Finite Group Databasebeta

← #34056205

Subgroups — #34056205

Order 19072.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011940C211yesmaximal, characteristic, complemented
2C22×#14558724C211yesmaximal, characteristic, complemented
3#23750288C211yesmaximal, characteristic, complemented
4#23750269C211yesmaximal, characteristic
5#23750016C211yesmaximal, characteristic, complemented
6#23749870C211yesmaximal, characteristic, complemented
7#23749864C211yesmaximal, characteristic, complemented
8#23749846C211yesmaximal, characteristic, complemented
9#23749828C211yesmaximal, characteristic, complemented
10#23749788C211yesmaximal, characteristic, complemented
11#23749783C211yesmaximal, characteristic, complemented
12#23749762C211yesmaximal, characteristic, complemented
13#23749722C211yesmaximal, characteristic, complemented
14#23749693C211yesmaximal, characteristic, complemented
15#450×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18C2×Q8×D149C2211yescharacteristic, complemented
19#18011940—24no—
20C2×Dic596C2211yescharacteristic, complemented
21C2×Dic596C2211yescharacteristic, complemented
22C2×#14558726C2211yescharacteristic, complemented
23C2×#14558724—24no—
24C2×#14558724C2211yescharacteristic
25C2×#14558724C2211yescharacteristic
26C2×#14558724C2211yescharacteristic
27C2×#14558724C2211yescharacteristic
28C2×#14558719C2211yescharacteristic, complemented
29C22×#11924746C2211yescharacteristic
30#18011910—21no—
31#18011909C2211yescharacteristic, complemented
32#18011898C2211yescharacteristic
33#18011892—21no—
34#18011891C2211yescharacteristic, complemented
35#18011890C2211yescharacteristic
36#18011889—21no—
37#18011888—21no—
38#18011883—21no—
39#18011882C2211yescharacteristic
40#18011880—21no—
41#18011876C2211yescharacteristic, complemented
42D4×Dic149C2211yescharacteristic
43C4×C22⋊D149C2211yescharacteristic
44#18011871—21no—
45C2×C22⋊Dic149—21no—
46#18011844C2211yescharacteristic, complemented
47#18011840C2211yescharacteristic, complemented
48#18011836C2211yescharacteristic, complemented
49#18011836C2211yescharacteristic, complemented
50#18011835C2211yescharacteristic, complemented
51#18011834C2211yescharacteristic, complemented
52#18011823C2211yescharacteristic, complemented
53#18011821C2211yescharacteristic, complemented
54C22×D4×C149C2211yescharacteristic
55C2×SD16×C149C2211yescharacteristic
56C2×SD16×C149C2211yescharacteristic
57C22⋊Q8×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#102×C149C2211yescharacteristic
60C22⋊C8×C149C2211yescharacteristic
61#14558735—22no—
62#14558735—41no—
63C2×Dic298—21no—
64C2×Dic298—22no—
65C2×Dic298—21no—
66C2×Dic298—41no—
67C2×Dic298C2311yescharacteristic
68C2×Dic298C2311yescharacteristic
69C2×Dic298C2311yescharacteristic
70Q8×D149—22no—
71Q8×D149—41no—
72C2×C22⋊D149—21no—
73C2×C22⋊D149—21no—
74C2×C22⋊D149D411yescharacteristic
75C22×Dic149—21no—
76C22×Dic149—21no—
77C22×Dic149—21no—
78C2×C4×D149—21no—
79C2×C4×D149C2311yescharacteristic
80Dic596—22no—
81Dic596—41no—
82#14558726—22no—
83#14558724—22no—
84#14558724—22no—
85#14558724—22no—
86#14558724D414yescomplemented
87#14558719—22no—
88C2×#11924746—22no—
89C2×#11924746C2311yescharacteristic
90C2×#11924746C2311yescharacteristic
91C4⋊Dic149—21no—
92C4⋊Dic149C2311yescharacteristic
93#14558715—21no—
94#14558715—21no—
95#14558715—21no—
96#14558715—21no—
97#14558715D411yescharacteristic
98C22⋊Dic149—21no—
99C22⋊Dic149—21no—
100C22⋊Dic149—21no—
101C22⋊Dic149—21no—
102C22⋊Dic149—21no—
103C22⋊Dic149D411yescharacteristic
104#14558713—21no—
105#14558713D411yescharacteristic
106C4×Dic149—21no—
