Finite Group Databasebeta

← #30608769

Subgroups — #30608769

Order 15616.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840712C211yesmaximal, characteristic
2C2×#16840709C211yesmaximal, characteristic
3#21461000C211yesmaximal, characteristic
4#21461000C211yesmaximal, characteristic
5#21460999C211yesmaximal, characteristic, complemented
6#21460999C211yesmaximal, characteristic, complemented
7#21460999C211yesmaximal, characteristic, complemented
8#21460998C211yesmaximal, characteristic, complemented
9#21460997C211yesmaximal, characteristic, complemented
10#21460996C211yesmaximal, characteristic, complemented
11#21460995C211yesmaximal, characteristic, complemented
12#21460994C211yesmaximal, characteristic, complemented
13#21460992C211yesmaximal, characteristic
14#21460992C211yesmaximal, characteristic
15#388×D61C211yesmaximal, characteristic
16C24×#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C22⋊#6923C2211yescharacteristic
21C22×C22⋊#6923C2211yescharacteristic
22C22×C22⋊#6923C2211yescharacteristic
23C22×C4×#6923C2211yescharacteristic
24C22×C4×#6923C2211yescharacteristic
25C22×C4×#6923C2211yescharacteristic
26#16840712C418yescomplemented
27#16840709C418yescomplemented
28C2×(C2×#6923)⋊C4C2211yescharacteristic
29C2×(C2×#6923)⋊C4C2211yescharacteristic
30C2×(C2×#6923)⋊C4C2211yescharacteristic
31C2×(C2×#6923)⋊C4C2211yescharacteristic
32C2×(C2×#6923)⋊C4C2211yescharacteristic
33C2×(C2×#6923)⋊C4C2211yescharacteristic
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36C2×(C2×#6923)⋊C4C2211yescharacteristic
37C2×(C2×#6923)⋊C4C2211yescharacteristic
38C2×(C2×#6923)⋊C4C2211yescharacteristic
39C2×(C2×#6923)⋊C4C2211yescharacteristic
40C2×(C2×#6923)⋊C4C2211yescharacteristic
41C2×(C2×#6923)⋊C4C2211yescharacteristic
42C2×(C2×#6923)⋊C4C2211yescharacteristic
43C2×(C2×#6923)⋊C4C2211yescharacteristic
44C2×(C2×#6923)⋊C4C2211yescharacteristic
45C2×(C2×#6923)⋊C4C2211yescharacteristic
46C2×C4⋊C4×D61C2211yescharacteristic
47C2×C22⋊C4×D61C2211yescharacteristic
48C2×C22⋊C4×D61C2211yescharacteristic
49C2×C22⋊C4×D61C2211yescharacteristic
50C2×C42×D61C2211yescharacteristic
51#16839656C411yescharacteristic, complemented
52#16839655C411yescharacteristic, complemented
53#16839654C411yescharacteristic, complemented
54#16839653C411yescharacteristic, complemented
55#16839652C411yescharacteristic, complemented
56#16839651C411yescharacteristic, complemented
57#16839650C411yescharacteristic, complemented
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60C61×#388C411yescharacteristic, complemented
61C23×#6923—41no—
62C23×#6923—41no—
63C23×#6923—41no—
64C23×#6923—41no—
65C23×#6923—41no—
66C23×#6923—41no—
67C23×#6923C2×C414yes—
68C23×#6923C2311yescharacteristic
69C23×#6923C2311yescharacteristic
70C23×#6923C2311yescharacteristic
71C23×#6923C2311yescharacteristic
72C23×#6923C2311yescharacteristic
73C23×#6923C2311yescharacteristic
74C23×#6923C2311yescharacteristic
75C23×#6923C2311yescharacteristic
76C2×C4⋊#6923—41no—
77C2×C4⋊#6923—41no—
78C2×C4⋊#6923—41no—
