Finite Group Databasebeta

← #21435756

Subgroups — #21435756

Order 7552.

482 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273759C211yesmaximal, characteristic, complemented
2#16838071C211yesmaximal, characteristic
3Q8×C22⋊D59C211yesmaximal, characteristic, complemented
4#16837773C211yesmaximal, characteristic, complemented
5#16837648C211yesmaximal, characteristic, complemented
6#16837645C211yesmaximal, characteristic, complemented
7#16837610C211yesmaximal, characteristic, complemented
8#16837600C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837563C211yesmaximal, characteristic, complemented
11#16837541C211yesmaximal, characteristic, complemented
12#16837539C211yesmaximal, characteristic, complemented
13Q16×Dic59C211yesmaximal, characteristic, complemented
14#16837478C211yesmaximal, characteristic, complemented
15C2×#137×C59C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18#14273759—24no—
19C2×#11745672C2211yescharacteristic
20C2×#11745660C2211yescharacteristic
21C2×#11745670C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23C2×#11745671C2211yescharacteristic
24C2×#11745659C2211yescharacteristic
25#14273725—21no—
26#14273725C2211yescharacteristic
27#14273723—21no—
28#14273723C2211yescharacteristic
29#14273706—21no—
30#14273706C2211yescharacteristic
31#14273703—21no—
32#14273703C2211yescharacteristic
33#14273701—21no—
34#14273701C2211yescharacteristic
35#14273698—21no—
36#14273698C2211yescharacteristic
37Q8×Dic59C2211yescharacteristic
38Q8×Dic59C2211yescharacteristic
39C4×C22⋊D59—21no—
40C4×C22⋊D59—21no—
41C4×C22⋊D59C2211yescharacteristic
42#14273661C2211yescharacteristic
43Dic59⋊C8C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273651C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273648C2211yescharacteristic
50C22⋊(C59⋊C8)C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C8×Dic59C2211yescharacteristic
53C2×#41×C59C2211yescharacteristic
54C22×Q8×C59C2211yescharacteristic
55#137×C59—24no—
56C2×Q16×C59C2211yescharacteristic
57C2×Q16×C59C2211yescharacteristic
58C2×SD16×C59C2211yescharacteristic
59C2×SD16×C59C2211yescharacteristic
60C2×M16×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×Q8×C59C2311yescharacteristic
69C2×D4×C59—21no—
70C2×D4×C59C2311yescharacteristic
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59C2311yescharacteristic
74C2×C22⋊D59—21no—
75C2×C22⋊D59—21no—
76C2×C22⋊D59—21no—
77C2×C22⋊D59—21no—
78C2×C22⋊D59D411yescharacteristic
79#11745689—22no—
80#11745689—41no—
81Q8×D59—22no—
82Q8×D59—41no—
83C2×D236—21no—
84C2×D236C2311yescharacteristic
85C2×C4×D59—21no—
86C2×C4×D59—21no—
87C2×C4×D59C2311yescharacteristic
88C2×Dic118—21no—
89C2×Dic118C2311yescharacteristic
90Q16×C59—22no—
91Q16×C59D414yescomplemented
92SD16×C59—22no—
93SD16×C59—22no—
94M16×C59—22no—
95C2×C8×C59C2311yescharacteristic
96C2×C8×C59C2311yescharacteristic
97C22⋊Dic59—21no—
98C22⋊Dic59—21no—
99C22⋊Dic59D411yescharacteristic
100#11745672—22no—
101#11745671—22no—
102#11745671—41no—
103#11745670—41no—
104(C2×D59)⋊C4—21no—
105(C2×D59)⋊C4—21no—
106(C2×D59)⋊C4D411yescharacteristic
107C4⋊Dic59—21no—
