Finite Group Databasebeta

← #26237016

Subgroups — #26237016

Order 12032.

1058 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#20252604C211yesmaximal, characteristic
2C2×#15689243C211yesmaximal, characteristic, complemented
3C22×#13093950C211yesmaximal, characteristic, complemented
4#20251834C211yesmaximal, characteristic, complemented
5#20244280C211yesmaximal, characteristic, complemented
6#20244098C211yesmaximal, characteristic, complemented
7#20244036C211yesmaximal, characteristic, complemented
8#20243832C211yesmaximal, characteristic, complemented
9#20243718C211yesmaximal, characteristic, complemented
10#20243715C211yesmaximal, characteristic, complemented
11#20243662C211yesmaximal, characteristic, complemented
12#20243593C211yesmaximal, characteristic, complemented
13#20243234C211yesmaximal, characteristic, complemented
14#20243152C211yesmaximal, characteristic, complemented
15C47×#2933C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C2×#13094044C2211yescharacteristic
18C2×#13094044C2211yescharacteristic
19C2×#13094030C2211yescharacteristic
20C2×#13094030C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22#15689283C411yescharacteristic, complemented
23#15689283C411yescharacteristic, complemented
24#15689278C411yescharacteristic, complemented
25#15689273C411yescharacteristic, complemented
26#15689266C411yescharacteristic, complemented
27#15689266C411yescharacteristic, complemented
28#15689261C411yescharacteristic, complemented
29#15689256C411yescharacteristic, complemented
30#15689243—24no—
31C2×#13093959C2211yescharacteristic, complemented
32C2×#13093959C2211yescharacteristic, complemented
33C2×#13093951C2211yescharacteristic, complemented
34C2×#13093951C2211yescharacteristic, complemented
35C2×#13093950—24no—
36C2×#13093950C2211yescharacteristic
37C2×#13093950C2211yescharacteristic
38C2×#13093950C2211yescharacteristic
39C2×#13093950C2211yescharacteristic
40#15689117C2211yescharacteristic
41#15689117C2211yescharacteristic
42#15689089C2211yescharacteristic
43#15689089C2211yescharacteristic
44#15689088—21no—
45#15689088—21no—
46#15689087C2211yescharacteristic
47#15689085—21no—
48C2×C22⋊(C47⋊C8)C2211yescharacteristic
49C22⋊C8×D47—21no—
50C2×#13093934C2211yescharacteristic, complemented
51C2×#13093934C2211yescharacteristic, complemented
52#15688887C2211yescharacteristic, complemented
53#15688887C2211yescharacteristic, complemented
54#15688882C2211yescharacteristic, complemented
55#15688882C2211yescharacteristic, complemented
56#15688877C2211yescharacteristic, complemented
57#15688877C2211yescharacteristic, complemented
58C2×#131×C47C2211yescharacteristic, complemented
59C22×M16×C47C2211yescharacteristic
60C47×#525C2211yescharacteristic
61C47×#436—21no—
62C47×#435—21no—
63C47×#435—21no—
64C8×D4×C47—21no—
65C47×#424C2211yescharacteristic, complemented
66C47×#408C2211yescharacteristic, complemented
67C2×C22⋊C8×C47C2211yescharacteristic
68C47×#405C2211yescharacteristic, complemented
69C2×#10625350—21no—
