Finite Group Databasebeta

← #34055802

Subgroups — #34055802

Order 19072.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750246C211yesmaximal, characteristic, complemented
2#23750201C211yesmaximal, characteristic, complemented
3#23750019C211yesmaximal, characteristic, complemented
4#23750009C211yesmaximal, characteristic, complemented
5#23749985C211yesmaximal, characteristic, complemented
6#23749976C211yesmaximal, characteristic, complemented
7#23749848C211yesmaximal, characteristic, complemented
8#23749841C211yesmaximal, characteristic, complemented
9#23749836C211yesmaximal, characteristic, complemented
10#23749831C211yesmaximal, characteristic, complemented
11#23749789C211yesmaximal, characteristic, complemented
12#23749783C211yesmaximal, characteristic, complemented
13#23749772C211yesmaximal, characteristic
14#23749766C211yesmaximal, characteristic, complemented
15#433×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18C2×Dic596C2211yescharacteristic
19C2×Dic596C2211yescharacteristic
20C2×Dic596C2211yescharacteristic
21C2×#14558725C2211yescharacteristic
22C2×#14558725C2211yescharacteristic
23C2×#14558725C2211yescharacteristic
24C2×#14558725C2211yescharacteristic
25C2×D1192C2211yescharacteristic
26#18011911C2211yescharacteristic
27#18011911C2211yescharacteristic
28#18011911C2211yescharacteristic
29#18011906—21no—
30#18011899C2211yescharacteristic
31#18011899C2211yescharacteristic
32#18011899C2211yescharacteristic
33#18011897—21no—
34#18011895—21no—
35#18011895—21no—
36#18011893—21no—
37#18011891—21no—
38#18011891—21no—
39#18011890C2211yescharacteristic
40#18011889—21no—
41#18011885C2211yescharacteristic
42C4×Dic298C2211yescharacteristic
43C4×D596C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011836C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011833C2211yescharacteristic
52#117×C149C2211yescharacteristic
53C4⋊C8×C149C2211yescharacteristic
54C4⋊C8×C149C2211yescharacteristic
55C22⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57#97×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61C2×Dic298—21no—
62C2×Dic298—21no—
63C2×Dic298—41no—
64C2×Dic298—41no—
65C2×Dic298C2311yescharacteristic
66C2×Dic298C2311yescharacteristic
67C2×Dic298C2311yescharacteristic
68C2×Dic298C2311yescharacteristic
69C2×D596C2311yescharacteristic
70C2×D596C2311yescharacteristic
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C22×Dic149—21no—
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76Dic596—41no—
77Dic596—41no—
78Dic596—41no—
79#14558725—41no—
80#14558725—41no—
81#14558725—41no—
82#14558725—41no—
83D1192—41no—
84C4⋊Dic149—21no—
85C4⋊Dic149—21no—
86C4⋊Dic149—21no—
87C4⋊Dic149—21no—
88C4⋊Dic149—21no—
89C4⋊Dic149C2311yescharacteristic
90C4⋊Dic149C2311yescharacteristic
91#14558715—21no—
92#14558715—21no—
93C22⋊Dic149—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101#14558713—21no—
102C4×Dic149—21no—
103C22×C4×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149D411yescharacteristic
109C4⋊C4×C149D411yescharacteristic
110C22⋊C4×C149D411yescharacteristic
111C22⋊C4×C149D411yescharacteristic
112C42×C149C2311yescharacteristic
113C42×C149C2311yescharacteristic
114C22×D149—21no—
115C22×D149—21no—
116Dic298—21no—
117Dic298—21no—
118Dic298—21no—
119Dic298—21no—
120Dic298—21no—
121Dic298—21no—
122Dic298—21no—
123Dic298—21no—
124Dic298—42no—
125Dic298—81no—
126D596—21no—
127D596—21no—
128D596—21no—
129D596—21no—
130C22⋊D149—42no—
131C22⋊D149—81no—
132C2×Dic149—21no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149—21no—
138C2×Dic149—42no—
139C4×D149—42no—
140C4×D149—81no—
141C23×C149C2×D411yescharacteristic
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2411yescharacteristic
150C8×C149—21no—
151C8×C149—21no—
152C8×C149—21no—
153C8×C149—21no—
154C22×C149—21no—
155C22×C149—21no—
156C22×C149—21no—
157C22×C149C22×D411yescharacteristic
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—21no—
167C4×C149—21no—
168C4×C149—21no—
169C4×C149H(5,𝔽2)11yescharacteristic
170C4×C149H(5,𝔽2)11yescharacteristic
171Dic149—41no—
172Dic149—41no—
173Dic149—41no—
174Dic149—41no—
175Dic149—41no—
176Dic149—41no—
177C2×C149—41no—
178C2×C149#53511yescharacteristic
