Finite Group Databasebeta

← #30608759

Subgroups — #30608759

Order 15616.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840713C211yesmaximal, characteristic
2C2×#16840711C211yesmaximal, characteristic
3C2×C4⋊C4×#6923C211yesmaximal, characteristic
4C2×C4×C4⋊#6923C211yesmaximal, characteristic
5#21460999C211yesmaximal, characteristic
6#21460999C211yesmaximal, characteristic
7#21460999C211yesmaximal, characteristic
8#21460999C211yesmaximal, characteristic
9#21460999C211yesmaximal, characteristic
10#21460998C211yesmaximal, characteristic
11C4×(C2×#6923)⋊C4C211yesmaximal, characteristic
12#95×#6923C211yesmaximal, characteristic
13#95×#6923C211yesmaximal, characteristic
14#95×#6923C211yesmaximal, characteristic
15#387×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4×#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
22C22×C4×#6923C2211yescharacteristic
23C22×C4×#6923C2211yescharacteristic
24C22×C4×#6923C2211yescharacteristic
25C22×C4×#6923C2211yescharacteristic
26C22×C4×#6923C2211yescharacteristic
27C22×C4×#6923C2211yescharacteristic
28#16840713C418yescomplemented
29#16840711C418yescomplemented
30C4⋊C4×#6923—24no—
31C4×C4⋊#6923—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×C4⋊C4×D61C2211yescharacteristic
50C2×C42×D61C2211yescharacteristic
51#16839649C411yescharacteristic, complemented
52#16839648C411yescharacteristic, complemented
53#16839647C411yescharacteristic, complemented
54#16839646C411yescharacteristic, complemented
55#16839645C411yescharacteristic, complemented
56#16839644C411yescharacteristic, complemented
57#16839643C411yescharacteristic, complemented
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60#95×D61C2211yescharacteristic
61#95×D61C2211yescharacteristic
62C61×#387C411yescharacteristic, 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—41no—
78C2×C4⋊#6923—41no—
79C2×C4⋊#6923C2×C414yes—
80C2×C4⋊#6923C2×C414yes—
81C2×C4⋊#6923C2×C414yes—
82C2×C4⋊#6923C2×C414yes—
83C2×C4×#6923—22no—
84C2×C4×#6923—22no—
85C2×C4×#6923—22no—
86C2×C4×#6923—22no—
87C2×C4×#6923—22no—
88C2×C4×#6923—22no—
89C2×C4×#6923—22no—
90C2×C4×#6923—22no—
91C2×C4×#6923—22no—
92C2×C4×#6923—22no—
93C2×C4×#6923—22no—
94C2×C4×#6923—22no—
95C2×C4×#6923—22no—
96C2×C4×#6923—22no—
97C2×C4×#6923—41no—
98C2×C4×#6923—41no—
99C2×C4×#6923—41no—
100C2×C4×#6923—41no—
101C2×C4×#6923—41no—
102C2×C4×#6923—41no—
103C2×C4×#6923—41no—
104C2×C4×#6923—41no—
105C2×C4×#6923C2×C414yes—
106C2×C4×#6923C2×C414yes—
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—41no—
114(C2×#6923)⋊C4—41no—
115(C2×#6923)⋊C4C2×C414yes—
116(C2×#6923)⋊C4C2×C414yes—
117(C2×#6923)⋊C4C2×C414yes—
118(C2×#6923)⋊C4C2×C414yes—
119(C2×#6923)⋊C4C2×C414yes—
120(C2×#6923)⋊C4C2×C414yes—
121(C2×#6923)⋊C4D414yes—
122(C2×#6923)⋊C4Q814yes—
123C22×C4×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126C22×C4×D61C2311yescharacteristic
127C22×C4×D61C2311yescharacteristic
128C22×C4×D61C2311yescharacteristic
129C22×C4×D61C2311yescharacteristic
