Finite Group Databasebeta

← #30608754

Subgroups — #30608754

Order 15616.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840712C211yesmaximal, characteristic
2C2×C4⋊C4×#6923C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×#6923C211yesmaximal, characteristic
4C2×C22⋊C4×#6923C211yesmaximal, characteristic
5#21461000C211yesmaximal, characteristic
6#21461000C211yesmaximal, characteristic
7#21460999C211yesmaximal, characteristic, complemented
8#21460998C211yesmaximal, characteristic, complemented
9#21460994C211yesmaximal, characteristic, complemented
10#21460994C211yesmaximal, characteristic, complemented
11#21460992C211yesmaximal, characteristic
12C4×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
13C4×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
14#95×#6923C211yesmaximal, characteristic, complemented
15#388×D61C211yesmaximal, characteristic
16C24×#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C22⋊#6923C2211yescharacteristic
19C22×C22⋊#6923C2211yescharacteristic
20C22×C22⋊#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
22C22×C4×#6923C2211yescharacteristic
23C22×C4×#6923C2211yescharacteristic
24C22×C4×#6923C2211yescharacteristic
25C22×C4×#6923C2211yescharacteristic
26C22×C4×#6923C2211yescharacteristic
27C22×C4×#6923C2211yescharacteristic
28#16840712C418yescomplemented
29C4⋊C4×#6923—24no—
30C22⋊C4×#6923—24no—
31C22⋊C4×#6923C418yescomplemented
32C2×(C2×#6923)⋊C4C2211yescharacteristic
33C2×(C2×#6923)⋊C4C2211yescharacteristic
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
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×C4⋊C4×D61C2211yescharacteristic
49C2×C22⋊C4×D61C2211yescharacteristic
50C2×C22⋊C4×D61C2211yescharacteristic
51C2×C22⋊C4×D61C2211yescharacteristic
52C2×C42×D61C2211yescharacteristic
53#16839656C411yescharacteristic, complemented
54#16839655C411yescharacteristic, complemented
55#16839654C411yescharacteristic, complemented
56#16839653C411yescharacteristic, complemented
57#16839652C411yescharacteristic, complemented
58#16839651C411yescharacteristic, complemented
59#16839650C411yescharacteristic, complemented
60#95×D61C2211yescharacteristic
61#95×D61C2211yescharacteristic
62C61×#388C411yescharacteristic, complemented
63C23×#6923—22no—
64C23×#6923—22no—
65C23×#6923—22no—
66C23×#6923—22no—
67C23×#6923—41no—
68C23×#6923—41no—
69C23×#6923C2×C414yes—
70C23×#6923C2311yescharacteristic
71C23×#6923C2311yescharacteristic
72C23×#6923C2311yescharacteristic
73C23×#6923C2311yescharacteristic
74C23×#6923C2311yescharacteristic
75C23×#6923C2311yescharacteristic
76C23×#6923C2311yescharacteristic
77C23×#6923C2311yescharacteristic
78C2×C4⋊#6923—22no—
79C2×C4⋊#6923—22no—
80C2×C4⋊#6923C2×C414yescomplemented
81C2×C22⋊#6923—22no—
82C2×C22⋊#6923—22no—
83C2×C22⋊#6923—22no—
84C2×C22⋊#6923—22no—
85C2×C22⋊#6923—41no—
86C2×C22⋊#6923—41no—
87C2×C22⋊#6923C2×C414yes—
