Finite Group Databasebeta

← #46839860

Subgroups — #46839860

Order 34688.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22576137C211yesmaximal, characteristic
2C2×#22576125C211yesmaximal, characteristic, complemented
3#31773839C211yesmaximal, characteristic, complemented
4#31773835C211yesmaximal, characteristic, complemented
5#31773825C211yesmaximal, characteristic
6#31773801C211yesmaximal, characteristic, complemented
7#31773794C211yesmaximal, characteristic, complemented
8#31773790C211yesmaximal, characteristic
9#31773785C211yesmaximal, characteristic
10#31773784C211yesmaximal, characteristic, complemented
11#31773782C211yesmaximal, characteristic, complemented
12#31773761C211yesmaximal, characteristic, complemented
13#31773755C211yesmaximal, characteristic
14C22⋊C4×Dic271C211yesmaximal, characteristic
15#397×C271C211yesmaximal, characteristic
16C22×Dic542C2211yescharacteristic
17C23×Dic271C2211yescharacteristic
18#22576137—24no—
19#22576125—24no—
20C2×C4⋊Dic271C2211yescharacteristic
21C2×C4⋊Dic271C2211yescharacteristic
22C2×Dic271⋊C4C2211yescharacteristic
23C2×Dic271⋊C4C2211yescharacteristic
24C2×Dic271⋊C4C2211yescharacteristic
25C2×Dic271⋊C4C2211yescharacteristic
26C2×Dic271⋊C4C2211yescharacteristic
27C2×Dic271⋊C4C2211yescharacteristic
28C2×C22⋊Dic271C2211yescharacteristic
29C2×C22⋊Dic271C2211yescharacteristic
30C2×C22⋊Dic271C2211yescharacteristic
31C2×C4×Dic271C2211yescharacteristic
32C2×C4×Dic271C2211yescharacteristic
33C2×C4×Dic271C2211yescharacteristic
34C2×C4×Dic271C2211yescharacteristic
35C271⋊#95C2211yescharacteristic
36C271⋊#95C2211yescharacteristic
37C271⋊#95C2211yescharacteristic
38C271⋊#95C2211yescharacteristic
39C271⋊#95C2211yescharacteristic
40C271⋊#95C2211yescharacteristic
41C271⋊#95C2211yescharacteristic
42C271⋊#95C2211yescharacteristic
43C271⋊#95C2211yescharacteristic
44C271⋊#95C2211yescharacteristic
45C271⋊#95C2211yescharacteristic
46C2×C4⋊C4×C271C2211yescharacteristic
47C2×C22⋊C4×C271C2211yescharacteristic
48C2×C22⋊C4×C271C2211yescharacteristic
49C2×C22⋊C4×C271C2211yescharacteristic
50#95×C271C2211yescharacteristic
51#95×C271C2211yescharacteristic
52#95×C271C2211yescharacteristic
53C2×Dic542—22no—
54C2×Dic542—22no—
55C2×Dic542D414yes—
56C22×Dic271—22no—
57C22×Dic271—22no—
58C22×Dic271—22no—
59C22×Dic271C2311yescharacteristic
60C22×Dic271C2311yescharacteristic
61C22×Dic271C2311yescharacteristic
62C22×Dic271C2311yescharacteristic
63C22×Dic271C2311yescharacteristic
64C22×Dic271C2311yescharacteristic
65C22×Dic271C2311yescharacteristic
66C22×Dic271C2311yescharacteristic
67C4⋊Dic271—22no—
68C4⋊Dic271—22no—
69Dic271⋊C4—22no—
70Dic271⋊C4—22no—
71Dic271⋊C4—22no—
72Dic271⋊C4—22no—
73Dic271⋊C4—22no—
74Dic271⋊C4—22no—
75C22⋊Dic271—22no—
76C22⋊Dic271—22no—
77C22⋊Dic271—22no—
78C4×Dic271—22no—
79C4×Dic271—22no—
80C4×Dic271—22no—
81C4×Dic271—22no—
82C24×C271C2311yescharacteristic
83C22×C4×C271C2311yescharacteristic
84C22×C4×C271C2311yescharacteristic
85C22×C4×C271C2311yescharacteristic
86C22×C4×C271C2311yescharacteristic
87C22×C4×C271C2311yescharacteristic
88C22×C4×C271C2311yescharacteristic
89C4⋊C4×C271—22no—
90C22⋊C4×C271—22no—
91C22⋊C4×C271—22no—
92C22⋊C4×C271—22no—
93Dic542—28no—
94C2×Dic271—21no—
95C2×Dic271—21no—
96C2×Dic271—21no—
97C2×Dic271—21no—
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—44no—
114C2×Dic271C2×D412yes—
115C2×Dic271C2×D412yes—
116C2×Dic271#4112yes—
117C2×Dic271#4112yes—
118C2×Dic271#4112yes—
119C23×C271—21no—
120C23×C271—21no—
121C23×C271—21no—
122C23×C271—21no—
123C23×C271—21no—
124C23×C271—21no—
125C23×C271#4112yes—
126C23×C271C2411yescharacteristic
127C2×C4×C271—21no—
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—
145C22×C271—22no—
146C22×C271—22no—
147C22×C271—22no—
148C22×C271—41no—
149C22×C271—41no—
150C22×C271—41no—
151C22×C271—41no—
152C22×C271C22×D411yescharacteristic
153C22×C271C2×#4111yescharacteristic
154C22×C271C2×#4111yescharacteristic
155C22×C271C2×#4111yescharacteristic
156C22×C271C2×#4111yescharacteristic
157C22×C2712−1+411yescharacteristic
158C22×C2712−1+411yescharacteristic
159C4×C271—22no—
160C4×C271—41no—
161C4×C271—41no—
162C4×C271—41no—
163C4×C271—41no—
164C4×C271—41no—
165Dic271—22no—
166Dic271—22no—
167Dic271—41no—
168Dic271—41no—
169Dic271—41no—
170Dic271—41no—
