Finite Group Databasebeta

← #21435652

Subgroups — #21435652

Order 7552.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 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#16838057C211yesmaximal, characteristic, complemented
4#16837797C211yesmaximal, characteristic, complemented
5#16837646C211yesmaximal, characteristic, complemented
6#16837641C211yesmaximal, characteristic, complemented
7#16837614C211yesmaximal, characteristic, complemented
8#16837612C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837562C211yesmaximal, characteristic, complemented
11#16837558C211yesmaximal, characteristic, complemented
12#16837545C211yesmaximal, characteristic, complemented
13#16837500C211yesmaximal, 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×#11745672C2211yescharacteristic
23C2×#11745672C2211yescharacteristic
24C2×#11745670C2211yescharacteristic
25C2×#11745670C2211yescharacteristic
26C2×#11745671C2211yescharacteristic
27C2×#11745671C2211yescharacteristic
28C2×#11745669C2211yescharacteristic
29C2×#11745664C2211yescharacteristic
30C22×C59⋊C8C2211yescharacteristic
31#14273727C2211yescharacteristic
32#14273709—21no—
33#14273709—21no—
34#14273706C2211yescharacteristic
35#14273706C2211yescharacteristic
36#14273698—21no—
37C4×D236C2211yescharacteristic
38C4⋊C4×D59—21no—
39#14273660C2211yescharacteristic
40C4⋊(C59⋊C8)C2211yescharacteristic
41#14273651C2211yescharacteristic
42#14273651C2211yescharacteristic
43#14273650C2211yescharacteristic
44#14273650C2211yescharacteristic
45#14273648C2211yescharacteristic
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—
78#11745685—22no—
79#11745685—22no—
80#11745685—41no—
81#11745685—41no—
82C2×D236C2311yescharacteristic
83C2×C4×D59—21no—
84C2×C4×D59—21no—
85C2×C4×D59—21no—
86C2×Dic118C2311yescharacteristic
87C2×Dic118C2311yescharacteristic
88C4⋊C4×C59—21no—
89C4⋊C4×C59—21no—
90C4⋊C4×C59D411yescharacteristic
91C4⋊C4×C59C2311yescharacteristic
92C22⋊C4×C59—21no—
93C22⋊C4×C59—21no—
94C22⋊C4×C59—21no—
95C22⋊C4×C59—21no—
96C22⋊C4×C59D411yescharacteristic
97C22⋊C4×C59D411yescharacteristic
98C42×C59—21no—
99C42×C59C2311yescharacteristic
100C22⋊Dic59—21no—
101C22⋊Dic59—21no—
102#11745672—22no—
103#11745672—22no—
104#11745672—22no—
105#11745672—41no—
106#11745671—22no—
107#11745671D414yescomplemented
108#11745670—22no—
109#11745670—41no—
110#11745669—22no—
111(C2×D59)⋊C4—21no—
112C4⋊Dic59—21no—
113C4⋊Dic59—21no—
114C4⋊Dic59C2311yescharacteristic
115Dic59⋊C4—21no—
116Dic59⋊C4—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—
127Q8×C59—21no—
128Q8×C59—21no—
129Q8×C59—21no—
130Q8×C59—42no—
131Q8×C59C2×D412yes—
132D4×C59—21no—
133D4×C59—21no—
134D4×C59—41no—
135D4×C59—42no—
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—21no—
143C2×C4×C59—21no—
144C2×C4×C59—42no—
145C2×C4×C59—42no—
146C2×C4×C59C2×D411yescharacteristic
147C2×C4×C59C2×D411yescharacteristic
148C2×C4×C59C2×D411yescharacteristic
149C2×C4×C59C2×D411yescharacteristic
150C2×C4×C59C2411yescharacteristic
151C22⋊D59—42no—
152C22⋊D59—42no—
153C2×Dic59—21no—
154C2×Dic59—21no—
155C2×Dic59—21no—
156D236—21no—
157D236C2×D412yes—
158C4×D59—42no—
159C4×D59—42no—
160C4×D59—42no—
161Dic118—21no—
162Dic118—21no—
163Dic118—21no—
164Dic118—21no—
165C59⋊C8—21no—
166C59⋊C8—21no—
167C59⋊C8—21no—
168C59⋊C8C2×D412yes—
169C22×C59—21no—
170C22×C59—21no—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59—21no—
174C22×C59—21no—
175C22×C59—41no—
176C22×C59—41no—
177C22×C59—41no—
178C22×C59C22×D411yescharacteristic
179C2×D59—22no—
180C2×D59—41no—
181C2×D59—41no—
182C4×C59—21no—
183C4×C59—21no—
184C4×C59—22no—
185C4×C59—21no—
186C4×C59—21no—
187C4×C59—41no—
188C4×C59—41no—
189C4×C59C22×D411yescharacteristic
190C4×C59H(5,𝔽2)11yescharacteristic
191Dic59—41no—
192Dic59—41no—
193Dic59—41no—
194#3269—591nomaximal, Sylow
195C2×C59—41no—
196C2×C59—41no—
197C2×C59—81no—
198C2×C59D4211yescharacteristic
199C2×C59#57511yescharacteristic
200C2×C59#57811yescharacteristic
201D59—42no—
202C2×#137—591no—
203C2×#135—591no—