88C2×C22⋊#6923C2×C414yes—
89C2×C22⋊#6923C2×C414yes—
90C2×C4×#6923—22no—
91C2×C4×#6923—22no—
92C2×C4×#6923—22no—
93C2×C4×#6923—22no—
94C2×C4×#6923—22no—
95C2×C4×#6923—22no—
96C2×C4×#6923—22no—
97C2×C4×#6923—22no—
98C2×C4×#6923—22no—
99C2×C4×#6923—22no—
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×#6923—41no—
107C2×C4×#6923—41no—
108C2×C4×#6923C2×C414yes—
109C2×C4×#6923C2×C414yes—
110C2×C4×#6923C2×C414yescomplemented
111(C2×#6923)⋊C4—22no—
112(C2×#6923)⋊C4—22no—
113(C2×#6923)⋊C4—22no—
114(C2×#6923)⋊C4—22no—
115(C2×#6923)⋊C4—22no—
116(C2×#6923)⋊C4—22no—
117(C2×#6923)⋊C4—22no—
118(C2×#6923)⋊C4—22no—
119(C2×#6923)⋊C4—22no—
120(C2×#6923)⋊C4—41no—
121(C2×#6923)⋊C4—41no—
122(C2×#6923)⋊C4C2×C414yes—
123(C2×#6923)⋊C4C2×C414yes—
124(C2×#6923)⋊C4C2×C414yescomplemented
125(C2×#6923)⋊C4C2×C414yescomplemented
126(C2×#6923)⋊C4D414yes—
127C24×D61C2311yescharacteristic
128C22×C4×D61C2311yescharacteristic
129C22×C4×D61C2311yescharacteristic
130C22×C4×D61C2311yescharacteristic
131C22×C4×D61C2311yescharacteristic
132C22×C4×D61C2311yescharacteristic
133C22×C4×D61C2311yescharacteristic
134C2×C4⋊Dic61C2×C411yescharacteristic, complemented
135C2×#11758196C2×C411yescharacteristic, complemented
136C2×#11758196C2×C411yescharacteristic, complemented
137C4⋊C4×D61—22no—
138C4⋊C4×D61—22no—
139C2×C22⋊Dic61C2×C411yescharacteristic
140C2×C22⋊Dic61C2×C411yescharacteristic
141C2×C22⋊Dic61C2×C411yescharacteristic
142C2×#11758198C2×C411yescharacteristic
143C2×#11758198C2×C411yescharacteristic
144C2×#11758198C2×C411yescharacteristic
145C2×#11758198C2×C411yescharacteristic
146C2×#11758198C2×C411yescharacteristic
147C2×#11758198C2×C411yescharacteristic
148C22⋊C4×D61—22no—
149C22⋊C4×D61—22no—
150C22⋊C4×D61—41no—
151C22⋊C4×D61—41no—
152C22⋊C4×D61C2×C414yes—
153C22⋊C4×D61C2×C414yes—
154C2×C4×Dic61C2×C411yescharacteristic, complemented
155C2×C4×Dic61C2×C411yescharacteristic, complemented
156C2×C4×Dic61C2×C411yescharacteristic, complemented
157C42×D61—41no—
158C42×D61—41no—
159#14519684C2×C411yescharacteristic, complemented
160#14519684C2×C411yescharacteristic, complemented
161#14519684C2×C411yescharacteristic, complemented
162#14519684C2×C411yescharacteristic, complemented
163#14519684C2×C411yescharacteristic, complemented
164#14519684C2×C411yescharacteristic, complemented
165C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
166C2×C22⋊C4×C61C2×C411yescharacteristic
167C2×C22⋊C4×C61C2×C411yescharacteristic
168C2×C22⋊C4×C61C2×C411yescharacteristic
169C2×C42×C61C2×C411yescharacteristic, complemented
170#95×C61C2×C411yescharacteristic, complemented
171#95×C61C2×C411yescharacteristic, complemented
172C24×C61C22×C411yescharacteristic
173C23×D61—21no—
174C23×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61C22×C411yescharacteristic
186C23×D61C22×C412yes—
187C23×D61C22×C412yes—
188C23×D61C2411yescharacteristic
