Finite Group Databasebeta

← #21430639

Subgroups — #21430639

Order 7552.

562 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273712C211yesmaximal, characteristic, complemented
2C2×#14273705C211yesmaximal, characteristic, complemented
3#16837331C211yesmaximal, characteristic, complemented
4#16837320C211yesmaximal, characteristic, complemented
5#16837315C211yesmaximal, characteristic, complemented
6#16837315C211yesmaximal, characteristic, complemented
7#16837312C211yesmaximal, characteristic
8#16837303C211yesmaximal, characteristic, complemented
9#16837292C211yesmaximal, characteristic, complemented
10#16837284C211yesmaximal, characteristic, complemented
11#16837280C211yesmaximal, characteristic, complemented
12#16837280C211yesmaximal, characteristic, complemented
13#16837280C211yesmaximal, characteristic, complemented
14#16837261C211yesmaximal, characteristic, complemented
15C59×#400C211yesmaximal, characteristic, complemented
16C22×Dic118C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C22×D236C2211yescharacteristic
19C22×D236C2211yescharacteristic
20C22×C4×D59C2211yescharacteristic
21C22×C4×D59C2211yescharacteristic
22#14273712—24no—
23#14273705—24no—
24C2×Dic59⋊C4C2211yescharacteristic
25C2×Dic59⋊C4C2211yescharacteristic
26C2×Dic59⋊C4C2211yescharacteristic
27C2×(C2×D59)⋊C4C2211yescharacteristic
28C2×(C2×D59)⋊C4C2211yescharacteristic
29C2×(C2×D59)⋊C4C2211yescharacteristic
30C2×(C2×D59)⋊C4C2211yescharacteristic
31C2×(C2×D59)⋊C4C2211yescharacteristic
32C2×(C2×D59)⋊C4C2211yescharacteristic
33C2×(C2×D59)⋊C4C2211yescharacteristic
34C2×(C2×D59)⋊C4C2211yescharacteristic
35C2×(C2×D59)⋊C4C2211yescharacteristic
36C2×(C2×D59)⋊C4C2211yescharacteristic
37C2×(C2×D59)⋊C4C2211yescharacteristic
38C2×(C2×D59)⋊C4C2211yescharacteristic
39C2×(C2×D59)⋊C4C2211yescharacteristic
40C2×C4×Dic59C2211yescharacteristic
41C59⋊#95C2211yescharacteristic
42C59⋊#95C2211yescharacteristic
43C59⋊#95C2211yescharacteristic
44C59⋊#95C2211yescharacteristic
45C59⋊#95C2211yescharacteristic
46C2×C4⋊C4×C59C2211yescharacteristic
47C2×C4⋊C4×C59C2211yescharacteristic
48#95×C59C2211yescharacteristic
49#95×C59C2211yescharacteristic
50#95×C59C2211yescharacteristic
51#95×C59C2211yescharacteristic
52#95×C59C2211yescharacteristic
53C23×D59C2311yescharacteristic
54C23×D59C2311yescharacteristic
55C23×D59C2311yescharacteristic
56C22×C4×C59C2311yescharacteristic
57C22×C4×C59C2311yescharacteristic
58C22×C4×C59C2311yescharacteristic
59C22×C4×C59C2311yescharacteristic
60C22×C4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C22×C4×C59C2311yescharacteristic
63C22×Dic59C2311yescharacteristic
64C22×Dic59C2311yescharacteristic
65C22×Dic59C2311yescharacteristic
66C22×Dic59C2311yescharacteristic
67C22×Dic59C2311yescharacteristic
68C2×D236—22no—
69C2×D236—22no—
70C2×D236—22no—
71C2×D236—22no—
72C2×D236—22no—
73C2×D236—41no—
74C2×D236—41no—
75C2×D236—41no—
76C2×D236—41no—
77C2×C4×D59—22no—
78C2×C4×D59—22no—
79C2×C4×D59—22no—
80C2×C4×D59—41no—
81C2×C4×D59—41no—
82C2×C4×D59—41no—
83C2×Dic118—22no—
84C2×Dic118—41no—
85C2×Dic118—41no—
86C4⋊C4×C59—22no—
87C4⋊C4×C59—22no—
88(C2×D59)⋊C4—22no—
89(C2×D59)⋊C4—22no—
90(C2×D59)⋊C4—22no—
91(C2×D59)⋊C4—22no—
92(C2×D59)⋊C4—22no—
93(C2×D59)⋊C4—22no—
94(C2×D59)⋊C4—41no—
95(C2×D59)⋊C4—41no—
96(C2×D59)⋊C4—41no—
97(C2×D59)⋊C4—41no—
98(C2×D59)⋊C4—41no—