108C4⋊Dic59—21no—
109C4⋊Dic59C2311yescharacteristic
110C4⋊Dic59C2311yescharacteristic
111Dic59⋊C4—21no—
112Dic59⋊C4—21no—
113Dic59⋊C4—21no—
114Dic59⋊C4—21no—
115Dic59⋊C4D411yescharacteristic
116C4×Dic59—21no—
117C4×Dic59—21no—
118C4×Dic59C2311yescharacteristic
119C2×C59⋊C8C2311yescharacteristic
120C2×C59⋊C8C2311yescharacteristic
121#11745660—22no—
122#11745659—22no—
123C23×C59—21no—
124C23×C59C2×D411yescharacteristic
125C22×D59—21no—
126C22×D59C2×D411yescharacteristic
127Q8×C59—21no—
128Q8×C59—21no—
129Q8×C59—21no—
130Q8×C59—21no—
131Q8×C59—42no—
132Q8×C59C2×D412yes—
133Q8×C59C2×D412yes—
134D4×C59—21no—
135D4×C59—21no—
136D4×C59—42no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—42no—
143C2×C4×C59—42no—
144C2×C4×C59C2×D411yescharacteristic
145C2×C4×C59C2411yescharacteristic
146C22⋊D59—22no—
147C22⋊D59—42no—
148C22⋊D59—81no—
149C22⋊D59—81no—
150C22⋊D59—81no—
151C2×Dic59—21no—
152C2×Dic59—21no—
153C2×Dic59—21no—
154C2×Dic59C2×D411yescharacteristic
155C2×Dic59C2×D411yescharacteristic
156C2×Dic59C2×D411yescharacteristic
157D236—21no—
158D236—21no—
159D236—42no—
160C4×D59—21no—
161C4×D59—21no—
162C4×D59—42no—
163C4×D59—42no—
164Dic118—21no—
165Dic118—21no—
166Dic118—42no—
167C8×C59—21no—
168C8×C59C2×D412yes—
169C59⋊C8—21no—
170C59⋊C8—21no—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59—21no—
174C22×C59—41no—
175C22×C59—41no—
176C22×C59—41no—
177C22×C59C22×D411yescharacteristic
178C2×D59—21no—
179C2×D59—21no—
180C2×D59—21no—
181C2×D59—41no—
182C2×D59—41no—
183C2×D59—41no—
184C4×C59—22no—
185C4×C59—22no—
186C4×C59—21no—
187C4×C59—41no—
188C4×C59C22×D411yescharacteristic
189C4×C59H(5,𝔽2)11yescharacteristic
190Dic59—21no—
191Dic59—21no—
192Dic59—41no—
193Dic59—41no—
194Dic59—41no—
195Dic59#13712yescomplemented
196#3278—591nomaximal, Sylow
197C2×C59—41no—
198C2×C59—81no—
199C2×C59D4211yescharacteristic
200C2×C59C2×#13711yescharacteristic
201C2×C59#57711yescharacteristic
202D59—41no—
203D59—81no—
204C2×#137—591no—
205C2×#137D5911yescharacteristic, complemented
206#550—591no—
207D4×Q8—591no—
208#492—591no—
209#468—591no—
210#468—591no—
211#462—591no—
212#460—591no—
213#452—591no—
214#452—591no—
215#448—591no—
216#448—591no—
217C4×Q16—591no—
218#436—591no—
219C59#327811yescharacteristic, complemented, Sylow
220C2×#41—591no—
221C2×#41C2×D5911yescharacteristic
222C22×Q8—591no—
223C22×Q8C2×D5911yescharacteristic
224#137—24no—
225#137—1184no—
226C2×Q16—591no—
227C2×Q16C2×D5911yescharacteristic
228C2×Q16C2×D5911yescharacteristic
229C2×SD16—591no—
230C2×SD16—591no—
231C2×SD16—591no—
232C2×SD16—591no—
233C2×SD16C2×D5911yescharacteristic
234C2×SD16C2×D5911yescharacteristic
235C2×M16—591no—
236C2×M16C2×D5911yescharacteristic
237C4⋊Q8—591no—
238C4⋊Q8—1181no—
239#127—591no—
240#127—1181no—
241C22⋊Q8—591no—
242C22⋊Q8—591no—
243C22⋊Q8—1181no—
244C22⋊Q8—1181no—
245#121—591no—
246#121—591no—
247#121—1181no—
248#121—1181no—
249C4×Q8—591no—
250C4×Q8—591no—
251C4×D4—591no—
252C4×D4—1181no—
253C4×D4—1181no—
254#107—591no—
255C4⋊C8—591no—
256#103—591no—
257#103—591no—
258#103—591no—
259#103—591no—
260#102—591no—
261#102—591no—
