Finite Group Databasebeta

← #34054216

Subgroups — #34054216

Order 19072.

458 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011943C211yesmaximal, characteristic
2C2×Q16×D149C211yesmaximal, characteristic, complemented
3#23750200C211yesmaximal, characteristic
4#23750101C211yesmaximal, characteristic, complemented
5#23749850C211yesmaximal, characteristic, complemented
6#23749849C211yesmaximal, characteristic, complemented
7#23749848C211yesmaximal, characteristic, complemented
8#23749847C211yesmaximal, characteristic, complemented
9#23749834C211yesmaximal, characteristic, complemented
10#23749833C211yesmaximal, characteristic, complemented
11#23749832C211yesmaximal, characteristic, complemented
12#23749650C211yesmaximal, characteristic, complemented
13#23749632C211yesmaximal, characteristic, complemented
14#23749620C211yesmaximal, characteristic
15#462×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic
18C2×Q8×D149C2211yescharacteristic
19#18011943—24no—
20C2×Dic596C2211yescharacteristic
21C2×#14558726C2211yescharacteristic
22C2×#14558726C2211yescharacteristic
23C2×#14558726C2211yescharacteristic
24Q16×D149—24no—
25C2×#14558725C2211yescharacteristic
26C2×#14558723C2211yescharacteristic
27C2×#14558719C2211yescharacteristic
28C2×C8×D149C2211yescharacteristic
29#18011909C2211yescharacteristic
30#18011900C2211yescharacteristic
31#18011899C2211yescharacteristic
32#18011896—21no—
33#18011896—21no—
34#18011889—21no—
35#18011889—21no—
36Q8×Dic149C2211yescharacteristic
37C4×Dic298—21no—
38C4×Dic298C2211yescharacteristic
39#18011876—21no—
40#18011876C2211yescharacteristic
41#18011869—21no—
42#18011869C2211yescharacteristic
43#18011868—21no—
44#18011868C2211yescharacteristic
45C4⋊#11924746C2211yescharacteristic
46#18011840C2211yescharacteristic
47#18011840C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011835C2211yescharacteristic
50#18011835C2211yescharacteristic
51#18011834C2211yescharacteristic
52#18011833C2211yescharacteristic
53#18011831C2211yescharacteristic
54C2×Q16×C149C2211yescharacteristic
55C2×Q16×C149C2211yescharacteristic
56C4⋊Q8×C149C2211yescharacteristic
57C4×Q8×C149C2211yescharacteristic
58C4⋊C8×C149C2211yescharacteristic
59#103×C149C2211yescharacteristic
60#103×C149C2211yescharacteristic
61#14558737—22no—
62#14558737—22no—
63C2×Dic298—21no—
64C2×Dic298—21no—
65C2×Dic298C2311yescharacteristic
66C2×Dic298C2311yescharacteristic
67Q8×D149—22no—
68Q8×D149—22no—
69Q8×D149—22no—
70Q8×D149D414yes—
71C2×D596—21no—
72C2×D596C2311yescharacteristic
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76C2×C4×D149C2311yescharacteristic
77Dic596—22no—
78#14558726—22no—
79#14558726—22no—
80#14558726—22no—
81#14558725—22no—
82#14558723—22no—
83#14558719—22no—
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C8×D149—22no—
87C4⋊Dic149—21no—
88C4⋊Dic149C2311yescharacteristic
89#14558715—21no—
90#14558715—21no—
91#14558715—21no—
92#14558715—21no—
93#14558715D411yescharacteristic
94#14558715D411yescharacteristic
