Finite Group Databasebeta

← #34054835

Subgroups — #34054835

Order 19072.

430 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#23750170C211yesmaximal, characteristic, complemented
2#41×Dic149C211yesmaximal, characteristic, complemented
3#23749950C211yesmaximal, characteristic, complemented
4#23749946C211yesmaximal, characteristic, complemented
5#23749908C211yesmaximal, characteristic, complemented
6#23749903C211yesmaximal, characteristic, complemented
7#23749823C211yesmaximal, characteristic, complemented
8#23749818C211yesmaximal, characteristic, complemented
9#23749770C211yesmaximal, characteristic, complemented
10#23749737C211yesmaximal, characteristic, complemented
11#23749734C211yesmaximal, characteristic, complemented
12#23749728C211yesmaximal, characteristic, complemented
13#23749726C211yesmaximal, characteristic, complemented
14#23749679C211yesmaximal, characteristic, complemented
15#449×C149C211yesmaximal, characteristic, complemented
16C2×#14558735—21no—
17C2×#14558723C2211yescharacteristic
18C2×#14558721C2211yescharacteristic
19#18011910C2211yescharacteristic
20#18011907C2211yescharacteristic
21#18011897—21no—
22#18011885C2211yescharacteristic
23#18011883—21no—
24Q8×Dic149C2211yescharacteristic
25Q8×Dic149C2211yescharacteristic
26D4×Dic149—21no—
27D4×Dic149—21no—
28D4×Dic149C2211yescharacteristic
29D4×Dic149C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31#18011873C2211yescharacteristic
32#18011871—21no—
33#18011870—21no—
34#18011870C2211yescharacteristic
35C2×C4×Dic149—21no—
36C2×C4×Dic149C2211yescharacteristic
37#18011845C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic
51#18011821C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C2×D8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558735—44no—
60C2×Dic298—21no—
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C22×Dic149—21no—
66C22×Dic149—21no—
67C22×Dic149—21no—
68C22×Dic149D411yescharacteristic
69C22×Dic149D411yescharacteristic
70C2×C4×D149—21no—
71#14558723—22no—
72#14558721—22no—
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C4⋊Dic149—21no—
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81C22⋊Dic149—21no—
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85#14558713—21no—
86#14558713—21no—
87C4×Dic149—21no—
88C4×Dic149—21no—
89C4×Dic149—21no—
90C4×Dic149D411yescharacteristic
91C4×Dic149D411yescharacteristic
92C4×Dic149C2311yescharacteristic
93C4×Dic149C2311yescharacteristic
94#41×C149—22no—
95#41×C149—22no—
96C2×Q8×C149C2311yescharacteristic
97C2×D4×C149—21no—
98C2×D4×C149—21no—
99C2×D4×C149C2311yescharacteristic
100C2×D4×C149C2311yescharacteristic
101C22×C4×C149—21no—
102C22×C4×C149C2311yescharacteristic
103SD16×C149—22no—
104D8×C149—22no—
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C22⋊C4×C149—21no—
109C22×D149—21no—
110Dic298—42no—
111D596—21no—
112D596—21no—
113C22⋊D149—42no—
114C22⋊D149—42no—
115C22⋊D149—42no—
116C2×Dic149—22no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—41no—
121C2×Dic149—42no—
122C2×Dic149—42no—
123C2×Dic149—42no—
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C4×D149—42no—
129#11924746—21no—
130#11924746—21no—
131C23×C149—21no—
132C23×C149—21no—
133C23×C149C2×D411yescharacteristic
134Q8×C149—21no—
135Q8×C149#4112yescomplemented
136D4×C149—24no—
137D4×C149—21no—
138D4×C149—21no—
139D4×C149—21no—
140D4×C149—42no—
141D4×C149#4112yescomplemented
142C2×C4×C149—24no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2411yescharacteristic
149C8×C149—21no—
150C8×C149—21no—
151C22×C149—21no—
152C22×C149—22no—
153C22×C149—21no—
154C22×C149—21no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149C22×D411yescharacteristic
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C4×C149—21no—
165C4×C149—22no—
166C4×C149—41no—
167C4×C149C2×#4111yescharacteristic
168C4×C149C2×#4111yescharacteristic
169Dic149—21no—
170Dic149—21no—
171Dic149—21no—
172Dic149—41no—
173Dic149—41no—
174Dic149—41no—
175Dic149AGL(1,ℤ/8)12yes—
176C2×C149—41no—
177C2×C149—42no—
178C2×C149—81no—
179C2×C149#52511yescharacteristic
180C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C149#57511yescharacteristic
182D149—81no—