171Dic271—41no—
172Dic271#12314yes—
173C2×C271—42no—
174C2×C271C2×#12311yescharacteristic
175C2×C271#52911yescharacteristic
176C2×C271#54111yescharacteristic
177C2×C271#54811yescharacteristic
178C2×C271#54811yescharacteristic
179C2×C271#55211yescharacteristic
180C2×C271#55611yescharacteristic
181C271#242111yescharacteristic, complemented, Sylow
182#2421—2711nomaximal, Sylow
183C2×C22⋊Q8—2711no—
184C2×C4×Q8—2711no—
185#400—2711no—
186#400—2711no—
187#397—2711no—
188#397D27111yescharacteristic
189#391—2711no—
190#389—2711no—
191#388—2711no—
192#388—2711no—
193#387—2711no—
194#387—2711no—
195#382—2711no—
196#380—2711no—
197C4×C22⋊C4—2711no—
198C22×Q8—2711no—
199C23×C4—2711no—
200C22⋊Q8—5424no—
201C4×Q8—5424no—
202C2×C4⋊C4—2711no—
203C2×C4⋊C4—2711no—
204C2×C4⋊C4—2711no—
205C2×C4⋊C4—2711no—
206C2×C4⋊C4—2711no—
207C2×C4⋊C4—2711no—
208C2×C4⋊C4—2711no—
209C2×C4⋊C4—2711no—
210C2×C4⋊C4C2×D27111yescharacteristic
211C2×C22⋊C4—2711no—
212C2×C22⋊C4—2711no—
213C2×C22⋊C4—2711no—
214C2×C22⋊C4C2×D27111yescharacteristic
215C2×C22⋊C4C2×D27111yescharacteristic
216C2×C22⋊C4C2×D27111yescharacteristic
217C2×C42—2711no—
218C2×C42—2711no—
219C2×C42—2711no—
220C2×C42—2711no—
221#95—2711no—
222#95—2711no—
223#95—2711no—
224#95—2711no—
225#95—2711no—
226#95—2711no—
227#95—2711no—
228#95—2711no—
229#95—2711no—
230#95—2711no—
231#95—2711no—
232#95C2×D27111yescharacteristic
233#95C2×D27111yescharacteristic
234#95C2×D27111yescharacteristic
235C24C22×D27111yescharacteristic
236C2×Q8—2714no—
237C2×Q8—5422no—
238C2×Q8—5422no—
239C22×C4—2711no—
240C22×C4—2711no—
241C22×C4—2711no—
242C22×C4—2711no—
243C22×C4—2711no—
244C22×C4—2711no—
245C22×C4—2711no—
246C22×C4—2711no—
247C22×C4—5422no—
248C22×C4—5422no—
249C22×C4—5422no—
250C22×C4C22×D27111yescharacteristic
251C22×C4C22×D27111yescharacteristic
252C22×C4C22×D27111yescharacteristic
253C22×C4C22×D27111yescharacteristic
254C22×C4C22×D27111yescharacteristic
255C22×C4C22×D27111yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—5422no—
258C4⋊C4—5422no—
259C4⋊C4—5422no—
260C4⋊C4—5422no—
261C4⋊C4—5422no—
262C4⋊C4—5422no—
263C4⋊C4—5422no—
264C4⋊C4—5422no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—5422no—
269C22⋊C4—5422no—
270C22⋊C4—5422no—
271C42—5422no—
272C42—5422no—
273C42—5422no—
274C42—5422no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23#1686465312yes—
282C23C23×D27111yescharacteristic
283Q8—5428no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
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—2712no—
302C2×C4—2712no—
303C2×C4—2712no—
304C2×C4—2712no—
305C2×C4—2712no—
306C2×C4—5421no—
307C2×C4—5421no—
308C2×C4—5421no—
309C2×C4—5421no—
310C2×C4—5421no—
311C2×C4—5421no—
312C2×C4—5421no—
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—5421no—
324C2×C4—5421no—
325C2×C4—10844no—
326C2×C4D4×D27112yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22C2×D4×D27111yescharacteristic
335C22#41×D27111yescharacteristic
336C22#41×D27111yescharacteristic
337C22#41×D27111yescharacteristic
338C22C2×#1686465311yescharacteristic
339C22#2257620711yescharacteristic
340C22#2257620711yescharacteristic
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—2714no—
348C4—5422no—
349C4—5422no—
350C4—10841no—
351C4—10841no—
352C4—10841no—
353C4—10841no—
354C4—10841no—
355C2—42no—
356C2#123×D27111yescharacteristic
357C2#3177442411yescharacteristic
358C2#3177450411yescharacteristic
359C2#3177455311yescharacteristic
360C2#3177455511yescharacteristic
361C2#3177458411yescharacteristic
362C2#3177461411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D271
commutator, socle, cosocleC23×C271C24
Fitting#397×C271C2
prime radicalC24×C271C23
hypercenter#397D271
hypocenterC271#2421
LCSG ▷ C23×C271 ▷ C271
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#22576125C2semidirect
3. #31773839C2semidirect
4. #31773835C2semidirect
6. #31773801C2semidirect
7. #31773794C2semidirect
10. #31773784C2semidirect
11. #31773782C2semidirect
12. #31773761C2semidirect
181. C271#2421semidirect

Maximal subgroups

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

subgroupindex
C2×#225761372
C2×#225761252
#317738392
#317738352
#317738252
#317738012
#317737942
#317737902
#317737852
#317737842
#317737822
#317737612
#317737552
C22⋊C4×Dic2712
#397×C2712
#2421271