Finite Group Databasebeta

← #21436267

Subgroups — #21436267

Order 7552.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838098C211yesmaximal, characteristic
2#16837770C211yesmaximal, characteristic, complemented
3#16837740C211yesmaximal, characteristic, complemented
4#16837735C211yesmaximal, characteristic, complemented
5#16837709C211yesmaximal, characteristic, complemented
6#16837650C211yesmaximal, characteristic, complemented
7#16837633C211yesmaximal, characteristic, complemented
8#16837604C211yesmaximal, characteristic, complemented
9#16837541C211yesmaximal, characteristic, complemented
10#16837541C211yesmaximal, characteristic, complemented
11#16837500C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837411C211yesmaximal, characteristic, complemented
14C2×#14273651C211yesmaximal, characteristic, complemented
15D4×Q8×C59C211yesmaximal, characteristic, complemented
16C2×#11745671C2211yescharacteristic
17C2×#11745671C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19C2×#11745664C2211yescharacteristic
20C22×C59⋊C8C2211yescharacteristic
21#14273722—21no—
22#14273719C2211yescharacteristic
23#14273709—21no—
24#14273701C2211yescharacteristic
25#14273701C2211yescharacteristic
26#14273699—21no—
27C4×D236C2211yescharacteristic
28(C22⋊D59)⋊C4—21no—
29#14273686C2211yescharacteristic
30C2×C4⋊Dic59C2211yescharacteristic
31#14273660C2211yescharacteristic
32#14273660C2211yescharacteristic
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#14273647C2211yescharacteristic
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
73C2×C22⋊D59—21no—
74C2×C22⋊D59—21no—
75C22×Dic59—21no—
76C2×D236C2311yescharacteristic
77C2×C4×D59—21no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59D411yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C22⋊C4×C59D411yescharacteristic
88C22⋊C4×C59D411yescharacteristic
89C42×C59—21no—
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92#11745671—22no—
93#11745671—41no—
94#11745671—41no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
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
113C22×D59—21no—
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—21no—
119Q8×C59—42no—
120Q8×C59—42no—
121Q8×C59#4112yes—
122D4×C59—22no—
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—21no—
131C2×C4×C59—42no—
132C2×C4×C59—42no—
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2411yescharacteristic
138C22⋊D59—42no—
139C22⋊D59—81no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—81no—
144D236—21no—
145D236—21no—
146C4×D59—81no—
147C59⋊C8—21no—
148C59⋊C8—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59#13712yes—
157C22×C59C22×D411yescharacteristic
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—22no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—41no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59C2×#4111yescharacteristic
170C4×C59H(5,𝔽2)11yescharacteristic
171Dic59—41no—
172Dic59—41no—
173Dic59—41no—
174#3320—591nomaximal, Sylow
175C2×C59—22no—
176C2×C59—41no—
177C2×C59#54611yescharacteristic
178C2×C59C2×#13711yescharacteristic
179C2×C59#57711yescharacteristic
180D59—81no—
181#553—591no—
182D4×Q8D5911yescharacteristic, complemented
183#491—591no—
184#485—591no—
185#484—591no—
186#479—591no—
187#468—591no—
188#465—591no—
189#461—591no—
190#448—591no—
191#448—591no—
192#440—591no—
193#435—591no—
194#419—591no—
195C2×#103—591no—
196C59#332011yescharacteristic, complemented, Sylow
197C22×Q8C2×D5911yescharacteristic
198C22×Q8C2×D5911yescharacteristic
199C2×SD16—591no—
200C2×SD16—591no—
201C2×SD16—591no—
202C2×M16—591no—
203C22×C8—591no—
204C4⋊Q8—21no—
205C4⋊Q8C2×D5911yescharacteristic
206#126—1181no—
207#125—591no—
208#123—1181no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D5911yescharacteristic
212C22⋊Q8C2×D5911yescharacteristic
213#121—591no—
214#121—591no—
215#121—1181no—
216C4×Q8C2×D5911yescharacteristic
217C4×D4—21no—
218C4×D4—591no—
219C4×D4—1181no—
220C4×D4C2×D5911yescharacteristic
221#117—591no—
222C2×C4⋊C4—591no—
223#107—591no—
224#107—591no—
225#106—591no—
226C4⋊C8—591no—
227#103—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#102—591no—
237C22⋊C8—591no—
238C22⋊C8—591no—
239#97—591no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8C22×D5911yescharacteristic
247C2×Q8C22×D5911yescharacteristic
248C2×Q8C22×D5911yescharacteristic
249C2×D4—591no—
250C2×D4—1181no—
251C2×D4—1181no—
252C2×D4C22⋊D5911yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1181no—
256C22×C4—1181no—
257C22×C4C22×D5911yescharacteristic
258C22×C4C22×D5911yescharacteristic
259SD16—1182no—
260SD16—2361no—
261SD16—2361no—
262M16—2361no—
263C2×C8—591no—
264C2×C8—591no—
265C2×C8—591no—
266C2×C8—591no—
267C2×C8—2361no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—591no—
274C4⋊C4—591no—
275C4⋊C4—591no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4C22⋊D5911yescharacteristic
280C4⋊C4C22×D5911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4C22⋊D5911yescharacteristic
288C22⋊C4C22⋊D5911yescharacteristic
289C42—21no—
290C42—1181no—
291C42C22×D5911yescharacteristic
292C23—1181no—
293C23C2×C22⋊D5911yescharacteristic
294C23C2×C22⋊D5911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—42no—
302Q8#1174568712yes—
303D4—22no—
304D4—1181no—
305D4—1181no—
306D4—4721no—
307D4—2362no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—1181no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—4721no—
322C2×C4—4721no—
323C2×C4C2×C22⋊D5911yescharacteristic
324C2×C4C2×C22⋊D5911yescharacteristic
325C2×C4C2×C22⋊D5911yescharacteristic
326C2×C4C2×C22⋊D5911yescharacteristic
327C2×C4C23×D5911yescharacteristic
328C8—1181no—
329C8—1181no—
330C8—1181no—
331C8—1181no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—2361no—
338C22—2361no—
339C22—2361no—
340C22#1427375812yes—
341C22C22×C22⋊D5911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—2361no—
351C4—2361no—
352C4—2361no—
353C4C2×#1174568711yescharacteristic
354C4#1427377211yescharacteristic
355C2—22no—
356C2—41no—
357C2—4721no—
358C2#1683804611yescharacteristic
359C2C2×#1427375811yescharacteristic
360C2#1683821011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingD4×Q8×C59C2
socleC22×C59C22×D4
hypercenterD4×Q8D59
hypocenterC59#3320
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. #16837735C2semidirect
5. #16837709C2semidirect
6. #16837650C2semidirect
7. #16837633C2semidirect
8. #16837604C2semidirect
9. #16837541C2semidirect
10. #16837541C2semidirect
11. #16837500C2semidirect
12. #16837474C2semidirect
13. #16837411C2semidirect
14. C2×#14273651C2semidirect
15. D4×Q8×C59C2semidirect
182. D4×Q8D59semidirect
196. C59#3320semidirect