Finite Group Databasebeta

← #44402711

Subgroups — #44402711

Order 29056.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20300256C211yesmaximal, characteristic
2C2×C4×C22⋊D227C211yesmaximal, characteristic, complemented
3C22×(C2×D227)⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D227C211yesmaximal, characteristic, complemented
5#28408932C211yesmaximal, characteristic, complemented
6#28408923C211yesmaximal, characteristic, complemented
7#28408922C211yesmaximal, characteristic, complemented
8#28408912C211yesmaximal, characteristic, complemented
9#28408911C211yesmaximal, characteristic, complemented
10#28408908C211yesmaximal, characteristic, complemented
11#28408905C211yesmaximal, characteristic, complemented
12#28408903C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic227C211yesmaximal, characteristic, complemented
14C4×(C2×D227)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×D4×C227C211yesmaximal, characteristic, complemented
16C24×D227C2211yescharacteristic
17C22×C22⋊D227C2211yescharacteristic
18C22×C22⋊D227C2211yescharacteristic
19C23×Dic227C2211yescharacteristic
20C22×C4×D227C2211yescharacteristic
21C22×C4×D227C2211yescharacteristic
22#20300256C418yescomplemented
23C4×C22⋊D227—24no—
24C2×Dic227⋊C4C2211yescharacteristic, complemented
25C2×Dic227⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic227C2211yescharacteristic
27C2×C22⋊Dic227C2211yescharacteristic
28C2×C22⋊Dic227C2211yescharacteristic, complemented
29C2×C22⋊Dic227C2211yescharacteristic, complemented
30C2×(C2×D227)⋊C4—24no—
31C2×(C2×D227)⋊C4C2211yescharacteristic
32C2×(C2×D227)⋊C4C2211yescharacteristic
33C2×(C2×D227)⋊C4C2211yescharacteristic
34C2×(C2×D227)⋊C4C2211yescharacteristic
35C2×(C2×D227)⋊C4C2211yescharacteristic
36C2×(C2×D227)⋊C4C2211yescharacteristic
37C2×(C2×D227)⋊C4C2211yescharacteristic
38C2×(C2×D227)⋊C4C2211yescharacteristic
39C22⋊C4×D227—24no—
40C2×C4×Dic227C2211yescharacteristic, complemented
41C2×C4×Dic227C2211yescharacteristic, complemented
42C227⋊#95C2211yescharacteristic, complemented
43C227⋊#95C2211yescharacteristic, complemented
44C227⋊#95C2211yescharacteristic, complemented
45C227⋊#95C2211yescharacteristic, complemented
46C227⋊#95C2211yescharacteristic, complemented
47C227⋊#95C2211yescharacteristic, complemented
48C22×D4×C227C2211yescharacteristic
49C23×C4×C227C2211yescharacteristic
50C23×C4×C227C2211yescharacteristic, complemented
51C4×D4×C227—24no—
52C2×C4⋊C4×C227C2211yescharacteristic, complemented
53C2×C22⋊C4×C227C2211yescharacteristic
54C2×C22⋊C4×C227C2211yescharacteristic, complemented
55C2×C42×C227C2211yescharacteristic, complemented
56C23×D227—22no—
57C23×D227—22no—
58C23×D227—22no—
59C23×D227—22no—
60C23×D227—41no—
61C23×D227—41no—
62C23×D227C2×C414yescomplemented