130C2×C4⋊Dic61C2×C411yescharacteristic
131C2×C4⋊Dic61C2×C411yescharacteristic
132C2×#11758196C2×C411yescharacteristic
133C2×#11758196C2×C411yescharacteristic
134C2×#11758196C2×C411yescharacteristic
135C2×#11758196C2×C411yescharacteristic
136C4⋊C4×D61—22no—
137C4⋊C4×D61—22no—
138C4⋊C4×D61C2×C414yes—
139C4⋊C4×D61C2×C414yes—
140C2×C4×Dic61C2×C411yescharacteristic
141C2×C4×Dic61C2×C411yescharacteristic
142C2×C4×Dic61C2×C411yescharacteristic
143C42×D61—22no—
144C42×D61—22no—
145#14519684C2×C411yescharacteristic
146#14519684C2×C411yescharacteristic
147#14519684C2×C411yescharacteristic
148#14519684C2×C411yescharacteristic
149#14519684C2×C411yescharacteristic
150#14519684C2×C411yescharacteristic
151#14519684C2×C411yescharacteristic
152#14519684C2×C411yescharacteristic
153#14519684C2×C411yescharacteristic
154#14519684C2×C411yescharacteristic
155#14519684C2×C411yescharacteristic
156#14519684C2×C411yescharacteristic
157C2×C4⋊C4×C61C2×C411yescharacteristic
158C2×C4⋊C4×C61C2×C411yescharacteristic
159C2×C42×C61C2×C411yescharacteristic
160#95×C61C2×C411yescharacteristic
161#95×C61C2×C411yescharacteristic
162#95×C61C2×C411yescharacteristic
163#95×C61C2×C411yescharacteristic
164C23×D61C2411yescharacteristic
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—21no—
169C22×#6923—21no—
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
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×#6923C22×C412yes—
206C22×#6923C22×C412yes—
207C22×#6923C22×C412yes—
208C22×#6923C22×C412yes—
209C22×#6923C22×C412yes—
210C22×#6923C22×C412yes—
211C22×#6923C22×C412yes—
212C22×#6923C22×C412yes—
213C22×#6923C2×D412yes—
214C22×#6923C2×D412yes—
215C22×#6923C2×Q812yes—
216C22×#6923C2×Q812yes—
217C22×#6923#4112yes—
218C22×#6923#4112yes—
219C22×#6923#4112yes—
220C22×#6923#4112yes—
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C22×C411yescharacteristic
227C22×C4×C61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C22×Dic61C22×C411yescharacteristic
230C22×Dic61C22×C411yescharacteristic
231C22×Dic61C22×C411yescharacteristic
232C22×Dic61C22×C411yescharacteristic
233C22×Dic61C22×C411yescharacteristic
234C22×Dic61C22×C411yescharacteristic
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
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×D61C22×C412yes—
268C2×C4×D61C22×C412yes—
269C2×C4×D61C22×C412yes—
270C2×C4×D61C22×C412yes—
271C2×C4×D61C22×C412yes—
272C2×C4×D61C22×C412yes—
273C2×C4×D61C2×D412yes—
274C2×C4×D61C2×Q812yes—
275C2×C4×D61#4112yes—
276C2×C4×D61#4112yes—
277C4⋊#6923—28no—
278C4⋊#6923—28no—
279C4⋊#6923—28no—
280C4⋊#6923—44no—
281C4×#6923—28no—
282C4×#6923—44no—
283C4×#6923—44no—
284C4×#6923—44no—
285C4×#6923—44no—
286C4×#6923—44no—
287C4×#6923—44no—
288C4×#6923—44no—
289C4⋊C4×C61—22no—
290C4⋊C4×C61C4214yescomplemented
291C42×C61—22no—
292C4⋊Dic61—22no—
293C4⋊Dic61C4214yescomplemented
294#11758196—22no—
295#11758196—22no—
296#11758196C4214yescomplemented
297#11758196C4214yescomplemented
298C4×Dic61—22no—
