Finite Group Databasebeta

← #34056273

Subgroups — #34056273

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×#18011933C211yesmaximal, characteristic, complemented
3#23750293C211yesmaximal, characteristic, complemented
4#23750285C211yesmaximal, characteristic, complemented
5#23750011C211yesmaximal, characteristic, complemented
6#23749879C211yesmaximal, characteristic, complemented
7#23749850C211yesmaximal, characteristic, complemented
8#23749824C211yesmaximal, characteristic, complemented
9#23749785C211yesmaximal, characteristic, complemented
10#23749771C211yesmaximal, characteristic, complemented
11#23749768C211yesmaximal, characteristic, complemented
12#23749765C211yesmaximal, characteristic, complemented
13#23749731C211yesmaximal, characteristic, complemented
14#23749696C211yesmaximal, characteristic, complemented
15#465×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558736C2211yescharacteristic
18C2×#14558735C2211yescharacteristic
19C2×Q8×D149C2211yescharacteristic
20#18011940—24no—
21#18011933—24no—
22C2×Dic596C2211yescharacteristic
23C2×#14558726C2211yescharacteristic
24C2×#14558725C2211yescharacteristic
25C2×#14558725C2211yescharacteristic
26C2×#14558724C2211yescharacteristic
27C2×#14558723C2211yescharacteristic
28C2×D1192C2211yescharacteristic
29C2×#14558721C2211yescharacteristic
30C2×#14558719C2211yescharacteristic
31#18011907—21no—
32#18011907C2211yescharacteristic
33#18011900C2211yescharacteristic
34#18011897—21no—
35#18011889—21no—
36#18011886C2211yescharacteristic
37#18011886C2211yescharacteristic
38#18011884—21no—
39#18011884—21no—
40#18011883—21no—
41#18011876C2211yescharacteristic
42#18011876C2211yescharacteristic
43#18011873—21no—
44C4×C22⋊D149C2211yescharacteristic
45#18011871—21no—
46#18011840C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011834C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011831C2211yescharacteristic
51C22⋊#11924746C2211yescharacteristic
52#18011823C2211yescharacteristic
53#18011821C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C22×C8×C149C2211yescharacteristic
56C22⋊Q8×C149C2211yescharacteristic
57#121×C149C2211yescharacteristic
58#106×C149C2211yescharacteristic
59#103×C149C2211yescharacteristic
60#102×C149C2211yescharacteristic
61#14558736—22no—
62#14558736—22no—
63#14558736—41no—
64#14558736—41no—
65#14558735—22no—
66#14558735—41no—
67C2×Dic298—21no—
68C2×Dic298C2311yescharacteristic
69C2×Dic298C2311yescharacteristic
70Q8×D149—22no—
71Q8×D149—41no—
72C2×D596—21no—
73C2×D596—21no—
74C2×D596C2311yescharacteristic
75C2×D596C2311yescharacteristic
76C2×C22⋊D149—21no—
77C2×C22⋊D149—21no—
78C2×C22⋊D149—21no—
79C2×C22⋊D149—21no—
80C2×C22⋊D149—21no—
81C2×C22⋊D149D411yescharacteristic
82C22×Dic149—21no—
83C2×C4×D149—21no—
84C2×C4×D149—21no—
85C2×C4×D149—21no—
86C2×C4×D149C2311yescharacteristic
87Dic596D414yescomplemented
88#14558726—22no—
89#14558725—22no—
90#14558725—22no—
91#14558724—22no—
92#14558723—41no—
93D1192—22no—
94#14558721—41no—
95#14558719—22no—
96C2×#11924746C2311yescharacteristic
97C2×#11924746C2311yescharacteristic
98#14558715—21no—
99#14558715—21no—
100#14558715D411yescharacteristic
101C22⋊Dic149D411yescharacteristic
102#14558713—21no—
103#14558713—21no—
104#14558713—21no—
105#14558713—21no—
106#14558713D411yescharacteristic
107C4×Dic149—21no—
108C4×Dic149—21no—
109C4×Dic149C2311yescharacteristic
110C2×Q8×C149C2311yescharacteristic
111C2×D4×C149—21no—
112C2×D4×C149C2311yescharacteristic
113C22×C4×C149C2311yescharacteristic
114SD16×C149—22no—
115C2×C8×C149—22no—
116C2×C8×C149C2311yescharacteristic
117C2×C8×C149C2311yescharacteristic
118C4⋊C4×C149—21no—
119C4⋊C4×C149C2311yescharacteristic
120C4⋊C4×C149C2311yescharacteristic
121C22⋊C4×C149—21no—
122C22⋊C4×C149—21no—
123C22×D149—21no—
124C22×D149—21no—
125C22×D149C2×D411yescharacteristic
126Dic298—21no—
127Dic298—21no—
128Dic298—42no—
129Dic298C2×D412yes—
130Dic298C2×D412yes—
131D596—21no—
132D596—21no—
133D596—21no—
134D596—21no—
135D596—42no—
136D596—81no—
137C22⋊D149—41no—
138C22⋊D149—42no—
139C22⋊D149—42no—
140C22⋊D149—42no—
141C22⋊D149—42no—
142C22⋊D149—81no—
143C2×Dic149—21no—
144C2×Dic149—21no—
145C2×Dic149—42no—
146C2×Dic149C2×D411yescharacteristic
147C2×Dic149C2×D411yescharacteristic
148C2×Dic149C2×D411yescharacteristic
149C4×D149—21no—
150C4×D149—21no—
151C4×D149—42no—
152C4×D149—42no—
153C4×D149—42no—
154#11924746—21no—
155#11924746—21no—
156C23×C149—21no—
157C23×C149C2×D411yescharacteristic
158Q8×C149—21no—
159Q8×C149—21no—
160D4×C149—21no—
