Finite Group Databasebeta

← #30609419

Subgroups — #30609419

Order 15616.

1406 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461008C211yesmaximal, characteristic, complemented
2#21461006C211yesmaximal, characteristic, complemented
3#21461005C211yesmaximal, characteristic, complemented
4#21461004C211yesmaximal, characteristic, complemented
5#21461003C211yesmaximal, characteristic
6#21461002C211yesmaximal, characteristic
7#21461000C211yesmaximal, characteristic
8#21460995C211yesmaximal, characteristic, complemented
9#21460995C211yesmaximal, characteristic, complemented
10#21460994C211yesmaximal, characteristic, complemented
11#21460994C211yesmaximal, characteristic, complemented
12#21460992C211yesmaximal, characteristic
13#21460992C211yesmaximal, characteristic
14#21460992C211yesmaximal, characteristic
15#388×D61C211yesmaximal, characteristic
16C24×#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C22⋊#6923C2211yescharacteristic
19C22×C22⋊#6923C2211yescharacteristic
20C22×C22⋊#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
22C2×(C2×#6923)⋊C4C2211yescharacteristic
23C2×(C2×#6923)⋊C4C2211yescharacteristic
24C2×(C2×#6923)⋊C4C2211yescharacteristic
25C2×(C2×#6923)⋊C4C2211yescharacteristic
26C2×(C2×#6923)⋊C4C2211yescharacteristic
27C2×(C2×#6923)⋊C4C2211yescharacteristic
28C2×(C2×#6923)⋊C4C2211yescharacteristic
29C2×(C2×#6923)⋊C4C2211yescharacteristic
30C2×(C2×#6923)⋊C4C2211yescharacteristic
31C2×(C2×#6923)⋊C4C2211yescharacteristic
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×C4⋊C4×D61C2211yescharacteristic
45C2×C22⋊C4×D61C2211yescharacteristic
46C2×C22⋊C4×D61C2211yescharacteristic
47C2×C22⋊C4×D61C2211yescharacteristic
48C2×C42×D61C2211yescharacteristic
49#16839656C411yescharacteristic, complemented
50#16839655C411yescharacteristic, complemented
51#16839654C411yescharacteristic, complemented
52#16839653C411yescharacteristic, complemented
53#16839652C411yescharacteristic, complemented
54#16839651C411yescharacteristic, complemented
55#16839650C411yescharacteristic, complemented
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58C61×#388C411yescharacteristic, complemented
59C23×#6923—22no—
60C23×#6923—22no—
61C23×#6923—22no—
62C23×#6923—41no—
63C23×#6923—41no—
64C23×#6923—41no—
65C23×#6923—41no—
66C23×#6923C2311yescharacteristic
67C23×#6923C2311yescharacteristic
68C23×#6923C2311yescharacteristic
69C23×#6923C2311yescharacteristic
70C23×#6923C2311yescharacteristic
71C23×#6923C2311yescharacteristic
72C23×#6923C2311yescharacteristic
73C23×#6923C2311yescharacteristic
74C2×C4⋊#6923—41no—
75C2×C4⋊#6923—41no—
76C2×C4⋊#6923—41no—
77C2×C22⋊#6923—22no—
78C2×C22⋊#6923—22no—
79C2×C22⋊#6923—22no—
80C2×C22⋊#6923—22no—
81C2×C22⋊#6923—22no—
82C2×C22⋊#6923—41no—
83C2×C22⋊#6923—41no—
84C2×C22⋊#6923—41no—
85C2×C22⋊#6923—41no—
86C2×C4×#6923—22no—
87C2×C4×#6923—22no—
88C2×C4×#6923—41no—
89(C2×#6923)⋊C4—22no—
90(C2×#6923)⋊C4—22no—
91(C2×#6923)⋊C4—22no—
92(C2×#6923)⋊C4—22no—
93(C2×#6923)⋊C4—22no—
94(C2×#6923)⋊C4—22no—
95(C2×#6923)⋊C4—41no—
