Finite Group Databasebeta

← #46846565

Subgroups — #46846565

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#31774502C211yesmaximal, characteristic, complemented
2#31774377C211yesmaximal, characteristic, complemented
3#31774216C211yesmaximal, characteristic, complemented
4#31774211C211yesmaximal, characteristic, complemented
5#31774205C211yesmaximal, characteristic, complemented
6#31774198C211yesmaximal, characteristic, complemented
7#31774098C211yesmaximal, characteristic, complemented
8#31774093C211yesmaximal, characteristic, complemented
9#31774044C211yesmaximal, characteristic, complemented
10#31774044C211yesmaximal, characteristic, complemented
11#31774010C211yesmaximal, characteristic, complemented
12#31773999C211yesmaximal, characteristic, complemented
13C4×#16864643C211yesmaximal, characteristic, complemented
14C4×D2168C211yesmaximal, characteristic, complemented
15#433×C271C211yesmaximal, characteristic, complemented
16C2×#16864654C2211yescharacteristic
17C2×#16864643C2211yescharacteristic
18C2×#16864643C2211yescharacteristic
19C2×D2168C2211yescharacteristic
20C2×D2168C2211yescharacteristic
21#22576157C2211yescharacteristic
22#22576152C2211yescharacteristic
23#22576145—21no—
24#22576145—21no—
25#22576134C2211yescharacteristic
26#22576134C2211yescharacteristic
27#22576133—21no—
28#22576133—21no—
29C4×Dic542C2211yescharacteristic
30C4×Dic542C2211yescharacteristic
31C4×D1084C2211yescharacteristic
32C4×D1084C2211yescharacteristic
33C4×D1084C2211yescharacteristic
34C4×D1084C2211yescharacteristic
35(C22⋊D271)⋊C4—21no—
36(C22⋊D271)⋊C4—21no—
37#22576118—21no—
38C2×C4⋊Dic271C2211yescharacteristic
39C4⋊C4×D271—21no—
40#22576094C2211yescharacteristic
41#22576094C2211yescharacteristic
42#22576092C2211yescharacteristic
43#22576092C2211yescharacteristic
44#22576085C2211yescharacteristic
45#22576085C2211yescharacteristic
46#22576082C2211yescharacteristic
47#22576082C2211yescharacteristic
48#22576082C2211yescharacteristic
49#22576082C2211yescharacteristic
50#22576082C2211yescharacteristic
51#22576082C2211yescharacteristic
52#117×C271C2211yescharacteristic
53C4⋊C8×C271C2211yescharacteristic
54C4⋊C8×C271C2211yescharacteristic
55C22⋊C8×C271C2211yescharacteristic
56C22⋊C8×C271C2211yescharacteristic
57#97×C271C2211yescharacteristic
58C4×C8×C271C2211yescharacteristic
59#16864654—22no—
60#16864654—22no—
61C2×Dic542C2311yescharacteristic
62C2×D1084—21no—
63C2×D1084—21no—
64C2×D1084C2311yescharacteristic
65C2×D1084C2311yescharacteristic
66C2×D1084C2311yescharacteristic
67C2×C22⋊D271—21no—
68C2×C22⋊D271—21no—
69C2×C22⋊D271—21no—
70C22×Dic271—21no—
71C2×C4×D271—21no—
72C2×C4×D271—21no—
73C2×C4×D271—21no—
74C2×C4×D271—21no—
75C2×C4×D271—21no—
76#16864643—22no—
77#16864643—22no—
78D2168—22no—
79D2168—22no—
80C4⋊Dic271—21no—
81C4⋊Dic271C2311yescharacteristic
82C4⋊Dic271C2311yescharacteristic
83C4⋊Dic271C2311yescharacteristic
84C4⋊Dic271C2311yescharacteristic
85Dic271⋊C4—21no—
86Dic271⋊C4—21no—
87Dic271⋊C4—21no—
88Dic271⋊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)⋊C4—21no—
94(C2×D271)⋊C4—21no—
95C4×Dic271—21no—
96C4×Dic271—21no—
97C22×C4×C271C2311yescharacteristic
98C2×C8×C271C2311yescharacteristic
99C2×C8×C271C2311yescharacteristic
100C2×C8×C271C2311yescharacteristic
101C2×C8×C271C2311yescharacteristic
102C4⋊C4×C271D411yescharacteristic
103C4⋊C4×C271D411yescharacteristic
104C22⋊C4×C271D411yescharacteristic
105C22⋊C4×C271D411yescharacteristic
106C42×C271C2311yescharacteristic
107C42×C271C2311yescharacteristic
108C22×D271—21no—
109C22×D271—21no—
110C22×D271—21no—
111Dic542—21no—
112Dic542#4112yes—
113D1084—21no—
114D1084—21no—
115D1084—21no—
116D1084—21no—
117D1084—21no—
118D1084—81no—
119D1084—81no—
120D1084#4112yes—
121C22⋊D271—24no—
122C22⋊D271—81no—
123C22⋊D271—81no—
124C2×Dic271—21no—
125C2×Dic271—21no—
126C2×Dic271—21no—
127C2×Dic271—21no—
128C2×Dic271—21no—
129C2×Dic271—81no—
130C4×D271—24no—
131C4×D271—81no—
132C4×D271—81no—
133C4×D271—81no—
134C4×D271—81no—
135C23×C271C2×D411yescharacteristic
136C2×C4×C271—21no—
137C2×C4×C271—21no—
138C2×C4×C271C2×D411yescharacteristic
139C2×C4×C271C2×D411yescharacteristic
140C2×C4×C271C2×D411yescharacteristic
141C2×C4×C271C2×D411yescharacteristic
142C2×C4×C271C2×D411yescharacteristic