70C2×#10625350—21no—
71C2×#10625350—22no—
72C2×#10625350—22no—
73C2×#10625350—41no—
74C2×#10625350—41no—
75C2×#10625350C2×C411yescharacteristic
76C2×#10625350C2×C411yescharacteristic
77C2×#10625350C2311yescharacteristic
78C2×#10625350C2311yescharacteristic
79C22×Dic94C2×C411yescharacteristic
80C22×D188C2×C411yescharacteristic
81C22×C22⋊D47—21no—
82C23×Dic47—21no—
83C22×C4×D47—21no—
84#13094044—22no—
85#13094044—22no—
86#13094044—41no—
87#13094044—41no—
88C2×#10625337C2×C411yescharacteristic, complemented
89C2×#10625337C2×C411yescharacteristic, complemented
90C2×#10625335C2×C411yescharacteristic, complemented
91C2×#10625335C2×C411yescharacteristic, complemented
92C2×#10625336C2×C411yescharacteristic, complemented
93C2×#10625336C2×C411yescharacteristic, complemented
94C2×#10625334C2×C411yescharacteristic, complemented
95C2×#10625334C2×C411yescharacteristic, complemented
96#13094030—22no—
97#13094030—22no—
98#13094030—41no—
99#13094030—41no—
100C2×#10625329C2311yescharacteristic
101C2×#10625329C2311yescharacteristic
102C2×#10625324—21no—
103C2×#10625324—21no—
104C22×C47⋊C8C2311yescharacteristic
105C22×C47⋊C8C2311yescharacteristic
106C2×C8×D47—21no—
107C2×C8×D47—21no—
108C2×C4×Dic47—22no—
109C2×C4×Dic47—21no—
110C2×C4×Dic47—41no—
111C2×C4×Dic47C2311yescharacteristic
112C2×C4×Dic47C2311yescharacteristic
113#13093959—22no—
114#13093959—41no—
115#13093951—22no—
116#13093951—41no—
117#13093950—22no—
118#13093950—22no—
119#13093950—22no—
120#13093950D414yescomplemented
121#13093947C2×C411yescharacteristic, complemented
122#13093947C2×C411yescharacteristic, complemented
123#13093947C2×C411yescharacteristic, complemented
124#13093947C2×C411yescharacteristic, complemented
125#13093944C2×C411yescharacteristic, complemented
126#13093944C2×C411yescharacteristic, complemented
127#13093944C2×C411yescharacteristic, complemented
128#13093944C2×C411yescharacteristic, complemented
129C22⋊(C47⋊C8)—21no—
130C22⋊(C47⋊C8)—21no—
131C22⋊(C47⋊C8)C2×C411yescharacteristic
132C22⋊(C47⋊C8)C2×C411yescharacteristic
133C22⋊(C47⋊C8)C2×C411yescharacteristic
134C22⋊(C47⋊C8)C2×C411yescharacteristic
135(C2×D47)⋊C8—21no—
136(C2×D47)⋊C8—21no—
137(C2×D47)⋊C8—21no—
138(C2×D47)⋊C8—21no—
139#13093934—22no—
140#13093934—41no—
141C2×#41×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143#131×C47—22no—
144#131×C47—41no—
145C2×M16×C47—21no—
146C2×M16×C47—21no—
147C2×M16×C47—22no—
148C2×M16×C47—41no—
149C2×M16×C47C2311yescharacteristic
150C2×M16×C47C2311yescharacteristic
151C22×C8×C47—21no—
152C22×C8×C47—21no—
153C22×C8×C47C2311yescharacteristic
154C22×C8×C47C2311yescharacteristic
155#123×C47—21no—
156C22⋊Q8×C47C2×C411yescharacteristic
157C22⋊Q8×C47C2×C411yescharacteristic
158#121×C47C2×C411yescharacteristic
159#121×C47C2×C411yescharacteristic
160#120×C47—21no—
161C4×D4×C47—21no—
162C4×D4×C47—21no—
163#117×C47C2311yescharacteristic
164C4⋊C8×C47—21no—
165C4⋊C8×C47—21no—
166C22⋊C8×C47—21no—
167C22⋊C8×C47—21no—
168C22⋊C8×C47D411yescharacteristic
