Finite Group Databasebeta

← #30609345

Subgroups — #30609345

Order 15616.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840713C211yesmaximal, characteristic, complemented
2C2×#16840712C211yesmaximal, characteristic
3C2×#16840709C211yesmaximal, characteristic
4C2×#16840709C211yesmaximal, characteristic
5C2×#16840709C211yesmaximal, characteristic
6C2×#16840708C211yesmaximal, characteristic, complemented
7#21461007C211yesmaximal, characteristic, complemented
8#21461007C211yesmaximal, characteristic, complemented
9#21461005C211yesmaximal, characteristic, complemented
10#21461004C211yesmaximal, characteristic, complemented
11#21461002C211yesmaximal, characteristic
12#21461002C211yesmaximal, characteristic
13#21460999C211yesmaximal, characteristic, complemented
14#21460995C211yesmaximal, characteristic, complemented
15#388×D61C211yesmaximal, characteristic
16C24×#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21C22×C4⋊#6923C2211yescharacteristic
22C22×C4⋊#6923C2211yescharacteristic
23C22×C4⋊#6923C2211yescharacteristic
24C22×C4⋊#6923C2211yescharacteristic
25C22×C4⋊#6923C2211yescharacteristic
26C22×C22⋊#6923C2211yescharacteristic
27C22×C22⋊#6923C2211yescharacteristic
28C22×C22⋊#6923C2211yescharacteristic
29C22×C4×#6923C2211yescharacteristic
30#16840713—24no—
31#16840712—24no—
32#16840709—24no—
33#16840709—24no—
34#16840709—24no—
35#16840708—24no—
36C2×(C2×#6923)⋊C4C2211yescharacteristic
37C2×(C2×#6923)⋊C4C2211yescharacteristic
38C2×(C2×#6923)⋊C4C2211yescharacteristic
39C2×(C2×#6923)⋊C4C2211yescharacteristic
40C2×(C2×#6923)⋊C4C2211yescharacteristic
41C2×(C2×#6923)⋊C4C2211yescharacteristic
42C2×(C2×#6923)⋊C4C2211yescharacteristic
43C2×(C2×#6923)⋊C4C2211yescharacteristic
44C2×(C2×#6923)⋊C4C2211yescharacteristic
45C2×(C2×#6923)⋊C4C2211yescharacteristic
46C2×(C2×#6923)⋊C4C2211yescharacteristic
47C2×(C2×#6923)⋊C4C2211yescharacteristic
48C2×(C2×#6923)⋊C4C2211yescharacteristic
49C2×(C2×#6923)⋊C4C2211yescharacteristic
50C2×C4⋊C4×D61C2211yescharacteristic
51C2×C22⋊C4×D61C2211yescharacteristic
52C2×C22⋊C4×D61C2211yescharacteristic
53C2×C22⋊C4×D61C2211yescharacteristic
54C2×C42×D61C2211yescharacteristic
55#16839656C411yescharacteristic, complemented
56#16839655C411yescharacteristic, complemented
57#16839654C411yescharacteristic, complemented
58#16839653C411yescharacteristic, complemented
59#16839652C411yescharacteristic, complemented
60#16839651C411yescharacteristic, complemented
61#16839650C411yescharacteristic, complemented
62#95×D61C2211yescharacteristic
63#95×D61C2211yescharacteristic
64C61×#388C411yescharacteristic, complemented
65C23×#6923—22no—
66C23×#6923—22no—
67C23×#6923—22no—
68C23×#6923—41no—
69C23×#6923—41no—
70C23×#6923—41no—
71C23×#6923—41no—
72C23×#6923C2311yescharacteristic
73C23×#6923C2311yescharacteristic
74C23×#6923C2311yescharacteristic
75C23×#6923C2311yescharacteristic
76C23×#6923C2311yescharacteristic
77C23×#6923C2311yescharacteristic
78C23×#6923C2311yescharacteristic
79C23×#6923C2311yescharacteristic
80C2×C4⋊#6923—22no—
81C2×C4⋊#6923—22no—
82C2×C4⋊#6923—22no—
83C2×C4⋊#6923—22no—
84C2×C4⋊#6923—22no—
