Finite Group Databasebeta

← #21436141

Subgroups — #21436141

Order 7552.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic118C211yesmaximal, characteristic
2#16837772C211yesmaximal, characteristic, complemented
3#16837743C211yesmaximal, characteristic, complemented
4#16837732C211yesmaximal, characteristic, complemented
5#16837706C211yesmaximal, characteristic, complemented
6#16837658C211yesmaximal, characteristic, complemented
7#16837641C211yesmaximal, characteristic, complemented
8#16837612C211yesmaximal, characteristic, complemented
9#16837557C211yesmaximal, characteristic, complemented
10#16837557C211yesmaximal, characteristic, complemented
11#16837507C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic
13#16837410C211yesmaximal, characteristic, complemented
14C2×#14273650C211yesmaximal, characteristic, complemented
15C59×#552C211yesmaximal, characteristic
16C22×Dic118C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745672C2211yescharacteristic
20C2×#11745672C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22C22×C59⋊C8C2211yescharacteristic
23#14273727C2211yescharacteristic
24#14273726—21no—
25#14273706C2211yescharacteristic
26#14273706C2211yescharacteristic
27#14273704—21no—
28#14273704—21no—
29C4×Dic118C2211yescharacteristic
30D4×Dic59—21no—
31#14273660C2211yescharacteristic
32#14273658C2211yescharacteristic
33#14273658C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273651C2211yescharacteristic
36#14273650C2211yescharacteristic
37#14273650C2211yescharacteristic
38#14273650C2211yescharacteristic
39#14273650C2211yescharacteristic
40#14273650C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273650C2211yescharacteristic
43#14273650C2211yescharacteristic
44#14273650C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48#126×C59—21no—
49#125×C59—21no—
50#125×C59C2211yescharacteristic
51#123×C59—21no—
52C22⋊Q8×C59C2211yescharacteristic
53C22⋊Q8×C59C2211yescharacteristic
54C4×Q8×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic
56#117×C59—21no—
57#117×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59D411yescharacteristic
61C22×C4×C59—21no—
62C22×C4×C59C2311yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C22×Dic59—21no—
65C22×Dic59—21no—
66C2×Dic118—22no—
67C2×Dic118—22no—
68C2×Dic118—21no—
69C2×Dic118—21no—
70C2×Dic118—41no—
71C2×Dic118—41no—
72C2×Dic118C2311yescharacteristic
73C2×Dic118C2311yescharacteristic
74C2×Dic118C2311yescharacteristic
75C4⋊C4×C59—21no—
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59D411yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C22⋊C4×C59—21no—
88C22⋊C4×C59D411yescharacteristic
89C22⋊C4×C59D411yescharacteristic
90C42×C59—21no—
91C42×C59—21no—
92C42×C59C2311yescharacteristic
93C22⋊Dic59—21no—
94C22⋊Dic59—21no—
95#11745672—22no—
96#11745672—41no—
97#11745672—41no—
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105#11745664—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59C2×D411yescharacteristic
112C23×C59C2×D411yescharacteristic
113Q8×C59—21no—
114Q8×C59—21no—
115D4×C59—22no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—42no—
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2411yescharacteristic
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—42no—
135C2×Dic59—42no—
136Dic118—21no—
137Dic118—21no—
138Dic118—21no—
139Dic118—21no—
140Dic118—21no—
141Dic118—42no—
142Dic118—42no—
143Dic118#4112yes—
144C59⋊C8—21no—
145C59⋊C8—21no—
146C59⋊C8—21no—
147C59⋊C8—21no—
148C22×C59—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59#13712yes—
154C22×C59C22×D411yescharacteristic
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—41no—
160C4×C59—41no—
161C4×C59—41no—
162C4×C59—41no—
163C4×C59C2×#4111yescharacteristic
164C4×C59H(5,𝔽2)11yescharacteristic
