Finite Group Databasebeta

← #34055770

Subgroups — #34055770

Order 19072.

364 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#23750235C211yesmaximal, characteristic, complemented
2#23750199C211yesmaximal, characteristic
3#23750018C211yesmaximal, characteristic, complemented
4#23750003C211yesmaximal, characteristic, complemented
5#23749992C211yesmaximal, characteristic, complemented
6#23749981C211yesmaximal, characteristic, complemented
7#23749850C211yesmaximal, characteristic, complemented
8#23749849C211yesmaximal, characteristic, complemented
9#23749834C211yesmaximal, characteristic, complemented
10#23749833C211yesmaximal, characteristic, complemented
11#23749789C211yesmaximal, characteristic
12#23749785C211yesmaximal, characteristic
13#23749781C211yesmaximal, characteristic, complemented
14#23749683C211yesmaximal, characteristic, complemented
15#451×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558726C2211yescharacteristic
20C2×#14558726C2211yescharacteristic
21C2×#14558725C2211yescharacteristic
22C2×#14558723C2211yescharacteristic
23#18011909C2211yescharacteristic
24#18011909C2211yescharacteristic
25#18011909C2211yescharacteristic
26#18011904—21no—
27#18011904—21no—
28#18011902—21no—
29#18011902C2211yescharacteristic
30#18011901—21no—
31#18011900C2211yescharacteristic
32#18011900C2211yescharacteristic
33#18011894—21no—
34#18011894—21no—
35#18011890C2211yescharacteristic
36#18011887—21no—
37#18011887—21no—
38Q8×Dic149C2211yescharacteristic
39#18011876C2211yescharacteristic
40#18011870C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C22×Q8×C149C2211yescharacteristic
53C2×Q16×C149C2211yescharacteristic
54C2×Q16×C149C2211yescharacteristic
55C22⋊Q8×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61C2×Dic298C2311yescharacteristic
62C2×Dic298C2311yescharacteristic
63C2×D596C2311yescharacteristic
64C2×C22⋊D149—21no—
65C2×C4×D149—21no—
66Dic596—41no—
67#14558726—41no—
68#14558726—41no—
69#14558726—41no—
70#14558725—41no—
71#14558723—41no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149D411yescharacteristic
77C4⋊Dic149D411yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149D411yescharacteristic
90C22⋊Dic149D411yescharacteristic
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C4×Dic149C2311yescharacteristic
98C4×Dic149C2311yescharacteristic
99C2×Q8×C149—21no—
100C2×Q8×C149—41no—
101C2×Q8×C149—41no—
102C2×Q8×C149C2311yescharacteristic
103C2×Q8×C149C2311yescharacteristic
104C2×Q8×C149C2311yescharacteristic
105C22×C4×C149—21no—
106C22×C4×C149C2311yescharacteristic
107Q16×C149—41no—
108Q16×C149—41no—
109C2×C8×C149C2311yescharacteristic
110C2×C8×C149C2311yescharacteristic
111C4⋊C4×C149—21no—
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149—21no—
115Dic298—21no—
116Dic298—21no—
117Dic298—21no—
118Dic298—21no—
119D596—21no—
120D596—21no—
121C22⋊D149—42no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C4×D149—42no—
130#11924746—21no—
131#11924746—21no—
132C23×C149C2×D411yescharacteristic
133Q8×C149—21no—
134Q8×C149—21no—
135Q8×C149—21no—
136Q8×C149—21no—
137Q8×C149—21no—
138Q8×C149—21no—
139Q8×C149—42no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—42no—
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2411yescharacteristic
149C8×C149—21no—
150C8×C149—21no—
151C22×C149—21no—
152C22×C149—21no—
153C22×C149—21no—
154C22×C149C22×D411yescharacteristic
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C4×C149—21no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149H(5,𝔽2)11yescharacteristic
164C4×C149H(5,𝔽2)11yescharacteristic
165Dic149—21no—
166Dic149—21no—
167Dic149—21no—
168Dic149—21no—
169Dic149—41no—
170Dic149—41no—
171Dic149—41no—
172C2×C149—41no—
173C2×C149#53511yescharacteristic
174C2×C149#57811yescharacteristic