85C2×C4⋊#6923—22no—
86C2×C4⋊#6923—22no—
87C2×C4⋊#6923—22no—
88C2×C4⋊#6923—22no—
89C2×C4⋊#6923—22no—
90C2×C4⋊#6923—22no—
91C2×C4⋊#6923—22no—
92C2×C4⋊#6923—22no—
93C2×C4⋊#6923—22no—
94C2×C4⋊#6923—41no—
95C2×C4⋊#6923—41no—
96C2×C4⋊#6923—41no—
97C2×C4⋊#6923—41no—
98C2×C4⋊#6923—41no—
99C2×C4⋊#6923—41no—
100C2×C4⋊#6923—41no—
101C2×C4⋊#6923—41no—
102C2×C4⋊#6923—41no—
103C2×C4⋊#6923—41no—
104C2×C4⋊#6923—41no—
105C2×C4⋊#6923—41no—
106C2×C4⋊#6923D414yes—
107C2×C22⋊#6923—22no—
108C2×C22⋊#6923—22no—
109C2×C22⋊#6923—22no—
110C2×C22⋊#6923—22no—
111C2×C22⋊#6923—22no—
112C2×C22⋊#6923—41no—
113C2×C22⋊#6923—41no—
114C2×C22⋊#6923—41no—
115C2×C22⋊#6923—41no—
116C2×C4×#6923—22no—
117C2×C4×#6923—22no—
118C2×C4×#6923—41no—
119(C2×#6923)⋊C4—22no—
120(C2×#6923)⋊C4—22no—
121(C2×#6923)⋊C4—22no—
122(C2×#6923)⋊C4—22no—
123(C2×#6923)⋊C4—22no—
124(C2×#6923)⋊C4—22no—
125(C2×#6923)⋊C4—22no—
126(C2×#6923)⋊C4—22no—
127(C2×#6923)⋊C4—22no—
128(C2×#6923)⋊C4—22no—
129(C2×#6923)⋊C4—41no—
130(C2×#6923)⋊C4—41no—
131(C2×#6923)⋊C4—41no—
132(C2×#6923)⋊C4D414yes—
133C24×D61C2311yescharacteristic
134C22×C4×D61C2311yescharacteristic
135C22×C4×D61C2311yescharacteristic
136C22×C4×D61C2311yescharacteristic
137C22×C4×D61C2311yescharacteristic
138C22×C4×D61C2311yescharacteristic
139C22×C4×D61C2311yescharacteristic
140C2×C4⋊Dic61C2×C411yescharacteristic, complemented
141C2×#11758196C2×C411yescharacteristic, complemented
142C2×#11758196C2×C411yescharacteristic, complemented
143C4⋊C4×D61—22no—
144C4⋊C4×D61—22no—
145C2×C22⋊Dic61C2×C411yescharacteristic
146C2×C22⋊Dic61C2×C411yescharacteristic
147C2×C22⋊Dic61C2×C411yescharacteristic
148C2×#11758198C2×C411yescharacteristic
149C2×#11758198C2×C411yescharacteristic
150C2×#11758198C2×C411yescharacteristic
151C2×#11758198C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C22⋊C4×D61—22no—
155C22⋊C4×D61—22no—
156C22⋊C4×D61—22no—
157C22⋊C4×D61—22no—
158C22⋊C4×D61D414yes—
159C22⋊C4×D61Q814yes—
160C2×C4×Dic61C2×C411yescharacteristic, complemented
161C2×C4×Dic61C2×C411yescharacteristic, complemented
162C2×C4×Dic61C2×C411yescharacteristic, complemented
163C42×D61—22no—
164C42×D61—22no—
165#14519684C2×C411yescharacteristic, complemented
166#14519684C2×C411yescharacteristic, complemented
167#14519684C2×C411yescharacteristic, complemented
168#14519684C2×C411yescharacteristic, complemented
169#14519684C2×C411yescharacteristic, complemented
170#14519684C2×C411yescharacteristic, complemented
171C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
172C2×C22⋊C4×C61C2×C411yescharacteristic
173C2×C22⋊C4×C61C2×C411yescharacteristic
174C2×C22⋊C4×C61C2×C411yescharacteristic
175C2×C42×C61C2×C411yescharacteristic, complemented
176#95×C61C2×C411yescharacteristic, complemented
177#95×C61C2×C411yescharacteristic, complemented
178C24×C61C22×C411yescharacteristic
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61C22×C411yescharacteristic
192C23×D61C2×D412yes—
193C23×D61C2×Q812yes—
194C23×D61C2411yescharacteristic
195C22×#6923—21no—
196C22×#6923—21no—
197C22×#6923—21no—
198C22×#6923—21no—
199C22×#6923—21no—
200C22×#6923—21no—
