Finite Group Databasebeta

← #30609343

Subgroups — #30609343

Order 15616.

1650 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×#16840709C211yesmaximal, characteristic
3C2×#16840709C211yesmaximal, characteristic
4C2×#16840706C211yesmaximal, characteristic, complemented
5#21461007C211yesmaximal, characteristic, complemented
6#21461007C211yesmaximal, characteristic, complemented
7#21461005C211yesmaximal, characteristic, complemented
8#21461004C211yesmaximal, characteristic, complemented
9#21461002C211yesmaximal, characteristic
10#21461002C211yesmaximal, characteristic
11#21460999C211yesmaximal, characteristic, complemented
12#21460997C211yesmaximal, characteristic, complemented
13#21460996C211yesmaximal, characteristic, complemented
14#21460992C211yesmaximal, characteristic
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×C22⋊#6923C2211yescharacteristic
25C22×C22⋊#6923C2211yescharacteristic
26C22×C22⋊#6923C2211yescharacteristic
27C22×C4×#6923C2211yescharacteristic
28#16840712—24no—
29#16840709—24no—
30#16840709—24no—
31#16840706—24no—
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—41no—
67C23×#6923—41no—
68C23×#6923—41no—
69C23×#6923—41no—
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⋊#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—41no—
90C2×C4⋊#6923—41no—
91C2×C4⋊#6923—41no—
92C2×C4⋊#6923—41no—
93C2×C4⋊#6923—41no—
94C2×C4⋊#6923—41no—
95C2×C4⋊#6923—41no—
96C2×C4⋊#6923—41no—
97C2×C4⋊#6923—41no—
98C2×C4⋊#6923—41no—
99C2×C22⋊#6923—22no—
100C2×C22⋊#6923—22no—
101C2×C22⋊#6923—22no—
102C2×C22⋊#6923—22no—
103C2×C22⋊#6923—22no—
104C2×C22⋊#6923—41no—
105C2×C22⋊#6923—41no—
106C2×C22⋊#6923—41no—
107C2×C22⋊#6923—41no—
108C2×C4×#6923—22no—
109C2×C4×#6923—22no—
110C2×C4×#6923—41no—
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—41no—
120(C2×#6923)⋊C4—41no—
121(C2×#6923)⋊C4—41no—
122(C2×#6923)⋊C4—41no—
123(C2×#6923)⋊C4—41no—
124(C2×#6923)⋊C4—41no—
125(C2×#6923)⋊C4—41no—
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—41no—
138C4⋊C4×D61—41no—
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×D61D414yes—
153C22⋊C4×D61Q814yes—
154C2×C4×Dic61C2×C411yescharacteristic, complemented
155C2×C4×Dic61C2×C411yescharacteristic, complemented
156C2×C4×Dic61C2×C411yescharacteristic, complemented
157C42×D61—22no—
158C42×D61—22no—
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×D61C2×D412yes—
187C23×D61C2×Q812yes—
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—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—44no—
242C22×#6923—44no—
243C22×#6923—44no—
244C22×#6923—44no—
245C22×#6923—44no—
246C22×#6923—44no—
247C22×#6923—44no—
248C22×#6923C2×D412yes—
249C22×#6923C2×D412yes—
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×D61C2×D412yes—
295C2×C4×D61C2×D412yes—
296C2×C4×D61C2×D412yes—
297C2×C4×D61C2×Q812yes—
298C2×C4×D61C2×Q812yes—
299C2×C4×D61#4112yes—
300C22⋊#6923—44no—
301C22⋊#6923—44no—
302C22⋊#6923—44no—
303C4⋊#6923—44no—
304C4⋊#6923—44no—
305C4⋊#6923—44no—
306C4⋊#6923—44no—
307C4⋊#6923—44no—
308C4⋊#6923—44no—
309C4⋊#6923—44no—
310C4×#6923—44no—
311C4⋊C4×C61—41no—
312C22⋊C4×C61—22no—
313C22⋊C4×C61—41no—
314C22⋊C4×C61C4⋊C414yescomplemented
