Finite Group Databasebeta

← #46840042

Subgroups — #46840042

Order 34688.

528 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22576137C211yesmaximal, characteristic
2C2×#22576119C211yesmaximal, characteristic
3#31773839C211yesmaximal, characteristic, complemented
4#31773831C211yesmaximal, characteristic, complemented
5#31773829C211yesmaximal, characteristic, complemented
6#31773818C211yesmaximal, characteristic, complemented
7#31773801C211yesmaximal, characteristic, complemented
8#31773794C211yesmaximal, characteristic, complemented
9#31773784C211yesmaximal, characteristic, complemented
10#31773780C211yesmaximal, characteristic, complemented
11#31773772C211yesmaximal, characteristic
12#31773769C211yesmaximal, characteristic
13#31773755C211yesmaximal, characteristic
14C2×C271⋊#95C211yesmaximal, characteristic
15#381×C271C211yesmaximal, characteristic
16C22×Dic542C2211yescharacteristic
17C23×Dic271C2211yescharacteristic
18C23×Dic271C2211yescharacteristic
19#22576137—24no—
20#22576119—24no—
21C2×C4⋊Dic271C2211yescharacteristic
22C2×C4⋊Dic271C2211yescharacteristic
23C2×C4⋊Dic271C2211yescharacteristic
24C2×C4⋊Dic271C2211yescharacteristic
25C2×C4⋊Dic271C2211yescharacteristic
26C2×Dic271⋊C4C2211yescharacteristic
27C2×Dic271⋊C4C2211yescharacteristic
28C2×Dic271⋊C4C2211yescharacteristic
29C2×Dic271⋊C4C2211yescharacteristic
30C2×Dic271⋊C4C2211yescharacteristic
31C2×Dic271⋊C4C2211yescharacteristic
32C2×C22⋊Dic271C2211yescharacteristic
33C2×C22⋊Dic271C2211yescharacteristic
34C2×C4×Dic271C2211yescharacteristic
35C2×C4×Dic271C2211yescharacteristic
36C271⋊#95C2211yescharacteristic
37C271⋊#95C2211yescharacteristic
38C271⋊#95C2211yescharacteristic
39C271⋊#95C2211yescharacteristic
40C271⋊#95C2211yescharacteristic
41C271⋊#95C2211yescharacteristic
42C271⋊#95C2211yescharacteristic
43C271⋊#95C2211yescharacteristic
44C271⋊#95C2211yescharacteristic
45C271⋊#95C2211yescharacteristic
46C23×C4×C271C2211yescharacteristic
47C2×C22⋊C4×C271C2211yescharacteristic
48C2×C22⋊C4×C271C2211yescharacteristic
49#95×C271C2211yescharacteristic
50#95×C271C2211yescharacteristic
51#95×C271C2211yescharacteristic
52#95×C271C2211yescharacteristic
53C2×Dic542—22no—
54C2×Dic542—22no—
55C2×Dic542—41no—
56C22×Dic271—22no—
57C22×Dic271—22no—
58C22×Dic271—22no—
59C22×Dic271—22no—
60C22×Dic271—41no—
61C22×Dic271—41no—
62C22×Dic271C2311yescharacteristic
63C22×Dic271C2311yescharacteristic
64C22×Dic271C2311yescharacteristic
65C22×Dic271C2311yescharacteristic
66C22×Dic271C2311yescharacteristic
67C22×Dic271C2311yescharacteristic
68C22×Dic271C2311yescharacteristic
69C22×Dic271C2311yescharacteristic
70C4⋊Dic271—22no—
71C4⋊Dic271—22no—
72C4⋊Dic271—22no—
73C4⋊Dic271—22no—
74C4⋊Dic271—41no—
75Dic271⋊C4—22no—
76Dic271⋊C4—22no—
77Dic271⋊C4—22no—
78Dic271⋊C4—22no—
79Dic271⋊C4—41no—
80Dic271⋊C4—41no—
81C22⋊Dic271—22no—
82C22⋊Dic271D414yes—
83C4×Dic271—22no—
84C4×Dic271—22no—
85C24×C271C2311yescharacteristic
86C22×C4×C271—22no—
87C22×C4×C271—22no—
88C22×C4×C271Q814yescomplemented
89C22×C4×C271C2311yescharacteristic
90C22×C4×C271C2311yescharacteristic
91C22×C4×C271C2311yescharacteristic
92C22×C4×C271C2311yescharacteristic
93C22×C4×C271C2311yescharacteristic