79C2×C4⋊#6923—41no—
80C2×C4⋊#6923—41no—
81C2×C4⋊#6923—41no—
82C2×C4⋊#6923C2×C414yes—
83C2×C4⋊#6923C2×C414yes—
84C2×C4⋊#6923C2×C414yescomplemented
85C2×C22⋊#6923—41no—
86C2×C22⋊#6923—41no—
87C2×C22⋊#6923—41no—
88C2×C22⋊#6923—41no—
89C2×C22⋊#6923—41no—
90C2×C22⋊#6923—41no—
91C2×C22⋊#6923C2×C414yes—
92C2×C22⋊#6923C2×C414yes—
93C2×C22⋊#6923C2×C414yes—
94C2×C4×#6923—41no—
95C2×C4×#6923—41no—
96C2×C4×#6923—41no—
97C2×C4×#6923—41no—
98C2×C4×#6923—41no—
99C2×C4×#6923—41no—
100C2×C4×#6923—41no—
101C2×C4×#6923—41no—
102C2×C4×#6923C2×C414yescomplemented
103(C2×#6923)⋊C4—41no—
104(C2×#6923)⋊C4—41no—
105(C2×#6923)⋊C4—41no—
106(C2×#6923)⋊C4—41no—
107(C2×#6923)⋊C4—41no—
108(C2×#6923)⋊C4—41no—
109(C2×#6923)⋊C4—41no—
110(C2×#6923)⋊C4—41no—
111(C2×#6923)⋊C4—41no—
112(C2×#6923)⋊C4—41no—
113(C2×#6923)⋊C4—41no—
114(C2×#6923)⋊C4—41no—
115(C2×#6923)⋊C4—41no—
116(C2×#6923)⋊C4—41no—
117(C2×#6923)⋊C4C2×C414yes—
118(C2×#6923)⋊C4C2×C414yes—
119(C2×#6923)⋊C4C2×C414yescomplemented
120(C2×#6923)⋊C4C2×C414yescomplemented
121C24×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126C22×C4×D61C2311yescharacteristic
127C22×C4×D61C2311yescharacteristic
128C2×C4⋊Dic61C2×C411yescharacteristic, complemented
129C2×#11758196C2×C411yescharacteristic, complemented
130C2×#11758196C2×C411yescharacteristic, complemented
131C4⋊C4×D61—41no—
132C4⋊C4×D61—41no—
133C2×C22⋊Dic61C2×C411yescharacteristic
134C2×C22⋊Dic61C2×C411yescharacteristic
135C2×C22⋊Dic61C2×C411yescharacteristic
136C2×#11758198C2×C411yescharacteristic
137C2×#11758198C2×C411yescharacteristic
138C2×#11758198C2×C411yescharacteristic
139C2×#11758198C2×C411yescharacteristic
140C2×#11758198C2×C411yescharacteristic
141C2×#11758198C2×C411yescharacteristic
142C22⋊C4×D61—41no—
143C22⋊C4×D61—41no—
144C22⋊C4×D61—41no—
145C22⋊C4×D61—41no—
146C22⋊C4×D61C2×C414yes—
147C22⋊C4×D61C2×C414yes—
148C2×C4×Dic61C2×C411yescharacteristic, complemented
149C2×C4×Dic61C2×C411yescharacteristic, complemented
150C2×C4×Dic61C2×C411yescharacteristic, complemented
151C42×D61—41no—
152C42×D61—41no—
153#14519684C2×C411yescharacteristic, complemented
154#14519684C2×C411yescharacteristic, complemented
155#14519684C2×C411yescharacteristic, complemented
156#14519684C2×C411yescharacteristic, complemented
157#14519684C2×C411yescharacteristic, complemented
158#14519684C2×C411yescharacteristic, complemented
159C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
160C2×C22⋊C4×C61C2×C411yescharacteristic
161C2×C22⋊C4×C61C2×C411yescharacteristic
162C2×C22⋊C4×C61C2×C411yescharacteristic
163C2×C42×C61C2×C411yescharacteristic, complemented
164#95×C61C2×C411yescharacteristic, complemented
165#95×C61C2×C411yescharacteristic, complemented
166C24×C61C22×C411yescharacteristic
167C23×D61—21no—
168C23×D61—21no—
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×D61C22×C411yescharacteristic
180C23×D61C22×C412yes—
181C23×D61C22×C412yes—
182C23×D61C2411yescharacteristic
183C22×#6923—21no—
184C22×#6923—21no—
185C22×#6923—21no—
186C22×#6923—21no—
