Finite Group Databasebeta

← #30609353

Subgroups — #30609353

Order 15616.

1498 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840712C211yesmaximal, characteristic
2C2×#16840712C211yesmaximal, characteristic
3C2×#16840711C211yesmaximal, characteristic, complemented
4C2×#16840708C211yesmaximal, characteristic, complemented
5#21461005C211yesmaximal, characteristic, complemented
6#21461004C211yesmaximal, characteristic, complemented
7#21461002C211yesmaximal, characteristic
8#21461002C211yesmaximal, characteristic
9#21461002C211yesmaximal, characteristic
10#21461002C211yesmaximal, characteristic
11#21460999C211yesmaximal, characteristic, complemented
12#21460999C211yesmaximal, characteristic, complemented
13#21460999C211yesmaximal, characteristic, complemented
14#21460995C211yesmaximal, characteristic, complemented
15#388×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21C22×C4⋊#6923C2211yescharacteristic
22C22×C22⋊#6923C2211yescharacteristic
23C22×C22⋊#6923C2211yescharacteristic
24C22×C22⋊#6923C2211yescharacteristic
25C22×C22⋊#6923C2211yescharacteristic
26C22×C4×#6923C2211yescharacteristic
27C22×C4×#6923C2211yescharacteristic
28#16840712—24no—
29#16840712—24no—
30#16840711—24no—
31#16840708—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×#6923C2311yescharacteristic
64C23×#6923C2311yescharacteristic
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C23×#6923C2311yescharacteristic
68C23×#6923C2311yescharacteristic
69C23×#6923C2311yescharacteristic
70C23×#6923C2311yescharacteristic
71C2×C4⋊#6923—22no—
72C2×C4⋊#6923—22no—
73C2×C4⋊#6923—22no—
74C2×C4⋊#6923—22no—
75C2×C4⋊#6923—22no—
76C2×C4⋊#6923—22no—
77C2×C4⋊#6923—22no—
78C2×C4⋊#6923—22no—
79C2×C4⋊#6923—22no—
80C2×C4⋊#6923—41no—
81C2×C4⋊#6923—41no—
82C2×C4⋊#6923—41no—
83C2×C4⋊#6923—41no—
84C2×C4⋊#6923—41no—
85C2×C4⋊#6923—41no—
86C2×C4⋊#6923—41no—
87C2×C4⋊#6923—41no—
88C2×C4⋊#6923D414yes—
89C2×C22⋊#6923—22no—
90C2×C22⋊#6923—22no—
91C2×C22⋊#6923—22no—
92C2×C22⋊#6923—22no—
93C2×C22⋊#6923—41no—
94C2×C22⋊#6923—41no—
95C2×C22⋊#6923—41no—
96C2×C22⋊#6923—41no—
97C2×C22⋊#6923—41no—
98C2×C22⋊#6923—41no—
99C2×C22⋊#6923—41no—
100C2×C22⋊#6923—41no—
101C2×C4×#6923—22no—
102C2×C4×#6923—22no—
103C2×C4×#6923—22no—
104C2×C4×#6923—41no—
105C2×C4×#6923—41no—
106C2×C4×#6923—41no—
107(C2×#6923)⋊C4—22no—
108(C2×#6923)⋊C4—22no—
109(C2×#6923)⋊C4—22no—
110(C2×#6923)⋊C4—22no—
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—41no—
118(C2×#6923)⋊C4—41no—
119(C2×#6923)⋊C4—41no—
120(C2×#6923)⋊C4—41no—
121(C2×#6923)⋊C4—41no—
122(C2×#6923)⋊C4D414yes—
123C24×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126C22×C4×D61C2311yescharacteristic
127C22×C4×D61C2311yescharacteristic
128C22×C4×D61C2311yescharacteristic
129C22×C4×D61C2311yescharacteristic
130C2×C4⋊Dic61C2×C411yescharacteristic
131C2×#11758196C2×C411yescharacteristic
132C2×#11758196C2×C411yescharacteristic
133C4⋊C4×D61—22no—
134C4⋊C4×D61—22no—
135C2×C22⋊Dic61C2×C411yescharacteristic
136C2×C22⋊Dic61C2×C411yescharacteristic
137C2×C22⋊Dic61C2×C411yescharacteristic
138C2×#11758198C2×C411yescharacteristic
139C2×#11758198C2×C411yescharacteristic
