Finite Group Databasebeta

← #29646316

Subgroups — #29646316

Order 15616.

996 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840466C211yesmaximal, characteristic
2#21454855C211yesmaximal, characteristic
3#21454850C211yesmaximal, characteristic
4#21444183C211yesmaximal, characteristic, complemented
5#21444181C211yesmaximal, characteristic, complemented
6#21444181C211yesmaximal, characteristic, complemented
7#21444173C211yesmaximal, characteristic, complemented
8#21444173C211yesmaximal, characteristic, complemented
9#21444161C211yesmaximal, characteristic, complemented
10#21444148C211yesmaximal, characteristic, complemented
11#21444147C211yesmaximal, characteristic, complemented
12#21444141C211yesmaximal, characteristic, complemented
13C2×#16839487C211yesmaximal, characteristic, complemented
14#324×D61C211yesmaximal, characteristic, complemented
15C61×#1472C211yesmaximal, characteristic, complemented
16#16840466—21no—
17#16840466—21no—
18#16840466—21no—
19#16840466—21no—
20#16840466—21no—
21#16840466—21no—
22#16840466—21no—
23#16840466—21no—
24C2×#14519775C411yescharacteristic
25C2×#14519767C411yescharacteristic
26C2×#14519767C2211yescharacteristic
27C2×#14519755C411yescharacteristic
28C2×#14519755C2211yescharacteristic
29C2×#14519754C411yescharacteristic
30C2×#14519754C411yescharacteristic
31C2×#14519753C411yescharacteristic
32C2×#14519742C2211yescharacteristic
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×#14519737C411yescharacteristic
35C2×#14519737C411yescharacteristic
36C22×#11758196C2211yescharacteristic
37C2×C4⋊C4×D61C2211yescharacteristic
38#16839838—21no—
39#16839837—21no—
40#16839836—21no—
41#16839833—21no—
42#16839831—21no—
43#16839830—21no—
44C8×C22⋊D61—21no—
45#16839825—21no—
46#16839816C2211yescharacteristic
47#16839816C2211yescharacteristic
48#16839812C2211yescharacteristic
49#16839812C2211yescharacteristic
50#16839726C2211yescharacteristic
51#16839724C2211yescharacteristic
52#16839724C2211yescharacteristic
53C2×C22⋊#92418C2211yescharacteristic
54C22⋊C8×D61C2211yescharacteristic
55C22⋊C8×D61C2211yescharacteristic
56#16839488C2211yescharacteristic
57#16839488C2211yescharacteristic
58#16839488C2211yescharacteristic
59#16839488C2211yescharacteristic
60#16839487C2211yescharacteristic
61#16839487C2211yescharacteristic
62#16839487C2211yescharacteristic
63#16839487C2211yescharacteristic
64#16839487C2211yescharacteristic
65#16839487C2211yescharacteristic
66#16839487C2211yescharacteristic
67#16839487C2211yescharacteristic
68C2×C22⋊Q8×C61C2211yescharacteristic
69C61×#407C2211yescharacteristic
70C2×C22⋊C8×C61C2211yescharacteristic
71C61×#324C2211yescharacteristic
72C61×#324C2211yescharacteristic
73C61×#324C2211yescharacteristic
74C61×#324C2211yescharacteristic
75C22×Dic122C2×C411yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×C22⋊D61C2×C411yescharacteristic
78C23×Dic61C2×C411yescharacteristic
79C23×Dic61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C2×#11758194—21no—
84C2×#11758189—21no—
85C2×#11758189—21no—
86C22×#92418—21no—
87C2×C8×D61—21no—
88C2×C8×D61—21no—
89#14519775—21no—
90#14519775—21no—
91#14519775—21no—
92#14519775—21no—
93#14519767—21no—
94#14519767—21no—
95#14519767—21no—
96#14519767—21no—
97#14519767—21no—
98#14519767—21no—
99#14519767—21no—
100#14519767—21no—
101#14519755—21no—
102#14519755—21no—
103#14519755—21no—
104#14519755—21no—
105#14519755—21no—
106#14519755—21no—
107#14519755—21no—
108#14519755—21no—
109#14519754—21no—
110#14519754—21no—
111#14519754—21no—
112#14519754—21no—
113#14519754—21no—
114#14519754—21no—
115#14519754—21no—
116#14519754—21no—