99(C2×D59)⋊C4—41no—
100(C2×D59)⋊C4—41no—
101Dic59⋊C4—22no—
102Dic59⋊C4—41no—
103Dic59⋊C4D414yescomplemented
104C4×Dic59—41no—
105C23×C59C2411yescharacteristic
106C22×D59—21no—
107C22×D59—21no—
108C22×D59—21no—
109C22×D59—21no—
110C22×D59—21no—
111C22×D59—21no—
112C22×D59—21no—
113C22×D59—21no—
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—21no—
117C22×D59—21no—
118C22×D59—21no—
119C22×D59—21no—
120C22×D59—21no—
121C22×D59—21no—
122C22×D59—21no—
123C22×D59—21no—
124C22×D59—21no—
125C22×D59#4112yes—
126C22×D59#4112yes—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
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—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59C2×D412yes—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—21no—
151C2×Dic59—21no—
152C2×Dic59—21no—
153C2×Dic59—21no—
154C2×Dic59—21no—
155C2×Dic59—21no—
156C2×Dic59—21no—
157C2×Dic59—21no—
158C2×Dic59—21no—
159C2×Dic59—21no—
160C2×Dic59—21no—
161C2×Dic59C2×D412yes—
162C2×Dic59C2×D412yes—
163D236—44no—
164D236—44no—
165D236—44no—
166C4×D59—44no—
167C4×D59—44no—
168Dic118—44no—
169C22×C59C22×D411yescharacteristic
170C22×C59C2×#4111yescharacteristic
171C22×C59C2×#4111yescharacteristic
172C22×C59H(5,𝔽2)11yescharacteristic
173C22×C59H(5,𝔽2)11yescharacteristic
174C22×C59H(5,𝔽2)11yescharacteristic
175C22×C592−1+411yescharacteristic
176C2×D59—22no—
177C2×D59—22no—
178C2×D59—22no—
179C2×D59—22no—
180C2×D59—22no—
181C2×D59—22no—
182C2×D59—41no—
183C2×D59—41no—
184C2×D59—41no—
185C2×D59—41no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—41no—
189C2×D59—41no—
190C2×D59—41no—
191C2×D59—41no—
192C2×D59—41no—
193C2×D59—41no—
194C2×D59—41no—
195C2×D59—41no—
196C2×D59—41no—
197C4×C59—22no—
198C4×C59—41no—
199C4×C59—41no—
200C4×C59—41no—
201C4×C59—41no—
202C4×C59—41no—
203C4×C59—41no—
204Dic59—22no—
205Dic59—22no—
206Dic59—41no—
207Dic59—41no—
208Dic59—41no—
209#2696—591nomaximal, Sylow
210C2×C59#53511yescharacteristic
211C2×C59#53811yescharacteristic
212C2×C59#53911yescharacteristic
213C2×C59#54611yescharacteristic
214C2×C59#54811yescharacteristic
215C2×C59#55111yescharacteristic
216C2×C59#56211yescharacteristic
217D59—42no—
218D59—42no—
219D59—81no—
220C2×#123—591no—
221C2×C22⋊Q8—591no—
222#400D5911yescharacteristic, complemented
223#397—591no—
224#394—591no—
225#393—591no—
226#393—591no—
227#392—591no—
228#390—591no—
229#388—591no—
230#387—591no—
231#386—591no—
232#386—591no—
233#386—591no—
234#380—591no—
235C59#269611yescharacteristic, complemented, Sylow
236C22×Q8—591no—
237C22×D4—591no—
238C22×D4—591no—
239C22×D4—591no—
240C23×C4—591no—
241C23×C4—591no—
242#123—1184no—
243C22⋊Q8—1184no—
244C2×C4⋊C4—591no—
245C2×C4⋊C4—591no—
246C2×C4⋊C4—591no—
247C2×C4⋊C4C2×D5911yescharacteristic
248C2×C4⋊C4C2×D5911yescharacteristic
249C2×C22⋊C4—591no—
250C2×C22⋊C4—591no—
251C2×C22⋊C4—591no—
252C2×C22⋊C4—591no—
253C2×C22⋊C4—591no—
254C2×C22⋊C4—591no—
255C2×C22⋊C4—591no—
256C2×C22⋊C4—591no—
257C2×C22⋊C4—591no—
258C2×C22⋊C4—591no—
259C2×C22⋊C4—591no—
260C2×C22⋊C4—591no—
261C2×C22⋊C4—591no—
262C2×C42—591no—
263#95—591no—
264#95—591no—
265#95—591no—
266#95—591no—
267#95—591no—
268#95C2×D5911yescharacteristic
269#95C2×D5911yescharacteristic
270#95C2×D5911yescharacteristic
271#95C2×D5911yescharacteristic
272#95C2×D5911yescharacteristic
273C24—591no—
274C24—591no—