175C2×C149#57811yescharacteristic
176D149—81no—
177C149#322311yescharacteristic, complemented, Sylow
178#3223—1491nomaximal, Sylow
179#541—1491no—
180#536—1491no—
181#497—1491no—
182#494—1491no—
183#491—1491no—
184#488—1491no—
185#464—1491no—
186#464—1491no—
187#462—1491no—
188#462—1491no—
189#452—1491no—
190#452—1491no—
191#451—1491no—
192#451D14911yescharacteristic, complemented
193#433—1491no—
194C2×#41—1491no—
195C22×Q8C2×D14911yescharacteristic
196C2×Q16—1491no—
197C2×Q16—1491no—
198C2×Q16—1491no—
199C2×Q16—1491no—
200C2×Q16C2×D14911yescharacteristic
201C2×Q16C2×D14911yescharacteristic
202C2×SD16—1491no—
203C2×SD16—1491no—
204C4⋊Q8—1491no—
205C4⋊Q8—1491no—
206C4⋊Q8—1491no—
207#126—2981no—
208#126—2981no—
209#125—2981no—
210#125—2981no—
211#125—1491no—
212#124—1491no—
213#124—1491no—
214#123—2981no—
215#123—2981no—
216C22⋊Q8—2981no—
217C22⋊Q8—2981no—
218C22⋊Q8—1491no—
219C22⋊Q8C2×D14911yescharacteristic
220C4×Q8—1491no—
221C4×Q8—1491no—
222#117—1491no—
223C4⋊C8—1491no—
224C4⋊C8—1491no—
225#103—1491no—
226#103—1491no—
227#103—1491no—
228#103—1491no—
229#103C2×D14911yescharacteristic
230#103C2×D14911yescharacteristic
231#102—1491no—
232#102—1491no—
233C22⋊C8—1491no—
234C22⋊C8C2×D14911yescharacteristic
235#97—1491no—
236C4×C8—1491no—
237#41—5961no—
238#41—5961no—
239C2×Q8—21no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—1491no—
243C2×Q8—1491no—
244C2×Q8C22×D14911yescharacteristic
245C2×Q8C22×D14911yescharacteristic
246C2×Q8C22×D14911yescharacteristic
247C2×D4—2981no—
248C2×D4—1491no—
249C22×C4—21no—
250C22×C4—2981no—
251C22×C4C22×D14911yescharacteristic
252Q16—41no—
253Q16—41no—
254Q16—5961no—
255Q16—5961no—
256Q16—5961no—
257Q16—5961no—
258SD16—5961no—
259SD16—5961no—
260C2×C8—1491no—
261C2×C8—1491no—
262C2×C8C22×D14911yescharacteristic
263C2×C8C22×D14911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—1491no—
277C4⋊C4—1491no—
278C4⋊C4—1491no—
279C4⋊C4C22×D14911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—1491no—
287C22⋊C4—1491no—
288C42—2981no—
289C42—2981no—
290C42—1491no—
291C42—1491no—
292C23—2981no—
293C23D4×D14911yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—2981no—
302Q8—2981no—
303Q8—2981no—
304Q8—2981no—
305D4—2981no—
306D4—2981no—
307D4—5962no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—5962no—
319C2×C4—1491no—
320C2×C4—1491no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4D4×D14911yescharacteristic
324C2×C4C23×D14911yescharacteristic
325C8—21no—
326C8—21no—
327C8—2981no—
328C8—2981no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—5961no—
333C22—5961no—
334C22—5961no—
335C22C2×D4×D14911yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—2981no—
342C4—2981no—
343C4—2981no—
344C4—2981no—
345C4—5961no—
346C4—5961no—
347C4—5961no—
348C4#1801195611yescharacteristic
349C4#1801195611yescharacteristic
350C2—41no—
351C2—11921no—
352C2#2375019011yescharacteristic
353C2#2375043811yescharacteristic
354C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#451×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558736C22
hypercenter#451D149
hypocenterC149#3223
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #23750235C2semidirect
3. #23750018C2semidirect
4. #23750003C2semidirect
5. #23749992C2semidirect
6. #23749981C2semidirect
7. #23749850C2semidirect
8. #23749849C2semidirect
9. #23749834C2semidirect
10. #23749833C2semidirect
13. #23749781C2semidirect
14. #23749683C2semidirect
15. #451×C149C2semidirect
177. C149#3223semidirect
192. #451D149semidirect

Maximal subgroups

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

subgroupindex
#237502352
#237501992
#237500182
#237500032
#237499922
#237499812
#237498502
#237498492
#237498342
#237498332
#237497892
#237497852
#237497812
#237496832
#451×C1492
#3223149