117#14519753—21no—
118#14519753—21no—
119#14519753—21no—
120#14519753—21no—
121#14519742—21no—
122#14519742—21no—
123#14519742—21no—
124#14519742—21no—
125C4×C22⋊D61D411yescharacteristic
126C4×C22⋊D61D411yescharacteristic
127C4×C22⋊D61D411yescharacteristic
128C4×C22⋊D61D411yescharacteristic
129C4×C22⋊D61D411yescharacteristic
130C4×C22⋊D61D411yescharacteristic
131C4×C22⋊D61D411yescharacteristic
132C4×C22⋊D61D411yescharacteristic
133#14519737—21no—
134#14519737—21no—
135#14519737—21no—
136#14519737—21no—
137#14519737—21no—
138#14519737—21no—
139#14519737—21no—
140#14519737—21no—
141C2×C4⋊Dic61C2×C411yescharacteristic
142C2×C4⋊Dic61C2×C411yescharacteristic
143C2×#11758196—21no—
144C2×#11758196—21no—
145C2×#11758196—21no—
146C2×#11758196—21no—
147C2×#11758196C2×C411yescharacteristic
148C2×#11758196C2×C411yescharacteristic
149C2×#11758196C2×C411yescharacteristic
150C2×#11758196C2×C411yescharacteristic
151C2×#11758196C2×C411yescharacteristic
152C2×#11758196C2×C411yescharacteristic
153C2×#11758196C2×C411yescharacteristic
154C2×#11758196C2×C411yescharacteristic
155C2×#11758196C2×C411yescharacteristic
156C2×#11758196C2311yescharacteristic
157C2×#11758196C2311yescharacteristic
158C4⋊C4×D61—21no—
159C4⋊C4×D61—21no—
160C4⋊C4×D61—21no—
161C4⋊C4×D61—21no—
162C2×C22⋊Dic61C2×C411yescharacteristic
163C2×#11758198C2×C411yescharacteristic
164C2×#11758198C2×C411yescharacteristic
165C2×#11758198C2×C411yescharacteristic
166C2×C4×Dic61C2×C411yescharacteristic
167C2×C4×Dic61C2×C411yescharacteristic
168C2×C4×Dic61C2311yescharacteristic
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418—21no—
174C22⋊#92418—21no—
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177C22⋊#92418C2311yescharacteristic
178C22⋊#92418C2311yescharacteristic
179#14519689—21no—
180#14519689—21no—
181#14519689—21no—
182#14519689—21no—
183#14519687—21no—
184#14519687—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C22×Q8×C61C2×C411yescharacteristic
188C23×C4×C61C2311yescharacteristic
189C2×M16×C61—21no—
190C22×C8×C61—21no—
191C22⋊Q8×C61—21no—
192C22⋊Q8×C61—21no—
193C22⋊Q8×C61—21no—
194C22⋊Q8×C61—21no—
195C2×C4⋊C4×C61C2×C411yescharacteristic
196C2×C4⋊C4×C61C2311yescharacteristic
197C2×C4⋊C4×C61C2311yescharacteristic
198C2×C22⋊C4×C61C2×C411yescharacteristic
199C2×C22⋊C4×C61C2×C411yescharacteristic
200C22⋊C8×C61—21no—
201C22⋊C8×C61—21no—
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204C22⋊C8×C61C2311yescharacteristic
205C22⋊C8×C61C2311yescharacteristic
206C24×C61C22×C411yescharacteristic
207C23×D61C22×C411yescharacteristic
208C2×Q8×C61—21no—
209C2×Q8×C61—21no—
210C2×Q8×C61—81no—
211C22×C4×C61—81no—
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2411yescharacteristic
222C2×C22⋊D61—24no—
223C2×C22⋊D61C22⋊C411yescharacteristic
224C2×C22⋊D61C22⋊C411yescharacteristic
225C2×C22⋊D61C22⋊C411yescharacteristic
226C2×C22⋊D61C22⋊C411yescharacteristic
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—22no—
232C22×Dic61—41no—
233C22×Dic61—81no—
234C22×Dic61C22×C411yescharacteristic
235C22×Dic61C22×C411yescharacteristic
236C22×Dic61C22×C411yescharacteristic
237C22×Dic61C22×C411yescharacteristic
238C22×Dic61C22×C411yescharacteristic
239C22×Dic61C22×C411yescharacteristic
240C22×Dic61C22×C411yescharacteristic
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—22no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—41no—
247C2×C4×D61—81no—
248C2×C4×D61—81no—
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×Dic122—21no—
254C2×Dic122—21no—
255C2×Dic122—22no—
256C2×Dic122—21no—
257C2×Dic122—21no—
258C2×Dic122—41no—
259C2×Dic122—81no—
