Finite Group Databasebeta

← #46839640

Subgroups — #46839640

Order 34688.

528 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Dic542C211yesmaximal, characteristic, complemented
2C2×#22576117C211yesmaximal, characteristic
3#31773838C211yesmaximal, characteristic, complemented
4#31773832C211yesmaximal, characteristic
5#31773831C211yesmaximal, characteristic, complemented
6#31773828C211yesmaximal, characteristic, complemented
7#31773821C211yesmaximal, characteristic
8#31773819C211yesmaximal, characteristic
9#31773817C211yesmaximal, characteristic, complemented
10#31773810C211yesmaximal, characteristic
11C4×Dic271⋊C4C211yesmaximal, characteristic, complemented
12C4×Dic271⋊C4C211yesmaximal, characteristic, complemented
13C4×(C2×D271)⋊C4C211yesmaximal, characteristic
14C4×(C2×D271)⋊C4C211yesmaximal, characteristic
15C4×C4⋊C4×C271C211yesmaximal, characteristic, complemented
16C22×Dic542C2211yescharacteristic
17C22×C4×D271C2211yescharacteristic
18C4×Dic542—24no—
19#22576117—24no—
20C2×C4⋊Dic271C2211yescharacteristic
21C2×Dic271⋊C4C2211yescharacteristic
22C2×Dic271⋊C4C2211yescharacteristic
23C2×Dic271⋊C4C2211yescharacteristic
24C2×Dic271⋊C4C2211yescharacteristic
25C2×Dic271⋊C4C2211yescharacteristic
26C2×Dic271⋊C4C2211yescharacteristic
27C2×Dic271⋊C4C2211yescharacteristic
28C2×Dic271⋊C4C2211yescharacteristic
29C2×(C2×D271)⋊C4C2211yescharacteristic
30C2×(C2×D271)⋊C4C2211yescharacteristic
31C2×(C2×D271)⋊C4C2211yescharacteristic
32C2×(C2×D271)⋊C4C2211yescharacteristic
33C2×(C2×D271)⋊C4C2211yescharacteristic
34C2×(C2×D271)⋊C4C2211yescharacteristic
35C2×C4×Dic271C2211yescharacteristic
36C2×C4×Dic271C2211yescharacteristic
37C2×C4×Dic271C2211yescharacteristic
38C271⋊#95C2211yescharacteristic
39C271⋊#95C2211yescharacteristic
40C271⋊#95C2211yescharacteristic
41C271⋊#95C2211yescharacteristic
42C271⋊#95C2211yescharacteristic
43C271⋊#95C2211yescharacteristic
44C271⋊#95C2211yescharacteristic
45C271⋊#95C2211yescharacteristic
46C2×C4⋊C4×C271C2211yescharacteristic
47C2×C4⋊C4×C271C2211yescharacteristic
48C2×C42×C271C2211yescharacteristic
49C2×C42×C271C2211yescharacteristic
50C2×C42×C271C2211yescharacteristic
51#95×C271C2211yescharacteristic
52#95×C271C2211yescharacteristic
53C23×D271C2311yescharacteristic
54C2×Dic542—22no—
55C2×Dic542—22no—
56C2×Dic542—22no—
57C22×Dic271C2311yescharacteristic
58C22×Dic271C2311yescharacteristic
59C22×Dic271C2311yescharacteristic
60C22×Dic271C2311yescharacteristic
61C22×Dic271C2311yescharacteristic
62C22×Dic271C2311yescharacteristic
63C22×Dic271C2311yescharacteristic
64C2×C4×D271—22no—
65C2×C4×D271—22no—
66C2×C4×D271Q814yescomplemented
67C4⋊Dic271—22no—
68Dic271⋊C4—22no—
69Dic271⋊C4—22no—
70Dic271⋊C4—22no—
71Dic271⋊C4—22no—
72Dic271⋊C4—22no—
73Dic271⋊C4—22no—
74Dic271⋊C4—22no—
75Dic271⋊C4—22no—
76(C2×D271)⋊C4—22no—
77(C2×D271)⋊C4—22no—
78(C2×D271)⋊C4—22no—
79(C2×D271)⋊C4—22no—
80(C2×D271)⋊C4—22no—
81(C2×D271)⋊C4—22no—
82C4×Dic271—22no—
83C4×Dic271—22no—
84C4×Dic271D414yes—
85C22×C4×C271C2311yescharacteristic
