Finite Group Databasebeta

← #29700780

Subgroups — #29700780

Order 15616.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455037C211yesmaximal, characteristic
2C2×#16839876C211yesmaximal, characteristic, complemented
3#21454544C211yesmaximal, characteristic, complemented
4#21454268C211yesmaximal, characteristic, complemented
5#21446704C211yesmaximal, characteristic, complemented
6#21446520C211yesmaximal, characteristic, complemented
7#21446470C211yesmaximal, characteristic, complemented
8#21446262C211yesmaximal, characteristic, complemented
9#21446144C211yesmaximal, characteristic, complemented
10#21446143C211yesmaximal, characteristic, complemented
11#21446092C211yesmaximal, characteristic, complemented
12#21446024C211yesmaximal, characteristic, complemented
13#21445657C211yesmaximal, characteristic, complemented
14C4×C22⋊#92418C211yesmaximal, characteristic, complemented
15C22×#104×C61C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519785C2211yescharacteristic, complemented
19C2×#14519784C2211yescharacteristic
20C2×#14519784C2211yescharacteristic
21#16840273C2211yescharacteristic
22#16839924C411yescharacteristic, complemented
23#16839924C411yescharacteristic, complemented
24#16839918C411yescharacteristic, complemented
25#16839913C411yescharacteristic, complemented
26#16839907C411yescharacteristic, complemented
27#16839907C411yescharacteristic, complemented
28#16839901C411yescharacteristic, complemented
29#16839896C411yescharacteristic, complemented
30#16839876—24no—
31#16839838—21no—
32#16839833—21no—
33#16839831—21no—
34C8×C22⋊D61—21no—
35C2×#14519712C2211yescharacteristic, complemented
36C2×#14519712C2211yescharacteristic, complemented
37#16839790C2211yescharacteristic, complemented
38C2×#14519705C2211yescharacteristic, complemented
39C2×#14519705C2211yescharacteristic, complemented
40#16839758C2211yescharacteristic
41#16839758C2211yescharacteristic
42#16839730C2211yescharacteristic, complemented
43#16839729—21no—
44#16839729—21no—
45#16839729C2211yescharacteristic
46#16839729C2211yescharacteristic
47#16839726—21no—
48#16839726C2211yescharacteristic
49C2×C22⋊#92418—21no—
50C2×C22⋊#92418C2211yescharacteristic
51C2×C22⋊#92418C2211yescharacteristic
52#16839720C2211yescharacteristic, complemented
53C2×C4×#92418C2211yescharacteristic, complemented
54C2×C4×#92418C2211yescharacteristic, complemented
55#16839526C2211yescharacteristic, complemented
56#16839526C2211yescharacteristic, complemented
57#16839522C2211yescharacteristic, complemented
58#16839522C2211yescharacteristic, complemented
59#16839517C2211yescharacteristic, complemented
60#16839517C2211yescharacteristic, complemented
61C22×#41×C61C2211yescharacteristic
62C22×M16×C61C2211yescharacteristic
63C22×C42×C61C2211yescharacteristic
64C2×#104×C61—24no—
65C2×#104×C61C2211yescharacteristic
66C2×#104×C61C2211yescharacteristic
67C2×#104×C61C2211yescharacteristic
68C2×#104×C61C2211yescharacteristic
69C2×#11758222C2311yescharacteristic
70#14519797—22no—
71#14519797—22no—
72#14519797—41no—
73#14519797—41no—
74C2×#11758202C2×C411yescharacteristic, complemented
75C2×#11758202C2×C411yescharacteristic, complemented
76C2×#11758200C2×C411yescharacteristic, complemented
77C2×#11758200C2×C411yescharacteristic, complemented
78C2×#11758201C2×C411yescharacteristic, complemented
79C2×#11758201C2×C411yescharacteristic, complemented
80C2×#11758199C2×C411yescharacteristic, complemented
81C2×#11758199C2×C411yescharacteristic, complemented
82#14519785—22no—
83#14519785—41no—
84#14519784—22no—
85#14519784—22no—
86#14519784—41no—
87#14519784—41no—
88C2×#11758194—21no—
89C2×#11758194—21no—
90C2×#11758194C2311yescharacteristic
91C2×#11758194C2311yescharacteristic
92C2×#11758189—21no—
93C22×#92418—21no—
94C22×#92418—21no—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C2×C8×D61—21no—
100#14519760—21no—