299C4×Dic61—22no—
300C4×Dic61—22no—
301C23×C61C23×C411yescharacteristic
302C22×D61C23×C411yescharacteristic
303C22×D61C23×C411yescharacteristic
304C22×D61C22×D411yescharacteristic
305C22×D61C22×Q811yescharacteristic
306C22×D61C2×#4111yescharacteristic
307C22×D61C2×#4111yescharacteristic
308C22×D61C2×#4111yescharacteristic
309C22×D61C2×#4111yescharacteristic
310C22×D61C2×#4111yescharacteristic
311C22×D61C2×#4111yescharacteristic
312C22×D61H(5,𝔽2)11yescharacteristic
313C22×D61H(5,𝔽2)11yescharacteristic
314C22×D612−1+411yescharacteristic
315C22×D612−1+411yescharacteristic
316C2×#6923—22no—
317C2×#6923—22no—
318C2×#6923—22no—
319C2×#6923—22no—
320C2×#6923—22no—
321C2×#6923—22no—
322C2×#6923—22no—
323C2×#6923—22no—
324C2×#6923—22no—
325C2×#6923—22no—
326C2×#6923—22no—
327C2×#6923—22no—
328C2×#6923—22no—
329C2×#6923—22no—
330C2×#6923—22no—
331C2×#6923—22no—
332C2×#6923—22no—
333C2×#6923—22no—
334C2×#6923—22no—
335C2×#6923—22no—
336C2×#6923—22no—
337C2×#6923—22no—
338C2×#6923—22no—
339C2×#6923—22no—
340C2×#6923—22no—
341C2×#6923—22no—
342C2×#6923—22no—
343C2×#6923—22no—
344C2×#6923—22no—
345C2×#6923—22no—
346C2×#6923—22no—
347C2×#6923—22no—
348C2×#6923—22no—
349C2×#6923—22no—
350C2×#6923—22no—
351C2×#6923—22no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—41no—
361C2×#6923—41no—
362C2×#6923—41no—
363C2×#6923—41no—
364C2×#6923—41no—
365C2×#6923—41no—
366C2×#6923—41no—
367C2×#6923—41no—
368C2×#6923C4×D414yes—
369C2×#6923C4×D414yes—
370C2×#6923C4×Q814yes—
371C2×#6923C4×Q814yes—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61C2×C4212yes—
389C2×C4×C61C2×C4212yes—
390C2×C4×C61C2×C4212yes—
391C2×C4×C61C4×D412yes—
392C2×C4×C61C4×Q812yes—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—21no—
399C2×Dic61—21no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—21no—
408C2×Dic61—21no—
409C2×Dic61C2×C4212yes—
410C2×Dic61C2×C4212yes—
411C2×Dic61C2×C4212yes—
412C2×Dic61C4×D412yes—
413C2×Dic61C4×Q812yes—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—22no—
420C4×D61—22no—
421C4×D61—22no—
422C4×D61—22no—
423C4×D61—22no—
424C4×D61—22no—
425C4×D61—22no—
426C4×D61—22no—
427C4×D61—22no—
428C4×D61—22no—
429C4×D61—22no—
430C4×D61—22no—
431C4×D61—22no—
432C4×D61—22no—
433C4×D61—22no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61—41no—
437C4×D61—41no—
438C4×D61—41no—
439C4×D61—41no—
440C4×D61—41no—
441C4×D61—41no—
442#13825—611nomaximal, Sylow
443C22×C61C22×C4211yescharacteristic
444C22×C61C2×C4×D411yescharacteristic
445C22×C61C2×C4×Q811yescharacteristic
446C22×C61C4×#4111yescharacteristic
447C22×C61C4×#4111yescharacteristic
448C22×C61#52011yescharacteristic
449C22×C61#52011yescharacteristic
450C2×D61C2×C4×D411yescharacteristic
451C2×D61C2×C4×D411yescharacteristic
452C2×D61C2×C4×Q811yescharacteristic
453C2×D61C2×C4×Q811yescharacteristic
454C2×D61C4×#4111yescharacteristic
455C2×D61C4×#4111yescharacteristic
456C2×D61C4×#4111yescharacteristic
457C2×D61C4×#4111yescharacteristic
