Finite Group Databasebeta

← #34052855

Subgroups — #34052855

Order 19072.

416 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23749565C211yesmaximal, characteristic, complemented
2#23749564C211yesmaximal, characteristic, complemented
3#23749554C211yesmaximal, characteristic, complemented
4#23749546C211yesmaximal, characteristic, complemented
5#23749541C211yesmaximal, characteristic
6#23749541C211yesmaximal, characteristic
7#23749540C211yesmaximal, characteristic
8#23749538C211yesmaximal, characteristic, complemented
9#23749538C211yesmaximal, characteristic, complemented
10#23749537C211yesmaximal, characteristic, complemented
11#23749537C211yesmaximal, characteristic, complemented
12#23749529C211yesmaximal, characteristic, complemented
13#23749515C211yesmaximal, characteristic, complemented
14#23749513C211yesmaximal, characteristic, complemented
15#397×C149C211yesmaximal, characteristic, complemented
16C22×Dic298C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18C22×C22⋊D149C2211yescharacteristic
19C2×C4⋊Dic149C2211yescharacteristic
20C2×C4⋊Dic149C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×C22⋊Dic149C2211yescharacteristic
24C2×C22⋊Dic149C2211yescharacteristic
25C2×C22⋊Dic149C2211yescharacteristic
26C2×#14558713C2211yescharacteristic
27C2×#14558713C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×C4×Dic149C2211yescharacteristic
33#18011818C2211yescharacteristic
34#18011818C2211yescharacteristic
35#18011818C2211yescharacteristic
36#18011818C2211yescharacteristic
37#18011818C2211yescharacteristic
38#18011818C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44C2×C4⋊C4×C149C2211yescharacteristic
45C2×C22⋊C4×C149C2211yescharacteristic
46C2×C22⋊C4×C149C2211yescharacteristic
47C2×C22⋊C4×C149C2211yescharacteristic
48#95×C149C2211yescharacteristic
49#95×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51C23×D149C2311yescharacteristic
52C2×Dic298—22no—
53C2×Dic298—41no—
54C2×Dic298—41no—
55C2×Dic298—41no—
56C2×Dic298—41no—
57C2×Dic298—41no—
58C2×C22⋊D149—41no—
59C2×C22⋊D149—41no—
60C2×C22⋊D149—41no—
61C22×Dic149C2311yescharacteristic
62C22×Dic149C2311yescharacteristic
63C22×Dic149C2311yescharacteristic
64C22×Dic149C2311yescharacteristic
65C22×Dic149C2311yescharacteristic
66C22×Dic149C2311yescharacteristic
67C22×Dic149C2311yescharacteristic
68C4⋊Dic149—41no—
69C4⋊Dic149—41no—
70#14558715—41no—
71#14558715—41no—
72C22⋊Dic149—22no—
73C22⋊Dic149—41no—
74C22⋊Dic149—41no—
75#14558713—22no—
76#14558713—41no—
77#14558713—41no—
78#14558713—41no—
79#14558713—41no—
80#14558713—41no—
81C4×Dic149—41no—
82C24×C149C2311yescharacteristic
83C22×C4×C149C2311yescharacteristic
84C22×C4×C149C2311yescharacteristic
85C22×C4×C149C2311yescharacteristic
86C22×C4×C149C2311yescharacteristic
87C22×C4×C149C2311yescharacteristic
88C22×C4×C149C2311yescharacteristic
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—
100Dic298—44no—
101Dic298—44no—
102C22⋊D149—44no—
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—21no—
122C2×Dic149—21no—
123C2×Dic149#4112yes—
124C23×C149—21no—
125C23×C149—21no—
126C23×C149—21no—
127C23×C149—21no—
128C23×C149—21no—
129C23×C149—21no—
130C23×C149—21no—
131C23×C149C2411yescharacteristic
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—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149C2×#4111yescharacteristic
158C22×C149H(5,𝔽2)11yescharacteristic
159C22×C149H(5,𝔽2)11yescharacteristic
160C22×C149H(5,𝔽2)11yescharacteristic
161C22×C149H(5,𝔽2)11yescharacteristic
162C22×C1492−1+411yescharacteristic
163C22×C1492−1+411yescharacteristic
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—41no—
171C4×C149—41no—
172C4×C149—41no—
173C4×C149—41no—
174C4×C149—41no—
175C4×C149—41no—
176C4×C149—41no—
177Dic149—22no—
178Dic149—41no—
179Dic149—41no—
180Dic149—41no—
181Dic149—41no—
182Dic149—41no—
183Dic149—41no—
184C2×C149—81no—
185C2×C149#53811yescharacteristic
186C2×C149#54211yescharacteristic
187C2×C149#54211yescharacteristic
