Finite Group Databasebeta

← #34052772

Subgroups — #34052772

Order 19072.

472 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23749566C211yesmaximal, characteristic, complemented
2#23749554C211yesmaximal, characteristic, complemented
3#23749551C211yesmaximal, characteristic, complemented
4#23749543C211yesmaximal, characteristic, complemented
5#23749543C211yesmaximal, characteristic, complemented
6#23749542C211yesmaximal, characteristic, complemented
7#23749542C211yesmaximal, characteristic, complemented
8#23749538C211yesmaximal, characteristic, complemented
9#23749538C211yesmaximal, characteristic, complemented
10#23749538C211yesmaximal, characteristic, complemented
11#23749535C211yesmaximal, characteristic
12#23749503C211yesmaximal, characteristic, complemented
13#23749503C211yesmaximal, characteristic, complemented
14#23749496C211yesmaximal, characteristic, complemented
15#400×C149C211yesmaximal, characteristic, complemented
16C22×Dic298C2211yescharacteristic
17C22×D596C2211yescharacteristic
18C22×D596C2211yescharacteristic
19C22×D596C2211yescharacteristic
20C22×C4×D149C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558713C2211yescharacteristic
24C2×#14558713C2211yescharacteristic
25C2×#14558713C2211yescharacteristic
26C2×#14558713C2211yescharacteristic
27C2×#14558713C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×#14558713C2211yescharacteristic
36C2×#14558713C2211yescharacteristic
37#18011818C2211yescharacteristic
38#18011818C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44C2×C4⋊C4×C149C2211yescharacteristic
45C2×C4⋊C4×C149C2211yescharacteristic
46#95×C149C2211yescharacteristic
47#95×C149C2211yescharacteristic
48#95×C149C2211yescharacteristic
49#95×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51C23×D149C2311yescharacteristic
52C23×D149C2311yescharacteristic
53C23×D149C2311yescharacteristic
54C2×Dic298—41no—
55C2×Dic298—41no—
56C2×Dic298—41no—
57C2×D596—22no—
58C2×D596—22no—
59C2×D596—41no—
60C2×D596—41no—
61C2×D596—41no—
62C2×D596—41no—
63C2×D596—41no—
64C2×D596—41no—
65C2×D596—41no—
66C22×Dic149C2311yescharacteristic
67C22×Dic149C2311yescharacteristic
68C22×Dic149C2311yescharacteristic
69C22×Dic149C2311yescharacteristic
70C22×Dic149C2311yescharacteristic
71C2×C4×D149—41no—
72C2×C4×D149—41no—
73C2×C4×D149—41no—
74#14558715—41no—
75#14558715—41no—
76#14558713—22no—
77#14558713—41no—
78#14558713—41no—
79#14558713—41no—
80#14558713—41no—
81#14558713—41no—
82#14558713—41no—
83#14558713—41no—
84#14558713—41no—
85#14558713—41no—
86#14558713—41no—
87#14558713—41no—
88#14558713—41no—
89#14558713—41no—
90C22×C4×C149C2311yescharacteristic
91C22×C4×C149C2311yescharacteristic
92C22×C4×C149C2311yescharacteristic
93C22×C4×C149C2311yescharacteristic
94C22×C4×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96C22×C4×C149C2311yescharacteristic
97C4⋊C4×C149—41no—
98C4⋊C4×C149—41no—
99C22×D149—21no—
100C22×D149—21no—
101C22×D149—21no—
102C22×D149—21no—
103C22×D149—21no—
104C22×D149—21no—
105C22×D149—21no—
106C22×D149—21no—
107C22×D149—21no—
108C22×D149—21no—