63C23×D227C2311yescharacteristic
64C23×D227C2311yescharacteristic
65C2×C22⋊D227—22no—
66C2×C22⋊D227—22no—
67C2×C22⋊D227—41no—
68C2×C22⋊D227—41no—
69C2×C22⋊D227C2×C414yescomplemented
70C2×C22⋊D227C2×C414yescomplemented
71C22×Dic227—22no—
72C22×Dic227—22no—
73C22×Dic227—41no—
74C22×Dic227C2311yescharacteristic
75C22×Dic227C2311yescharacteristic
76C22×Dic227C2311yescharacteristic
77C22×Dic227C2311yescharacteristic
78C22×Dic227C2311yescharacteristic
79C22×Dic227C2311yescharacteristic
80C2×C4×D227—22no—
81C2×C4×D227—22no—
82C2×C4×D227—22no—
83C2×C4×D227—22no—
84C2×C4×D227—41no—
85C2×C4×D227—41no—
86Dic227⋊C4—22no—
87Dic227⋊C4—41no—
88C22⋊Dic227—22no—
89C22⋊Dic227—22no—
90C22⋊Dic227—41no—
91C22⋊Dic227C2×C414yescomplemented
92(C2×D227)⋊C4—22no—
93(C2×D227)⋊C4—22no—
94(C2×D227)⋊C4—22no—
95(C2×D227)⋊C4—22no—
96(C2×D227)⋊C4—22no—
97(C2×D227)⋊C4C2×C414yescomplemented
98(C2×D227)⋊C4C2×C414yescomplemented
99(C2×D227)⋊C4D414yescomplemented
100C4×Dic227—22no—
101C4×Dic227—41no—
102C24×C227C2311yescharacteristic
103C24×C227C2311yescharacteristic
104C2×D4×C227—22no—
105C2×D4×C227—22no—
106C2×D4×C227C2×C414yescomplemented
107C22×C4×C227—22no—
108C22×C4×C227—22no—
109C22×C4×C227—22no—
110C22×C4×C227—22no—
111C22×C4×C227—41no—
112C22×C4×C227—41no—
113C22×C4×C227C2311yescharacteristic
114C22×C4×C227C2311yescharacteristic
115C22×C4×C227C2311yescharacteristic
116C22×C4×C227C2311yescharacteristic
117C22×C4×C227C2311yescharacteristic
118C4⋊C4×C227—22no—
119C22⋊C4×C227—22no—
120C22⋊C4×C227D414yescomplemented
121C42×C227—22no—
122C22×D227—21no—
123C22×D227—21no—
124C22×D227—21no—
125C22×D227—21no—
126C22×D227—28no—
127C22×D227—21no—
128C22×D227—21no—
129C22×D227—21no—
130C22×D227—21no—
131C22×D227—21no—
132C22×D227—21no—
133C22×D227—28no—
134C22×D227—44no—
135C22×D227—44no—
136C22×D227—44no—
137C22×D227—44no—
138C22×D227—44no—
139C22×D227C22×C412yes—
140C22×D227C22×C412yes—
141C22×D227C2×D412yes—
142C22×D227#4112yes—
143C22⋊D227—28no—
144C22⋊D227—44no—
145C2×Dic227—21no—
146C2×Dic227—21no—
147C2×Dic227—21no—
148C2×Dic227—21no—
149C2×Dic227—21no—
150C2×Dic227—21no—
151C2×Dic227—21no—
152C2×Dic227—21no—
153C2×Dic227—21no—
154C2×Dic227—21no—
155C2×Dic227—21no—
156C2×Dic227—21no—
157C2×Dic227—21no—
158C2×Dic227—21no—
159C2×Dic227—21no—
160C2×Dic227—44no—
161C2×Dic227C22×C412yes—
162C2×Dic227C22×C412yes—
163C2×Dic227C2×D412yes—
164C4×D227—44no—
165C4×D227—44no—
166C23×C227—21no—
167C23×C227—21no—
168C23×C227—21no—
169C23×C227—21no—
170C23×C227—21no—
171C23×C227—21no—
172C23×C227—21no—
173C23×C227—21no—
174C23×C227—21no—
175C23×C227—21no—
176C23×C227C22×C412yes—
177C23×C227C22×C412yes—
178C23×C227C2×D412yes—
179C23×C227#4112yes—
180C23×C227C2411yescharacteristic
181D4×C227—28no—
