Finite Group Databasebeta

← #30620142

Subgroups — #30620142

Order 15616.

1544 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462557C212yesmaximal, complemented
2C2×#16840748C211yesmaximal, characteristic, complemented
3C22×#14519837C211yesmaximal, characteristic, complemented
4#21461963C212yesmaximal, complemented
5#21461846C212yesmaximal, complemented
6#21461845C212yesmaximal, complemented
7#21461683C211yesmaximal, characteristic, complemented
8#21461655C211yesmaximal, characteristic, complemented
9#21461651C211yesmaximal, characteristic, complemented
10C4×#14519837C211yesmaximal, characteristic, complemented
11C2×#16840402C211yesmaximal, characteristic
12C2×D61⋊M16C2212yescomplemented
13C22×#11758217C2212yes—
14#16840795—22no—
15#16840794—22no—
16#16840791—22no—
17#16840789—22no—
18#16840765C2212yescomplemented
19#16840748—24no—
20C2×#14519838C2212yescomplemented
21C2×#14519838C2212yescomplemented
22C2×#14519837—24no—
23C2×#14519837C2211yescharacteristic
24C2×#14519837C2212yes—
25C2×#14519837C2211yescharacteristic
26C2×#14519837C2211yescharacteristic
27C2×#14519837C2212yes—
28C2×#14519837C2211yescharacteristic
29#16840734C2212yescomplemented
30#16840732C2212yes—
31C4×#11758217C2212yescomplemented
32#16840642C2212yescomplemented
33#16840642C2212yescomplemented
34C22×#11758222C2211yescharacteristic
35C23×C22⋊D61C2211yescharacteristic
36#16840402—22no—
37#16840402—22no—
38#16840402—22no—
39#16840402—22no—
40C2×#14519763C2211yescharacteristic
41C2×#14519760C411yescharacteristic
42C2×#14519759C411yescharacteristic
43C2×#14519754C2211yescharacteristic
44C2×#14519751C411yescharacteristic
45C2×#14519750C411yescharacteristic
46C2×#14519750C2211yescharacteristic
47C2×#14519747C411yescharacteristic
48C2×#14519746C411yescharacteristic
49C2×C4×C22⋊D61C2211yescharacteristic
50C2×#14519737C2211yescharacteristic
51C2×C22⋊C4×D61C411yescharacteristic
52C22×C22⋊C4×C61C411yescharacteristic
53C2×#11758213—22no—
54D61⋊M16—24no—
55D61⋊M16—42no—
56C2×#11758217—22no—
57C2×#11758217—24no—
58C2×#11758217—42no—
59C2×#11758217C2312yes—
60C2×#11758217C2312yes—
61C2×#11758217C2312yes—
62C2×#11758217C2312yes—
63C2×D61⋊C8—22no—
64C22×#92420—22no—
65#14519844—22no—
66C4⋊#92420—22no—
67#14519838—24no—
68#14519838—42no—
69#14519837—22no—
70#14519837—22no—
71#14519837—22no—
72#14519837—24no—
73#14519837—42no—
74#14519837D414yescomplemented
75#14519834—22no—
76#14519834—22no—
77C22⋊#92420—22no—
78C22⋊#92420—22no—
79#14519832—22no—
80C4×#92420—22no—
81C24×D61C2×C411yescharacteristic
82C2×#11758222—22no—
83C2×#11758222—22no—
84C2×#11758222—22no—
85C2×#11758222—22no—
86C2×#11758222—42no—
87C22×Dic122C2311yescharacteristic
88C22×D244C2×C411yescharacteristic
89C22×D244C2×C411yescharacteristic
90C22×C22⋊D61—22no—
91C22×C22⋊D61—22no—
92C22×C22⋊D61—22no—
93C22×C22⋊D61—22no—
94C22×C22⋊D61—42no—
95C22×C22⋊D61C2×C411yescharacteristic
96C22×C22⋊D61C2×C411yescharacteristic
97C22×C22⋊D61C2×C411yescharacteristic
98C22×C22⋊D61C2×C411yescharacteristic
99C22×C22⋊D61C2×C411yescharacteristic
100C22×C22⋊D61C2311yescharacteristic
