Finite Group Databasebeta

← #34056275

Subgroups — #34056275

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×#18011940C211yesmaximal, characteristic, complemented
2C2×#18011930C211yesmaximal, characteristic, complemented
3#23750295C211yesmaximal, characteristic, complemented
4#23750283C211yesmaximal, characteristic, complemented
5#23749875C211yesmaximal, characteristic, complemented
6#23749851C211yesmaximal, characteristic, complemented
7#23749844C211yesmaximal, characteristic, complemented
8#23749822C211yesmaximal, characteristic, complemented
9#23749784C211yesmaximal, characteristic, complemented
10#23749767C211yesmaximal, characteristic, complemented
11#23749767C211yesmaximal, characteristic, complemented
12#23749762C211yesmaximal, characteristic, complemented
13#23749733C211yesmaximal, characteristic, complemented
14#23749698C211yesmaximal, characteristic, complemented
15#496×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C2×#14558735C2211yescharacteristic
19C2×Q8×D149C2211yescharacteristic
20#18011940—24no—
21#18011930—24no—
22C2×Dic596C2211yescharacteristic
23C2×#14558726C2211yescharacteristic
24C2×#14558724C2211yescharacteristic
25C2×#14558724C2211yescharacteristic
26C2×#14558724C2211yescharacteristic
27C2×#14558719C2211yescharacteristic
28C2×C8×D149C2211yescharacteristic
29#18011907—21no—
30#18011897—21no—
31#18011888—21no—
32#18011887C2211yescharacteristic
33#18011884—21no—
34#18011883—21no—
35#18011883—21no—
36#18011882C2211yescharacteristic
37#18011882C2211yescharacteristic
38#18011882C2211yescharacteristic
39C4×Dic298C2211yescharacteristic
40C4×Dic298C2211yescharacteristic
41C4×D596C2211yescharacteristic
42D4×Dic149—21no—
43#18011871—21no—
44#18011843C2211yescharacteristic
45C4⋊#11924746C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011835C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011832C2211yescharacteristic
51#18011832C2211yescharacteristic
52#18011823C2211yescharacteristic
53#18011823C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C2×SD16×C149C2211yescharacteristic
56C2×D8×C149C2211yescharacteristic
57C2×D8×C149C2211yescharacteristic
58#127×C149C2211yescharacteristic
59#124×C149C2211yescharacteristic
60#97×C149C2211yescharacteristic
61#14558735—22no—
62#14558735—22no—
63#14558735—22no—
64#14558735—41no—
65#14558735—41no—
66#14558735—41no—
67C2×Dic298—21no—
68C2×Dic298C2311yescharacteristic
69C2×Dic298C2311yescharacteristic
70Q8×D149—22no—
71Q8×D149—41no—
72C2×D596D411yescharacteristic
73C2×C22⋊D149—21no—
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76C2×C22⋊D149—21no—
77C2×C22⋊D149—21no—
78C2×C22⋊D149—21no—
79C22×Dic149—21no—
80C22×Dic149—21no—
81C22×Dic149—21no—
82C2×C4×D149—21no—
83C2×C4×D149C2311yescharacteristic
84C2×C4×D149C2311yescharacteristic
85Dic596D414yescomplemented
86#14558726—22no—
87#14558724—22no—
88#14558724—22no—
89#14558724—22no—
90#14558719—22no—
91C2×#11924746C2311yescharacteristic
92C2×#11924746C2311yescharacteristic
93C8×D149—22no—
94C4⋊Dic149D411yescharacteristic
95C4⋊Dic149C2311yescharacteristic
96C4⋊Dic149C2311yescharacteristic
97#14558715—21no—
98#14558715—21no—
99#14558715—21no—