96(C2×#6923)⋊C4—41no—
97(C2×#6923)⋊C4—41no—
98(C2×#6923)⋊C4—41no—
99(C2×#6923)⋊C4—41no—
100(C2×#6923)⋊C4—41no—
101(C2×#6923)⋊C4—41no—
102(C2×#6923)⋊C4—41no—
103(C2×#6923)⋊C4—41no—
104(C2×#6923)⋊C4—41no—
105(C2×#6923)⋊C4—41no—
106(C2×#6923)⋊C4—41no—
107(C2×#6923)⋊C4—41no—
108(C2×#6923)⋊C4—41no—
109(C2×#6923)⋊C4—41no—
110(C2×#6923)⋊C4—41no—
111C24×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C2×C4⋊Dic61C2×C411yescharacteristic, complemented
119C2×#11758196C2×C411yescharacteristic, complemented
120C2×#11758196C2×C411yescharacteristic, complemented
121C4⋊C4×D61—41no—
122C4⋊C4×D61—41no—
123C2×C22⋊Dic61C2×C411yescharacteristic
124C2×C22⋊Dic61C2×C411yescharacteristic
125C2×C22⋊Dic61C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×#11758198C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×#11758198C2×C411yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×#11758198C2×C411yescharacteristic
132C22⋊C4×D61—22no—
133C22⋊C4×D61—22no—
134C22⋊C4×D61—41no—
135C22⋊C4×D61—41no—
136C22⋊C4×D61—41no—
137C22⋊C4×D61—41no—
138C2×C4×Dic61C2×C411yescharacteristic, complemented
139C2×C4×Dic61C2×C411yescharacteristic, complemented
140C2×C4×Dic61C2×C411yescharacteristic, complemented
141C42×D61—41no—
142C42×D61—41no—
143#14519684C2×C411yescharacteristic, complemented
144#14519684C2×C411yescharacteristic, complemented
145#14519684C2×C411yescharacteristic, complemented
146#14519684C2×C411yescharacteristic, complemented
147#14519684C2×C411yescharacteristic, complemented
148#14519684C2×C411yescharacteristic, complemented
149C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
150C2×C22⋊C4×C61C2×C411yescharacteristic
151C2×C22⋊C4×C61C2×C411yescharacteristic
152C2×C22⋊C4×C61C2×C411yescharacteristic
153C2×C42×C61C2×C411yescharacteristic, complemented
154#95×C61C2×C411yescharacteristic, complemented
155#95×C61C2×C411yescharacteristic, complemented
156C24×C61C22×C411yescharacteristic
157C23×D61—21no—
158C23×D61—21no—
159C23×D61—21no—
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61C22×C411yescharacteristic
170C23×D61#4112yes—
171C23×D61#4112yes—
172C23×D61C2411yescharacteristic
173C22×#6923—21no—
174C22×#6923—21no—
175C22×#6923—21no—
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—21no—
182C22×#6923—21no—
183C22×#6923—21no—
184C22×#6923—21no—
185C22×#6923—21no—
186C22×#6923—21no—
187C22×#6923—21no—
188C22×#6923—21no—
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—44no—
226C22×#6923—44no—
227C22×#6923—44no—
228C22×#6923—44no—
229C22×#6923—44no—
230C22×#6923—44no—
231C22×#6923—44no—
232C22×#6923#4112yes—
233C22×#6923#4112yes—
234C22×#6923#4112yes—
235C22×#6923#4112yes—
236C22×C4×C61C22×C411yescharacteristic
237C22×C4×C61C22×C411yescharacteristic
238C22×C4×C61C22×C411yescharacteristic
239C22×C4×C61C22×C411yescharacteristic
240C22×C4×C61C22×C411yescharacteristic
241C22×C4×C61C22×C411yescharacteristic
242C22×Dic61C22×C411yescharacteristic
243C22×Dic61C22×C411yescharacteristic
244C22×Dic61C22×C411yescharacteristic
245C22×Dic61C22×C411yescharacteristic