189C22×#6923—21no—
190C22×#6923—21no—
191C22×#6923—21no—
192C22×#6923—21no—
193C22×#6923—21no—
194C22×#6923—21no—
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—28no—
230C22×#6923—28no—
231C22×#6923—44no—
232C22×#6923—44no—
233C22×#6923—44no—
234C22×#6923—44no—
235C22×#6923—44no—
236C22×#6923C22×C412yes—
237C22×#6923C22×C412yes—
238C22×#6923C22×C412yes—
239C22×#6923C22×C412yes—
240C22×#6923C22×C412yes—
241C22×#6923C22×C412yes—
242C22×#6923C22×C412yes—
243C22×#6923C22×C412yes—
244C22×#6923C2×D412yes—
245C22×#6923C2×D412yes—
246C22×#6923#4112yes—
247C22×#6923#4112yes—
248C22×#6923#4112yes—
249C22×#6923#4112yes—
250C22×#6923#4112yes—
251C22×#6923#4112yes—
252C22×C4×C61C22×C411yescharacteristic
253C22×C4×C61C22×C411yescharacteristic
254C22×C4×C61C22×C411yescharacteristic
255C22×C4×C61C22×C411yescharacteristic
256C22×C4×C61C22×C411yescharacteristic
257C22×C4×C61C22×C411yescharacteristic
258C22×Dic61C22×C411yescharacteristic
259C22×Dic61C22×C411yescharacteristic
260C22×Dic61C22×C411yescharacteristic
261C22×Dic61C22×C411yescharacteristic
262C22×Dic61C22×C411yescharacteristic
263C22×Dic61C22×C411yescharacteristic
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
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×D61C22×C412yes—
295C2×C4×D61C22×C412yes—
296C2×C4×D61C22×C412yes—
297C2×C4×D61C22×C412yes—
298C2×C4×D61C2×D412yes—
299C2×C4×D61#4112yes—
300C22⋊#6923—28no—
301C22⋊#6923—28no—
302C22⋊#6923—44no—
303C4⋊#6923—28no—
304C4×#6923—28no—
305C4×#6923—44no—
306C4×#6923—44no—
307C4×#6923—44no—
308C4×#6923—44no—
309C4×#6923—44no—
310C4×#6923—44no—
311C4⋊C4×C61—22no—
312C22⋊C4×C61—22no—
313C22⋊C4×C61—41no—
314C22⋊C4×C61C4214yescomplemented
315C42×C61—41no—
316C22⋊Dic61—22no—
317C22⋊Dic61—41no—
318C22⋊Dic61C4214yescomplemented
319#11758198—22no—
320#11758198—22no—
321#11758198—41no—
322#11758198—41no—
323#11758198C4214yescomplemented
324#11758198C4214yescomplemented
325C4⋊Dic61—22no—
326#11758196—22no—
327#11758196—22no—
328C4×Dic61—41no—
329C4×Dic61—41no—
330C4×Dic61—41no—
331C23×C61—21no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61C2×C4212yes—
338C23×C61C23×C411yescharacteristic
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—41no—
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×D61C2×C4212yes—
374C22×D61C23×C411yescharacteristic
375C22×D61C23×C411yescharacteristic
376C22×D61C22×D411yescharacteristic
377C22×D61C2×#4111yescharacteristic
378C22×D61C2×#4111yescharacteristic
379C22×D61C2×#4111yescharacteristic
380C22×D61C2×#4111yescharacteristic
381C22×D61C2×#4111yescharacteristic
382C22×D61C2×#4111yescharacteristic
383C22×D61C2×#4111yescharacteristic
384C22×D61H(5,𝔽2)11yescharacteristic
385C22×D61H(5,𝔽2)11yescharacteristic
386C22×D61H(5,𝔽2)11yescharacteristic
387C22×D612−1+411yescharacteristic
388C2×#6923—22no—
389C2×#6923—22no—
390C2×#6923—22no—
