Finite Group Databasebeta

← #30602987

Subgroups — #30602987

Order 15616.

1286 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
2C22×#14519831C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊#6923C211yesmaximal, characteristic
4C2×(C2×#6923)⋊C8C211yesmaximal, characteristic, complemented
5C2×(C2×#6923)⋊C8C211yesmaximal, characteristic, complemented
6C2×(C2×#6923)⋊C8C211yesmaximal, characteristic, complemented
7C2×C22⋊C8×D61C211yesmaximal, characteristic
8C22×D61⋊C8C2211yescharacteristic
9C22×D61⋊C8C2211yescharacteristic
10C22×C22⋊#6923C412yes—
11C22×C4×#6923C2211yescharacteristic
12C22×C4×#6923C2211yescharacteristic
13C2×#14519834C412yescomplemented
14D61⋊(C22⋊C8)—22no—
15D61⋊(C22⋊C8)—22no—
16C2×C22⋊#92420C412yescomplemented
17C2×#14519831—22no—
18C2×#14519831—22no—
19C2×#14519831—22no—
20C4×C22⋊#6923—22no—
21C4×C22⋊#6923—22no—
22C2×(C2×#6923)⋊C4C412yes—
23(C2×#6923)⋊C8—22no—
24(C2×#6923)⋊C8—22no—
25(C2×#6923)⋊C8—22no—
26C23×C4×D61C2211yescharacteristic
27C22×C8×D61C2211yescharacteristic
28C22×C8×D61C2211yescharacteristic
29C2×C22⋊#92418C411yescharacteristic, complemented
30C2×#14519689C411yescharacteristic, complemented
31C2×#14519689C411yescharacteristic, complemented
32C22⋊C8×D61—22no—
33C22⋊C8×D61—22no—
34C2×C22⋊C8×C61C411yescharacteristic, complemented
35C23×#6923C2×C412yes—
36C23×#6923C2×C412yes—
37C2×D61⋊C8—21no—
38C2×D61⋊C8—21no—
39C2×D61⋊C8—21no—
40C2×D61⋊C8—21no—
41C2×D61⋊C8—21no—
42C2×D61⋊C8—21no—
43C2×D61⋊C8—21no—
44C2×D61⋊C8—21no—
45C2×D61⋊C8—21no—
46C2×D61⋊C8—21no—
47C2×D61⋊C8D412yes—
48C2×D61⋊C8D412yes—
49C22×#92420C2×C412yes—
50C22×#92420C2×C412yes—
51C2×C22⋊#6923—24no—
52C2×C22⋊#6923—24no—
53C2×C22⋊#6923—24no—
54C2×C4×#6923—21no—
55C2×C4×#6923—21no—
56C2×C4×#6923—21no—
57C2×C4×#6923—21no—
58C2×C4×#6923—21no—
59C2×C4×#6923—21no—
60C2×C4×#6923—21no—
61C2×C4×#6923—21no—
62C2×C4×#6923—21no—
63C2×C4×#6923—21no—
64C2×C4×#6923D412yes—
65C2×C4×#6923D412yes—
66#14519834—24no—
67C22⋊#92420—24no—
68#14519831—28no—
69(C2×#6923)⋊C4—24no—
70C24×D61C2×C411yescharacteristic
71C23×Dic61C2×C411yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61—21no—
78C22×C4×D61—21no—
79C22×C4×D61—21no—
80C22×C4×D61—21no—
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2×C411yescharacteristic
85C22×C4×D61C2×C411yescharacteristic
86C22×C4×D61C2×C411yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C22×#92418C2×C411yescharacteristic
89C22×#92418C2×C411yescharacteristic
90C2×C8×D61—21no—
91C2×C8×D61—21no—
92C2×C8×D61—21no—
93C2×C8×D61—21no—
94C2×C8×D61—21no—
95C2×C8×D61—21no—
96C2×C8×D61—21no—
97C2×C8×D61—21no—
98C2×C8×D61—21no—
99C2×C8×D61—21no—
100C2×C8×D61D412yes—
101C2×C8×D61D412yes—
102C22⋊#92418—22no—
103#14519689—22no—
104#14519689—22no—
105C23×C4×C61C2×C411yescharacteristic
106C22×C8×C61C2×C411yescharacteristic
107C22×C8×C61C2×C411yescharacteristic
108C22⋊C8×C61—22no—
109C24×C61C4211yescharacteristic
110C23×D61—21no—
111C23×D61—21no—
112C23×D61—21no—
113C23×D61—21no—
114C23×D61—21no—
115C23×D61—21no—
116C23×D61—22no—
117C23×D61—22no—
118C23×D61—22no—
119C23×D61C4211yescharacteristic
120C23×D61M1614yes—
121C23×D61C22×C411yescharacteristic