246C22×Dic61C22×C411yescharacteristic
247C22×Dic61C22×C411yescharacteristic
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
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—
284C22⋊#6923—44no—
285C22⋊#6923—44no—
286C22⋊#6923—44no—
287C4⋊#6923—44no—
288C4×#6923—44no—
289C4⋊C4×C61—41no—
290C22⋊C4×C61—22no—
291C22⋊C4×C61—41no—
292C22⋊C4×C61—41no—
293C42×C61—41no—
294C22⋊Dic61—22no—
295C22⋊Dic61—41no—
296C22⋊Dic61—41no—
297#11758198—22no—
298#11758198—22no—
299#11758198—41no—
300#11758198—41no—
301#11758198—41no—
302#11758198—41no—
303C4⋊Dic61—41no—
304#11758196—41no—
305#11758196—41no—
306C4×Dic61—41no—
307C4×Dic61—41no—
308C4×Dic61—41no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—21no—
315C23×C61#11712yes—
316C23×C61C23×C411yescharacteristic
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—41no—
339C22×D61—41no—
340C22×D61—41no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61#11712yes—
352C22×D61C2×#4111yescharacteristic
353C22×D61C2×#4111yescharacteristic
354C22×D61C2×#4111yescharacteristic
355C22×D61C2×#4111yescharacteristic
356C22×D61C2×#4111yescharacteristic
357C22×D61C2×#4111yescharacteristic
358C22×D61H(5,𝔽2)11yescharacteristic
359C22×D61H(5,𝔽2)11yescharacteristic
360C22×D61H(5,𝔽2)11yescharacteristic
361C22×D61H(5,𝔽2)11yescharacteristic
362C22×D61H(5,𝔽2)11yescharacteristic
363C22×D61H(5,𝔽2)11yescharacteristic
364C22×D612−1+411yescharacteristic
365C22×D612−1+411yescharacteristic
366C2×#6923—22no—
367C2×#6923—22no—
368C2×#6923—22no—
369C2×#6923—22no—
370C2×#6923—22no—
371C2×#6923—22no—
372C2×#6923—22no—
373C2×#6923—22no—
374C2×#6923—22no—
375C2×#6923—22no—
376C2×#6923—22no—
377C2×#6923—22no—
378C2×#6923—416no—
379C2×#6923—41no—
380C2×#6923—41no—
381C2×#6923—41no—
382C2×#6923—41no—
383C2×#6923—41no—
384C2×#6923—41no—
385C2×#6923—41no—
386C2×#6923—41no—
387C2×#6923—41no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923—41no—
396C2×#6923—41no—
397C2×#6923—41no—
398C2×#6923—41no—
399C2×#6923—41no—
400C2×#6923—41no—
401C2×#6923—41no—
402C2×#6923—41no—
403C2×#6923—41no—
404C2×#6923—41no—
405C2×#6923—41no—
406C2×#6923—41no—
407C2×#6923—41no—
408C2×#6923—41no—
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×C4×C61—21no—
424C2×C4×C61—21no—
425C2×C4×C61—21no—
426C2×C4×C61—21no—
427C2×C4×C61—21no—
428C2×C4×C61—21no—
429C2×C4×C61—21no—
430C2×C4×C61—21no—
431C2×C4×C61—21no—
432C2×C4×C61—21no—
433C2×C4×C61—21no—
434C2×C4×C61—21no—
435C2×C4×C61—21no—
436C2×C4×C61—21no—
437C2×C4×C61—21no—
438C2×C4×C61—21no—
439C2×C4×C61—21no—
440C2×C4×C61—21no—
441C2×Dic61—21no—
442C2×Dic61—21no—
443C2×Dic61—21no—
444C2×Dic61—21no—
445C2×Dic61—21no—
446C2×Dic61—21no—
447C2×Dic61—21no—
448C2×Dic61—21no—
449C2×Dic61—21no—
450C2×Dic61—21no—
451C2×Dic61—21no—
452C2×Dic61—21no—
453C2×Dic61—21no—
454C2×Dic61—21no—
455C2×Dic61—21no—
456C2×Dic61—21no—
457C2×Dic61—21no—
458C2×Dic61—21no—
459C4×D61—41no—
460C4×D61—41no—
461C4×D61—41no—
462C4×D61—41no—
463C4×D61—41no—
464C4×D61—41no—
465C4×D61—41no—
466C4×D61—41no—
467C4×D61—41no—