140C2×#11758198C2×C411yescharacteristic
141C2×#11758198C2×C411yescharacteristic
142C2×#11758198C2×C411yescharacteristic
143C2×#11758198C2×C411yescharacteristic
144C22⋊C4×D61—22no—
145C22⋊C4×D61—22no—
146C22⋊C4×D61—22no—
147C22⋊C4×D61—22no—
148C22⋊C4×D61—22no—
149C22⋊C4×D61—22no—
150C2×C4×Dic61C2×C411yescharacteristic
151C2×C4×Dic61C2×C411yescharacteristic
152C2×C4×Dic61C2×C411yescharacteristic
153C42×D61—22no—
154C42×D61—22no—
155#14519684C2×C411yescharacteristic
156#14519684C2×C411yescharacteristic
157#14519684C2×C411yescharacteristic
158#14519684C2×C411yescharacteristic
159#14519684C2×C411yescharacteristic
160#14519684C2×C411yescharacteristic
161C2×C4⋊C4×C61C2×C411yescharacteristic
162C2×C22⋊C4×C61C2×C411yescharacteristic
163C2×C22⋊C4×C61C2×C411yescharacteristic
164C2×C22⋊C4×C61C2×C411yescharacteristic
165C2×C42×C61C2×C411yescharacteristic
166#95×C61C2×C411yescharacteristic
167#95×C61C2×C411yescharacteristic
168C24×C61C22×C411yescharacteristic
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
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×D61C22×C411yescharacteristic
184C23×D61C2411yescharacteristic
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—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×#6923C2×D412yes—
238C22×#6923C2×D412yes—
239C22×#6923C2×D412yes—
240C22×#6923C2×D412yes—
241C22×C4×C61C22×C411yescharacteristic
242C22×C4×C61C22×C411yescharacteristic
243C22×C4×C61C22×C411yescharacteristic
244C22×C4×C61C22×C411yescharacteristic
245C22×C4×C61C22×C411yescharacteristic
246C22×C4×C61C22×C411yescharacteristic
247C22×Dic61C22×C411yescharacteristic
248C22×Dic61C22×C411yescharacteristic
249C22×Dic61C22×C411yescharacteristic
250C22×Dic61C22×C411yescharacteristic
251C22×Dic61C22×C411yescharacteristic
252C22×Dic61C22×C411yescharacteristic
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×D61C2×D412yes—
284C2×C4×D61C2×D412yes—
285C2×C4×D61#4112yes—
286C2×C4×D61#4112yes—
287C2×C4×D61#4112yes—
288C2×C4×D61#4112yes—
289C22⋊#6923—44no—
290C22⋊#6923—44no—
291C22⋊#6923—44no—
292C22⋊#6923—44no—
293C4⋊#6923—44no—
294C4⋊#6923—44no—
295C4⋊#6923—44no—
296C4⋊#6923—44no—
297C4⋊#6923—44no—
298C4⋊#6923—44no—
299C4×#6923—44no—
300C4×#6923—44no—
301C4⋊C4×C61—22no—
302C22⋊C4×C61—22no—
303C22⋊C4×C61—22no—
304C22⋊C4×C61—22no—
305C42×C61—22no—
306C22⋊Dic61—22no—
307C22⋊Dic61—22no—
308C22⋊Dic61—22no—
309#11758198—22no—
310#11758198—22no—
311#11758198—22no—
312#11758198—22no—
313#11758198—22no—
314#11758198—22no—
315C4⋊Dic61—22no—
316#11758196—22no—
317#11758196—22no—
318C4×Dic61—22no—
319C4×Dic61—22no—
320C4×Dic61—22no—
321C23×C61—21no—
322C23×C61—21no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61C23×C411yescharacteristic
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—21no—
332C22×D61—21no—
333C22×D61—21no—
334C22×D61—21no—
335C22×D61—21no—
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—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61C22×D411yescharacteristic
365C22×D61C22×D411yescharacteristic
366C22×D61C2×#4111yescharacteristic
367C22×D61C2×#4111yescharacteristic