169C22⋊C8×C47D411yescharacteristic
170C22⋊C8×C47D411yescharacteristic
171C22⋊C8×C47D411yescharacteristic
172#97×C47—21no—
173C4×C8×C47—21no—
174C24×C47#4111yescharacteristic
175C23×D47—21no—
176#41×C47—21no—
177#41×C47—21no—
178#41×C47—21no—
179#41×C47—21no—
180C2×Q8×C47C22×C411yescharacteristic
181C2×D4×C47—21no—
182C2×D4×C47—21no—
183C2×D4×C47—21no—
184C2×D4×C47C22×C411yescharacteristic
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47C22×C411yescharacteristic
191C22×C4×C47C22×C411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47#4111yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—21no—
197C2×C22⋊D47—21no—
198C2×C22⋊D47—21no—
199C2×C22⋊D47—21no—
200C2×C22⋊D47—42no—
201C2×C22⋊D47—42no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—42no—
206C22×Dic47—42no—
207C22×Dic47—42no—
208#10625350—21no—
209#10625350—21no—
210#10625350—21no—
211#10625350—21no—
212#10625350—21no—
213#10625350—21no—
214#10625350—22no—
215#10625350—22no—
216#10625350—41no—
217#10625350—41no—
218#10625350—42no—
219#10625350—42no—
220#10625350—42no—
221#10625350—42no—
222#10625350C2×D412yes—
223#10625350#4112yes—
224C2×D188—22no—
225C2×D188—21no—
226C2×D188—41no—
227C2×D188C22×C411yescharacteristic
228C2×D188C22×C411yescharacteristic
229C2×C4×D47—21no—
230C2×C4×D47—21no—
231C2×C4×D47—21no—
232C2×C4×D47—21no—
233C2×C4×D47—42no—
234C2×C4×D47—42no—
235C2×Dic94—22no—
236C2×Dic94—21no—
237C2×Dic94—41no—
238C2×Dic94C22×C411yescharacteristic
239C2×Dic94C22×C411yescharacteristic
240M16×C47—21no—
241M16×C47—21no—
242M16×C47—21no—
243M16×C47—42no—
244M16×C47—42no—
245M16×C47C2×D412yes—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47—21no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47—42no—
253C2×C8×C47—42no—
254C2×C8×C47C2×D411yescharacteristic
255C2×C8×C47C2×D411yescharacteristic
256C2×C8×C47C2×D411yescharacteristic
257C2×C8×C47C2×D411yescharacteristic
258C4⋊C4×C47—21no—
259C4⋊C4×C47—21no—
260C4⋊C4×C47C22×C411yescharacteristic
261C4⋊C4×C47C22×C411yescharacteristic
262C22⋊C4×C47—21no—
263C22⋊C4×C47—21no—
264C22⋊C4×C47—21no—
265C22⋊C4×C47—21no—
266C22⋊C4×C47—21no—
267C42×C47—21no—
268#10625337—22no—
269#10625337—41no—
270#10625336—22no—
271#10625336—41no—
272#10625335—22no—
273#10625335—41no—
274#10625334—22no—
275#10625334—41no—
276C4×Dic47—21no—
277C4×Dic47—21no—
278C4×Dic47—21no—
279C4×Dic47—42no—
280C4×Dic47C2×D412yes—
281#10625329—21no—
282#10625329—21no—
283#10625329—21no—
284#10625329—21no—
285C2×C47⋊C8—21no—
286C2×C47⋊C8—21no—
287C2×C47⋊C8—21no—
288C2×C47⋊C8—21no—
289C2×C47⋊C8—21no—
290C2×C47⋊C8—21no—
291C2×C47⋊C8C22×C411yescharacteristic
292C2×C47⋊C8C22×C411yescharacteristic
293C2×C47⋊C8C22×C411yescharacteristic
294C2×C47⋊C8C22×C411yescharacteristic
295#10625324—42no—
296#10625324—42no—
297C8×D47—42no—
298C8×D47—42no—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—22no—
302C23×C47—21no—
303C23×C47—41no—
304C23×C47C4×D411yescharacteristic
305C23×C47C4×D411yescharacteristic
306C23×C47C2×#4111yescharacteristic