122C22×#6923—22no—
123C22×#6923—22no—
124C22×#6923—22no—
125C22×#6923—22no—
126C22×#6923—22no—
127C22×#6923—22no—
128C22×#6923—22no—
129C22×#6923—22no—
130C22×#6923—22no—
131C22×#6923—22no—
132C22×#6923—22no—
133C22×#6923—22no—
134C22×#6923C22⋊C414yes—
135C22×#6923M1614yes—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61C4211yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61C4211yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—41no—
171C2×C4×D61—41no—
172C2×C4×D61—41no—
173C2×C4×D61—41no—
174C2×C4×D61—41no—
175C2×C4×D61—41no—
176C2×C4×D61—41no—
177C2×C4×D61—41no—
178C2×C4×D61—41no—
179C2×C4×D61—41no—
180C2×C4×D61—41no—
181C2×C4×D61—41no—
182C2×C4×D61—41no—
183C2×C4×D61—41no—
184C2×C4×D61—41no—
185C2×C4×D61—41no—
186C2×C4×D61C2×D411yescharacteristic
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61C2×D411yescharacteristic
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2×D411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61#4111yescharacteristic
193C2×C4×D61#4111yescharacteristic
194C2×C4×D61#4111yescharacteristic
195C2×C4×D61#4111yescharacteristic
196C2×C4×D61#4111yescharacteristic
197C2×C4×D61#4111yescharacteristic
198C22⋊#6923—216no—
199C2×#92420—22no—
200C2×#92420—22no—
201C2×#92420—22no—
202C2×#92420—22no—
203C2×#92420—22no—
204C2×#92420C22⋊C414yescomplemented
205C4×#6923—22no—
206C4×#6923—22no—
207C4×#6923—22no—
208C4×#6923—22no—
209C4×#6923—41no—
210C4×#6923—41no—
211C4×#6923—41no—
212C4×#6923—41no—
213D61⋊C8—22no—
214D61⋊C8—22no—
215D61⋊C8—22no—
216D61⋊C8—22no—
217D61⋊C8—41no—
218D61⋊C8—41no—
219D61⋊C8—41no—
220D61⋊C8—41no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61C22⋊C412yescomplemented
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418C22⋊C412yescomplemented
233C8×D61—22no—
234C8×D61—22no—
235C8×D61—22no—
236C8×D61—22no—
237C8×D61—41no—
238C8×D61—41no—
239C8×D61—41no—
240C8×D61—41no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61#9712yescomplemented
248C23×C61C2×C4211yescharacteristic
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—24no—
256C22×D61—24no—
257C22×D61—24no—
258C22×D61—24no—
259C22×D61—24no—
260C22×D61—24no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61#9712yescomplemented
272C22×D61C2×C22⋊C411yescharacteristic
273C22×D61#11711yescharacteristic
274C22×D61C4×D411yescharacteristic
275C22×D61C4×D411yescharacteristic
276C22×D61C4×D411yescharacteristic
277C22×D61C4×D411yescharacteristic
278C22×D61C2×M1612yes—
279C22×D61C2×M1612yes—
280C22×D61#13112yes—
281C22×D61#13112yes—
282C2×#6923—24no—
283C2×#6923—24no—
284C2×#6923—24no—
285C2×#6923—24no—
286C2×#6923—24no—
287C2×#6923—24no—
288C2×#6923—42no—
289C2×#6923—42no—
290C2×#6923—42no—
291C2×#6923—42no—
292C2×#6923—42no—
293C2×#6923—42no—
294C2×#6923—42no—
295C2×#6923—42no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61C2×C22⋊C411yescharacteristic
304C2×C4×C61#11711yescharacteristic
305C2×C4×C61C4×D411yescharacteristic
306C2×C4×C61C4×D411yescharacteristic
307C2×C4×C61C4×D411yescharacteristic
308C2×C4×C61C4×D411yescharacteristic
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61C2×C22⋊C411yescharacteristic