368C22×D61C2×#4111yescharacteristic
369C22×D61C2×#4111yescharacteristic
370C22×D61H(5,𝔽2)11yescharacteristic
371C22×D61H(5,𝔽2)11yescharacteristic
372C22×D61H(5,𝔽2)11yescharacteristic
373C22×D61H(5,𝔽2)11yescharacteristic
374C22×D612−1+411yescharacteristic
375C22×D612−1+411yescharacteristic
376C22×D612−1+411yescharacteristic
377C22×D612−1+411yescharacteristic
378C2×#6923—22no—
379C2×#6923—22no—
380C2×#6923—22no—
381C2×#6923—22no—
382C2×#6923—22no—
383C2×#6923—22no—
384C2×#6923—22no—
385C2×#6923—22no—
386C2×#6923—22no—
387C2×#6923—22no—
388C2×#6923—22no—
389C2×#6923—22no—
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×#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×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×C4×C61—21no—
442C2×C4×C61—21no—
443C2×C4×C61—21no—
444C2×C4×C61—21no—
445C2×C4×C61—21no—
446C2×C4×C61—21no—
447C2×C4×C61—21no—
448C2×C4×C61—21no—
449C2×C4×C61#11712yes—
450C2×C4×C61C4×D412yes—
451C2×C4×C61C4×D412yes—
452C2×Dic61—21no—
453C2×Dic61—21no—
454C2×Dic61—21no—
455C2×Dic61—21no—
456C2×Dic61—21no—
457C2×Dic61—21no—
458C2×Dic61—21no—
459C2×Dic61—21no—
460C2×Dic61—21no—
461C2×Dic61—21no—
462C2×Dic61—21no—
463C2×Dic61—21no—
464C2×Dic61—21no—
465C2×Dic61—21no—
466C2×Dic61—21no—
467C2×Dic61#11712yes—
468C2×Dic61C4×D412yes—
469C2×Dic61C4×D412yes—
470C4×D61—22no—
471C4×D61—22no—
472C4×D61—22no—
473C4×D61—22no—
474C4×D61—22no—
475C4×D61—22no—
476C4×D61—22no—
477C4×D61—22no—
478C4×D61—22no—
479C4×D61—22no—
480C4×D61—22no—
481C4×D61—22no—
482C4×D61—41no—
483C4×D61—41no—
484C4×D61—41no—
485C4×D61—41no—
486C4×D61—41no—
487C4×D61—41no—
488C4×D61—41no—
489C4×D61—41no—
490C4×D61—41no—
491C4×D61—41no—
492C4×D61—41no—
493C4×D61—41no—
494#14413—611nomaximal, Sylow
495C22×C61—41no—
496C22×C61—41no—
497C22×C61—41no—
498C22×C61—41no—
499C22×C61—41no—
500C22×C61—41no—
501C22×C61—41no—
502C22×C61C2×#11711yescharacteristic
503C22×C61C2×C4×D411yescharacteristic
504C22×C61C2×C4×D411yescharacteristic
505C22×C61#52011yescharacteristic
506C22×C61#52011yescharacteristic
507C22×C61#52011yescharacteristic
508C22×C61#52011yescharacteristic
509C2×D61—41no—
510C2×D61—41no—
511C2×D61—41no—
512C2×D61—41no—
513C2×D61—41no—
514C2×D61—41no—
515C2×D61—41no—
516C2×D61—81no—
517C2×D61—81no—
518C2×D61—81no—
519C2×D61—81no—
520C2×D61—81no—
521C2×D61—81no—
522C2×D61—81no—
523C2×D61—81no—
524C2×D61#53411yescharacteristic
525C2×D61#53511yescharacteristic
526C2×D61#53611yescharacteristic
527C2×D61#53611yescharacteristic
528C2×D61#53911yescharacteristic
529C2×D61#53911yescharacteristic
530C2×D61#54011yescharacteristic
531C2×D61#54111yescharacteristic
532C2×D61#54211yescharacteristic
533C2×D61#54211yescharacteristic
534C2×D61#54211yescharacteristic
535C2×D61#54211yescharacteristic
536C2×D61D4211yescharacteristic
537C2×D61#54611yescharacteristic
538C2×D61#54711yescharacteristic
539C2×D61#54711yescharacteristic
540C2×D61#54811yescharacteristic
541C2×D61#54811yescharacteristic
542C2×D61#55011yescharacteristic
543C2×D61#55211yescharacteristic
544C2×D61#55311yescharacteristic
545C2×D61#55311yescharacteristic
546C2×D61#55511yescharacteristic