307C22×D47—21no—
308C22×D47—21no—
309C22×D47—42no—
310C22×D47—42no—
311C22×D47—81no—
312Q8×C47—21no—
313Q8×C47—21no—
314D4×C47—21no—
315D4×C47—21no—
316D4×C47—41no—
317D4×C47—41no—
318D4×C47—42no—
319D4×C47—81no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47C4×D411yescharacteristic
336C2×C4×C47C4×D411yescharacteristic
337C2×C4×C47C23×C411yescharacteristic
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C22×D411yescharacteristic
340C2×C4×C47C2×#4111yescharacteristic
341C2×C4×C47H(5,𝔽2)11yescharacteristic
342C2×C4×C47H(5,𝔽2)11yescharacteristic
343C22⋊D47—22no—
344C22⋊D47—22no—
345C22⋊D47—42no—
346C22⋊D47—42no—
347C22⋊D47—41no—
348C22⋊D47—41no—
349C2×Dic47—21no—
350C2×Dic47—22no—
351C2×Dic47—21no—
352C2×Dic47—22no—
353C2×Dic47—42no—
354C2×Dic47—41no—
355C2×Dic47—41no—
356C2×Dic47—41no—
357C2×Dic47—48no—
358C2×Dic47—41no—
359D188—21no—
360D188—21no—
361D188—21no—
362D188—42no—
363D188C4×D412yes—
364C4×D47—22no—
365C4×D47—22no—
366C4×D47—42no—
367C4×D47—42no—
368C4×D47—41no—
369C4×D47—41no—
370Dic94—21no—
371Dic94—21no—
372Dic94—21no—
373Dic94—42no—
374Dic94C4×D412yes—
375C8×C47—21no—
376C8×C47—21no—
377C8×C47—22no—
378C8×C47—21no—
379C8×C47—21no—
380C8×C47—41no—
381C47⋊C8—21no—
382C47⋊C8—21no—
383C47⋊C8—21no—
384C47⋊C8—21no—
385C47⋊C8—41no—
386C47⋊C8—41no—
387#22886—471nomaximal, Sylow
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—21no—
391C22×C47—21no—
392C22×C47—21no—
393C22×C47—21no—
394C22×C47—21no—
395C22×C47—42no—
396C22×C47—42no—
397C22×C47—41no—
398C22×C47—41no—
399C22×C47—41no—
400C22×C47#44412yescomplemented
401C22×C47C2×C4×D411yescharacteristic
402C22×C47#54611yescharacteristic
403C22×C47#55111yescharacteristic
404C2×D47—22no—
405C2×D47—41no—
406C2×D47—41no—
407C2×D47—41no—
408C2×D47—41no—
409C2×D47—41no—
410C2×D47—84no—
411C4×C47—21no—
412C4×C47—21no—
413C4×C47—41no—
414C4×C47—41no—
415C4×C47—41no—
416C4×C47C2×C4×D411yescharacteristic
417C4×C47#51811yescharacteristic
418C4×C47D4211yescharacteristic
419C4×C47#54611yescharacteristic
420Dic47—22no—
421Dic47—42no—
422Dic47—42no—
423Dic47—41no—
424#3002—471no—
425C2×#444—471no—
426#2933D4711yescharacteristic, complemented
427C22×#104—471no—
428#2880—471no—
429#1975—471no—
430#1938—471no—
431#1929—471no—
432#1896—471no—
433#1876—471no—
434#1876—471no—
435#1866—471no—
436#1855—471no—
437#1765—471no—
438#1749—471no—
439C2×C47—21no—
440C2×C47—22no—
441C2×C47—21no—
442C2×C47—41no—
443C2×C47—81no—
444C2×C47#235811yescharacteristic
445C2×C47C2×#44411yescharacteristic
446C2×C47#295611yescharacteristic
447D47—42no—
448D47—81no—
449C22×#41—471no—
450C2×#135—471no—
451C2×#135—471no—
452C2×#131—471no—
453C2×#131—471no—
454C2×#131C2×D4711yescharacteristic, complemented
455C22×M16C2×D4711yescharacteristic
456#525C2×D4711yescharacteristic
457C22×C42—471no—
458#452—471no—
459#452—471no—
460#451—471no—
461#450—471no—
462#449—471no—
463#449—471no—
464#448—471no—
465#447—471no—
466#444—944no—
467#436—21no—
468#435—21no—
469#435—21no—
470C8×D4—21no—
471C2×#108—471no—
