Finite Group Databasebeta

← #34057759

Subgroups — #34057759

Order 19072.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750360C211yesmaximal, characteristic, complemented
2#23750348C211yesmaximal, characteristic, complemented
3#23750019C211yesmaximal, characteristic, complemented
4#23750014C211yesmaximal, characteristic
5#23750009C211yesmaximal, characteristic, complemented
6#23749848C211yesmaximal, characteristic, complemented
7#23749848C211yesmaximal, characteristic, complemented
8#23749841C211yesmaximal, characteristic, complemented
9#23749841C211yesmaximal, characteristic, complemented
10#23749831C211yesmaximal, characteristic, complemented
11#23749826C211yesmaximal, characteristic, complemented
12#23749738C211yesmaximal, characteristic, complemented
13#23749733C211yesmaximal, characteristic, complemented
14C4×#14558725C211yesmaximal, characteristic, complemented
15#446×C149C211yesmaximal, characteristic, complemented
16C2×Dic596C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558725C2211yescharacteristic
22C2×#14558725C2211yescharacteristic
23C2×D1192C2211yescharacteristic
24C2×D1192C2211yescharacteristic
25#18011911C2211yescharacteristic
26#18011908C2211yescharacteristic
27#18011906—21no—
28#18011906—21no—
29#18011900—21no—
30#18011899C2211yescharacteristic
31#18011899C2211yescharacteristic
32#18011899C2211yescharacteristic
33#18011899C2211yescharacteristic
34#18011896—21no—
35#18011896—21no—
36#18011887—21no—
37C4×Dic298C2211yescharacteristic
38C4×Dic298C2211yescharacteristic
39C4×Dic298C2211yescharacteristic
40C4×D596C2211yescharacteristic
41C4×D596C2211yescharacteristic
42C4×D596C2211yescharacteristic
43#18011873—21no—
44#18011869—21no—
45#18011843C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011833C2211yescharacteristic
52C4×Q8×C149C2211yescharacteristic
53C4⋊C8×C149C2211yescharacteristic
54C4⋊C8×C149C2211yescharacteristic
55C4⋊C8×C149C2211yescharacteristic
56#97×C149C2211yescharacteristic
57#97×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59C2×Dic298C2311yescharacteristic
60C2×Dic298C2311yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×D596—21no—
63C2×D596—21no—
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70Dic596—22no—
71Dic596—41no—
72#14558725—22no—
73#14558725—41no—
74#14558725—41no—
75#14558725—41no—
76#14558725—41no—
77D1192—22no—
78D1192—41no—
79C4⋊Dic149—21no—
80C4⋊Dic149—21no—
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97C4×Dic149—21no—
98C4×Dic149—21no—
99C4×Dic149—21no—
100C2×Q8×C149D411yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C4⋊C4×C149D411yescharacteristic
106C4⋊C4×C149D411yescharacteristic
107C4⋊C4×C149D411yescharacteristic
108C42×C149C2311yescharacteristic
109C42×C149C2311yescharacteristic
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—21no—
114Dic298—21no—
115Dic298—21no—
116Dic298—21no—
117Dic298—21no—
118Dic298—21no—
119Dic298—21no—
120D596—21no—
121D596—21no—
122D596—21no—
123D596—21no—
124D596—21no—
125D596—21no—
126D596—42no—
127D596—81no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C4×D149—42no—
134C4×D149—81no—
135C4×D149—81no—
136Q8×C149—41no—
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2411yescharacteristic
144C8×C149—21no—
145C8×C149—21no—
146C8×C149—21no—
147C8×C149#4112yes—
148C22×C149C22×D411yescharacteristic
149C2×D149—41no—
150C2×D149—41no—
151C2×D149—41no—
152C2×D149—41no—
153C2×D149—41no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C4×C149—21no—
159C4×C149—21no—
160C4×C149—21no—
161C4×C149—21no—
162C4×C149—21no—
163C4×C149—21no—
164C4×C149C2×#4111yescharacteristic
165C4×C149H(5,𝔽2)11yescharacteristic
166Dic149—41no—
167Dic149—41no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171C2×C149#55011yescharacteristic
172C2×C149#57511yescharacteristic
173C2×C149#57711yescharacteristic
174D149—81no—
175D149—81no—
176D149—81no—
177C149#340111yescharacteristic, complemented, Sylow
178#3401—1491nomaximal, Sylow
179#559—1491no—
180#556—1491no—
181#497—1491no—
182#496—1491no—