547C2×D61#55611yescharacteristic
548C2×D61#56011yescharacteristic
549C2×D61#56311yescharacteristic
550C2×D61#56311yescharacteristic
551C2×D61#56311yescharacteristic
552#6923—42no—
553#6923—42no—
554#6923—42no—
555#6923—42no—
556#6923—81no—
557#6923—81no—
558#6923—81no—
559#6923—81no—
560C4×C61—22no—
561C4×C61—22no—
562C4×C61—22no—
563C4×C61—41no—
564C4×C61—41no—
565C4×C61—41no—
566Dic61—22no—
567Dic61—22no—
568Dic61—22no—
569Dic61—41no—
570Dic61—41no—
571Dic61—41no—
572C2×#388—611no—
573C2×#388—611no—
574C2×#388—611no—
575C2×#387—611no—
576C2×#384—611no—
577#1442—611no—
578#1441—611no—
579#1439—611no—
580#1439—611no—
581#1439—611no—
582#1439—611no—
583#1436—611no—
584#1436—611no—
585#1436—611no—
586#1434—611no—
587C2×C61—81no—
588C2×C61#231411yescharacteristic
589C2×C61#232211yescharacteristic
590C2×C61#232611yescharacteristic
591C2×C61#235211yescharacteristic
592C2×C61#235411yescharacteristic
593C2×C61#236111yescharacteristic
594C2×C61#238311yescharacteristic
595D61—81no—
596D61#267311yescharacteristic
597D61#267411yescharacteristic
598D61#271611yescharacteristic
599D61#271811yescharacteristic
600D61#272111yescharacteristic
601D61#273111yescharacteristic
602D61#279311yescharacteristic
603D61#279511yescharacteristic
604C22×C4⋊C4—611no—
605C22×C4⋊C4—611no—
606C22×C4⋊C4—611no—
607C22×C4⋊C4—611no—
608C22×C4⋊C4—611no—
609C22×C4⋊C4—611no—
610C22×C4⋊C4—611no—
611C22×C22⋊C4—611no—
612C22×C22⋊C4—611no—
613C22×C22⋊C4—611no—
614C22×C22⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C42—611no—
619C22×C42—611no—
620C22×C42—611no—
621#388—611no—
622#388—611no—
623#388—611no—
624#388—611no—
625#388—611no—
626#388—611no—
627#388—611no—
628#388—1224no—
629#388—1224no—
630#388#692311yescharacteristic, complemented
631#387—1224no—
632#384—1224no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95—611no—
644C2×#95—611no—
645C2×#95—611no—
646C2×#95—611no—
647C2×#95—611no—
648C2×#95—611no—
649C2×#95—611no—
650C2×#95—611no—
651C61#1441311yescharacteristic, complemented, Sylow
652C25—611no—
653C23×C4—611no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—611no—
659C23×C4—611no—
660C23×C4—611no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—611no—
665C23×C4—611no—
666C23×C4—611no—
667C2×C4⋊C4—611no—
668C2×C4⋊C4—611no—
669C2×C4⋊C4—611no—
670C2×C4⋊C4—614no—
671C2×C4⋊C4—1222no—
672C2×C4⋊C4—1222no—
673C2×C4⋊C4—1222no—
674C2×C4⋊C4—1222no—
675C2×C4⋊C4—1222no—
676C2×C4⋊C4—1222no—
677C2×C4⋊C4—1222no—
678C2×C4⋊C4—1222no—
679C2×C4⋊C4—1222no—
680C2×C4⋊C4—1222no—
681C2×C4⋊C4—1222no—
682C2×C4⋊C4—2441no—
683C2×C4⋊C4—2441no—
684C2×C4⋊C4—2441no—
685C2×C4⋊C4—2441no—
686C2×C4⋊C4—2441no—
687C2×C4⋊C4—2441no—
688C2×C4⋊C4—2441no—
689C2×C4⋊C4—2441no—
690C2×C4⋊C4C2×#692311yescharacteristic
691C2×C22⋊C4—611no—
692C2×C22⋊C4—611no—
693C2×C22⋊C4—611no—
694C2×C22⋊C4—611no—
695C2×C22⋊C4—611no—
696C2×C22⋊C4—611no—
697C2×C22⋊C4—611no—
698C2×C22⋊C4—611no—
699C2×C22⋊C4—611no—
700C2×C22⋊C4—1222no—
701C2×C22⋊C4—1222no—
702C2×C22⋊C4—1222no—
703C2×C22⋊C4—1222no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1222no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—2441no—
