Finite Group Databasebeta

← #34056281

Subgroups — #34056281

Order 19072.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011944C211yesmaximal, characteristic, complemented
2C2×#18011933C211yesmaximal, characteristic, complemented
3#23750296C211yesmaximal, characteristic, complemented
4#23750284C211yesmaximal, characteristic, complemented
5#23750014C211yesmaximal, characteristic, complemented
6#23749878C211yesmaximal, characteristic, complemented
7#23749854C211yesmaximal, characteristic, complemented
8#23749848C211yesmaximal, characteristic, complemented
9#23749826C211yesmaximal, characteristic, complemented
10#23749789C211yesmaximal, characteristic, complemented
11#23749772C211yesmaximal, characteristic, complemented
12#23749772C211yesmaximal, characteristic, complemented
13#23749766C211yesmaximal, characteristic, complemented
14#23749733C211yesmaximal, characteristic, complemented
15#435×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558736C2211yescharacteristic
18C2×#14558736C2211yescharacteristic
19C22×Dic298C2211yescharacteristic
20#18011944—24no—
21#18011933—24no—
22C2×Dic596C2211yescharacteristic
23C2×Dic596C2211yescharacteristic
24C2×#14558725C2211yescharacteristic
25C2×#14558725C2211yescharacteristic
26C2×#14558725C2211yescharacteristic
27C2×#14558725C2211yescharacteristic
28C2×#14558725C2211yescharacteristic
29C2×D1192C2211yescharacteristic
30C2×D1192C2211yescharacteristic
31#18011908C2211yescharacteristic
32#18011907—21no—
33#18011899C2211yescharacteristic
34#18011897—21no—
35#18011890C2211yescharacteristic
36#18011889—21no—
37#18011885C2211yescharacteristic
38#18011885C2211yescharacteristic
39#18011885C2211yescharacteristic
40#18011884—21no—
41#18011884—21no—
42#18011883—21no—
43C4×Dic298C2211yescharacteristic
44C4×Dic298C2211yescharacteristic
45#18011873—21no—
46#18011871—21no—
47#18011843C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011836C2211yescharacteristic
50#18011836C2211yescharacteristic
51#18011833C2211yescharacteristic
52#18011833C2211yescharacteristic
53#18011833C2211yescharacteristic
54C2×M16×C149C2211yescharacteristic
55C22×C8×C149C2211yescharacteristic
56C4×D4×C149C2211yescharacteristic
57C4⋊C8×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59C22⋊C8×C149C2211yescharacteristic
60#97×C149C2211yescharacteristic
61#14558736—22no—
62#14558736—22no—
63#14558736—22no—
64#14558736—41no—
65#14558736—41no—
66#14558736—41no—
67C2×Dic298—22no—
68C2×Dic298—21no—
69C2×Dic298—41no—
70C2×Dic298C2311yescharacteristic
71C2×Dic298C2311yescharacteristic
72C2×Dic298C2311yescharacteristic
73C2×D596—21no—
74C2×D596—21no—
75C2×D596C2311yescharacteristic
76C2×D596C2311yescharacteristic
77C2×D596C2311yescharacteristic
78C2×C22⋊D149—21no—
79C2×C22⋊D149—21no—
80C2×C22⋊D149—21no—
81C2×C22⋊D149—21no—
82C2×C22⋊D149—21no—
83C2×C22⋊D149—21no—
84C22×Dic149—21no—
85C2×C4×D149—21no—
86C2×C4×D149—21no—
87C2×C4×D149—21no—
88Dic596—22no—
89Dic596D414yescomplemented
90#14558725—22no—
91#14558725—22no—
92#14558725—22no—
93#14558725—22no—
94#14558725—41no—
95D1192—22no—
96D1192—41no—
97C4⋊Dic149C2311yescharacteristic
98C4⋊Dic149C2311yescharacteristic
99#14558715—21no—
100#14558715—21no—
101#14558715—21no—
102C22⋊Dic149—21no—
103#14558713—21no—
104#14558713—21no—
105#14558713—21no—
106#14558713—21no—
107#14558713—21no—
108C4×Dic149—21no—
109C4×Dic149—21no—
110C2×D4×C149D411yescharacteristic