315C42×C61—22no—
316C22⋊Dic61—22no—
317C22⋊Dic61—41no—
318C22⋊Dic61C4⋊C414yescomplemented
319#11758198—22no—
320#11758198—22no—
321#11758198—41no—
322#11758198—41no—
323#11758198C4⋊C414yescomplemented
324#11758198C4⋊C414yescomplemented
325C4⋊Dic61—41no—
326#11758196—41no—
327#11758196—41no—
328C4×Dic61—22no—
329C4×Dic61—22no—
330C4×Dic61—22no—
331C23×C61—21no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61C2×C4⋊C412yes—
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×C4⋊C412yes—
374C22×D61C22×D411yescharacteristic
375C22×D61C22×D411yescharacteristic
376C22×D61C22×Q811yescharacteristic
377C22×D61C2×#4111yescharacteristic
378C22×D61C2×#4111yescharacteristic
379C22×D61C2×#4111yescharacteristic
380C22×D61H(5,𝔽2)11yescharacteristic
381C22×D61H(5,𝔽2)11yescharacteristic
382C22×D61H(5,𝔽2)11yescharacteristic
383C22×D61H(5,𝔽2)11yescharacteristic
384C22×D61H(5,𝔽2)11yescharacteristic
385C22×D612−1+411yescharacteristic
386C22×D612−1+411yescharacteristic
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—416no—
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×#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×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×C4⋊C412yes—
461C2×C4×C61C2×C4⋊C412yes—
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×C4⋊C412yes—
479C2×Dic61C2×C4⋊C412yes—
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#14403—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×C4⋊C411yescharacteristic
514C22×C61C2×C4×D411yescharacteristic
515C22×C61C4×#4111yescharacteristic
516C22×C61#51811yescharacteristic
517C22×C61#52011yescharacteristic
518C22×C61#52011yescharacteristic
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×D61#53511yescharacteristic
536C2×D61#53511yescharacteristic
537C2×D61#53611yescharacteristic
538C2×D61#53711yescharacteristic
539C2×D61#53811yescharacteristic
540C2×D61#53911yescharacteristic
541C2×D61#54011yescharacteristic
542C2×D61#54111yescharacteristic
543C2×D61#54211yescharacteristic
544C2×D61#54211yescharacteristic
545C2×D61#54411yescharacteristic
546C2×D61#54411yescharacteristic
547C2×D61D4211yescharacteristic
548C2×D61#54611yescharacteristic
549C2×D61#54611yescharacteristic
550C2×D61#54611yescharacteristic
551C2×D61#54711yescharacteristic
552C2×D61#54711yescharacteristic
553C2×D61D4×Q811yescharacteristic
554C2×D61#55111yescharacteristic
555C2×D61#55211yescharacteristic
556C2×D61#55411yescharacteristic
557C2×D61#55411yescharacteristic
558C2×D61#55411yescharacteristic
559C2×D61H(3,𝔽4)11yescharacteristic
560C2×D61#56211yescharacteristic
561C2×D61#56211yescharacteristic
562C2×D61#56311yescharacteristic
563#6923—42no—
564#6923—42no—
565#6923—42no—
566#6923—42no—
567#6923—81no—
568#6923—81no—
569#6923—81no—
570#6923—81no—
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×#385—611no—
586C2×#385—611no—
587C2×#382—611no—
588#1444—611no—
589#1444—611no—
590#1442—611no—
591#1441—611no—
592#1439—611no—
593#1439—611no—
594#1436—611no—
595C4⋊#95—611no—
596C4⋊#95—611no—
597C22⋊#95—611no—
598C2×C61—42no—
599C2×C61#231711yescharacteristic
600C2×C61#232411yescharacteristic
601C2×C61#233411yescharacteristic