472C2×#108—471no—
473#424C2×D4711yescharacteristic, complemented
474C2×#104—471no—
475C2×#104—471no—
476C2×#104—471no—
477C2×#104—471no—
478C2×#104—471no—
479C2×#104—471no—
480C2×#104—944no—
481#416—471no—
482#416—471no—
483#408—471no—
484#408—471no—
485#408—941no—
486#408—941no—
487#408C2×D4711yescharacteristic, complemented
488#407—471no—
489#407—941no—
490C2×C22⋊C8—471no—
491C2×C22⋊C8—941no—
492C2×C22⋊C8C2×D4711yescharacteristic
493#405C2×D4711yescharacteristic, complemented
494C2×#97—471no—
495C2×#97—471no—
496#341—471no—
497#341—471no—
498#339—471no—
499#339—471no—
500#336—471no—
501#336—471no—
502C47#2288611yescharacteristic, complemented, Sylow
503C2×#41—471no—
504C2×#41—471no—
505C2×#41—471no—
506C2×#41—471no—
507C2×#41—942no—
508C2×#41—942no—
509C2×#41—941no—
510C2×#41—941no—
511C2×#41—1881no—
512C2×#41—1881no—
513C2×#41C22×D4711yescharacteristic
514C22×Q8—471no—
515C22×D4—471no—
516C22×D4—941no—
517C23×C4—941no—
518C23×C4—941no—
519C23×C4C22×D4711yescharacteristic
520#135—942no—
521#135—942no—
522#135—1881no—
523#135—1881no—
524C2×Q16—471no—
525C2×Q16—471no—
526C2×SD16—471no—
527C2×SD16—471no—
528C2×SD16—471no—
529C2×SD16—471no—
530C2×D8—471no—
531C2×D8—471no—
532#131—22no—
533#131—41no—
534#131—942no—
535#131—942no—
536#131—1881no—
537#131—1881no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—22no—
541C2×M16—41no—
542C2×M16—471no—
543C2×M16—471no—
544C2×M16—941no—
545C2×M16—941no—
546C2×M16C22×D4711yescharacteristic
547C2×M16C22×D4711yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—471no—
551C22×C8—471no—
552C22×C8—941no—
553C22×C8—941no—
554C22×C8C22×D4711yescharacteristic
555C22×C8C22×D4711yescharacteristic
556#123—21no—
557C22⋊Q8C4×D4711yescharacteristic
558C22⋊Q8C4×D4711yescharacteristic
559#121C4×D4711yescharacteristic
560#121C4×D4711yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D4711yescharacteristic
565C2×C42—471no—
566C2×C42—471no—
567C2×C42—942no—
568C2×C42—941no—
569C2×C42—1881no—
570#108—942no—
571#108—1881no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—474no—
575#104—942no—
576#104—942no—
577#104—942no—
578#104—942no—
579#104—1881no—
580#103—471no—
581#103—471no—
582#103—471no—
583#103—471no—
584#102—471no—
585#102—471no—
586#102—471no—
587#102—471no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—471no—
591C22⋊C8—471no—
592C22⋊C8—471no—
593C22⋊C8—471no—
594C22⋊C8—941no—
595C22⋊C8—941no—
596C22⋊C8—941no—
597C22⋊C8—941no—
598C22⋊C8—941no—
599C22⋊C8—941no—
600C22⋊C8C22⋊D4711yescharacteristic
601C22⋊C8C22⋊D4711yescharacteristic
602C22⋊C8C22⋊D4711yescharacteristic
603C22⋊C8C22⋊D4711yescharacteristic
604#97—21no—
605#97—942no—
606#97—1881no—
607C4×C8—21no—
608C24—941no—
609C24#1062535011yescharacteristic
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—472no—
615#41—472no—
616#41—942no—
617#41—942no—
618#41—941no—
619#41—941no—
620#41—941no—
621#41—941no—
622#41—941no—
623#41—941no—
624#41—1882no—
625#41—1882no—
626#41—1881no—
627#41—1881no—
628#41—1882no—
