Finite Group Databasebeta

← #34056201

Subgroups — #34056201

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
2Q8×C22⋊D149C211yesmaximal, characteristic, complemented
3#23750269C211yesmaximal, characteristic
4#23750016C211yesmaximal, characteristic, complemented
5#23749868C211yesmaximal, characteristic, complemented
6#23749866C211yesmaximal, characteristic, complemented
7#23749845C211yesmaximal, characteristic, complemented
8#23749828C211yesmaximal, characteristic, complemented
9#23749784C211yesmaximal, characteristic, complemented
10#23749781C211yesmaximal, characteristic, complemented
11#23749776C211yesmaximal, characteristic, complemented
12#23749762C211yesmaximal, characteristic, complemented
13#23749726C211yesmaximal, characteristic, complemented
14#23749696C211yesmaximal, characteristic, complemented
15C22×SD16×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic, complemented
18#18011940—24no—
19C2×Dic596C2211yescharacteristic, complemented
20C2×#14558726C2211yescharacteristic, complemented
21C2×#14558726C2211yescharacteristic, complemented
22C2×#14558724C2211yescharacteristic
23C2×#14558724C2211yescharacteristic
24C2×#14558719C2211yescharacteristic, complemented
25#18011909—21no—
26#18011909C2211yescharacteristic, complemented
27#18011898C2211yescharacteristic
28#18011892—21no—
29#18011890—21no—
30#18011890C2211yescharacteristic
31#18011890C2211yescharacteristic
32#18011887—21no—
33#18011887C2211yescharacteristic, complemented
34#18011883—21no—
35#18011882C2211yescharacteristic
36#18011880—21no—
37Q8×Dic149C2211yescharacteristic, complemented
38D4×Dic149C2211yescharacteristic
39C4×C22⋊D149—21no—
40C4×C22⋊D149C2211yescharacteristic
41C2×C22⋊Dic149—21no—
42#18011845C2211yescharacteristic, complemented
43#18011840C2211yescharacteristic, complemented
44#18011836C2211yescharacteristic, complemented
45#18011836C2211yescharacteristic, complemented
46#18011835C2211yescharacteristic, complemented
47#18011835C2211yescharacteristic, complemented
48#18011832C2211yescharacteristic
49#18011832C2211yescharacteristic
50C22⋊#11924746C2211yescharacteristic
51#18011823C2211yescharacteristic, complemented
52#18011821C2211yescharacteristic, complemented
53C22×Q8×C149C2211yescharacteristic
54C22×D4×C149C2211yescharacteristic
55C2×SD16×C149—24no—
56C2×SD16×C149C2211yescharacteristic
57C2×SD16×C149C2211yescharacteristic
58C2×SD16×C149C2211yescharacteristic
59C2×SD16×C149C2211yescharacteristic
60C22×C8×C149C2211yescharacteristic
61#14558735—22no—
62#14558735—41no—
63C2×Dic298—21no—
64C2×Dic298C2311yescharacteristic
65C2×Dic298C2311yescharacteristic
66Q8×D149—22no—
67Q8×D149—41no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149D411yescharacteristic
71C22×Dic149—21no—
72C22×Dic149—21no—
73C2×C4×D149—21no—
74C2×C4×D149C2311yescharacteristic
75Dic596—22no—
76#14558726—22no—
77#14558726—41no—
78#14558724—22no—
79#14558724—41no—
80#14558719—22no—
81C2×#11924746C2311yescharacteristic
82C2×#11924746C2311yescharacteristic
83C4⋊Dic149—21no—
84C4⋊Dic149C2311yescharacteristic
85C4⋊Dic149C2311yescharacteristic
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89#14558715—21no—
90#14558715—21no—
91#14558715D411yescharacteristic
92C22⋊Dic149—21no—
93C22⋊Dic149—21no—
94C22⋊Dic149—21no—
95C22⋊Dic149—21no—
96C22⋊Dic149—21no—
97C22⋊Dic149—21no—
98C22⋊Dic149D411yescharacteristic
99#14558713—21no—
100#14558713D411yescharacteristic
101C4×Dic149—21no—
102C4×Dic149C2311yescharacteristic
103C24×C149—21no—
104C2×Q8×C149—21no—
105C2×Q8×C149—22no—
106C2×Q8×C149—41no—
107C2×Q8×C149C2311yescharacteristic
108C2×Q8×C149C2311yescharacteristic
109C2×D4×C149—22no—
110C2×D4×C149—21no—
111C2×D4×C149—41no—
112C2×D4×C149C2311yescharacteristic
113C2×D4×C149C2311yescharacteristic
114C22×C4×C149—21no—
115C22×C4×C149C2311yescharacteristic
116SD16×C149—22no—
117SD16×C149—22no—
118SD16×C149—22no—
119SD16×C149D414yescomplemented
120C2×C8×C149—22no—
121C2×C8×C149C2311yescharacteristic
122C2×C8×C149C2311yescharacteristic
123C22×D149C2×D411yescharacteristic
124Dic298—21no—
125Dic298—21no—
126Dic298—21no—
127Dic298—21no—
128Dic298—42no—
129C22⋊D149—22no—
130C22⋊D149—42no—
131C22⋊D149—81no—
132C2×Dic149—21no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—42no—
137C2×Dic149—81no—
138C2×Dic149C2×D411yescharacteristic
139C2×Dic149C2×D411yescharacteristic
140C2×Dic149C2×D411yescharacteristic
141C4×D149—21no—
142C4×D149—21no—
143C4×D149—42no—
144#11924746—21no—
145#11924746—21no—
146C23×C149—21no—
147C23×C149—21no—
148C23×C149—42no—
149C23×C149—42no—
150C23×C149—81no—