260M16×C61—81no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—81no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊Dic61C22⋊C411yescharacteristic
277C22⋊Dic61C22⋊C411yescharacteristic
278C22⋊Dic61C22⋊C411yescharacteristic
279C22⋊Dic61C22⋊C411yescharacteristic
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198C22⋊C411yescharacteristic
285#11758198C22⋊C411yescharacteristic
286#11758198C22⋊C411yescharacteristic
287#11758198C22⋊C411yescharacteristic
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196C22⋊C411yescharacteristic
313#11758196C22⋊C411yescharacteristic
314#11758196C22⋊C411yescharacteristic
315#11758196C22⋊C411yescharacteristic
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324#11758194—81no—
325C2×#92418—21no—
326C2×#92418—21no—
327C2×#92418—21no—
328C2×#92418—21no—
329C2×#92418—81no—
330#11758189—81no—
331#11758189—81no—
332C8×D61—81no—
333C8×D61—81no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—22no—
337C23×C61—41no—
338C23×C61C2×C22⋊C411yescharacteristic
339C23×C61C2×C22⋊C411yescharacteristic
340C23×C61C23×C411yescharacteristic
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—22no—
344C22×D61—41no—
345C22×D61C2×C22⋊C411yescharacteristic
346C22×D61C2×C22⋊C411yescharacteristic
347Q8×C61—81no—
348Q8×C61—81no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C22⋊D61—22no—
370C22⋊D61—22no—
371C22⋊D61—22no—
372C22⋊D61#10114yes—
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—22no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—41no—
384C2×Dic61—42no—
385C2×Dic61—42no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—81no—
389C2×Dic61—81no—
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61#13112yes—
397C4×D61—41no—
398C4×D61—41no—
399C4×D61—41no—
400C4×D61—41no—
401C4×D61—42no—
402C4×D61—42no—
403C4×D61—81no—
404C4×D61—81no—
405Dic122—42no—
406Dic122—42no—
407Dic122—81no—
408Dic122—81no—
409C8×C61—41no—
410C8×C61—41no—
411C8×C61—41no—
412C8×C61—41no—
413#92418—41no—
414#92418—41no—
415#92418—41no—
416#92418—41no—
417#17426—611nomaximal, Sylow
418C22×C61—21no—
419C22×C61—21no—
420C22×C61—21no—
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61C2×#10112yes—
428C22×C61C22×C22⋊C411yescharacteristic
429C22×C61C2×#13111yescharacteristic
430C22×C61#56811yescharacteristic
431C2×D61—21no—
432C2×D61—21no—
433C2×D61—21no—
434C2×D61—21no—
435C2×D61—21no—
436C2×D61—42no—
437C2×D61—42no—
438C2×D61C2×#10112yes—
439C4×C61—21no—
440C4×C61—21no—
441C4×C61—21no—
442C4×C61—21no—
443C4×C61—41no—
444C4×C61—41no—
445C4×C61—41no—
446C4×C61—41no—
447Dic61—22no—
448Dic61—21no—
449Dic61—21no—
450Dic61—21no—
451Dic61—21no—
452Dic61—21no—
453Dic61—41no—
454Dic61—41no—
455Dic61—41no—
456Dic61C2×#10112yes—
457C2×#554—611no—
458#2974—611no—
459#2974—611no—
460#1472—611no—
461#1472—611no—
462#1472—611no—
463#1472D6111yescharacteristic, complemented
464#1470—611no—
465#1470—611no—
466#1467—611no—
467#1463—611no—
468#1463—611no—
469#1461—611no—
470C2×#324—611no—
471C2×#324—611no—
472C2×C61—21no—
473C2×C61—21no—
474C2×C61—22no—
475C2×C61—41no—
476C2×C61#288011yescharacteristic
477C2×C61#288311yescharacteristic
478C2×C61C22×#10111yescharacteristic
479D61—22no—
480D61—41no—
481#554—1221no—
482#554—1221no—
483#554—1221no—
484#554—1221no—
485#554—1221no—
486#554—1221no—
487#554—1221no—
488#554—1221no—
489C2×C4⋊Q8—611no—
490C2×#125—611no—
491C2×#125—611no—
492C2×C22⋊Q8—611no—
493C2×C22⋊Q8—611no—
494C2×C22⋊Q8—611no—
495C2×C22⋊Q8—611no—
496C2×C22⋊Q8—611no—
497C2×C22⋊Q8C2×D6111yescharacteristic
498C2×C4×Q8—611no—
499C2×C4×D4—611no—
500C2×C4×D4—611no—
501C2×C4×D4—611no—
502C22×C4⋊C4—611no—