188C2×C149H(3,𝔽4)11yescharacteristic
189C2×C149#56211yescharacteristic
190C2×C149#56211yescharacteristic
191C2×C149#56311yescharacteristic
192D149—81no—
193C149#283211yescharacteristic, complemented, Sylow
194#2832—1491nomaximal, Sylow
195#400—1491no—
196#400—1491no—
197#397—1491no—
198#397D14911yescharacteristic, complemented
199#395—1491no—
200#394—1491no—
201#394—1491no—
202#394—1491no—
203#393—1491no—
204#393—1491no—
205#393—1491no—
206#393—1491no—
207#391—1491no—
208#388—1491no—
209#388—1491no—
210C22×Q8—1491no—
211C22×Q8—1491no—
212C22×D4—1491no—
213C2×C4⋊C4—1491no—
214C2×C4⋊C4—1491no—
215C2×C4⋊C4—1491no—
216C2×C4⋊C4—1491no—
217C2×C4⋊C4C2×D14911yescharacteristic
218C2×C22⋊C4—1491no—
219C2×C22⋊C4—1491no—
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⋊C4C2×D14911yescharacteristic
228C2×C22⋊C4C2×D14911yescharacteristic
229C2×C22⋊C4C2×D14911yescharacteristic
230C2×C42—1491no—
231#95—1491no—
232#95—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
243#95C2×D14911yescharacteristic
244#95C2×D14911yescharacteristic
245C24—1491no—
246C24C22×D14911yescharacteristic
247C2×Q8—2982no—
248C2×Q8—5961no—
249C2×Q8—5961no—
250C2×Q8—5961no—
251C2×Q8—5961no—
252C2×Q8—5961no—
253C2×D4—5961no—
254C2×D4—5961no—
255C2×D4—5961no—
256C22×C4—1491no—
257C22×C4—1491no—
258C22×C4—1491no—
259C22×C4—1491no—
260C22×C4—1491no—
261C22×C4—1491no—
262C22×C4—1491no—
263C22×C4C22×D14911yescharacteristic
264C22×C4C22×D14911yescharacteristic
265C22×C4C22×D14911yescharacteristic
266C22×C4C22×D14911yescharacteristic
267C22×C4C22×D14911yescharacteristic
268C22×C4C22×D14911yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—5961no—
271C4⋊C4—5961no—
272C4⋊C4—5961no—
273C4⋊C4—5961no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—2982no—
278C22⋊C4—2982no—
279C22⋊C4—5961no—
280C22⋊C4—5961no—
281C22⋊C4—5961no—
282C22⋊C4—5961no—
283C22⋊C4—5961no—
284C22⋊C4—5961no—
285C22⋊C4—5961no—
286C42—5961no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—2981no—
295C23—2981no—
296C23—2981no—
297C23—2981no—
298C23—2981no—
299C23—2981no—
300C23—2981no—
301C23C23×D14911yescharacteristic
302Q8—5964no—
303Q8—5964no—
304D4—5964no—
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—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
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—2981no—
340C2×C4—2981no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—1492no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—5961no—
352C22—5961no—
353C22—5961no—
354C22—5961no—
355C22—5961no—
356C22—5961no—
357C22—5961no—
358C22#41×D14911yescharacteristic
359C22#1801195611yescharacteristic
360C22#1801195611yescharacteristic
361C22#1801195711yescharacteristic
362C22#1801195711yescharacteristic
363C22#1801195811yescharacteristic
364C22#1801195811yescharacteristic
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—2982no—
372C4—5961no—
373C4—5961no—
374C4—5961no—
375C4—5961no—
376C4—5961no—
377C4—5961no—
378C2—81no—
379C2—11921no—
380C2#2375021111yescharacteristic
381C2#2375024111yescharacteristic
382C2#2375024311yescharacteristic
383C2#2375036711yescharacteristic
384C2#2375037011yescharacteristic
385C2#2375037211yescharacteristic
386C2#2375037711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#397×C149C2
prime radicalC22×C22⋊D149C22
hypercenter#397D149
hypocenterC149#2832
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #23749565C2semidirect
2. #23749564C2semidirect
3. #23749554C2semidirect
4. #23749546C2semidirect
8. #23749538C2semidirect
9. #23749538C2semidirect
10. #23749537C2semidirect
11. #23749537C2semidirect
12. #23749529C2semidirect
13. #23749515C2semidirect
14. #23749513C2semidirect
15. #397×C149C2semidirect
193. C149#2832semidirect
198. #397D149semidirect

Maximal subgroups

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

subgroupindex
#237495652
#237495642
#237495542
#237495462
#237495412
#237495402
#237495382
#237495372
#237495292
#237495152
#237495132
#397×C1492
#2832149