262C22⋊C8—591no—
263C22⋊C8—591no—
264C4×C8—591no—
265#41—22no—
266#41—41no—
267#41—1182no—
268#41—2361no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—591no—
273C2×Q8—1181no—
274C2×Q8—1182no—
275C2×Q8—2361no—
276C2×Q8C22×D5911yescharacteristic
277C2×Q8C22×D5911yescharacteristic
278C2×Q8C22×D5911yescharacteristic
279C2×D4—21no—
280C2×D4—591no—
281C2×D4—591no—
282C2×D4—1181no—
283C2×D4—1181no—
284C2×D4—1181no—
285C2×D4—1181no—
286C2×D4—1181no—
287C2×D4C22×D5911yescharacteristic
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—591no—
291C22×C4—1181no—
292C22×C4—1181no—
293C22×C4C22×D5911yescharacteristic
294Q16—22no—
295Q16—1182no—
296Q16C22⋊D5914yescomplemented
297SD16—22no—
298SD16—22no—
299SD16—1182no—
300SD16—1182no—
301SD16—2361no—
302SD16—2361no—
303M16—22no—
304M16—1182no—
305C2×C8—591no—
306C2×C8—591no—
307C2×C8C22×D5911yescharacteristic
308C2×C8C22×D5911yescharacteristic
309C4⋊C4—591no—
310C4⋊C4—591no—
311C4⋊C4—591no—
312C4⋊C4—1181no—
313C4⋊C4—1181no—
314C4⋊C4—1181no—
315C4⋊C4—1181no—
316C4⋊C4—1181no—
317C4⋊C4—1181no—
318C22⋊C4—591no—
319C22⋊C4—591no—
320C22⋊C4—1181no—
321C22⋊C4—1181no—
322C22⋊C4—1181no—
323C22⋊C4—1181no—
324C42—591no—
325C42—1181no—
326C42—1181no—
327C23—21no—
328C23—591no—
329C23—1181no—
330C23D4×D5911yescharacteristic
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—21no—
335Q8—42no—
336Q8—1181no—
337Q8—1181no—
338Q8—2362no—
339Q8C2×C22⋊D5912yes—
340Q8C2×C22⋊D5912yes—
341D4—21no—
342D4—21no—
343D4—42no—
344D4—1182no—
345D4—1181no—
346D4—1181no—
347D4—4721no—
348D4—4721no—
349D4—4721no—
350D4—2362no—
351D4—2362no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—591no—
360C2×C4—591no—
361C2×C4—591no—
362C2×C4—1181no—
363C2×C4—1181no—
364C2×C4—1181no—
365C2×C4—1181no—
366C2×C4—1181no—
367C2×C4—2362no—
368C2×C4—2362no—
369C2×C4D4×D5911yescharacteristic
370C2×C4C23×D5911yescharacteristic
371C8—21no—
372C8—1181no—
373C8—1181no—
374C8C2×C22⋊D5912yes—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—1181no—
382C22—1181no—
383C22—1181no—
384C22—2361no—
385C22—2361no—
386C22—2361no—
387C22C2×D4×D5911yescharacteristic
388C4—21no—
389C4—22no—
390C4—22no—
391C4—41no—
392C4—592no—
393C4—1181no—
394C4—1181no—
395C4—2361no—
396C4—2361no—
397C4—2361no—
398C4C22×C22⋊D5911yescharacteristic
399C4#1427377211yescharacteristic
400C2—41no—
401C2—81no—
402C2—4721no—
403C2—2361no—
404C2D4×C22⋊D5911yescharacteristic
405C2#137×D5911yescharacteristic
406C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#137×C59C2
socleC22×C59C22×D4
hypercenterC2×#137D59
hypocenterC59#3278
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#14273759C2semidirect
3. Q8×C22⋊D59C2semidirect
4. #16837773C2semidirect
5. #16837648C2semidirect
6. #16837645C2semidirect
7. #16837610C2semidirect
8. #16837600C2semidirect
9. #16837564C2semidirect
10. #16837563C2semidirect
11. #16837541C2semidirect
12. #16837539C2semidirect
13. Q16×Dic59C2semidirect
14. #16837478C2semidirect
15. C2×#137×C59C2semidirect
91. Q16×C59D4semidirect
195. Dic59#137semidirect
205. C2×#137D59semidirect
219. C59#3278semidirect
296. Q16C22⋊D59semidirect