Finite Group Databasebeta

← #21435602

Subgroups — #21435602

Order 7552.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273757C211yesmaximal, characteristic, complemented
2C22×#11745670C211yesmaximal, characteristic, complemented
3D4×Dic118C211yesmaximal, characteristic, complemented
4#16837797C211yesmaximal, characteristic, complemented
5#16837646C211yesmaximal, characteristic, complemented
6#16837641C211yesmaximal, characteristic, complemented
7#16837621C211yesmaximal, characteristic, complemented
8#16837607C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837557C211yesmaximal, characteristic, complemented
11#16837553C211yesmaximal, characteristic, complemented
12#16837540C211yesmaximal, characteristic, complemented
13#16837502C211yesmaximal, characteristic, complemented
14#16837474C211yesmaximal, characteristic, complemented
15C59×#546C211yesmaximal, characteristic
16C22×Dic118C2211yescharacteristic
17C22×Dic118C2211yescharacteristic, complemented
18#14273757—24no—
19C2×#11745672C2211yescharacteristic, complemented
20C2×#11745672C2211yescharacteristic, complemented
21C2×#11745672C2211yescharacteristic, complemented
22C2×#11745670—24no—
23C2×#11745670C2211yescharacteristic
24C2×#11745670C2211yescharacteristic
25C2×#11745670C2211yescharacteristic
26C2×#11745670C2211yescharacteristic
27C2×#11745670C2211yescharacteristic
28C2×#11745670C2211yescharacteristic
29C2×#11745664C2211yescharacteristic, complemented
30C22×C59⋊C8C2211yescharacteristic
31#14273727C2211yescharacteristic, complemented
32#14273726—21no—
33#14273706C2211yescharacteristic
34#14273706C2211yescharacteristic, complemented
35#14273704—21no—
36#14273704—21no—
37C4×Dic118C2211yescharacteristic, complemented
38D4×Dic59—21no—
39#14273660C2211yescharacteristic, complemented
40C4⋊(C59⋊C8)C2211yescharacteristic, complemented
41#14273651C2211yescharacteristic, complemented
42#14273650C2211yescharacteristic, complemented
43#14273650C2211yescharacteristic, complemented
44#14273650C2211yescharacteristic, complemented
45#14273648C2211yescharacteristic
46#14273648C2211yescharacteristic
47C22⋊(C59⋊C8)C2211yescharacteristic
48C22⋊(C59⋊C8)C2211yescharacteristic, complemented
49#14273638C2211yescharacteristic, complemented
50C2×#41×C59C2211yescharacteristic
51C22×D4×C59C2211yescharacteristic
52#124×C59C2211yescharacteristic
53#123×C59—21no—
54C22⋊Q8×C59C2211yescharacteristic
55#121×C59—21no—
56#121×C59C2211yescharacteristic
57#120×C59—21no—
58C4×D4×C59C2211yescharacteristic
59C4×D4×C59C2211yescharacteristic
60C2×C22⋊C4×C59—21no—
61C24×C59—21no—
62#41×C59—22no—
63#41×C59—41no—
64C2×Q8×C59C2311yescharacteristic
65C2×D4×C59—22no—
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59—41no—
70C2×D4×C59D411yescharacteristic
71C2×D4×C59C2311yescharacteristic
72C2×D4×C59C2311yescharacteristic
73C22×C4×C59—21no—
74C22×C4×C59—21no—
75C22×C4×C59C2311yescharacteristic
76C22×C4×C59C2311yescharacteristic
77C22×Dic59—21no—
78C22×Dic59—21no—
79C2×Dic118—22no—
80C2×Dic118—22no—
81C2×Dic118—21no—
82C2×Dic118—21no—
83C2×Dic118—41no—
84C2×Dic118—41no—
85C2×Dic118C2311yescharacteristic
86C2×Dic118C2311yescharacteristic
87C2×Dic118C2311yescharacteristic
88C4⋊C4×C59—21no—
89C4⋊C4×C59D411yescharacteristic
90C4⋊C4×C59C2311yescharacteristic
91C22⋊C4×C59—21no—
92C22⋊C4×C59—21no—
93C22⋊C4×C59—21no—