101#14519756C2×C411yescharacteristic
102#14519756C2×C411yescharacteristic
103#14519751C2×C411yescharacteristic
104#14519751C2×C411yescharacteristic
105#14519746—21no—
106C4×C22⋊D61—21no—
107C4×C22⋊D61—21no—
108#14519736C2311yescharacteristic
109#14519712—22no—
110#14519712—41no—
111#14519706—21no—
112#14519706—21no—
113#14519705—22no—
114#14519705—41no—
115#14519701C2×C411yescharacteristic, complemented
116#14519701C2×C411yescharacteristic, complemented
117#14519701C2×C411yescharacteristic, complemented
118#14519701C2×C411yescharacteristic, complemented
119#14519698C2×C411yescharacteristic, complemented
120#14519698C2×C411yescharacteristic, complemented
121#14519698C2×C411yescharacteristic, complemented
122#14519698C2×C411yescharacteristic, complemented
123C22⋊#92418—21no—
124C22⋊#92418—21no—
125C22⋊#92418—21no—
126C22⋊#92418—21no—
127C22⋊#92418—21no—
128C22⋊#92418—21no—
129C22⋊#92418C2×C411yescharacteristic
130C22⋊#92418C2×C411yescharacteristic
131C22⋊#92418C2×C411yescharacteristic
132C22⋊#92418C2×C411yescharacteristic
133C22⋊#92418D411yescharacteristic
134C22⋊#92418D411yescharacteristic
135C22⋊#92418D411yescharacteristic
136C22⋊#92418D411yescharacteristic
137#14519689—21no—
138#14519689—21no—
139#14519687—21no—
140C4×#92418—22no—
141C4×#92418—41no—
142C8×Dic61—21no—
143C2×#41×C61—21no—
144C2×#41×C61—21no—
145C2×#41×C61—22no—
146C2×#41×C61—22no—
147C2×#41×C61—41no—
148C2×#41×C61—41no—
149C2×#41×C61C2×C411yescharacteristic
150C2×#41×C61C2×C411yescharacteristic
151C2×#41×C61C2311yescharacteristic
152C2×#41×C61C2311yescharacteristic
153C22×Q8×C61C2×C411yescharacteristic
154C22×D4×C61—21no—
155C22×D4×C61C2×C411yescharacteristic
156C23×C4×C61—21no—
157C23×C4×C61—21no—
158C23×C4×C61C2311yescharacteristic
159C2×M16×C61—21no—
160C2×M16×C61—22no—
161C2×M16×C61—41no—
162C2×M16×C61C2311yescharacteristic
163C2×M16×C61C2311yescharacteristic
164C22×C8×C61—21no—
165C2×C42×C61—22no—
166C2×C42×C61—21no—
167C2×C42×C61—41no—
168C2×C42×C61C2311yescharacteristic
169C2×C42×C61C2311yescharacteristic
170#104×C61—22no—
171#104×C61—22no—
172#104×C61—22no—
173#104×C61D414yescomplemented
174C24×C61—21no—
175C24×C61#4111yescharacteristic
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—22no—
179#41×C61—22no—
180#41×C61—21no—
181#41×C61—21no—
182#41×C61—21no—
183#41×C61—21no—
184#41×C61—42no—
185#41×C61—42no—
186#41×C61—41no—
187#41×C61—41no—
188#41×C61—42no—
189#41×C61—42no—
190#41×C61C2×D412yes—
191#41×C61#4112yes—
192C2×Q8×C61—21no—
193C2×Q8×C61—22no—
194C2×Q8×C61—41no—
195C2×Q8×C61C22×C411yescharacteristic
196C2×Q8×C61C22×C411yescharacteristic
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—41no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61C22×C411yescharacteristic
207C2×D4×C61C22×C411yescharacteristic
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—24no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—42no—
221C22×C4×C61—42no—
222C22×C4×C61—42no—
223C22×C4×C61—42no—
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61#4111yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233#11758222—21no—
234#11758222—21no—
235#11758222—21no—
236#11758222—21no—
237C2×D244C22×C411yescharacteristic
238C2×C4×D61—21no—
239C2×Dic122C22×C411yescharacteristic
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—42no—
244M16×C61C2×D412yes—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—42no—
248C42×C61—21no—
249C42×C61—21no—
250C42×C61—21no—
251C42×C61—42no—
252C42×C61C2×D412yes—
253C22⋊Dic61—21no—
254C22⋊Dic61—21no—
255C22⋊Dic61—21no—
256#11758202—22no—
257#11758202—41no—
258#11758201—22no—
259#11758201—41no—
260#11758200—22no—
261#11758200—41no—
262#11758199—22no—
263#11758199—41no—
264#11758198—21no—
265#11758198—21no—
266C4⋊Dic61C22×C411yescharacteristic
267C4⋊Dic61C22×C411yescharacteristic
268#11758196—21no—
269#11758196—21no—
270C4×Dic61—21no—