165Dic59—22no—
166Dic59—41no—
167Dic59—41no—
168Dic59—41no—
169#3312—591nomaximal, Sylow
170C2×C59—22no—
171C2×C59—41no—
172C2×C59#54611yescharacteristic
173C2×C59C2×#13711yescharacteristic
174C2×C59#57811yescharacteristic
175#552D5911yescharacteristic
176D4×Q8—591no—
177#491—591no—
178#485—591no—
179#483—591no—
180#479—591no—
181#470—591no—
182#467—591no—
183#462—591no—
184#451—591no—
185#451—591no—
186#441—591no—
187#435—591no—
188#419—591no—
189C2×#103—591no—
190C59#331211yescharacteristic, complemented, Sylow
191C22×Q8—591no—
192C22×Q8—591no—
193C2×Q16—591no—
194C2×Q16—591no—
195C2×Q16—591no—
196C2×M16—591no—
197C22×C8—591no—
198C4⋊Q8—591no—
199C4⋊Q8—1181no—
200#126—21no—
201#125—21no—
202#125C2×D5911yescharacteristic
203#123—21no—
204C22⋊Q8—591no—
205C22⋊Q8—591no—
206C22⋊Q8—1181no—
207C22⋊Q8—1181no—
208C22⋊Q8C2×D5911yescharacteristic
209C22⋊Q8C2×D5911yescharacteristic
210C4×Q8—591no—
211C4×Q8C2×D5911yescharacteristic
212C4×D4—1181no—
213C4×D4C2×D5911yescharacteristic
214#117—21no—
215#117C2×D5911yescharacteristic
216C2×C4⋊C4C2×D5911yescharacteristic
217#107—591no—
218#106—591no—
219#106—591no—
220C4⋊C8—591no—
221#103—591no—
222#103—591no—
223#103—591no—
224#103—591no—
225#103—591no—
226#103—591no—
227#103—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231C22⋊C8—591no—
232C22⋊C8—591no—
233#97—591no—
234C2×Q8—591no—
235C2×Q8—591no—
236C2×Q8—591no—
237C2×Q8—1182no—
238C2×Q8—1182no—
239C2×Q8—1181no—
240C2×Q8—1181no—
241C2×Q8—2361no—
242C2×Q8—2361no—
243C2×Q8C22×D5911yescharacteristic
244C2×D4C22⋊D5911yescharacteristic
245C22×C4—21no—
246C22×C4—1181no—
247C22×C4—1181no—
248C22×C4C22×D5911yescharacteristic
249C22×C4C22×D5911yescharacteristic
250Q16—1182no—
251Q16—2361no—
252Q16—2361no—
253M16—2361no—
254C2×C8—591no—
255C2×C8—591no—
256C2×C8—591no—
257C2×C8—591no—
258C2×C8—2361no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—591no—
266C4⋊C4—1181no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4C22⋊D5911yescharacteristic
272C4⋊C4C22×D5911yescharacteristic
273C4⋊C4C22×D5911yescharacteristic
274C4⋊C4C22×D5911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4C22⋊D5911yescharacteristic
281C22⋊C4C22⋊D5911yescharacteristic
282C42—21no—
283C42—21no—
284C42—1181no—
285C42C22×D5911yescharacteristic
286C23C2×C22⋊D5911yescharacteristic
287C23C2×C22⋊D5911yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—592no—
291Q8—1181no—
292Q8—1181no—
293Q8—1181no—
294Q8—1181no—
295Q8—1181no—
296Q8—2362no—
297Q8—2362no—
298D4—22no—
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—42no—
308C2×C4—1181no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—1181no—
312C2×C4—2362no—
313C2×C4—2362no—
314C2×C4C2×C22⋊D5911yescharacteristic
315C2×C4C2×C22⋊D5911yescharacteristic
316C2×C4C2×C22⋊D5911yescharacteristic
317C2×C4C2×C22⋊D5911yescharacteristic
318C2×C4C23×D5911yescharacteristic
319C8—1181no—
320C8—1181no—
321C8—1181no—
322C8—1181no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#1427375712yes—
329C22C22×C22⋊D5911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—1182no—
339C4—2361no—
340C4—2361no—
341C4—2361no—
342C4#41×D5911yescharacteristic
343C4#1427377311yescharacteristic
344C2—22no—
345C2—41no—
346C2#1683804011yescharacteristic
347C2C2×#1427375711yescharacteristic
348C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#552C2
socleC22×C59C22×D4
hypercenter#552D59
hypocenterC59#3312
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #16837772C2semidirect
3. #16837743C2semidirect
4. #16837732C2semidirect
5. #16837706C2semidirect
6. #16837658C2semidirect
7. #16837641C2semidirect
8. #16837612C2semidirect
9. #16837557C2semidirect
10. #16837557C2semidirect
11. #16837507C2semidirect
13. #16837410C2semidirect
14. C2×#14273650C2semidirect
190. C59#3312semidirect