109C22×D149—21no—
110C22×D149—21no—
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—21no—
114C22×D149—21no—
115C22×D149—21no—
116C22×D149—21no—
117C22×D149—21no—
118C22×D149—21no—
119C22×D149#4112yes—
120Dic298—44no—
121D596—44no—
122D596—44no—
123D596—44no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C4×D149—44no—
140C23×C149C2411yescharacteristic
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149—21no—
158C2×C4×C149—21no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C22×C149C2×#4111yescharacteristic
163C22×C149H(5,𝔽2)11yescharacteristic
164C22×C149H(5,𝔽2)11yescharacteristic
165C22×C149H(5,𝔽2)11yescharacteristic
166C22×C149H(5,𝔽2)11yescharacteristic
167C22×C149H(5,𝔽2)11yescharacteristic
168C22×C1492−1+411yescharacteristic
169C2×D149—22no—
170C2×D149—22no—
171C2×D149—22no—
172C2×D149—41no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C2×D149—41no—
178C2×D149—41no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—41no—
184C2×D149—41no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C2×D149—41no—
189C2×D149—41no—
190C4×C149—41no—
191C4×C149—41no—
192C4×C149—41no—
193C4×C149—41no—
194C4×C149—41no—
195C4×C149—41no—
196C4×C149—41no—
197Dic149—41no—
198Dic149—41no—
199Dic149—41no—
200Dic149—41no—
201Dic149—41no—
202C2×C149#53811yescharacteristic
203C2×C149#53811yescharacteristic
204C2×C149#53911yescharacteristic
205C2×C149#56011yescharacteristic
206C2×C149H(3,𝔽4)11yescharacteristic
207C2×C149#56211yescharacteristic
208C2×C149#56211yescharacteristic
209D149—42no—
210D149—81no—
211D149—81no—
212C149#282411yescharacteristic, complemented, Sylow
213#2824—1491nomaximal, Sylow
214#400—1491no—
215#400D14911yescharacteristic, complemented
216#397—1491no—
217#397—1491no—
218#394—1491no—
219#394—1491no—
220#394—1491no—
221#394—1491no—
222#393—1491no—
223#393—1491no—
224#393—1491no—
225#392—1491no—
226#386—1491no—
227#386—1491no—
228#385—1491no—
229C22×Q8—1491no—
230C22×D4—1491no—
231C22×D4—1491no—
232C22×D4—1491no—
233C23×C4—1491no—
234C2×C4⋊C4—1491no—
235C2×C4⋊C4—1491no—
236C2×C4⋊C4C2×D14911yescharacteristic
237C2×C4⋊C4C2×D14911yescharacteristic
238C2×C22⋊C4—1491no—
239C2×C22⋊C4—1491no—
240C2×C22⋊C4—1491no—
241C2×C22⋊C4—1491no—
242C2×C22⋊C4—1491no—
243C2×C22⋊C4—1491no—
244C2×C22⋊C4—1491no—
245C2×C22⋊C4—1491no—
246C2×C22⋊C4—1491no—
247C2×C22⋊C4—1491no—
248C2×C22⋊C4—1491no—
249C2×C22⋊C4—1491no—
250C2×C22⋊C4—1491no—
251C2×C22⋊C4—1491no—
252#95—1491no—
253#95—1491no—
254#95—1491no—
255#95—1491no—
256#95—1491no—
257#95—1491no—
258#95—1491no—
259#95C2×D14911yescharacteristic
260#95C2×D14911yescharacteristic
261#95C2×D14911yescharacteristic
262#95C2×D14911yescharacteristic
263#95C2×D14911yescharacteristic
264C24—1491no—
265C24—1491no—
266C24—1491no—
267C2×Q8—5961no—
268C2×Q8—5961no—
269C2×Q8—5961no—
270C2×D4—2982no—
271C2×D4—2982no—
272C2×D4—5961no—
273C2×D4—5961no—
274C2×D4—5961no—
275C2×D4—5961no—
276C2×D4—5961no—
277C2×D4—5961no—
278C2×D4—5961no—
279C22×C4—5961no—
280C22×C4—5961no—
281C22×C4—5961no—
282C22×C4—1491no—
283C22×C4—1491no—
284C22×C4—1491no—
285C22×C4—1491no—