271#11758194—21no—
272#11758194—21no—
273#11758194—21no—
274#11758194—21no—
275#11758194—42no—
276#11758194—42no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—42no—
288C2×#92418—42no—
289C2×#92418C22×C411yescharacteristic
290C2×#92418C22×C411yescharacteristic
291C2×#92418C22×C411yescharacteristic
292C2×#92418C22×C411yescharacteristic
293C2×#92418C2×D411yescharacteristic
294C2×#92418C2×D411yescharacteristic
295C2×#92418C2×D411yescharacteristic
296C2×#92418C2×D411yescharacteristic
297#11758189—42no—
298C8×D61—42no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—22no—
303C23×C61—21no—
304C23×C61—41no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—81no—
308C23×C61C4×D411yescharacteristic
309C23×C61C4×D411yescharacteristic
310C23×C61C2×#4111yescharacteristic
311C22×D61—21no—
312Q8×C61—21no—
313Q8×C61—21no—
314Q8×C61—21no—
315Q8×C61—42no—
316Q8×C61C4×D412yes—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—21no—
320D4×C61—21no—
321D4×C61—21no—
322D4×C61—42no—
323D4×C61—42no—
324D4×C61—42no—
325D4×C61—41no—
326D4×C61—41no—
327D4×C61C4×D412yes—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—21no—
331C2×C4×C61—22no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—22no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—22no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—22no—
345C2×C4×C61—21no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61—48no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61C4×D411yescharacteristic
355C2×C4×C61C4×D411yescharacteristic
356C2×C4×C61C23×C411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C2×#4111yescharacteristic
360C2×C4×C61H(5,𝔽2)11yescharacteristic
361C2×C4×C61H(5,𝔽2)11yescharacteristic
362C22⋊D61—41no—
363C22⋊D61—41no—
364C22⋊D61—42no—
365C22⋊D61—81no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369D244—21no—
370D244—21no—
371C4×D61—41no—
372C4×D61—41no—
373Dic122—21no—
374Dic122—21no—
375C8×C61—22no—
376C8×C61—41no—
377#92418—21no—
378#92418—21no—
379#92418—21no—
380#92418—21no—
381#92418—21no—
382#92418—21no—
383#92418—21no—
384#92418—21no—
385#92418—41no—
386#92418—41no—
387#22888—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—22no—
394C22×C61—21no—
395C22×C61—21no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—84no—
404C22×C61#44312yescomplemented
405C22×C61C2×C4×D411yescharacteristic
406C22×C61#54611yescharacteristic
407C22×C61#55111yescharacteristic
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C4×C61—24no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—22no—
415C4×C61—42no—
416C4×C61—41no—
417C4×C61C2×C4×D411yescharacteristic
418C4×C61#51811yescharacteristic
419C4×C61D4211yescharacteristic
420C4×C61#54611yescharacteristic
421Dic61—41no—
422Dic61—41no—
423Dic61—41no—
424#3002—611no—
425C2×#443—611no—
426#2933—611no—
427C22×#104D6111yescharacteristic, complemented
428#2880—611no—
429#1974—611no—
430#1937—611no—
431#1929—611no—
432#1896—611no—
433#1876—611no—
434#1876—611no—
435#1866—611no—
436#1855—611no—
437#1764—611no—
438C4×C22⋊C8—611no—
439C2×C61—21no—
440C2×C61—22no—
441C2×C61—21no—
442C2×C61—41no—
443C2×C61—42no—
444C2×C61—81no—
445C2×C61#235811yescharacteristic
446C2×C61C2×#44311yescharacteristic
447C2×C61#295611yescharacteristic
448D61—81no—
449C22×#41C2×D6111yescharacteristic
450C2×#135—611no—
451C2×#135—611no—
452C2×#131—611no—
453C2×#131—611no—
454C2×#131—611no—
455C22×M16C2×D6111yescharacteristic
456#525—611no—
457C22×C42C2×D6111yescharacteristic
458#452—611no—
459#452—611no—
460#451—611no—
461#450—611no—
462#449—611no—
463#449—611no—
464#448—611no—
465#447—611no—
466#443—1224no—
467#436—1221no—
468#435—1221no—
469#435—1221no—
470C8×D4—1221no—
471C2×#108—611no—
472C2×#108—611no—
473#424—611no—
474C2×#104—24no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104C2×D6111yescharacteristic
478C2×#104C2×D6111yescharacteristic