503C22×C4⋊C4—611no—
504#436—1221no—
505#436—1221no—
506#435—1221no—
507#435—1221no—
508#435—1221no—
509#435—1221no—
510C8×D4—1221no—
511C8×D4—1221no—
512#432—611no—
513#432—611no—
514#431—611no—
515#431—611no—
516#407—611no—
517#407—611no—
518#407—611no—
519#407C2×D6111yescharacteristic
520C2×C22⋊C8—611no—
521C2×C22⋊C8—611no—
522C2×C22⋊C8—611no—
523C2×C22⋊C8C2×D6111yescharacteristic
524#324—611no—
525#324—611no—
526#324—611no—
527#324—611no—
528#324—611no—
529#324—611no—
530#324—611no—
531#324—611no—
532#324—611no—
533#324—611no—
534#324—611no—
535#324—611no—
536#324C2×D6111yescharacteristic
537#324C2×D6111yescharacteristic
538#324C2×D6111yescharacteristic
539#324C2×D6111yescharacteristic
540C61#1742611yescharacteristic, complemented, Sylow
541C22×Q8—611no—
542C22×Q8—611no—
543C22×Q8C4×D6111yescharacteristic
544C22×D4—611no—
545C23×C4—611no—
546C23×C4—611no—
547C23×C4—611no—
548C23×C4—611no—
549C23×C4—611no—
550C23×C4C22×D6111yescharacteristic
551C2×M16—21no—
552C2×M16—1221no—
553C2×M16—1221no—
554C2×M16—1221no—
555C22×C8—21no—
556C22×C8—1221no—
557C22×C8—1221no—
558C22×C8—1221no—
559C4⋊Q8—1221no—
560C4⋊Q8—1221no—
561C4⋊Q8—1221no—
562C4⋊Q8—1221no—
563#125—1221no—
564#125—1221no—
565#125—1221no—
566#125—1221no—
567#125—1221no—
568#125—1221no—
569#125—1221no—
570#125—1221no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—1221no—
576C22⋊Q8—1221no—
577C22⋊Q8—1221no—
578C22⋊Q8—1221no—
579C22⋊Q8—1221no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583C22⋊Q8—1221no—
584C22⋊Q8—1221no—
585C22⋊Q8—1221no—
586C22⋊Q8—1221no—
587C22⋊Q8—1221no—
588C22⋊Q8—1221no—
589C22⋊Q8—1221no—
590C22⋊Q8—1221no—
591C22⋊Q8—1221no—
592C22⋊Q8—1221no—
593C22⋊Q8—1221no—
594C22⋊Q8—1221no—
595C4×Q8—1221no—
596C4×Q8—1221no—
597C4×Q8—1221no—
598C4×Q8—1221no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—611no—
603C4×D4—611no—
604C4×D4—611no—
605C4×D4—611no—
606C4×D4—611no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4—1221no—
615C2×C4⋊C4—611no—
616C2×C4⋊C4—611no—
617C2×C4⋊C4—611no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—611no—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4—1221no—
632C2×C4⋊C4—1221no—
633C2×C4⋊C4—1221no—
634C2×C4⋊C4—1221no—
635C2×C4⋊C4—1221no—
636C2×C4⋊C4C4×D6111yescharacteristic
637C2×C4⋊C4C22×D6111yescharacteristic
638C2×C4⋊C4C22×D6111yescharacteristic
639C2×C22⋊C4—611no—
640C2×C22⋊C4—611no—
641C2×C22⋊C4—611no—
642C2×C22⋊C4—611no—
643C2×C22⋊C4C4×D6111yescharacteristic
644C2×C22⋊C4C4×D6111yescharacteristic
645C2×C42—611no—
646C2×C42—611no—
647C2×C42—611no—
648C4⋊C8—1221no—
649C4⋊C8—1221no—
650C4⋊C8—1221no—
651C4⋊C8—1221no—
652C22⋊C8—21no—
653C22⋊C8—21no—
654C22⋊C8—611no—
655C22⋊C8—611no—
656C22⋊C8—611no—
657C22⋊C8—611no—
658C22⋊C8—1221no—
659C22⋊C8—1221no—
660C22⋊C8—1221no—
661C22⋊C8—1221no—
662C22⋊C8—1221no—
663C22⋊C8—1221no—
664C22⋊C8C22×D6111yescharacteristic
665C22⋊C8C22×D6111yescharacteristic
666C22⋊C8C22×D6111yescharacteristic
667C22⋊C8C22×D6111yescharacteristic
668#97—1221no—
669#97—1221no—
670C4×C8—1221no—
671C4×C8—1221no—
672C24—611no—
673C24C2×C4×D6111yescharacteristic
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—81no—
677C2×Q8—1221no—
678C2×Q8—1221no—
679C2×Q8—1221no—
680C2×Q8—1221no—
681C2×Q8—1222no—
682C2×Q8—4881no—
683C2×Q8—2441no—
684C2×D4—611no—
685C2×D4—611no—
686C2×D4—611no—
687C2×D4—611no—
688C2×D4—1224no—
689C22×C4—81no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—1222no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1222no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—4881no—
712C22×C4—4881no—
713C22×C4—4881no—
714C22×C4—2441no—
715C22×C4—2441no—
