Finite Group Databasebeta

← #21436147

Subgroups — #21436147

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
1#16838092C211yesmaximal, characteristic
2#16837770C211yesmaximal, characteristic, complemented
3#16837740C211yesmaximal, characteristic, complemented
4#16837730C211yesmaximal, characteristic, complemented
5#16837709C211yesmaximal, characteristic, complemented
6#16837658C211yesmaximal, characteristic, complemented
7#16837641C211yesmaximal, characteristic, complemented
8#16837609C211yesmaximal, characteristic, complemented
9#16837558C211yesmaximal, characteristic, complemented
10#16837558C211yesmaximal, characteristic, complemented
11#16837507C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic
13#16837411C211yesmaximal, characteristic, complemented
14C2×#14273651C211yesmaximal, characteristic, complemented
15D4×Q8×C59C211yesmaximal, characteristic
16C2×#11745672C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745664C2211yescharacteristic
20C22×C59⋊C8C2211yescharacteristic
21#14273720—21no—
22#14273719C2211yescharacteristic
23#14273717—21no—
24#14273708—21no—
25#14273706C2211yescharacteristic
26#14273706C2211yescharacteristic
27C4×Dic118C2211yescharacteristic
28#14273686C2211yescharacteristic
29#14273683—21no—
30C2×C4⋊Dic59C2211yescharacteristic
31#14273660C2211yescharacteristic
32#14273658C2211yescharacteristic
33#14273658C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273651C2211yescharacteristic
36#14273651C2211yescharacteristic
37#14273651C2211yescharacteristic
38#14273651C2211yescharacteristic
39#14273651C2211yescharacteristic
40#14273651C2211yescharacteristic
41#14273651C2211yescharacteristic
42#14273651C2211yescharacteristic
43#14273651C2211yescharacteristic
44#14273650C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48C22×Q8×C59C2211yescharacteristic
49C22×Q8×C59C2211yescharacteristic
50C4⋊Q8×C59—21no—
51C4⋊Q8×C59C2211yescharacteristic
52C22⋊Q8×C59—21no—
53C22⋊Q8×C59—21no—
54C22⋊Q8×C59C2211yescharacteristic
55C22⋊Q8×C59C2211yescharacteristic
56C4×Q8×C59C2211yescharacteristic
57C4×D4×C59—21no—
58C4×D4×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59—21no—
61C2×Q8×C59—22no—
62C2×Q8×C59—22no—
63C2×Q8×C59—41no—
64C2×Q8×C59—41no—
65C2×Q8×C59C2311yescharacteristic
66C2×Q8×C59C2311yescharacteristic
67C2×Q8×C59C2311yescharacteristic
68C2×D4×C59D411yescharacteristic
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59C2311yescharacteristic
72C22×C4×C59C2311yescharacteristic
73C22×Dic59—21no—
74C2×Dic118C2311yescharacteristic
75C4⋊C4×C59—21no—
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59D411yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C22⋊C4×C59—21no—
83C22⋊C4×C59—21no—
84C22⋊C4×C59D411yescharacteristic
85C22⋊C4×C59D411yescharacteristic
86C42×C59—21no—
87C42×C59C2311yescharacteristic
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91#11745672—22no—
92#11745672—41no—
93#11745672—41no—
94C4⋊Dic59—21no—
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103C4×Dic59—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—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—42no—
119Q8×C59—42no—
120Q8×C59#4112yes—
121D4×C59—22no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—42no—
131C2×C4×C59—42no—
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2411yescharacteristic
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—42no—
142Dic118—21no—
143Dic118—21no—
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—22no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—41no—
161C4×C59—41no—
162C4×C59—41no—
163C4×C59C2×#4111yescharacteristic
164C4×C59H(5,𝔽2)11yescharacteristic
165Dic59—41no—
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#552—591no—
176D4×Q8D5911yescharacteristic
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×Q8C2×D5911yescharacteristic
192C22×Q8C2×D5911yescharacteristic
193C2×Q16—591no—
194C2×Q16—591no—
195C2×Q16—591no—
196C2×M16—591no—
197C22×C8—591no—
198C4⋊Q8—21no—
199C4⋊Q8C2×D5911yescharacteristic
200#126—1181no—
201#125—591no—
202#125—1181no—
203#123—1181no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C22⋊Q8—591no—
207C22⋊Q8—591no—
208C22⋊Q8C2×D5911yescharacteristic
209C22⋊Q8C2×D5911yescharacteristic
210C4×Q8—591no—
211C4×Q8C2×D5911yescharacteristic
212C4×D4—21no—
213C4×D4C2×D5911yescharacteristic
214#117—591no—
215#117—1181no—
216C2×C4⋊C4—591no—
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—21no—
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—591no—
241C2×Q8C22×D5911yescharacteristic
242C2×Q8C22×D5911yescharacteristic
243C2×Q8C22×D5911yescharacteristic
244C2×D4C22⋊D5911yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
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—591no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4C22⋊D5911yescharacteristic
274C4⋊C4C22×D5911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4C22⋊D5911yescharacteristic
281C22⋊C4C22⋊D5911yescharacteristic
282C42—21no—
283C42—1181no—
284C42—1181no—
285C42C22×D5911yescharacteristic
286C23C2×C22⋊D5911yescharacteristic
287C23C2×C22⋊D5911yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—42no—
295Q8—1181no—
296Q8—1181no—
297Q8#1174568712yes—
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—42no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—1181no—
312C2×C4—1181no—
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#1427375812yes—
329C22C22×C22⋊D5911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—22no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—2361no—
339C4—2361no—
340C4—2361no—
341C4—2361no—
342C4C2×#1174568711yescharacteristic
343C4#1427377211yescharacteristic
344C2—22no—
345C2—41no—
346C2#1683804611yescharacteristic
347C2C2×#1427375811yescharacteristic
348C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingD4×Q8×C59C2
socleC22×C59C22×D4
hypercenterD4×Q8D59
hypocenterC59#3312
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #16837770C2semidirect
3. #16837740C2semidirect
4. #16837730C2semidirect
5. #16837709C2semidirect
6. #16837658C2semidirect
7. #16837641C2semidirect
8. #16837609C2semidirect
9. #16837558C2semidirect
10. #16837558C2semidirect
11. #16837507C2semidirect
13. #16837411C2semidirect
14. C2×#14273651C2semidirect
190. C59#3312semidirect