86C22×C4×C271C2311yescharacteristic
87C22×C4×C271C2311yescharacteristic
88C22×C4×C271C2311yescharacteristic
89C22×C4×C271C2311yescharacteristic
90C22×C4×C271C2311yescharacteristic
91C22×C4×C271C2311yescharacteristic
92C4⋊C4×C271—22no—
93C4⋊C4×C271—22no—
94C42×C271—22no—
95C42×C271—22no—
96C42×C271—22no—
97C22×D271—21no—
98C22×D271—21no—
99C22×D271—21no—
100C22×D271—21no—
101C22×D271—21no—
102C22×D271—21no—
103C22×D271C2×Q812yes—
104Dic542—28no—
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—21no—
119C2×Dic271—21no—
120C2×Dic271—21no—
121C2×Dic271C2×D412yes—
122C2×Dic271C2×D412yes—
123C2×Dic271C2×Q812yes—
124C2×Dic271#4112yes—
125C2×Dic271#4112yes—
126C4×D271—28no—
127C23×C271C2411yescharacteristic
128C2×C4×C271—21no—
129C2×C4×C271—21no—
130C2×C4×C271—21no—
131C2×C4×C271—21no—
132C2×C4×C271—21no—
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×C271C2×D412yes—
145C2×C4×C271C2×Q812yes—
146C2×C4×C271#4112yes—
147C2×C4×C271#4112yes—
148C2×C4×C271#4112yes—
149C22×C271C22×D411yescharacteristic
150C22×C271C22×Q811yescharacteristic
151C22×C271C2×#4111yescharacteristic
152C22×C271C2×#4111yescharacteristic
153C22×C271C2×#4111yescharacteristic
154C22×C271C2×#4111yescharacteristic
155C22×C271C2×#4111yescharacteristic
156C2×D271—22no—
157C2×D271—22no—
158C2×D271—22no—
159C2×D271—41no—
160C2×D271—41no—
161C2×D271—41no—
162C2×D271—41no—
163C4×C271—22no—
164C4×C271—22no—
165C4×C271—41no—
166C4×C271—41no—
167C4×C271—41no—
168C4×C271—41no—
169C4×C271C22⋊Q814yes—
170Dic271—22no—
171Dic271—22no—
172Dic271—22no—
173Dic271—22no—
174Dic271—22no—
175Dic271—41no—
176Dic271—41no—
177C2×C271C2×C22⋊Q811yescharacteristic
178C2×C271#52511yescharacteristic
179C2×C271#52911yescharacteristic
180C2×C271#52911yescharacteristic
181C2×C271#53211yescharacteristic
182C2×C271#53311yescharacteristic
183C2×C271#53311yescharacteristic
184D271—42no—
185C271#239611yescharacteristic, complemented, Sylow
186#2396—2711nomaximal, Sylow
187C2×C4×Q8—2711no—
188C2×#117—2711no—
189#400—2711no—
190#399—2711no—
191#398—2711no—
192#398—2711no—
193#396—2711no—
194#396—2711no—
195#395—2711no—
196#393—2711no—
197C4×C4⋊C4—2711no—
198C4×C4⋊C4—2711no—
199C4×C4⋊C4D27111yescharacteristic, complemented
200C4×C22⋊C4—2711no—
201C4×C22⋊C4—2711no—
202C22×Q8—2711no—
203C23×C4—2711no—
204C4×Q8—5424no—
205#117—5424no—
206C2×C4⋊C4—2711no—
207C2×C4⋊C4—2711no—
208C2×C4⋊C4—2711no—
209C2×C4⋊C4—2711no—
210C2×C4⋊C4—2711no—
211C2×C4⋊C4—2711no—
212C2×C4⋊C4—2711no—
213C2×C4⋊C4—2711no—
214C2×C4⋊C4—2711no—
215C2×C4⋊C4C2×D27111yescharacteristic
216C2×C4⋊C4C2×D27111yescharacteristic
217C2×C22⋊C4—2711no—
218C2×C22⋊C4—2711no—
219C2×C22⋊C4—2711no—
220C2×C22⋊C4—2711no—
221C2×C22⋊C4—2711no—
222C2×C22⋊C4—2711no—
223C2×C42—2711no—
224C2×C42—2711no—
225C2×C42—2711no—
226C2×C42C2×D27111yescharacteristic
227C2×C42C2×D27111yescharacteristic
228C2×C42C2×D27111yescharacteristic
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
239C24—2711no—
240C2×Q8—5422no—
241C2×Q8—5422no—
242C2×Q8—5422no—
243C22×C4—2711no—
244C22×C4—2711no—