182C2×C4×C227—21no—
183C2×C4×C227—21no—
184C2×C4×C227—21no—
185C2×C4×C227—21no—
186C2×C4×C227—21no—
187C2×C4×C227—21no—
188C2×C4×C227—21no—
189C2×C4×C227—21no—
190C2×C4×C227—21no—
191C2×C4×C227—21no—
192C2×C4×C227—21no—
193C2×C4×C227—44no—
194C2×C4×C227—44no—
195C2×C4×C227C22×C412yes—
196C2×C4×C227C2×D412yes—
197C2×C4×C227C2×D412yes—
198C2×C4×C227C2×D412yes—
199C22×C227—22no—
200C22×C227—22no—
201C22×C227—22no—
202C22×C227—22no—
203C22×C227—22no—
204C22×C227—22no—
205C22×C227—22no—
206C22×C227—22no—
207C22×C227—22no—
208C22×C227—41no—
209C22×C227—41no—
210C22×C227—41no—
211C22×C227—41no—
212C22×C227C4×D414yescomplemented
213C22×C227C23×C411yescharacteristic
214C22×C227C22×D411yescharacteristic
215C22×C227C22×D411yescharacteristic
216C22×C227C2×#4111yescharacteristic
217C22×C227C2×#4111yescharacteristic
218C22×C227H(5,𝔽2)11yescharacteristic
219C22×C227H(5,𝔽2)11yescharacteristic
220C2×D227—22no—
221C2×D227—22no—
222C2×D227—22no—
223C2×D227—22no—
224C2×D227—22no—
225C2×D227—22no—
226C2×D227—22no—
227C2×D227—22no—
228C2×D227—22no—
229C2×D227—416no—
230C2×D227—41no—
231C2×D227—41no—
232C2×D227—41no—
233C2×D227—41no—
234C2×D227C4×D414yescomplemented
235C4×C227—22no—
236C4×C227—22no—
237C4×C227—22no—
238C4×C227—22no—
239C4×C227—41no—
240Dic227—22no—
241Dic227—22no—
242Dic227—22no—
243Dic227—41no—
244Dic227—41no—
245Dic227—41no—
246C2×C227—24no—
247C2×C227—42no—
248C2×C227C2×C4×D411yescharacteristic
249C2×C227C2×C4×D411yescharacteristic
250C2×C227#51811yescharacteristic
251C2×C227D4211yescharacteristic
252C2×C227#54611yescharacteristic
253C2×C227#54611yescharacteristic
254C2×C227#55111yescharacteristic
255D227—24no—
256D227—42no—
257C227#235811yescharacteristic, complemented, Sylow
258#2358—2271nomaximal, Sylow
259C2×#120—2271no—
260C2×C4×D4—2271no—
261C2×C4×D4D22711yescharacteristic, complemented
262C22×C22⋊C4—2271no—
263C22×C22⋊C4—2271no—
264#390—2271no—
265#388—2271no—
266#388—2271no—
267#386—2271no—
268#386—2271no—
269#386—2271no—
270#385—2271no—
271#385—2271no—
272C4×C22⋊C4—2271no—
273C4×C22⋊C4—2271no—
274C25—2271no—
275C22×D4—2271no—
276C22×D4—2271no—
277C22×D4C2×D22711yescharacteristic
278C23×C4—2271no—
279C23×C4—2271no—
280C23×C4—2271no—
281C23×C4C2×D22711yescharacteristic
282C23×C4C2×D22711yescharacteristic, complemented
283#120—2278no—
284C4×D4—24no—
285C4×D4—4544no—
286C2×C4⋊C4—2271no—
287C2×C4⋊C4—2271no—
288C2×C4⋊C4C2×D22711yescharacteristic, complemented
289C2×C22⋊C4—4544no—
290C2×C22⋊C4—4544no—
291C2×C22⋊C4—2271no—
292C2×C22⋊C4—2271no—
293C2×C22⋊C4—2271no—
294C2×C22⋊C4—2271no—
295C2×C22⋊C4—2271no—
296C2×C22⋊C4—2271no—
297C2×C22⋊C4—2271no—
298C2×C22⋊C4—2271no—
299C2×C22⋊C4—2271no—
300C2×C22⋊C4—2271no—
301C2×C22⋊C4—2271no—
302C2×C22⋊C4—2271no—
303C2×C22⋊C4C2×D22711yescharacteristic