458C2×D61#51811yescharacteristic
459C2×D61#51911yescharacteristic
460C2×D61#52011yescharacteristic
461C2×D61#52011yescharacteristic
462C2×D61#54611yescharacteristic
463C2×D61#54611yescharacteristic
464C2×D61#54711yescharacteristic
465C2×D61D4×Q811yescharacteristic
466C2×D61#55111yescharacteristic
467C2×D61#55111yescharacteristic
468C2×D61#55211yescharacteristic
469C2×D61#55211yescharacteristic
470C2×D61#55211yescharacteristic
471C2×D61#55211yescharacteristic
472C2×D61#55311yescharacteristic
473C2×D61#55311yescharacteristic
474C2×D61#55411yescharacteristic
475C2×D61#55411yescharacteristic
476C2×D61#55611yescharacteristic
477C2×D61#55711yescharacteristic
478#6923—24no—
479#6923—24no—
480#6923—24no—
481#6923—24no—
482#6923—42no—
483#6923—42no—
484#6923—42no—
485#6923—42no—
486C4×C61—22no—
487C4×C61—22no—
488C4×C61—22no—
489C4×C61—22no—
490C4×C61—22no—
491C4×C61—41no—
492C4×C61—41no—
493Dic61—22no—
494Dic61—22no—
495Dic61—22no—
496Dic61—22no—
497Dic61—22no—
498Dic61—41no—
499Dic61—41no—
500C2×#389—611no—
501C2×#387—611no—
502C2×#387—611no—
503C2×C4×C4⋊C4—611no—
504C2×C4×C4⋊C4—611no—
505#1436—611no—
506#1436—611no—
507#1436—611no—
508#1436—611no—
509#1436—611no—
510#1436—611no—
511C4×#95—611no—
512C4×#95—611no—
513C4×#95—611no—
514C4×#95—611no—
515C2×C61C42×D411yescharacteristic
516C2×C61C42×Q811yescharacteristic
517C2×C61#227411yescharacteristic
518C2×C61#235911yescharacteristic
519C2×C61#236011yescharacteristic
520C2×C61#237011yescharacteristic
521C2×C61#237311yescharacteristic
522D61#235911yescharacteristic
523D61#236011yescharacteristic
524D61#236411yescharacteristic
525D61#236511yescharacteristic
526D61#236811yescharacteristic
527D61#237011yescharacteristic
528D61#237111yescharacteristic
529D61#237311yescharacteristic
530C22×C4⋊C4—611no—
531C22×C4⋊C4—611no—
532C22×C4⋊C4—611no—
533C22×C4⋊C4—611no—
534C22×C4⋊C4—611no—
535C22×C4⋊C4—611no—
536C22×C42—611no—
537C22×C42—611no—
538C22×C42—611no—
539C22×C42—611no—
540C22×C42—611no—
541C22×C42—611no—
542C22×C42—611no—
543C22×C42—611no—
544C22×C42—611no—
545#389—618no—
546#387—618no—
547#387—611no—
548#387—611no—
549#387—611no—
550#387—611no—
551#387—611no—
552#387—611no—
553#387—611no—
554#387#692311yescharacteristic, complemented
555C4×C4⋊C4—1224no—
556C4×C4⋊C4—1224no—
557C2×#95—611no—
558C2×#95—611no—
559C2×#95—611no—
560C2×#95—611no—
561C2×#95—611no—
562C2×#95—611no—
563C2×#95—611no—
564C2×#95—611no—
565C2×#95—611no—
566C2×#95—611no—
567C2×#95—611no—
568C2×#95—611no—
569C2×#95—611no—
570C2×#95—611no—
571C2×#95—611no—
572C2×#95—611no—
573C2×#95—611no—
574C2×#95—611no—
575C2×#95—611no—
576C2×#95—611no—
577C61#1382511yescharacteristic, complemented, Sylow
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—611no—
586C23×C4—611no—
587C23×C4—611no—
588C23×C4—611no—
589C23×C4—611no—
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—611no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—614no—
597C2×C4⋊C4—614no—
598C2×C4⋊C4—614no—
599C2×C4⋊C4—614no—
