Finite Group Databasebeta

← #34056272

Subgroups — #34056272

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×#18011941C211yesmaximal, characteristic, complemented
2C2×#18011931C211yesmaximal, characteristic, complemented
3#23750284C211yesmaximal, characteristic, complemented
4#23750012C211yesmaximal, characteristic, complemented
5#23749876C211yesmaximal, characteristic, complemented
6#23749852C211yesmaximal, characteristic, complemented
7#23749847C211yesmaximal, characteristic, complemented
8#23749822C211yesmaximal, characteristic, complemented
9#23749787C211yesmaximal, characteristic, complemented
10#23749770C211yesmaximal, characteristic, complemented
11#23749768C211yesmaximal, characteristic, complemented
12#23749763C211yesmaximal, characteristic, complemented
13#23749730C211yesmaximal, characteristic, complemented
14#23749697C211yesmaximal, characteristic, complemented
15#550×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18#18011941—24no—
19#18011931—24no—
20C2×#14558726C2211yescharacteristic
21C2×#14558726C2211yescharacteristic
22C2×#14558724C2211yescharacteristic
23C2×#14558724C2211yescharacteristic
24C2×#14558724C2211yescharacteristic
25C2×#14558724C2211yescharacteristic
26C2×#14558723C2211yescharacteristic
27C2×#14558721C2211yescharacteristic
28C2×#14558721C2211yescharacteristic
29C2×#14558720C2211yescharacteristic
30C22×#11924746C2211yescharacteristic
31#18011899C2211yescharacteristic
32#18011897—21no—
33#18011890C2211yescharacteristic
34#18011889—21no—
35#18011885C2211yescharacteristic
36#18011883—21no—
37C4×Dic298C2211yescharacteristic
38#18011871—21no—
39#18011842C2211yescharacteristic
40C4⋊#11924746C2211yescharacteristic
41#18011835C2211yescharacteristic
42#18011834C2211yescharacteristic
43#18011834C2211yescharacteristic
44#18011832C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011831C2211yescharacteristic
47C22⋊#11924746C2211yescharacteristic
48C22⋊#11924746C2211yescharacteristic
49#18011822C2211yescharacteristic
50C2×#41×C149C2211yescharacteristic
51C2×#41×C149C2211yescharacteristic
52#127×C149—21no—
53#127×C149C2211yescharacteristic
54#121×C149—21no—
55#121×C149—21no—
56#121×C149C2211yescharacteristic
57#121×C149C2211yescharacteristic
58C4×Q8×C149C2211yescharacteristic
59C4×D4×C149—21no—
60C4×D4×C149C2211yescharacteristic
61#14558736—22no—
62#14558736—41no—
63C2×Dic298—22no—
64C2×Dic298—21no—
65C2×Dic298—41no—
66C2×Dic298C2311yescharacteristic
67C2×Dic298C2311yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C22×Dic149—21no—
72C2×C4×D149—21no—
73#14558726—22no—
74#14558726D414yescomplemented
75#14558724—22no—
76#14558724—22no—
77#14558724—22no—
78#14558724—41no—
79#14558723—22no—
80#14558721—22no—
81#14558721—41no—
82#14558720—22no—
83C2×#11924746—22no—
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C2×#11924746C2311yescharacteristic
87C2×#11924746C2311yescharacteristic
88C4⋊Dic149C2311yescharacteristic
89#14558715—21no—
90#14558715—21no—
91C22⋊Dic149—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95C4×Dic149—21no—
96#41×C149—22no—
97#41×C149—22no—
98#41×C149—41no—
99#41×C149—41no—
100C2×Q8×C149C2311yescharacteristic
101C2×D4×C149—21no—
102C2×D4×C149—21no—
103C2×D4×C149—21no—
104C2×D4×C149—21no—
105C2×D4×C149—21no—
106C2×D4×C149—21no—
107C2×D4×C149D411yescharacteristic
108C2×D4×C149C2311yescharacteristic
109C2×D4×C149C2311yescharacteristic
110C22×C4×C149—21no—
111C22×C4×C149—21no—
112C22×C4×C149C2311yescharacteristic
113C22×C4×C149C2311yescharacteristic
114C4⋊C4×C149—21no—
115C4⋊C4×C149D411yescharacteristic
116C4⋊C4×C149C2311yescharacteristic
117C22⋊C4×C149—21no—
118C22⋊C4×C149—21no—
119C22⋊C4×C149D411yescharacteristic
120C22⋊C4×C149D411yescharacteristic
121C42×C149—21no—
122C42×C149C2311yescharacteristic
123C22×D149—21no—
124Dic298—21no—
125Dic298—21no—
126Dic298—21no—
127Dic298—42no—
128Dic298C2×D412yes—
129D596—21no—
130D596—21no—
131C22⋊D149—42no—
132C22⋊D149—42no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—42no—
137C4×D149—42no—
138#11924746—21no—
139#11924746—21no—
140#11924746—21no—
141#11924746C2×D412yes—
142C23×C149—21no—
143C23×C149—21no—
144C23×C149C2×D411yescharacteristic
145C23×C149C2×D411yescharacteristic
146Q8×C149—21no—
147Q8×C149C2×D412yes—
148D4×C149—21no—
149D4×C149—21no—
150D4×C149—21no—
151D4×C149—21no—
152D4×C149—41no—
153D4×C149—42no—
154D4×C149—42no—
155D4×C149—42no—
156D4×C149—81no—
157D4×C149—81no—
158D4×C149—81no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—42no—
166C2×C4×C149—42no—
167C2×C4×C149C2×D411yescharacteristic