183C149#311511yescharacteristic, complemented, Sylow
184#3115—1491nomaximal, Sylow
185#532—1491no—
186C4×#41—1491no—
187#482—1491no—
188#482—1491no—
189#475—1491no—
190#474—1491no—
191#460—1491no—
192#459—1491no—
193#449—1491no—
194#449D14911yescharacteristic, complemented
195#442—1491no—
196#442—1491no—
197#440—1491no—
198#440—1491no—
199#432—1491no—
200C2×#41—2981no—
201C2×#41C2×D14911yescharacteristic
202C2×SD16—1491no—
203C2×SD16C2×D14911yescharacteristic
204C2×D8—1491no—
205C2×D8C2×D14911yescharacteristic
206C4⋊Q8—1491no—
207#127—1491no—
208#124—2981no—
209#121—2981no—
210#121—1491no—
211#121C2×D14911yescharacteristic
212C4×Q8—1491no—
213C4×Q8—1491no—
214C4×D4—2981no—
215C4×D4—2981no—
216C4×D4—2981no—
217C4×D4—1491no—
218C4×D4—1491no—
219C4×D4—1491no—
220C4×D4—1491no—
221#117—2981no—
222#117—1491no—
223C2×C42—2981no—
224C2×C42—1491no—
225#107—1491no—
226#107—1491no—
227#106—1491no—
228#106—1491no—
229C4⋊C8—1491no—
230C4⋊C8—1491no—
231#103—1491no—
232#103C2×D14911yescharacteristic
233#102—1491no—
234#102—1491no—
235#102—1491no—
236#102—1491no—
237#102—1491no—
238#102C2×D14911yescharacteristic
239C22⋊C8—1491no—
240C22⋊C8C2×D14911yescharacteristic
241#97—1491no—
242#97—1491no—
243#41—22no—
244#41—22no—
245#41—5964no—
246C2×Q8—2981no—
247C2×Q8C22×D14911yescharacteristic
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—2981no—
251C2×D4—2981no—
252C2×D4—2981no—
253C2×D4—1491no—
254C2×D4C22×D14911yescharacteristic
255C2×D4C22×D14911yescharacteristic
256C22×C4—21no—
257C22×C4—2981no—
258C22×C4—2981no—
259C22×C4—2981no—
260C22×C4—2981no—
261C22×C4—1491no—
262C22×C4—1491no—
263C22×C4C22×D14911yescharacteristic
264SD16—22no—
265SD16—2982no—
266D8—22no—
267D8—2982no—
268C2×C8—1491no—
269C2×C8—1491no—
270C2×C8C22×D14911yescharacteristic
271C2×C8C22×D14911yescharacteristic
272C4⋊C4—2981no—
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—1491no—
276C4⋊C4—1491no—
277C4⋊C4—1491no—
278C4⋊C4C22×D14911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C42—2981no—
287C42—2981no—
288C42—2981no—
289C42—1491no—
290C42—1491no—
291C42—1491no—
292C42—1491no—
293C23—21no—
294C23—21no—
295C23—2981no—
296C23D4×D14911yescharacteristic
297Q8—21no—
298Q8—5962no—
299Q8#1455873512yescomplemented
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—42no—
305D4—2981no—
306D4—2981no—
307D4—5962no—
308D4—5962no—
309D4—5962no—
310D4#1455873512yescomplemented
311C2×C4—24no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—2982no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—5962no—
321C2×C4—5961no—
322C2×C4—5962no—
323C2×C4—5962no—
324C2×C4—5962no—
325C2×C4—1491no—
326C2×C4—1491no—
327C2×C4—1491no—
328C2×C4—1491no—
329C2×C4D4×D14911yescharacteristic
330C2×C4C23×D14911yescharacteristic
331C8—21no—
332C8—21no—
333C8—2981no—
334C8—2981no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22C2×D4×D14911yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—2981no—
352C4—2981no—
353C4—2981no—
354C4—5961no—
355C4—5961no—
356C4—5961no—
357C4—1492no—
358C4C2×#1455873511yescharacteristic
359C4C2×#1455873511yescharacteristic
360C2—41no—
361C2—42no—
362C2—81no—
363C2—11921no—
364C2#2375013111yescharacteristic
365C2AGL(1,ℤ/8)×D14911yescharacteristic
366C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#449×C149C2
socleC22×C149C22×D4
hypercenter#449D149
hypocenterC149#3115
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23750170C2semidirect
2. #41×Dic149C2semidirect
3. #23749950C2semidirect
4. #23749946C2semidirect
5. #23749908C2semidirect
6. #23749903C2semidirect
7. #23749823C2semidirect
8. #23749818C2semidirect
9. #23749770C2semidirect
10. #23749737C2semidirect
11. #23749734C2semidirect
12. #23749728C2semidirect
13. #23749726C2semidirect
14. #23749679C2semidirect
15. #449×C149C2semidirect
135. Q8×C149#41semidirect
141. D4×C149#41semidirect
183. C149#3115semidirect
194. #449D149semidirect
299. Q8#14558735semidirect
310. D4#14558735semidirect

Maximal subgroups

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

subgroupindex
#237501702
#41×Dic1492
#237499502
#237499462
#237499082
#237499032
#237498232
#237498182
#237497702
#237497372
#237497342
#237497282
#237497262
#237496792
#449×C1492
#3115149