Finite Group Databasebeta

← #44402578

Subgroups — #44402578

Order 29056.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20300245C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D227C211yesmaximal, characteristic
3C2×C22⋊C4×D227C211yesmaximal, characteristic
4#28408926C211yesmaximal, characteristic, complemented
5#28408925C211yesmaximal, characteristic, complemented
6#28408920C211yesmaximal, characteristic, complemented
7#28408906C211yesmaximal, characteristic, complemented
8#28408903C211yesmaximal, characteristic, complemented
9#28408894C211yesmaximal, characteristic, complemented
10#28408889C211yesmaximal, characteristic, complemented
11#28408887C211yesmaximal, characteristic
12C4×(C2×D227)⋊C4C211yesmaximal, characteristic, complemented
13#28408879C211yesmaximal, characteristic, complemented
14#28408879C211yesmaximal, characteristic, complemented
15#388×C227C211yesmaximal, characteristic, complemented
16C24×D227C2211yescharacteristic
17C22×C4×D227C2211yescharacteristic
18C22×C4×D227C2211yescharacteristic
19C22×C4×D227C2211yescharacteristic
20C22×C4×D227C2211yescharacteristic
21#20300245—24no—
22C2×C4⋊Dic227C2211yescharacteristic, complemented
23C2×Dic227⋊C4C2211yescharacteristic, complemented
24C2×Dic227⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic227C2211yescharacteristic
26C2×C22⋊Dic227C2211yescharacteristic
27C2×C22⋊Dic227C2211yescharacteristic
28C2×(C2×D227)⋊C4C2211yescharacteristic
29C2×(C2×D227)⋊C4C2211yescharacteristic
30C2×(C2×D227)⋊C4C2211yescharacteristic
31C2×(C2×D227)⋊C4C2211yescharacteristic
32C2×(C2×D227)⋊C4C2211yescharacteristic
33C2×(C2×D227)⋊C4C2211yescharacteristic
34C2×(C2×D227)⋊C4C2211yescharacteristic
35C2×(C2×D227)⋊C4C2211yescharacteristic
36C22⋊C4×D227—24no—
37C22⋊C4×D227C418yescomplemented
38C2×C4×Dic227C2211yescharacteristic, complemented
39C2×C4×Dic227C2211yescharacteristic, complemented
40C2×C4×Dic227C2211yescharacteristic, complemented
41C227⋊#95C2211yescharacteristic, complemented
42C227⋊#95C2211yescharacteristic, complemented
43C227⋊#95C2211yescharacteristic, complemented
44C227⋊#95C2211yescharacteristic, complemented
45C227⋊#95C2211yescharacteristic, complemented
46C227⋊#95C2211yescharacteristic, complemented
47C2×C4⋊C4×C227C2211yescharacteristic, complemented
48C2×C22⋊C4×C227C2211yescharacteristic
49C2×C22⋊C4×C227C2211yescharacteristic
50C2×C22⋊C4×C227C2211yescharacteristic
51C2×C42×C227C2211yescharacteristic, complemented
52#95×C227C2211yescharacteristic, complemented
53#95×C227C2211yescharacteristic, complemented
54C23×D227—22no—
55C23×D227—22no—
56C23×D227—22no—
57C23×D227—22no—
58C23×D227—41no—
59C23×D227—41no—
60C23×D227C2×C414yes—
61C23×D227C2311yescharacteristic
62C23×D227C2311yescharacteristic
63C22×Dic227C2311yescharacteristic
64C22×Dic227C2311yescharacteristic
65C22×Dic227C2311yescharacteristic
66C22×Dic227C2311yescharacteristic
67C22×Dic227C2311yescharacteristic
68C22×Dic227C2311yescharacteristic
69C2×C4×D227—22no—
70C2×C4×D227—22no—
71C2×C4×D227—22no—
72C2×C4×D227—22no—
73C2×C4×D227—22no—
74C2×C4×D227—22no—
75C2×C4×D227—41no—