100C22⋊Dic149—21no—
101C22⋊Dic149—21no—
102C22⋊Dic149—21no—
103#14558713—21no—
104#14558713D411yescharacteristic
105#14558713D411yescharacteristic
106C4×Dic149—21no—
107C4×Dic149—21no—
108C2×Q8×C149C2311yescharacteristic
109C2×D4×C149—21no—
110C2×D4×C149—21no—
111C2×D4×C149C2311yescharacteristic
112C2×D4×C149C2311yescharacteristic
113C2×D4×C149C2311yescharacteristic
114SD16×C149—22no—
115SD16×C149—41no—
116D8×C149—22no—
117D8×C149—41no—
118C2×C8×C149C2311yescharacteristic
119C2×C8×C149C2311yescharacteristic
120C22⋊C4×C149—21no—
121C22⋊C4×C149—21no—
122C42×C149C2311yescharacteristic
123C22×D149C2×D411yescharacteristic
124C22×D149C2×D411yescharacteristic
125Dic298—21no—
126Dic298—21no—
127Dic298—42no—
128Dic298C2×D412yes—
129Dic298C2×D412yes—
130D596—41no—
131C22⋊D149—42no—
132C22⋊D149—42no—
133C22⋊D149—42no—
134C22⋊D149—42no—
135C22⋊D149—81no—
136C22⋊D149—81no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C2×Dic149—21no—
140C2×Dic149—21no—
141C2×Dic149—42no—
142C2×Dic149—42no—
143C2×Dic149—42no—
144C2×Dic149C2×D411yescharacteristic
145C2×Dic149C2×D411yescharacteristic
146C4×D149—21no—
147C4×D149—21no—
148C4×D149—21no—
149C4×D149—21no—
150C4×D149—42no—
151#11924746—21no—
152#11924746—21no—
153C23×C149—21no—
154C23×C149—21no—
155C23×C149—21no—
156Q8×C149—21no—
157Q8×C149—21no—
158D4×C149—21no—
159D4×C149—21no—
160D4×C149—21no—
161D4×C149—21no—
162D4×C149—21no—
163D4×C149—21no—
164D4×C149—42no—
165D4×C149—81no—
166C2×C4×C149—21no—
167C2×C4×C149C2×D411yescharacteristic
168C2×C4×C149C2×D411yescharacteristic
169C2×C4×C149C2411yescharacteristic
170C8×C149—21no—
171C8×C149C2×D412yes—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149—41no—
179C22×C149—41no—
180C22×C149—41no—
181C22×C149C22×D411yescharacteristic
182C2×D149—21no—
183C2×D149—21no—
184C2×D149—21no—
185C2×D149—21no—
186C2×D149—21no—
187C2×D149—21no—
188C4×C149—21no—
189C4×C149—21no—
190C4×C149—41no—
191C4×C149C22×D411yescharacteristic
192C4×C149H(5,𝔽2)11yescharacteristic
193Dic149—21no—
194Dic149—21no—
195Dic149—22no—
196Dic149—22no—
197Dic149—41no—
198Dic149—41no—
199C2×C149—81no—
200C2×C149—81no—
201C2×C149—81no—
202C2×C149D4211yescharacteristic
203C2×C149#57511yescharacteristic
204C2×C149#57711yescharacteristic
205D149—41no—
206D149—41no—
207C149#327111yescharacteristic, complemented, Sylow
208#3271—1491nomaximal, Sylow
209C2×#137—1491no—
210C2×#135—1491no—
211#550—1491no—
212#548—1491no—
213#496D14911yescharacteristic, complemented
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#435—1491no—
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×SD16C2×D14911yescharacteristic
236C2×SD16C2×D14911yescharacteristic
237C2×D8C2×D14911yescharacteristic
238C2×D8C2×D14911yescharacteristic
239C2×M16—1491no—
240C22×C8—1491no—
241#127—2981no—
242#127C2×D14911yescharacteristic
243#124—2981no—
244#124C2×D14911yescharacteristic
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×D4—1491no—
258#106—1491no—
259C4⋊C8—1491no—
260#103—1491no—
261#103—1491no—
262#103—1491no—
263#102—1491no—
264#102—1491no—
265#102—1491no—
266C22⋊C8—1491no—
267C22⋊C8—1491no—
268#97C2×D14911yescharacteristic