187C22×#6923—21no—
188C22×#6923—21no—
189C22×#6923—21no—
190C22×#6923—21no—
191C22×#6923—21no—
192C22×#6923—21no—
193C22×#6923—21no—
194C22×#6923—21no—
195C22×#6923—21no—
196C22×#6923—21no—
197C22×#6923—21no—
198C22×#6923—21no—
199C22×#6923—21no—
200C22×#6923—21no—
201C22×#6923—21no—
202C22×#6923—21no—
203C22×#6923—21no—
204C22×#6923—21no—
205C22×#6923—21no—
206C22×#6923—21no—
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—21no—
215C22×#6923—21no—
216C22×#6923—21no—
217C22×#6923—21no—
218C22×#6923—21no—
219C22×#6923—21no—
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—21no—
226C22×#6923—21no—
227C22×#6923—21no—
228C22×#6923—21no—
229C22×#6923—21no—
230C22×#6923—21no—
231C22×#6923—44no—
232C22×#6923—44no—
233C22×#6923—44no—
234C22×#6923—44no—
235C22×#6923—44no—
236C22×#6923—44no—
237C22×#6923—44no—
238C22×#6923C22×C412yes—
239C22×#6923C22×C412yes—
240C22×#6923C22×C412yes—
241C22×#6923C22×C412yes—
242C22×#6923C22×C412yes—
243C22×#6923C22×C412yes—
244C22×#6923C22×C412yes—
245C22×#6923C22×C412yes—
246C22×C4×C61C22×C411yescharacteristic
247C22×C4×C61C22×C411yescharacteristic
248C22×C4×C61C22×C411yescharacteristic
249C22×C4×C61C22×C411yescharacteristic
250C22×C4×C61C22×C411yescharacteristic
251C22×C4×C61C22×C411yescharacteristic
252C22×Dic61C22×C411yescharacteristic
253C22×Dic61C22×C411yescharacteristic
254C22×Dic61C22×C411yescharacteristic
255C22×Dic61C22×C411yescharacteristic
256C22×Dic61C22×C411yescharacteristic
257C22×Dic61C22×C411yescharacteristic
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—21no—
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×D61C22×C412yes—
291C2×C4×D61C22×C412yes—
292C2×C4×D61C22×C412yes—
293C2×C4×D61C22×C412yes—
294C22⋊#6923—44no—
295C22⋊#6923—44no—
296C22⋊#6923—44no—
297C4⋊#6923—44no—
298C4⋊#6923—44no—
299C4⋊#6923—44no—
300C4×#6923—44no—
301C4×#6923—44no—
302C4×#6923—44no—
303C4⋊C4×C61—41no—
304C22⋊C4×C61—41no—
305C22⋊C4×C61—41no—
306C22⋊C4×C61C4214yescomplemented
307C42×C61—41no—
308C22⋊Dic61—41no—
309C22⋊Dic61—41no—
310C22⋊Dic61C4214yescomplemented
311#11758198—41no—
312#11758198—41no—
313#11758198—41no—
314#11758198—41no—
315#11758198C4214yescomplemented
316#11758198C4214yescomplemented
317C4⋊Dic61—41no—
318#11758196—41no—
319#11758196—41no—
320C4×Dic61—41no—
321C4×Dic61—41no—
322C4×Dic61—41no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—21no—
329C23×C61C2×C4212yes—
330C23×C61C23×C411yescharacteristic
331C22×D61—21no—
332C22×D61—21no—
333C22×D61—21no—
334C22×D61—21no—
335C22×D61—21no—
336C22×D61—21no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
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×D61—41no—
365C22×D61C2×C4212yes—
366C22×D61C23×C411yescharacteristic
367C22×D61C23×C411yescharacteristic
368C22×D61H(5,𝔽2)11yescharacteristic
369C22×D61H(5,𝔽2)11yescharacteristic
370C22×D61H(5,𝔽2)11yescharacteristic
371C22×D61H(5,𝔽2)11yescharacteristic
372C22×D61H(5,𝔽2)11yescharacteristic
373C22×D61H(5,𝔽2)11yescharacteristic
374C22×D61H(5,𝔽2)11yescharacteristic