111C22×C4×C149C2311yescharacteristic
112C22×C4×C149C2311yescharacteristic
113M16×C149—22no—
114C2×C8×C149—22no—
115C2×C8×C149C2311yescharacteristic
116C2×C8×C149C2311yescharacteristic
117C2×C8×C149C2311yescharacteristic
118C2×C8×C149C2311yescharacteristic
119C4⋊C4×C149D411yescharacteristic
120C22⋊C4×C149D411yescharacteristic
121C22⋊C4×C149D411yescharacteristic
122C42×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149—21no—
125C22×D149—21no—
126Dic298—21no—
127Dic298—21no—
128Dic298—21no—
129Dic298—21no—
130Dic298—42no—
131Dic298C2×D412yes—
132Dic298C2×D412yes—
133D596—21no—
134D596—21no—
135D596—21no—
136D596—21no—
137D596—21no—
138D596—21no—
139D596—42no—
140D596—81no—
141C22⋊D149—42no—
142C22⋊D149—42no—
143C22⋊D149—42no—
144C22⋊D149—42no—
145C22⋊D149—81no—
146C22⋊D149—81no—
147C2×Dic149—21no—
148C2×Dic149—21no—
149C2×Dic149—21no—
150C2×Dic149—21no—
151C2×Dic149—21no—
152C2×Dic149—42no—
153C4×D149—42no—
154C4×D149—42no—
155C4×D149—42no—
156C23×C149C2×D411yescharacteristic
157C23×C149C2×D411yescharacteristic
158D4×C149—41no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149C2×D411yescharacteristic
164C2×C4×C149C2×D411yescharacteristic
165C2×C4×C149C2×D411yescharacteristic
166C2×C4×C149C2×D411yescharacteristic
167C2×C4×C149C2411yescharacteristic
168C8×C149—21no—
169C8×C149—21no—
170C8×C149—21no—
171C8×C149C2×D412yes—
172C22×C149—21no—
173C22×C149—21no—
174C22×C149—21no—
175C22×C149—21no—
176C22×C149—21no—
177C22×C149—21no—
178C22×C149C22×D411yescharacteristic
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—41no—
184C2×D149—41no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C4×C149—21no—
189C4×C149—21no—
190C4×C149—21no—
191C4×C149—21no—
192C4×C149C22×D411yescharacteristic
193C4×C149H(5,𝔽2)11yescharacteristic
194Dic149—22no—
195Dic149—22no—
196Dic149—41no—
197Dic149—41no—
198Dic149—41no—
199C2×C149—41no—
200C2×C149—41no—
201C2×C149D4211yescharacteristic
202C2×C149#57511yescharacteristic
203C2×C149#57711yescharacteristic
204D149—81no—
205D149—81no—
206D149—81no—
207C149#327111yescharacteristic, complemented, Sylow
208#3271—1491nomaximal, Sylow
209C2×#137—1491no—
210C2×#135—1491no—
211#550—1491no—
212#548—1491no—
213#496—1491no—
214#469—1491no—
215#465—1491no—
216#464—1491no—
217#460—1491no—
218#452—1491no—
219#449—1491no—
220#449—1491no—
221#448—1491no—
222#441—1491no—
223#435D14911yescharacteristic, complemented
224C2×#41—1491no—
225C2×#41—1491no—
226C2×#41—1491no—
227C22×Q8—1491no—
228#137—2984no—
229#135—2984no—
230C2×Q16—1491no—
231C2×Q16—1491no—
232C2×SD16—1491no—
233C2×SD16—1491no—
234C2×SD16—1491no—
235C2×SD16—1491no—
236C2×SD16—1491no—
237C2×D8—1491no—
238C2×D8—1491no—
239C2×M16C2×D14911yescharacteristic
240C22×C8C2×D14911yescharacteristic
241#127—2981no—
242#127—1491no—
243#124—2981no—
244#124—1491no—
245C22⋊Q8—2981no—
246C22⋊Q8—1491no—
247#121—2981no—
248#121—2981no—
249#121—2981no—
250#121—1491no—
251#121—1491no—
252#121—1491no—
253C4×Q8—1491no—
254C4×Q8—1491no—
255C4×D4—2981no—
256C4×D4—2981no—
257C4×D4C2×D14911yescharacteristic
258#106—1491no—
259C4⋊C8C2×D14911yescharacteristic
260#103—1491no—
261#103—1491no—
262#103—1491no—
263#102—1491no—
264#102—1491no—
265#102—1491no—
266C22⋊C8C2×D14911yescharacteristic
267C22⋊C8C2×D14911yescharacteristic
268#97C2×D14911yescharacteristic
269#41—2982no—
270#41—2982no—
271#41—2982no—
272#41—5961no—
273#41—5961no—