286C22×C4—1491no—
287C22×C4C22×D14911yescharacteristic
288C22×C4C22×D14911yescharacteristic
289C22×C4C22×D14911yescharacteristic
290C22×C4C22×D14911yescharacteristic
291C22×C4C22×D14911yescharacteristic
292C22×C4C22×D14911yescharacteristic
293C22×C4C22×D14911yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—5961no—
297C4⋊C4—5961no—
298C22⋊C4—2982no—
299C22⋊C4—5961no—
300C22⋊C4—5961no—
301C22⋊C4—5961no—
302C22⋊C4—5961no—
303C22⋊C4—5961no—
304C22⋊C4—5961no—
305C22⋊C4—5961no—
306C22⋊C4—5961no—
307C22⋊C4—5961no—
308C22⋊C4—5961no—
309C22⋊C4—5961no—
310C22⋊C4—5961no—
311C22⋊C4—5961no—
312C23—2981no—
313C23—2981no—
314C23—2981no—
315C23—2981no—
316C23—2981no—
317C23—2981no—
318C23—2981no—
319C23—2981no—
320C23—2981no—
321C23—2981no—
322C23—2981no—
323C23—2981no—
324C23—2981no—
325C23—2981no—
326C23—2981no—
327C23—2981no—
328C23—2981no—
329C23—2981no—
330C23—2981no—
331C23—2981no—
332C23—1492no—
333C23C23×D14911yescharacteristic
334Q8—5964no—
335D4—5964no—
336D4—5964no—
337D4—5964no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
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—2981no—
360C2×C4—2981no—
361C2×C4—2981no—
362C2×C4—2981no—
363C2×C4—2981no—
364C2×C4—2981no—
365C2×C4—2981no—
366C2×C4—2981no—
367C2×C4—2981no—
368C2×C4—2981no—
369C2×C4—2981no—
370C2×C4—2981no—
371C2×C4—2981no—
372C2×C4—2981no—
373C2×C4—2981no—
374C2×C4—5964no—
375C22—2982no—
376C22—2982no—
377C22—2982no—
378C22—5961no—
379C22—5961no—
380C22—5961no—
381C22—5961no—
382C22—5961no—
383C22—5961no—
384C22—5961no—
385C22—5961no—
386C22—5961no—
387C22—5961no—
388C22—5961no—
389C22—5961no—
390C22—5961no—
391C22—5961no—
392C22—5961no—
393C22—5961no—
394C22—5961no—
395C22—5961no—
396C22#41×D14911yescharacteristic
397C22#1801195611yescharacteristic
398C22#1801195711yescharacteristic
399C22#1801195711yescharacteristic
400C22#1801195711yescharacteristic
401C22#1801195711yescharacteristic
402C22#1801195911yescharacteristic
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—5961no—
411C4—5961no—
412C4—5961no—
413C4—5961no—
414C4—5961no—
415C2—5962no—
416C2—11921no—
417C2—11921no—
418C2#2375021111yescharacteristic
419C2#2375021411yescharacteristic
420C2#2375022311yescharacteristic
421C2#2375036611yescharacteristic
422C2#2375036711yescharacteristic
423C2#2375037111yescharacteristic
424C2#2375037311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#400×C149C2
prime radical#23749535C2
hypercenter#400D149
hypocenterC149#2824
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #23749566C2semidirect
2. #23749554C2semidirect
3. #23749551C2semidirect
4. #23749543C2semidirect
5. #23749543C2semidirect
6. #23749542C2semidirect
7. #23749542C2semidirect
8. #23749538C2semidirect
9. #23749538C2semidirect
10. #23749538C2semidirect
12. #23749503C2semidirect
13. #23749503C2semidirect
14. #23749496C2semidirect
15. #400×C149C2semidirect
212. C149#2824semidirect
215. #400D149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237495662
#237495542
#237495512
#237495432
#237495422
#237495382
#237495352
#237495032
#237494962
#400×C1492
#2824149