245C22×C4—2711no—
246C22×C4—2711no—
247C22×C4—2711no—
248C22×C4—2714no—
249C22×C4—2711no—
250C22×C4—2711no—
251C22×C4—5422no—
252C22×C4—5422no—
253C22×C4C22×D27111yescharacteristic
254C22×C4C22×D27111yescharacteristic
255C22×C4C22×D27111yescharacteristic
256C22×C4C22×D27111yescharacteristic
257C22×C4C22×D27111yescharacteristic
258C22×C4C22×D27111yescharacteristic
259C22×C4C22×D27111yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—5422no—
263C4⋊C4—5422no—
264C4⋊C4—5422no—
265C4⋊C4—5422no—
266C4⋊C4—5422no—
267C4⋊C4—5422no—
268C4⋊C4—5422no—
269C4⋊C4—5422no—
270C4⋊C4—5422no—
271C22⋊C4—5422no—
272C22⋊C4—5422no—
273C22⋊C4—5422no—
274C22⋊C4—5422no—
275C22⋊C4—5422no—
276C22⋊C4—5422no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—2714no—
281C42—5422no—
282C42—5422no—
283C23—2712no—
284C23—5421no—
285C23—5421no—
286C23—5421no—
287C23—5421no—
288C23—5421no—
289C23—5421no—
290C23C23×D27111yescharacteristic
291Q8—5428no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
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—2712no—
309C2×C4—2712no—
310C2×C4—2712no—
311C2×C4—2712no—
312C2×C4—2712no—
313C2×C4—5421no—
314C2×C4—5421no—
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—5428no—
324C2×C4—5421no—
325C2×C4—5421no—
326C2×C4—5421no—
327C2×C4—5421no—
328C2×C4—5421no—
329C2×C4—5421no—
330C2×C4D4×D27112yes—
331C2×C4Q8×D27112yes—
332C2×C4#1686465412yes—
333C2×C4#1686465412yes—
334C2×C4#1686465412yes—
335C22—5422no—
336C22—5422no—
337C22—5422no—
338C22—10841no—
339C22—10841no—
340C22—10841no—
341C22—10841no—
342C22C2×D4×D27111yescharacteristic
343C22C2×Q8×D27111yescharacteristic
344C22#41×D27111yescharacteristic
345C22#41×D27111yescharacteristic
346C22C2×#1686465411yescharacteristic
347C22C2×#1686465411yescharacteristic
348C22C2×#1686465411yescharacteristic
349C4—22no—
350C4—22no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—5422no—
356C4—5422no—
357C4—5422no—
358C4—5422no—
359C4—5422no—
360C4—10841no—
361C4—10841no—
362C4#2257613814yes—
363C2—10842no—
364C2C2×#2257613811yescharacteristic
365C2#3177440611yescharacteristic
366C2#3177442511yescharacteristic
367C2#3177443111yescharacteristic
368C2#3177444411yescharacteristic
369C2#3177445111yescharacteristic
370C2#3177445111yescharacteristic
subgroupG/H
centerC22×C4C22×D271
commutator, socle, cosocleC23×C271C24
FrattiniC23C23×D271
FittingC4×C4⋊C4×C271C2
prime radicalC23×D271C23
hypercenterC4×C4⋊C4D271
hypocenterC271#2396
LCSG ▷ C23×C271 ▷ C271
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic542C2semidirect
3. #31773838C2semidirect
5. #31773831C2semidirect
6. #31773828C2semidirect
9. #31773817C2semidirect
11. C4×Dic271⋊C4C2semidirect
12. C4×Dic271⋊C4C2semidirect
15. C4×C4⋊C4×C271C2semidirect
66. C2×C4×D271Q8semidirect
185. C271#2396semidirect
199. C4×C4⋊C4D271semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic5422
C2×#225761172
#317738382
#317738322
#317738312
#317738282
#317738212
#317738192
#317738172
#317738102
C4×Dic271⋊C42
C4×(C2×D271)⋊C42
C4×C4⋊C4×C2712
#2396271