204#548D5911yescharacteristic, complemented
205#547—591no—
206#497—591no—
207#468—591no—
208#467—591no—
209#463—591no—
210#462—591no—
211#452—591no—
212#452—591no—
213#451—591no—
214#449—591no—
215#440—591no—
216#435—591no—
217C59#326911yescharacteristic, complemented, Sylow
218C2×#41—591no—
219C2×#41—591no—
220C2×#41C2×D5911yescharacteristic
221C22×Q8C2×D5911yescharacteristic
222#137—1184no—
223#135—1184no—
224C2×Q16—591no—
225C2×Q16—591no—
226C2×Q16—591no—
227C2×Q16—591no—
228C2×SD16—591no—
229C2×SD16—591no—
230C2×SD16—591no—
231C2×SD16—591no—
232C2×D8—591no—
233C2×M16—591no—
234C22×C8—591no—
235C4⋊Q8—591no—
236#124—21no—
237#124C2×D5911yescharacteristic
238#123—1181no—
239#123—1181no—
240C22⋊Q8—21no—
241C22⋊Q8—591no—
242C22⋊Q8—591no—
243C22⋊Q8C2×D5911yescharacteristic
244#121—21no—
245#121—1181no—
246#121C2×D5911yescharacteristic
247C4×Q8C2×D5911yescharacteristic
248C4×D4—21no—
249C4×D4—591no—
250C4×D4C2×D5911yescharacteristic
251C2×C4⋊C4—1181no—
252#107—591no—
253C4⋊C8—591no—
254#103—591no—
255#103—591no—
256#103—591no—
257#103—591no—
258#102—591no—
259#102—591no—
260C22⋊C8—591no—
261C22⋊C8—591no—
262#97—591no—
263#41—22no—
264#41—41no—
265#41—1182no—
266#41—1182no—
267#41—2361no—
268#41—2361no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—591no—
273C2×Q8—591no—
274C2×Q8C22×D5911yescharacteristic
275C2×Q8C22×D5911yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—591no—
279C2×D4—1181no—
280C2×D4—1181no—
281C2×D4C22⋊D5911yescharacteristic
282C2×D4C22×D5911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—1181no—
286C22×C4—1181no—
287C22×C4—1181no—
288C22×C4C22×D5911yescharacteristic
289C22×C4C22×D5911yescharacteristic
290Q16—1182no—
291Q16—1182no—
292Q16—1182no—
293Q16—2361no—
294SD16—594no—
295SD16—1182no—
296SD16—1182no—
297SD16—2361no—
298D8—1182no—
299M16—1182no—
300C2×C8—591no—
301C2×C8—591no—
302C2×C8—591no—
303C2×C8—591no—
304C2×C8—1182no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—591no—
308C4⋊C4—1181no—
309C4⋊C4—1181no—
310C4⋊C4—1181no—
311C4⋊C4—1181no—
312C4⋊C4C22⋊D5911yescharacteristic
313C4⋊C4C22×D5911yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—21no—
318C22⋊C4—1181no—
319C22⋊C4—1181no—
320C22⋊C4—1181no—
321C22⋊C4C22⋊D5911yescharacteristic
322C22⋊C4C22⋊D5911yescharacteristic
323C42—21no—
324C42C22×D5911yescharacteristic
325C23—21no—
326C23—1181no—
327C23C2×C22⋊D5911yescharacteristic
328C23C2×C22⋊D5911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—1181no—
334Q8—1181no—
335Q8—1181no—
336Q8—1181no—
337Q8D4×D5912yes—
338D4—21no—
339D4—21no—
340D4—41no—
341D4—42no—
342D4—42no—
343D4—592no—
344D4—1181no—
345D4—2362no—
346D4—2362no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—1181no—
357C2×C4—1181no—
358C2×C4—1181no—
359C2×C4—2362no—
360C2×C4—2362no—
361C2×C4—2362no—
362C2×C4C2×C22⋊D5911yescharacteristic
363C2×C4C2×C22⋊D5911yescharacteristic
364C2×C4C2×C22⋊D5911yescharacteristic
365C2×C4C2×C22⋊D5911yescharacteristic
366C2×C4C23×D5911yescharacteristic
367C8—592no—
368C8—1181no—
369C8—1181no—
370C8—1181no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—1182no—
381C22—2361no—
382C22—2361no—
383C22C22×C22⋊D5911yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—2361no—
392C4—2361no—
393C4—2361no—
394C4C2×D4×D5911yescharacteristic
395C4#1427377211yescharacteristic
396C2—41no—
397C2—41no—
398C2—81no—
399C2—2362no—
400C2D4×C22⋊D5911yescharacteristic
401C2#1683820011yescharacteristic
402C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#548C2
socleC22×C59C22×D4
hypercenter#548D59
hypocenterC59#3269
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. #16838057C2semidirect
4. #16837797C2semidirect
5. #16837646C2semidirect
6. #16837641C2semidirect
7. #16837614C2semidirect
8. #16837612C2semidirect
9. #16837564C2semidirect
10. #16837562C2semidirect
11. #16837558C2semidirect
12. #16837545C2semidirect
13. #16837500C2semidirect
14. #16837474C2semidirect
15. C59×#548C2semidirect
107. #11745671D4semidirect
204. #548D59semidirect
217. C59#3269semidirect