Finite Group Databasebeta

← #46846558

Subgroups — #46846558

Order 34688.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774500C211yesmaximal, characteristic, complemented
2#31774378C211yesmaximal, characteristic, complemented
3#31774210C211yesmaximal, characteristic, complemented
4#31774207C211yesmaximal, characteristic, complemented
5#31774196C211yesmaximal, characteristic, complemented
6#31774096C211yesmaximal, characteristic, complemented
7#31774091C211yesmaximal, characteristic, complemented
8#31774044C211yesmaximal, characteristic, complemented
9#31774040C211yesmaximal, characteristic, complemented
10#31774008C211yesmaximal, characteristic, complemented
11#31773994C211yesmaximal, characteristic, complemented
12#31773984C211yesmaximal, characteristic, complemented
13#31773977C211yesmaximal, characteristic, complemented
14#31773955C211yesmaximal, characteristic, complemented
15#481×C271C211yesmaximal, characteristic, complemented
16C2×#16864654C2211yescharacteristic
17C2×#16864643C2211yescharacteristic
18C2×#16864642C2211yescharacteristic
19C2×D2168C2211yescharacteristic
20C2×#16864639C2211yescharacteristic
21#22576156C2211yescharacteristic
22#22576151C2211yescharacteristic
23#22576144—21no—
24#22576142—21no—
25#22576134C2211yescharacteristic
26#22576132—21no—
27#22576131—21no—
28#22576125C2211yescharacteristic
29#22576125C2211yescharacteristic
30D4×Dic271C2211yescharacteristic
31#22576122C2211yescharacteristic
32#22576122C2211yescharacteristic
33#22576122C2211yescharacteristic
34C4×C22⋊D271—21no—
35C4×C22⋊D271—21no—
36#22576119C2211yescharacteristic
37#22576118—21no—
38C4⋊C4×D271—21no—
39#22576093C2211yescharacteristic
40#22576093C2211yescharacteristic
41Dic271⋊C8C2211yescharacteristic
42Dic271⋊C8C2211yescharacteristic
43#22576085C2211yescharacteristic
44#22576083C2211yescharacteristic
45#22576082C2211yescharacteristic
46#22576080C2211yescharacteristic
47#22576080C2211yescharacteristic
48#22576080C2211yescharacteristic
49C22⋊(C271⋊C8)C2211yescharacteristic
50#22576070C2211yescharacteristic
51C8×Dic271C2211yescharacteristic
52#121×C271C2211yescharacteristic
53C2×C4⋊C4×C271C2211yescharacteristic
54#106×C271C2211yescharacteristic
55#106×C271C2211yescharacteristic
56#102×C271C2211yescharacteristic
57#102×C271C2211yescharacteristic
58C22⋊C8×C271C2211yescharacteristic
59#16864654—22no—
60#16864654—22no—
61C2×Dic542C2311yescharacteristic
62C2×D1084C2311yescharacteristic
63C2×D1084C2311yescharacteristic
64C2×C22⋊D271—21no—
65C2×C22⋊D271—21no—
66C2×C22⋊D271—21no—
67C2×C22⋊D271—21no—
68C22×Dic271—21no—
69C2×C4×D271—21no—
70C2×C4×D271—21no—
71C2×C4×D271—21no—
72C2×C4×D271—21no—
73#16864643—22no—
74#16864642—22no—
75D2168—22no—
76#16864639—22no—
77C2×C271⋊C8C2311yescharacteristic
78C2×C271⋊C8C2311yescharacteristic
79C4⋊Dic271—21no—
80C4⋊Dic271D411yescharacteristic
81C4⋊Dic271D411yescharacteristic
82C4⋊Dic271C2311yescharacteristic
83Dic271⋊C4—21no—
84Dic271⋊C4—21no—
85Dic271⋊C4—21no—
86C22⋊Dic271—21no—
87C22⋊Dic271D411yescharacteristic
88C22⋊Dic271D411yescharacteristic
89(C2×D271)⋊C4—21no—
90(C2×D271)⋊C4—21no—