629#41—1882no—
630C2×Q8—471no—
631C2×Q8—471no—
632C2×Q8—942no—
633C2×Q8—941no—
634C2×Q8—1881no—
635C2×Q8C2×C4×D4711yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—471no—
640C2×D4—471no—
641C2×D4—942no—
642C2×D4—941no—
643C2×D4—941no—
644C2×D4—941no—
645C2×D4—941no—
646C2×D4—941no—
647C2×D4—1881no—
648C2×D4—1882no—
649C2×D4—1882no—
650C2×D4C2×C4×D4711yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—941no—
657C22×C4—941no—
658C22×C4—941no—
659C22×C4—941no—
660C22×C4—941no—
661C22×C4—941no—
662C22×C4—941no—
663C22×C4—1882no—
664C22×C4—1882no—
665C22×C4—1882no—
666C22×C4—1882no—
667C22×C4—1882no—
668C22×C4C2×C4×D4711yescharacteristic
669C22×C4C2×C4×D4711yescharacteristic
670C22×C4#1062535011yescharacteristic
671C22×C4C2×C22⋊D4711yescharacteristic
672C22×C4C2×C22⋊D4711yescharacteristic
673C22×C4C23×D4711yescharacteristic
674Q16—942no—
675Q16—1881no—
676SD16—942no—
677SD16—942no—
678SD16—1881no—
679SD16—1881no—
680D8—942no—
681D8—1881no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—42no—
687M16—941no—
688M16—941no—
689M16—941no—
690M16—941no—
691M16—1882no—
692M16—1882no—
693M16D4×D4712yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—471no—
703C2×C8—471no—
704C2×C8—471no—
705C2×C8—471no—
706C2×C8—941no—
707C2×C8—941no—
708C2×C8—941no—
709C2×C8—941no—
710C2×C8—941no—
711C2×C8—941no—
712C2×C8—1882no—
713C2×C8—1882no—
714C2×C8C2×C22⋊D4711yescharacteristic
715C2×C8C2×C22⋊D4711yescharacteristic
716C2×C8C2×C22⋊D4711yescharacteristic
717C2×C8C2×C22⋊D4711yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C2×C4×D4711yescharacteristic
721C4⋊C4C2×C4×D4711yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—472no—
729C42—941no—
730C42—941no—
731C42—941no—
732C42—1882no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—941no—
739C23—941no—
740C23—3761no—
741C23—1882no—
742C23—1882no—
743C23C4×C22⋊D4711yescharacteristic
744C23C4×C22⋊D4711yescharacteristic
745C23C2×#1062535011yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—472no—
749Q8—941no—
750Q8—941no—
751Q8—941no—
752Q8—1882no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—81no—
759D4—472no—
760D4—942no—
761D4—942no—
762D4—941no—
763D4—941no—
764D4—941no—
765D4—1882no—
766D4—1882no—
767D4—1882no—
768D4—1881no—
769D4—1881no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—941no—
786C2×C4—942no—
787C2×C4—942no—
788C2×C4—942no—
789C2×C4—942no—
790C2×C4—941no—
791C2×C4—1882no—
792C2×C4—1882no—
793C2×C4—1882no—
794C2×C4—1881no—
795C2×C4—1881no—
796C2×C4—1881no—
797C2×C4—1888no—
798C2×C4—1881no—
799C2×C4—1881no—
800C2×C4—1881no—
801C2×C4C4×C22⋊D4711yescharacteristic
802C2×C4C4×C22⋊D4711yescharacteristic
803C2×C4C22×C4×D4711yescharacteristic
804C2×C4C2×D4×D4711yescharacteristic
805C2×C4C22×C22⋊D4711yescharacteristic
806C2×C4#41×D4711yescharacteristic
807C2×C4#1309406911yescharacteristic
808C2×C4#1309407011yescharacteristic
809C8—21no—
810C8—21no—
811C8—22no—
812C8—21no—
813C8—21no—
814C8—41no—
815C8—941no—
816C8—941no—
817C8—941no—