179C2×C149#57711yescharacteristic
180C2×C149#57811yescharacteristic
181D149—81no—
182D149—81no—
183C149#322511yescharacteristic, complemented, Sylow
184#3225—1491nomaximal, Sylow
185#542—1491no—
186#536—1491no—
187#497—1491no—
188#495—1491no—
189#489—1491no—
190#487—1491no—
191#464—1491no—
192#463—1491no—
193#462—1491no—
194#461—1491no—
195#452—1491no—
196#451—1491no—
197#449—1491no—
198#448—1491no—
199#433D14911yescharacteristic, complemented
200C2×#41—1491no—
201C22×Q8—1491no—
202C2×Q16—1491no—
203C2×Q16—1491no—
204C2×Q16—1491no—
205C2×SD16—1491no—
206C2×SD16—1491no—
207C2×SD16—1491no—
208C2×SD16—1491no—
209C2×D8—1491no—
210C4⋊Q8—1491no—
211C4⋊Q8—1491no—
212C4⋊Q8—1491no—
213#126—2981no—
214#124—2981no—
215#124—1491no—
216#124—1491no—
217#124—1491no—
218#123—2981no—
219#123—2981no—
220#123—2981no—
221C22⋊Q8—2981no—
222C22⋊Q8—2981no—
223C22⋊Q8—2981no—
224C22⋊Q8—1491no—
225#121—1491no—
226C4×Q8—1491no—
227C4×D4—1491no—
228#117C2×D14911yescharacteristic
229C4⋊C8C2×D14911yescharacteristic
230C4⋊C8C2×D14911yescharacteristic
231#103—1491no—
232#103—1491no—
233#103—1491no—
234#103—1491no—
235#103—1491no—
236#103—1491no—
237#102—1491no—
238#102—1491no—
239C22⋊C8C2×D14911yescharacteristic
240C22⋊C8C2×D14911yescharacteristic
241#97C2×D14911yescharacteristic
242C4×C8C2×D14911yescharacteristic
243#41—5961no—
244#41—5961no—
245C2×Q8—2981no—
246C2×Q8—2981no—
247C2×Q8—5961no—
248C2×Q8—5961no—
249C2×Q8—1491no—
250C2×Q8—1491no—
251C2×Q8—1491no—
252C2×Q8—1491no—
253C2×D4—2981no—
254C2×D4—2981no—
255C2×D4—1491no—
256C2×D4—1491no—
257C22×C4—2981no—
258C22×C4—2981no—
259C22×C4—2981no—
260C22×C4C22×D14911yescharacteristic
261Q16—5961no—
262Q16—5961no—
263Q16—5961no—
264SD16—5961no—
265SD16—5961no—
266SD16—5961no—
267SD16—5961no—
268D8—5961no—
269C2×C8C22×D14911yescharacteristic
270C2×C8C22×D14911yescharacteristic
271C2×C8C22×D14911yescharacteristic
272C2×C8C22×D14911yescharacteristic
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—2981no—
279C4⋊C4—2981no—
280C4⋊C4—1491no—
281C4⋊C4—1491no—
282C4⋊C4D59611yescharacteristic
283C4⋊C4D59611yescharacteristic
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4D59611yescharacteristic
294C22⋊C4D59611yescharacteristic
295C42—2981no—
296C42C22×D14911yescharacteristic
297C42C22×D14911yescharacteristic
298C23—2981no—
299C23—2981no—
300C23C2×D59611yescharacteristic
301Q8—2981no—
302Q8—2981no—
303Q8—2981no—
304Q8—2981no—
305Q8—2981no—
306Q8—2981no—
307Q8—2981no—
308Q8—2981no—
309Q8—5962no—
310Q8—11921no—
311D4—2981no—
312D4—2981no—
313D4—2981no—
314D4—2981no—
315D4—5962no—
316D4—11921no—
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—5962no—
326C2×C4—5962no—
327C2×C4—11921no—
328C2×C4C2×D59611yescharacteristic
329C2×C4C2×D59611yescharacteristic
330C2×C4C2×D59611yescharacteristic
331C2×C4C2×D59611yescharacteristic
332C2×C4C2×D59611yescharacteristic
333C2×C4C23×D14911yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—5961no—
342C22—5961no—
343C22—5961no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22C22×D59611yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—5961no—
354C4—5961no—
355C4—5961no—
356C4—5961no—
357C4—5961no—
358C4—5961no—
359C4#1801195711yescharacteristic
360C4#1801195711yescharacteristic
361C2—41no—
362C2—11921no—
363C2—11921no—
364C2#2375019411yescharacteristic
365C2#2375043711yescharacteristic
366C2#2375044211yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#433×C149C2
socleC22×C149C22×D4
prime radical#23749772C2
hypercenter#433D149
hypocenterC149#3225
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23750246C2semidirect
2. #23750201C2semidirect
3. #23750019C2semidirect
4. #23750009C2semidirect
5. #23749985C2semidirect
6. #23749976C2semidirect
7. #23749848C2semidirect
8. #23749841C2semidirect
9. #23749836C2semidirect
10. #23749831C2semidirect
11. #23749789C2semidirect
12. #23749783C2semidirect
14. #23749766C2semidirect
15. #433×C149C2semidirect
183. C149#3225semidirect
199. #433D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237502012
#237500192
#237500092
#237499852
#237499762
#237498482
#237498412
#237498362
#237498312
#237497892
#237497832
#237497722
#237497662
#433×C1492
#3225149