275C24—591no—
276C2×Q8—1182no—
277C2×Q8—2361no—
278C2×Q8—2361no—
279C2×D4—1182no—
280C2×D4—1182no—
281C2×D4—1182no—
282C2×D4—1182no—
283C2×D4—1182no—
284C2×D4—2361no—
285C2×D4—2361no—
286C2×D4—2361no—
287C2×D4—2361no—
288C22×C4—591no—
289C22×C4—591no—
290C22×C4—591no—
291C22×C4—591no—
292C22×C4—591no—
293C22×C4—1182no—
294C22×C4—1182no—
295C22×C4—1182no—
296C22×C4—2361no—
297C22×C4—2361no—
298C22×C4—2361no—
299C22×C4C22×D5911yescharacteristic
300C22×C4C22×D5911yescharacteristic
301C22×C4C22×D5911yescharacteristic
302C22×C4C22×D5911yescharacteristic
303C22×C4C22×D5911yescharacteristic
304C22×C4C22×D5911yescharacteristic
305C22×C4C22×D5911yescharacteristic
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—594no—
309C4⋊C4—1182no—
310C4⋊C4—2361no—
311C22⋊C4—1182no—
312C22⋊C4—1182no—
313C22⋊C4—1182no—
314C22⋊C4—1182no—
315C22⋊C4—1182no—
316C22⋊C4—1182no—
317C22⋊C4—2361no—
318C22⋊C4—2361no—
319C22⋊C4—2361no—
320C22⋊C4—2361no—
321C22⋊C4—2361no—
322C22⋊C4—2361no—
323C22⋊C4—2361no—
324C42—2361no—
325C23—592no—
326C23—592no—
327C23—1181no—
328C23—1181no—
329C23—1181no—
330C23—1181no—
331C23—1181no—
332C23—1181no—
333C23—1181no—
334C23—1181no—
335C23—1181no—
336C23—1181no—
337C23—1181no—
338C23—1181no—
339C23—1181no—
340C23—1181no—
341C23—1181no—
342C23—1181no—
343C23—1181no—
344C23—1181no—
345C23—1181no—
346C23C23×D5911yescharacteristic
347Q8—2364no—
348D4—2364no—
349D4—2364no—
350D4—2364no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—592no—
372C2×C4—592no—
373C2×C4—1181no—
374C2×C4—1181no—
375C2×C4—1181no—
376C2×C4—1181no—
377C2×C4—1181no—
378C2×C4—1181no—
379C2×C4—1181no—
380C2×C4—1181no—
381C2×C4—1181no—
382C2×C4—1181no—
383C2×C4—1181no—
384C2×C4—1181no—
385C2×C4—1181no—
386C2×C4—2364no—
387C2×C4—2364no—
388C2×C4D4×D5912yes—
389C22—1182no—
390C22—1182no—
391C22—1182no—
392C22—1182no—
393C22—1182no—
394C22—1182no—
395C22—2361no—
396C22—2361no—
397C22—2361no—
398C22—2361no—
399C22—2361no—
400C22—2361no—
401C22—2361no—
402C22—2361no—
403C22—2361no—
404C22—2361no—
405C22—2361no—
406C22—2361no—
407C22—2361no—
408C22—2361no—
409C22—2361no—
410C22C2×D4×D5911yescharacteristic
411C22#41×D5911yescharacteristic
412C22#41×D5911yescharacteristic
413C22#1427377311yescharacteristic
414C22#1427377311yescharacteristic
415C22#1427377311yescharacteristic
416C22#1427377511yescharacteristic
417C4—22no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—1182no—
425C4—1182no—
426C4—2361no—
427C4—2361no—
428C4—2361no—
429C2—4721no—
430C2—2362no—
431C2—2362no—
432C2#1683797011yescharacteristic
433C2#1683799111yescharacteristic
434C2#1683800011yescharacteristic
435C2#1683804411yescharacteristic
436C2#1683806211yescharacteristic
437C2#1683807711yescharacteristic
438C2#1683815011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#400C2
hypercenter#400D59
hypocenterC59#2696
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#14273712C2semidirect
2. C2×#14273705C2semidirect
3. #16837331C2semidirect
4. #16837320C2semidirect
5. #16837315C2semidirect
6. #16837315C2semidirect
8. #16837303C2semidirect
9. #16837292C2semidirect
10. #16837284C2semidirect
11. #16837280C2semidirect
12. #16837280C2semidirect
13. #16837280C2semidirect
14. #16837261C2semidirect
15. C59×#400C2semidirect
103. Dic59⋊C4D4semidirect
222. #400D59semidirect
235. C59#2696semidirect