201C22×#6923—21no—
202C22×#6923—21no—
203C22×#6923—21no—
204C22×#6923—21no—
205C22×#6923—21no—
206C22×#6923—21no—
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—21no—
215C22×#6923—21no—
216C22×#6923—21no—
217C22×#6923—21no—
218C22×#6923—21no—
219C22×#6923—21no—
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—21no—
226C22×#6923—21no—
227C22×#6923—21no—
228C22×#6923—21no—
229C22×#6923—21no—
230C22×#6923—21no—
231C22×#6923—21no—
232C22×#6923—21no—
233C22×#6923—21no—
234C22×#6923—21no—
235C22×#6923—21no—
236C22×#6923—21no—
237C22×#6923—21no—
238C22×#6923—21no—
239C22×#6923—21no—
240C22×#6923—21no—
241C22×#6923—21no—
242C22×#6923—21no—
243C22×#6923—21no—
244C22×#6923—21no—
245C22×#6923—21no—
246C22×#6923—21no—
247C22×#6923—44no—
248C22×#6923—44no—
249C22×#6923—44no—
250C22×#6923—44no—
251C22×#6923—44no—
252C22×#6923—44no—
253C22×#6923—44no—
254C22×#6923C2×D412yes—
255C22×#6923C2×D412yes—
256C22×#6923C2×D412yes—
257C22×#6923C2×D412yes—
258C22×C4×C61C22×C411yescharacteristic
259C22×C4×C61C22×C411yescharacteristic
260C22×C4×C61C22×C411yescharacteristic
261C22×C4×C61C22×C411yescharacteristic
262C22×C4×C61C22×C411yescharacteristic
263C22×C4×C61C22×C411yescharacteristic
264C22×Dic61C22×C411yescharacteristic
265C22×Dic61C22×C411yescharacteristic
266C22×Dic61C22×C411yescharacteristic
267C22×Dic61C22×C411yescharacteristic
268C22×Dic61C22×C411yescharacteristic
269C22×Dic61C22×C411yescharacteristic
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—21no—
284C2×C4×D61—21no—
285C2×C4×D61—21no—
286C2×C4×D61—21no—
287C2×C4×D61—21no—
288C2×C4×D61—21no—
289C2×C4×D61—21no—
290C2×C4×D61—21no—
291C2×C4×D61—21no—
292C2×C4×D61—21no—
293C2×C4×D61—21no—
294C2×C4×D61—21no—
295C2×C4×D61—21no—
296C2×C4×D61—21no—
297C2×C4×D61—21no—
298C2×C4×D61C2×D412yes—
299C2×C4×D61C2×D412yes—
300C2×C4×D61C2×D412yes—
301C2×C4×D61C2×D412yes—
302C2×C4×D61C2×Q812yes—
303C2×C4×D61C2×Q812yes—
304C2×C4×D61#4112yes—
305C2×C4×D61#4112yes—
306C22⋊#6923—44no—
307C22⋊#6923—44no—
308C22⋊#6923—44no—
309C4⋊#6923—44no—
310C4⋊#6923—44no—
311C4⋊#6923—44no—
312C4⋊#6923—44no—
313C4⋊#6923—44no—
314C4⋊#6923—44no—
315C4⋊#6923—44no—
316C4⋊#6923—44no—
317C4⋊#6923—44no—
318C4×#6923—44no—
319C4⋊C4×C61—22no—
320C22⋊C4×C61—22no—
321C22⋊C4×C61—22no—
322C22⋊C4×C61C4⋊C414yescomplemented
323C42×C61—22no—
324C22⋊Dic61—22no—
325C22⋊Dic61—22no—
326C22⋊Dic61C4⋊C414yescomplemented
327#11758198—22no—
328#11758198—22no—
329#11758198—22no—
330#11758198—22no—
331#11758198C4⋊C414yescomplemented
332#11758198C4⋊C414yescomplemented
333C4⋊Dic61—22no—
334#11758196—22no—
335#11758196—22no—
336C4×Dic61—22no—
337C4×Dic61—22no—
338C4×Dic61—22no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—21no—
344C23×C61—21no—
345C23×C61C2×C4⋊C412yes—
346C23×C61C23×C411yescharacteristic
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—21no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61C2×C4⋊C412yes—
382C22×D61C22×D411yescharacteristic
383C22×D61C22×D411yescharacteristic
384C22×D61C22×D411yescharacteristic
385C22×D61C22×Q811yescharacteristic
386C22×D61C2×#4111yescharacteristic
