Finite Group Databasebeta

← #21435682

Subgroups — #21435682

Order 7552.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273758C211yesmaximal, characteristic, complemented
2C2×#14273747C211yesmaximal, characteristic, complemented
3#16838073C211yesmaximal, characteristic, complemented
4#16837792C211yesmaximal, characteristic, complemented
5#16837653C211yesmaximal, characteristic, complemented
6#16837633C211yesmaximal, characteristic, complemented
7#16837621C211yesmaximal, characteristic, complemented
8#16837602C211yesmaximal, characteristic, complemented
9#16837562C211yesmaximal, characteristic, complemented
10#16837547C211yesmaximal, characteristic, complemented
11#16837545C211yesmaximal, characteristic, complemented
12#16837541C211yesmaximal, characteristic, complemented
13#16837507C211yesmaximal, characteristic, complemented
14#16837474C211yesmaximal, characteristic, complemented
15C59×#548C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745685C2211yescharacteristic
18#14273758—24no—
19#14273747—24no—
20C2×#11745672C2211yescharacteristic
21C2×#11745672C2211yescharacteristic
22C2×#11745670C2211yescharacteristic
23C2×#11745671C2211yescharacteristic
24C2×#11745671C2211yescharacteristic
25C2×#11745671C2211yescharacteristic
26C2×#11745671C2211yescharacteristic
27C2×#11745669C2211yescharacteristic
28C2×#11745669C2211yescharacteristic
29C2×#11745664C2211yescharacteristic
30C22×C59⋊C8C2211yescharacteristic
31#14273724C2211yescharacteristic
32#14273723—21no—
33#14273701C2211yescharacteristic
34#14273701C2211yescharacteristic
35#14273700—21no—
36#14273700—21no—
37C4×Dic118C2211yescharacteristic
38#14273689—21no—
39#14273658C2211yescharacteristic
40C4⋊(C59⋊C8)C2211yescharacteristic
41#14273651C2211yescharacteristic
42#14273651C2211yescharacteristic
43#14273650C2211yescharacteristic
44#14273648C2211yescharacteristic
45#14273647C2211yescharacteristic
46#14273647C2211yescharacteristic
47C22⋊(C59⋊C8)C2211yescharacteristic
48C22⋊(C59⋊C8)C2211yescharacteristic
49#14273638C2211yescharacteristic
50C2×#41×C59C2211yescharacteristic
51C22×Q8×C59C2211yescharacteristic
52#124×C59—21no—
53#124×C59C2211yescharacteristic
54C22⋊Q8×C59—21no—
55C22⋊Q8×C59C2211yescharacteristic
56#121×C59—21no—
57#121×C59C2211yescharacteristic
58C4×Q8×C59C2211yescharacteristic
59C4×D4×C59—21no—
60C4×D4×C59C2211yescharacteristic
61#41×C59—22no—
62#41×C59—41no—
63C2×Q8×C59—21no—
64C2×Q8×C59—22no—
65C2×Q8×C59—41no—
66C2×Q8×C59C2311yescharacteristic
67C2×Q8×C59C2311yescharacteristic
68C2×D4×C59—21no—
69C2×D4×C59—21no—
70C2×D4×C59D411yescharacteristic
71C2×D4×C59C2311yescharacteristic
72C22×C4×C59—21no—
73C22×C4×C59—21no—
74C22×C4×C59C2311yescharacteristic
75C22×C4×C59C2311yescharacteristic
76C2×C22⋊D59—21no—
77C2×C22⋊D59—21no—
78C2×C22⋊D59—21no—
79C2×C22⋊D59—21no—
80#11745685—22no—
81#11745685—22no—
82#11745685—41no—
83#11745685—41no—
84C2×D236—21no—
85C2×D236—21no—
86C2×D236C2311yescharacteristic
87C2×D236C2311yescharacteristic
88C2×C4×D59—21no—
89C2×C4×D59—21no—
90C2×Dic118C2311yescharacteristic
91C4⋊C4×C59—21no—
92C4⋊C4×C59—21no—
93C4⋊C4×C59D411yescharacteristic
94C4⋊C4×C59C2311yescharacteristic
95C22⋊C4×C59—21no—
96C22⋊C4×C59—21no—
97C22⋊C4×C59—21no—