143C2×C4×C271C2411yescharacteristic
144C8×C271—21no—
145C8×C271—21no—
146C8×C271—21no—
147C8×C271—21no—
148C22×C271—21no—
149C22×C271—21no—
150C22×C271—21no—
151C22×C271C22×D411yescharacteristic
152C2×D271—22no—
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—21no—
162C4×C271—21no—
163C4×C271—21no—
164C4×C271—21no—
165C4×C271—21no—
166C4×C271C2×#4111yescharacteristic
167C4×C271C2×#4111yescharacteristic
168Dic271—22no—
169Dic271—41no—
170Dic271—41no—
171Dic271—41no—
172Dic271—41no—
173C2×C271—41no—
174C2×C271#52511yescharacteristic
175C2×C271#57611yescharacteristic
176C2×C271#57711yescharacteristic
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#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#433D27111yescharacteristic, complemented
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—2711no—
208#121—5421no—
209#121—5421no—
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—5421no—
219#117C2×D27111yescharacteristic
220C2×C4⋊C4—2711no—
221C2×C4⋊C4—5421no—
222#107—2711no—
223#107—2711no—
224#106—2711no—
225#106—2711no—
226C4⋊C8C2×D27111yescharacteristic
227C4⋊C8C2×D27111yescharacteristic
228#103—2711no—
229#103—2711no—
230#102—2711no—
231#102—2711no—
232#102—2711no—
233#102—2711no—
234#102—2711no—
235#102—2711no—
236C22⋊C8C2×D27111yescharacteristic
237C22⋊C8C2×D27111yescharacteristic
238#97C2×D27111yescharacteristic
239C4×C8C2×D27111yescharacteristic
240#41—5422no—
241#41—5422no—
242C2×Q8—2711no—
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—5421no—
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×C8C22×D27111yescharacteristic
263C2×C8C22×D27111yescharacteristic
264C2×C8C22×D27111yescharacteristic
265C2×C8C22×D27111yescharacteristic
266C4⋊C4—2711no—
267C4⋊C4—2711no—
268C4⋊C4—2711no—
269C4⋊C4—2711no—
270C4⋊C4—5421no—
271C4⋊C4—5421no—
272C4⋊C4—5421no—
273C4⋊C4—5421no—
274C4⋊C4—5421no—
275C4⋊C4D108411yescharacteristic
276C4⋊C4D108411yescharacteristic
277C22⋊C4—5421no—
278C22⋊C4—5421no—
279C22⋊C4—5421no—
280C22⋊C4—5421no—
281C22⋊C4—5421no—
282C22⋊C4—5421no—
283C22⋊C4D108411yescharacteristic
284C22⋊C4D108411yescharacteristic
285C42—5421no—
286C42—5421no—
287C42C22×D27111yescharacteristic
288C42C22×D27111yescharacteristic
289C23—5421no—
290C23—5421no—
291C23—5421no—
292C23C2×D108411yescharacteristic
293Q8—2712no—
294Q8—5421no—
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—5424no—
309C2×C4—5421no—
310C2×C4—5421no—
311C2×C4—5421no—
312C2×C4—5421no—
313C2×C4—5421no—
314C2×C4—21681no—
315C2×C4—21681no—
316C2×C4—21681no—
317C2×C4—21681no—
318C2×C4—21681no—
319C2×C4C2×D108411yescharacteristic
320C2×C4C2×D108411yescharacteristic
321C2×C4C2×D108411yescharacteristic
322C2×C4C2×D108411yescharacteristic
323C2×C4C2×D108411yescharacteristic
324C2×C4C23×D27111yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—5422no—
333C22—10841no—
334C22—10841no—
335C22—10841no—
336C22—10841no—
337C22—10841no—
338C22—10841no—
339C22—10841no—
340C22—10841no—
341C22C22×D108411yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—5422no—
348C4—10841no—
349C4—10841no—
350C4—10841no—
351C4—10841no—
352C4#41×D27111yescharacteristic
353C4#41×D27111yescharacteristic
354C2—41no—
355C2—10842no—
356C2—21681no—
357C2—21681no—
358C2#3177440911yescharacteristic
359C2#3177470211yescharacteristic
360C2#3177470911yescharacteristic
subgroupG/H
centerC22C22×D1084
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#433×C271C2
socleC22×C271C22×D4
hypercenter#433D271
hypocenterC271#3119
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #31774502C2semidirect
2. #31774377C2semidirect
3. #31774216C2semidirect
4. #31774211C2semidirect
5. #31774205C2semidirect
6. #31774198C2semidirect
7. #31774098C2semidirect
8. #31774093C2semidirect
9. #31774044C2semidirect
10. #31774044C2semidirect
11. #31774010C2semidirect
12. #31773999C2semidirect
13. C4×#16864643C2semidirect
14. C4×D2168C2semidirect
15. #433×C271C2semidirect
180. C271#3119semidirect
196. #433D271semidirect

Maximal subgroups

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

subgroupindex
#317745022
#317743772
#317742162
#317742112
#317742052
#317741982
#317740982
#317740932
#317740442
#317740102
#317739992
C4×#168646432
C4×D21682
#433×C2712
#3119271