Finite Group Databasebeta

← #30608740

Subgroups — #30608740

Order 15616.

1602 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840711C211yesmaximal, characteristic
2C2×C4⋊C4×#6923C211yesmaximal, characteristic
3C2×C4⋊C4×#6923C211yesmaximal, characteristic
4C2×#16840698C211yesmaximal, characteristic
5#21460999C211yesmaximal, characteristic
6#21460999C211yesmaximal, characteristic
7#21460999C211yesmaximal, characteristic
8#21460998C211yesmaximal, characteristic
9#21460994C211yesmaximal, characteristic
10#21460994C211yesmaximal, characteristic
11#21460994C211yesmaximal, characteristic
12C4×(C2×#6923)⋊C4C211yesmaximal, 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
26#16840711C418yescomplemented
27C4⋊C4×#6923—24no—
28C4⋊C4×#6923C418yescomplemented
29#16840698—24no—
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×(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⋊#6923C2×C414yes—
76C2×C4⋊#6923C2×C414yes—
77C2×C4×#6923—22no—
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—22no—
90C2×C4×#6923—22no—
91C2×C4×#6923—22no—
92C2×C4×#6923—22no—
93C2×C4×#6923—41no—
94C2×C4×#6923—41no—
95C2×C4×#6923—41no—
96C2×C4×#6923—41no—
97C2×C4×#6923C2×C414yes—
98C2×C4×#6923C2×C414yes—
99C2×C4×#6923C2×C414yes—
100C2×C4×#6923C2×C414yes—
101(C2×#6923)⋊C4—22no—
102(C2×#6923)⋊C4—22no—
103(C2×#6923)⋊C4—22no—
104(C2×#6923)⋊C4—22no—
105(C2×#6923)⋊C4—22no—
106(C2×#6923)⋊C4—22no—
107(C2×#6923)⋊C4—22no—
108(C2×#6923)⋊C4—22no—
109(C2×#6923)⋊C4—22no—
110(C2×#6923)⋊C4—41no—
111(C2×#6923)⋊C4—41no—
112(C2×#6923)⋊C4C2×C414yes—
113(C2×#6923)⋊C4C2×C414yes—
114(C2×#6923)⋊C4C2×C414yes—
115(C2×#6923)⋊C4C2×C414yes—
116(C2×#6923)⋊C4C2×C414yes—
117(C2×#6923)⋊C4C2×C414yes—
118(C2×#6923)⋊C4D414yes—
119C22×C4×D61C2311yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126C2×C4⋊Dic61C2×C411yescharacteristic
127C2×C4⋊Dic61C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C2×#11758196C2×C411yescharacteristic
131C2×#11758196C2×C411yescharacteristic
132C4⋊C4×D61—22no—
133C4⋊C4×D61—22no—
134C4⋊C4×D61C2×C414yes—
135C4⋊C4×D61C2×C414yes—
136C2×C4×Dic61C2×C411yescharacteristic
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61C2×C411yescharacteristic
139C42×D61—22no—
140C42×D61—22no—
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
143#14519684C2×C411yescharacteristic
144#14519684C2×C411yescharacteristic
145#14519684C2×C411yescharacteristic
146#14519684C2×C411yescharacteristic
147#14519684C2×C411yescharacteristic
148#14519684C2×C411yescharacteristic
149#14519684C2×C411yescharacteristic
150#14519684C2×C411yescharacteristic
151#14519684C2×C411yescharacteristic
152#14519684C2×C411yescharacteristic
153C2×C4⋊C4×C61C2×C411yescharacteristic
154C2×C4⋊C4×C61C2×C411yescharacteristic
155C2×C42×C61C2×C411yescharacteristic
156#95×C61C2×C411yescharacteristic
157#95×C61C2×C411yescharacteristic
158#95×C61C2×C411yescharacteristic
159#95×C61C2×C411yescharacteristic
160C23×D61C2411yescharacteristic
161C22×#6923—21no—
162C22×#6923—21no—
163C22×#6923—21no—
164C22×#6923—21no—
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×#6923C22×C412yes—
202C22×#6923C22×C412yes—
203C22×#6923C22×C412yes—
204C22×#6923C22×C412yes—
205C22×#6923C22×C412yes—
206C22×#6923C22×C412yes—
207C22×#6923C22×C412yes—
208C22×#6923C22×C412yes—
209C22×#6923C2×D412yes—
210C22×#6923C2×D412yes—
211C22×#6923#4112yes—
212C22×#6923#4112yes—
213C22×#6923#4112yes—
214C22×#6923#4112yes—
215C22×#6923#4112yes—
216C22×#6923#4112yes—
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C22×Dic61C22×C411yescharacteristic
230C22×Dic61C22×C411yescharacteristic
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
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×D61C22×C412yes—