375C22×D61H(5,𝔽2)11yescharacteristic
376C22×D612−1+411yescharacteristic
377C22×D612−1+411yescharacteristic
378C22×D612−1+411yescharacteristic
379C22×D612−1+411yescharacteristic
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—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—22no—
401C2×#6923—22no—
402C2×#6923—22no—
403C2×#6923—22no—
404C2×#6923—416no—
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×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—21no—
450C2×C4×C61—21no—
451C2×C4×C61—21no—
452C2×C4×C61—21no—
453C2×C4×C61C2×C4212yes—
454C2×C4×C61C2×C4212yes—
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—21no—
468C2×Dic61—21no—
469C2×Dic61—21no—
470C2×Dic61—21no—
471C2×Dic61C2×C4212yes—
472C2×Dic61C2×C4212yes—
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—41no—
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—
494C4×D61—41no—
495C4×D61—41no—
496C4×D61—41no—
497#13831—611nomaximal, Sylow
498C22×C61—22no—
499C22×C61—22no—
500C22×C61—22no—
501C22×C61—41no—
502C22×C61—41no—
503C22×C61—41no—
504C22×C61—41no—
505C22×C61C22×C4211yescharacteristic
506C22×C61#51811yescharacteristic
507C22×C61#51811yescharacteristic
508C22×C61#52011yescharacteristic
509C22×C61#52011yescharacteristic
510C22×C61#52011yescharacteristic
511C22×C61#52011yescharacteristic
512C2×D61—22no—
513C2×D61—22no—
514C2×D61—22no—
515C2×D61—41no—
516C2×D61—41no—
517C2×D61—41no—
518C2×D61—41no—
519C2×D61—42no—
520C2×D61—42no—
521C2×D61—42no—
522C2×D61—42no—
523C2×D61—42no—
524C2×D61—42no—
525C2×D61—42no—
526C2×D61—42no—
527C2×D61#51811yescharacteristic
528C2×D61#51811yescharacteristic
529C2×D61#51811yescharacteristic
530C2×D61#51811yescharacteristic
531C2×D61#51811yescharacteristic
532C2×D61#51911yescharacteristic
533C2×D61#52011yescharacteristic
534C2×D61#52011yescharacteristic
535C2×D61#52011yescharacteristic
536C2×D61#52011yescharacteristic
537C2×D61#52011yescharacteristic
538C2×D61#52011yescharacteristic
539C2×D61#56011yescharacteristic
540C2×D61#56011yescharacteristic
541C2×D61#56011yescharacteristic
542C2×D61#56011yescharacteristic
543C2×D61H(3,𝔽4)11yescharacteristic
544C2×D61#56211yescharacteristic
545C2×D61#56211yescharacteristic
546C2×D61#56211yescharacteristic
547C2×D61#56211yescharacteristic
548C2×D61#56211yescharacteristic
549C2×D61#56211yescharacteristic
550C2×D61#56311yescharacteristic
551C2×D61#56311yescharacteristic
552C2×D61#56311yescharacteristic
553C2×D61#56311yescharacteristic
554C2×D61#56311yescharacteristic
555#6923—42no—
556#6923—42no—
557#6923—42no—
558#6923—42no—
559#6923—42no—
560#6923—42no—
561#6923—42no—
562#6923—42no—
563C4×C61—22no—
564C4×C61—22no—
565C4×C61—41no—
566C4×C61—41no—
567C4×C61—41no—
568C4×C61—41no—
569Dic61—22no—
570Dic61—22no—
571Dic61—41no—
572Dic61—41no—
573Dic61—41no—
574Dic61—41no—
575C2×#388—611no—
576C2×#388—611no—
577C2×#385—611no—
578#1437—611no—
579#1437—611no—
580#1436—611no—
581#1436—611no—
582#1436—611no—
583#1436—611no—
584C4⋊#95—611no—
585C4⋊#95—611no—
586#1434—611no—
587#1434—611no—