387C22×D61C2×#4111yescharacteristic
388C22×D61H(5,𝔽2)11yescharacteristic
389C22×D61H(5,𝔽2)11yescharacteristic
390C22×D61H(5,𝔽2)11yescharacteristic
391C22×D61H(5,𝔽2)11yescharacteristic
392C22×D612−1+411yescharacteristic
393C22×D612−1+411yescharacteristic
394C22×D612−1+411yescharacteristic
395C22×D612−1+411yescharacteristic
396C2×#6923—22no—
397C2×#6923—22no—
398C2×#6923—22no—
399C2×#6923—22no—
400C2×#6923—22no—
401C2×#6923—22no—
402C2×#6923—22no—
403C2×#6923—22no—
404C2×#6923—22no—
405C2×#6923—22no—
406C2×#6923—22no—
407C2×#6923—22no—
408C2×#6923—416no—
409C2×#6923—41no—
410C2×#6923—41no—
411C2×#6923—41no—
412C2×#6923—41no—
413C2×#6923—41no—
414C2×#6923—41no—
415C2×#6923—41no—
416C2×#6923—41no—
417C2×#6923—41no—
418C2×#6923—41no—
419C2×#6923—41no—
420C2×#6923—41no—
421C2×#6923—41no—
422C2×#6923—41no—
423C2×#6923—41no—
424C2×#6923—41no—
425C2×#6923—41no—
426C2×#6923—41no—
427C2×#6923—41no—
428C2×#6923—41no—
429C2×#6923—41no—
430C2×#6923—41no—
431C2×#6923—41no—
432C2×#6923—41no—
433C2×#6923—41no—
434C2×#6923—41no—
435C2×#6923—41no—
436C2×#6923—41no—
437C2×#6923—41no—
438C2×#6923—41no—
439C2×#6923—41no—
440C2×#6923—41no—
441C2×#6923—41no—
442C2×#6923—41no—
443C2×#6923—41no—
444C2×#6923—41no—
445C2×#6923—41no—
446C2×#6923—41no—
447C2×#6923—41no—
448C2×#6923—41no—
449C2×#6923—41no—
450C2×#6923—41no—
451C2×#6923—41no—
452C2×#6923—41no—
453C2×C4×C61—21no—
454C2×C4×C61—21no—
455C2×C4×C61—21no—
456C2×C4×C61—21no—
457C2×C4×C61—21no—
458C2×C4×C61—21no—
459C2×C4×C61—21no—
460C2×C4×C61—21no—
461C2×C4×C61—21no—
462C2×C4×C61—21no—
463C2×C4×C61—21no—
464C2×C4×C61—21no—
465C2×C4×C61—21no—
466C2×C4×C61—21no—
467C2×C4×C61C2×C4⋊C412yes—
468C2×C4×C61C2×C4⋊C412yes—
469C2×C4×C61C4×D412yes—
470C2×C4×C61C4×D412yes—
471C2×Dic61—21no—
472C2×Dic61—21no—
473C2×Dic61—21no—
474C2×Dic61—21no—
475C2×Dic61—21no—
476C2×Dic61—21no—
477C2×Dic61—21no—
478C2×Dic61—21no—
479C2×Dic61—21no—
480C2×Dic61—21no—
481C2×Dic61—21no—
482C2×Dic61—21no—
483C2×Dic61—21no—
484C2×Dic61—21no—
485C2×Dic61C2×C4⋊C412yes—
486C2×Dic61C2×C4⋊C412yes—
487C2×Dic61C4×D412yes—
488C2×Dic61C4×D412yes—
489C4×D61—22no—
490C4×D61—22no—
491C4×D61—22no—
492C4×D61—22no—
493C4×D61—22no—
494C4×D61—22no—
495C4×D61—22no—
496C4×D61—22no—
497C4×D61—22no—
498C4×D61—22no—
499C4×D61—22no—
500C4×D61—22no—
501C4×D61—22no—
502C4×D61—22no—
503C4×D61—22no—
504C4×D61—22no—
505C4×D61—41no—
506C4×D61—41no—
507C4×D61—41no—
508C4×D61—41no—
509C4×D61—41no—
510C4×D61—41no—
511C4×D61—41no—
512C4×D61—41no—
513#14405—611nomaximal, Sylow
514C22×C61—22no—
515C22×C61—22no—
516C22×C61—22no—
517C22×C61—41no—
518C22×C61—41no—
519C22×C61—41no—
520C22×C61—41no—
521C22×C61C22×C4⋊C411yescharacteristic
522C22×C61C2×C4×D411yescharacteristic
523C22×C61C2×C4×D411yescharacteristic
524C22×C61#52011yescharacteristic
525C22×C61#52011yescharacteristic
526C22×C61#52011yescharacteristic
527C22×C61#52011yescharacteristic
528C2×D61—22no—
529C2×D61—22no—
530C2×D61—22no—
531C2×D61—41no—
532C2×D61—41no—
533C2×D61—41no—
534C2×D61—41no—
535C2×D61—42no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61#53411yescharacteristic