468C4×D61—41no—
469C4×D61—41no—
470C4×D61—41no—
471C4×D61—41no—
472C4×D61—41no—
473C4×D61—41no—
474C4×D61—41no—
475C4×D61—41no—
476C4×D61—41no—
477C4×D61—41no—
478C4×D61—41no—
479C4×D61—41no—
480C4×D61—41no—
481C4×D61—41no—
482C4×D61—41no—
483#14479—611nomaximal, Sylow
484C22×C61—22no—
485C22×C61—22no—
486C22×C61—22no—
487C22×C61—41no—
488C22×C61—41no—
489C22×C61—41no—
490C22×C61—41no—
491C22×C61C2×#11711yescharacteristic
492C22×C61C4×#4111yescharacteristic
493C22×C61C4×#4111yescharacteristic
494C22×C61#51811yescharacteristic
495C22×C61#51811yescharacteristic
496C22×C61#52011yescharacteristic
497C22×C61#52011yescharacteristic
498C2×D61—22no—
499C2×D61—22no—
500C2×D61—22no—
501C2×D61—41no—
502C2×D61—41no—
503C2×D61—41no—
504C2×D61—41no—
505C2×D61—42no—
506C2×D61—42no—
507C2×D61—42no—
508C2×D61—42no—
509C2×D61—42no—
510C2×D61—42no—
511C2×D61—42no—
512C2×D61—42no—
513C2×D61#53811yescharacteristic
514C2×D61#53811yescharacteristic
515C2×D61#53811yescharacteristic
516C2×D61#53811yescharacteristic
517C2×D61#53911yescharacteristic
518C2×D61#53911yescharacteristic
519C2×D61#53911yescharacteristic
520C2×D61#53911yescharacteristic
521C2×D61#54011yescharacteristic
522C2×D61#54111yescharacteristic
523C2×D61#54211yescharacteristic
524C2×D61#54211yescharacteristic
525C2×D61#55111yescharacteristic
526C2×D61#55111yescharacteristic
527C2×D61#55111yescharacteristic
528C2×D61#55111yescharacteristic
529C2×D61#55111yescharacteristic
530C2×D61#55111yescharacteristic
531C2×D61#55211yescharacteristic
532C2×D61#55211yescharacteristic
533C2×D61#55311yescharacteristic
534C2×D61#55311yescharacteristic
535C2×D61#55511yescharacteristic
536C2×D61#55511yescharacteristic
537C2×D61#56011yescharacteristic
538C2×D61#56011yescharacteristic
539C2×D61#56211yescharacteristic
540C2×D61#56211yescharacteristic
541#6923—42no—
542#6923—42no—
543#6923—42no—
544#6923—42no—
545#6923—81no—
546#6923—81no—
547#6923—81no—
548#6923—81no—
549C4×C61—41no—
550C4×C61—41no—
551C4×C61—41no—
552C4×C61—41no—
553C4×C61—41no—
554C4×C61—41no—
555Dic61—41no—
556Dic61—41no—
557Dic61—41no—
558Dic61—41no—
559Dic61—41no—
560Dic61—41no—
561C2×#388—611no—
562#1445—611no—
563#1443—611no—
564#1442—611no—
565#1441—611no—
566#1440—611no—
567#1439—611no—
568#1437—611no—
569#1434—611no—
570#1434—611no—
571#1434—611no—
572#1434—611no—
573C22⋊#95—611no—
574C22⋊#95—611no—
575C22⋊#95—611no—
576C2×C61—42no—
577C2×C61#231811yescharacteristic
578C2×C61#233411yescharacteristic
579C2×C61#233511yescharacteristic
580C2×C61#234311yescharacteristic
581C2×C61#235311yescharacteristic
582C2×C61#237211yescharacteristic
583C2×C61#237711yescharacteristic
584D61—42no—
585D61#273511yescharacteristic
586D61#273711yescharacteristic
587D61#274311yescharacteristic
588D61#274411yescharacteristic
589D61#274611yescharacteristic
590D61#274711yescharacteristic
591D61#275611yescharacteristic
592D61#278111yescharacteristic
593C24×C4—611no—
594C22×C4⋊C4—611no—
595C22×C4⋊C4—611no—
596C22×C22⋊C4—611no—
597C22×C22⋊C4—611no—
598C22×C22⋊C4—611no—