479C2×#104C2×D6111yescharacteristic
480C2×#104C2×D6111yescharacteristic
481#416—611no—
482#416—611no—
483#408—611no—
484#408—611no—
485#408—611no—
486#408—1221no—
487#408—1221no—
488#407—611no—
489#407—1221no—
490C2×C22⋊C8—611no—
491C2×C22⋊C8—611no—
492C2×C22⋊C8—1221no—
493#405—611no—
494C2×C4×C8—611no—
495C2×C4×C8—611no—
496#341—611no—
497#341—611no—
498#339—611no—
499#339—611no—
500#336—611no—
501#336—611no—
502C61#2288811yescharacteristic, complemented, Sylow
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—611no—
510C2×#41C4×D6111yescharacteristic
511C2×#41C4×D6111yescharacteristic
512C2×#41C22×D6111yescharacteristic
513C2×#41C22×D6111yescharacteristic
514C22×Q8C4×D6111yescharacteristic
515C22×D4—21no—
516C22×D4C4×D6111yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C22×D6111yescharacteristic
520#135—1222no—
521#135—1222no—
522#135—2441no—
523#135—2441no—
524C2×Q16—611no—
525C2×Q16—611no—
526C2×SD16—611no—
527C2×SD16—611no—
528C2×SD16—611no—
529C2×SD16—611no—
530C2×D8—611no—
531C2×D8—611no—
532#131—1222no—
533#131—1222no—
534#131—1222no—
535#131—2441no—
536#131—2441no—
537#131—2441no—
538C2×M16—21no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—611no—
542C2×M16—611no—
543C2×M16—1221no—
544C2×M16—1221no—
545C2×M16—1221no—
546C2×M16C22×D6111yescharacteristic
547C2×M16C22×D6111yescharacteristic
548C22×C8—21no—
549C22×C8—611no—
550C22×C8—611no—
551C22×C8—611no—
552C22×C8—611no—
553C22×C8—1221no—
554C22×C8—1221no—
555C22×C8—1221no—
556#123—1221no—
557C22⋊Q8—611no—
558C22⋊Q8—611no—
559#121—611no—
560#121—611no—
561#120—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564#117—611no—
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C22×D6111yescharacteristic
569C2×C42C22×D6111yescharacteristic
570#108—1222no—
571#108—2441no—
572C4⋊C8—1221no—
573C4⋊C8—1221no—
574#104—22no—
575#104—22no—
576#104—22no—
577#104—1222no—
578#104—2441no—
579#104C22⋊D6114yescomplemented
580#103—611no—
581#103—611no—
582#103—611no—
583#103—611no—
584#102—611no—
585#102—611no—
586#102—611no—
587#102—611no—
588C22⋊C8—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
595C22⋊C8—611no—
596C22⋊C8—1221no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601C22⋊C8—1221no—
602C22⋊C8—1221no—
603C22⋊C8—1221no—
604#97—1221no—
605C4×C8—1221no—
606C4×C8—1222no—
607C4×C8—2441no—
608C24—21no—
609C24#1175822411yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—42no—
619#41—42no—
620#41—41no—
621#41—41no—
622#41—42no—
623#41—42no—
624#41—1221no—
625#41—1221no—
626#41—1221no—
627#41—1221no—
628#41#1175822212yes—
629#41C2×C22⋊D6112yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8—611no—
634C2×Q8C2×C4×D6111yescharacteristic
635C2×Q8C2×C4×D6111yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—611no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4C2×C4×D6111yescharacteristic
650C2×D4C2×C4×D6111yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—1221no—
668C22×C4C2×C4×D6111yescharacteristic
669C22×C4C2×C4×D6111yescharacteristic
670C22×C4D4×D6111yescharacteristic
671C22×C4D4×D6111yescharacteristic
672C22×C4#1175822411yescharacteristic
673C22×C4C23×D6111yescharacteristic
674Q16—1222no—
675Q16—2441no—
676SD16—1222no—
677SD16—1222no—
678SD16—2441no—
679SD16—2441no—
680D8—1222no—
681D8—2441no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—1221no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—2442no—
691M16—2442no—
692M16—2442no—
693M16C2×C22⋊D6112yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—42no—
697C2×C8—611no—
698C2×C8—611no—
699C2×C8—611no—
700C2×C8—611no—
701C2×C8—611no—
702C2×C8—611no—
703C2×C8—611no—
704C2×C8—611no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—2442no—
716C2×C8—2442no—
717C2×C8—2442no—
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C22⋊C4—1221no—