317C2×Dic61#11711yescharacteristic
318C2×Dic61C4×D411yescharacteristic
319C2×Dic61C4×D411yescharacteristic
320C2×Dic61C4×D411yescharacteristic
321C2×Dic61C4×D411yescharacteristic
322C4×D61—41no—
323C4×D61—41no—
324C4×D61—41no—
325C4×D61—41no—
326C4×D61—41no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61#12011yescharacteristic
335C4×D61#12111yescharacteristic
336C4×D61#12111yescharacteristic
337C4×D61#12111yescharacteristic
338C4×D61#12111yescharacteristic
339C4×D61#12111yescharacteristic
340C4×D61#12111yescharacteristic
341C4×D61#12311yescharacteristic
342C4×D61#12311yescharacteristic
343C4×D61#12311yescharacteristic
344C4×D61#12411yescharacteristic
345C4×D61#12411yescharacteristic
346C4×D61#12411yescharacteristic
347C4×D61#12611yescharacteristic
348C4×D61#12611yescharacteristic
349C4×D61#12711yescharacteristic
350#92420—24no—
351#92420—42no—
352C8×C61—22no—
353C8×C61—41no—
354#92418—22no—
355#92418—41no—
356#10922—611nomaximal, Sylow
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61C4×C22⋊C411yescharacteristic
365C22×C61C4×C22⋊C411yescharacteristic
366C22×C61C4×C22⋊C411yescharacteristic
367C22×C61C2×#9711yescharacteristic
368C22×C61C4×M1611yescharacteristic
369C22×C61#40511yescharacteristic
370C22×C61#40511yescharacteristic
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—44no—
379C2×D61—44no—
380C2×D61—44no—
381C2×D61—44no—
382C2×D61#38611yescharacteristic
383C2×D61#38811yescharacteristic
384C2×D61#38811yescharacteristic
385C2×D61#39011yescharacteristic
386C2×D61#40712yes—
387C2×D61#40812yes—
388C2×D61#43212yes—
389C2×D61#43312yes—
390C2×D61#43512yes—
391C2×D61#43512yes—
392C2×D61#43512yes—
393C2×D61#43512yes—
394C2×D61#43512yes—
395C2×D61#43512yes—
396C2×D61#43612yes—
397C2×D61#43612yes—
398#6923—44no—
399#6923—44no—
400C4×C61—41no—
401C4×C61#38611yescharacteristic
402C4×C61#38811yescharacteristic
403C4×C61#38811yescharacteristic
404C4×C61#39011yescharacteristic
405Dic61—41no—
406Dic61#38611yescharacteristic
407Dic61#38811yescharacteristic
408Dic61#38811yescharacteristic
409Dic61#39011yescharacteristic
410C22×C22⋊C8—611no—
411C22×C22⋊C8—611no—
412C22×#97—611no—
413C2×C4×C22⋊C4—611no—
414C2×#336—611no—
415C2×#336—611no—
416C2×#336—611no—
417C2×C61—42no—
418C2×C61#143711yescharacteristic
419C2×C61#174911yescharacteristic
420C2×C61#175011yescharacteristic
421C2×C61#175211yescharacteristic
422C2×C61#175211yescharacteristic
423C2×C61#175311yescharacteristic
424C2×C61#175311yescharacteristic
425D61—42no—
426D61#187012yes—
427D61#192412yes—
428D61#192412yes—
429D61#195512yes—
430C24×C4—611no—
431C23×C8—611no—
432C23×C8—611no—
433C23×C8—611no—
434C23×C8—611no—
435C22×C22⋊C4—612no—
436C22×C42—611no—
437C22×C42—611no—
438C2×C22⋊C8—612no—
439C2×C22⋊C8—612no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—1222no—
444C2×C22⋊C8—1222no—
445C2×C22⋊C8—1222no—
446C2×C22⋊C8—1222no—
447C2×C22⋊C8#692311yescharacteristic, complemented
448C2×#97—1222no—
449C2×#97—1222no—
450C2×#97—1222no—
451C4×C22⋊C4—1222no—
452C4×C22⋊C4—1222no—
453C2×#95—612no—
454#336—1222no—
455#336—1222no—
456#336—1222no—
457C61#1092211yescharacteristic, complemented, Sylow
458C25—611no—
