Finite Group Databasebeta

← #29700765

Subgroups — #29700765

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455037C211yesmaximal, characteristic
2C2×#16839881C211yesmaximal, characteristic, complemented
3#21454544C211yesmaximal, characteristic, complemented
4#21454268C211yesmaximal, characteristic, complemented
5#21446704C211yesmaximal, characteristic, complemented
6#21446527C211yesmaximal, characteristic, complemented
7#21446470C211yesmaximal, characteristic, complemented
8#21446267C211yesmaximal, characteristic, complemented
9#21446144C211yesmaximal, characteristic, complemented
10#21446143C211yesmaximal, characteristic, complemented
11#21446092C211yesmaximal, characteristic, complemented
12#21446024C211yesmaximal, characteristic, complemented
13#21445657C211yesmaximal, characteristic, complemented
14#21445585C211yesmaximal, characteristic, complemented
15C2×C61×#421C211yesmaximal, 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#16839881—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×#14519688C2211yescharacteristic, 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
63C2×#117×C61C2211yescharacteristic
64C61×#421—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
75C2×#11758202C2×C411yescharacteristic
76C2×#11758200C2×C411yescharacteristic
77C2×#11758200C2×C411yescharacteristic
78C2×#11758201C2×C411yescharacteristic
79C2×#11758201C2×C411yescharacteristic
80C2×#11758199C2×C411yescharacteristic
81C2×#11758199C2×C411yescharacteristic
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
116#14519701C2×C411yescharacteristic
117#14519701C2×C411yescharacteristic
118#14519701C2×C411yescharacteristic
119#14519698C2×C411yescharacteristic
120#14519698C2×C411yescharacteristic
121#14519698C2×C411yescharacteristic
122#14519698C2×C411yescharacteristic
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#14519688—22no—
140#14519687—21no—
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×C61C2311yescharacteristic
158C2×M16×C61—21no—
159C2×M16×C61—22no—
160C2×M16×C61—41no—
161C2×M16×C61C2311yescharacteristic
162C2×M16×C61C2311yescharacteristic
163C22×C8×C61—21no—
164#117×C61—22no—
165#117×C61—41no—
166C2×C4⋊C4×C61—21no—
167C2×C22⋊C4×C61—21no—
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—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—42no—
220C22×C4×C61—42no—
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61#4111yescharacteristic
226C22×C4×C61C2411yescharacteristic
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230#11758222—21no—
231#11758222—21no—
232#11758222—21no—
233#11758222—21no—
234C2×D244C22×C411yescharacteristic
235C2×C4×D61—21no—
236C2×Dic122C22×C411yescharacteristic
237M16×C61—21no—
238M16×C61—21no—
239M16×C61—21no—
240M16×C61—42no—
241M16×C61C2×D412yes—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—42no—
245C4⋊C4×C61—42no—
246C22⋊C4×C61—42no—
247C42×C61—21no—
248C42×C61—21no—
249C42×C61—21no—
250C42×C61C2×D412yes—
251C22⋊Dic61—21no—
252C22⋊Dic61—21no—
253C22⋊Dic61—21no—
254#11758202—22no—
255#11758202—41no—
256#11758201—22no—
257#11758201—41no—
258#11758200—22no—
259#11758200—41no—
260#11758199—22no—
261#11758199—41no—
262#11758198—21no—
263#11758198—21no—
264C4⋊Dic61C22×C411yescharacteristic
265C4⋊Dic61C22×C411yescharacteristic
266#11758196—21no—
267#11758196—21no—
268C4×Dic61—21no—
269#11758194—21no—
270#11758194—21no—
271#11758194—21no—
272#11758194—21no—
273#11758194—42no—
274#11758194—42no—
275C2×#92418—21no—
276C2×#92418—21no—
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—42no—
286C2×#92418—42no—
287C2×#92418C22×C411yescharacteristic
288C2×#92418C22×C411yescharacteristic
289C2×#92418C22×C411yescharacteristic
290C2×#92418C22×C411yescharacteristic
291C2×#92418C2×D411yescharacteristic
292C2×#92418C2×D411yescharacteristic
293C2×#92418C2×D411yescharacteristic
294C2×#92418C2×D411yescharacteristic
295#11758189—42no—
296C8×D61—42no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61—81no—
306C23×C61C4×D411yescharacteristic
307C23×C61C4×D411yescharacteristic
308C23×C61C2×#4111yescharacteristic
309C22×D61—21no—
310Q8×C61—21no—
311Q8×C61—21no—
312Q8×C61—21no—
313Q8×C61—42no—
314Q8×C61C4×D412yes—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—21no—
318D4×C61—21no—
319D4×C61—21no—
320D4×C61—42no—
321D4×C61—42no—
322D4×C61—42no—
323D4×C61—41no—
324D4×C61—41no—
325D4×C61C4×D412yes—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—22no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—22no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—22no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61—42no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61C4×D411yescharacteristic