602C2×C61D4×C4⋊C411yescharacteristic
603C2×C61#234911yescharacteristic
604C2×C61#235911yescharacteristic
605C2×C61#237911yescharacteristic
606D61—42no—
607D61#267011yescharacteristic
608D61#267211yescharacteristic
609D61#269811yescharacteristic
610D61#270411yescharacteristic
611D61#270611yescharacteristic
612D61#272011yescharacteristic
613D61#276311yescharacteristic
614D61#276811yescharacteristic
615C24×C4—611no—
616C22×C4⋊C4—611no—
617C22×C4⋊C4—611no—
618C22×C4⋊C4—611no—
619C22×C4⋊C4—611no—
620C22×C4⋊C4—611no—
621C22×C4⋊C4—611no—
622C22×C4⋊C4—611no—
623C22×C4⋊C4—611no—
624C22×C22⋊C4—611no—
625C22×C22⋊C4—611no—
626C22×C22⋊C4—611no—
627C22×C22⋊C4—611no—
628C22×C22⋊C4—611no—
629C22×C22⋊C4—611no—
630C22×C42—611no—
631C22×C42—611no—
632#388—611no—
633#388—611no—
634#388—611no—
635#388—611no—
636#388—611no—
637#388—611no—
638#388—611no—
639#388—1224no—
640#388#692311yescharacteristic, complemented
641#385—1224no—
642#385—1224no—
643#382—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#1440311yescharacteristic, 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—611no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—1222no—
679C23×C4—1222no—
680C23×C4—1222no—
681C23×C4—2441no—
682C23×C4—2441no—
683C23×C4—2441no—
684C23×C4—2441no—
685C2×C4⋊C4—611no—
686C2×C4⋊C4—611no—
687C2×C4⋊C4—611no—
688C2×C4⋊C4—1222no—
689C2×C4⋊C4—1222no—
690C2×C4⋊C4—1222no—
691C2×C4⋊C4—1222no—
692C2×C4⋊C4—1222no—
693C2×C4⋊C4—1222no—
694C2×C4⋊C4—1222no—
695C2×C4⋊C4—1222no—
696C2×C4⋊C4—1222no—
697C2×C4⋊C4—1222no—
698C2×C4⋊C4—1222no—
699C2×C4⋊C4—2441no—
700C2×C4⋊C4—2441no—
701C2×C4⋊C4—2441no—
702C2×C4⋊C4—2441no—
703C2×C4⋊C4—2441no—
704C2×C4⋊C4—2441no—
705C2×C4⋊C4—2441no—
706C2×C4⋊C4—2441no—
707C2×C4⋊C4—2441no—
708C2×C4⋊C4—2441no—
709C2×C4⋊C4—2441no—
710C2×C4⋊C4—2441no—
711C2×C4⋊C4C2×#692311yescharacteristic, complemented
712C2×C22⋊C4—611no—
713C2×C22⋊C4—611no—
714C2×C22⋊C4—611no—
715C2×C22⋊C4—614no—
716C2×C22⋊C4—614no—
717C2×C22⋊C4—611no—
718C2×C22⋊C4—611no—
719C2×C22⋊C4—611no—
720C2×C22⋊C4—611no—
721C2×C22⋊C4—611no—
722C2×C22⋊C4—611no—
723C2×C22⋊C4—1222no—
724C2×C22⋊C4—1222no—
725C2×C22⋊C4—1222no—
726C2×C22⋊C4—1222no—
727C2×C22⋊C4—1222no—
728C2×C22⋊C4—1222no—
729C2×C22⋊C4—1222no—
730C2×C22⋊C4—2441no—
731C2×C22⋊C4—2441no—
732C2×C22⋊C4—2441no—
733C2×C22⋊C4—2441no—
734C2×C22⋊C4—2441no—
735C2×C22⋊C4—2441no—
736C2×C22⋊C4C2×#692311yescharacteristic
737C2×C22⋊C4C2×#692311yescharacteristic
738C2×C22⋊C4C2×#692311yescharacteristic
739C2×C42—611no—
740C2×C42—611no—
741C2×C42—611no—
742C2×C42—1222no—
743C2×C42—1222no—
744C2×C42—1222no—
745C2×C42—1222no—
746C2×C42—2441no—
747C2×C42C2×#692311yescharacteristic, complemented
748#95—614no—
749#95—611no—
750#95—611no—
751#95—611no—
752#95—611no—
753#95—611no—
754#95—611no—
755#95—1222no—
756#95—1222no—
757#95—1222no—
758#95—1222no—
759#95—1222no—
760#95—1222no—
761#95—1222no—
762#95—1222no—
763#95—2441no—
764#95—2441no—
765#95—2441no—
766#95—2441no—
767#95—2441no—
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—611no—
790C22×C4—611no—
791C22×C4—611no—
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—612no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—611no—