76C2×C4×D227—41no—
77C2×C4×D227—41no—
78C2×C4×D227—41no—
79C2×C4×D227C2×C414yescomplemented
80C2×C4×D227C2×C414yescomplemented
81C4⋊Dic227—41no—
82Dic227⋊C4—22no—
83Dic227⋊C4—22no—
84C22⋊Dic227—22no—
85C22⋊Dic227—41no—
86C22⋊Dic227C2×C414yescomplemented
87(C2×D227)⋊C4—22no—
88(C2×D227)⋊C4—22no—
89(C2×D227)⋊C4—22no—
90(C2×D227)⋊C4—22no—
91(C2×D227)⋊C4—22no—
92(C2×D227)⋊C4C2×C414yes—
93(C2×D227)⋊C4C2×C414yes—
94(C2×D227)⋊C4D414yes—
95C4×Dic227—22no—
96C4×Dic227—41no—
97C4×Dic227—41no—
98C24×C227C2311yescharacteristic
99C22×C4×C227C2311yescharacteristic
100C22×C4×C227C2311yescharacteristic
101C22×C4×C227C2311yescharacteristic
102C22×C4×C227C2311yescharacteristic
103C22×C4×C227C2311yescharacteristic
104C22×C4×C227C2311yescharacteristic
105C4⋊C4×C227—41no—
106C22⋊C4×C227—22no—
107C22⋊C4×C227—41no—
108C22⋊C4×C227C2×C414yescomplemented
109C42×C227—22no—
110C22×D227—21no—
111C22×D227—21no—
112C22×D227—21no—
113C22×D227—21no—
114C22×D227—21no—
115C22×D227—21no—
116C22×D227—21no—
117C22×D227—21no—
118C22×D227—28no—
119C22×D227—28no—
120C22×D227—44no—
121C22×D227—44no—
122C22×D227—44no—
123C22×D227—44no—
124C22×D227—44no—
125C22×D227C22×C412yes—
126C22×D227C22×C412yes—
127C22×D227C2×D412yes—
128C22×D227#4112yes—
129C22×D227#4112yes—
130C22×D227#4112yes—
131C2×Dic227—21no—
132C2×Dic227—21no—
133C2×Dic227—21no—
134C2×Dic227—21no—
135C2×Dic227—21no—
136C2×Dic227—21no—
137C2×Dic227—21no—
138C2×Dic227—21no—
139C2×Dic227—21no—
140C2×Dic227—21no—
141C2×Dic227—21no—
142C2×Dic227—21no—
143C2×Dic227—21no—
144C2×Dic227—21no—
145C2×Dic227—21no—
146C2×Dic227C22×C412yes—
147C2×Dic227C22×C412yes—
148C2×Dic227C2×D412yes—
149C4×D227—28no—
150C4×D227—44no—
151C4×D227—44no—
152C4×D227—44no—
153C23×C227—21no—
154C23×C227—21no—
155C23×C227—21no—
156C23×C227—21no—
157C23×C227—21no—
158C23×C227—21no—
159C23×C227C22×C412yes—
160C23×C227C2411yescharacteristic
161C2×C4×C227—21no—
162C2×C4×C227—21no—
163C2×C4×C227—21no—
164C2×C4×C227—21no—
165C2×C4×C227—21no—
166C2×C4×C227—21no—
167C2×C4×C227—21no—
168C2×C4×C227—21no—
169C2×C4×C227—21no—
170C2×C4×C227—21no—
171C2×C4×C227—21no—
172C2×C4×C227—21no—
173C2×C4×C227—21no—
174C2×C4×C227—21no—
175C2×C4×C227—21no—
176C2×C4×C227C22×C412yes—
177C2×C4×C227C22×C412yes—
178C2×C4×C227C2×D412yes—
179C22×C227—22no—
180C22×C227—22no—
181C22×C227—22no—
182C22×C227—41no—
183C22×C227—41no—
184C22×C227—41no—
185C22×C227—41no—
186C22×C227C23×C411yescharacteristic
187C22×C227C22×D411yescharacteristic
188C22×C227C2×#4111yescharacteristic
189C22×C227C2×#4111yescharacteristic
190C22×C227C2×#4111yescharacteristic
191C22×C227H(5,𝔽2)11yescharacteristic
192C22×C227H(5,𝔽2)11yescharacteristic
193C2×D227—22no—
194C2×D227—22no—
195C2×D227—22no—
196C2×D227—22no—
197C2×D227—22no—
198C2×D227—22no—
199C2×D227—22no—
200C2×D227—22no—
201C2×D227—22no—
202C2×D227—22no—
203C2×D227—22no—
204C2×D227—22no—
205C2×D227—416no—
206C2×D227#11714yescomplemented
207C2×D227C4×D414yes—
208C4×C227—22no—
209C4×C227—22no—
210C4×C227—22no—
211C4×C227—41no—
212C4×C227—41no—
213C4×C227—41no—
214Dic227—22no—
215Dic227—22no—
216Dic227—22no—
217Dic227—41no—