91(C2×D271)⋊C4—21no—
92(C2×D271)⋊C4—21no—
93C4×Dic271—21no—
94C4×Dic271—21no—
95C4×Dic271C2311yescharacteristic
96C4×Dic271C2311yescharacteristic
97C2×D4×C271—21no—
98C2×D4×C271C2311yescharacteristic
99C22×C4×C271—21no—
100C22×C4×C271C2311yescharacteristic
101C2×C8×C271C2311yescharacteristic
102C2×C8×C271C2311yescharacteristic
103C4⋊C4×C271—21no—
104C4⋊C4×C271C2311yescharacteristic
105C4⋊C4×C271C2311yescharacteristic
106C4⋊C4×C271C2311yescharacteristic
107C22⋊C4×C271—21no—
108C22×D271—21no—
109C22×D271—21no—
110Dic542—21no—
111Dic542#4112yes—
112D1084—21no—
113D1084—21no—
114D1084—21no—
115D1084#4112yes—
116C22⋊D271—24no—
117C22⋊D271—81no—
118C22⋊D271—81no—
119C22⋊D271—81no—
120C2×Dic271—21no—
121C2×Dic271—21no—
122C2×Dic271—81no—
123C2×Dic271C2×D411yescharacteristic
124C2×Dic271C2×D411yescharacteristic
125C2×Dic271C2×D411yescharacteristic
126C2×Dic271C2×D411yescharacteristic
127C4×D271—24no—
128C4×D271—81no—
129C4×D271—81no—
130C4×D271—81no—
131C271⋊C8—21no—
132C271⋊C8—21no—
133C23×C271—21no—
134C23×C271C2×D411yescharacteristic
135D4×C271—21no—
136D4×C271—21no—
137D4×C271—81no—
138C2×C4×C271—21no—
139C2×C4×C271—21no—
140C2×C4×C271—21no—
141C2×C4×C271—21no—
142C2×C4×C271—21no—
143C2×C4×C271—81no—
144C2×C4×C271C2×D411yescharacteristic
145C2×C4×C271C2411yescharacteristic
146C8×C271—21no—
147C8×C271—21no—
148C22×C271—21no—
149C22×C271—21no—
150C22×C271—21no—
151C22×C271—41no—
152C22×C271—41no—
153C22×C271—41no—
154C22×C271C22×D411yescharacteristic
155C2×D271—22no—
156C2×D271—41no—
157C2×D271—41no—
158C2×D271—41no—
159C2×D271—41no—
160C2×D271—41no—
161C4×C271—21no—
162C4×C271—41no—
163C4×C271—41no—
164C4×C271—41no—
165C4×C271C2×#4111yescharacteristic
166C4×C271C2×#4111yescharacteristic
167Dic271—22no—
168Dic271—21no—
169Dic271—21no—
170Dic271—21no—
171Dic271—21no—
172Dic271—41no—
173C2×C271—41no—
174C2×C271—81no—
175C2×C271#52511yescharacteristic
176C2×C271#57611yescharacteristic
177C2×C271#57711yescharacteristic
178D271—42no—
179D271—81no—
180C271#311911yescharacteristic, complemented, Sylow
181#3119—2711nomaximal, Sylow
182#540—2711no—
183#520—2711no—
184#481D27111yescharacteristic, complemented
185#480—2711no—
186#479—2711no—
187#478—2711no—
188#460—2711no—
189#459—2711no—
190#449—2711no—
191#449—2711no—
192#442—2711no—
193#440—2711no—
194C4×SD16—2711no—
195C4×D8—2711no—
196#433—2711no—
197C2×#41—2711no—
198C2×SD16—2711no—
199C2×SD16—2711no—
200C2×D8—2711no—
201C2×D8—2711no—
202#127—2711no—
203#125—2711no—
204#123—5421no—
205#123—5421no—
206#121—2711no—
207#121—5421no—
208#121—5421no—
209#121C2×D27111yescharacteristic
210C4×Q8—2711no—
211C4×Q8—2711no—
212C4×D4—2711no—
213C4×D4—2711no—
214C4×D4—2711no—
215C4×D4—2711no—
216C4×D4—5421no—
217C4×D4—5421no—
218#117—2711no—
219#117—5421no—
220C2×C4⋊C4—5421no—
221C2×C4⋊C4C2×D27111yescharacteristic
222#107—2711no—
223#107—2711no—
224#106C2×D27111yescharacteristic
225#106C2×D27111yescharacteristic
226C4⋊C8—2711no—
227C4⋊C8—2711no—
228#103—2711no—
229#103—2711no—
230#102—2711no—
231#102—2711no—
232#102—2711no—
233#102—2711no—
234#102C2×D27111yescharacteristic