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713D411yescharacteristic
101#14558713D411yescharacteristic
102C4×Dic149—21no—
103C4×Dic149—21no—
104C4×Dic149—21no—
105C4×Dic149—21no—
106C4×Dic149C2311yescharacteristic
107C2×Q8×C149C2311yescharacteristic
108C2×Q8×C149C2311yescharacteristic
109C2×Q8×C149C2311yescharacteristic
110Q16×C149—22no—
111Q16×C149—22no—
112C2×C8×C149C2311yescharacteristic
113C2×C8×C149C2311yescharacteristic
114C4⋊C4×C149—21no—
115C4⋊C4×C149—21no—
116C4⋊C4×C149—21no—
117C4⋊C4×C149C2311yescharacteristic
118C42×C149—21no—
119C42×C149C2311yescharacteristic
120C22×D149—21no—
121C22×D149C2×D411yescharacteristic
122Dic298—21no—
123Dic298—24no—
124Dic298—21no—
125Dic298—21no—
126Dic298—42no—
127Dic298C2×D412yes—
128D596—21no—
129D596—21no—
130D596—42no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149—21no—
134C2×Dic149C2×D411yescharacteristic
135C2×Dic149C2×D411yescharacteristic
136C2×Dic149C2×D411yescharacteristic
137C4×D149—24no—
138C4×D149—42no—
139C4×D149—42no—
140C4×D149C2×D412yes—
141C4×D149#4112yes—
142#11924746—21no—
143#11924746—21no—
144Q8×C149—21no—
145Q8×C149—21no—
146Q8×C149—21no—
147Q8×C149—21no—
148Q8×C149—21no—
149Q8×C149C2×D412yes—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149C2×D411yescharacteristic
155C2×C4×C149C2×D411yescharacteristic
156C2×C4×C149C2411yescharacteristic
157C8×C149—21no—
158C8×C149—21no—
159C22×C149C22×D411yescharacteristic
160C2×D149—21no—
161C2×D149—21no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C2×D149#12112yes—
166C4×C149—22no—
167C4×C149—21no—
168C4×C149—21no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149—41no—
172C4×C149C22×D411yescharacteristic
173C4×C149C2×#4111yescharacteristic
174Dic149—22no—
175Dic149—21no—
176Dic149—21no—
177Dic149—41no—
178Dic149—41no—
179Dic149#12112yes—
180C2×C149C2×#12111yescharacteristic
181C2×C149#57811yescharacteristic
182C2×C149#57811yescharacteristic
183D149—22no—
184D149—81no—
185C149#304411yescharacteristic, complemented, Sylow
186#3044—1491nomaximal, Sylow
187C2×#137—1491no—
188C22×Q16—1491no—
189#536—1491no—
190#519—1491no—
191#464—1491no—
192#464—1491no—
193#464—1491no—
194#464—1491no—
195#462—1491no—
196#462—1491no—
197#462—1491no—
198#462D14911yescharacteristic, complemented
199#424—1491no—
200#419—1491no—
201#416—1491no—
202C2×#41—1491no—
203C22×Q8—1491no—
204C22×Q8—1491no—
205#137—2984no—
206C2×Q16—2984no—
207C2×Q16—1491no—
208C2×Q16—1491no—
209C2×Q16—1491no—
210C2×Q16—1491no—
211C2×Q16C2×D14911yescharacteristic
212C2×Q16C2×D14911yescharacteristic
213C2×SD16—1491no—
214C2×SD16—1491no—
215C2×M16—1491no—
216C22×C8—1491no—
217C4⋊Q8—1491no—
218C4⋊Q8C2×D14911yescharacteristic
219#124—1491no—
220#124—1491no—
221#123—2981no—
222#123—2981no—
223C22⋊Q8—2981no—
224C22⋊Q8—2981no—
225C4×Q8—2981no—
226C4×Q8—2981no—
227C4×Q8—1491no—
228C4×Q8—1491no—
229C4×Q8—1491no—
230C4×Q8C2×D14911yescharacteristic
231#117—2981no—
232#117—2981no—
233#117—1491no—
234#117—1491no—
235C4⋊C8—1491no—
236C4⋊C8—1491no—
237C4⋊C8—1491no—
238C4⋊C8C2×D14911yescharacteristic