94C22⋊C4×C59—21no—
95C22⋊C4×C59—21no—
96C22⋊C4×C59D411yescharacteristic
97C22⋊C4×C59D411yescharacteristic
98C42×C59C2311yescharacteristic
99C22⋊Dic59—21no—
100C22⋊Dic59—21no—
101#11745672—22no—
102#11745672—22no—
103#11745672—41no—
104#11745670—22no—
105#11745670—22no—
106#11745670—22no—
107#11745670—22no—
108#11745670—41no—
109#11745670D414yescomplemented
110C4⋊Dic59—21no—
111C4⋊Dic59—21no—
112C4⋊Dic59C2311yescharacteristic
113Dic59⋊C4—21no—
114Dic59⋊C4—21no—
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×C59—21no—
125C23×C59—42no—
126C23×C59—42no—
127C23×C59—81no—
128C23×C59C2×D411yescharacteristic
129C23×C59C2×D411yescharacteristic
130Q8×C59—21no—
131Q8×C59—21no—
132D4×C59—22no—
133D4×C59—21no—
134D4×C59—21no—
135D4×C59—21no—
136D4×C59—42no—
137D4×C59—42no—
138D4×C59—81no—
139D4×C59C2×D412yes—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—42no—
147C2×C4×C59—81no—
148C2×C4×C59C2×D411yescharacteristic
149C2×C4×C59C2×D411yescharacteristic
150C2×C4×C59C2×D411yescharacteristic
151C2×C4×C59C2×D411yescharacteristic
152C2×C4×C59C2411yescharacteristic
153C2×Dic59—21no—
154C2×Dic59—21no—
155C2×Dic59—21no—
156C2×Dic59—21no—
157C2×Dic59—42no—
158C2×Dic59—42no—
159Dic118—21no—
160Dic118—21no—
161Dic118—21no—
162Dic118—21no—
163Dic118—21no—
164Dic118—42no—
165Dic118—42no—
166Dic118C2×D412yes—
167C59⋊C8—21no—
168C59⋊C8—21no—
169C59⋊C8—21no—
170C59⋊C8C2×D412yes—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59—21no—
174C22×C59—22no—
175C22×C59—21no—
176C22×C59—21no—
177C22×C59—41no—
178C22×C59—41no—
179C22×C59—41no—
180C22×C59—41no—
181C22×C59—41no—
182C22×C59—84no—
183C22×C59#13712yescomplemented
184C22×C59C22×D411yescharacteristic
185C4×C59—21no—
186C4×C59—21no—
187C4×C59—21no—
188C4×C59—21no—
189C4×C59—41no—
190C4×C59—41no—
191C4×C59C22×D411yescharacteristic
192C4×C59H(5,𝔽2)11yescharacteristic
193Dic59—22no—
194Dic59—41no—
195Dic59—41no—
196Dic59—41no—
197#3266—591nomaximal, Sylow
198C2×C59—22no—
199C2×C59—41no—
200C2×C59—42no—
201C2×C59—81no—
202C2×C59D4211yescharacteristic
203C2×C59C2×#13711yescharacteristic
204C2×C59#57711yescharacteristic
205C2×#137—591no—
206C22×SD16—591no—
207D4×Q8—591no—
208#546D5911yescharacteristic
209#497—591no—
210#468—591no—
211#467—591no—
212#464—591no—
213#461—591no—
214#452—591no—
215#451—591no—
216#450—591no—
217#448—591no—
218#440—591no—
219#435—591no—
220C59#326611yescharacteristic, complemented, Sylow
221C2×#41C2×D5911yescharacteristic
222C22×Q8—591no—
223C22×Q8—591no—
224C22×D4C2×D5911yescharacteristic
225#137—1184no—
226C2×Q16—591no—
227C2×Q16—591no—
228C2×Q16—591no—
229C2×SD16—591no—
230C2×SD16—591no—
231C2×SD16—591no—
232C2×SD16—591no—
233C2×SD16—591no—
234C2×SD16—591no—
235C2×SD16—1184no—
236C2×M16—591no—
237C22×C8—591no—
238C4⋊Q8—591no—
239C4⋊Q8—1181no—
240#124C2×D5911yescharacteristic
241#123—21no—
242C22⋊Q8—591no—
243C22⋊Q8—591no—
244C22⋊Q8—1181no—
245C22⋊Q8—1181no—
246C22⋊Q8C2×D5911yescharacteristic
247#121—21no—
248#121C2×D5911yescharacteristic
249#120—21no—
250C4×Q8—591no—
251C4×D4—1181no—
252C4×D4C2×D5911yescharacteristic
253C4×D4C2×D5911yescharacteristic
254C2×C22⋊C4—21no—
255#107—591no—
256C4⋊C8—591no—
257#103—591no—
258#103—591no—
259#103—591no—
260#103—591no—
261#102—591no—
262#102—591no—
263C22⋊C8—591no—
264C22⋊C8—591no—
265#97—591no—
266C24—21no—
267#41—22no—
268#41—41no—
