Finite Group Databasebeta

← #34054961

Subgroups — #34054961

Order 19072.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750248C211yesmaximal, characteristic, complemented
2#23750108C211yesmaximal, characteristic, complemented
3#23749953C211yesmaximal, characteristic, complemented
4#23749944C211yesmaximal, characteristic, complemented
5#23749913C211yesmaximal, characteristic, complemented
6#23749908C211yesmaximal, characteristic, complemented
7#23749849C211yesmaximal, characteristic, complemented
8#23749842C211yesmaximal, characteristic, complemented
9#23749770C211yesmaximal, characteristic
10#23749734C211yesmaximal, characteristic, complemented
11#23749732C211yesmaximal, characteristic, complemented
12SD16×Dic149C211yesmaximal, characteristic, complemented
13#23749710C211yesmaximal, characteristic, complemented
14#23749683C211yesmaximal, characteristic, complemented
15#452×C149C211yesmaximal, characteristic, complemented
16C2×#14558723C2211yescharacteristic
17C2×#14558721C2211yescharacteristic
18#18011910C2211yescharacteristic
19#18011906—21no—
20#18011900C2211yescharacteristic
21#18011897—21no—
22#18011893—21no—
23#18011891—21no—
24#18011885C2211yescharacteristic
25Q8×Dic149C2211yescharacteristic
26Q8×Dic149C2211yescharacteristic
27Q8×Dic149C2211yescharacteristic
28D4×Dic149—21no—
29D4×Dic149—21no—
30D4×Dic149C2211yescharacteristic
31D4×Dic149C2211yescharacteristic
32#18011873C2211yescharacteristic
33#18011870—21no—
34#18011870C2211yescharacteristic
35C2×C4⋊Dic149—21no—
36C2×C4⋊Dic149C2211yescharacteristic
37#18011843C2211yescharacteristic
38#18011843C2211yescharacteristic
39#18011842C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×Q16×C149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C22⋊Q8×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×D596C2311yescharacteristic
61C2×C22⋊D149—21no—
62C22×Dic149—21no—
63C22×Dic149—21no—
64C22×Dic149—21no—
65C2×C4×D149—21no—
66#14558723—22no—
67#14558721—22no—
68C2×#11924746C2311yescharacteristic
69C2×#11924746C2311yescharacteristic
70C4⋊Dic149—21no—
71C4⋊Dic149—21no—
72C4⋊Dic149—21no—
73C4⋊Dic149—21no—
74C4⋊Dic149D411yescharacteristic
75C4⋊Dic149D411yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80C22⋊Dic149—21no—
81C22⋊Dic149—21no—
82C22⋊Dic149D411yescharacteristic
83C22⋊Dic149D411yescharacteristic
84#14558713—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88C4×Dic149—21no—
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149C2311yescharacteristic
92C4×Dic149C2311yescharacteristic
93#41×C149—22no—
94#41×C149—22no—
95C2×Q8×C149C2311yescharacteristic
96C2×Q8×C149C2311yescharacteristic
97C2×D4×C149—21no—
98C2×D4×C149C2311yescharacteristic
99C22×C4×C149—21no—
100C22×C4×C149C2311yescharacteristic
101Q16×C149—22no—
102SD16×C149—22no—
103C2×C8×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C4⋊C4×C149—21no—
106C4⋊C4×C149C2311yescharacteristic
107C22⋊C4×C149—21no—
108C22×D149—21no—
109Dic298—81no—
110D596—21no—
111D596—21no—
112C22⋊D149—81no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—81no—
117C2×Dic149—81no—
118C2×Dic149—81no—
119C2×Dic149C2×D411yescharacteristic
120C2×Dic149C2×D411yescharacteristic
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C4×D149—81no—
124#11924746—21no—
125#11924746—21no—
126C23×C149—21no—
127C23×C149C2×D411yescharacteristic
128Q8×C149—21no—
129Q8×C149—21no—
130Q8×C149—21no—
131Q8×C149#4112yes—
132D4×C149—24no—
133D4×C149—21no—
134D4×C149#4112yes—
135C2×C4×C149—24no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2411yescharacteristic
143C8×C149—21no—
144C8×C149—21no—
145C22×C149—21no—
146C22×C149—22no—
147C22×C149—21no—
148C22×C149—21no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149C22×D411yescharacteristic
152C2×D149—41no—
153C2×D149—41no—
154C2×D149—41no—
155C4×C149—21no—
156C4×C149—22no—
157C4×C149—41no—
158C4×C149—41no—
159C4×C149C2×#4111yescharacteristic
160C4×C149C2×#4111yescharacteristic
161Dic149—21no—
162Dic149—21no—
163Dic149—21no—
164Dic149—21no—
165Dic149—41no—
166Dic149—41no—
167Dic149—41no—
168C2×C149—41no—