391C2×#6923—22no—
392C2×#6923—22no—
393C2×#6923—22no—
394C2×#6923—22no—
395C2×#6923—22no—
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—22no—
409C2×#6923—22no—
410C2×#6923—22no—
411C2×#6923—22no—
412C2×#6923—22no—
413C2×#6923—22no—
414C2×#6923—22no—
415C2×#6923—22no—
416C2×#6923—22no—
417C2×#6923—22no—
418C2×#6923—22no—
419C2×#6923—22no—
420C2×#6923—22no—
421C2×#6923—22no—
422C2×#6923—22no—
423C2×#6923—22no—
424C2×#6923—416no—
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#11714yes—
442C2×#6923#11714yes—
443C2×#6923C4×D414yes—
444C2×#6923C4×D414yes—
445C2×C4×C61—21no—
446C2×C4×C61—21no—
447C2×C4×C61—21no—
448C2×C4×C61—21no—
449C2×C4×C61—21no—
450C2×C4×C61—21no—
451C2×C4×C61—21no—
452C2×C4×C61—21no—
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×C61C2×C4212yes—
461C2×C4×C61C2×C4212yes—
462C2×C4×C61C4×D412yes—
463C2×Dic61—21no—
464C2×Dic61—21no—
465C2×Dic61—21no—
466C2×Dic61—21no—
467C2×Dic61—21no—
468C2×Dic61—21no—
469C2×Dic61—21no—
470C2×Dic61—21no—
471C2×Dic61—21no—
472C2×Dic61—21no—
473C2×Dic61—21no—
474C2×Dic61—21no—
475C2×Dic61—21no—
476C2×Dic61—21no—
477C2×Dic61—21no—
478C2×Dic61C2×C4212yes—
479C2×Dic61C2×C4212yes—
480C2×Dic61C4×D412yes—
481C4×D61—22no—
482C4×D61—22no—
483C4×D61—22no—
484C4×D61—22no—
485C4×D61—22no—
486C4×D61—22no—
487C4×D61—22no—
488C4×D61—22no—
489C4×D61—22no—
490C4×D61—22no—
491C4×D61—22no—
492C4×D61—22no—
493C4×D61—41no—
494C4×D61—41no—
495C4×D61—41no—
496C4×D61—41no—
497C4×D61—41no—
498C4×D61—41no—
499C4×D61—41no—
500C4×D61—41no—
501C4×D61—41no—
502C4×D61—41no—
503C4×D61—41no—
504C4×D61—41no—
505#13822—611nomaximal, Sylow
506C22×C61—22no—
507C22×C61—22no—
508C22×C61—22no—
509C22×C61—41no—
510C22×C61—41no—
511C22×C61—41no—
512C22×C61—41no—
513C22×C61C22×C4211yescharacteristic
514C22×C61C2×C4×D411yescharacteristic
515C22×C61C4×#4111yescharacteristic
516C22×C61C4×#4111yescharacteristic
517C22×C61C4×#4111yescharacteristic
518C22×C61#51811yescharacteristic
519C22×C61#52011yescharacteristic
520C2×D61—22no—
521C2×D61—22no—
522C2×D61—22no—
523C2×D61—41no—
524C2×D61—41no—
525C2×D61—41no—
526C2×D61—41no—
527C2×D61—42no—
528C2×D61—42no—
529C2×D61—42no—
530C2×D61—42no—
531C2×D61—42no—
532C2×D61—42no—
533C2×D61—42no—
534C2×D61—42no—
535C2×D61C2×#11711yescharacteristic
536C2×D61C2×#11711yescharacteristic
537C2×D61C2×C4×D411yescharacteristic
538C2×D61C2×C4×D411yescharacteristic
539C2×D61C4×#4111yescharacteristic
540C2×D61C4×#4111yescharacteristic
541C2×D61C4×#4111yescharacteristic
542C2×D61C4×#4111yescharacteristic
543C2×D61#51811yescharacteristic
544C2×D61#51811yescharacteristic
545C2×D61#52011yescharacteristic
546C2×D61#52011yescharacteristic
547C2×D61#54611yescharacteristic
548C2×D61#54611yescharacteristic
549C2×D61#54611yescharacteristic
550C2×D61#54811yescharacteristic
551C2×D61#55111yescharacteristic
552C2×D61#55111yescharacteristic