544C2×D61#53511yescharacteristic
545C2×D61#53511yescharacteristic
546C2×D61#53611yescharacteristic
547C2×D61#53611yescharacteristic
548C2×D61#53611yescharacteristic
549C2×D61#53911yescharacteristic
550C2×D61#53911yescharacteristic
551C2×D61#54211yescharacteristic
552C2×D61#54211yescharacteristic
553C2×D61#54411yescharacteristic
554C2×D61#54411yescharacteristic
555C2×D61D4211yescharacteristic
556C2×D61D4211yescharacteristic
557C2×D61D4211yescharacteristic
558C2×D61#54711yescharacteristic
559C2×D61#54711yescharacteristic
560C2×D61#54711yescharacteristic
561C2×D61#54811yescharacteristic
562C2×D61D4×Q811yescharacteristic
563C2×D61D4×Q811yescharacteristic
564C2×D61#55311yescharacteristic
565C2×D61#55411yescharacteristic
566C2×D61#55411yescharacteristic
567C2×D61#56011yescharacteristic
568C2×D61#56311yescharacteristic
569C2×D61#56311yescharacteristic
570C2×D61#56311yescharacteristic
571#6923—42no—
572#6923—42no—
573#6923—42no—
574#6923—42no—
575#6923—81no—
576#6923—81no—
577#6923—81no—
578#6923—81no—
579C4×C61—22no—
580C4×C61—22no—
581C4×C61—22no—
582C4×C61—22no—
583C4×C61—41no—
584C4×C61—41no—
585Dic61—22no—
586Dic61—22no—
587Dic61—22no—
588Dic61—22no—
589Dic61—41no—
590Dic61—41no—
591C2×#389—611no—
592C2×#388—611no—
593C2×#388—611no—
594C2×#385—611no—
595C2×#385—611no—
596C2×#385—611no—
597C2×#384—611no—
598#1444—611no—
599#1444—611no—
600#1442—611no—
601#1441—611no—
602#1439—611no—
603#1439—611no—
604#1436—611no—
605#1434—611no—
606C2×C61—42no—
607C2×C61#231711yescharacteristic
608C2×C61#232211yescharacteristic
609C2×C61#232611yescharacteristic
610C2×C61D4×C4⋊C411yescharacteristic
611C2×C61D4×C4⋊C411yescharacteristic
612C2×C61#236111yescharacteristic
613C2×C61#238311yescharacteristic
614D61—42no—
615D61#266911yescharacteristic
616D61#267411yescharacteristic
617D61#267711yescharacteristic
618D61#268011yescharacteristic
619D61#271811yescharacteristic
620D61#272011yescharacteristic
621D61#272911yescharacteristic
622D61#279011yescharacteristic
623C24×C4—611no—
624C22×C4⋊C4—611no—
625C22×C4⋊C4—611no—
626C22×C4⋊C4—611no—
627C22×C4⋊C4—611no—
628C22×C4⋊C4—611no—
629C22×C4⋊C4—611no—
630C22×C4⋊C4—611no—
631C22×C4⋊C4—611no—
632C22×C4⋊C4—611no—
633C22×C4⋊C4—611no—
634C22×C22⋊C4—611no—
635C22×C22⋊C4—611no—
636C22×C22⋊C4—611no—
637C22×C22⋊C4—611no—
638C22×C22⋊C4—611no—
639C22×C22⋊C4—611no—
640C22×C42—611no—
641C22×C42—611no—
642#389—1224no—
643#388—611no—
644#388—611no—
645#388—611no—
646#388—611no—
647#388—611no—
648#388—611no—
649#388—611no—
650#388—1224no—
651#388#692311yescharacteristic, complemented
652#385—1224no—
653#385—1224no—
654#385—1224no—
655#384—1224no—
656C2×#95—611no—
657C2×#95—611no—
658C2×#95—611no—
659C2×#95—611no—
660C2×#95—611no—
661C2×#95—611no—
662C2×#95—611no—
663C2×#95—611no—
664C2×#95—611no—
665C2×#95—611no—
666C2×#95—611no—
667C2×#95—611no—
668C2×#95—611no—
669C2×#95—611no—
670C2×#95—611no—
671C2×#95—611no—
672C61#1440511yescharacteristic, complemented, Sylow
673C25—611no—
674C23×C4—611no—
675C23×C4—611no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—611no—
680C23×C4—611no—
681C23×C4—611no—
682C23×C4—611no—