151C23×C149C2×D411yescharacteristic
152Q8×C149—21no—
153Q8×C149—21no—
154Q8×C149—21no—
155Q8×C149—42no—
156Q8×C149C2×D412yes—
157D4×C149—21no—
158D4×C149—21no—
159D4×C149—21no—
160D4×C149—42no—
161D4×C149C2×D412yes—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—42no—
167C2×C4×C149C2×D411yescharacteristic
168C2×C4×C149C2411yescharacteristic
169C8×C149—21no—
170C8×C149C2×D412yes—
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—22no—
187C4×C149—41no—
188C4×C149C22×D411yescharacteristic
189C4×C149H(5,𝔽2)11yescharacteristic
190Dic149—21no—
191Dic149—21no—
192Dic149—21no—
193Dic149—41no—
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×SD16D14911yescharacteristic, complemented
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#450—1491no—
218#448—1491no—
219#440—1491no—
220#435—1491no—
221C2×#41—1491no—
222C22×Q8—1491no—
223C22×Q8C2×D14911yescharacteristic
224C22×D4C2×D14911yescharacteristic
225#137—2984no—
226C2×Q16—1491no—
227C2×Q16—1491no—
228C2×Q16—1491no—
229C2×SD16—24no—
230C2×SD16—1491no—
231C2×SD16—1491no—
232C2×SD16C2×D14911yescharacteristic
233C2×SD16C2×D14911yescharacteristic
234C2×SD16C2×D14911yescharacteristic
235C2×SD16C2×D14911yescharacteristic
236C2×M16—1491no—
237C22×C8C2×D14911yescharacteristic
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⋊Q8—1491no—
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#102—1491no—
262#102—1491no—
263C22⋊C8—1491no—
264C22⋊C8—1491no—
265#97—1491no—
266C24—21no—
267#41—2982no—
268#41—5961no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—2981no—
273C2×Q8—2982no—
274C2×Q8—5961no—
275C2×Q8—1491no—
276C2×Q8—1491no—
277C2×Q8C22×D14911yescharacteristic
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—21no—
288C22×C4—2981no—
289C22×C4—2981no—
290C22×C4—2981no—
291C22×C4—1491no—
292C22×C4C22×D14911yescharacteristic
293Q16—2982no—
294Q16—2982no—
295Q16—5961no—
296SD16—22no—
297SD16—22no—
298SD16—22no—
299SD16—2982no—
300SD16—5961no—
301SD16C22⋊D14914yescomplemented
302M16—2982no—
303C2×C8—22no—
304C2×C8—1491no—
305C2×C8—1491no—
306C2×C8C22×D14911yescharacteristic
307C2×C8C22×D14911yescharacteristic
308C4⋊C4—2981no—
309C4⋊C4—2981no—
310C4⋊C4—2981no—
311C4⋊C4—2981no—
312C4⋊C4—2981no—
313C4⋊C4—2981no—
314C4⋊C4—1491no—
315C4⋊C4—1491no—
316C4⋊C4—1491no—
317C22⋊C4—2981no—
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—21no—
338Q8—42no—
339Q8—2981no—
340Q8—2981no—
341Q8—2981no—
342Q8—2981no—
343Q8—5962no—
344Q8C2×C22⋊D14912yes—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—2982no—
350D4—5962no—
351D4—11921no—
352D4C2×C22⋊D14912yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—2981no—
359C2×C4—2981no—
360C2×C4—2981no—
361C2×C4—2981no—
362C2×C4—2981no—
363C2×C4—2981no—
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—2981no—
374C8—2981no—
375C8C2×C22⋊D14912yes—
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—22no—
392C4—41no—
393C4—2981no—
394C4—2981no—
395C4—2981no—
396C4—5961no—
397C4—5961no—
398C4—5961no—
399C4—5961no—
400C4C22×C22⋊D14911yescharacteristic
401C4#1801195611yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—5961no—
406C2D4×C22⋊D14911yescharacteristic
407C2C2×#1801194011yescharacteristic
408C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC22×SD16×C149C2
socleC22×C149C22×D4
prime radical#23750269C2
hypercenterC22×SD16D149
hypocenterC149#3266
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#18011940C2semidirect
2. Q8×C22⋊D149C2semidirect
4. #23750016C2semidirect
5. #23749868C2semidirect
6. #23749866C2semidirect
7. #23749845C2semidirect
8. #23749828C2semidirect
9. #23749784C2semidirect
10. #23749781C2semidirect
11. #23749776C2semidirect
12. #23749762C2semidirect
13. #23749726C2semidirect
14. #23749696C2semidirect
15. C22×SD16×C149C2semidirect
17. C2×Q8×D149C22semidirect
19. C2×Dic596C22semidirect
20. C2×#14558726C22semidirect
21. C2×#14558726C22semidirect
24. C2×#14558719C22semidirect
26. #18011909C22semidirect
33. #18011887C22semidirect
37. Q8×Dic149C22semidirect
42. #18011845C22semidirect
43. #18011840C22semidirect
44. #18011836C22semidirect
45. #18011836C22semidirect
46. #18011835C22semidirect
47. #18011835C22semidirect
51. #18011823C22semidirect
52. #18011821C22semidirect
119. SD16×C149D4semidirect
180. C22×C149#137semidirect
204. C149#3266semidirect
207. C22×SD16D149semidirect
301. SD16C22⋊D149semidirect
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
Q8×C22⋊D1492
#237502692
#237500162
#237498682
#237498662
#237498452
#237498282
#237497842
#237497812
#237497762
#237497622
#237497262
#237496962
C22×SD16×C1492
#3266149