266C2×C4×D61C22×C412yes—
267C2×C4×D61C22×C412yes—
268C2×C4×D61C22×C412yes—
269C2×C4×D61C22×C412yes—
270C2×C4×D61C22×C412yes—
271C2×C4×D61C2×D412yes—
272C2×C4×D61#4112yes—
273C4⋊#6923—28no—
274C4⋊#6923—28no—
275C4×#6923—28no—
276C4×#6923—28no—
277C4×#6923—28no—
278C4×#6923—28no—
279C4×#6923—44no—
280C4×#6923—44no—
281C4×#6923—44no—
282C4×#6923—44no—
283C4⋊C4×C61—22no—
284C4⋊C4×C61C4214yescomplemented
285C42×C61—22no—
286C4⋊Dic61—22no—
287C4⋊Dic61C4214yescomplemented
288#11758196—22no—
289#11758196—22no—
290#11758196C4214yescomplemented
291#11758196C4214yescomplemented
292C4×Dic61—22no—
293C4×Dic61—22no—
294C4×Dic61—22no—
295C23×C61C23×C411yescharacteristic
296C22×D61C23×C411yescharacteristic
297C22×D61C23×C411yescharacteristic
298C22×D61C22×D411yescharacteristic
299C22×D61C2×#4111yescharacteristic
300C22×D61C2×#4111yescharacteristic
301C22×D61C2×#4111yescharacteristic
302C22×D61C2×#4111yescharacteristic
303C22×D61C2×#4111yescharacteristic
304C22×D61C2×#4111yescharacteristic
305C22×D61C2×#4111yescharacteristic
306C22×D61H(5,𝔽2)11yescharacteristic
307C22×D612−1+411yescharacteristic
308C22×D612−1+411yescharacteristic
309C22×D612−1+411yescharacteristic
310C2×#6923—22no—
311C2×#6923—22no—
312C2×#6923—22no—
313C2×#6923—22no—
314C2×#6923—22no—
315C2×#6923—22no—
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—41no—
347C2×#6923—41no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
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#11714yes—
363C2×#6923#11714yes—
364C2×#6923C4×D414yes—
365C2×#6923C4×D414yes—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
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×C61C2×C4212yes—
384C2×C4×C61C2×C4212yes—
385C2×C4×C61C2×C4212yes—
386C2×C4×C61C4×D412yes—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
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×Dic61C2×C4212yes—
405C2×Dic61C2×C4212yes—
406C2×Dic61C2×C4212yes—
407C2×Dic61C4×D412yes—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
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—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436#13815—611nomaximal, Sylow
437C22×C61C22×C4211yescharacteristic
438C22×C61C2×C4×D411yescharacteristic
439C22×C61C4×#4111yescharacteristic
440C22×C61C4×#4111yescharacteristic
441C22×C61C4×#4111yescharacteristic
442C22×C61#51911yescharacteristic
443C22×C61#52011yescharacteristic
444C2×D61C2×#11711yescharacteristic
445C2×D61C2×#11711yescharacteristic
446C2×D61C2×C4×D411yescharacteristic
447C2×D61C2×C4×D411yescharacteristic
448C2×D61C4×#4111yescharacteristic
449C2×D61C4×#4111yescharacteristic
450C2×D61C4×#4111yescharacteristic
451C2×D61C4×#4111yescharacteristic
452C2×D61#51911yescharacteristic
453C2×D61#51911yescharacteristic
454C2×D61#52011yescharacteristic
455C2×D61#52011yescharacteristic
456C2×D61#54611yescharacteristic
457C2×D61#54711yescharacteristic
458C2×D61#54711yescharacteristic
459C2×D61#54811yescharacteristic
460C2×D61#55111yescharacteristic
461C2×D61#55111yescharacteristic
462C2×D61#55211yescharacteristic
463C2×D61#55211yescharacteristic
464C2×D61#55211yescharacteristic
465C2×D61#55211yescharacteristic
466C2×D61#55211yescharacteristic
467C2×D61#55211yescharacteristic
468C2×D61#55211yescharacteristic
469C2×D61#55311yescharacteristic
470C2×D61#55611yescharacteristic
471C2×D61#55611yescharacteristic
472#6923—24no—
473#6923—24no—
474#6923—24no—
475#6923—24no—
476#6923—42no—
477#6923—42no—
478#6923—42no—
479#6923—42no—
480C4×C61—22no—
481C4×C61—22no—
482C4×C61—22no—
483C4×C61—22no—
484C4×C61—41no—
485C4×C61—41no—
486C4×C61—41no—
487Dic61—22no—
488Dic61—22no—
489Dic61—22no—
490Dic61—22no—