683C23×C4—611no—
684C23×C4—611no—
685C23×C4—611no—
686C23×C4—611no—
687C23×C4—611no—
688C23×C4—1222no—
689C23×C4—1222no—
690C23×C4—1222no—
691C23×C4—2441no—
692C23×C4—2441no—
693C23×C4—2441no—
694C23×C4—2441no—
695C2×C4⋊C4—611no—
696C2×C4⋊C4—611no—
697C2×C4⋊C4—611no—
698C2×C4⋊C4—614no—
699C2×C4⋊C4—1222no—
700C2×C4⋊C4—1222no—
701C2×C4⋊C4—1222no—
702C2×C4⋊C4—1222no—
703C2×C4⋊C4—1222no—
704C2×C4⋊C4—1222no—
705C2×C4⋊C4—1222no—
706C2×C4⋊C4—1222no—
707C2×C4⋊C4—1222no—
708C2×C4⋊C4—1222no—
709C2×C4⋊C4—1222no—
710C2×C4⋊C4—1222no—
711C2×C4⋊C4—1222no—
712C2×C4⋊C4—1222no—
713C2×C4⋊C4—1222no—
714C2×C4⋊C4—1222no—
715C2×C4⋊C4—2441no—
716C2×C4⋊C4—2441no—
717C2×C4⋊C4—2441no—
718C2×C4⋊C4—2441no—
719C2×C4⋊C4—2441no—
720C2×C4⋊C4—2441no—
721C2×C4⋊C4—2441no—
722C2×C4⋊C4—2441no—
723C2×C4⋊C4—2441no—
724C2×C4⋊C4—2441no—
725C2×C4⋊C4—2441no—
726C2×C4⋊C4—2441no—
727C2×C4⋊C4C2×#692311yescharacteristic, complemented
728C2×C22⋊C4—611no—
729C2×C22⋊C4—611no—
730C2×C22⋊C4—611no—
731C2×C22⋊C4—614no—
732C2×C22⋊C4—614no—
733C2×C22⋊C4—611no—
734C2×C22⋊C4—611no—
735C2×C22⋊C4—611no—
736C2×C22⋊C4—611no—
737C2×C22⋊C4—611no—
738C2×C22⋊C4—611no—
739C2×C22⋊C4—1222no—
740C2×C22⋊C4—1222no—
741C2×C22⋊C4—1222no—
742C2×C22⋊C4—1222no—
743C2×C22⋊C4—1222no—
744C2×C22⋊C4—1222no—
745C2×C22⋊C4—1222no—
746C2×C22⋊C4—1222no—
747C2×C22⋊C4—1222no—
748C2×C22⋊C4—2441no—
749C2×C22⋊C4—2441no—
750C2×C22⋊C4—2441no—
751C2×C22⋊C4—2441no—
752C2×C22⋊C4C2×#692311yescharacteristic
753C2×C22⋊C4C2×#692311yescharacteristic
754C2×C22⋊C4C2×#692311yescharacteristic
755C2×C42—611no—
756C2×C42—611no—
757C2×C42—611no—
758C2×C42—1222no—
759C2×C42—1222no—
760C2×C42—1222no—
761C2×C42—1222no—
762C2×C42—2441no—
763C2×C42C2×#692311yescharacteristic, complemented
764#95—614no—
765#95—611no—
766#95—611no—
767#95—611no—
768#95—611no—
769#95—611no—
770#95—611no—
771#95—1222no—
772#95—1222no—
773#95—1222no—
774#95—1222no—
775#95—1222no—
776#95—1222no—
777#95—1222no—
778#95—1222no—
779#95—1222no—
780#95—1222no—
781#95—2441no—
782#95—2441no—
783#95—2441no—
784#95C2×#692311yescharacteristic, complemented
785#95C2×#692311yescharacteristic, complemented
786C24—611no—
787C24—612no—
788C24—612no—
789C24—611no—
790C24—1221no—
791C24—1221no—
792C24—1221no—
793C24—1221no—
794C24—1221no—
795C24—1221no—
796C24—1221no—
797C24—1221no—
798C24—1221no—
799C24—1221no—
800C24—1221no—
801C24—1221no—
802C24C22×#692311yescharacteristic
803C22×C4—611no—
804C22×C4—611no—
805C22×C4—611no—
806C22×C4—611no—
807C22×C4—612no—
808C22×C4—612no—
809C22×C4—612no—
810C22×C4—612no—
811C22×C4—612no—
812C22×C4—612no—
813C22×C4—612no—
814C22×C4—612no—
815C22×C4—612no—
816C22×C4—612no—
817C22×C4—612no—
818C22×C4—612no—
819C22×C4—611no—
820C22×C4—611no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1221no—
889C22×C4—1221no—
890C22×C4—1221no—
891C22×C4—1221no—
892C22×C4—1221no—
893C22×C4—1221no—
894C22×C4—1221no—
895C22×C4—1221no—
896C22×C4—1221no—
897C22×C4—1221no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—2444no—
902C22×C4—2444no—
903C22×C4—2444no—
904C22×C4—2444no—
905C22×C4—2444no—
906C22×C4—2444no—
907C22×C4—2444no—
