4—611no—
493C22×D4—611no—
494C22×D4C4×D6111yescharacteristic
495C22×D4C4×D6111yescharacteristic
496C22×D4C4×D6111yescharacteristic
497C23×C4—611no—
498C23×C4C22×D6111yescharacteristic
499C23×C4C22×D6111yescharacteristic
500C23×C4C22×D6111yescharacteristic
501C2×M16—22no—
502C2×M16—22no—
503C2×M16—41no—
504C2×M16—1222no—
505C2×M16—1222no—
506C2×M16—1222no—
507C2×M16—1222no—
508C2×M16—2441no—
509C2×M16—2441no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8—611no—
514C22×C8—611no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—1222no—
518C22×C8—1222no—
519C22×C8—2441no—
520C22×C8C22×D6111yescharacteristic
521C22×C8C22×D6111yescharacteristic
522C22×C8C22×D6111yescharacteristic
523C22×C8C22×D6111yescharacteristic
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—2441no—
529C4×D4—2441no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—611no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4—611no—
541C2×C22⋊C4—611no—
542C2×C22⋊C4—611no—
543C2×C22⋊C4—611no—
544C2×C22⋊C4—611no—
545C2×C42—611no—
546C2×C42—611no—
547C2×C42—611no—
548C4⋊C8—1222no—
549C4⋊C8—1222no—
550C4⋊C8—2441no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—614no—
555C22⋊C8—1222no—
556C22⋊C8—1222no—
557C22⋊C8—1222no—
558C22⋊C8—1222no—
559C22⋊C8—1222no—
560C22⋊C8—2441no—
561C22⋊C8C22⋊D6114yescomplemented
562C4×C8—1222no—
563C4×C8—1222no—
564C4×C8—2441no—
565#95—611no—
566#95—611no—
567#95—611no—
568#95—611no—
569#95—611no—
570#95—611no—
571C24—611no—
572C24C2×C4×D6111yescharacteristic
573C24C2×C4×D6111yescharacteristic
574C24C2×C4×D6111yescharacteristic
575#41—44no—
576#41—44no—
577#41—44no—
578#41—44no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—41no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—1222no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—2441no—
597C2×D4—2441no—
598C2×D4—2441no—
599C2×D4—2441no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4C2×C4×D6111yescharacteristic
628C22×C4C2×C4×D6111yescharacteristic
629C22×C4C2×C4×D6111yescharacteristic
630C22×C4#1175822212yes—
631C22×C4D4×D6112yes—
632C22×C4#1175822412yes—
633C22×C4C2×C22⋊D6112yes—
634C22×C4C23×D6111yescharacteristic
635M16—44no—
636M16—2444no—
637M16—2444no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—44no—
649C2×C8—612no—
650C2×C8—612no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—2444no—
662C2×C8C2×C22⋊D6112yes—
663C2×C8C2×C22⋊D6112yes—
664C4⋊C4—1222no—
665C4⋊C4—1222no—
666C4⋊C4—2441no—
667C22⋊C4—1222no—
668C22⋊C4—1222no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—1222no—
672C22⋊C4—1222no—
673C22⋊C4—1222no—
674C22⋊C4—1222no—
675C22⋊C4—1222no—
676C22⋊C4—1222no—
677C22⋊C4—2441no—
678C22⋊C4—2441no—
679C42—1221no—
680C42—1221no—
681C42—1221no—
682C42—1221no—
683C42—1221no—
684C42—1221no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23#1451973712yes—
712C23C4×C22⋊D6112yes—
713C23C22×C4×D6111yescharacteristic
714Q8—44no—
715D4—44no—
716D4—44no—
717D4—44no—
718D4—2444no—
719D4—2444no—
720D4—2444no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—612no—
741C2×C4—612no—
742C2×C4—612no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4#1451973712yes—
766C2×C4C4×C22⋊D6112yes—
767C2×C4C2×D4×D6111yescharacteristic
768C2×C4C22×C22⋊D6111yescharacteristic
769C2×C4C2×#1175822411yescharacteristic
770C2×C4C2×#1175822211yescharacteristic
771C2×C4#1451982211yescharacteristic
772C2×C4#1451982211yescharacteristic
773C8—22no—
774C8—22no—
775C8—41no—
776C8—41no—
777C8—1222no—
778C8—1222no—
779C8—2441no—
780C8—2441no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—2441no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22—2441no—
809C22C2×#1451973711yescharacteristic
810C22C2×C4×C22⋊D6111yescharacteristic
811C22#1684023511yescharacteristic
812C22#131×D6111yescharacteristic
813C22#131×D6111yescharacteristic
814C22#131×D6111yescharacteristic
815C22#1684052711yescharacteristic
816C4—22no—
817C4—22no—
818C4—41no—
819C4—1222no—
820C4—1222no—
821C4—1222no—
822C4—2441no—
823C4—2441no—
824C4—2441no—
825C4—2441no—
826C4D4×C22⋊D6111yescharacteristic
827C4#1684040211yescharacteristic
828C4#1684040611yescharacteristic
829C4#1684043811yescharacteristic
830C2—42no—
831C2—42no—
832C2—81no—
833C2—4881no—
834C2#2144879811yescharacteristic
835C2#2145452711yescharacteristic
836C2#2145452911yescharacteristic
837C2#2145454111yescharacteristic
838C2#2145454911yescharacteristic
839C2#2145486211yescharacteristic
840C2#2145488311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC2×C61×#408C2
prime radical#21449032C2
cosocleC22×C4×C61C24
hypercenterC2×#408D61
hypocenterC61#22853
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C2×#16839838C2semidirect
2. C2×#16839837C2semidirect
3. C2×#16839729C2semidirect
5. #21446611C2semidirect
6. #21446428C2semidirect
7. #21446422C2semidirect
8. #21446113C2semidirect
9. #21446111C2semidirect
10. #21446109C2semidirect
11. #21446002C2semidirect
12. #21446001C2semidirect
13. #21445593C2semidirect
14. C8×C22⋊Dic61C2semidirect
15. C2×C61×#408C2semidirect
110. C22⋊#92418D4semidirect
149. C22⋊C8×C61D4semidirect
413. C2×#408D61semidirect
483. C61#22853semidirect
561. C22⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398382
C2×#168398372
C2×#168397292
#214490322
#214466112
#214464282
#214464222
#214461132
#214461112
#214461092
#214460022
#214460012
#214455932
C8×C22⋊Dic612
C2×C61×#4082
#2285361