491Dic61—41no—
492Dic61—41no—
493Dic61—41no—
494C2×#387—611no—
495C2×#387—611no—
496C2×C4×C4⋊C4—611no—
497C2×C4×C4⋊C4—611no—
498C2×#376—611no—
499#1436—611no—
500#1436—611no—
501#1436—611no—
502#1436—611no—
503#1434—611no—
504#1434—611no—
505#1434—611no—
506C4×#95—611no—
507C4×#95—611no—
508C4×#95—611no—
509C2×C61C4×#11711yescharacteristic
510C2×C61C42×D411yescharacteristic
511C2×C61#227611yescharacteristic
512C2×C61#235911yescharacteristic
513C2×C61#236211yescharacteristic
514C2×C61#237111yescharacteristic
515C2×C61#237311yescharacteristic
516D61#234311yescharacteristic
517D61#234411yescharacteristic
518D61#235211yescharacteristic
519D61#235611yescharacteristic
520D61#235911yescharacteristic
521D61#236211yescharacteristic
522D61#237111yescharacteristic
523D61#237311yescharacteristic
524C22×C4⋊C4—611no—
525C22×C4⋊C4—611no—
526C22×C4⋊C4—611no—
527C22×C4⋊C4—611no—
528C22×C42—611no—
529C22×C42—611no—
530C22×C42—611no—
531C22×C42—611no—
532C22×C42—611no—
533C22×C42—611no—
534C22×C42—611no—
535C22×C42—611no—
536C22×C42—611no—
537#387—618no—
538#387—611no—
539#387—611no—
540#387—611no—
541#387—611no—
542#387—611no—
543#387—611no—
544#387—611no—
545#387#692311yescharacteristic, complemented
546C4×C4⋊C4—618no—
547C4×C4⋊C4—1224no—
548#376—1224no—
549C2×#95—611no—
550C2×#95—611no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95—611no—
555C2×#95—611no—
556C2×#95—611no—
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—
571C61#1381511yescharacteristic, complemented, Sylow
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
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—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—614no—
591C2×C4⋊C4—614no—
592C2×C4⋊C4—614no—
593C2×C4⋊C4—614no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—611no—
597C2×C4⋊C4—1222no—
598C2×C4⋊C4—1222no—
599C2×C4⋊C4—1222no—
600C2×C4⋊C4—1222no—
601C2×C4⋊C4—1222no—
602C2×C4⋊C4—1222no—
603C2×C4⋊C4C2×#692311yescharacteristic
604C2×C4⋊C4C2×#692311yescharacteristic
605C2×C42—614no—
606C2×C42—614no—
607C2×C42—614no—
608C2×C42—614no—
609C2×C42—611no—
610C2×C42—611no—
611C2×C42—611no—
612C2×C42—1222no—
613C2×C42—1222no—
614C2×C42—1222no—
615C2×C42—1222no—
616C2×C42—1222no—
617C2×C42—1222no—
618C2×C42—1222no—
619C2×C42—1222no—
620C2×C42—1222no—
621C2×C42—1222no—
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—2441no—
631C2×C42—2441no—
632C2×C42—2441no—
633C2×C42—2441no—
634C2×C42C2×#692311yescharacteristic
635#95—614no—
636#95—614no—
637#95—614no—
638#95—614no—
639#95—614no—
640#95—614no—
641#95—614no—
642#95—611no—
643#95—611no—
644#95—611no—
645#95—611no—
646#95—611no—
647#95—611no—
648#95—611no—
649#95—611no—
650#95—611no—
651#95—611no—
652#95—611no—
653#95—611no—
654#95—1222no—
655#95—1222no—
656#95—1222no—
657#95—1222no—
658#95—1222no—
659#95—1222no—
660#95—1222no—
661#95—1222no—
662#95—1222no—
663#95—2441no—
664#95—2441no—
665#95C2×#692311yescharacteristic
666#95C2×#692311yescharacteristic
667#95C2×#692311yescharacteristic
668#95C2×#692311yescharacteristic
669C24—611no—
670C22×C4—612no—
671C22×C4—612no—
672C22×C4—612no—
673C22×C4—612no—
674C22×C4—612no—
675C22×C4—612no—
676C22×C4—612no—
677C22×C4—612no—
678C22×C4—612no—
679C22×C4—612no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—611no—
686C22×C4—612no—
687C22×C4—612no—
688C22×C4—612no—
689C22×C4—612no—
690C22×C4—612no—
691C22×C4—612no—
692C22×C4—612no—
693C22×C4—612no—
694C22×C4—612no—
695C22×C4—612no—
696C22×C4—612no—
697C22×C4—612no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
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×C4C22×#692311yescharacteristic
776C22×C4C22×#692311yescharacteristic