352C2×C4×C61C4×D411yescharacteristic
353C2×C4×C61C23×C411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C2×#4111yescharacteristic
357C2×C4×C61H(5,𝔽2)11yescharacteristic
358C2×C4×C61H(5,𝔽2)11yescharacteristic
359C22⋊D61—42no—
360C22⋊D61—41no—
361C22⋊D61—41no—
362C22⋊D61—81no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366D244—21no—
367D244—21no—
368C4×D61—41no—
369C4×D61—41no—
370Dic122—21no—
371Dic122—21no—
372C8×C61—22no—
373C8×C61—41no—
374#92418—21no—
375#92418—21no—
376#92418—21no—
377#92418—21no—
378#92418—21no—
379#92418—21no—
380#92418—21no—
381#92418—21no—
382#92418—41no—
383#92418—41no—
384#22887—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—22no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—81no—
400C22×C61—81no—
401C22×C61—84no—
402C22×C61C2×C4×D411yescharacteristic
403C22×C61#54611yescharacteristic
404C22×C61#55111yescharacteristic
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—22no—
411C4×C61—42no—
412C4×C61—41no—
413C4×C61—81no—
414C4×C61C2×C4×D411yescharacteristic
415C4×C61#51811yescharacteristic
416C4×C61D4211yescharacteristic
417C4×C61#54611yescharacteristic
418Dic61—41no—
419Dic61—41no—
420Dic61—41no—
421#3002—611no—
422C2×#444—611no—
423#2933—611no—
424C2×#421D6111yescharacteristic, complemented
425#2880—611no—
426#1974—611no—
427#1938—611no—
428#1929—611no—
429#1897—611no—
430#1876—611no—
431#1876—611no—
432#1866—611no—
433#1855—611no—
434#1764—611no—
435#1750—611no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—41no—
439C2×C61—41no—
440C2×C61—42no—
441C2×C61—81no—
442C2×C61#235811yescharacteristic
443C2×C61#295511yescharacteristic
444C2×C61#295711yescharacteristic
445D61—81no—
446C22×#41C2×D6111yescharacteristic
447C2×#135—611no—
448C2×#135—611no—
449C2×#131—611no—
450C2×#131—611no—
451C2×#131—611no—
452C22×M16C2×D6111yescharacteristic
453#525—611no—
454C2×#117C2×D6111yescharacteristic
455#452—611no—
456#452—611no—
457#451—611no—
458#450—611no—
459#449—611no—
460#449—611no—
461#448—611no—
462#447—611no—
463#444—1224no—
464#436—1221no—
465#435—1221no—
466#435—1221no—
467C8×D4—1221no—
468C2×#108—611no—
469C2×#108—611no—
470#424—611no—
471#421—24no—
472C2×#104—611no—
473C2×#104—611no—
474C2×#104C2×D6111yescharacteristic
475C2×#104C2×D6111yescharacteristic
476C2×#104C2×D6111yescharacteristic
477C2×#104C2×D6111yescharacteristic
478#416—611no—
479#416—611no—
480#408—611no—
481#408—611no—
482#408—611no—
483#408—1221no—
484#408—1221no—
485#407—611no—
486#407—1221no—
487C2×C22⋊C8—611no—
488C2×C22⋊C8—611no—
489C2×C22⋊C8—1221no—
490#405—611no—
491C2×#97—611no—
492C2×C4×C8—611no—
493#341—611no—
494#341—611no—
495#339—611no—
496#339—611no—
497#336—611no—
498#336—611no—
499C61#2288711yescharacteristic, complemented, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—611no—
507C2×#41C4×D6111yescharacteristic
508C2×#41C4×D6111yescharacteristic
509C2×#41C22×D6111yescharacteristic
510C2×#41C22×D6111yescharacteristic
511C22×Q8C4×D6111yescharacteristic
512C22×D4—21no—
513C22×D4C4×D6111yescharacteristic
514C23×C4—21no—
515C23×C4C22×D6111yescharacteristic
516#135—1222no—
517#135—1222no—
518#135—2441no—
519#135—2441no—
520C2×Q16—611no—
521C2×Q16—611no—
522C2×SD16—611no—
523C2×SD16—611no—
524C2×SD16—611no—
525C2×SD16—611no—
526C2×D8—611no—
527C2×D8—611no—
528#131—1222no—
529#131—1222no—
530#131—1222no—
531#131—2441no—
532#131—2441no—
533#131—2441no—
534C2×M16—21no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—611no—
538C2×M16—611no—
539C2×M16—1221no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16C22×D6111yescharacteristic
543C2×M16C22×D6111yescharacteristic
544C22×C8—21no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—611no—
548C22×C8—611no—
549C22×C8—1221no—
550C22×C8—1221no—
551C22×C8—1221no—
552#123—1221no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555#121—611no—
556#121—611no—
557#120—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560#117—22no—
561#117—41no—
562#117—611no—
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C22×D6111yescharacteristic
566C2×C42C22×D6111yescharacteristic
567#108—1222no—
568#108—2441no—
569C4⋊C8—1221no—
570C4⋊C8—1221no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—1222no—
575#104—2441no—
576#104C22⋊D6114yescomplemented
577#103—611no—
578#103—611no—
579#103—611no—
580#103—611no—
581#102—611no—
582#102—611no—
583#102—611no—
584#102—611no—
585C22⋊C8—611no—
586C22⋊C8—611no—
587C22⋊C8—611no—
588C22⋊C8—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—1221no—
