Finite Group Databasebeta

← #34052910

Subgroups — #34052910

Order 19072.

400 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23749563C211yesmaximal, characteristic, complemented
2#23749560C211yesmaximal, characteristic, complemented
3#23749560C211yesmaximal, characteristic, complemented
4#23749558C211yesmaximal, characteristic, complemented
5#23749555C211yesmaximal, characteristic, complemented
6#23749553C211yesmaximal, characteristic, complemented
7#23749552C211yesmaximal, characteristic, complemented
8#23749548C211yesmaximal, characteristic, complemented
9#23749541C211yesmaximal, characteristic
10#23749540C211yesmaximal, characteristic
11#23749540C211yesmaximal, characteristic
12#23749522C211yesmaximal, characteristic, complemented
13#23749515C211yesmaximal, characteristic, complemented
14#23749513C211yesmaximal, characteristic, complemented
15#396×C149C211yesmaximal, characteristic, complemented
16C22×C22⋊D149C2211yescharacteristic
17C2×C4⋊Dic149C2211yescharacteristic
18C2×C4⋊Dic149C2211yescharacteristic
19C2×#14558715C2211yescharacteristic
20C2×#14558715C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×C22⋊Dic149C2211yescharacteristic
26C2×C22⋊Dic149C2211yescharacteristic
27C2×C22⋊Dic149C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×C4×Dic149C2211yescharacteristic
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
46C2×C4⋊C4×C149C2211yescharacteristic
47C2×C22⋊C4×C149C2211yescharacteristic
48C2×C22⋊C4×C149C2211yescharacteristic
49C2×C22⋊C4×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51C23×D149C2311yescharacteristic
52C2×C22⋊D149—41no—
53C2×C22⋊D149—41no—
54C2×C22⋊D149—41no—
55C22×Dic149C2311yescharacteristic
56C22×Dic149C2311yescharacteristic
57C22×Dic149C2311yescharacteristic
58C22×Dic149C2311yescharacteristic
59C22×Dic149C2311yescharacteristic
60C22×Dic149C2311yescharacteristic
61C22×Dic149C2311yescharacteristic
62C4⋊Dic149—41no—
63C4⋊Dic149—41no—
64#14558715—22no—
65#14558715—41no—
66#14558715—41no—
67#14558715—41no—
68#14558715—41no—
69#14558715—41no—
70C22⋊Dic149—22no—
71C22⋊Dic149—41no—
72C22⋊Dic149—41no—
73#14558713—22no—
74#14558713—41no—
75#14558713—41no—
76#14558713—41no—
77#14558713—41no—
78#14558713—41no—
79C4×Dic149—41no—
80C24×C149C2311yescharacteristic
81C22×C4×C149C2311yescharacteristic
82C22×C4×C149C2311yescharacteristic
83C22×C4×C149C2311yescharacteristic
84C22×C4×C149C2311yescharacteristic
85C22×C4×C149C2311yescharacteristic
86C22×C4×C149C2311yescharacteristic
87C4⋊C4×C149—41no—
88C4⋊C4×C149—41no—
89C4⋊C4×C149—41no—
90C22⋊C4×C149—41no—
91C22⋊C4×C149—41no—
92C22⋊C4×C149—41no—
93C22×D149—21no—
94C22×D149—21no—
95C22×D149—21no—
96C22×D149—21no—
97C22×D149—21no—
98C22×D149—21no—
99C22×D149—21no—
100C22⋊D149—44no—
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×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149#4112yes—
122C23×C149—21no—
123C23×C149—21no—
124C23×C149—21no—
125C23×C149—21no—
126C23×C149—21no—
127C23×C149—21no—
128C23×C149—21no—
129C23×C149C2411yescharacteristic
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×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C22×C149—41no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149C2×#4111yescharacteristic
156C22×C149H(5,𝔽2)11yescharacteristic
157C22×C149H(5,𝔽2)11yescharacteristic
158C22×C149H(5,𝔽2)11yescharacteristic
159C22×C149H(5,𝔽2)11yescharacteristic
160C22×C1492−1+411yescharacteristic
161C22×C1492−1+411yescharacteristic
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149—41no—
172C4×C149—41no—
173C4×C149—41no—
174C4×C149—41no—
175Dic149—22no—
176Dic149—41no—
177Dic149—41no—
178Dic149—41no—
179Dic149—41no—
180Dic149—41no—
181Dic149—41no—
182C2×C149—81no—
183C2×C149#53911yescharacteristic
184C2×C149#54011yescharacteristic
185C2×C149#54211yescharacteristic
186C2×C149#56011yescharacteristic
187C2×C149#56211yescharacteristic
188C2×C149#56211yescharacteristic
189C2×C149#56311yescharacteristic
190D149—81no—
191C149#283711yescharacteristic, complemented, Sylow