600C2×C4⋊C4—614no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—614no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4—2441no—
614C2×C4⋊C4—2441no—
615C2×C4⋊C4C2×#692311yescharacteristic
616C2×C4⋊C4C2×#692311yescharacteristic
617C2×C42—614no—
618C2×C42—611no—
619C2×C42—611no—
620C2×C42—611no—
621C2×C42—614no—
622C2×C42—1222no—
623C2×C42—1222no—
624C2×C42—1222no—
625C2×C42—1222no—
626C2×C42—1222no—
627C2×C42—1222no—
628C2×C42—1222no—
629C2×C42—1222no—
630C2×C42—1222no—
631C2×C42—1222no—
632C2×C42—1222no—
633C2×C42—1222no—
634C2×C42—1222no—
635C2×C42—1222no—
636C2×C42—1222no—
637C2×C42—1222no—
638C2×C42—2441no—
639C2×C42—2441no—
640C2×C42—2441no—
641C2×C42—2441no—
642C2×C42—2441no—
643C2×C42—2441no—
644C2×C42—2441no—
645C2×C42—2441no—
646C2×C42C2×#692311yescharacteristic
647#95—614no—
648#95—614no—
649#95—614no—
650#95—614no—
651#95—614no—
652#95—614no—
653#95—614no—
654#95—614no—
655#95—611no—
656#95—611no—
657#95—611no—
658#95—611no—
659#95—611no—
660#95—611no—
661#95—611no—
662#95—611no—
663#95—611no—
664#95—611no—
665#95—611no—
666#95—611no—
667#95—1222no—
668#95—1222no—
669#95—1222no—
670#95—1222no—
671#95—1222no—
672#95—1222no—
673#95—2441no—
674#95—2441no—
675#95C2×#692311yescharacteristic
676#95C2×#692311yescharacteristic
677#95C2×#692311yescharacteristic
678#95C2×#692311yescharacteristic
679C24—611no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—612no—
683C22×C4—612no—
684C22×C4—612no—
685C22×C4—612no—
686C22×C4—612no—
687C22×C4—612no—
688C22×C4—612no—
689C22×C4—612no—
690C22×C4—612no—
691C22×C4—612no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—612no—
698C22×C4—612no—
699C22×C4—612no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—612no—
707C22×C4—612no—
708C22×C4—612no—
709C22×C4—612no—
710C22×C4—612no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
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×C4C22×#692311yescharacteristic
786C22×C4C22×#692311yescharacteristic
787C22×C4C22×#692311yescharacteristic
788C22×C4C22×#692311yescharacteristic
789C22×C4C22×#692311yescharacteristic
790C22×C4C22×#692311yescharacteristic
791C22×C4C22×#692311yescharacteristic
792C4⋊C4—22no—
793C4⋊C4—614no—
794C4⋊C4—614no—
795C4⋊C4—614no—
796C4⋊C4—1222no—
797C4⋊C4—1222no—
798C4⋊C4—1228no—
799C4⋊C4—1228no—
800C4⋊C4—1228no—
801C4⋊C4—1222no—
802C4⋊C4—2444no—
803C4⋊C4C4×#692314yescomplemented
804C42—22no—
805C42—1222no—
806C42—1222no—
807C42—1228no—
808C42—1222no—
809C42—2444no—
810C42—2444no—
811C42—2444no—
812C42—2444no—
813C42—2444no—
814C42—2444no—
815C42—2444no—
816C23—611no—
817C23—611no—
818C23—611no—
819C23—611no—
820C23—611no—
821C23—611no—
822C23—611no—
823C23—611no—
824C23—611no—
825C23—611no—
826C23—611no—
827C23—611no—
828C23—611no—
829C23—611no—
830C23C23×#692311yescharacteristic
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—614no—
848C2×C4—614no—
849C2×C4—614no—
850C2×C4—614no—
851C2×C4—612no—
852C2×C4—612no—
853C2×C4—612no—
854C2×C4—612no—
