Finite Group Databasebeta

← #46846570

Subgroups — #46846570

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#31774503C211yesmaximal, characteristic, complemented
2#31774379C211yesmaximal, characteristic, complemented
3#31774217C211yesmaximal, characteristic, complemented
4#31774212C211yesmaximal, characteristic, complemented
5#31774194C211yesmaximal, characteristic, complemented
6#31774097C211yesmaximal, characteristic, complemented
7#31774093C211yesmaximal, characteristic, complemented
8#31774045C211yesmaximal, characteristic, complemented
9#31774045C211yesmaximal, characteristic, complemented
10#31774008C211yesmaximal, characteristic, complemented
11#31774000C211yesmaximal, characteristic, complemented
12#31773982C211yesmaximal, characteristic, complemented
13#31773979C211yesmaximal, characteristic, complemented
14#31773957C211yesmaximal, characteristic, complemented
15#479×C271C211yesmaximal, characteristic, complemented
16C2×#16864655C2211yescharacteristic
17C2×#16864641C2211yescharacteristic
18C2×#16864641C2211yescharacteristic
19C2×D2168C2211yescharacteristic
20C2×D2168C2211yescharacteristic
21#22576157C2211yescharacteristic
22#22576145—21no—
23#22576145—21no—
24#22576135—21no—
25#22576135—21no—
26#22576135C2211yescharacteristic
27#22576135C2211yescharacteristic
28Q8×Dic271C2211yescharacteristic
29C4×D1084—21no—
30C4×D1084C2211yescharacteristic
31#22576122—21no—
32#22576122C2211yescharacteristic
33#22576122C2211yescharacteristic
34#22576122C2211yescharacteristic
35#22576117—21no—
36#22576117C2211yescharacteristic
37C4⋊C4×D271—21no—
38C4⋊C4×D271C2211yescharacteristic
39#22576093C2211yescharacteristic
40#22576091C2211yescharacteristic
41C4⋊(C271⋊C8)C2211yescharacteristic
42#22576082C2211yescharacteristic
43#22576082C2211yescharacteristic
44#22576080C2211yescharacteristic
45#22576080C2211yescharacteristic
46#22576080C2211yescharacteristic
47#22576080C2211yescharacteristic
48(C2×D271)⋊C8C2211yescharacteristic
49(C2×D271)⋊C8C2211yescharacteristic
50#22576070C2211yescharacteristic
51C8×Dic271C2211yescharacteristic
52#125×C271C2211yescharacteristic
53C4×Q8×C271C2211yescharacteristic
54#107×C271C2211yescharacteristic
55#106×C271C2211yescharacteristic
56C4⋊C8×C271C2211yescharacteristic
57#103×C271C2211yescharacteristic
58#103×C271C2211yescharacteristic
59#16864655—22no—
60#16864655—22no—
61C2×D1084—21no—
62C2×D1084—21no—
63C2×D1084—21no—
64C2×D1084—21no—
65C2×D1084—21no—
66C2×D1084C2311yescharacteristic
67C2×D1084C2311yescharacteristic
68C2×D1084C2311yescharacteristic
69C2×C4×D271—21no—
70C2×C4×D271—21no—
71C2×C4×D271—21no—
72C2×C4×D271—21no—
73C2×C4×D271—21no—
74C2×C4×D271—21no—
75C2×C4×D271C2311yescharacteristic
76#16864641—22no—
77#16864641—22no—
78D2168—22no—
79D2168—22no—
80C2×C271⋊C8C2311yescharacteristic
81C2×C271⋊C8C2311yescharacteristic
82C4⋊Dic271—21no—
83C4⋊Dic271C2311yescharacteristic
84Dic271⋊C4—21no—
85Dic271⋊C4D411yescharacteristic