269C2×Q8—591no—
270C2×Q8—591no—
271C2×Q8—591no—
272C2×Q8—1182no—
273C2×Q8—1182no—
274C2×Q8—1181no—
275C2×Q8—1181no—
276C2×Q8—2361no—
277C2×Q8—2361no—
278C2×Q8C22×D5911yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4C22⋊D5911yescharacteristic
285C2×D4C22×D5911yescharacteristic
286C2×D4C22×D5911yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—1181no—
290C22×C4—1181no—
291C22×C4C22×D5911yescharacteristic
292C22×C4C22×D5911yescharacteristic
293Q16—1182no—
294Q16—1182no—
295Q16—2361no—
296SD16—594no—
297SD16—1182no—
298SD16—1182no—
299SD16—1182no—
300SD16—1182no—
301SD16—2361no—
302M16—1182no—
303C2×C8—591no—
304C2×C8—591no—
305C2×C8—591no—
306C2×C8—591no—
307C2×C8—1182no—
308C4⋊C4—21no—
309C4⋊C4—591no—
310C4⋊C4—1181no—
311C4⋊C4—1181no—
312C4⋊C4—1181no—
313C4⋊C4—1181no—
314C4⋊C4—1181no—
315C4⋊C4C22⋊D5911yescharacteristic
316C4⋊C4C22×D5911yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—1181no—
323C22⋊C4—1181no—
324C22⋊C4C22⋊D5911yescharacteristic
325C22⋊C4C22⋊D5911yescharacteristic
326C42—1181no—
327C42C22×D5911yescharacteristic
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23C2×C22⋊D5911yescharacteristic
334C23C2×C22⋊D5911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—592no—
338Q8—1181no—
339Q8—1181no—
340Q8—1181no—
341Q8—1181no—
342Q8—1181no—
343Q8—2362no—
344Q8—2362no—
345D4—22no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—42no—
351D4—81no—
352D4D4×D5912yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—1181no—
362C2×C4—1181no—
363C2×C4—1181no—
364C2×C4—1181no—
365C2×C4—2362no—
366C2×C4—2362no—
367C2×C4C2×C22⋊D5911yescharacteristic
368C2×C4C2×C22⋊D5911yescharacteristic
369C2×C4C2×C22⋊D5911yescharacteristic
370C2×C4C2×C22⋊D5911yescharacteristic
371C2×C4C23×D5911yescharacteristic
372C8—592no—
373C8—1181no—
374C8—1181no—
375C8—1181no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—84no—
388C22#1427375712yescomplemented
389C22C22×C22⋊D5911yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—1182no—
397C4—2361no—
398C4—2361no—
399C4—2361no—
400C4C2×D4×D5911yescharacteristic
401C4#1427377211yescharacteristic
402C2—22no—
403C2—41no—
404C2—42no—
405C2—81no—
406C2D4×C22⋊D5911yescharacteristic
407C2C2×#1427375711yescharacteristic
408C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#546C2
socleC22×C59C22×D4
hypercenter#546D59
hypocenterC59#3266
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#14273757C2semidirect
2. C22×#11745670C2semidirect
3. D4×Dic118C2semidirect
4. #16837797C2semidirect
5. #16837646C2semidirect
6. #16837641C2semidirect
7. #16837621C2semidirect
8. #16837607C2semidirect
9. #16837564C2semidirect
10. #16837557C2semidirect
11. #16837553C2semidirect
12. #16837540C2semidirect
13. #16837502C2semidirect
14. #16837474C2semidirect
17. C22×Dic118C22semidirect
19. C2×#11745672C22semidirect
20. C2×#11745672C22semidirect
21. C2×#11745672C22semidirect
29. C2×#11745664C22semidirect
31. #14273727C22semidirect
34. #14273706C22semidirect
37. C4×Dic118C22semidirect
39. #14273660C22semidirect
40. C4⋊(C59⋊C8)C22semidirect
41. #14273651C22semidirect
42. #14273650C22semidirect
43. #14273650C22semidirect
44. #14273650C22semidirect
48. C22⋊(C59⋊C8)C22semidirect
49. #14273638C22semidirect
109. #11745670D4semidirect
183. C22×C59#137semidirect
220. C59#3266semidirect
388. C22#14273757semidirect