Finite Group Databasebeta

← #34054867

Subgroups — #34054867

Order 19072.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750160C211yesmaximal, characteristic
2C4×Q8×D149C211yesmaximal, characteristic, complemented
3#23749962C211yesmaximal, characteristic, complemented
4#23749945C211yesmaximal, characteristic
5#23749929C211yesmaximal, characteristic, complemented
6#23749848C211yesmaximal, characteristic, complemented
7#23749847C211yesmaximal, characteristic, complemented
8#23749782C211yesmaximal, characteristic, complemented
9#23749765C211yesmaximal, characteristic
10#23749731C211yesmaximal, characteristic, complemented
11#23749729C211yesmaximal, characteristic, complemented
12#23749728C211yesmaximal, characteristic, complemented
13#23749724C211yesmaximal, characteristic, complemented
14#23749681C211yesmaximal, characteristic, complemented
15#479×C149C211yesmaximal, characteristic, complemented
16C2×Q8×D149C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21#18011906—21no—
22#18011899C2211yescharacteristic
23#18011896—21no—
24#18011891C2211yescharacteristic
25#18011886C2211yescharacteristic
26Q8×Dic149C2211yescharacteristic
27C4×Dic298—21no—
28C4×Dic298C2211yescharacteristic
29#18011876—21no—
30#18011876C2211yescharacteristic
31#18011876C2211yescharacteristic
32#18011873—21no—
33#18011873C2211yescharacteristic
34#18011869—21no—
35C4⋊C4×D149—21no—
36C4⋊C4×D149C2211yescharacteristic
37C42×D149—21no—
38C42×D149C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011834C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic
51#18011821C2211yescharacteristic
52#125×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61C2×Dic298C2311yescharacteristic
62Q8×D149—22no—
63Q8×D149—22no—
64C2×D596—21no—
65C2×D596C2311yescharacteristic
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149D411yescharacteristic
70C2×C4×D149D411yescharacteristic
71C2×C4×D149C2311yescharacteristic
72Dic596—22no—
73#14558726—22no—
74#14558725—22no—
75#14558723—22no—
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C4⋊Dic149—21no—
79C4⋊Dic149—21no—
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90C4×Dic149—21no—
91C4×Dic149—21no—
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149D411yescharacteristic
95C4×Dic149D411yescharacteristic
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C4⋊C4×C149—21no—
101C4⋊C4×C149—21no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C42×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149C2×D411yescharacteristic
110Dic298—24no—
111Dic298—21no—
112Dic298—21no—
113Dic298—21no—
114Dic298#4112yes—
115D596—21no—
116D596—21no—
117D596—42no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C4×D149—24no—
125C4×D149—22no—
126C4×D149—21no—
127C4×D149—21no—
128C4×D149—41no—
129C4×D149—42no—
130C4×D149—42no—
131#11924746—21no—
132#11924746—21no—
133Q8×C149—21no—
134Q8×C149#4112yes—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2411yescharacteristic
142C8×C149—21no—
143C8×C149—21no—
144C22×C149C22×D411yescharacteristic
145C2×D149—21no—
146C2×D149—21no—
147C2×D149—41no—
148C2×D149—41no—
149C2×D149—41no—
150C2×D149#13712yes—
151C4×C149—22no—
152C4×C149—21no—
153C4×C149—21no—
154C4×C149—41no—
155C4×C149—41no—
156C4×C149—41no—
157C4×C149C2×#4111yescharacteristic
158C4×C149C2×#4111yescharacteristic
159Dic149—22no—
160Dic149—21no—
161Dic149—21no—
162Dic149—21no—
163Dic149—41no—
164Dic149—41no—
165C2×C149#52511yescharacteristic
166C2×C149C2×#13711yescharacteristic
167C2×C149#57511yescharacteristic
168D149—22no—
169D149—81no—
170C149#311711yescharacteristic, complemented, Sylow
171#3117—1491nomaximal, Sylow
172#529—1491no—
173C2×C4×Q8—1491no—
174#484—1491no—
175#481—1491no—
176#479—1491no—
177#479D14911yescharacteristic, complemented