107C4×Dic149C2311yescharacteristic
108C24×C149—21no—
109C2×Q8×C149C2311yescharacteristic
110C2×D4×C149—22no—
111C2×D4×C149—21no—
112C2×D4×C149—41no—
113C2×D4×C149C2311yescharacteristic
114C2×D4×C149C2311yescharacteristic
115C22×C4×C149C2311yescharacteristic
116SD16×C149—22no—
117SD16×C149—41no—
118C2×C8×C149C2311yescharacteristic
119C2×C8×C149C2311yescharacteristic
120C4⋊C4×C149—21no—
121C4⋊C4×C149C2311yescharacteristic
122C22⋊C4×C149—21no—
123C22×D149C2×D411yescharacteristic
124Dic298—21no—
125Dic298—21no—
126Dic298—21no—
127Dic298—21no—
128Dic298—21no—
129Dic298—42no—
130Dic298—42no—
131Dic298C2×D412yes—
132C22⋊D149—22no—
133C22⋊D149—42no—
134C22⋊D149—81no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C2×Dic149—42no—
140C2×Dic149—42no—
141C2×Dic149—81no—
142C2×Dic149C2×D411yescharacteristic
143C2×Dic149C2×D411yescharacteristic
144C2×Dic149C2×D411yescharacteristic
145C4×D149—21no—
146C4×D149—21no—
147C4×D149—42no—
148#11924746—21no—
149#11924746C2×D412yes—
150C23×C149—21no—
151C23×C149—21no—
152C23×C149—42no—
153C23×C149—42no—
154C23×C149—81no—
155C23×C149C2×D411yescharacteristic
156Q8×C149—21no—
157Q8×C149—21no—
158D4×C149—21no—
159D4×C149—21no—
160D4×C149—21no—
161D4×C149—42no—
162D4×C149C2×D412yes—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—21no—
167C2×C4×C149C2×D411yescharacteristic
168C2×C4×C149C2411yescharacteristic
169C8×C149—21no—
170C8×C149—21no—
171C22×C149—21no—
172C22×C149—21no—
173C22×C149—22no—
174C22×C149—41no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149—41no—
179C22×C149—84no—
180C22×C149#13712yescomplemented
181C22×C149C22×D411yescharacteristic
182C2×D149—21no—
183C2×D149—21no—
184C2×D149—21no—
185C4×C149—21no—
186C4×C149—41no—
187C4×C149—41no—
188C4×C149C22×D411yescharacteristic
189C4×C149H(5,𝔽2)11yescharacteristic
190Dic149—21no—
191Dic149—22no—
192Dic149—21no—
193Dic149—21no—
194Dic149—41no—
195Dic149—41no—
196Dic149—41no—
197C2×C149—22no—
198C2×C149—42no—
199C2×C149—81no—
200C2×C149D4211yescharacteristic
201C2×C149C2×#13711yescharacteristic
202C2×C149#57711yescharacteristic
203D149—41no—
204C149#326611yescharacteristic, complemented, Sylow
205#3266—1491nomaximal, Sylow
206C2×#137—1491no—
207C22×SD16—1491no—
208D4×Q8—1491no—
209#546—1491no—
210#497—1491no—
211#468—1491no—
212#467—1491no—
213#464—1491no—
214#461—1491no—
215#452—1491no—
216#451—1491no—
217#450D14911yescharacteristic, complemented
218#448—1491no—
219#440—1491no—
220#435—1491no—
221C2×#41—1491no—
222C22×Q8—1491no—
223C22×Q8—1491no—
224C22×D4C2×D14911yescharacteristic
225#137—2984no—
226C2×Q16—1491no—
227C2×Q16—1491no—
228C2×Q16—1491no—
229C2×SD16—2984no—
230C2×SD16—1491no—
231C2×SD16—1491no—
232C2×SD16—1491no—
233C2×SD16—1491no—
234C2×SD16C2×D14911yescharacteristic
235C2×SD16C2×D14911yescharacteristic
236C2×M16—1491no—
237C22×C8—1491no—
238C4⋊Q8—2981no—
239C4⋊Q8—1491no—
240#124—1491no—
241#123—2981no—
242C22⋊Q8—2981no—
243C22⋊Q8—2981no—
244C22⋊Q8—1491no—
245C22⋊Q8—1491no—
246C22⋊Q8C2×D14911yescharacteristic
247#121—2981no—
248#121—1491no—
249#120—2981no—
250C4×Q8—1491no—
251C4×D4—2981no—
252C4×D4—1491no—
253C4×D4—1491no—
254C2×C22⋊C4—2981no—
255#107—1491no—
256C4⋊C8—1491no—
257#103—1491no—
258#103—1491no—
259#103—1491no—
260#103—1491no—
261#102C2×D14911yescharacteristic
262#102C2×D14911yescharacteristic
263C22⋊C8—1491no—
264C22⋊C8C2×D14911yescharacteristic
265#97—1491no—
266C24—21no—
267#41—2982no—
268#41—5961no—
269C2×Q8—2981no—
270C2×Q8—2982no—
271C2×Q8—2981no—
272C2×Q8—2982no—
273C2×Q8—5961no—
274C2×Q8—5961no—
275C2×Q8—1491no—
276C2×Q8—1491no—
277C2×Q8—1491no—