235#102C2×D27111yescharacteristic
236C22⋊C8—2711no—
237C22⋊C8C2×D27111yescharacteristic
238#97—2711no—
239C4×C8—2711no—
240#41—5422no—
241#41—5422no—
242C2×Q8—2711no—
243C2×D4—21no—
244C2×D4—2711no—
245C2×D4—2711no—
246C2×D4—5421no—
247C2×D4—5421no—
248C2×D4—5421no—
249C2×D4—5421no—
250C2×D4C22×D27111yescharacteristic
251C22×C4—21no—
252C22×C4—5421no—
253C22×C4—5421no—
254C22×C4—5421no—
255C22×C4—5421no—
256C22×C4—5421no—
257C22×C4C22×D27111yescharacteristic
258SD16—5422no—
259SD16—5422no—
260D8—5422no—
261D8—5422no—
262C2×C8—2711no—
263C2×C8—2711no—
264C2×C8C22×D27111yescharacteristic
265C2×C8C22×D27111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—2711no—
268C4⋊C4—2711no—
269C4⋊C4—2711no—
270C4⋊C4—5421no—
271C4⋊C4—5421no—
272C4⋊C4—5421no—
273C4⋊C4—5421no—
274C4⋊C4C22×D27111yescharacteristic
275C4⋊C4C22×D27111yescharacteristic
276C4⋊C4C22×D27111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2711no—
279C22⋊C4—2711no—
280C22⋊C4—5421no—
281C22⋊C4—5421no—
282C22⋊C4—5421no—
283C22⋊C4—5421no—
284C22⋊C4—5421no—
285C42—2711no—
286C42—2711no—
287C42—5421no—
288C42—5421no—
289C23—21no—
290C23—5421no—
291C23—5421no—
292C23D4×D27111yescharacteristic
293Q8—2712no—
294Q8—5421no—
295D4—21no—
296D4—21no—
297D4—81no—
298D4—2712no—
299D4—5424no—
300D4—5421no—
301D4—5421no—
302D4—5421no—
303D4—21681no—
304D4—21681no—
305D4—21681no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—2711no—
313C2×C4—2711no—
314C2×C4—2711no—
315C2×C4—2711no—
316C2×C4—5424no—
317C2×C4—5421no—
318C2×C4—5421no—
319C2×C4—21681no—
320C2×C4—21681no—
321C2×C4—21681no—
322C2×C4—21681no—
323C2×C4D4×D27111yescharacteristic
324C2×C4C23×D27111yescharacteristic
325C8—21no—
326C8—21no—
327C8—5421no—
328C8—5421no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—5422no—
336C22—10841no—
337C22—10841no—
338C22—10841no—
339C22—10841no—
340C22—10841no—
341C22C2×D4×D27111yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—5422no—
347C4—5421no—
348C4—5421no—
349C4—5421no—
350C4—5421no—
351C4—10841no—
352C4#41×D27111yescharacteristic
353C4#41×D27111yescharacteristic
354C2—41no—
355C2—81no—
356C2—10842no—
357C2—21681no—
358C2#3177440511yescharacteristic
359C2#3177470111yescharacteristic
360C2#3177470311yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#481×C271C2
socleC22×C271C22×D4
hypercenter#481D271
hypocenterC271#3119
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #31774500C2semidirect
2. #31774378C2semidirect
3. #31774210C2semidirect
4. #31774207C2semidirect
5. #31774196C2semidirect
6. #31774096C2semidirect
7. #31774091C2semidirect
8. #31774044C2semidirect
9. #31774040C2semidirect
10. #31774008C2semidirect
11. #31773994C2semidirect
12. #31773984C2semidirect
13. #31773977C2semidirect
14. #31773955C2semidirect
15. #481×C271C2semidirect
180. C271#3119semidirect
184. #481D271semidirect

Maximal subgroups

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

subgroupindex
#317745002
#317743782
#317742102
#317742072
#317741962
#317740962
#317740912
#317740442
#317740402
#317740082
#317739942
#317739842
#317739772
#317739552
#481×C2712
#3119271