599C22×C22⋊C4—611no—
600C22×C22⋊C4—611no—
601C22×C22⋊C4—611no—
602C22×C42—611no—
603C22×C42—611no—
604#388—611no—
605#388—611no—
606#388—611no—
607#388—611no—
608#388—611no—
609#388—611no—
610#388—611no—
611#388#692311yescharacteristic, complemented
612C2×#95—611no—
613C2×#95—611no—
614C2×#95—611no—
615C2×#95—611no—
616C2×#95—611no—
617C2×#95—611no—
618C2×#95—611no—
619C2×#95—611no—
620C2×#95—611no—
621C2×#95—611no—
622C2×#95—611no—
623C2×#95—611no—
624C2×#95—611no—
625C2×#95—611no—
626C2×#95—611no—
627C2×#95—611no—
628C2×#95—611no—
629C2×#95—611no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C61#1447911yescharacteristic, complemented, Sylow
637C25—611no—
638C23×C4—611no—
639C23×C4—611no—
640C23×C4—611no—
641C23×C4—611no—
642C23×C4—611no—
643C23×C4—611no—
644C23×C4—611no—
645C23×C4—611no—
646C23×C4—611no—
647C23×C4—611no—
648C23×C4—611no—
649C23×C4—611no—
650C23×C4—611no—
651C23×C4—611no—
652C23×C4—1222no—
653C23×C4—1222no—
654C23×C4—1222no—
655C23×C4—2441no—
656C23×C4—2441no—
657C23×C4—2441no—
658C23×C4—2441no—
659C2×C4⋊C4—611no—
660C2×C4⋊C4—611no—
661C2×C4⋊C4—611no—
662C2×C4⋊C4—2441no—
663C2×C4⋊C4—2441no—
664C2×C4⋊C4—2441no—
665C2×C4⋊C4—2441no—
666C2×C4⋊C4—2441no—
667C2×C4⋊C4C2×#692311yescharacteristic, complemented
668C2×C22⋊C4—611no—
669C2×C22⋊C4—611no—
670C2×C22⋊C4—611no—
671C2×C22⋊C4—611no—
672C2×C22⋊C4—611no—
673C2×C22⋊C4—611no—
674C2×C22⋊C4—611no—
675C2×C22⋊C4—611no—
676C2×C22⋊C4—611no—
677C2×C22⋊C4—1222no—
678C2×C22⋊C4—1222no—
679C2×C22⋊C4—1222no—
680C2×C22⋊C4—1222no—
681C2×C22⋊C4—1222no—
682C2×C22⋊C4—1222no—
683C2×C22⋊C4—1222no—
684C2×C22⋊C4—2441no—
685C2×C22⋊C4—2441no—
686C2×C22⋊C4—2441no—
687C2×C22⋊C4—2441no—
688C2×C22⋊C4—2441no—
689C2×C22⋊C4—2441no—
690C2×C22⋊C4—2441no—
691C2×C22⋊C4—2441no—
692C2×C22⋊C4C2×#692311yescharacteristic
693C2×C22⋊C4C2×#692311yescharacteristic
694C2×C22⋊C4C2×#692311yescharacteristic
695C2×C42—611no—
696C2×C42—611no—
697C2×C42—611no—
698C2×C42—1222no—
699C2×C42—1222no—
700C2×C42—2441no—
701C2×C42—2441no—
702C2×C42—2441no—
703C2×C42C2×#692311yescharacteristic, complemented
704#95—611no—
705#95—611no—
706#95—611no—
707#95—611no—
708#95—611no—
709#95—611no—
710#95—1222no—
711#95—1222no—
712#95—1222no—
713#95—1222no—
714#95—1222no—
715#95—1222no—
716#95—2441no—
717#95—2441no—
718#95—2441no—
719#95—2441no—
720#95—2441no—
721#95—2441no—
722#95—2441no—
723#95—2441no—
724#95—2441no—
725#95—2441no—
726#95—2441no—
727#95—2441no—
728#95—2441no—
729#95—2441no—
730#95—2441no—
731#95—2441no—
732#95C2×#692311yescharacteristic, complemented
733#95C2×#692311yescharacteristic, complemented
734C24—611no—
735C24—612no—
736C24—612no—
737C24—611no—
738C24—1221no—
739C24—1221no—
740C24—1221no—
741C24—1221no—
742C24—1221no—
743C24—1221no—
744C24—1221no—
745C24—1221no—
746C24—1221no—
747C24—1221no—
748C24—1221no—
749C24—1221no—
750C24C22×#692311yescharacteristic
751C22×C4—612no—
752C22×C4—612no—
753C22×C4—612no—
754C22×C4—612no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
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—1221no—