94C22×C4×C271C2311yescharacteristic
95C22⋊C4×C271—22no—
96C22⋊C4×C271—22no—
97Dic542—44no—
98C2×Dic271—21no—
99C2×Dic271—21no—
100C2×Dic271—21no—
101C2×Dic271—21no—
102C2×Dic271—21no—
103C2×Dic271—21no—
104C2×Dic271—21no—
105C2×Dic271—21no—
106C2×Dic271—21no—
107C2×Dic271—21no—
108C2×Dic271—21no—
109C2×Dic271—21no—
110C2×Dic271—21no—
111C2×Dic271—21no—
112C2×Dic271—21no—
113C2×Dic271—21no—
114C2×Dic271—21no—
115C2×Dic271—21no—
116C2×Dic271—21no—
117C2×Dic271—21no—
118C2×Dic271—44no—
119C2×Dic271—44no—
120C2×Dic271C2×D412yes—
121C2×Dic271C2×D412yes—
122C2×Dic271#4112yes—
123C2×Dic271#4112yes—
124C23×C271—21no—
125C23×C271—21no—
126C23×C271—21no—
127C23×C271—21no—
128C23×C271C2×D412yes—
129C23×C271C2×Q812yes—
130C23×C271#4112yes—
131C23×C271C2411yescharacteristic
132C2×C4×C271—28no—
133C2×C4×C271—21no—
134C2×C4×C271—21no—
135C2×C4×C271—21no—
136C2×C4×C271—21no—
137C2×C4×C271—21no—
138C2×C4×C271—21no—
139C2×C4×C271—21no—
140C2×C4×C271—21no—
141C2×C4×C271—21no—
142C2×C4×C271—21no—
143C2×C4×C271—21no—
144C2×C4×C271—21no—
145C2×C4×C271—21no—
146C2×C4×C271—21no—
147C2×C4×C271—21no—
148C2×C4×C271—21no—
149C2×C4×C271C2×Q812yes—
150C2×C4×C271C2×Q812yes—
151C22×C271—22no—
152C22×C271—22no—
153C22×C271—22no—
154C22×C271—22no—
155C22×C271—22no—
156C22×C271—22no—
157C22×C271C22⋊Q814yes—
158C22×C271C22×D411yescharacteristic
159C22×C271C22×Q811yescharacteristic
160C22×C271C2×#4111yescharacteristic
161C22×C271C2×#4111yescharacteristic
162C22×C271C2×#4111yescharacteristic
163C22×C271H(5,𝔽2)11yescharacteristic
164C22×C2712−1+411yescharacteristic
165C4×C271—22no—
166C4×C271—22no—
167C4×C271—41no—
168C4×C271—41no—
169C4×C271—41no—
170C4×C271—41no—
171Dic271—22no—
172Dic271—22no—
173Dic271—22no—
174Dic271—22no—
175Dic271—41no—
176Dic271—41no—
177Dic271—41no—
178Dic271—41no—
179C2×C271—24no—
180C2×C271C2×C22⋊Q811yescharacteristic
181C2×C271#53311yescharacteristic
182C2×C271#54411yescharacteristic
183C2×C271#54611yescharacteristic
184C2×C271#54711yescharacteristic
185C2×C271#55111yescharacteristic
186C2×C271#55211yescharacteristic
187C271#243811yescharacteristic, complemented, Sylow
188#2438—2711nomaximal, Sylow
189C2×C22⋊Q8—2711no—
190C2×#117—2711no—
191#400—2711no—
192#398—2711no—
193#398—2711no—
194#395—2711no—
195#391—2711no—
196#389—2711no—
197#387—2711no—
198#387—2711no—
199#385—2711no—
200#385—2711no—
201#381D27111yescharacteristic
202#380—2711no—
203C2×#95—2711no—
204C22×Q8—2711no—
205C23×C4—2711no—
206C23×C4—2711no—
207C23×C4C2×D27111yescharacteristic
208C22⋊Q8—5424no—
209#117—5424no—
210C2×C4⋊C4—2711no—
211C2×C4⋊C4—2711no—
212C2×C4⋊C4—2711no—
213C2×C4⋊C4—2711no—
214C2×C4⋊C4—2711no—
215C2×C4⋊C4—2711no—
216C2×C4⋊C4—2711no—
217C2×C4⋊C4—2711no—
218C2×C4⋊C4—2711no—
219C2×C4⋊C4—2711no—
220C2×C4⋊C4—2711no—
221C2×C22⋊C4—2711no—
222C2×C22⋊C4—2711no—
223C2×C22⋊C4C2×D27111yescharacteristic
224C2×C22⋊C4C2×D27111yescharacteristic
225C2×C42—2711no—
226C2×C42—2711no—
227#95—2711no—
228#95—2711no—
229#95—2711no—
230#95—2711no—
231#95—2711no—
232#95—2711no—
233#95—2711no—
234#95—2711no—
235#95—2711no—
236#95—2711no—
237#95C2×D27111yescharacteristic
238#95C2×D27111yescharacteristic
239#95C2×D27111yescharacteristic
240#95C2×D27111yescharacteristic