86Dic271⋊C4D411yescharacteristic
87(C2×D271)⋊C4—21no—
88(C2×D271)⋊C4—21no—
89(C2×D271)⋊C4—21no—
90(C2×D271)⋊C4—21no—
91(C2×D271)⋊C4—21no—
92(C2×D271)⋊C4—21no—
93(C2×D271)⋊C4D411yescharacteristic
94(C2×D271)⋊C4D411yescharacteristic
95C4×Dic271—21no—
96C4×Dic271C2311yescharacteristic
97C2×Q8×C271C2311yescharacteristic
98C2×C8×C271C2311yescharacteristic
99C2×C8×C271C2311yescharacteristic
100C4⋊C4×C271—21no—
101C4⋊C4×C271—21no—
102C4⋊C4×C271—21no—
103C4⋊C4×C271C2311yescharacteristic
104C4⋊C4×C271C2311yescharacteristic
105C4⋊C4×C271C2311yescharacteristic
106C42×C271—21no—
107C42×C271C2311yescharacteristic
108C22×D271—21no—
109C22×D271—21no—
110C22×D271—21no—
111C22×D271C2×D411yescharacteristic
112D1084—24no—
113D1084—21no—
114D1084—21no—
115D1084—21no—
116D1084—21no—
117D1084—21no—
118D1084—81no—
119D1084—81no—
120D1084—81no—
121D1084—81no—
122D1084#4112yes—
123C2×Dic271—21no—
124C2×Dic271C2×D411yescharacteristic
125C2×Dic271C2×D411yescharacteristic
126C2×Dic271C2×D411yescharacteristic
127C4×D271—24no—
128C4×D271—21no—
129C4×D271—21no—
130C4×D271—81no—
131C4×D271—81no—
132C4×D271—81no—
133C4×D271—81no—
134C4×D271—81no—
135C271⋊C8—21no—
136C271⋊C8—21no—
137Q8×C271—21no—
138Q8×C271#4112yes—
139C2×C4×C271—21no—
140C2×C4×C271—21no—
141C2×C4×C271—21no—
142C2×C4×C271—21no—
143C2×C4×C271C2×D411yescharacteristic
144C2×C4×C271C2×D411yescharacteristic
145C2×C4×C271C2411yescharacteristic
146C8×C271—21no—
147C8×C271—21no—
148C22×C271C22×D411yescharacteristic
149C2×D271—21no—
150C2×D271—22no—
151C2×D271—21no—
152C2×D271—21no—
153C2×D271—41no—
154C2×D271—41no—
155C2×D271—41no—
156C2×D271—41no—
157C2×D271—41no—
158C2×D271—41no—
159C2×D271—41no—
160C2×D271—41no—
161C4×C271—22no—
162C4×C271—21no—
163C4×C271—21no—
164C4×C271—41no—
165C4×C271—41no—
166C4×C271—41no—
167C4×C271C2×#4111yescharacteristic
168C4×C271C2×#4111yescharacteristic
169Dic271—21no—
170Dic271—21no—
171Dic271—21no—
172Dic271—41no—
173C2×C271#52511yescharacteristic
174C2×C271#57611yescharacteristic
175C2×C271#57711yescharacteristic
176D271—41no—
177D271—42no—
178D271—81no—
179D271—81no—
180C271#311911yescharacteristic, complemented, Sylow
181#3119—2711nomaximal, Sylow
182#540—2711no—
183#520—2711no—
184#481—2711no—
185#480—2711no—
186#479D27111yescharacteristic, complemented
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#125C2×D27111yescharacteristic
204#123—5421no—
205#123—5421no—
206#121—2711no—
207#121—2711no—
208#121—5421no—
209#121—5421no—
210C4×Q8—2711no—
211C4×Q8C2×D27111yescharacteristic
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—2711no—
221C2×C4⋊C4—5421no—
222#107—2711no—
223#107C2×D27111yescharacteristic
224#106—2711no—
225#106C2×D27111yescharacteristic
226C4⋊C8—2711no—
227C4⋊C8C2×D27111yescharacteristic
228#103C2×D27111yescharacteristic
229#103C2×D27111yescharacteristic
230#102—2711no—
231#102—2711no—
232#102—2711no—
233#102—2711no—
234#102—2711no—
235#102—2711no—
236C22⋊C8—2711no—