269#41—2982no—
270#41—2982no—
271#41—2982no—
272#41—5961no—
273#41—5961no—
274#41—5961no—
275C2×Q8—2981no—
276C2×Q8—2982no—
277C2×Q8—5961no—
278C2×Q8—1491no—
279C2×Q8—1491no—
280C2×Q8C22×D14911yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—2981no—
284C2×D4—2981no—
285C2×D4—2981no—
286C2×D4—2981no—
287C2×D4—2981no—
288C2×D4—2981no—
289C2×D4—1491no—
290C2×D4C22×D14911yescharacteristic
291C2×D4C22×D14911yescharacteristic
292C2×D4C22×D14911yescharacteristic
293C22×C4—2981no—
294C22×C4—2981no—
295C22×C4—2981no—
296C22×C4—2981no—
297C22×C4—1491no—
298C22×C4—1491no—
299Q16—2982no—
300Q16—1494no—
301SD16—22no—
302SD16—41no—
303SD16—2982no—
304SD16—2982no—
305SD16—2982no—
306D8—22no—
307D8—41no—
308M16—2982no—
309C2×C8—2982no—
310C2×C8—1491no—
311C2×C8—1491no—
312C2×C8C22×D14911yescharacteristic
313C2×C8C22×D14911yescharacteristic
314C4⋊C4—2981no—
315C4⋊C4—2981no—
316C4⋊C4—2981no—
317C4⋊C4—1491no—
318C4⋊C4—1491no—
319C4⋊C4—1491no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—2981no—
323C22⋊C4—2981no—
324C22⋊C4—2981no—
325C22⋊C4—2981no—
326C22⋊C4—1491no—
327C22⋊C4—1491no—
328C42—2981no—
329C42—2981no—
330C42C22×D14911yescharacteristic
331C23—21no—
332C23—21no—
333C23—21no—
334C23—1491no—
335C23—1491no—
336Q8—21no—
337Q8—21no—
338Q8—2981no—
339Q8—2981no—
340Q8—5962no—
341Q8—1492no—
342Q8—1492no—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—81no—
351D4—5961no—
352D4—5962no—
353D4—5962no—
354D4—5962no—
355D4—5962no—
356D4—11921no—
357D4—11921no—
358C2×C4—21no—
359C2×C4—2981no—
360C2×C4—2981no—
361C2×C4—2981no—
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×C4—1491no—
372C2×C4—1491no—
373C2×C4D4×D14911yescharacteristic
374C2×C4D4×D14911yescharacteristic
375C2×C4C23×D14911yescharacteristic
376C8—21no—
377C8—2981no—
378C8—2981no—
379C8D4×D14912yes—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—2981no—
390C22—2981no—
391C22—2981no—
392C22—2981no—
393C22—2981no—
394C22—2981no—
395C22C2×D4×D14911yescharacteristic
396C4—21no—
397C4—21no—
398C4—41no—
399C4—2981no—
400C4—2981no—
401C4—2982no—
402C4—2982no—
403C4—5961no—
404C4—5961no—
405C4C2×D4×D14911yescharacteristic
406C4#1801195611yescharacteristic
407C2—81no—
408C2—81no—
409C2—81no—
410C2—5961no—
411C2—5961no—
412C2#2375026011yescharacteristic
413C2#2375042111yescharacteristic
414C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#496×C149C2
socleC22×C149C22×D4
hypercenter#496D149
hypocenterC149#3271
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#18011940C2semidirect
2. C2×#18011930C2semidirect
3. #23750295C2semidirect
4. #23750283C2semidirect
5. #23749875C2semidirect
6. #23749851C2semidirect
7. #23749844C2semidirect
8. #23749822C2semidirect
9. #23749784C2semidirect
10. #23749767C2semidirect
11. #23749767C2semidirect
12. #23749762C2semidirect
13. #23749733C2semidirect
14. #23749698C2semidirect
15. #496×C149C2semidirect
85. Dic596D4semidirect
207. C149#3271semidirect
213. #496D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119402
C2×#180119302
#237502952
#237502832
#237498752
#237498512
#237498442
#237498222
#237497842
#237497672
#237497622
#237497332
#237496982
#496×C1492
#3271149