101C22×C22⋊D61C2311yescharacteristic
102C23×Dic61C2311yescharacteristic
103C22×C4×D61C2×C411yescharacteristic
104C22×C4×D61C2×C411yescharacteristic
105C22×C4×D61C2311yescharacteristic
106#14519763—22no—
107#14519763—22no—
108#14519760—22no—
109#14519760—22no—
110#14519759—22no—
111#14519759—22no—
112#14519754—22no—
113#14519754—22no—
114#14519751—22no—
115#14519751—22no—
116#14519750—22no—
117#14519750—22no—
118#14519750—22no—
119#14519750—22no—
120#14519747—22no—
121#14519747—22no—
122#14519746—22no—
123#14519746—22no—
124C4×C22⋊D61—22no—
125C4×C22⋊D61—22no—
126#14519737D412yes—
127#14519737D412yes—
128#14519737D412yes—
129#14519737D412yes—
130C2×C4⋊Dic61C2×C411yescharacteristic
131C2×#11758196C2×C411yescharacteristic
132C2×#11758196C2×C411yescharacteristic
133C2×#11758196C2311yescharacteristic
134C2×C22⋊Dic61C2×C411yescharacteristic
135C2×C22⋊Dic61C2×C411yescharacteristic
136C2×C22⋊Dic61C2×C411yescharacteristic
137C2×#11758198C2×C411yescharacteristic
138C2×#11758198C2×C411yescharacteristic
139C2×#11758198C2×C411yescharacteristic
140C2×#11758198C2×C411yescharacteristic
141C2×#11758198C2×C411yescharacteristic
142C22⋊C4×D61—21no—
143C22⋊C4×D61—21no—
144C22⋊C4×D61—21no—
145C22⋊C4×D61—21no—
146C2×C4×Dic61C2311yescharacteristic
147C25×C61C2×C411yescharacteristic
148C23×C4×C61C2×C411yescharacteristic
149C23×C4×C61C2×C411yescharacteristic
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61C2×C411yescharacteristic
155C2×C22⋊C4×C61C2×C411yescharacteristic
156C2×C22⋊C4×C61C2×C411yescharacteristic
157C2×C22⋊C4×C61C2×C411yescharacteristic
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—22no—
161C24×C61—41no—
162C24×C61—42no—
163C24×C61—81no—
164C24×C61C22×C411yescharacteristic
165C24×C61C22×C411yescharacteristic
166C24×C61C22×C411yescharacteristic
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—22no—
170C23×D61—41no—
171C23×D61—42no—
172C23×D61—81no—
173C23×D61C22×C411yescharacteristic
174C23×D61C22×C411yescharacteristic
175C23×D61C22×C411yescharacteristic
176C22×C4×C61—22no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—41no—
182C22×C4×C61—81no—
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C22×C411yescharacteristic
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—22no—
194C2×C22⋊D61—22no—
195C2×C22⋊D61—21no—
196C2×C22⋊D61—22no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—44no—
201C2×C22⋊D61—44no—
202C2×C22⋊D61—44no—
203C2×C22⋊D61—44no—
204C2×C22⋊D61—41no—
205C2×C22⋊D61—41no—
206C2×C22⋊D61—41no—
207C2×C22⋊D61—42no—
208C2×C22⋊D61—81no—
209C2×C22⋊D61C22⋊C412yes—
210C2×C22⋊D61C22⋊C412yes—
211C2×C22⋊D61C2×D412yes—
212C2×C22⋊D61#4112yes—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—22no—
216C22×Dic61C22×C411yescharacteristic
217C22×Dic61C22×C411yescharacteristic
218C22×Dic61C22×C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C2×D412yes—
221C22×Dic61C2×D412yes—
222C22×Dic61C2411yescharacteristic
223#11758222—44no—
224#11758222—44no—
225#11758222—44no—
226#11758222—44no—
227C2×D244—22no—
228C2×D244—22no—
229C2×D244—22no—