711C2×C22⋊C4—2441no—
712C2×C22⋊C4—2441no—
713C2×C22⋊C4—2441no—
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—611no—
722C2×C42—611no—
723C2×C42—611no—
724C2×C42—1222no—
725C2×C42—1222no—
726C2×C42—1222no—
727C2×C42—1222no—
728C2×C42—1222no—
729C2×C42—2441no—
730C2×C42—2441no—
731C2×C42—2441no—
732C2×C42C2×#692311yescharacteristic
733#95—614no—
734#95—611no—
735#95—611no—
736#95—611no—
737#95—611no—
738#95—611no—
739#95—611no—
740#95—1222no—
741#95—1222no—
742#95—1222no—
743#95—1222no—
744#95—1222no—
745#95—1222no—
746#95—1222no—
747#95—1222no—
748#95—1222no—
749#95—1222no—
750#95—2441no—
751#95—2441no—
752#95—2441no—
753#95—2441no—
754#95—2441no—
755#95C2×#692311yescharacteristic
756#95C2×#692311yescharacteristic
757C24—611no—
758C24—611no—
759C24—1221no—
760C24—1221no—
761C24—1221no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24—1221no—
766C24—1221no—
767C24—1221no—
768C24—1221no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24C22×#692311yescharacteristic
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—611no—
777C22×C4—612no—
778C22×C4—612no—
779C22×C4—612no—
780C22×C4—612no—
781C22×C4—612no—
782C22×C4—612no—
783C22×C4—612no—
784C22×C4—612no—
785C22×C4—612no—
786C22×C4—612no—
787C22×C4—611no—
788C22×C4—611no—
789C22×C4—611no—
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—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×C4C22×#692311yescharacteristic
873C22×C4C22×#692311yescharacteristic
874C22×C4C22×#692311yescharacteristic
875C22×C4C22×#692311yescharacteristic
876C22×C4C22×#692311yescharacteristic
877C22×C4C22×#692311yescharacteristic
878C4⋊C4—22no—
879C4⋊C4—1222no—
880C4⋊C4—1222no—
881C4⋊C4—1222no—
882C4⋊C4—2444no—
883C4⋊C4—2444no—
884C4⋊C4—2444no—
885C4⋊C4—2444no—
886C4⋊C4—2444no—
887C4⋊C4—2444no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—1222no—
892C22⋊C4—1222no—
893C22⋊C4—1222no—
894C22⋊C4—1222no—
895C22⋊C4—1222no—
896C22⋊C4—1222no—
897C22⋊C4—1222no—
898C22⋊C4—1222no—
899C22⋊C4—1222no—
900C22⋊C4—2444no—
901C22⋊C4—2444no—
902C22⋊C4—2444no—
903C22⋊C4—2444no—
904C42—22no—
905C42—1222no—
906C42—1222no—
907C42—1222no—
908C42—2444no—
909C42—2444no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—611no—
918C23—611no—
919C23—611no—
920C23—611no—
921C23—611no—
922C23—611no—
923C23—611no—
924C23—611no—
925C23—611no—
926C23—611no—
927C23—611no—
928C23—611no—
929C23—611no—
930C23—611no—
931C23—1221no—
932C23—1221no—
933C23—1221no—
934C23—1221no—
935C23—1221no—
936C23—1221no—
937C23—1221no—
938C23—2441no—
939C23—2441no—
940C23—2441no—
941C23—2441no—
942C23—2441no—
943C23—2441no—
944C23—2441no—
945C23—2441no—
946C23—2441no—
947C23—2441no—
948C23—2441no—
949C23—2441no—
950C23—2441no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23C23×#692311yescharacteristic
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—612no—
983C2×C4—612no—
984C2×C4—612no—
985C2×C4—1222no—
986C2×C4—1222no—
987C2×C4—1222no—
988C2×C4—1222no—
989C2×C4—1222no—
990C2×C4—1222no—
991C2×C4—1222no—
992C2×C4—1222no—
993C2×C4—1222no—
994C2×C4—1222no—
995C2×C4—1222no—
996C2×C4—1222no—