848C22×C4—1221no—
849C22×C4—2444no—
850C22×C4—2444no—
851C22×C4—2444no—
852C22×C4—2444no—
853C22×C4—2444no—
854C22×C4—2444no—
855C22×C4—2444no—
856C22×C4C22×#692311yescharacteristic
857C22×C4C22×#692311yescharacteristic
858C22×C4C22×#692311yescharacteristic
859C22×C4C22×#692311yescharacteristic
860C22×C4C22×#692311yescharacteristic
861C22×C4C22×#692311yescharacteristic
862C4⋊C4—41no—
863C4⋊C4—2441no—
864C4⋊C4—2441no—
865C4⋊C4—2441no—
866C4⋊C4—2444no—
867C22⋊C4—22no—
868C22⋊C4—41no—
869C22⋊C4—41no—
870C22⋊C4—1222no—
871C22⋊C4—1222no—
872C22⋊C4—1222no—
873C22⋊C4—2441no—
874C22⋊C4—2441no—
875C22⋊C4—2441no—
876C22⋊C4—2441no—
877C22⋊C4—2441no—
878C22⋊C4—2441no—
879C22⋊C4—2444no—
880C22⋊C4—2444no—
881C22⋊C4—2444no—
882C42—41no—
883C42—2441no—
884C42—2441no—
885C42—2441no—
886C42—2444no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—611no—
894C23—611no—
895C23—611no—
896C23—611no—
897C23—611no—
898C23—611no—
899C23—611no—
900C23—611no—
901C23—611no—
902C23—611no—
903C23—611no—
904C23—611no—
905C23—611no—
906C23—611no—
907C23—612no—
908C23—1222no—
909C23—1222no—
910C23—1222no—
911C23—1222no—
912C23—1222no—
913C23—1222no—
914C23—1222no—
915C23—1222no—
916C23—1222no—
917C23—1222no—
918C23—1222no—
919C23—1222no—
920C23—1221no—
921C23—1221no—
922C23—1221no—
923C23—1221no—
924C23—1221no—
925C23—1221no—
926C23—2441no—
927C23—2441no—
928C23—2441no—
929C23—2441no—
930C23—2441no—
931C23—2441no—
932C23—2441no—
933C23—2441no—
934C23—2441no—
935C23—2441no—
936C23—2441no—
937C23—2441no—
938C23—2441no—
939C23—2441no—
940C23—2441no—
941C23—2441no—
942C23#1451985612yes—
943C23C23×#692311yescharacteristic
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—1222no—
963C2×C4—1222no—
964C2×C4—1222no—
965C2×C4—1222no—
966C2×C4—1222no—
967C2×C4—1222no—
968C2×C4—1222no—
969C2×C4—1222no—
970C2×C4—1222no—
971C2×C4—1222no—
972C2×C4—1222no—
973C2×C4—1222no—
974C2×C4—1221no—
975C2×C4—1221no—
976C2×C4—1221no—
977C2×C4—1221no—
978C2×C4—1221no—
979C2×C4—1221no—
980C2×C4—1221no—
981C2×C4—1221no—
982C2×C4—1221no—
983C2×C4—1221no—
984C2×C4—1221no—
985C2×C4—1221no—
986C2×C4—1221no—
987C2×C4—1221no—
988C2×C4—1221no—
989C2×C4—1221no—
990C2×C4—1221no—
991C2×C4—1221no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4—2441no—
1000C2×C4—2441no—
1001C2×C4—2441no—
1002C2×C4—2441no—
1003C2×C4—2441no—
1004C2×C4—2441no—
1005C2×C4—2441no—
1006C2×C4—2441no—
1007C2×C4—2441no—
1008C2×C4—2441no—
1009C2×C4—2441no—
1010C2×C4—2441no—
1011C2×C4—2441no—
1012C2×C4—2441no—
1013C2×C4—2441no—
1014C2×C4—2441no—
1015C2×C4—2441no—
1016C2×C4—2441no—
1017C2×C4—2441no—
1018C2×C4—2441no—
1019C2×C4—2441no—
1020C2×C4—2441no—
1021C2×C4—2441no—
1022C2×C4—2441no—
1023C2×C4—2441no—
1024C2×C4—2441no—
1025C2×C4—2441no—
1026C2×C4—2441no—
1027C2×C4—2441no—
1028C2×C4—2441no—
1029C2×C4—2441no—
1030C2×C4—2441no—
1031C2×C4—2441no—
1032C2×C4—2441no—
1033C2×C4—2441no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—24416no—
1061C22—22no—
1062C22—22no—
1063C22—22no—
1064C22—41no—
1065C22—41no—