230C2×D244—41no—
231C2×D244—81no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—41no—
241C2×C4×D61—81no—
242C2×C4×D61C2×D412yes—
243C2×C4×D61C2×D412yes—
244C2×Dic122—21no—
245C2×Dic122—22no—
246C2×Dic122—21no—
247C2×Dic122—22no—
248#11758217—22no—
249#11758217—22no—
250#11758217—22no—
251#11758217—22no—
252#11758217—22no—
253#11758217—22no—
254#11758217—22no—
255#11758217—44no—
256#11758217C2×D414yes—
257C2×#92420—22no—
258C2×#92420—22no—
259C2×#92420—22no—
260C2×#92420—22no—
261C2×#92420—44no—
262#11758213—44no—
263D61⋊C8—44no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61C22⋊C411yescharacteristic
271C22⋊C4×C61C22⋊C411yescharacteristic
272C22⋊C4×C61C22⋊C411yescharacteristic
273C22⋊C4×C61C22⋊C411yescharacteristic
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61—22no—
277C22⋊Dic61—22no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—22no—
283#11758198—22no—
284#11758198C22⋊C412yes—
285#11758198C22⋊C412yes—
286C4⋊Dic61—22no—
287#11758196—22no—
288#11758196—22no—
289#11758196C22⋊C412yes—
290#11758196C22⋊C412yes—
291C4×Dic61C2×D412yes—
292C4×Dic61C2×D412yes—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—22no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—41no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—42no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—42no—
310C23×C61—81no—
311C23×C61—81no—
312C23×C61—84no—
313C23×C61—84no—
314C23×C61C2×C22⋊C411yescharacteristic
315C23×C61C2×C22⋊C411yescharacteristic
316C23×C61C4×D412yes—
317C23×C61C23×C411yescharacteristic
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—81no—
336C22×D61—81no—
337C22×D61—84no—
338C22×D61—84no—
339C22×D61C2×C22⋊C412yes—
340C22×D61C4×D412yes—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—41no—
348C2×C4×C61—42no—
349C2×C4×C61—42no—
350C2×C4×C61—41no—
351C2×C4×C61—81no—
352C2×C4×C61—81no—
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C2×C22⋊C411yescharacteristic
357C22⋊D61—24no—
358C22⋊D61—24no—
359C22⋊D61—24no—
360C22⋊D61—42no—
361C22⋊D61—44no—
362C22⋊D61—44no—
363C22⋊D61—44no—
364C22⋊D61—42no—
365C22⋊D61—42no—
366C22⋊D61—82no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61C2×C22⋊C412yes—
380C2×Dic61C2×C22⋊C412yes—
381C2×Dic61C22×D411yescharacteristic
382C2×Dic61C22×D412yes—
383C2×Dic61C2×#4111yescharacteristic
384C2×Dic61H(5,𝔽2)12yes—
385D244—44no—
386D244—82no—
387C4×D61—22no—
388C4×D61—22no—
389C4×D61—22no—
390C4×D61—22no—
391C4×D61—42no—
392C4×D61—42no—
393C4×D61—81no—
394C4×D61—81no—
395Dic122—42no—
396Dic122—42no—
397#92420—24no—
398#92420—42no—
399#92420—42no—
400#92420—42no—
401#22408—611nomaximal, Sylow
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61—22no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—42no—
411C22×C61—42no—
412C22×C61—42no—
413C22×C61—42no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—84no—
420C22×C61—81no—
421C22×C61—81no—
422C22×C61—84no—
423C22×C61#41312yescomplemented
424C22×C61C22×C22⋊C411yescharacteristic
425C22×C61C2×C4×D411yescharacteristic
426C22×C61#51811yescharacteristic