997C2×C4—1221no—
998C2×C4—1221no—
999C2×C4—1221no—
1000C2×C4—1221no—
1001C2×C4—1221no—
1002C2×C4—1221no—
1003C2×C4—1222no—
1004C2×C4—1222no—
1005C2×C4—1222no—
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—1221no—
1016C2×C4—1221no—
1017C2×C4—1221no—
1018C2×C4—1221no—
1019C2×C4—1221no—
1020C2×C4—1221no—
1021C2×C4—1221no—
1022C2×C4—1221no—
1023C2×C4—1221no—
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—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#1451985612yes—
1081C2×C4D4×#692312yes—
1082C2×C4D4×#692312yes—
1083C22—41no—
1084C22—41no—
1085C22—41no—
1086C22—41no—
1087C22—41no—
1088C22—41no—
1089C22—41no—
1090C22—611no—
1091C22—611no—
1092C22—611no—
1093C22—611no—
1094C22—611no—
1095C22—611no—
1096C22—611no—
1097C22—611no—
1098C22—611no—
1099C22—611no—
1100C22—611no—
1101C22—611no—
1102C22—611no—
1103C22—611no—
1104C22—611no—
1105C22—611no—
1106C22—611no—
1107C22—611no—
1108C22—611no—
1109C22—611no—
1110C22—611no—
1111C22—611no—
1112C22—611no—
1113C22—611no—
1114C22—611no—
1115C22—611no—
1116C22—611no—
1117C22—611no—
1118C22—4881no—
1119C22—4881no—
1120C22—4881no—
1121C22—4881no—
1122C22—4881no—
1123C22—4881no—
1124C22—4881no—
1125C22—4881no—
1126C22—2441no—
1127C22—2441no—
1128C22—2441no—
1129C22—2441no—
1130C22—2441no—
1131C22—2441no—
1132C22—2441no—
1133C22C2×#1451985611yescharacteristic
1134C22C2×D4×#692311yescharacteristic
1135C22C2×D4×#692311yescharacteristic
1136C22#1684083111yescharacteristic
1137C22#1684083111yescharacteristic
1138C22#1684083111yescharacteristic
1139C22#1684083111yescharacteristic
1140C4—22no—
1141C4—22no—
1142C4—22no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—1222no—
1147C4—1222no—
1148C4—1222no—
1149C4—4881no—
1150C4—4881no—
1151C4—4881no—
1152C4—4881no—
1153C4—2442no—
1154C4—2442no—
1155C4—2442no—
1156C4—2442no—
1157C4—2441no—
1158C4—2441no—
1159C4—2441no—
1160C2—81no—
1161C2—611no—
1162C2—611no—
1163C2—611no—
1164C2—611no—
1165C2—611no—
1166C2—611no—
1167C2—611no—
1168C2—611no—
1169C2—4881no—
1170C2#2146229711yescharacteristic
1171C2#2146230511yescharacteristic
1172C2#2146230911yescharacteristic
1173C2#2146233511yescharacteristic
1174C2#2146233711yescharacteristic
1175C2#2146234411yescharacteristic
1176C2#2146236611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#388C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#388#6923
hypocenterC61#14413
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. C2×#16840711C2semidirect
4. C2×#16840708C2semidirect
5. #21461005C2semidirect
6. #21461004C2semidirect
11. #21460999C2semidirect
12. #21460999C2semidirect
13. #21460999C2semidirect
14. #21460995C2semidirect
53. #16839656C4semidirect
54. #16839655C4semidirect
55. #16839654C4semidirect
56. #16839653C4semidirect
57. #16839652C4semidirect
58. #16839651C4semidirect
59. #16839650C4semidirect
62. C61×#388C4semidirect
630. #388#6923semidirect
651. C61#14413semidirect

Maximal subgroups

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

subgroupindex
C2×#168407122
C2×#168407112
C2×#168407082
#214610052
#214610042
#214610022
#214609992
#214609952
#388×D612
#1441361