237C22⋊C8—2711no—
238#97—2711no—
239C4×C8—2711no—
240#41—5422no—
241#41—5422no—
242C2×Q8C22×D27111yescharacteristic
243C2×D4—2711no—
244C2×D4—2711no—
245C2×D4—2711no—
246C2×D4—5421no—
247C2×D4—5421no—
248C2×D4—5421no—
249C2×D4—5421no—
250C2×D4—5421no—
251C22×C4—2711no—
252C22×C4—5421no—
253C22×C4—5421no—
254C22×C4—5421no—
255C22×C4—5421no—
256C22×C4—5421no—
257C22×C4—5421no—
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—21no—
268C4⋊C4—21no—
269C4⋊C4—2711no—
270C4⋊C4—2711no—
271C4⋊C4—2711no—
272C4⋊C4—5421no—
273C4⋊C4—5421no—
274C4⋊C4C22×D27111yescharacteristic
275C4⋊C4C22×D27111yescharacteristic
276C4⋊C4C22×D27111yescharacteristic
277C22⋊C4—2711no—
278C22⋊C4—2711no—
279C22⋊C4—5421no—
280C22⋊C4—5421no—
281C22⋊C4—5421no—
282C22⋊C4—5421no—
283C22⋊C4—5421no—
284C22⋊C4—5421no—
285C42—21no—
286C42—2711no—
287C42—5421no—
288C42C22×D27111yescharacteristic
289C23—2711no—
290C23—5421no—
291C23—5421no—
292C23—5421no—
293Q8—21no—
294Q8#1686465512yes—
295D4—2712no—
296D4—5424no—
297D4—5421no—
298D4—5421no—
299D4—5421no—
300D4—5421no—
301D4—5421no—
302D4—21681no—
303D4—21681no—
304D4—21681no—
305D4—21681no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—2711no—
311C2×C4—2711no—
312C2×C4—2711no—
313C2×C4—5424no—
314C2×C4—5421no—
315C2×C4—5421no—
316C2×C4—5421no—
317C2×C4—21681no—
318C2×C4—21681no—
319C2×C4—21681no—
320C2×C4—21681no—
321C2×C4—21681no—
322C2×C4D4×D27111yescharacteristic
323C2×C4D4×D27111yescharacteristic
324C2×C4C23×D27111yescharacteristic
325C8—21no—
326C8—21no—
327C8—5421no—
328C8—5421no—
329C22—5422no—
330C22—5421no—
331C22—5421no—
332C22—5421no—
333C22—10841no—
334C22—10841no—
335C22—10841no—
336C22—10841no—
337C22—10841no—
338C22—10841no—
339C22—10841no—
340C22—10841no—
341C22C2×D4×D27111yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—5421no—
349C4—5421no—
350C4—5421no—
351C4—10841no—
352C4#41×D27111yescharacteristic
353C4C2×#1686465511yescharacteristic
354C2—10841no—
355C2—10842no—
356C2—21681no—
357C2—21681no—
358C2#3177441011yescharacteristic
359C2#3177469911yescharacteristic
360C2#3177470611yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#479×C271C2
socleC22×C271C22×D4
hypercenter#479D271
hypocenterC271#3119
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #31774503C2semidirect
2. #31774379C2semidirect
3. #31774217C2semidirect
4. #31774212C2semidirect
5. #31774194C2semidirect
6. #31774097C2semidirect
7. #31774093C2semidirect
8. #31774045C2semidirect
9. #31774045C2semidirect
10. #31774008C2semidirect
11. #31774000C2semidirect
12. #31773982C2semidirect
13. #31773979C2semidirect
14. #31773957C2semidirect
15. #479×C271C2semidirect
180. C271#3119semidirect
186. #479D271semidirect

Maximal subgroups

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

subgroupindex
#317745032
#317743792
#317742172
#317742122
#317741942
#317740972
#317740932
#317740452
#317740082
#317740002
#317739822
#317739792
#317739572
#479×C2712
#3119271