427C2×D61—22no—
428C2×D61—22no—
429C2×D61—22no—
430C2×D61—22no—
431C2×D61—42no—
432C2×D61—41no—
433C2×D61—41no—
434C2×D61—42no—
435C2×D61—41no—
436C2×D61—41no—
437C2×D61—41no—
438C2×D61—81no—
439C2×D61—81no—
440C2×D61—84no—
441C2×D61—84no—
442C2×D61—81no—
443C2×D61—81no—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—41no—
449C4×C61—41no—
450Dic61—22no—
451Dic61—22no—
452Dic61—41no—
453Dic61—41no—
454Dic61D4212yes—
455Dic61#54612yes—
456C2×#546—611no—
457D4×M16—612no—
458C2×#413—611no—
459C22×#100—611no—
460#1967—612no—
461#1901—612no—
462#1900—612no—
463#1800—611no—
464#1785—611no—
465#1783—611no—
466C4×#100—611no—
467C2×C61—21no—
468C2×C61—21no—
469C2×C61—22no—
470C2×C61—41no—
471C2×C61—42no—
472C2×C61—81no—
473C2×C61D4×C22⋊C411yescharacteristic
474C2×C61C2×#41311yescharacteristic
475C2×C61#288811yescharacteristic
476D61—42no—
477D61—42no—
478D61—81no—
479C22×#41—611no—
480C23×D4—611no—
481C22×M16—612no—
482C22×M16—612no—
483#546—1222no—
484#546—1222no—
485#546—1222no—
486#546—1222no—
487C2×#124—611no—
488C2×#123—611no—
489C2×#123—611no—
490C2×C22⋊Q8—611no—
491C2×#121—611no—
492C2×#121—611no—
493C2×#121—611no—
494C2×#120—611no—
495C2×#120—611no—
496C2×C4×D4—611no—
497C2×C4×D4—611no—
498C22×C22⋊C4—611no—
499C22×C22⋊C4#692311yescharacteristic
500#436—1222no—
501#435—1222no—
502#435—1222no—
503C8×D4—1222no—
504#423—612no—
505#413—1224no—
506C2×#101—612no—
507C2×#101—612no—
508C2×#100—611no—
509C2×#100—611no—
510C2×#100—611no—
511C2×#100—612no—
512C2×#100—611no—
513C2×#100—612no—
514C2×#100—1224no—
515#407—612no—
516#407—612no—
517C4×M16—612no—
518#343—612no—
519#343—612no—
520C61#2240811yescharacteristic, complemented, Sylow
521C25—611no—
522C25C2×#692311yescharacteristic
523C2×#41—1222no—
524C2×#41—1222no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—2442no—
528C22×Q8—611no—
529C22×D4—611no—
530C22×D4—611no—
531C22×D4—611no—
532C22×D4—611no—
533C22×D4—611no—
534C22×D4—611no—
535C22×D4—611no—
536C22×D4—611no—
537C22×D4—611no—
538C22×D4—1222no—
539C22×D4—1222no—
540C22×D4—1222no—
541C22×D4—1222no—
542C22×D4—2442no—
543C23×C4—611no—
544C23×C4—611no—
545C23×C4—611no—
546C23×C4—611no—
547C23×C4C2×#692311yescharacteristic
548C23×C4C2×#692311yescharacteristic
549C2×M16—612no—
550C2×M16—612no—
551C2×M16—612no—
552C2×M16—612no—
553C2×M16—1222no—
554C2×M16—1222no—
555C2×M16—1224no—
556C2×M16—1224no—
557C2×M16—2442no—
558C2×M16—2442no—
559C22×C8—1222no—
560C22×C8—1222no—
561#124—1222no—
562#124—1222no—
563#123—1222no—
564#123—1222no—
565#123—1222no—
566#123—1222no—
567C22⋊Q8—1222no—
568C22⋊Q8—1222no—
569#121—1222no—
570#121—1222no—
571#121—1222no—
572#121—1222no—
573#121—1222no—
574#121—1222no—
575#120—1222no—
576#120—1222no—
577#120—1222no—
578#120—1222no—
579C4×D4—612no—
580C4×D4—612no—
581C4×D4—612no—
582C4×D4—612no—
583C4×D4—1222no—
584C4×D4—1222no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—611no—
594C2×C22⋊C4—611no—
595C2×C22⋊C4—611no—
596C2×C22⋊C4—611no—
597C2×C22⋊C4—611no—
598C2×C22⋊C4—611no—
599C2×C22⋊C4—611no—
