Finite Group Databasebeta

← #34057763

Subgroups — #34057763

Order 19072.

368 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#23750357C211yesmaximal, characteristic, complemented
2#23750344C211yesmaximal, characteristic, complemented
3#23750018C211yesmaximal, characteristic, complemented
4#23750013C211yesmaximal, characteristic
5#23749845C211yesmaximal, characteristic, complemented
6#23749844C211yesmaximal, characteristic, complemented
7#23749842C211yesmaximal, characteristic, complemented
8#23749837C211yesmaximal, characteristic, complemented
9#23749828C211yesmaximal, characteristic, complemented
10#23749823C211yesmaximal, characteristic, complemented
11#23749755C211yesmaximal, characteristic, complemented
12#23749737C211yesmaximal, characteristic, complemented
13#23749732C211yesmaximal, characteristic, complemented
14C4×#14558725C211yesmaximal, characteristic, complemented
15#495×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21#18011909C2211yescharacteristic
22#18011907C2211yescharacteristic
23#18011904—21no—
24#18011904—21no—
25#18011900C2211yescharacteristic
26#18011898C2211yescharacteristic
27#18011897—21no—
28#18011895—21no—
29#18011893—21no—
30#18011888—21no—
31Q8×Dic149C2211yescharacteristic
32Q8×Dic149C2211yescharacteristic
33C4×Dic298C2211yescharacteristic
34C4×Dic298C2211yescharacteristic
35C4×D596C2211yescharacteristic
36D4×Dic149C2211yescharacteristic
37D4×Dic149C2211yescharacteristic
38#18011871—21no—
39#18011867—21no—
40#18011843C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011821C2211yescharacteristic
51#18011821C2211yescharacteristic
52C2×Q16×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C2×D8×C149C2211yescharacteristic
56#124×C149C2211yescharacteristic
57#124×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59C2×Dic298D411yescharacteristic
60C2×Dic298C2311yescharacteristic
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C22×Dic149—21no—
65C22×Dic149—21no—
66C2×C4×D149—21no—
67#14558726—41no—
68#14558725—22no—
69#14558724—41no—
70#14558723—41no—
71#14558721—41no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149D411yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715D411yescharacteristic
83#14558715D411yescharacteristic
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91C4×Dic149—21no—
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149C2311yescharacteristic
95C4×Dic149C2311yescharacteristic
96C2×Q8×C149C2311yescharacteristic
97C2×Q8×C149C2311yescharacteristic
98C2×D4×C149C2311yescharacteristic
99C2×D4×C149C2311yescharacteristic
100Q16×C149—22no—
101SD16×C149—41no—
102SD16×C149—41no—
103D8×C149—22no—
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C22⋊C4×C149—21no—
108C22⋊C4×C149—21no—
109C22⋊C4×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112Dic298—21no—
113Dic298—21no—
114Dic298—41no—
115D596—21no—
116D596—21no—
117C22⋊D149—42no—
118C22⋊D149—81no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—42no—
123C2×Dic149—81no—
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C4×D149—81no—
129#11924746—21no—
130#11924746—21no—
131C23×C149—21no—
132C23×C149—21no—
133Q8×C149—21no—
134Q8×C149—21no—
135Q8×C149—21no—
136Q8×C149—21no—
137D4×C149—21no—
138D4×C149—21no—
139D4×C149—21no—
140D4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—21no—
147C8×C149#4112yes—
148C22×C149—41no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149C22×D411yescharacteristic
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C4×C149—21no—
159C4×C149—21no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149C2×#4111yescharacteristic
163C4×C149H(5,𝔽2)11yescharacteristic
164Dic149—21no—
165Dic149—21no—
166Dic149—21no—
167Dic149—21no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171C2×C149—81no—
172C2×C149—81no—
173C2×C149#55011yescharacteristic
174C2×C149#57511yescharacteristic
175C2×C149#57711yescharacteristic
176D149—81no—