723C22⋊C4—1221no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—42no—
731C42—1221no—
732C42C2×C22⋊D6112yes—
733C23—21no—
734C23—22no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—81no—
742C23—1221no—
743C23#1451973711yescharacteristic
744C23#1451973711yescharacteristic
745C23C2×#1175822411yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—42no—
750Q8—1221no—
751Q8—1221no—
752Q8C4×C22⋊D6112yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—1221no—
764D4—1221no—
765D4—4881no—
766D4—2442no—
767D4—2441no—
768D4—2441no—
769D4C4×C22⋊D6112yes—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4#1451973711yescharacteristic
802C2×C4#1451973711yescharacteristic
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C22×C22⋊D6111yescharacteristic
806C2×C4C2×#1175822211yescharacteristic
807C2×C4#1451982211yescharacteristic
808C2×C4#1451982211yescharacteristic
809C8—22no—
810C8—41no—
811C8—1221no—
812C8—1221no—
813C8—1221no—
814C8—1221no—
815C8—1221no—
816C8—1221no—
817C8—1221no—
818C8—1221no—
819C8—2441no—
820C8—2441no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—84no—
837C22—2441no—
838C22—2441no—
839C22—2441no—
840C22#1683987612yescomplemented
841C22C2×#1451973711yescharacteristic
842C22#1684040611yescharacteristic
843C22#1684043811yescharacteristic
844C4—24no—
845C4—21no—
846C4—21no—
847C4—22no—
848C4—42no—
849C4—41no—
850C4—2441no—
851C4—2441no—
852C4—2441no—
853C4C2×C4×C22⋊D6111yescharacteristic
854C4#1684023511yescharacteristic
855C4D4×C22⋊D6111yescharacteristic
856C4#1684040211yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—4881no—
864C2#2144879811yescharacteristic
865C2C2×#1683987611yescharacteristic
866C2#2145472511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#104×C61C2
socleC22×C61C2×C4×D4
prime radical#21455037C2
cosocleC22×C4×C61C24
hypercenterC22×#104D61
hypocenterC61#22888
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#16839876C2semidirect
3. #21454544C2semidirect
4. #21454268C2semidirect
5. #21446704C2semidirect
6. #21446520C2semidirect
7. #21446470C2semidirect
8. #21446262C2semidirect
9. #21446144C2semidirect
10. #21446143C2semidirect
11. #21446092C2semidirect
12. #21446024C2semidirect
13. #21445657C2semidirect
14. C4×C22⋊#92418C2semidirect
15. C22×#104×C61C2semidirect
18. C2×#14519785C22semidirect
22. #16839924C4semidirect
23. #16839924C4semidirect
24. #16839918C4semidirect
25. #16839913C4semidirect
26. #16839907C4semidirect
27. #16839907C4semidirect
28. #16839901C4semidirect
29. #16839896C4semidirect
35. C2×#14519712C22semidirect
36. C2×#14519712C22semidirect
37. #16839790C22semidirect
38. C2×#14519705C22semidirect
39. C2×#14519705C22semidirect
42. #16839730C22semidirect
52. #16839720C22semidirect
53. C2×C4×#92418C22semidirect
54. C2×C4×#92418C22semidirect
55. #16839526C22semidirect
56. #16839526C22semidirect
57. #16839522C22semidirect
58. #16839522C22semidirect
59. #16839517C22semidirect
60. #16839517C22semidirect
74. C2×#11758202C2×C4semidirect
75. C2×#11758202C2×C4semidirect
76. C2×#11758200C2×C4semidirect
77. C2×#11758200C2×C4semidirect
78. C2×#11758201C2×C4semidirect
79. C2×#11758201C2×C4semidirect
80. C2×#11758199C2×C4semidirect
81. C2×#11758199C2×C4semidirect
115. #14519701C2×C4semidirect
116. #14519701C2×C4semidirect
117. #14519701C2×C4semidirect
118. #14519701C2×C4semidirect
119. #14519698C2×C4semidirect
120. #14519698C2×C4semidirect
121. #14519698C2×C4semidirect
122. #14519698C2×C4semidirect
173. #104×C61D4semidirect
404. C22×C61#443semidirect
427. C22×#104D61semidirect
502. C61#22888semidirect
579. #104C22⋊D61semidirect
840. C22#16839876semidirect

Maximal subgroups

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

subgroupindex
#214550372
C2×#168398762
#214545442
#214542682
#214467042
#214465202
#214464702
#214462622
#214461442
#214461432
#214460922
#214460242
#214456572
C4×C22⋊#924182
C22×#104×C612
#2288861