818C8—941no—
819C8—1881no—
820C8—1881no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—942no—
834C22—3764no—
835C22—1881no—
836C22—1881no—
837C22—1881no—
838C22—1881no—
839C22—1881no—
840C22#1568924312yescomplemented
841C22C2×C4×C22⋊D4711yescharacteristic
842C22#1568976911yescharacteristic
843C22#1568980211yescharacteristic
844C4—21no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—942no—
850C4—1882no—
851C4—1882no—
852C4—1881no—
853C4C4×D4×D4711yescharacteristic
854C4#1568959511yescharacteristic
855C4D4×C22⋊D4711yescharacteristic
856C4#1568976111yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—3761no—
863C2—1882no—
864C2#2024636511yescharacteristic
865C2C2×#1568924311yescharacteristic
866C2#2025229511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2933C2
socleC22×C47C2×C4×D4
prime radical#20252604C2
cosocleC22×C4×C47C24
hypercenter#2933D47
hypocenterC47#22886
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#15689243C2semidirect
3. C22×#13093950C2semidirect
4. #20251834C2semidirect
5. #20244280C2semidirect
6. #20244098C2semidirect
7. #20244036C2semidirect
8. #20243832C2semidirect
9. #20243718C2semidirect
10. #20243715C2semidirect
11. #20243662C2semidirect
12. #20243593C2semidirect
13. #20243234C2semidirect
14. #20243152C2semidirect
15. C47×#2933C2semidirect
22. #15689283C4semidirect
23. #15689283C4semidirect
24. #15689278C4semidirect
25. #15689273C4semidirect
26. #15689266C4semidirect
27. #15689266C4semidirect
28. #15689261C4semidirect
29. #15689256C4semidirect
31. C2×#13093959C22semidirect
32. C2×#13093959C22semidirect
33. C2×#13093951C22semidirect
34. C2×#13093951C22semidirect
50. C2×#13093934C22semidirect
51. C2×#13093934C22semidirect
52. #15688887C22semidirect
53. #15688887C22semidirect
54. #15688882C22semidirect
55. #15688882C22semidirect
56. #15688877C22semidirect
57. #15688877C22semidirect
58. C2×#131×C47C22semidirect
65. C47×#424C22semidirect
66. C47×#408C22semidirect
68. C47×#405C22semidirect
88. C2×#10625337C2×C4semidirect
89. C2×#10625337C2×C4semidirect
90. C2×#10625335C2×C4semidirect
91. C2×#10625335C2×C4semidirect
92. C2×#10625336C2×C4semidirect
93. C2×#10625336C2×C4semidirect
94. C2×#10625334C2×C4semidirect
95. C2×#10625334C2×C4semidirect
120. #13093950D4semidirect
121. #13093947C2×C4semidirect
122. #13093947C2×C4semidirect
123. #13093947C2×C4semidirect
124. #13093947C2×C4semidirect
125. #13093944C2×C4semidirect
126. #13093944C2×C4semidirect
127. #13093944C2×C4semidirect
128. #13093944C2×C4semidirect
400. C22×C47#444semidirect
426. #2933D47semidirect
454. C2×#131C2×D47semidirect
473. #424C2×D47semidirect
487. #408C2×D47semidirect
493. #405C2×D47semidirect
502. C47#22886semidirect
840. C22#15689243semidirect

Maximal subgroups

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

subgroupindex
#202526042
C2×#156892432
C22×#130939502
#202518342
#202442802
#202440982
#202440362
#202438322
#202437182
#202437152
#202436622
#202435932
#202432342
#202431522
C47×#29332
#2288647