Finite Group Databasebeta

← #34052950

Subgroups — #34052950

Order 19072.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23749566C211yesmaximal, characteristic, complemented
2#23749562C211yesmaximal, characteristic
3#23749559C211yesmaximal, characteristic, complemented
4#23749558C211yesmaximal, characteristic, complemented
5#23749558C211yesmaximal, characteristic, complemented
6#23749557C211yesmaximal, characteristic, complemented
7#23749549C211yesmaximal, characteristic
8#23749547C211yesmaximal, characteristic
9#23749546C211yesmaximal, characteristic, complemented
10#23749546C211yesmaximal, characteristic, complemented
11#23749538C211yesmaximal, characteristic
12#23749487C211yesmaximal, characteristic
13#23749484C211yesmaximal, characteristic
14#23749482C211yesmaximal, characteristic
15#400×C149C211yesmaximal, characteristic, complemented
16C22×Dic298C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18C2×C4⋊Dic149C2211yescharacteristic
19C2×C4⋊Dic149C2211yescharacteristic
20C2×C4⋊Dic149C2211yescharacteristic
21C2×C4⋊Dic149C2211yescharacteristic
22C2×C4⋊Dic149C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×#14558715C2211yescharacteristic
27C2×#14558715C2211yescharacteristic
28C2×#14558715C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35#18011818C2211yescharacteristic
36#18011818C2211yescharacteristic
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
52C2×Dic298—41no—
53C2×Dic298—41no—
54C2×Dic298—41no—
55C22×Dic149C2311yescharacteristic
56C22×Dic149C2311yescharacteristic
57C22×Dic149C2311yescharacteristic
58C22×Dic149C2311yescharacteristic
59C22×Dic149C2311yescharacteristic
60C22×Dic149C2311yescharacteristic
61C22×Dic149C2311yescharacteristic
62C2×C4×D149—41no—
63C2×C4×D149—41no—
64C2×C4×D149Q814yescomplemented
65C4⋊Dic149—41no—
66C4⋊Dic149—41no—
67C4⋊Dic149—41no—
68C4⋊Dic149—41no—
69C4⋊Dic149—41no—
70#14558715—41no—
71#14558715—41no—
72#14558715—41no—
73#14558715—41no—
74#14558715—41no—
75#14558715—41no—
76#14558713—41no—
77#14558713—41no—
78#14558713—41no—
79#14558713—41no—
80#14558713—41no—
81#14558713—41no—
82C22×C4×C149C2311yescharacteristic
83C22×C4×C149C2311yescharacteristic
84C22×C4×C149C2311yescharacteristic
85C22×C4×C149C2311yescharacteristic
86C22×C4×C149C2311yescharacteristic
87C22×C4×C149C2311yescharacteristic
88C22×C4×C149C2311yescharacteristic
89C4⋊C4×C149—41no—
90C4⋊C4×C149—41no—
91C22×D149—21no—
92C22×D149—21no—
93C22×D149—21no—
94C22×D149—21no—
95C22×D149—21no—
96C22×D149—21no—
97C22×D149C2×Q812yes—
98Dic298—44no—
99C2×Dic149—21no—
100C2×Dic149—21no—
101C2×Dic149—21no—
102C2×Dic149—21no—
103C2×Dic149—21no—
104C2×Dic149—21no—
105C2×Dic149—21no—
106C2×Dic149—21no—
107C2×Dic149—21no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149C2×Q812yes—
120C4×D149—44no—
121C23×C149C2411yescharacteristic
122C2×C4×C149—21no—
123C2×C4×C149—21no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149C2×Q812yes—
143C22×C149C22×Q811yescharacteristic
144C22×C149H(5,𝔽2)11yescharacteristic
145C22×C149H(5,𝔽2)11yescharacteristic
146C22×C149H(5,𝔽2)11yescharacteristic
147C22×C149H(5,𝔽2)11yescharacteristic
148C22×C1492−1+411yescharacteristic
149C22×C1492−1+411yescharacteristic
150C2×D149—22no—
151C2×D149—22no—
152C2×D149—22no—
153C2×D149—41no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C4×C149—22no—
158C4×C149—41no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149—41no—
164Dic149—22no—
165Dic149—41no—
166Dic149—41no—
167Dic149—41no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171C2×C149#54311yescharacteristic
172C2×C149#54411yescharacteristic
173C2×C149#54411yescharacteristic
174C2×C149#56011yescharacteristic
175C2×C149#56211yescharacteristic
176C2×C149#56211yescharacteristic
177C2×C149#56311yescharacteristic
178D149—42no—