304C2×C22⋊C4C2×D22711yescharacteristic, complemented
305C2×C42—2271no—
306C2×C42—2271no—
307C2×C42C2×D22711yescharacteristic, complemented
308#95—2271no—
309#95—2271no—
310#95—2271no—
311#95—2271no—
312#95—2271no—
313#95—2271no—
314C24—9081no—
315C24—9081no—
316C24—4542no—
317C24—4542no—
318C24—4542no—
319C24—4542no—
320C24—2274no—
321C24—2271no—
322C24—2271no—
323C24C22×D22711yescharacteristic
324C24C22×D22711yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—9081no—
328C2×D4—9081no—
329C2×D4—4542no—
330C2×D4—4542no—
331C2×D4—2274no—
332C2×D4—2274no—
333C2×D4C4×D22714yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—9081no—
341C22×C4—9081no—
342C22×C4—9081no—
343C22×C4—4542no—
344C22×C4—4542no—
345C22×C4—4542no—
346C22×C4—4542no—
347C22×C4—4542no—
348C22×C4—4542no—
349C22×C4—2271no—
350C22×C4—2271no—
351C22×C4—2271no—
352C22×C4—2271no—
353C22×C4—2271no—
354C22×C4—2271no—
355C22×C4C22×D22711yescharacteristic
356C22×C4C22×D22711yescharacteristic
357C22×C4C22×D22711yescharacteristic
358C22×C4C22×D22711yescharacteristic
359C22×C4C22×D22711yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—9081no—
362C4⋊C4—4542no—
363C22⋊C4—22no—
364C22⋊C4—9081no—
365C22⋊C4—4542no—
366C22⋊C4—4542no—
367C22⋊C4—4542no—
368C22⋊C4—4542no—
369C22⋊C4—4542no—
370C22⋊C4—4542no—
371C22⋊C4—4542no—
372C22⋊C4—2274no—
373C22⋊C4—2274no—
374C22⋊C4—2274no—
375C22⋊C4—2274no—
376C22⋊C4C22⋊D22714yescomplemented
377C42—22no—
378C42—9081no—
379C42—4542no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—9084no—
391C23—9084no—
392C23—9084no—
393C23—9084no—
394C23—9084no—
395C23—4548no—
396C23—4541no—
397C23—4541no—
398C23—4541no—
399C23—4541no—
400C23—4541no—
401C23—4541no—
402C23—4548no—
403C23—4541no—
404C23—4541no—
405C23—4541no—
406C23—4541no—
407C23—2272no—
408C23—2272no—
409C23—2272no—
410C23—2272no—
411C23C2×C4×D22712yes—
412C23C2×C4×D22712yes—
413C23C2×C22⋊D22712yes—
414C23#1681388412yes—
415C23C23×D22711yescharacteristic
416D4—28no—
417D4—9084no—
418D4—4548no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—9084no—
433C2×C4—9084no—
434C2×C4—9084no—
435C2×C4—4541no—
436C2×C4—4541no—
437C2×C4—4541no—
438C2×C4—4541no—
439C2×C4—4541no—
440C2×C4—4541no—
441C2×C4—4541no—
442C2×C4—4541no—
443C2×C4—4541no—
444C2×C4—4541no—
445C2×C4—4541no—
446C2×C4—4541no—
447C2×C4—4541no—
448C2×C4—4541no—
449C2×C4—4541no—
450C2×C4—2272no—
451C2×C4—2272no—
452C2×C4—2272no—
453C2×C4C2×C4×D22712yes—
454C2×C4D4×D22712yes—
455C2×C4C2×C22⋊D22712yes—
456C2×C4C2×C22⋊D22712yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—90816no—
471C22—9081no—
472C22—9081no—
473C22—9081no—
474C22—9081no—
475C22—4542no—
476C22—4542no—
477C22—4542no—
478C22—4542no—
479C22—4542no—
480C22—4542no—
481C22—4542no—
482C22—4542no—