183#495—1491no—
184#464—1491no—
185#464—1491no—
186#463—1491no—
187#463—1491no—
188#461—1491no—
189#460—1491no—
190#446D14911yescharacteristic, complemented
191#442—1491no—
192#441—1491no—
193C4×SD16—1491no—
194C2×Q16—1491no—
195C2×Q16—1491no—
196C2×SD16—1491no—
197C2×SD16—1491no—
198C2×SD16—1491no—
199C2×SD16—1491no—
200C2×SD16—1491no—
201C2×D8—1491no—
202C2×D8—1491no—
203C4⋊Q8—1491no—
204#127—1491no—
205#126—2981no—
206#126—2981no—
207#124—2981no—
208#124—1491no—
209#124—1491no—
210#124—1491no—
211#124—1491no—
212#123—2981no—
213#123—2981no—
214C22⋊Q8—2981no—
215C4×Q8—1491no—
216C4×Q8—1491no—
217C4×Q8—1491no—
218C4×Q8C2×D14911yescharacteristic
219C4×D4—2981no—
220C4×D4—1491no—
221C4×D4—1491no—
222C4×D4—1491no—
223#117—2981no—
224#106—1491no—
225C4⋊C8C2×D14911yescharacteristic
226C4⋊C8C2×D14911yescharacteristic
227C4⋊C8C2×D14911yescharacteristic
228#103—1491no—
229#103—1491no—
230#103—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#97C2×D14911yescharacteristic
235#97C2×D14911yescharacteristic
236C4×C8C2×D14911yescharacteristic
237C2×Q8—1491no—
238C2×Q8—1491no—
239C2×Q8—1491no—
240C2×Q8D59611yescharacteristic
241C2×D4—2981no—
242C2×D4—2981no—
243C2×D4—1491no—
244C2×D4—1491no—
245C2×D4—1491no—
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4—2981no—
249Q16—2982no—
250Q16—5961no—
251SD16—2982no—
252SD16—5961no—
253SD16—5961no—
254SD16—5961no—
255SD16—5961no—
256D8—2982no—
257D8—5961no—
258C2×C8C22×D14911yescharacteristic
259C2×C8C22×D14911yescharacteristic
260C2×C8C22×D14911yescharacteristic
261C2×C8C22×D14911yescharacteristic
262C4⋊C4—2981no—
263C4⋊C4—2981no—
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—1491no—
268C4⋊C4—1491no—
269C4⋊C4D59611yescharacteristic
270C4⋊C4D59611yescharacteristic
271C4⋊C4D59611yescharacteristic
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C42—2981no—
284C42—2981no—
285C42—2981no—
286C42C22×D14911yescharacteristic
287C42C22×D14911yescharacteristic
288C42C22×D14911yescharacteristic
289C23—2981no—
290C23—2981no—
291C23—2981no—
292Q8—41no—
293Q8—2981no—
294Q8—2981no—
295Q8—2981no—
296Q8—2981no—
297Q8—2981no—
298Q8—2981no—
299D4—2981no—
300D4—2981no—
301D4—2981no—
302D4—2981no—
303D4—2981no—
304D4—2981no—
305D4—5962no—
306D4—11921no—
307C2×C4—2981no—
308C2×C4—2981no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—5962no—
313C2×C4—11921no—
314C2×C4—11921no—
315C2×C4C2×D59611yescharacteristic
316C2×C4C2×D59611yescharacteristic
317C2×C4C2×D59611yescharacteristic
318C2×C4C2×D59611yescharacteristic
319C2×C4C2×D59611yescharacteristic
320C2×C4C2×D59611yescharacteristic
321C2×C4C23×D14911yescharacteristic
322C8—21no—
323C8—21no—
324C8—21no—
325C8#1455873712yes—
326C22—5961no—
327C22—5961no—
328C22—5961no—
329C22—5961no—
330C22—5961no—
331C22—5961no—
332C22—5961no—
333C22—5961no—
334C22—5961no—
335C22C22×D59611yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—5961no—
343C4—5961no—
344C4—5961no—
345C4—5961no—
346C4—5961no—
347C4C2×#1455873711yescharacteristic
348C4#1801195711yescharacteristic
349C2—11921no—
350C2—11921no—
351C2—11921no—
352C2#2375029711yescharacteristic
353C2#2375042511yescharacteristic
354C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#446×C149C2
socleC22×C149C22×D4
prime radical#23750014C2
hypercenter#446D149
hypocenterC149#3401
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #23750360C2semidirect
2. #23750348C2semidirect
3. #23750019C2semidirect
5. #23750009C2semidirect
6. #23749848C2semidirect
7. #23749848C2semidirect
8. #23749841C2semidirect
9. #23749841C2semidirect
10. #23749831C2semidirect
11. #23749826C2semidirect
12. #23749738C2semidirect
13. #23749733C2semidirect
14. C4×#14558725C2semidirect
15. #446×C149C2semidirect
177. C149#3401semidirect
190. #446D149semidirect

Maximal subgroups

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

subgroupindex
#237503602
#237503482
#237500192
#237500142
#237500092
#237498482
#237498412
#237498312
#237498262
#237497382
#237497332
C4×#145587252
#446×C1492
#3401149