588C22⋊#95—611no—
589C22⋊#95—611no—
590C2×C61—42no—
591C2×C61#227411yescharacteristic
592C2×C61#227511yescharacteristic
593C2×C61#227511yescharacteristic
594C2×C61#237611yescharacteristic
595C2×C61#237711yescharacteristic
596C2×C61#237911yescharacteristic
597C2×C61#238311yescharacteristic
598D61—42no—
599D61#237511yescharacteristic
600D61#237611yescharacteristic
601D61#237611yescharacteristic
602D61#237711yescharacteristic
603D61#237811yescharacteristic
604D61#237811yescharacteristic
605D61#237911yescharacteristic
606D61#238311yescharacteristic
607C24×C4—611no—
608C22×C4⋊C4—611no—
609C22×C4⋊C4—611no—
610C22×C4⋊C4—611no—
611C22×C4⋊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—
621C22×C42—611no—
622#388—618no—
623#388—611no—
624#388—611no—
625#388—611no—
626#388—611no—
627#388—611no—
628#388—611no—
629#388—611no—
630#388#692311yescharacteristic, complemented
631#385—618no—
632C2×#95—611no—
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—
651C2×#95—611no—
652C61#1383111yescharacteristic, complemented, Sylow
653C25—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—614no—
665C23×C4—611no—
666C23×C4—611no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—2441no—
670C23×C4—2441no—
671C23×C4—2441no—
672C23×C4—2441no—
673C23×C4—2441no—
674C23×C4—2441no—
675C2×C4⋊C4—614no—
676C2×C4⋊C4—614no—
677C2×C4⋊C4—614no—
678C2×C4⋊C4—611no—
679C2×C4⋊C4—611no—
680C2×C4⋊C4—611no—
681C2×C4⋊C4—2441no—
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⋊C4C2×#692311yescharacteristic, complemented
690C2×C22⋊C4—611no—
691C2×C22⋊C4—611no—
692C2×C22⋊C4—611no—
693C2×C22⋊C4—614no—
694C2×C22⋊C4—614no—
695C2×C22⋊C4—614no—
696C2×C22⋊C4—614no—
697C2×C22⋊C4—614no—
698C2×C22⋊C4—611no—
699C2×C22⋊C4—611no—
700C2×C22⋊C4—611no—
701C2×C22⋊C4—611no—
702C2×C22⋊C4—611no—
703C2×C22⋊C4—611no—
704C2×C22⋊C4—2441no—
705C2×C22⋊C4—2441no—
706C2×C22⋊C4—2441no—
707C2×C22⋊C4—2441no—
708C2×C22⋊C4—2441no—
709C2×C22⋊C4—2441no—
710C2×C22⋊C4—2441no—
711C2×C22⋊C4—2441no—
712C2×C22⋊C4—2441no—
713C2×C22⋊C4—2441no—
714C2×C22⋊C4C2×#692311yescharacteristic
715C2×C22⋊C4C2×#692311yescharacteristic
716C2×C22⋊C4C2×#692311yescharacteristic
717C2×C42—614no—
718C2×C42—611no—
719C2×C42—611no—
720C2×C42—611no—
721C2×C42—2441no—
722C2×C42—2441no—
723C2×C42—2441no—
724C2×C42—2441no—
725C2×C42—2441no—
726C2×C42—2441no—
727C2×C42—2441no—
728C2×C42—2441no—
729C2×C42—2441no—
730C2×C42—2441no—
731C2×C42C2×#692311yescharacteristic, complemented
732#95—614no—
733#95—614no—
734#95—614no—
735#95—614no—
736#95—611no—
737#95—611no—
738#95—611no—
739#95—611no—
740#95—611no—
741#95—611no—
742#95—2441no—
743#95—2441no—
744#95—2441no—
745#95—2441no—
746#95—2441no—
747#95—2441no—
748#95—2441no—
749#95—2441no—
750#95—2441no—
751#95—2441no—
752#95—2441no—
753#95—2441no—
754#95—2441no—
755#95—2441no—
756#95C2×#692311yescharacteristic, complemented
757#95C2×#692311yescharacteristic, complemented
758C24—611no—
759C24—612no—
760C24—612no—
761C24—611no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24—1221no—