594C22⋊C8—1221no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601#97—1221no—
602#97—1222no—
603C4×C8—1221no—
604C4×C8—2441no—
605C24—21no—
606C24#1175822411yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—42no—
616#41—42no—
617#41—41no—
618#41—41no—
619#41—42no—
620#41—42no—
621#41—1221no—
622#41—1221no—
623#41—1221no—
624#41—1221no—
625#41#1175822212yes—
626#41C2×C22⋊D6112yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8—611no—
631C2×Q8C2×C4×D6111yescharacteristic
632C2×Q8C2×C4×D6111yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—41no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—611no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4C2×C4×D6111yescharacteristic
647C2×D4C2×C4×D6111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—1221no—
662C22×C4C2×C4×D6111yescharacteristic
663C22×C4C2×C4×D6111yescharacteristic
664C22×C4D4×D6111yescharacteristic
665C22×C4D4×D6111yescharacteristic
666C22×C4#1175822411yescharacteristic
667C22×C4C23×D6111yescharacteristic
668Q16—1222no—
669Q16—2441no—
670SD16—1222no—
671SD16—1222no—
672SD16—2441no—
673SD16—2441no—
674D8—1222no—
675D8—2441no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—42no—
680M16—1221no—
681M16—1221no—
682M16—1221no—
683M16—1221no—
684M16—2442no—
685M16—2442no—
686M16—2442no—
687M16C2×C22⋊D6112yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—42no—
691C2×C8—611no—
692C2×C8—611no—
693C2×C8—611no—
694C2×C8—611no—
695C2×C8—611no—
696C2×C8—611no—
697C2×C8—611no—
698C2×C8—611no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—2442no—
710C2×C8—2442no—
711C2×C8—2442no—
712C4⋊C4—42no—
713C4⋊C4—611no—
714C4⋊C4—611no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C22⋊C4—42no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—1221no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—1221no—
727C42C2×C22⋊D6112yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—81no—
737C23—1221no—
738C23#1451973711yescharacteristic
739C23#1451973711yescharacteristic
740C23C2×#1175822411yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—42no—
745Q8—1221no—
746Q8—1221no—
747Q8C4×C22⋊D6112yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—1221no—
759D4—1221no—
760D4—4881no—
761D4—2442no—
762D4—2441no—
763D4—2441no—
764D4C4×C22⋊D6112yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4#1451973711yescharacteristic
796C2×C4#1451973711yescharacteristic
797C2×C4C22×C4×D6111yescharacteristic
798C2×C4C2×D4×D6111yescharacteristic
799C2×C4C22×C22⋊D6111yescharacteristic
800C2×C4C2×#1175822211yescharacteristic
801C2×C4#1451982211yescharacteristic
802C2×C4#1451982211yescharacteristic
803C8—22no—
804C8—41no—
805C8—1221no—
806C8—1221no—
807C8—1221no—
808C8—1221no—
809C8—1221no—
810C8—1221no—
811C8—1221no—
812C8—1221no—
813C8—2441no—
814C8—2441no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—84no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22C2×#1451973711yescharacteristic
836C22#1684040611yescharacteristic
837C22#1684043811yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—81no—
844C4—2441no—
845C4—2441no—
846C4—2441no—
847C4C2×C4×C22⋊D6111yescharacteristic
848C4#1684023511yescharacteristic
849C4D4×C22⋊D6111yescharacteristic
850C4#1684040211yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—4881no—
858C2#2144879811yescharacteristic
859C2#2145471811yescharacteristic
860C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#421C2
socleC22×C61C2×C4×D4
prime radical#21455037C2
cosocleC22×C4×C61C24
hypercenterC2×#421D61
hypocenterC61#22887
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16839881C2semidirect
3. #21454544C2semidirect
4. #21454268C2semidirect
5. #21446704C2semidirect
6. #21446527C2semidirect
7. #21446470C2semidirect
8. #21446267C2semidirect
9. #21446144C2semidirect
10. #21446143C2semidirect
11. #21446092C2semidirect
12. #21446024C2semidirect
13. #21445657C2semidirect
14. #21445585C2semidirect
15. C2×C61×#421C2semidirect
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×#14519688C22semidirect
54. C2×C4×#92418C22semidirect
55. #16839526C22semidirect
56. #16839526C22semidirect
57. #16839522C22semidirect
58. #16839522C22semidirect
59. #16839517C22semidirect
60. #16839517C22semidirect
173. #104×C61D4semidirect
424. C2×#421D61semidirect
499. C61#22887semidirect
576. #104C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214550372
C2×#168398812
#214545442
#214542682
#214467042
#214465272
#214464702
#214462672
#214461442
#214461432
#214460922
#214460242
#214456572
#214455852
C2×C61×#4212
#2288761