177C149#340111yescharacteristic, complemented, Sylow
178#3401—1491nomaximal, Sylow
179#559—1491no—
180#556—1491no—
181#497—1491no—
182#496—1491no—
183#495D14911yescharacteristic, complemented
184#464—1491no—
185#464—1491no—
186#463—1491no—
187#463—1491no—
188#461—1491no—
189#460—1491no—
190#446—1491no—
191#442—1491no—
192#441—1491no—
193C4×SD16—1491no—
194C2×Q16—1491no—
195C2×Q16C2×D14911yescharacteristic
196C2×SD16—1491no—
197C2×SD16—1491no—
198C2×SD16—1491no—
199C2×SD16C2×D14911yescharacteristic
200C2×SD16C2×D14911yescharacteristic
201C2×D8—1491no—
202C2×D8C2×D14911yescharacteristic
203C4⋊Q8—1491no—
204#127—1491no—
205#126—2981no—
206#126—2981no—
207#124—2981no—
208#124—1491no—
209#124—1491no—
210#124C2×D14911yescharacteristic
211#124C2×D14911yescharacteristic
212#123—2981no—
213#123—2981no—
214C22⋊Q8—2981no—
215C4×Q8—1491no—
216C4×Q8—1491no—
217C4×Q8—1491no—
218C4×Q8—1491no—
219C4×D4—2981no—
220C4×D4—1491no—
221C4×D4—1491no—
222C4×D4—1491no—
223#117—2981no—
224#106—1491no—
225C4⋊C8—1491no—
226C4⋊C8—1491no—
227C4⋊C8—1491no—
228#103—1491no—
229#103—1491no—
230#103—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#97—1491no—
235#97—1491no—
236C4×C8C2×D14911yescharacteristic
237C2×Q8—1491no—
238C2×Q8—1491no—
239C2×Q8C22×D14911yescharacteristic
240C2×Q8C22×D14911yescharacteristic
241C2×D4—2981no—
242C2×D4—2981no—
243C2×D4—1491no—
244C2×D4C22×D14911yescharacteristic
245C2×D4C22×D14911yescharacteristic
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4—2981no—
249Q16—22no—
250Q16—5961no—
251SD16—41no—
252SD16—41no—
253SD16—2982no—
254SD16—5961no—
255SD16—5961no—
256D8—22no—
257D8—5961no—
258C2×C8—1491no—
259C2×C8—1491no—
260C2×C8C22×D14911yescharacteristic
261C2×C8C22×D14911yescharacteristic
262C4⋊C4—2981no—
263C4⋊C4—2981no—
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—1491no—
268C4⋊C4—1491no—
269C4⋊C4—1491no—
270C4⋊C4—1491no—
271C4⋊C4—1491no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C42—2981no—
284C42—2981no—
285C42—2981no—
286C42—1491no—
287C42—1491no—
288C42C22×D14911yescharacteristic
289C23—21no—
290C23—21no—
291C23—2981no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—2981no—
297Q8—2981no—
298Q8—5961no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—2981no—
304D4—2981no—
305D4—5962no—
306D4—11921no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—5962no—
313C2×C4—1491no—
314C2×C4—1491no—
315C2×C4—1491no—
316C2×C4—1491no—
317C2×C4—11921no—
318C2×C4—11921no—
319C2×C4D4×D14911yescharacteristic
320C2×C4D4×D14911yescharacteristic
321C2×C4C23×D14911yescharacteristic
322C8—21no—
323C8—2981no—
324C8—2981no—
325C8#1455873512yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—5961no—
333C22—5961no—
334C22—5961no—
335C22C2×D4×D14911yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—2981no—
341C4—2981no—
342C4—2981no—
343C4—2981no—
344C4—5961no—
345C4—5961no—
346C4—5961no—
347C4C2×#1455873511yescharacteristic
348C4#1801195611yescharacteristic
349C2—81no—
350C2—81no—
351C2—11921no—
352C2#2375029511yescharacteristic
353C2#2375042211yescharacteristic
354C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#495×C149C2
socleC22×C149C22×D4
prime radical#23750013C2
hypercenter#495D149
hypocenterC149#3401
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #23750357C2semidirect
2. #23750344C2semidirect
3. #23750018C2semidirect
5. #23749845C2semidirect
6. #23749844C2semidirect
7. #23749842C2semidirect
8. #23749837C2semidirect
9. #23749828C2semidirect
10. #23749823C2semidirect
11. #23749755C2semidirect
12. #23749737C2semidirect
13. #23749732C2semidirect
14. C4×#14558725C2semidirect
15. #495×C149C2semidirect
177. C149#3401semidirect
183. #495D149semidirect

Maximal subgroups

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

subgroupindex
#237503572
#237503442
#237500182
#237500132
#237498452
#237498442
#237498422
#237498372
#237498282
#237498232
#237497552
#237497372
#237497322
C4×#145587252
#495×C1492
#3401149