766C24—1221no—
767C24—1221no—
768C24—1221no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24—1221no—
774C24C22×#692311yescharacteristic
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—612no—
788C22×C4—612no—
789C22×C4—611no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
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×C4—1221no—
873C22×C4—2444no—
874C22×C4—2444no—
875C22×C4—2444no—
876C22×C4—2444no—
877C22×C4—2444no—
878C22×C4—2444no—
879C22×C4—2444no—
880C22×C4C22×#692311yescharacteristic
881C22×C4C22×#692311yescharacteristic
882C22×C4C22×#692311yescharacteristic
883C22×C4C22×#692311yescharacteristic
884C22×C4C22×#692311yescharacteristic
885C22×C4C22×#692311yescharacteristic
886C4⋊C4—41no—
887C4⋊C4—2441no—
888C4⋊C4—2441no—
889C4⋊C4—2441no—
890C4⋊C4—2444no—
891C4⋊C4—2444no—
892C4⋊C4—2444no—
893C22⋊C4—41no—
894C22⋊C4—41no—
895C22⋊C4—614no—
896C22⋊C4—614no—
897C22⋊C4—614no—
898C22⋊C4—2441no—
899C22⋊C4—2441no—
900C22⋊C4—2441no—
901C22⋊C4—2441no—
902C22⋊C4—2441no—
903C22⋊C4—2441no—
904C22⋊C4—2444no—
905C22⋊C4—2444no—
906C22⋊C4—2444no—
907C22⋊C4C4×#692314yescomplemented
908C42—41no—
909C42—2441no—
910C42—2441no—
911C42—2441no—
912C42—2444no—
913C42—2444no—
914C42—2444no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—611no—
922C23—611no—
923C23—611no—
924C23—611no—
925C23—611no—
926C23—611no—
927C23—611no—
928C23—611no—
929C23—611no—
930C23—611no—
931C23—611no—
932C23—611no—
933C23—611no—
934C23—611no—
935C23—612no—
936C23—1222no—
937C23—1222no—
938C23—1222no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1222no—
943C23—1222no—
944C23—1222no—
945C23—1222no—
946C23—1222no—
947C23—1222no—
948C23—1221no—
949C23—1221no—
950C23—1221no—
951C23—1221no—
952C23—1221no—
953C23—1221no—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23—2441no—
967C23—2441no—
968C23—2441no—
969C23—2441no—
970C23C2×C4×#692312yes—
971C23C23×#692311yescharacteristic
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—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—612no—
989C2×C4—612no—
990C2×C4—1222no—
991C2×C4—1222no—
992C2×C4—1222no—
993C2×C4—1222no—
994C2×C4—1222no—
995C2×C4—1222no—
996C2×C4—1222no—
997C2×C4—1222no—
998C2×C4—1221no—
999C2×C4—1221no—
1000C2×C4—1221no—
1001C2×C4—1221no—
1002C2×C4—1222no—
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—1222no—
1016C2×C4—1222no—
1017C2×C4—1222no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1222no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1221no—
1027C2×C4—1221no—
1028C2×C4—1221no—
1029C2×C4—1221no—
1030C2×C4—1221no—
1031C2×C4—1221no—
1032C2×C4—1221no—
1033C2×C4—1221no—
1034C2×C4—1221no—
1035C2×C4—1221no—
1036C2×C4—1221no—
1037C2×C4—1221no—
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—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—24416no—
1087C2×C4C2×C4×#692312yes—
1088C2×C4C2×C4×#692312yes—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
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—611no—