600C2×C22⋊C4—611no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4C2×#692311yescharacteristic
606C2×C22⋊C4C2×#692311yescharacteristic
607C2×C22⋊C4C2×#692311yescharacteristic
608C2×C22⋊C4C2×#692311yescharacteristic
609C2×C42—611no—
610C4⋊C8—1222no—
611C4⋊C8—1222no—
612#101—1224no—
613#101—2442no—
614#100—614no—
615#100—1224no—
616#100—1222no—
617#100—1222no—
618#100—1222no—
619#100—2442no—
620C22⋊C8—1222no—
621C22⋊C8—1222no—
622C22⋊C8—1222no—
623C22⋊C8—1222no—
624#97—1222no—
625C4×C8—1222no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—41no—
630C24—42no—
631C24—81no—
632C24—611no—
633C24—611no—
634C24—611no—
635C24—1222no—
636C24—1221no—
637C24—1221no—
638C24—4881no—
639C24—2441no—
640C24—2442no—
641C24C22×#692311yescharacteristic
642C24C22×#692311yescharacteristic
643C24C22×#692311yescharacteristic
644#41—2444no—
645#41—2444no—
646#41—2444no—
647#41—2444no—
648C2×Q8—1221no—
649C2×Q8—1222no—
650C2×Q8—1222no—
651C2×Q8—1221no—
652C2×D4—612no—
653C2×D4—612no—
654C2×D4—612no—
655C2×D4—612no—
656C2×D4—1222no—
657C2×D4—1222no—
658C2×D4—1222no—
659C2×D4—1222no—
660C2×D4—1222no—
661C2×D4—1221no—
662C2×D4—1222no—
663C2×D4—1222no—
664C2×D4—1222no—
665C2×D4—1222no—
666C2×D4—1221no—
667C2×D4—1222no—
668C2×D4—1222no—
669C2×D4—1222no—
670C2×D4—1222no—
671C2×D4—1222no—
672C2×D4—4881no—
673C2×D4—4881no—
674C2×D4—2441no—
675C2×D4—2444no—
676C2×D4—2444no—
677C2×D4—2444no—
678C2×D4—2444no—
679C2×D4—2441no—
680C2×D4—2441no—
681C2×D4—2441no—
682C2×D4—2442no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—41no—
689C22×C4—81no—
690C22×C4—611no—
691C22×C4—612no—
692C22×C4—612no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—612no—
696C22×C4—612no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—1221no—
700C22×C4—1222no—
701C22×C4—1221no—
702C22×C4—1222no—
703C22×C4—1221no—
704C22×C4—1222no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—4881no—
711C22×C4—2441no—
712C22×C4C22×#692311yescharacteristic
713C22×C4C22×#692311yescharacteristic
714C22×C4C22×#692311yescharacteristic
715C22×C4C22×#692311yescharacteristic
716M16—614no—
717M16—1222no—
718M16—1222no—
719M16—1222no—
720M16—1222no—
721M16—1222no—
722M16—1222no—
723M16—1222no—
724M16—2444no—
725M16—2444no—
726C2×C8—1222no—
727C2×C8—1222no—
728C2×C8—1222no—
729C2×C8—1222no—
730C2×C8—2444no—
731C2×C8—2444no—
732C4⋊C4—612no—
733C4⋊C4—612no—
734C4⋊C4—1222no—
735C4⋊C4—1222no—
736C4⋊C4—1222no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—612no—
744C22⋊C4—612no—
745C22⋊C4—1222no—
746C22⋊C4—1222no—
747C22⋊C4—1222no—
748C22⋊C4—1222no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4C22⋊#692311yescharacteristic
756C22⋊C4C22⋊#692311yescharacteristic
757C22⋊C4C22⋊#692311yescharacteristic
758C22⋊C4C22⋊#692311yescharacteristic
759C42—612no—
760C42—612no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—41no—
770C23—42no—
771C23—42no—
772C23—41no—
773C23—41no—
774C23—42no—
775C23—41no—
776C23—41no—
777C23—42no—
778C23—81no—
779C23—81no—
780C23—84no—
781C23—84no—
782C23—612no—
783C23—612no—
784C23—1221no—
785C23—1221no—
786C23—1221no—
787C23—1221no—