553C2×D61#55211yescharacteristic
554C2×D61#55311yescharacteristic
555C2×D61#55311yescharacteristic
556C2×D61#55311yescharacteristic
557C2×D61#55311yescharacteristic
558C2×D61#55311yescharacteristic
559C2×D61#55611yescharacteristic
560C2×D61#55611yescharacteristic
561C2×D61#55911yescharacteristic
562C2×D61#55911yescharacteristic
563#6923—24no—
564#6923—24no—
565#6923—24no—
566#6923—24no—
567#6923—42no—
568#6923—42no—
569#6923—42no—
570#6923—42no—
571C4×C61—22no—
572C4×C61—22no—
573C4×C61—22no—
574C4×C61—41no—
575C4×C61—41no—
576C4×C61—41no—
577Dic61—22no—
578Dic61—22no—
579Dic61—22no—
580Dic61—41no—
581Dic61—41no—
582Dic61—41no—
583C2×#388—611no—
584C2×#388—611no—
585C2×C4×C4⋊C4—611no—
586C2×C4×C22⋊C4—611no—
587C2×C4×C22⋊C4—611no—
588#1437—611no—
589#1437—611no—
590#1436—611no—
591#1436—611no—
592#1434—611no—
593#1434—611no—
594C22⋊#95—611no—
595C4×#95—611no—
596C4×#95—611no—
597C4×#95—611no—
598C2×C61—42no—
599C2×C61C4×#11711yescharacteristic
600C2×C61C42×D411yescharacteristic
601C2×C61#227511yescharacteristic
602C2×C61#236411yescharacteristic
603C2×C61#236711yescharacteristic
604C2×C61#237311yescharacteristic
605C2×C61#237411yescharacteristic
606D61—42no—
607D61#234211yescharacteristic
608D61#234711yescharacteristic
609D61#235211yescharacteristic
610D61#235711yescharacteristic
611D61#236411yescharacteristic
612D61#236711yescharacteristic
613D61#237311yescharacteristic
614D61#237411yescharacteristic
615C24×C4—611no—
616C22×C4⋊C4—611no—
617C22×C4⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C22⋊C4—611no—
622C22×C22⋊C4—611no—
623C22×C22⋊C4—611no—
624C22×C42—611no—
625C22×C42—611no—
626C22×C42—611no—
627C22×C42—611no—
628C22×C42—611no—
629C22×C42—611no—
630C22×C42—611no—
631C22×C42—611no—
632#388—618no—
633#388—611no—
634#388—611no—
635#388—611no—
636#388—611no—
637#388—611no—
638#388—611no—
639#388—611no—
640#388#692311yescharacteristic, complemented
641C4×C4⋊C4—1224no—
642C4×C22⋊C4—618no—
643C4×C22⋊C4—1224no—
644C2×#95—611no—
645C2×#95—611no—
646C2×#95—611no—
647C2×#95—611no—
648C2×#95—611no—
649C2×#95—611no—
650C2×#95—611no—
651C2×#95—611no—
652C2×#95—611no—
653C2×#95—611no—
654C2×#95—611no—
655C2×#95—611no—
656C2×#95—611no—
657C2×#95—611no—
658C2×#95—611no—
659C2×#95—611no—
660C2×#95—611no—
661C2×#95—611no—
662C61#1382211yescharacteristic, complemented, Sylow
663C25—611no—
664C23×C4—611no—
665C23×C4—611no—
666C23×C4—611no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—611no—
670C23×C4—611no—
671C23×C4—611no—
672C23×C4—611no—
673C23×C4—611no—
674C23×C4—611no—
675C23×C4—614no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—1222no—
680C23×C4—1222no—
681C23×C4—1222no—
682C23×C4—1222no—
683C23×C4—2441no—
684C23×C4—2441no—
685C2×C4⋊C4—614no—
686C2×C4⋊C4—611no—
687C2×C4⋊C4—611no—
688C2×C4⋊C4—611no—
689C2×C4⋊C4—1222no—
690C2×C4⋊C4—1222no—
691C2×C4⋊C4—1222no—
692C2×C4⋊C4—1222no—