161D4×C149—21no—
162D4×C149—81no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—21no—
167C2×C4×C149—21no—
168C2×C4×C149C2×D411yescharacteristic
169C2×C4×C149C2411yescharacteristic
170C8×C149—21no—
171C8×C149C2×D412yes—
172C22×C149—21no—
173C22×C149—21no—
174C22×C149—21no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149C22×D411yescharacteristic
179C2×D149—21no—
180C2×D149—21no—
181C2×D149—21no—
182C2×D149—41no—
183C2×D149—41no—
184C2×D149—41no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C4×C149—21no—
189C4×C149—41no—
190C4×C149—41no—
191C4×C149—41no—
192C4×C149C22×D411yescharacteristic
193C4×C149H(5,𝔽2)11yescharacteristic
194Dic149—21no—
195Dic149—22no—
196Dic149—22no—
197Dic149—21no—
198Dic149—21no—
199C2×C149—41no—
200C2×C149—81no—
201C2×C149D4211yescharacteristic
202C2×C149#57511yescharacteristic
203C2×C149#57711yescharacteristic
204D149—41no—
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#465D14911yescharacteristic, complemented
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×SD16—1491no—
236C2×SD16C2×D14911yescharacteristic
237C2×D8—1491no—
238C2×D8—1491no—
239C2×M16—1491no—
240C22×C8C2×D14911yescharacteristic
241#127—2981no—
242#127—1491no—
243#124—2981no—
244#124—1491no—
245C22⋊Q8—2981no—
246C22⋊Q8C2×D14911yescharacteristic
247#121—2981no—
248#121—2981no—
249#121—2981no—
250#121—1491no—
251#121—1491no—
252#121C2×D14911yescharacteristic
253C4×Q8—1491no—
254C4×Q8—1491no—
255C4×D4—2981no—
256C4×D4—2981no—
257C4×D4—1491no—
258#106C2×D14911yescharacteristic
259C4⋊C8—1491no—
260#103—1491no—
261#103—1491no—
262#103C2×D14911yescharacteristic
263#102—1491no—
264#102—1491no—
265#102C2×D14911yescharacteristic
266C22⋊C8—1491no—
267C22⋊C8—1491no—
268#97—1491no—
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—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×D4C22×D14911yescharacteristic
293C22×C4—2981no—
294C22×C4—2981no—
295C22×C4—2981no—
296C22×C4—2981no—
297C22×C4—1491no—
298C22×C4C22×D14911yescharacteristic
299Q16—2982no—
300Q16—1494no—
301SD16—22no—
302SD16—2982no—
303SD16—2982no—
304SD16—2982no—
305SD16—5961no—
306D8—2982no—
307D8—5961no—
308M16—2982no—
309C2×C8—22no—
310C2×C8—1491no—
311C2×C8—1491no—
312C2×C8C22×D14911yescharacteristic
313C2×C8C22×D14911yescharacteristic
314C4⋊C4—21no—
315C4⋊C4—2981no—
316C4⋊C4—2981no—
317C4⋊C4—1491no—
318C4⋊C4C22×D14911yescharacteristic
319C4⋊C4C22×D14911yescharacteristic
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—
330C42—1491no—
331C23—21no—
332C23—2981no—
333C23—2981no—
334C23—1491no—
335C23D4×D14911yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—2981no—
339Q8—2981no—
340Q8—5962no—
341Q8—1492no—
342Q8—1492no—
343D4—21no—
344D4—21no—
345D4—81no—
346D4—2981no—
347D4—2981no—
348D4—2981no—
349D4—2981no—
350D4—5962no—
351D4—5961no—
352D4—5962no—
353D4—5962no—
354D4—5962no—
355D4—5962no—
356D4—11921no—
357D4—11921no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
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×C4—1491no—
374C2×C4D4×D14911yescharacteristic
375C2×C4C23×D14911yescharacteristic
376C8—21no—
377C8—2981no—
378C8—2981no—
379C8D4×D14912yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—2981no—
387C22—2981no—
388C22—2981no—
389C22—5961no—
390C22—5961no—
391C22—5961no—
392C22—5961no—
393C22—5961no—
394C22—5961no—
395C22C2×D4×D14911yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—2981no—
401C4—2981no—
402C4—2981no—
403C4—2982no—
404C4—2982no—
405C4C2×D4×D14911yescharacteristic
406C4#1801195711yescharacteristic
407C2—41no—
408C2—81no—
409C2—5961no—
410C2—11921no—
411C2—11921no—
412C2#2375025911yescharacteristic
413C2#2375042211yescharacteristic
414C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#465×C149C2
socleC22×C149C22×D4
hypercenter#465D149
hypocenterC149#3271
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#18011940C2semidirect
2. C2×#18011933C2semidirect
3. #23750293C2semidirect
4. #23750285C2semidirect
5. #23750011C2semidirect
6. #23749879C2semidirect
7. #23749850C2semidirect
8. #23749824C2semidirect
9. #23749785C2semidirect
10. #23749771C2semidirect
11. #23749768C2semidirect
12. #23749765C2semidirect
13. #23749731C2semidirect
14. #23749696C2semidirect
15. #465×C149C2semidirect
87. Dic596D4semidirect
207. C149#3271semidirect
215. #465D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119402
C2×#180119332
#237502932
#237502852
#237500112
#237498792
#237498502
#237498242
#237497852
#237497712
#237497682
#237497652
#237497312
#237496962
#465×C1492
#3271149