788C23—1221no—
789C23—1221no—
790C23—1221no—
791C23—4881no—
792C23—4881no—
793C23—4884no—
794C23—4884no—
795C23—2441no—
796C23—2441no—
797C23—2442no—
798C23—2442no—
799C23—2441no—
800C23—2441no—
801C23—2442no—
802C23—2441no—
803C23—2441no—
804C23—2442no—
805C23C2×C22⋊#692311yescharacteristic
806C23C2×C22⋊#692311yescharacteristic
807C23D4×#692312yes—
808C23C23×#692311yescharacteristic
809Q8—2442no—
810Q8—2442no—
811D4—1224no—
812D4—1224no—
813D4—1224no—
814D4—4882no—
815D4—4882no—
816D4—2444no—
817D4—2442no—
818D4—2442no—
819D4—2442no—
820D4—2444no—
821D4—2444no—
822D4—2444no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—612no—
836C2×C4—611no—
837C2×C4—611no—
838C2×C4—612no—
839C2×C4—612no—
840C2×C4—612no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—4881no—
856C2×C4—4881no—
857C2×C4—2442no—
858C2×C4—2442no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4C2×C22⋊#692311yescharacteristic
862C2×C4C2×C22⋊#692311yescharacteristic
863C2×C4C2×C22⋊#692311yescharacteristic
864C2×C4C2×C22⋊#692311yescharacteristic
865C8—1224no—
866C8—2442no—
867C8—2442no—
868C8—2442no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—22no—
874C22—21no—
875C22—21no—
876C22—21no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—84no—
887C22—81no—
888C22—81no—
889C22—84no—
890C22—1222no—
891C22—1222no—
892C22—1222no—
893C22—1222no—
894C22—4881no—
895C22—4881no—
896C22—4884no—
897C22—4881no—
898C22—4881no—
899C22—4884no—
900C22—2442no—
901C22—2442no—
902C22—2441no—
903C22—2441no—
904C22—2441no—
905C22—2441no—
906C22—2441no—
907C22#1684074812yescomplemented
908C22C22×C22⋊#692311yescharacteristic
909C22C2×D4×#692311yescharacteristic
910C22#1684082911yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—41no—
916C4—41no—
917C4—612no—
918C4—612no—
919C4—1222no—
920C4—1222no—
921C4—2441no—
922C4—2441no—
923C2—21no—
924C2—21no—
925C2—22no—
926C2—41no—
927C2—42no—
928C2—81no—
929C2—4881no—
930C2—2442no—
931C2—2442no—
932C2D4×C22⋊#692311yescharacteristic
933C2C2×#1684074811yescharacteristic
934C2#2146242911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840402C2
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61#22408
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #21462557C2semidirect
2. C2×#16840748C2semidirect
3. C22×#14519837C2semidirect
4. #21461963C2semidirect
5. #21461846C2semidirect
6. #21461845C2semidirect
7. #21461683C2semidirect
8. #21461655C2semidirect
9. #21461651C2semidirect
10. C4×#14519837C2semidirect
12. C2×D61⋊M16C22semidirect
18. #16840765C22semidirect
20. C2×#14519838C22semidirect
21. C2×#14519838C22semidirect
29. #16840734C22semidirect
31. C4×#11758217C22semidirect
32. #16840642C22semidirect
33. #16840642C22semidirect
74. #14519837D4semidirect
423. C22×C61#413semidirect
520. C61#22408semidirect
907. C22#16840748semidirect

Maximal subgroups

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

subgroupindex
#214625572
C2×#168407482
C22×#145198372
#214619632
#214618462
#214618452
#214616832
#214616552
#214616512
C4×#145198372
C2×#168404022
#2240861