98C22⋊C4×C59—21no—
99C22⋊C4×C59D411yescharacteristic
100C22⋊C4×C59D411yescharacteristic
101C42×C59—21no—
102C42×C59C2311yescharacteristic
103#11745672—22no—
104#11745672D414yescomplemented
105#11745671—22no—
106#11745671—22no—
107#11745671—22no—
108#11745671—41no—
109#11745670—22no—
110#11745669—22no—
111#11745669—41no—
112(C2×D59)⋊C4—21no—
113(C2×D59)⋊C4—21no—
114C4⋊Dic59C2311yescharacteristic
115Dic59⋊C4—21no—
116C4×Dic59—21no—
117#11745664—22no—
118C2×C59⋊C8—22no—
119C2×C59⋊C8C2311yescharacteristic
120C2×C59⋊C8C2311yescharacteristic
121C2×C59⋊C8C2311yescharacteristic
122C2×C59⋊C8C2311yescharacteristic
123C23×C59—21no—
124C23×C59C2×D411yescharacteristic
125C23×C59C2×D411yescharacteristic
126C22×D59—21no—
127C22×D59—21no—
128Q8×C59—21no—
129Q8×C59—21no—
130Q8×C59—21no—
131Q8×C59—42no—
132Q8×C59C2×D412yes—
133D4×C59—21no—
134D4×C59—21no—
135D4×C59—41no—
136D4×C59—42no—
137D4×C59—42no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—42no—
146C2×C4×C59—42no—
147C2×C4×C59C2×D411yescharacteristic
148C2×C4×C59C2×D411yescharacteristic
149C2×C4×C59C2×D411yescharacteristic
150C2×C4×C59C2×D411yescharacteristic
151C2×C4×C59C2411yescharacteristic
152C22⋊D59—42no—
153C22⋊D59—42no—
154C22⋊D59—81no—
155C22⋊D59—81no—
156C2×Dic59—21no—
157C2×Dic59—21no—
158D236—21no—
159D236—21no—
160D236—21no—
161D236—21no—
162D236—42no—
163D236—81no—
164C4×D59—42no—
165C4×D59—42no—
166Dic118—21no—
167Dic118C2×D412yes—
168C59⋊C8—21no—
169C59⋊C8—21no—
170C59⋊C8—21no—
171C59⋊C8C2×D412yes—
172C22×C59—21no—
173C22×C59—21no—
174C22×C59—21no—
175C22×C59—21no—
176C22×C59—21no—
177C22×C59—21no—
178C22×C59—41no—
179C22×C59—41no—
180C22×C59—41no—
181C22×C59C22×D411yescharacteristic
182C2×D59—41no—
183C2×D59—41no—
184C2×D59—41no—
185C2×D59—41no—
186C2×D59—41no—
187C2×D59—41no—
188C4×C59—21no—
189C4×C59—21no—
190C4×C59—22no—
191C4×C59—21no—
192C4×C59—21no—
193C4×C59—41no—
194C4×C59—41no—
195C4×C59C22×D411yescharacteristic
196C4×C59H(5,𝔽2)11yescharacteristic
197Dic59—22no—
198Dic59—41no—
199#3271—591nomaximal, Sylow
200C2×C59—41no—
201C2×C59—41no—
202C2×C59—81no—
203C2×C59D4211yescharacteristic
204C2×C59#57511yescharacteristic
205C2×C59#57711yescharacteristic
206D59—81no—
207D59—81no—
208C2×#137—591no—
209C2×#135—591no—
210#550—591no—
211#548D5911yescharacteristic, complemented
212#496—591no—
213#469—591no—
214#465—591no—
215#464—591no—
216#460—591no—
217#452—591no—
218#449—591no—
219#449—591no—
220#448—591no—
221#441—591no—
222#435—591no—
223C59#327111yescharacteristic, complemented, Sylow
224C2×#41—591no—
225C2×#41—591no—
226C2×#41C2×D5911yescharacteristic
227C22×Q8C2×D5911yescharacteristic
228#137—1184no—
229#135—1184no—
230C2×Q16—591no—
231C2×Q16—591no—
232C2×SD16—591no—
233C2×SD16—591no—
234C2×SD16—591no—
235C2×SD16—591no—
236C2×SD16—591no—
237C2×D8—591no—
238C2×D8—591no—
239C2×M16—591no—
240C22×C8—591no—
241#127—591no—
242#127—1181no—
243#124—21no—
244#124C2×D5911yescharacteristic
245C22⋊Q8—21no—
246C22⋊Q8C2×D5911yescharacteristic
247#121—21no—
248#121—591no—
249#121—591no—
250#121—1181no—
251#121—1181no—
252#121C2×D5911yescharacteristic
253C4×Q8—591no—
254C4×Q8C2×D5911yescharacteristic
255C4×D4—21no—
256C4×D4—1181no—
257C4×D4C2×D5911yescharacteristic