274#41—5961no—
275C2×Q8—2982no—
276C2×Q8—2981no—
277C2×Q8—5961no—
278C2×Q8—1491no—
279C2×Q8—1491no—
280C2×Q8—1491no—
281C2×D4—2981no—
282C2×D4—2981no—
283C2×D4—2981no—
284C2×D4—2981no—
285C2×D4—2981no—
286C2×D4—2981no—
287C2×D4—2981no—
288C2×D4—2981no—
289C2×D4—1491no—
290C2×D4—1491no—
291C2×D4—1491no—
292C2×D4D59611yescharacteristic
293C22×C4—2981no—
294C22×C4—2981no—
295C22×C4—2981no—
296C22×C4—2981no—
297C22×C4C22×D14911yescharacteristic
298C22×C4C22×D14911yescharacteristic
299Q16—2982no—
300Q16—1494no—
301SD16—2982no—
302SD16—2982no—
303SD16—2982no—
304SD16—2982no—
305SD16—5961no—
306D8—2982no—
307D8—5961no—
308M16—22no—
309C2×C8—22no—
310C2×C8C22×D14911yescharacteristic
311C2×C8C22×D14911yescharacteristic
312C2×C8C22×D14911yescharacteristic
313C2×C8C22×D14911yescharacteristic
314C4⋊C4—2981no—
315C4⋊C4—2981no—
316C4⋊C4—2981no—
317C4⋊C4—1491no—
318C4⋊C4—1491no—
319C4⋊C4D59611yescharacteristic
320C22⋊C4—2981no—
321C22⋊C4—2981no—
322C22⋊C4—2981no—
323C22⋊C4—2981no—
324C22⋊C4—2981no—
325C22⋊C4—2981no—
326C22⋊C4D59611yescharacteristic
327C22⋊C4D59611yescharacteristic
328C42—2981no—
329C42—2981no—
330C42C22×D14911yescharacteristic
331C23—2981no—
332C23—2981no—
333C23—2981no—
334C23C2×D59611yescharacteristic
335C23C2×D59611yescharacteristic
336Q8—2981no—
337Q8—2981no—
338Q8—2981no—
339Q8—2981no—
340Q8—5962no—
341Q8—1492no—
342Q8—1492no—
343D4—41no—
344D4—2981no—
345D4—2981no—
346D4—2981no—
347D4—2981no—
348D4—2981no—
349D4—2981no—
350D4—5962no—
351D4—5962no—
352D4—5962no—
353D4—5962no—
354D4—5962no—
355D4—11921no—
356D4—11921no—
357D4—11921no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—2981no—
363C2×C4—2981no—
364C2×C4—2981no—
365C2×C4—2981no—
366C2×C4—2981no—
367C2×C4—5962no—
368C2×C4—5962no—
369C2×C4—5962no—
370C2×C4—5962no—
371C2×C4C2×D59611yescharacteristic
372C2×C4C2×D59611yescharacteristic
373C2×C4C2×D59611yescharacteristic
374C2×C4C2×D59611yescharacteristic
375C2×C4C23×D14911yescharacteristic
376C8—21no—
377C8—21no—
378C8—21no—
379C8D4×D14912yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—5961no—
387C22—5961no—
388C22—5961no—
389C22—5961no—
390C22—5961no—
391C22—5961no—
392C22—5961no—
393C22—5961no—
394C22—5961no—
395C22C22×D59611yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—2982no—
401C4—2982no—
402C4—5961no—
403C4—5961no—
404C4—5961no—
405C4C2×D4×D14911yescharacteristic
406C4#1801195711yescharacteristic
407C2—41no—
408C2—41no—
409C2—11921no—
410C2—11921no—
411C2—11921no—
412C2D4×D59611yescharacteristic
413C2#2375042511yescharacteristic
414C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#435×C149C2
socleC22×C149C22×D4
hypercenter#435D149
hypocenterC149#3271
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#18011944C2semidirect
2. C2×#18011933C2semidirect
3. #23750296C2semidirect
4. #23750284C2semidirect
5. #23750014C2semidirect
6. #23749878C2semidirect
7. #23749854C2semidirect
8. #23749848C2semidirect
9. #23749826C2semidirect
10. #23749789C2semidirect
11. #23749772C2semidirect
12. #23749772C2semidirect
13. #23749766C2semidirect
14. #23749733C2semidirect
15. #435×C149C2semidirect
89. Dic596D4semidirect
207. C149#3271semidirect
223. #435D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119442
C2×#180119332
#237502962
#237502842
#237500142
#237498782
#237498542
#237498482
#237498262
#237497892
#237497722
#237497662
#237497332
#435×C1492
#3271149