777C22×C4C22×#692311yescharacteristic
778C22×C4C22×#692311yescharacteristic
779C22×C4C22×#692311yescharacteristic
780C22×C4C22×#692311yescharacteristic
781C22×C4C22×#692311yescharacteristic
782C4⋊C4—22no—
783C4⋊C4—614no—
784C4⋊C4—614no—
785C4⋊C4—614no—
786C4⋊C4—1222no—
787C4⋊C4—1222no—
788C4⋊C4—1228no—
789C4⋊C4—1228no—
790C4⋊C4—1222no—
791C4⋊C4C4×#692314yescomplemented
792C42—22no—
793C42—1222no—
794C42—1222no—
795C42—1228no—
796C42—1228no—
797C42—1228no—
798C42—1228no—
799C42—1222no—
800C42—2444no—
801C42—2444no—
802C42—2444no—
803C42—2444no—
804C23—611no—
805C23—611no—
806C23—611no—
807C23—611no—
808C23—611no—
809C23—611no—
810C23—611no—
811C23—611no—
812C23—611no—
813C23—611no—
814C23—611no—
815C23—611no—
816C23—611no—
817C23—611no—
818C23C23×#692311yescharacteristic
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—614no—
837C2×C4—614no—
838C2×C4—614no—
839C2×C4—614no—
840C2×C4—612no—
841C2×C4—612no—
842C2×C4—612no—
843C2×C4—612no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1222no—
850C2×C4—1222no—
851C2×C4—1222no—
852C2×C4—1222no—
853C2×C4—1222no—
854C2×C4—1222no—
855C2×C4—1222no—
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—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—1221no—
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—1222no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1221no—
905C2×C4—1221no—
906C2×C4—1221no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—1221no—
910C2×C4—1221no—
911C2×C4—1221no—
912C2×C4—1221no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
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×C4C2×C4×#692312yes—
942C2×C4C2×C4×#692312yes—
943C2×C4C2×C4×#692312yes—
944C2×C4D4×#692312yes—
945C22—611no—
946C22—611no—
947C22—611no—
948C22—611no—
949C22—611no—
950C22—611no—
951C22—611no—
952C22—611no—
953C22—611no—
954C22—611no—
955C22—611no—
956C22—611no—
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—
973C22C22×C4×#692311yescharacteristic
974C22C2×D4×#692311yescharacteristic
975C22#41×#692311yescharacteristic
976C22#41×#692311yescharacteristic
977C22#41×#692311yescharacteristic
978C22#1684083011yescharacteristic
979C22#1684083111yescharacteristic
980C4—22no—
981C4—22no—
982C4—22no—
983C4—22no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—1224no—
988C4—1224no—
989C4—1224no—
990C4—1224no—
991C4—1222no—
992C4—1222no—
993C4—1222no—
994C4—1222no—
995C4—2442no—
996C4—2442no—
997C4—2442no—
998C4—2442no—
999C4—2441no—
1000C4—2441no—
1001C4—2441no—
1002C2—611no—
1003C2—611no—
1004C2—611no—
1005C2—611no—
1006C2—611no—
1007C2—611no—
1008C2—611no—
1009C2—611no—
1010C2#117×#692311yescharacteristic
1011C2C4×D4×#692311yescharacteristic
1012C2#2146225911yescharacteristic
1013C2#2146234211yescharacteristic
1014C2#2146234511yescharacteristic
1015C2#2146235411yescharacteristic
1016C2#2146235611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C22×C42
FittingC61×#387C4
socleC23×C61C23×C4
prime radical, cosocleC23×D61C24
hypercenter#387#6923
hypocenterC61#13815
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
26. #16840711C4semidirect
28. C4⋊C4×#6923C4semidirect
51. #16839649C4semidirect
52. #16839648C4semidirect
53. #16839647C4semidirect
54. #16839646C4semidirect
55. #16839645C4semidirect
56. #16839644C4semidirect
57. #16839643C4semidirect
62. C61×#387C4semidirect
284. C4⋊C4×C61C42semidirect
287. C4⋊Dic61C42semidirect
290. #11758196C42semidirect
291. #11758196C42semidirect
545. #387#6923semidirect
571. C61#13815semidirect
791. C4⋊C4C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407112
C2×C4⋊C4×#69232
C2×#168406982
#214609992
#214609982
#214609942
C4×(C2×#6923)⋊C42
#95×#69232
#387×D612
#1381561