459C23×C4—611no—
460C23×C4—612no—
461C23×C4—612no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4—1221no—
470C23×C4—1221no—
471C23×C4—1221no—
472C23×C4—1221no—
473C23×C4—1221no—
474C23×C4—1221no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4—1221no—
478C23×C4C2×#692311yescharacteristic
479C22×C8—612no—
480C22×C8—612no—
481C22×C8—612no—
482C22×C8—611no—
483C22×C8—612no—
484C22×C8—612no—
485C22×C8—612no—
486C22×C8—611no—
487C22×C8—1221no—
488C22×C8—1221no—
489C22×C8—1221no—
490C22×C8—1221no—
491C22×C8—1221no—
492C22×C8—1221no—
493C22×C8—1221no—
494C22×C8—1221no—
495C22×C8—1221no—
496C22×C8—1221no—
497C22×C8—1221no—
498C22×C8—1221no—
499C22×C8—1221no—
500C22×C8—1221no—
501C22×C8—1221no—
502C22×C8—1221no—
503C22×C8—1221no—
504C22×C8—1221no—
505C22×C8—1221no—
506C22×C8—1221no—
507C22×C8C2×#692311yescharacteristic
508C22×C8C2×#692311yescharacteristic
509C2×C22⋊C4—1224no—
510C2×C22⋊C4—1224no—
511C2×C22⋊C4—1224no—
512C2×C42—612no—
513C2×C42—612no—
514C2×C42—1221no—
515C2×C42—1221no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42—1221no—
520C2×C42—1221no—
521C2×C42—1221no—
522C2×C42—1221no—
523C2×C42—1221no—
524C22⋊C8—22no—
525C22⋊C8—1222no—
526C22⋊C8—1222no—
527C22⋊C8—1224no—
528C22⋊C8—1224no—
529C22⋊C8—1222no—
530#97—1228no—
531#95—1224no—
532C24—611no—
533C24—614no—
534C24—611no—
535C24—1221no—
536C24—1222no—
537C24—1221no—
538C24—1221no—
539C24—1221no—
540C24—1221no—
541C24—1221no—
542C24—1222no—
543C24—1222no—
544C24C4×#692311yescharacteristic
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—614no—
565C22×C4—614no—
566C22×C4—611no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—2441no—
604C22×C4—2441no—
605C22×C4—2441no—
606C22×C4—2441no—
607C22×C4—2441no—
608C22×C4—2441no—
609C22×C4—2441no—
610C22×C4—2441no—
611C22×C4—2441no—
612C22×C4—2441no—
613C22×C4—2441no—
614C22×C4—2441no—
615C22×C4—2441no—
616C22×C4—2441no—
617C22×C4—2441no—
618C22×C4—2441no—
619C22×C4C4×#692311yescharacteristic
620C22×C4C22×#692311yescharacteristic
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—614no—
627C2×C8—612no—
628C2×C8—1222no—
629C2×C8—1222no—
630C2×C8—1222no—
631C2×C8—1222no—
632C2×C8—1222no—
633C2×C8—1222no—
634C2×C8—1222no—
635C2×C8—1222no—
636C2×C8—1222no—
637C2×C8—1222no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1222no—
641C2×C8—1222no—
642C2×C8—1222no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—2441no—
647C2×C8—2441no—
648C2×C8—2441no—
649C2×C8—2441no—
650C2×C8—2441no—
651C2×C8—2441no—
652C2×C8—2441no—
653C2×C8—2441no—
654C2×C8C22⋊#692312yescomplemented
655C22⋊C4—12216no—
656C42—1222no—
657C42—1222no—
658C42—1222no—
659C42—1222no—
660C42—2441no—
661C42—2441no—
662C42—2441no—
663C42—2441no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—612no—
671C23—612no—
672C23—612no—
673C23—612no—
674C23—611no—
675C23—611no—
676C23—611no—
677C23—611no—
678C23—611no—
679C23—611no—
680C23—612no—
681C23—1224no—
682C23—1224no—
683C23—1224no—
684C23—1224no—
685C23—1224no—
686C23—1224no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23—1221no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2442no—
698C23—2442no—
699C23—2442no—