716C22×C4C2×C4×D6111yescharacteristic
717C22×C4C2×C4×D6111yescharacteristic
718C22×C4C2×C4×D6111yescharacteristic
719C22×C4C2×C4×D6111yescharacteristic
720C22×C4C2×C4×D6111yescharacteristic
721C22×C4D4×D6111yescharacteristic
722C22×C4D4×D6111yescharacteristic
723C22×C4D4×D6111yescharacteristic
724C22×C4D4×D6111yescharacteristic
725C22×C4C23×D6111yescharacteristic
726M16—81no—
727M16—4881no—
728M16—4881no—
729M16—4881no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—81no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—4881no—
740C2×C8—4881no—
741C2×C8—4881no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—611no—
781C22⋊C4—611no—
782C22⋊C4—611no—
783C22⋊C4—611no—
784C22⋊C4—611no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C42—611no—
793C42—611no—
794C42—611no—
795C42—611no—
796C42—1221no—
797C42—1221no—
798C42—1221no—
799C42—1221no—
800C23—22no—
801C23—21no—
802C23—21no—
803C23—41no—
804C23—611no—
805C23—611no—
806C23—1222no—
807C23—1221no—
808C23—1221no—
809C23—2441no—
810C23C22⋊C4×D6111yescharacteristic
811C23C22⋊C4×D6111yescharacteristic
812C23C22×C4×D6111yescharacteristic
813Q8—81no—
814Q8—81no—
815Q8—4881no—
816Q8—4881no—
817Q8—2442no—
818Q8—2442no—
819D4—614no—
820D4—1222no—
821D4—1222no—
822D4—1222no—
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—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—611no—
840C2×C4—611no—
841C2×C4—611no—
842C2×C4—611no—
843C2×C4—611no—
844C2×C4—611no—
845C2×C4—612no—
846C2×C4—1222no—
847C2×C4—1221no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—4881no—
857C2×C4—4881no—
858C2×C4—4881no—
859C2×C4—4881no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2442no—
865C2×C4—2442no—
866C2×C4—2441no—
867C2×C4—2442no—
868C2×C4—2442no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4C22⋊C4×D6111yescharacteristic
872C2×C4C22⋊C4×D6111yescharacteristic
873C2×C4C2×D4×D6111yescharacteristic
874C2×C4C2×D4×D6111yescharacteristic
875C8—41no—
876C8—41no—
877C8—41no—
878C8—41no—
879C8—2441no—
880C8—2441no—
881C8—2441no—
882C8—2441no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—21no—
889C22—21no—
890C22—42no—
891C22—42no—
892C22—612no—
893C22—1221no—
894C22—1221no—
895C22—1221no—
896C22—1221no—
897C22—1221no—
898C22—2442no—
899C22—2442no—
900C22#101×D6112yes—
901C22C2×C22⋊C4×D6111yescharacteristic
902C22#131×D6111yescharacteristic
903C22#1684052711yescharacteristic
904C4—21no—
905C4—21no—
906C4—21no—
907C4—21no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—612no—
913C4—1222no—
914C4—1221no—
915C4—1221no—
916C4—1221no—
917C4—1221no—
918C4—1221no—
919C4—2441no—
920C4—2441no—
921C4—2441no—
922C2—21no—
923C2—21no—
924C2—22no—
925C2—41no—
926C2—1222no—
927C2—2441no—
928C2#2145426711yescharacteristic
929C2#2145427711yescharacteristic
930C2C2×#101×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1472C2
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1472D61
hypocenterC61#17426
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
4. #21444183C2semidirect
5. #21444181C2semidirect
6. #21444181C2semidirect
7. #21444173C2semidirect
8. #21444173C2semidirect
9. #21444161C2semidirect
10. #21444148C2semidirect
11. #21444147C2semidirect
12. #21444141C2semidirect
13. C2×#16839487C2semidirect
14. #324×D61C2semidirect
15. C61×#1472C2semidirect
463. #1472D61semidirect
540. C61#17426semidirect

Maximal subgroups

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

subgroupindex
C2×#168404662
#214548552
#214548502
#214441832
#214441812
#214441732
#214441612
#214441482
#214441472
#214441412
C2×#168394872
#324×D612
C61×#14722
#1742661