908C22×C4C22×#692311yescharacteristic
909C22×C4C22×#692311yescharacteristic
910C22×C4C22×#692311yescharacteristic
911C22×C4C22×#692311yescharacteristic
912C22×C4C22×#692311yescharacteristic
913C22×C4C22×#692311yescharacteristic
914C4⋊C4—22no—
915C4⋊C4—1222no—
916C4⋊C4—1222no—
917C4⋊C4—1222no—
918C4⋊C4—2444no—
919C4⋊C4—2444no—
920C4⋊C4—2444no—
921C4⋊C4—2444no—
922C4⋊C4—2444no—
923C4⋊C4—2444no—
924C4⋊C4—2444no—
925C4⋊C4—2444no—
926C4⋊C4—2444no—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—614no—
930C22⋊C4—614no—
931C22⋊C4—614no—
932C22⋊C4—1222no—
933C22⋊C4—1222no—
934C22⋊C4—1222no—
935C22⋊C4—1222no—
936C22⋊C4—1222no—
937C22⋊C4—1222no—
938C22⋊C4—2444no—
939C22⋊C4—2444no—
940C22⋊C4—2444no—
941C22⋊C4C4⋊#692314yescomplemented
942C42—22no—
943C42—1222no—
944C42—1222no—
945C42—1222no—
946C42—2444no—
947C23—21no—
948C23—21no—
949C23—21no—
950C23—21no—
951C23—21no—
952C23—21no—
953C23—611no—
954C23—611no—
955C23—611no—
956C23—611no—
957C23—611no—
958C23—611no—
959C23—611no—
960C23—611no—
961C23—611no—
962C23—611no—
963C23—611no—
964C23—611no—
965C23—611no—
966C23—611no—
967C23—612no—
968C23—1222no—
969C23—1222no—
970C23—1222no—
971C23—1222no—
972C23—1222no—
973C23—1222no—
974C23—1222no—
975C23—1222no—
976C23—1222no—
977C23—1222no—
978C23—1222no—
979C23—1222no—
980C23—1221no—
981C23—1221no—
982C23—1221no—
983C23—1221no—
984C23—1221no—
985C23—1221no—
986C23—2441no—
987C23—2441no—
988C23—2441no—
989C23—2441no—
990C23—2441no—
991C23—2441no—
992C23—2441no—
993C23—2441no—
994C23—2441no—
995C23—2441no—
996C23—2441no—
997C23—2441no—
998C23—2441no—
999C23—2441no—
1000C23—2441no—
1001C23—2441no—
1002C23C2×C4⋊#692312yes—
1003C23C23×#692311yescharacteristic
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—612no—
1019C2×C4—612no—
1020C2×C4—612no—
1021C2×C4—612no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1222no—
1036C2×C4—1222no—
1037C2×C4—1222no—
1038C2×C4—1221no—
1039C2×C4—1221no—
1040C2×C4—1221no—
1041C2×C4—1221no—
1042C2×C4—1221no—
1043C2×C4—1221no—
1044C2×C4—1221no—
1045C2×C4—1221no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—1222no—
1055C2×C4—1222no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1221no—
1059C2×C4—1221no—
1060C2×C4—1221no—
1061C2×C4—1221no—
1062C2×C4—1221no—
1063C2×C4—1221no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4—2441no—
1089C2×C4—2441no—
1090C2×C4—2441no—
1091C2×C4—2441no—
1092C2×C4—2441no—
1093C2×C4—2441no—
1094C2×C4—2441no—
1095C2×C4—2441no—
1096C2×C4—2441no—
1097C2×C4—2441no—
1098C2×C4—2441no—
1099C2×C4—2441no—
1100C2×C4—2441no—
1101C2×C4—2441no—
1102C2×C4—2441no—
1103C2×C4—2441no—
1104C2×C4—2441no—
1105C2×C4—2441no—
1106C2×C4—2441no—
1107C2×C4—2441no—
1108C2×C4—2441no—
1109C2×C4—2441no—
1110C2×C4—2441no—
1111C2×C4—2441no—
1112C2×C4—2441no—
1113C2×C4—2441no—
1114C2×C4—2441no—
1115C2×C4—2441no—
1116C2×C4—24416no—
1117C2×C4C2×C4⋊#692312yes—
1118C2×C4C2×C4⋊#692312yes—
1119C2×C4D4×#692312yes—
1120C2×C4D4×#692312yes—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—611no—
1129C22—611no—
1130C22—611no—
1131C22—611no—
1132C22—611no—
1133C22—611no—
1134C22—611no—