168C2×C4×C149C2×D411yescharacteristic
169C2×C4×C149C2×D411yescharacteristic
170C2×C4×C149C2×D411yescharacteristic
171C2×C4×C149C2411yescharacteristic
172C22×C149—21no—
173C22×C149—21no—
174C22×C149—21no—
175C22×C149—21no—
176C22×C149—21no—
177C22×C149—21no—
178C22×C149—41no—
179C22×C149—41no—
180C22×C149—41no—
181C22×C149—41no—
182C22×C149—41no—
183C22×C149—41no—
184C22×C149C22×D411yescharacteristic
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C4×C149—21no—
189C4×C149—21no—
190C4×C149—22no—
191C4×C149—21no—
192C4×C149—21no—
193C4×C149—41no—
194C4×C149C22×D411yescharacteristic
195C4×C149H(5,𝔽2)11yescharacteristic
196Dic149—22no—
197Dic149—41no—
198Dic149—41no—
199C2×C149—41no—
200C2×C149—41no—
201C2×C149—81no—
202C2×C149—81no—
203C2×C149D4211yescharacteristic
204C2×C149#57511yescharacteristic
205C2×C149#57711yescharacteristic
206D149—81no—
207C149#327111yescharacteristic, complemented, Sylow
208#3271—1491nomaximal, Sylow
209C2×#137—1491no—
210C2×#135—1491no—
211#550D14911yescharacteristic, complemented
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#435—1491no—
224C2×#41—1491no—
225C2×#41C2×D14911yescharacteristic
226C2×#41C2×D14911yescharacteristic
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×M16—1491no—
240C22×C8—1491no—
241#127—21no—
242#127C2×D14911yescharacteristic
243#124—2981no—
244#124—1491no—
245C22⋊Q8—2981no—
246C22⋊Q8—1491no—
247#121—21no—
248#121—21no—
249#121—2981no—
250#121—1491no—
251#121C2×D14911yescharacteristic
252#121C2×D14911yescharacteristic
253C4×Q8—1491no—
254C4×Q8C2×D14911yescharacteristic
255C4×D4—21no—
256C4×D4—2981no—
257C4×D4C2×D14911yescharacteristic
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#97—1491no—
269#41—22no—
270#41—22no—
271#41—41no—
272#41—41no—
273#41—2982no—
274#41—5961no—
275C2×Q8—2982no—
276C2×Q8—2981no—
277C2×Q8—5961no—
278C2×Q8—1491no—
279C2×Q8—1491no—
280C2×Q8C22×D14911yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—2981no—
288C2×D4—2981no—
289C2×D4—1491no—
290C2×D4C22⋊D14911yescharacteristic
291C2×D4C22×D14911yescharacteristic
292C2×D4C22×D14911yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
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—2982no—
309C2×C8—2982no—
310C2×C8—1491no—
311C2×C8—1491no—
312C2×C8—1491no—
313C2×C8—1491no—
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⋊C4C22⋊D14911yescharacteristic
327C22⋊C4C22⋊D14911yescharacteristic
328C42—21no—
329C42—2981no—
330C42C22×D14911yescharacteristic
331C23—21no—
332C23—21no—
333C23—2981no—
334C23C2×C22⋊D14911yescharacteristic
335C23C2×C22⋊D14911yescharacteristic
336Q8—21no—
337Q8—2981no—
338Q8—2981no—
339Q8—2981no—
340Q8—5962no—
341Q8—1492no—
342Q8D4×D14912yes—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—21no—
347D4—41no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—81no—
352D4—81no—
353D4—81no—
354D4—2981no—
355D4—2981no—
356D4—5962no—
357D4—5962no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—2981no—
367C2×C4—2981no—
368C2×C4—2981no—
369C2×C4—5962no—
370C2×C4—5962no—
371C2×C4C2×C22⋊D14911yescharacteristic
372C2×C4C2×C22⋊D14911yescharacteristic
373C2×C4C2×C22⋊D14911yescharacteristic
374C2×C4C2×C22⋊D14911yescharacteristic
375C2×C4C23×D14911yescharacteristic
376C8—2981no—
377C8—2981no—
378C8—2981no—
379C8—1492no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—5961no—
393C22—5961no—
394C22—5961no—
395C22C22×C22⋊D14911yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—22no—
401C4—41no—
402C4—2982no—
403C4—5961no—
404C4—5961no—
405C4C2×D4×D14911yescharacteristic
406C4#1801195611yescharacteristic
407C2—41no—
408C2—41no—
409C2—81no—
410C2—81no—
411C2—11921no—
412C2D4×C22⋊D14911yescharacteristic
413C2#2375042311yescharacteristic
414C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#550×C149C2
socleC22×C149C22×D4
hypercenter#550D149
hypocenterC149#3271
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#18011941C2semidirect
2. C2×#18011931C2semidirect
3. #23750284C2semidirect
4. #23750012C2semidirect
5. #23749876C2semidirect
6. #23749852C2semidirect
7. #23749847C2semidirect
8. #23749822C2semidirect
9. #23749787C2semidirect
10. #23749770C2semidirect
11. #23749768C2semidirect
12. #23749763C2semidirect
13. #23749730C2semidirect
14. #23749697C2semidirect
15. #550×C149C2semidirect
74. #14558726D4semidirect
207. C149#3271semidirect
211. #550D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119412
C2×#180119312
#237502842
#237500122
#237498762
#237498522
#237498472
#237498222
#237497872
#237497702
#237497682
#237497632
#237497302
#237496972
#550×C1492
#3271149