179C149#284111yescharacteristic, complemented, Sylow
180#2841—1491nomaximal, Sylow
181#400—1491no—
182#400D14911yescharacteristic, complemented
183#399—1491no—
184#398—1491no—
185#398—1491no—
186#398—1491no—
187#398—1491no—
188#396—1491no—
189#396—1491no—
190#395—1491no—
191#395—1491no—
192#393—1491no—
193#381—1491no—
194#380—1491no—
195#380—1491no—
196C22×Q8—1491no—
197C23×C4—1491no—
198C2×C4⋊C4—1491no—
199C2×C4⋊C4—1491no—
200C2×C4⋊C4—1491no—
201C2×C4⋊C4—1491no—
202C2×C4⋊C4—1491no—
203C2×C4⋊C4—1491no—
204C2×C4⋊C4—1491no—
205C2×C4⋊C4—1491no—
206C2×C4⋊C4—1491no—
207C2×C4⋊C4—1491no—
208C2×C4⋊C4—1491no—
209C2×C4⋊C4C2×D14911yescharacteristic
210C2×C4⋊C4C2×D14911yescharacteristic
211C2×C22⋊C4—1491no—
212C2×C22⋊C4—1491no—
213C2×C22⋊C4—1491no—
214C2×C22⋊C4—1491no—
215C2×C22⋊C4—1491no—
216C2×C22⋊C4—1491no—
217#95—1491no—
218#95—1491no—
219#95—1491no—
220#95—1491no—
221#95—1491no—
222#95—1491no—
223#95—1491no—
224#95—1491no—
225#95—1491no—
226#95C2×D14911yescharacteristic
227#95C2×D14911yescharacteristic
228#95C2×D14911yescharacteristic
229#95C2×D14911yescharacteristic
230#95C2×D14911yescharacteristic
231C24—1491no—
232C2×Q8—5961no—
233C2×Q8—5961no—
234C2×Q8—5961no—
235C22×C4—5961no—
236C22×C4—5961no—
237C22×C4—1491no—
238C22×C4—1491no—
239C22×C4—1491no—
240C22×C4—1491no—
241C22×C4—1491no—
242C22×C4—1491no—
243C22×C4—1491no—
244C22×C4—1494no—
245C22×C4C22×D14911yescharacteristic
246C22×C4C22×D14911yescharacteristic
247C22×C4C22×D14911yescharacteristic
248C22×C4C22×D14911yescharacteristic
249C22×C4C22×D14911yescharacteristic
250C22×C4C22×D14911yescharacteristic
251C22×C4C22×D14911yescharacteristic
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—5961no—
255C4⋊C4—5961no—
256C4⋊C4—5961no—
257C4⋊C4—5961no—
258C4⋊C4—5961no—
259C4⋊C4—5961no—
260C4⋊C4—5961no—
261C4⋊C4—5961no—
262C4⋊C4—5961no—
263C4⋊C4—5961no—
264C4⋊C4—5961no—
265C22⋊C4—5961no—
266C22⋊C4—5961no—
267C22⋊C4—5961no—
268C22⋊C4—5961no—
269C22⋊C4—5961no—
270C22⋊C4—5961no—
271C23—2981no—
272C23—2981no—
273C23—2981no—
274C23—2981no—
275C23—2981no—
276C23—2981no—
277C23—1492no—
278C23C23×D14911yescharacteristic
279Q8—5964no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—2981no—
307C2×C4—2981no—
308C2×C4—2981no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—5964no—
321C2×C4—1492no—
322C2×C4Q8×D14912yes—
323C22—2982no—
324C22—2982no—
325C22—2982no—
326C22—5961no—
327C22—5961no—
328C22—5961no—
329C22—5961no—
330C22C2×Q8×D14911yescharacteristic
331C22#1801195611yescharacteristic
332C22#1801195711yescharacteristic
333C22#1801195711yescharacteristic
334C22#1801195711yescharacteristic
335C22#1801195811yescharacteristic
336C22#1801195811yescharacteristic
337C4—22no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—2982no—
345C4—5961no—
346C4—5961no—
347C4—5961no—
348C4—5961no—
349C4—5961no—
350C4—5961no—
351C2—5962no—
352C2#2375025011yescharacteristic
353C2#2375025511yescharacteristic
354C2#2375025511yescharacteristic
355C2#2375036611yescharacteristic
356C2#2375036911yescharacteristic
357C2#2375037211yescharacteristic
358C2#2375037711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#400×C149C2
prime radicalC23×D149C23
hypercenter#400D149
hypocenterC149#2841
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #23749566C2semidirect
3. #23749559C2semidirect
4. #23749558C2semidirect
5. #23749558C2semidirect
6. #23749557C2semidirect
9. #23749546C2semidirect
10. #23749546C2semidirect
15. #400×C149C2semidirect
64. C2×C4×D149Q8semidirect
179. C149#2841semidirect
182. #400D149semidirect

Maximal subgroups

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

subgroupindex
#237495662
#237495622
#237495592
#237495582
#237495572
#237495492
#237495472
#237495462
#237495382
#237494872
#237494842
#237494822
#400×C1492
#2841149