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—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—2444no—
888C22×C4—2444no—
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—41no—
901C4⋊C4—2441no—
902C4⋊C4—2441no—
903C4⋊C4—2441no—
904C4⋊C4—2444no—
905C4⋊C4—2444no—
906C4⋊C4—2444no—
907C4⋊C4—2444no—
908C4⋊C4—2444no—
909C4⋊C4—2444no—
910C4⋊C4—2444no—
911C22⋊C4—22no—
912C22⋊C4—41no—
913C22⋊C4—614no—
914C22⋊C4—614no—
915C22⋊C4—614no—
916C22⋊C4—1222no—
917C22⋊C4—1222no—
918C22⋊C4—1222no—
919C22⋊C4—2441no—
920C22⋊C4—2441no—
921C22⋊C4—2441no—
922C22⋊C4—2444no—
923C22⋊C4—2444no—
924C22⋊C4—2444no—
925C22⋊C4C4⋊#692314yescomplemented
926C42—22no—
927C42—1222no—
928C42—1222no—
929C42—1222no—
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—612no—
1004C2×C4—612no—
1005C2×C4—612no—
1006C2×C4—1222no—
1007C2×C4—1222no—
1008C2×C4—1222no—
1009C2×C4—1222no—
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—1221no—
1019C2×C4—1221no—
1020C2×C4—1221no—
1021C2×C4—1221no—
1022C2×C4—1221no—
1023C2×C4—1221no—
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—1221no—
1037C2×C4—1221no—
1038C2×C4—1221no—
1039C2×C4—1221no—
1040C2×C4—1221no—
1041C2×C4—1221no—
1042C2×C4—1221no—
1043C2×C4—1221no—
1044C2×C4—1221no—
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—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
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—24416no—
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#1684082911yescharacteristic
1159C22#1684083111yescharacteristic
1160C22#1684083111yescharacteristic
1161C22#1684083111yescharacteristic
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—1222no—
1169C4—1222no—
1170C4—1222no—
1171C4—4881no—
1172C4—4881no—
1173C4—4881no—
1174C4—4881no—
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#2146230011yescharacteristic
1193C2#2146230711yescharacteristic
1194C2#2146231711yescharacteristic
1195C2D4×C4⋊#692311yescharacteristic
1196C2#2146233211yescharacteristic
1197C2#2146234211yescharacteristic
1198C2#2146236211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#388C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#388#6923
hypocenterC61#14403
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
4. C2×#16840706C2semidirect
5. #21461007C2semidirect
6. #21461007C2semidirect
7. #21461005C2semidirect
8. #21461004C2semidirect
11. #21460999C2semidirect
12. #21460997C2semidirect
13. #21460996C2semidirect
53. #16839656C4semidirect
54. #16839655C4semidirect
55. #16839654C4semidirect
56. #16839653C4semidirect
57. #16839652C4semidirect
58. #16839651C4semidirect
59. #16839650C4semidirect
62. C61×#388C4semidirect
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×C61C4⋊C4semidirect
318. C22⋊Dic61C4⋊C4semidirect
323. #11758198C4⋊C4semidirect
324. #11758198C4⋊C4semidirect
640. #388#6923semidirect
662. C61#14403semidirect
711. C2×C4⋊C4C2×#6923semidirect
747. C2×C42C2×#6923semidirect
770. #95C2×#6923semidirect
771. #95C2×#6923semidirect
925. 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×#168407092
C2×#168407062
#214610072
#214610052
#214610042
#214610022
#214609992
#214609972
#214609962
#214609922
#388×D612
#1440361