693C2×C4⋊C4C2×#692311yescharacteristic, complemented
694C2×C22⋊C4—611no—
695C2×C22⋊C4—611no—
696C2×C22⋊C4—611no—
697C2×C22⋊C4—614no—
698C2×C22⋊C4—614no—
699C2×C22⋊C4—614no—
700C2×C22⋊C4—614no—
701C2×C22⋊C4—611no—
702C2×C22⋊C4—611no—
703C2×C22⋊C4—611no—
704C2×C22⋊C4—614no—
705C2×C22⋊C4—611no—
706C2×C22⋊C4—611no—
707C2×C22⋊C4—611no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—2441no—
715C2×C22⋊C4—2441no—
716C2×C22⋊C4—2441no—
717C2×C22⋊C4—2441no—
718C2×C22⋊C4C2×#692311yescharacteristic
719C2×C22⋊C4C2×#692311yescharacteristic
720C2×C22⋊C4C2×#692311yescharacteristic
721C2×C42—614no—
722C2×C42—614no—
723C2×C42—614no—
724C2×C42—611no—
725C2×C42—611no—
726C2×C42—611no—
727C2×C42—1222no—
728C2×C42—1222no—
729C2×C42—1222no—
730C2×C42—1222no—
731C2×C42—1222no—
732C2×C42—1222no—
733C2×C42—1222no—
734C2×C42—1222no—
735C2×C42—1222no—
736C2×C42—1222no—
737C2×C42—2441no—
738C2×C42—2441no—
739C2×C42—2441no—
740C2×C42—2441no—
741C2×C42—2441no—
742C2×C42—2441no—
743C2×C42—2441no—
744C2×C42—2441no—
745C2×C42—2441no—
746C2×C42—2441no—
747C2×C42C2×#692311yescharacteristic, complemented
748#95—614no—
749#95—614no—
750#95—614no—
751#95—614no—
752#95—614no—
753#95—611no—
754#95—611no—
755#95—611no—
756#95—611no—
757#95—611no—
758#95—611no—
759#95—1222no—
760#95—1222no—
761#95—1222no—
762#95—1222no—
763#95—1222no—
764#95—1222no—
765#95—1222no—
766#95—1222no—
767#95—1222no—
768#95—2441no—
769#95—2441no—
770#95C2×#692311yescharacteristic, complemented
771#95C2×#692311yescharacteristic, complemented
772C24—611no—
773C24—612no—
774C24—612no—
775C24—611no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24—1221no—
783C24—1221no—
784C24—1221no—
785C24—1221no—
786C24—1221no—
787C24—1221no—
788C24C22×#692311yescharacteristic
789C22×C4—612no—
790C22×C4—612no—
791C22×C4—612no—
792C22×C4—612no—
793C22×C4—612no—
794C22×C4—612no—
795C22×C4—612no—
796C22×C4—612no—
797C22×C4—612no—
798C22×C4—612no—
799C22×C4—612no—
800C22×C4—612no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—612no—
805C22×C4—612no—
806C22×C4—612no—
807C22×C4—612no—
808C22×C4—612no—
809C22×C4—612no—
810C22×C4—612no—
811C22×C4—612no—
812C22×C4—612no—
813C22×C4—612no—
814C22×C4—611no—
815C22×C4—611no—
816C22×C4—611no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
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—1228no—
848C22×C4—1228no—
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—2444no—
890C22×C4—2444no—
891C22×C4—2444no—
892C22×C4—2444no—
893C22×C4—2444no—
894C22×C4C22×#692311yescharacteristic
895C22×C4C22×#692311yescharacteristic
896C22×C4C22×#692311yescharacteristic
897C22×C4C22×#692311yescharacteristic
898C22×C4C22×#692311yescharacteristic
899C22×C4C22×#692311yescharacteristic
900C4⋊C4—22no—
901C4⋊C4—1222no—
902C4⋊C4—1222no—
903C4⋊C4—1228no—
904C4⋊C4—1222no—
905C22⋊C4—22no—
906C22⋊C4—41no—
907C22⋊C4—614no—