178#464—1491no—
179#464—1491no—
180#451—1491no—
181#448—1491no—
182#441—1491no—
183#441—1491no—
184#440—1491no—
185#440—1491no—
186#432—1491no—
187C22×Q8—1491no—
188C2×Q16—1491no—
189C2×Q16—1491no—
190C2×SD16—1491no—
191C2×SD16—1491no—
192#126—2981no—
193#125C2×D14911yescharacteristic
194#124—1491no—
195#123—2981no—
196C22⋊Q8—1491no—
197#121—1491no—
198C4×Q8—2981no—
199C4×Q8—2981no—
200C4×Q8—1491no—
201C4×Q8—1491no—
202C4×Q8—1491no—
203C4×Q8—1491no—
204C4×Q8C2×D14911yescharacteristic
205C4×D4—2981no—
206C4×D4—1491no—
207#117—2981no—
208C2×C4⋊C4—2981no—
209C2×C4⋊C4—1491no—
210C2×C42—2981no—
211C2×C42—1491no—
212#107—1491no—
213#107C2×D14911yescharacteristic
214#106—1491no—
215#106C2×D14911yescharacteristic
216C4⋊C8—1491no—
217C4⋊C8C2×D14911yescharacteristic
218#103—1491no—
219#103—1491no—
220#103—1491no—
221#103—1491no—
222#103C2×D14911yescharacteristic
223#103C2×D14911yescharacteristic
224#102—1491no—
225#102—1491no—
226C22⋊C8—1491no—
227C22⋊C8—1491no—
228#97—1491no—
229#97—1491no—
230C2×Q8—2981no—
231C2×Q8—2982no—
232C2×Q8—2982no—
233C2×Q8—1491no—
234C2×Q8—1491no—
235C2×Q8C22×D14911yescharacteristic
236C2×D4—2981no—
237C2×D4—1491no—
238C22×C4—2981no—
239C22×C4—2981no—
240C22×C4—2981no—
241C22×C4—1491no—
242C22×C4—1491no—
243C22×C4—1491no—
244Q16—2982no—
245Q16—2982no—
246SD16—2982no—
247SD16—2982no—
248C2×C8—1491no—
249C2×C8—1491no—
250C2×C8C22×D14911yescharacteristic
251C2×C8C22×D14911yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—1491no—
262C4⋊C4C22×D14911yescharacteristic
263C4⋊C4C22×D14911yescharacteristic
264C4⋊C4C22×D14911yescharacteristic
265C22⋊C4—2981no—
266C22⋊C4—2981no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4—2981no—
270C42—21no—
271C42—2981no—
272C42—2981no—
273C42—2981no—
274C42—2981no—
275C42—1491no—
276C42—1491no—
277C42—1491no—
278C42C22×D14911yescharacteristic
279C23—2981no—
280C23—1491no—
281Q8—21no—
282Q8—2984no—
283Q8—2981no—
284Q8—2981no—
285Q8—2981no—
286Q8—1492no—
287Q8#1455873712yes—
288D4—2981no—
289D4—2981no—
290D4—5962no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—2984no—
296C2×C4—2982no—
297C2×C4—2981no—
298C2×C4—2981no—
299C2×C4—2981no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—5961no—
303C2×C4—5962no—
304C2×C4—5962no—
305C2×C4—1491no—
306C2×C4—1491no—
307C2×C4—1491no—
308C2×C4D4×D14911yescharacteristic
309C2×C4D4×D14911yescharacteristic
310C2×C4C23×D14911yescharacteristic
311C8—21no—
312C8—21no—
313C8—2981no—
314C8—2981no—
315C22—2981no—
316C22—2981no—
317C22—5961no—
318C22—5961no—
319C22—5961no—
320C22—1492no—
321C22C2×D4×D14911yescharacteristic
322C4—21no—
323C4—21no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—2981no—
329C4—2981no—
330C4—2982no—
331C4—2981no—
332C4—5961no—
333C4—5961no—
334C4#41×D14911yescharacteristic
335C4C2×#1455873711yescharacteristic
336C2—2982no—
337C2—11921no—
338C2#2375013811yescharacteristic
339C2#137×D14911yescharacteristic
340C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#479×C149C2
socleC22×C149C22×D4
prime radical#18011886C22
hypercenter#479D149
hypocenterC149#3117
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D149C2semidirect
3. #23749962C2semidirect
5. #23749929C2semidirect
6. #23749848C2semidirect
7. #23749847C2semidirect
8. #23749782C2semidirect
10. #23749731C2semidirect
11. #23749729C2semidirect
12. #23749728C2semidirect
13. #23749724C2semidirect
14. #23749681C2semidirect
15. #479×C149C2semidirect
170. C149#3117semidirect
177. #479D149semidirect

Maximal subgroups

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

subgroupindex
#237501602
C4×Q8×D1492
#237499622
#237499452
#237499292
#237498482
#237498472
#237497822
#237497652
#237497312
#237497292
#237497282
#237497242
#237496812
#479×C1492
#3117149