1119C22—611no—
1120C22—611no—
1121C22—611no—
1122C22—611no—
1123C22—611no—
1124C22—1222no—
1125C22—1222no—
1126C22—1222no—
1127C22—2442no—
1128C22—2442no—
1129C22—2442no—
1130C22—2442no—
1131C22—2442no—
1132C22—2442no—
1133C22—2442no—
1134C22—2442no—
1135C22—2441no—
1136C22—2441no—
1137C22—2441no—
1138C22—2441no—
1139C22C22×C4×#692311yescharacteristic
1140C22#1684082911yescharacteristic
1141C22#1684082911yescharacteristic
1142C22#1684083111yescharacteristic
1143C22#1684083111yescharacteristic
1144C22#1684083111yescharacteristic
1145C22#1684083111yescharacteristic
1146C4—22no—
1147C4—22no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—1222no—
1153C4—1222no—
1154C4—2442no—
1155C4—2442no—
1156C4—2442no—
1157C4—2442no—
1158C4—2442no—
1159C4—2442no—
1160C4—2442no—
1161C4—2442no—
1162C4—2441no—
1163C4—2441no—
1164C4—2441no—
1165C4—2441no—
1166C2—42no—
1167C2—611no—
1168C2—611no—
1169C2—611no—
1170C2—611no—
1171C2—611no—
1172C2—611no—
1173C2—611no—
1174C2—611no—
1175C2—2442no—
1176C2#2146225611yescharacteristic
1177C2#2146225811yescharacteristic
1178C2#2146225811yescharacteristic
1179C2#2146235911yescharacteristic
1180C2#2146236011yescharacteristic
1181C2#2146236211yescharacteristic
1182C2#2146236611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C22×C42
FittingC61×#388C4
socleC23×C61C23×C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#388#6923
hypocenterC61#13831
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
5. #21460999C2semidirect
6. #21460999C2semidirect
7. #21460999C2semidirect
8. #21460998C2semidirect
9. #21460997C2semidirect
10. #21460996C2semidirect
11. #21460995C2semidirect
12. #21460994C2semidirect
26. #16840712C4semidirect
27. #16840709C4semidirect
51. #16839656C4semidirect
52. #16839655C4semidirect
53. #16839654C4semidirect
54. #16839653C4semidirect
55. #16839652C4semidirect
56. #16839651C4semidirect
57. #16839650C4semidirect
60. C61×#388C4semidirect
84. C2×C4⋊#6923C2×C4semidirect
102. C2×C4×#6923C2×C4semidirect
119. (C2×#6923)⋊C4C2×C4semidirect
120. (C2×#6923)⋊C4C2×C4semidirect
128. C2×C4⋊Dic61C2×C4semidirect
129. C2×#11758196C2×C4semidirect
130. C2×#11758196C2×C4semidirect
148. C2×C4×Dic61C2×C4semidirect
149. C2×C4×Dic61C2×C4semidirect
150. C2×C4×Dic61C2×C4semidirect
153. #14519684C2×C4semidirect
154. #14519684C2×C4semidirect
155. #14519684C2×C4semidirect
156. #14519684C2×C4semidirect
157. #14519684C2×C4semidirect
158. #14519684C2×C4semidirect
159. C2×C4⋊C4×C61C2×C4semidirect
163. C2×C42×C61C2×C4semidirect
164. #95×C61C2×C4semidirect
165. #95×C61C2×C4semidirect
306. C22⋊C4×C61C42semidirect
310. C22⋊Dic61C42semidirect
315. #11758198C42semidirect
316. #11758198C42semidirect
630. #388#6923semidirect
652. C61#13831semidirect
689. C2×C4⋊C4C2×#6923semidirect
731. C2×C42C2×#6923semidirect
756. #95C2×#6923semidirect
757. #95C2×#6923semidirect
907. 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
#214610002
#214609992
#214609982
#214609972
#214609962
#214609952
#214609942
#214609922
#388×D612
#1383161