169C2×C149—42no—
170C2×C149#52511yescharacteristic
171C2×C149#57711yescharacteristic
172C2×C149#57711yescharacteristic
173D149—81no—
174C149#312511yescharacteristic, complemented, Sylow
175#3125—1491nomaximal, Sylow
176#542—1491no—
177#520—1491no—
178#483—1491no—
179#481—1491no—
180#476—1491no—
181#475—1491no—
182#464—1491no—
183#463—1491no—
184#452D14911yescharacteristic, complemented
185#449—1491no—
186#442—1491no—
187#441—1491no—
188C4×SD16—1491no—
189C4×SD16—1491no—
190#433—1491no—
191C2×#41C2×D14911yescharacteristic
192C2×Q16C2×D14911yescharacteristic
193C2×SD16—1491no—
194C2×SD16C2×D14911yescharacteristic
195C2×D8—1491no—
196C4⋊Q8—1491no—
197#126—2981no—
198#124—2981no—
199#124—1491no—
200#123—2981no—
201C22⋊Q8—2981no—
202C22⋊Q8C2×D14911yescharacteristic
203#121—1491no—
204C4×Q8—1491no—
205C4×Q8—1491no—
206C4×Q8—1491no—
207C4×D4—2981no—
208C4×D4—2981no—
209C4×D4—1491no—
210C4×D4—1491no—
211C4×D4—1491no—
212#117—2981no—
213#117—1491no—
214C2×C4⋊C4—2981no—
215C2×C4⋊C4—1491no—
216#106—1491no—
217#106—1491no—
218#106—1491no—
219#106—1491no—
220C4⋊C8—1491no—
221C4⋊C8—1491no—
222#103—1491no—
223#103—1491no—
224#103—1491no—
225#103C2×D14911yescharacteristic
226#102—1491no—
227#102—1491no—
228#102—1491no—
229#102C2×D14911yescharacteristic
230C22⋊C8—1491no—
231C22⋊C8C2×D14911yescharacteristic
232#97—1491no—
233C4×C8—1491no—
234#41—22no—
235#41—22no—
236C2×Q8—2981no—
237C2×Q8C22×D14911yescharacteristic
238C2×Q8C22×D14911yescharacteristic
239C2×D4—21no—
240C2×D4—2981no—
241C2×D4—1491no—
242C2×D4C22×D14911yescharacteristic
243C22×C4—21no—
244C22×C4—2981no—
245C22×C4—2981no—
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4C22×D14911yescharacteristic
249Q16—22no—
250SD16—22no—
251SD16—2982no—
252D8—2982no—
253C2×C8—1491no—
254C2×C8—1491no—
255C2×C8C22×D14911yescharacteristic
256C2×C8C22×D14911yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—2981no—
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—1491no—
264C4⋊C4—1491no—
265C4⋊C4—1491no—
266C4⋊C4—1491no—
267C4⋊C4—1491no—
268C4⋊C4C22×D14911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—1491no—
277C22⋊C4—1491no—
278C42—2981no—
279C42—2981no—
280C42—2981no—
281C42—1491no—
282C42—1491no—
283C23—21no—
284C23—2981no—
285C23D4×D14911yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—11921no—
290Q8#1455873512yes—
291D4—24no—
292D4—21no—
293D4—2981no—
294D4—2981no—
295D4—11921no—
296D4#1455873512yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—1491no—
307C2×C4—1491no—
308C2×C4—1491no—
309C2×C4—1491no—
310C2×C4—11921no—
311C2×C4—11921no—
312C2×C4—11921no—
313C2×C4—11921no—
314C2×C4D4×D14911yescharacteristic
315C2×C4C23×D14911yescharacteristic
316C8—21no—
317C8—21no—
318C8—2981no—
319C8—2981no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—5961no—
327C22—5961no—
328C22—5961no—
329C22C2×D4×D14911yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—2981no—
335C4—2981no—
336C4—2981no—
337C4—2981no—
338C4—5961no—
339C4—5961no—
340C4—5961no—
341C4C2×#1455873511yescharacteristic
342C4C2×#1455873511yescharacteristic
343C2—41no—
344C2—42no—
345C2—11921no—
346C2#2375013111yescharacteristic
347C2#2375043211yescharacteristic
348C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#452×C149C2
socleC22×C149C22×D4
prime radical#23749770C2
hypercenter#452D149
hypocenterC149#3125
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #23750248C2semidirect
2. #23750108C2semidirect
3. #23749953C2semidirect
4. #23749944C2semidirect
5. #23749913C2semidirect
6. #23749908C2semidirect
7. #23749849C2semidirect
8. #23749842C2semidirect
10. #23749734C2semidirect
11. #23749732C2semidirect
12. SD16×Dic149C2semidirect
13. #23749710C2semidirect
14. #23749683C2semidirect
15. #452×C149C2semidirect
174. C149#3125semidirect
184. #452D149semidirect

Maximal subgroups

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

subgroupindex
#237502482
#237501082
#237499532
#237499442
#237499132
#237499082
#237498492
#237498422
#237497702
#237497342
#237497322
SD16×Dic1492
#237497102
#237496832
#452×C1492
#3125149