908C22⋊C4—614no—
909C22⋊C4—614no—
910C22⋊C4—1222no—
911C22⋊C4—1222no—
912C22⋊C4—1228no—
913C22⋊C4—1228no—
914C22⋊C4—1222no—
915C22⋊C4—2441no—
916C22⋊C4—2441no—
917C22⋊C4—2441no—
918C22⋊C4—2444no—
919C22⋊C4C4×#692314yescomplemented
920C42—41no—
921C42—1228no—
922C42—2441no—
923C42—2441no—
924C42—2441no—
925C42—2444no—
926C42—2444no—
927C42—2444no—
928C42—2444no—
929C42—2444no—
930C42—2444no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—611no—
938C23—611no—
939C23—611no—
940C23—611no—
941C23—611no—
942C23—611no—
943C23—611no—
944C23—611no—
945C23—611no—
946C23—611no—
947C23—611no—
948C23—611no—
949C23—611no—
950C23—611no—
951C23—612no—
952C23—1222no—
953C23—1222no—
954C23—1222no—
955C23—1222no—
956C23—1222no—
957C23—1222no—
958C23—1222no—
959C23—1222no—
960C23—1222no—
961C23—1222no—
962C23—1222no—
963C23—1222no—
964C23—1221no—
965C23—1221no—
966C23—1221no—
967C23—1221no—
968C23—1221no—
969C23—1221no—
970C23—2441no—
971C23—2441no—
972C23—2441no—
973C23—2441no—
974C23—2441no—
975C23—2441no—
976C23—2441no—
977C23—2441no—
978C23—2441no—
979C23—2441no—
980C23—2441no—
981C23—2441no—
982C23—2441no—
983C23—2441no—
984C23—2441no—
985C23—2441no—
986C23C2×C4×#692312yes—
987C23C23×#692311yescharacteristic
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—614no—
1004C2×C4—614no—
1005C2×C4—614no—
1006C2×C4—614no—
1007C2×C4—612no—
1008C2×C4—612no—
1009C2×C4—612no—
1010C2×C4—1222no—
1011C2×C4—1222no—
1012C2×C4—1222no—
1013C2×C4—1222no—
1014C2×C4—1222no—
1015C2×C4—1222no—
1016C2×C4—1222no—
1017C2×C4—1222no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1222no—
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—1222no—
1039C2×C4—1222no—
1040C2×C4—1222no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—1221no—
1047C2×C4—1221no—
1048C2×C4—1221no—
1049C2×C4—1221no—
1050C2×C4—1221no—
1051C2×C4—1221no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—1222no—
1055C2×C4—1222no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—1222no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—1222no—
1063C2×C4—1222no—
1064C2×C4—1221no—
1065C2×C4—1221no—
1066C2×C4—1221no—
1067C2×C4—1221no—
1068C2×C4—1221no—
1069C2×C4—1221no—
1070C2×C4—1221no—
1071C2×C4—1221no—
1072C2×C4—1221no—
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—24416no—
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×C4C2×C4×#692312yes—
1103C2×C4C2×C4×#692312yes—
1104C2×C4D4×#692312yes—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—611no—
1113C22—611no—
1114C22—611no—
1115C22—611no—
1116C22—611no—
1117C22—611no—
1118C22—611no—
1119C22—611no—
1120C22—611no—
1121C22—611no—
1122C22—611no—
1123C22—611no—
1124C22—611no—
1125C22—611no—
1126C22—611no—
1127C22—611no—
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—1222no—
1141C22—1222no—
1142C22—1222no—
1143C22—2442no—
1144C22—2442no—
1145C22—2442no—
1146C22—2442no—