258#106—591no—
259C4⋊C8—591no—
260#103—591no—
261#103—591no—
262#103—591no—
263#102—591no—
264#102—591no—
265#102—591no—
266C22⋊C8—591no—
267C22⋊C8—591no—
268#97—591no—
269#41—22no—
270#41—41no—
271#41—1182no—
272#41—1182no—
273#41—2361no—
274#41—2361no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—591no—
279C2×Q8C22×D5911yescharacteristic
280C2×Q8C22×D5911yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—591no—
284C2×D4—591no—
285C2×D4—1181no—
286C2×D4—1181no—
287C2×D4—1181no—
288C2×D4—1181no—
289C2×D4—1181no—
290C2×D4—1181no—
291C2×D4C22⋊D5911yescharacteristic
292C2×D4C22×D5911yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—1181no—
296C22×C4—1181no—
297C22×C4C22×D5911yescharacteristic
298C22×C4C22×D5911yescharacteristic
299Q16—594no—
300Q16—1182no—
301SD16—1182no—
302SD16—1182no—
303SD16—1182no—
304SD16—1182no—
305SD16—2361no—
306D8—1182no—
307D8—2361no—
308M16—1182no—
309C2×C8—591no—
310C2×C8—591no—
311C2×C8—591no—
312C2×C8—591no—
313C2×C8—1182no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—591no—
317C4⋊C4—1181no—
318C4⋊C4C22⋊D5911yescharacteristic
319C4⋊C4C22×D5911yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—1181no—
325C22⋊C4—1181no—
326C22⋊C4C22⋊D5911yescharacteristic
327C22⋊C4C22⋊D5911yescharacteristic
328C42—21no—
329C42—1181no—
330C42C22×D5911yescharacteristic
331C23—21no—
332C23—1181no—
333C23—1181no—
334C23C2×C22⋊D5911yescharacteristic
335C23C2×C22⋊D5911yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—42no—
340Q8—592no—
341Q8—1181no—
342Q8D4×D5912yes—
343D4—21no—
344D4—21no—
345D4—41no—
346D4—42no—
347D4—42no—
348D4—1181no—
349D4—1181no—
350D4—1181no—
351D4—1181no—
352D4—4721no—
353D4—4721no—
354D4—4721no—
355D4—2362no—
356D4—2362no—
357D4—2362no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—1181no—
368C2×C4—1181no—
369C2×C4—2362no—
370C2×C4—2362no—
371C2×C4C2×C22⋊D5911yescharacteristic
372C2×C4C2×C22⋊D5911yescharacteristic
373C2×C4C2×C22⋊D5911yescharacteristic
374C2×C4C2×C22⋊D5911yescharacteristic
375C2×C4C23×D5911yescharacteristic
376C8—592no—
377C8—1181no—
378C8—1181no—
379C8—1181no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—2361no—
390C22—2361no—
391C22—2361no—
392C22—2361no—
393C22—2361no—
394C22—2361no—
395C22C22×C22⋊D5911yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—1182no—
404C4—2361no—
405C4C2×D4×D5911yescharacteristic
406C4#1427377211yescharacteristic
407C2—41no—
408C2—41no—
409C2—81no—
410C2—4721no—
411C2—4721no—
412C2D4×C22⋊D5911yescharacteristic
413C2#1683820011yescharacteristic
414C2#1683821011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#548C2
socleC22×C59C22×D4
hypercenter#548D59
hypocenterC59#3271
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14273758C2semidirect
2. C2×#14273747C2semidirect
3. #16838073C2semidirect
4. #16837792C2semidirect
5. #16837653C2semidirect
6. #16837633C2semidirect
7. #16837621C2semidirect
8. #16837602C2semidirect
9. #16837562C2semidirect
10. #16837547C2semidirect
11. #16837545C2semidirect
12. #16837541C2semidirect
13. #16837507C2semidirect
14. #16837474C2semidirect
15. C59×#548C2semidirect
104. #11745672D4semidirect
211. #548D59semidirect
223. C59#3271semidirect