855C2×C4—612no—
856C2×C4—1222no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—1222no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1221no—
901C2×C4—1221no—
902C2×C4—1221no—
903C2×C4—1221no—
904C2×C4—1221no—
905C2×C4—1221no—
906C2×C4—1221no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—1221no—
910C2×C4—1222no—
911C2×C4—1222no—
912C2×C4—1222no—
913C2×C4—1222no—
914C2×C4—1222no—
915C2×C4—1222no—
916C2×C4—1222no—
917C2×C4—1222no—
918C2×C4—1222no—
919C2×C4—1222no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1221no—
923C2×C4—1221no—
924C2×C4—1221no—
925C2×C4—1221no—
926C2×C4—1221no—
927C2×C4—1221no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4—2441no—
952C2×C4C2×C4×#692312yes—
953C2×C4C2×C4×#692312yes—
954C2×C4C2×C4×#692312yes—
955C2×C4D4×#692312yes—
956C2×C4Q8×#692312yes—
957C22—611no—
958C22—611no—
959C22—611no—
960C22—611no—
961C22—611no—
962C22—611no—
963C22—611no—
964C22—611no—
965C22—611no—
966C22—611no—
967C22—611no—
968C22—611no—
969C22—611no—
970C22—611no—
971C22—611no—
972C22—611no—
973C22—611no—
974C22—611no—
975C22—611no—
976C22—611no—
977C22—611no—
978C22—611no—
979C22—611no—
980C22—611no—
981C22—611no—
982C22—611no—
983C22—611no—
984C22—611no—
985C22C22×C4×#692311yescharacteristic
986C22C2×D4×#692311yescharacteristic
987C22C2×Q8×#692311yescharacteristic
988C22#41×#692311yescharacteristic
989C22#41×#692311yescharacteristic
990C22#1684083111yescharacteristic
991C22#1684083111yescharacteristic
992C4—22no—
993C4—22no—
994C4—22no—
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—1224no—
1000C4—1224no—
1001C4—1224no—
1002C4—1224no—
1003C4—1222no—
1004C4—1222no—
1005C4—1222no—
1006C4—1222no—
1007C4—1222no—
1008C4—2442no—
1009C4—2442no—
1010C4—2442no—
1011C4—2442no—
1012C4—2441no—
1013C4—2441no—
1014C2—611no—
1015C2—611no—
1016C2—611no—
1017C2—611no—
1018C2—611no—
1019C2—611no—
1020C2—611no—
1021C2—611no—
1022C2C4×D4×#692311yescharacteristic
1023C2C4×Q8×#692311yescharacteristic
1024C2#2146225611yescharacteristic
1025C2#2146234211yescharacteristic
1026C2#2146234311yescharacteristic
1027C2#2146235311yescharacteristic
1028C2#2146235611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C22×C42
FittingC61×#387C4
socleC23×C61C23×C4
prime radical, cosocleC23×D61C24
hypercenter#387#6923
hypocenterC61#13825
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
28. #16840713C4semidirect
29. #16840711C4semidirect
51. #16839649C4semidirect
52. #16839648C4semidirect
53. #16839647C4semidirect
54. #16839646C4semidirect
55. #16839645C4semidirect
56. #16839644C4semidirect
57. #16839643C4semidirect
62. C61×#387C4semidirect
290. C4⋊C4×C61C42semidirect
293. C4⋊Dic61C42semidirect
296. #11758196C42semidirect
297. #11758196C42semidirect
554. #387#6923semidirect
577. C61#13825semidirect
803. C4⋊C4C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407132
C2×#168407112
C2×C4⋊C4×#69232
C2×C4×C4⋊#69232
#214609992
#214609982
C4×(C2×#6923)⋊C42
#95×#69232
#387×D612
#1382561