192#2837—1491nomaximal, Sylow
193#400—1491no—
194#399—1491no—
195#399—1491no—
196#398—1491no—
197#398—1491no—
198#397—1491no—
199#397—1491no—
200#396—1491no—
201#396D14911yescharacteristic, complemented
202#394—1491no—
203#394—1491no—
204#394—1491no—
205#389—1491no—
206#388—1491no—
207#388—1491no—
208C22×D4—1491no—
209C2×C4⋊C4—1491no—
210C2×C4⋊C4—1491no—
211C2×C4⋊C4—1491no—
212C2×C4⋊C4—1491no—
213C2×C4⋊C4—1491no—
214C2×C4⋊C4—1491no—
215C2×C4⋊C4—1491no—
216C2×C4⋊C4—1491no—
217C2×C4⋊C4C2×D14911yescharacteristic
218C2×C4⋊C4C2×D14911yescharacteristic
219C2×C4⋊C4C2×D14911yescharacteristic
220C2×C22⋊C4—1491no—
221C2×C22⋊C4—1491no—
222C2×C22⋊C4—1491no—
223C2×C22⋊C4—1491no—
224C2×C22⋊C4—1491no—
225C2×C22⋊C4—1491no—
226C2×C22⋊C4—1491no—
227C2×C22⋊C4—1491no—
228C2×C22⋊C4—1491no—
229C2×C22⋊C4C2×D14911yescharacteristic
230C2×C22⋊C4C2×D14911yescharacteristic
231C2×C22⋊C4C2×D14911yescharacteristic
232C2×C42—1491no—
233#95—1491no—
234#95—1491no—
235#95—1491no—
236#95—1491no—
237#95—1491no—
238#95—1491no—
239#95—1491no—
240#95—1491no—
241#95—1491no—
242#95C2×D14911yescharacteristic
243C24—1491no—
244C24C22×D14911yescharacteristic
245C2×D4—5961no—
246C2×D4—5961no—
247C2×D4—5961no—
248C22×C4—1491no—
249C22×C4—1491no—
250C22×C4—1491no—
251C22×C4—1491no—
252C22×C4—1491no—
253C22×C4—1491no—
254C22×C4—1491no—
255C22×C4C22×D14911yescharacteristic
256C22×C4C22×D14911yescharacteristic
257C22×C4C22×D14911yescharacteristic
258C22×C4C22×D14911yescharacteristic
259C22×C4C22×D14911yescharacteristic
260C22×C4C22×D14911yescharacteristic
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—2982no—
265C4⋊C4—5961no—
266C4⋊C4—5961no—
267C4⋊C4—5961no—
268C4⋊C4—5961no—
269C4⋊C4—5961no—
270C4⋊C4—5961no—
271C4⋊C4—5961no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—2982no—
276C22⋊C4—2982no—
277C22⋊C4—5961no—
278C22⋊C4—5961no—
279C22⋊C4—5961no—
280C22⋊C4—5961no—
281C22⋊C4—5961no—
282C22⋊C4—5961no—
283C22⋊C4—5961no—
284C42—5961no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—2981no—
293C23—2981no—
294C23—2981no—
295C23—2981no—
296C23—2981no—
297C23—2981no—
298C23—2981no—
299C23C23×D14911yescharacteristic
300D4—5964no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—2981no—
320C2×C4—2981no—
321C2×C4—2981no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—2981no—
326C2×C4—2981no—
327C2×C4—2981no—
328C2×C4—2981no—
329C2×C4—2981no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—2981no—
339C2×C4—1492no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—5961no—
348C22—5961no—
349C22—5961no—
350C22—5961no—
351C22—5961no—
352C22—5961no—
353C22—5961no—
354C22#41×D14911yescharacteristic
355C22#1801195611yescharacteristic
356C22#1801195611yescharacteristic
357C22#1801195611yescharacteristic
358C22#1801195711yescharacteristic
359C22#1801195811yescharacteristic
360C22#1801195911yescharacteristic
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—2982no—
368C4—5961no—
369C4—5961no—
370C4—5961no—
371C4—5961no—
372C4—5961no—
373C4—5961no—
374C2—81no—
375C2—11921no—
376C2#2375022111yescharacteristic
377C2#2375022511yescharacteristic
378C2#2375024111yescharacteristic
379C2#2375036311yescharacteristic
380C2#2375037011yescharacteristic
381C2#2375037111yescharacteristic
382C2#2375037611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#396×C149C2
prime radicalC22×C22⋊D149C22
hypercenter#396D149
hypocenterC149#2837
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #23749563C2semidirect
2. #23749560C2semidirect
3. #23749560C2semidirect
4. #23749558C2semidirect
5. #23749555C2semidirect
6. #23749553C2semidirect
7. #23749552C2semidirect
8. #23749548C2semidirect
12. #23749522C2semidirect
13. #23749515C2semidirect
14. #23749513C2semidirect
15. #396×C149C2semidirect
191. C149#2837semidirect
201. #396D149semidirect

Maximal subgroups

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

subgroupindex
#237495632
#237495602
#237495582
#237495552
#237495532
#237495522
#237495482
#237495412
#237495402
#237495222
#237495152
#237495132
#396×C1492
#2837149