1147C22—2442no—
1148C22—2442no—
1149C22—2442no—
1150C22—2442no—
1151C22—2441no—
1152C22—2441no—
1153C22—2441no—
1154C22—2441no—
1155C22C22×C4×#692311yescharacteristic
1156C22C2×D4×#692311yescharacteristic
1157C22#41×#692311yescharacteristic
1158C22#41×#692311yescharacteristic
1159C22#41×#692311yescharacteristic
1160C22#1684082911yescharacteristic
1161C22#1684083111yescharacteristic
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—1224no—
1169C4—1224no—
1170C4—1224no—
1171C4—1224no—
1172C4—1222no—
1173C4—1222no—
1174C4—1222no—
1175C4—2442no—
1176C4—2442no—
1177C4—2442no—
1178C4—2442no—
1179C4—2441no—
1180C4—2441no—
1181C4—2441no—
1182C2—42no—
1183C2—611no—
1184C2—611no—
1185C2—611no—
1186C2—611no—
1187C2—611no—
1188C2—611no—
1189C2—611no—
1190C2—611no—
1191C2—2442no—
1192C2#117×#692311yescharacteristic
1193C2C4×D4×#692311yescharacteristic
1194C2#2146225811yescharacteristic
1195C2#2146234711yescharacteristic
1196C2#2146235011yescharacteristic
1197C2#2146235611yescharacteristic
1198C2#2146235711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C22×C42
FittingC61×#388C4
socleC23×C61C23×C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#388#6923
hypocenterC61#13822
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×#6923C2semidirect
7. #21460999C2semidirect
8. #21460998C2semidirect
9. #21460994C2semidirect
10. #21460994C2semidirect
12. C4×(C2×#6923)⋊C4C2semidirect
13. C4×(C2×#6923)⋊C4C2semidirect
14. #95×#6923C2semidirect
28. #16840712C4semidirect
31. C22⋊C4×#6923C4semidirect
53. #16839656C4semidirect
54. #16839655C4semidirect
55. #16839654C4semidirect
56. #16839653C4semidirect
57. #16839652C4semidirect
58. #16839651C4semidirect
59. #16839650C4semidirect
62. C61×#388C4semidirect
80. C2×C4⋊#6923C2×C4semidirect
110. C2×C4×#6923C2×C4semidirect
124. (C2×#6923)⋊C4C2×C4semidirect
125. (C2×#6923)⋊C4C2×C4semidirect
134. C2×C4⋊Dic61C2×C4semidirect
135. C2×#11758196C2×C4semidirect
136. C2×#11758196C2×C4semidirect
154. C2×C4×Dic61C2×C4semidirect
155. C2×C4×Dic61C2×C4semidirect
156. C2×C4×Dic61C2×C4semidirect
159. #14519684C2×C4semidirect
160. #14519684C2×C4semidirect
161. #14519684C2×C4semidirect
162. #14519684C2×C4semidirect
163. #14519684C2×C4semidirect
164. #14519684C2×C4semidirect
165. C2×C4⋊C4×C61C2×C4semidirect
169. C2×C42×C61C2×C4semidirect
170. #95×C61C2×C4semidirect
171. #95×C61C2×C4semidirect
314. C22⋊C4×C61C42semidirect
318. C22⋊Dic61C42semidirect
323. #11758198C42semidirect
324. #11758198C42semidirect
640. #388#6923semidirect
662. C61#13822semidirect
693. C2×C4⋊C4C2×#6923semidirect
747. C2×C42C2×#6923semidirect
770. #95C2×#6923semidirect
771. #95C2×#6923semidirect
919. C22⋊C4C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407122
C2×C4⋊C4×#69232
C2×C22⋊C4×#69232
#214610002
#214609992
#214609982
#214609942
#214609922
C4×(C2×#6923)⋊C42
#95×#69232
#388×D612
#1382261