483C22—4542no—
484C22—2274no—
485C22C4×C22⋊D22714yescomplemented
486C22C22×C4×D22711yescharacteristic
487C22C2×D4×D22711yescharacteristic
488C22C22×C22⋊D22711yescharacteristic
489C22#41×D22711yescharacteristic
490C22C2×#1681388411yescharacteristic
491C22#2030033311yescharacteristic
492C22#2030033411yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—9081no—
499C4—9081no—
500C4—9081no—
501C4—4542no—
502C4—4542no—
503C4—4542no—
504C2—24no—
505C2—42no—
506C2—9082no—
507C2—4544no—
508C2C4×D4×D22711yescharacteristic
509C2C2×C4×C22⋊D22711yescharacteristic
510C2#2840950411yescharacteristic
511C2D4×C22⋊D22711yescharacteristic
512C2#2840967011yescharacteristic
513C2#2840967811yescharacteristic
514C2#2840971111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D227
commutatorC22×C227C23×C4
FittingC2×C4×D4×C227C2
socle, cosocleC23×C227C24
prime radicalC2×#20300256C2
hypercenterC2×C4×D4D227
hypocenterC227#2358
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D227C2semidirect
3. C22×(C2×D227)⋊C4C2semidirect
4. C2×C22⋊C4×D227C2semidirect
5. #28408932C2semidirect
6. #28408923C2semidirect
7. #28408922C2semidirect
8. #28408912C2semidirect
9. #28408911C2semidirect
10. #28408908C2semidirect
11. #28408905C2semidirect
12. #28408903C2semidirect
13. C22⋊C4×Dic227C2semidirect
14. C4×(C2×D227)⋊C4C2semidirect
15. C2×C4×D4×C227C2semidirect
22. #20300256C4semidirect
24. C2×Dic227⋊C4C22semidirect
25. C2×Dic227⋊C4C22semidirect
28. C2×C22⋊Dic227C22semidirect
29. C2×C22⋊Dic227C22semidirect
40. C2×C4×Dic227C22semidirect
41. C2×C4×Dic227C22semidirect
42. C227⋊#95C22semidirect
43. C227⋊#95C22semidirect
44. C227⋊#95C22semidirect
45. C227⋊#95C22semidirect
46. C227⋊#95C22semidirect
47. C227⋊#95C22semidirect
50. C23×C4×C227C22semidirect
52. C2×C4⋊C4×C227C22semidirect
54. C2×C22⋊C4×C227C22semidirect
55. C2×C42×C227C22semidirect
62. C23×D227C2×C4semidirect
69. C2×C22⋊D227C2×C4semidirect
70. C2×C22⋊D227C2×C4semidirect
91. C22⋊Dic227C2×C4semidirect
97. (C2×D227)⋊C4C2×C4semidirect
98. (C2×D227)⋊C4C2×C4semidirect
99. (C2×D227)⋊C4D4semidirect
106. C2×D4×C227C2×C4semidirect
120. C22⋊C4×C227D4semidirect
212. C22×C227C4×D4semidirect
234. C2×D227C4×D4semidirect
257. C227#2358semidirect
261. C2×C4×D4D227semidirect
282. C23×C4C2×D227semidirect
288. C2×C4⋊C4C2×D227semidirect
304. C2×C22⋊C4C2×D227semidirect
307. C2×C42C2×D227semidirect
333. C2×D4C4×D227semidirect
376. C22⋊C4C22⋊D227semidirect
485. C22C4×C22⋊D227semidirect

Maximal subgroups

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

subgroupindex
C2×#203002562
C2×C4×C22⋊D2272
C22×(C2×D227)⋊C42
C2×C22⋊C4×D2272
#284089322
#284089232
#284089222
#284089122
#284089112
#284089082
#284089052
#284089032
C22⋊C4×Dic2272
C4×(C2×D227)⋊C42
C2×C4×D4×C2272
#2358227