218Dic227—41no—
219Dic227—41no—
220C2×C227—42no—
221C2×C227C2×#11711yescharacteristic
222C2×C227C2×C4×D411yescharacteristic
223C2×C227#51811yescharacteristic
224C2×C227#54611yescharacteristic
225C2×C227#54611yescharacteristic
226C2×C227#55111yescharacteristic
227C2×C227#55111yescharacteristic
228D227—24no—
229D227—24no—
230C227#234211yescharacteristic, complemented, Sylow
231#2342—2271nomaximal, Sylow
232C2×#117—2271no—
233C22×C22⋊C4—2271no—
234C22×C22⋊C4—2271no—
235#388—2271no—
236#388—2271no—
237#388—2271no—
238#388D22711yescharacteristic, complemented
239#385—2271no—
240#385—2271no—
241#381—2271no—
242#380—2271no—
243#379—2271no—
244C4×C22⋊C4—2271no—
245C4×C22⋊C4—2271no—
246C4×C22⋊C4—2271no—
247C25—2271no—
248C23×C4—2271no—
249C23×C4—2271no—
250C23×C4—2271no—
251C23×C4—2271no—
252#117—4544no—
253C2×C4⋊C4—2271no—
254C2×C4⋊C4—2271no—
255C2×C4⋊C4—2271no—
256C2×C4⋊C4C2×D22711yescharacteristic, complemented
257C2×C22⋊C4—4544no—
258C2×C22⋊C4—2271no—
259C2×C22⋊C4—2271no—
260C2×C22⋊C4—2271no—
261C2×C22⋊C4—2271no—
262C2×C22⋊C4—2271no—
263C2×C22⋊C4—2271no—
264C2×C22⋊C4—2271no—
265C2×C22⋊C4—2271no—
266C2×C22⋊C4—2271no—
267C2×C22⋊C4—2271no—
268C2×C22⋊C4—2271no—
269C2×C22⋊C4—2278no—
270C2×C22⋊C4C2×D22711yescharacteristic
271C2×C22⋊C4C2×D22711yescharacteristic
272C2×C22⋊C4C2×D22711yescharacteristic
273C2×C42—2271no—
274C2×C42—2271no—
275C2×C42—2271no—
276C2×C42C2×D22711yescharacteristic, complemented
277#95—2271no—
278#95—2271no—
279#95—2271no—
280#95—2271no—
281#95—2271no—
282#95—2271no—
283#95C2×D22711yescharacteristic, complemented
284#95C2×D22711yescharacteristic, complemented
285C24—9081no—
286C24—9081no—
287C24—4542no—
288C24—4542no—
289C24—4542no—
290C24—4542no—
291C24—2274no—
292C24—2271no—
293C24—2271no—
294C24C22×D22711yescharacteristic
295C22×C4—9081no—
296C22×C4—9081no—
297C22×C4—9081no—
298C22×C4—9081no—
299C22×C4—4542no—
300C22×C4—4542no—
301C22×C4—4542no—
302C22×C4—4542no—
303C22×C4—4542no—
304C22×C4—4542no—
305C22×C4—2274no—
306C22×C4—2271no—
307C22×C4—2271no—
308C22×C4—2271no—
309C22×C4—2271no—
310C22×C4—2271no—
311C22×C4—2271no—
312C22×C4—2274no—
313C22×C4C22×D22711yescharacteristic
314C22×C4C22×D22711yescharacteristic
315C22×C4C22×D22711yescharacteristic
316C22×C4C22×D22711yescharacteristic
317C22×C4C22×D22711yescharacteristic
318C22×C4C22×D22711yescharacteristic
319C4⋊C4—41no—
320C4⋊C4—9081no—
321C4⋊C4—4542no—
322C4⋊C4—4542no—
323C22⋊C4—22no—
324C22⋊C4—41no—
325C22⋊C4—9081no—
326C22⋊C4—4542no—
327C22⋊C4—4542no—
328C22⋊C4—4542no—
329C22⋊C4—4542no—
330C22⋊C4—4542no—
331C22⋊C4—4542no—
332C22⋊C4—2274no—
333C22⋊C4—2274no—
334C22⋊C4—2274no—
335C22⋊C4—2274no—
336C22⋊C4C4×D22714yescomplemented
337C42—22no—
338C42—9081no—
339C42—9081no—
340C42—4542no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—9084no—
348C23—9084no—
349C23—9084no—
350C23—9084no—
351C23—9084no—
352C23—4548no—
353C23—4548no—
354C23—4541no—
355C23—4541no—
356C23—4541no—
357C23—4541no—
358C23—4541no—
359C23—4541no—
360C23—4541no—
361C23—4541no—
362C23—2272no—
363C23—2272no—
364C23—2272no—
365C23—2272no—
366C23—2272no—