700C23—2442no—
701C23—2442no—
702C23—2442no—
703C23#1451983112yescomplemented
704C23C2×C4×#692311yescharacteristic
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—611no—
713C2×C4—611no—
714C2×C4—611no—
715C2×C4—611no—
716C2×C4—611no—
717C2×C4—611no—
718C2×C4—611no—
719C2×C4—611no—
720C2×C4—611no—
721C2×C4—611no—
722C2×C4—611no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—611no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—611no—
732C2×C4—611no—
733C2×C4—611no—
734C2×C4—1224no—
735C2×C4—1224no—
736C2×C4—1224no—
737C2×C4—1224no—
738C2×C4—1224no—
739C2×C4—1224no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4C2×C22⋊#692311yescharacteristic
768C2×C4#1451985611yescharacteristic
769C2×C4D4×#692311yescharacteristic
770C2×C4D4×#692311yescharacteristic
771C2×C4D4×#692311yescharacteristic
772C2×C4D4×#692311yescharacteristic
773C8—22no—
774C8—41no—
775C8—1224no—
776C8—1222no—
777C8—2442no—
778C8—2441no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—611no—
787C22—611no—
788C22—611no—
789C22—611no—
790C22—612no—
791C22—612no—
792C22—612no—
793C22—612no—
794C22—612no—
795C22—612no—
796C22—612no—
797C22—612no—
798C22—612no—
799C22—612no—
800C22—612no—
801C22—612no—
802C22—1222no—
803C22—1222no—
804C22—1222no—
805C22—2444no—
806C22—2444no—
807C22—2444no—
808C22—2444no—
809C22—2441no—
810C22—2441no—
811C22—2441no—
812C22—2441no—
813C22C4×C22⋊#692311yescharacteristic
814C22C22⋊C4×#692311yescharacteristic
815C22C22⋊C4×#692311yescharacteristic
816C22C2×#1451983111yescharacteristic
817C22M16×#692311yescharacteristic
818C22#1684072511yescharacteristic
819C22#1684072811yescharacteristic
820C4—41no—
821C4—611no—
822C4—611no—
823C4—611no—
824C4—611no—
825C4—2444no—
826C4—2444no—
827C4—2441no—
828C4#1684071011yescharacteristic
829C4#1684071211yescharacteristic
830C4#1684071211yescharacteristic
831C4#1684071411yescharacteristic
832C2—42no—
833C2—612no—
834C2—612no—
835C2—612no—
836C2—612no—
837C2—2442no—
838C2#2146100011yescharacteristic
839C2#2146154711yescharacteristic
840C2#2146155011yescharacteristic
841C2#2146155511yescharacteristic
842C2#2146155811yescharacteristic
843C2#2146155911yescharacteristic
844C2#2146156211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×#6923
commutator, socleC23×C61C2×C42
FittingC2×C22⋊C8×C61C4
prime radicalC24×D61C2×C4
cosocleC22×C4×D61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#10922
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#14519831C2semidirect
4. C2×(C2×#6923)⋊C8C2semidirect
5. C2×(C2×#6923)⋊C8C2semidirect
6. C2×(C2×#6923)⋊C8C2semidirect
13. C2×#14519834C4semidirect
16. C2×C22⋊#92420C4semidirect
29. C2×C22⋊#92418C4semidirect
30. C2×#14519689C4semidirect
31. C2×#14519689C4semidirect
34. C2×C22⋊C8×C61C4semidirect
204. C2×#92420C22⋊C4semidirect
226. C2×C8×C61C22⋊C4semidirect
232. C2×#92418C22⋊C4semidirect
247. C23×C61#97semidirect
271. C22×D61#97semidirect
447. C2×C22⋊C8#6923semidirect
457. C61#10922semidirect
654. C2×C8C22⋊#6923semidirect
703. C23#14519831semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊(C22⋊C8)2
C22×#145198312
C2×C4×C22⋊#69232
C2×(C2×#6923)⋊C82
C2×C22⋊C8×D612
#1092261