1135C22—611no—
1136C22—611no—
1137C22—611no—
1138C22—611no—
1139C22—611no—
1140C22—611no—
1141C22—611no—
1142C22—611no—
1143C22—611no—
1144C22—611no—
1145C22—611no—
1146C22—611no—
1147C22—611no—
1148C22—611no—
1149C22—611no—
1150C22—611no—
1151C22—611no—
1152C22—611no—
1153C22—611no—
1154C22—611no—
1155C22—611no—
1156C22—1222no—
1157C22—1222no—
1158C22—1222no—
1159C22—2442no—
1160C22—2442no—
1161C22—2442no—
1162C22—2442no—
1163C22—2442no—
1164C22—2442no—
1165C22—2442no—
1166C22—2442no—
1167C22—2441no—
1168C22—2441no—
1169C22—2441no—
1170C22—2441no—
1171C22C22×C4⋊#692311yescharacteristic
1172C22C2×D4×#692311yescharacteristic
1173C22C2×D4×#692311yescharacteristic
1174C22#1684083111yescharacteristic
1175C22#1684083111yescharacteristic
1176C22#1684083111yescharacteristic
1177C22#1684083111yescharacteristic
1178C4—22no—
1179C4—22no—
1180C4—22no—
1181C4—22no—
1182C4—41no—
1183C4—41no—
1184C4—1222no—
1185C4—1222no—
1186C4—1222no—
1187C4—1222no—
1188C4—4881no—
1189C4—4881no—
1190C4—4881no—
1191C4—4881no—
1192C4—2442no—
1193C4—2442no—
1194C4—2442no—
1195C4—2442no—
1196C4—2441no—
1197C4—2441no—
1198C2—42no—
1199C2—611no—
1200C2—611no—
1201C2—611no—
1202C2—611no—
1203C2—611no—
1204C2—611no—
1205C2—611no—
1206C2—611no—
1207C2—2442no—
1208C2#2146230011yescharacteristic
1209C2#2146230511yescharacteristic
1210C2#2146230911yescharacteristic
1211C2D4×C4⋊#692311yescharacteristic
1212C2D4×C4⋊#692311yescharacteristic
1213C2#2146234411yescharacteristic
1214C2#2146236611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#388C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#388#6923
hypocenterC61#14405
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#16840713C2semidirect
6. C2×#16840708C2semidirect
7. #21461007C2semidirect
8. #21461007C2semidirect
9. #21461005C2semidirect
10. #21461004C2semidirect
13. #21460999C2semidirect
14. #21460995C2semidirect
55. #16839656C4semidirect
56. #16839655C4semidirect
57. #16839654C4semidirect
58. #16839653C4semidirect
59. #16839652C4semidirect
60. #16839651C4semidirect
61. #16839650C4semidirect
64. C61×#388C4semidirect
140. C2×C4⋊Dic61C2×C4semidirect
141. C2×#11758196C2×C4semidirect
142. C2×#11758196C2×C4semidirect
160. C2×C4×Dic61C2×C4semidirect
161. C2×C4×Dic61C2×C4semidirect
162. C2×C4×Dic61C2×C4semidirect
165. #14519684C2×C4semidirect
166. #14519684C2×C4semidirect
167. #14519684C2×C4semidirect
168. #14519684C2×C4semidirect
169. #14519684C2×C4semidirect
170. #14519684C2×C4semidirect
171. C2×C4⋊C4×C61C2×C4semidirect
175. C2×C42×C61C2×C4semidirect
176. #95×C61C2×C4semidirect
177. #95×C61C2×C4semidirect
322. C22⋊C4×C61C4⋊C4semidirect
326. C22⋊Dic61C4⋊C4semidirect
331. #11758198C4⋊C4semidirect
332. #11758198C4⋊C4semidirect
651. #388#6923semidirect
672. C61#14405semidirect
727. C2×C4⋊C4C2×#6923semidirect
763. C2×C42C2×#6923semidirect
784. #95C2×#6923semidirect
785. #95C2×#6923semidirect
941. C22⋊C4C4⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407132
C2×#168407122
C2×#168407092
C2×#168407082
#214610072
#214610052
#214610042
#214610022
#214609992
#214609952
#388×D612
#1440561