239#103—1491no—
240#103—1491no—
241#103—1491no—
242#103—1491no—
243#103C2×D14911yescharacteristic
244#103C2×D14911yescharacteristic
245#102—1491no—
246#102—1491no—
247#41—2982no—
248#41—2982no—
249C2×Q8—2981no—
250C2×Q8—2981no—
251C2×Q8—2982no—
252C2×Q8—2982no—
253C2×Q8—2982no—
254C2×Q8—1494no—
255C2×Q8—1491no—
256C2×Q8—1491no—
257C2×Q8C22×D14911yescharacteristic
258C2×Q8C22×D14911yescharacteristic
259C2×Q8C22×D14911yescharacteristic
260C2×D4—2981no—
261C2×D4—1491no—
262C22×C4—2981no—
263C22×C4—2981no—
264C22×C4—2981no—
265C22×C4—1491no—
266Q16—22no—
267Q16—22no—
268Q16—2982no—
269Q16—2982no—
270Q16—2982no—
271Q16—2982no—
272SD16—2982no—
273SD16—2982no—
274M16—2982no—
275C2×C8—2982no—
276C2×C8—1491no—
277C2×C8—1491no—
278C2×C8C22×D14911yescharacteristic
279C2×C8C22×D14911yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—2981no—
286C4⋊C4—2981no—
287C4⋊C4—2981no—
288C4⋊C4—1491no—
289C4⋊C4—1491no—
290C4⋊C4—1491no—
291C4⋊C4C22×D14911yescharacteristic
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—1491no—
298C22⋊C4—1491no—
299C42—21no—
300C42—2981no—
301C42—2981no—
302C42—2981no—
303C42—2981no—
304C42—1491no—
305C42C22×D14911yescharacteristic
306C23—2981no—
307C23—1491no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—2984no—
314Q8—2981no—
315Q8—2981no—
316Q8—2981no—
317Q8—5962no—
318Q8—1492no—
319Q8D4×D14912yes—
320D4—2981no—
321D4—2981no—
322D4—5962no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—2984no—
328C2×C4—2981no—
329C2×C4—2981no—
330C2×C4—2981no—
331C2×C4—5962no—
332C2×C4—5962no—
333C2×C4—1491no—
334C2×C4—1491no—
335C2×C4—1491no—
336C2×C4—1492no—
337C2×C4—1492no—
338C2×C4D4×D14911yescharacteristic
339C2×C4D4×D14911yescharacteristic
340C2×C4C23×D14911yescharacteristic
341C8—21no—
342C8—21no—
343C8—2981no—
344C8—2981no—
345C22—2981no—
346C22—2981no—
347C22—5961no—
348C22—5961no—
349C22—5961no—
350C22—1492no—
351C22C2×D4×D14911yescharacteristic
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—2981no—
359C4—2981no—
360C4—2982no—
361C4—5961no—
362C4—5961no—
363C4—1492no—
364C4C2×D4×D14911yescharacteristic
365C4#41×D14911yescharacteristic
366C2—2982no—
367C2—11921no—
368C2#121×D14911yescharacteristic
369C2#2375043811yescharacteristic
370C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#462×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558737C22
hypercenter#462D149
hypocenterC149#3044
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. C2×Q16×D149C2semidirect
4. #23750101C2semidirect
5. #23749850C2semidirect
6. #23749849C2semidirect
7. #23749848C2semidirect
8. #23749847C2semidirect
9. #23749834C2semidirect
10. #23749833C2semidirect
11. #23749832C2semidirect
12. #23749650C2semidirect
13. #23749632C2semidirect
15. #462×C149C2semidirect
185. C149#3044semidirect
198. #462D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119432
C2×Q16×D1492
#237502002
#237501012
#237498502
#237498492
#237498482
#237498472
#237498342
#237498332
#237498322
#237496502
#237496322
#237496202
#462×C1492
#3044149