367C23—2272no—
368C23C2×C4×D22712yes—
369C23C23×D22711yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—9084no—
386C2×C4—9084no—
387C2×C4—9084no—
388C2×C4—4548no—
389C2×C4—4541no—
390C2×C4—4541no—
391C2×C4—4541no—
392C2×C4—4541no—
393C2×C4—4541no—
394C2×C4—4541no—
395C2×C4—4541no—
396C2×C4—4541no—
397C2×C4—4541no—
398C2×C4—4541no—
399C2×C4—4541no—
400C2×C4—4541no—
401C2×C4—4541no—
402C2×C4—4541no—
403C2×C4—4541no—
404C2×C4—2272no—
405C2×C4—2272no—
406C2×C4—2272no—
407C2×C4C2×C4×D22712yes—
408C2×C4C2×C4×D22712yes—
409C2×C4D4×D22712yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—90816no—
418C22—4542no—
419C22—4542no—
420C22—4542no—
421C22—4542no—
422C22—4542no—
423C22—4542no—
424C22—4542no—
425C22—4542no—
426C22—4542no—
427C22—4542no—
428C22—4542no—
429C22—4542no—
430C22—2274no—
431C22—2274no—
432C22C22×C4×D22711yescharacteristic
433C22C2×D4×D22711yescharacteristic
434C22#41×D22711yescharacteristic
435C22#41×D22711yescharacteristic
436C22#41×D22711yescharacteristic
437C22#2030033311yescharacteristic
438C22#2030033411yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—9081no—
446C4—9081no—
447C4—9081no—
448C4—4542no—
449C4—4542no—
450C4—4542no—
451C2—42no—
452C2—4544no—
453C2—4544no—
454C2#117×D22711yescharacteristic
455C2C4×D4×D22711yescharacteristic
456C2#2840950411yescharacteristic
457C2#2840967411yescharacteristic
458C2#2840967911yescharacteristic
459C2#2840970711yescharacteristic
460C2#2840971211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D227
commutatorC22×C227C23×C4
Fitting#388×C227C2
socle, cosocleC23×C227C24
prime radicalC24×D227C22
hypercenter#388D227
hypocenterC227#2342
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#20300245C2semidirect
4. #28408926C2semidirect
5. #28408925C2semidirect
6. #28408920C2semidirect
7. #28408906C2semidirect
8. #28408903C2semidirect
9. #28408894C2semidirect
10. #28408889C2semidirect
12. C4×(C2×D227)⋊C4C2semidirect
13. #28408879C2semidirect
14. #28408879C2semidirect
15. #388×C227C2semidirect
22. C2×C4⋊Dic227C22semidirect
23. C2×Dic227⋊C4C22semidirect
24. C2×Dic227⋊C4C22semidirect
37. C22⋊C4×D227C4semidirect
38. C2×C4×Dic227C22semidirect
39. C2×C4×Dic227C22semidirect
40. C2×C4×Dic227C22semidirect
41. C227⋊#95C22semidirect
42. C227⋊#95C22semidirect
43. C227⋊#95C22semidirect
44. C227⋊#95C22semidirect
45. C227⋊#95C22semidirect
46. C227⋊#95C22semidirect
47. C2×C4⋊C4×C227C22semidirect
51. C2×C42×C227C22semidirect
52. #95×C227C22semidirect
53. #95×C227C22semidirect
79. C2×C4×D227C2×C4semidirect
80. C2×C4×D227C2×C4semidirect
86. C22⋊Dic227C2×C4semidirect
108. C22⋊C4×C227C2×C4semidirect
206. C2×D227#117semidirect
230. C227#2342semidirect
238. #388D227semidirect
256. C2×C4⋊C4C2×D227semidirect
276. C2×C42C2×D227semidirect
283. #95C2×D227semidirect
284. #95C2×D227semidirect
336. C22⋊C4C4×D227semidirect

Maximal subgroups

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

subgroupindex
C2×#203002452
C2×C22⋊C4×D2272
#284089262
#284089252
#284089202
#284089062
#284089032
#284088942
#284088892
#284088872
C4×(C2×D227)⋊C42
#284088792
#388×C2272
#2342227