1066C22—41no—
1067C22—41no—
1068C22—611no—
1069C22—611no—
1070C22—611no—
1071C22—611no—
1072C22—611no—
1073C22—611no—
1074C22—611no—
1075C22—611no—
1076C22—611no—
1077C22—611no—
1078C22—611no—
1079C22—611no—
1080C22—611no—
1081C22—611no—
1082C22—611no—
1083C22—611no—
1084C22—611no—
1085C22—611no—
1086C22—611no—
1087C22—611no—
1088C22—611no—
1089C22—611no—
1090C22—611no—
1091C22—611no—
1092C22—611no—
1093C22—611no—
1094C22—611no—
1095C22—611no—
1096C22—1222no—
1097C22—1222no—
1098C22—1222no—
1099C22—2442no—
1100C22—2442no—
1101C22—2442no—
1102C22—2442no—
1103C22—2442no—
1104C22—2442no—
1105C22—2442no—
1106C22—2442no—
1107C22—2441no—
1108C22—2441no—
1109C22—2441no—
1110C22—2441no—
1111C22C2×#1451985611yescharacteristic
1112C22#41×#692311yescharacteristic
1113C22#41×#692311yescharacteristic
1114C22#1684082911yescharacteristic
1115C22#1684082911yescharacteristic
1116C22#1684083111yescharacteristic
1117C22#1684083111yescharacteristic
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—4881no—
1125C4—4881no—
1126C4—4881no—
1127C4—4881no—
1128C4—2442no—
1129C4—2442no—
1130C4—2442no—
1131C4—2442no—
1132C4—2441no—
1133C4—2441no—
1134C4—2441no—
1135C4—2441no—
1136C4—2441no—
1137C4—2441no—
1138C2—42no—
1139C2—611no—
1140C2—611no—
1141C2—611no—
1142C2—611no—
1143C2—611no—
1144C2—611no—
1145C2—611no—
1146C2—611no—
1147C2—2442no—
1148C2#2146230111yescharacteristic
1149C2#2146231711yescharacteristic
1150C2#2146231811yescharacteristic
1151C2#2146232611yescharacteristic
1152C2#2146233611yescharacteristic
1153C2#2146235511yescharacteristic
1154C2#2146236011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#388C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#388#6923
hypocenterC61#14479
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #21461008C2semidirect
2. #21461006C2semidirect
3. #21461005C2semidirect
4. #21461004C2semidirect
8. #21460995C2semidirect
9. #21460995C2semidirect
10. #21460994C2semidirect
11. #21460994C2semidirect
49. #16839656C4semidirect
50. #16839655C4semidirect
51. #16839654C4semidirect
52. #16839653C4semidirect
53. #16839652C4semidirect
54. #16839651C4semidirect
55. #16839650C4semidirect
58. C61×#388C4semidirect
118. C2×C4⋊Dic61C2×C4semidirect
119. C2×#11758196C2×C4semidirect
120. C2×#11758196C2×C4semidirect
138. C2×C4×Dic61C2×C4semidirect
139. C2×C4×Dic61C2×C4semidirect
140. C2×C4×Dic61C2×C4semidirect
143. #14519684C2×C4semidirect
144. #14519684C2×C4semidirect
145. #14519684C2×C4semidirect
146. #14519684C2×C4semidirect
147. #14519684C2×C4semidirect
148. #14519684C2×C4semidirect
149. C2×C4⋊C4×C61C2×C4semidirect
153. C2×C42×C61C2×C4semidirect
154. #95×C61C2×C4semidirect
155. #95×C61C2×C4semidirect
611. #388#6923semidirect
636. C61#14479semidirect
667. C2×C4⋊C4C2×#6923semidirect
703. C2×C42C2×#6923semidirect
732. #95C2×#6923semidirect
733. #95C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214610082
#214610062
#214610052
#214610042
#214610032
#214610022
#214610002
#214609952
#214609942
#214609922
#388×D612
#1447961