241C24C22×D27111yescharacteristic
242C2×Q8—5422no—
243C2×Q8—5422no—
244C2×Q8—10841no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—2711no—
248C22×C4—2711no—
249C22×C4—2711no—
250C22×C4—2711no—
251C22×C4—2711no—
252C22×C4—2711no—
253C22×C4—2711no—
254C22×C4—2711no—
255C22×C4—5422no—
256C22×C4—5422no—
257C22×C4—5422no—
258C22×C4—5422no—
259C22×C4—10841no—
260C22×C4—10841no—
261C22×C4Dic54214yescomplemented
262C22×C4C22×D27111yescharacteristic
263C22×C4C22×D27111yescharacteristic
264C22×C4C22×D27111yescharacteristic
265C22×C4C22×D27111yescharacteristic
266C22×C4C22×D27111yescharacteristic
267C22×C4C22×D27111yescharacteristic
268C4⋊C4—5422no—
269C4⋊C4—5422no—
270C4⋊C4—5422no—
271C4⋊C4—5422no—
272C4⋊C4—5422no—
273C4⋊C4—5422no—
274C4⋊C4—5422no—
275C4⋊C4—5422no—
276C4⋊C4—10841no—
277C4⋊C4—10841no—
278C4⋊C4—10841no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—2714no—
282C22⋊C4—5422no—
283C42—5422no—
284C42—5422no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23D4×D27112yes—
290C23C2×Dic54212yes—
291C23#1686465312yes—
292C23C23×D27111yescharacteristic
293Q8—10844no—
294C2×C4—28no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—2712no—
312C2×C4—2712no—
313C2×C4—2712no—
314C2×C4—2712no—
315C2×C4—5421no—
316C2×C4—5421no—
317C2×C4—5421no—
318C2×C4—5421no—
319C2×C4—5421no—
320C2×C4—5421no—
321C2×C4—5421no—
322C2×C4—5421no—
323C2×C4—5421no—
324C2×C4—5421no—
325C2×C4—5421no—
326C2×C4—5421no—
327C2×C4—5421no—
328C2×C4—5421no—
329C2×C4—5421no—
330C2×C4—5421no—
331C2×C4—5421no—
332C2×C4—5421no—
333C2×C4—5421no—
334C2×C4—5421no—
335C2×C4—10844no—
336C2×C4—10844no—
337C2×C4C2×Dic54212yes—
338C2×C4C2×Dic54212yes—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22#2257613714yes—
346C22C2×D4×D27111yescharacteristic
347C22C22×Dic54211yescharacteristic
348C22#41×D27111yescharacteristic
349C22#41×D27111yescharacteristic
350C22C2×#1686465311yescharacteristic
351C22#2257620611yescharacteristic
352C22#2257620711yescharacteristic
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—5422no—
360C4—5422no—
361C4—5422no—
362C4—5422no—
363C4—10841no—
364C4—10841no—
365C4—10841no—
366C4—10841no—
367C2—24no—
368C2C2×#2257613711yescharacteristic
369C2#3177445011yescharacteristic
370C2#3177452511yescharacteristic
371C2#3177453911yescharacteristic
372C2#3177454511yescharacteristic
373C2#3177457011yescharacteristic
374C2#3177458411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D271
commutator, socle, cosocleC23×C271C24
Fitting#381×C271C2
prime radicalC24×C271C23
hypercenter#381D271
hypocenterC271#2438
LCSG ▷ C23×C271 ▷ C271
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #31773839C2semidirect
4. #31773831C2semidirect
5. #31773829C2semidirect
6. #31773818C2semidirect
7. #31773801C2semidirect
8. #31773794C2semidirect
9. #31773784C2semidirect
10. #31773780C2semidirect
88. C22×C4×C271Q8semidirect
187. C271#2438semidirect
261. C22×C4Dic542semidirect

Maximal subgroups

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

subgroupindex
C2×#225761372
C2×#225761192
#317738392
#317738312
#317738292
#317738182
#317738012
#317737942
#317737842
#317737802
#317737722
#317737692
#317737552
C2×C271⋊#952
#381×C2712
#2438271