278C2×Q8C22×D14911yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—2981no—
283C2×D4—2981no—
284C2×D4—1491no—
285C2×D4C22×D14911yescharacteristic
286C2×D4C22×D14911yescharacteristic
287C22×C4—2981no—
288C22×C4—2981no—
289C22×C4—2981no—
290C22×C4—2981no—
291C22×C4—1491no—
292C22×C4C22×D14911yescharacteristic
293Q16—2982no—
294Q16—2982no—
295Q16—5961no—
296SD16—22no—
297SD16—41no—
298SD16—2982no—
299SD16—2982no—
300SD16—2982no—
301SD16—1494no—
302M16—2982no—
303C2×C8—2982no—
304C2×C8—1491no—
305C2×C8—1491no—
306C2×C8C22×D14911yescharacteristic
307C2×C8C22×D14911yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—2981no—
310C4⋊C4—2981no—
311C4⋊C4—2981no—
312C4⋊C4—2981no—
313C4⋊C4—2981no—
314C4⋊C4—1491no—
315C4⋊C4—1491no—
316C4⋊C4C22×D14911yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—2981no—
319C22⋊C4—2981no—
320C22⋊C4—2981no—
321C22⋊C4—2981no—
322C22⋊C4—2981no—
323C22⋊C4—2981no—
324C22⋊C4—1491no—
325C22⋊C4—1491no—
326C42—2981no—
327C42—1491no—
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—1491no—
334C23D4×D14911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—2981no—
338Q8—2981no—
339Q8—2981no—
340Q8—2981no—
341Q8—2981no—
342Q8—5962no—
343Q8—5962no—
344Q8—1492no—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—2982no—
350D4—5962no—
351D4—11921no—
352D4D4×D14912yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—2981no—
358C2×C4—2981no—
359C2×C4—2981no—
360C2×C4—2981no—
361C2×C4—2981no—
362C2×C4—2981no—
363C2×C4—5962no—
364C2×C4—5962no—
365C2×C4—5962no—
366C2×C4—1491no—
367C2×C4—1491no—
368C2×C4—1491no—
369C2×C4—11921no—
370C2×C4D4×D14911yescharacteristic
371C2×C4C23×D14911yescharacteristic
372C8—21no—
373C8—21no—
374C8—2981no—
375C8—1492no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—2981no—
386C22—2981no—
387C22—2981no—
388C22#1801194012yescomplemented
389C22C2×D4×D14911yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—2981no—
394C4—2981no—
395C4—2981no—
396C4—2982no—
397C4—5961no—
398C4—5961no—
399C4—5961no—
400C4C2×D4×D14911yescharacteristic
401C4#1801195611yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—5961no—
406C2#2375025711yescharacteristic
407C2C2×#1801194011yescharacteristic
408C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#450×C149C2
socleC22×C149C22×D4
prime radical#23750269C2
hypercenter#450D149
hypocenterC149#3266
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#18011940C2semidirect
2. C22×#14558724C2semidirect
3. #23750288C2semidirect
5. #23750016C2semidirect
6. #23749870C2semidirect
7. #23749864C2semidirect
8. #23749846C2semidirect
9. #23749828C2semidirect
10. #23749788C2semidirect
11. #23749783C2semidirect
12. #23749762C2semidirect
13. #23749722C2semidirect
14. #23749693C2semidirect
15. #450×C149C2semidirect
18. C2×Q8×D149C22semidirect
20. C2×Dic596C22semidirect
21. C2×Dic596C22semidirect
22. C2×#14558726C22semidirect
28. C2×#14558719C22semidirect
31. #18011909C22semidirect
34. #18011891C22semidirect
41. #18011876C22semidirect
46. #18011844C22semidirect
47. #18011840C22semidirect
48. #18011836C22semidirect
49. #18011836C22semidirect
50. #18011835C22semidirect
51. #18011834C22semidirect
52. #18011823C22semidirect
53. #18011821C22semidirect
86. #14558724D4semidirect
180. C22×C149#137semidirect
204. C149#3266semidirect
217. #450D149semidirect
388. C22#18011940semidirect

Maximal subgroups

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

subgroupindex
C2×#180119402
C22×#145587242
#237502882
#237502692
#237500162
#237498702
#237498642
#237498462
#237498282
#237497882
#237497832
#237497622
#237497222
#237496932
#450×C1492
#3266149