Finite Group Databasebeta

← #34055646

Subgroups — #34055646

Order 19072.

394 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
1#23750179C211yesmaximal, characteristic, complemented
2#23750174C211yesmaximal, characteristic
3#23750003C211yesmaximal, characteristic, complemented
4#23749996C211yesmaximal, characteristic, complemented
5#23749974C211yesmaximal, characteristic, complemented
6#23749970C211yesmaximal, characteristic, complemented
7#23749848C211yesmaximal, characteristic, complemented
8#23749847C211yesmaximal, characteristic, complemented
9#23749844C211yesmaximal, characteristic, complemented
10#23749790C211yesmaximal, characteristic, complemented
11#23749788C211yesmaximal, characteristic, complemented
12#23749786C211yesmaximal, characteristic, complemented
13#23749784C211yesmaximal, characteristic, complemented
14#23749677C211yesmaximal, characteristic, complemented
15#464×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C2×Dic596C2211yescharacteristic
19C2×#14558726C2211yescharacteristic
20C2×#14558726C2211yescharacteristic
21C2×#14558725C2211yescharacteristic
22C2×#14558724C2211yescharacteristic
23C2×#14558723C2211yescharacteristic
24#18011910C2211yescharacteristic
25#18011909C2211yescharacteristic
26#18011909C2211yescharacteristic
27#18011907C2211yescharacteristic
28#18011901—21no—
29#18011899C2211yescharacteristic
30#18011891C2211yescharacteristic
31#18011889—21no—
32#18011887C2211yescharacteristic
33#18011884—21no—
34#18011884—21no—
35C4×Dic298—21no—
36C4×Dic298C2211yescharacteristic
37#18011871—21no—
38#18011871—21no—
39#18011868—21no—
40C42×D149C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50C8×Dic149C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×Q16×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558737—41no—
60#14558737—41no—
61#14558735—41no—
62#14558735—41no—
63C2×Dic298—21no—
64C2×Dic298C2311yescharacteristic
65C2×Dic298C2311yescharacteristic
66C2×D596—21no—
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C22×Dic149—21no—
72C2×C4×D149—21no—
73C2×C4×D149D411yescharacteristic
74C2×C4×D149D411yescharacteristic
75C2×C4×D149C2311yescharacteristic
76Dic596—41no—
77#14558726—41no—
78#14558726—41no—
79#14558725—41no—
80#14558724—41no—
81#14558723—41no—
82C2×#11924746C2311yescharacteristic
83C2×#11924746C2311yescharacteristic
84C4⋊Dic149—21no—
85C4⋊Dic149C2311yescharacteristic
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89#14558715—21no—
90#14558715—21no—
91#14558715—21no—
92#14558715—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97C4×Dic149—21no—
98C4×Dic149D411yescharacteristic
99C4×Dic149D411yescharacteristic
100C4×Dic149C2311yescharacteristic
101C2×Q8×C149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103C2×D4×C149C2311yescharacteristic
104Q16×C149—41no—
105SD16×C149—41no—
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149—21no—
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C22⋊C4×C149—21no—
112C42×C149—21no—
113C42×C149C2311yescharacteristic
114C22×D149—21no—
115C22×D149C2×D411yescharacteristic
116Dic298—21no—
117Dic298—21no—
118Dic298—21no—
119Dic298—21no—
120Dic298—42no—
121D596—21no—
122D596—21no—
123D596—42no—
124C22⋊D149—42no—
125C22⋊D149—42no—
126C22⋊D149—42no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—42no—
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C2×Dic149C2×D411yescharacteristic
134C4×D149—21no—
135C4×D149—21no—
136C4×D149—22no—
137C4×D149—22no—
138C4×D149—42no—
139#11924746—21no—
140#11924746—21no—
141C23×C149—21no—
142Q8×C149—21no—
143Q8×C149—21no—
144Q8×C149—21no—
145Q8×C149—21no—
146D4×C149—21no—
147D4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2411yescharacteristic
154C8×C149—21no—
155C8×C149—21no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149C22×D411yescharacteristic
160C2×D149—21no—
161C2×D149—21no—
162C2×D149—21no—
163C2×D149—41no—
164C2×D149—41no—
165C2×D149—41no—
166C4×C149—21no—
167C4×C149—21no—
168C4×C149—41no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149H(5,𝔽2)11yescharacteristic
172C4×C149H(5,𝔽2)11yescharacteristic
173Dic149—21no—
174Dic149—41no—
175Dic149—41no—
176Dic149—41no—
177Dic149#13512yes—
178Dic149#13712yes—
179C2×C149—81no—
180C2×C149#53511yescharacteristic
181C2×C149C2×#13511yescharacteristic
182C2×C149C2×#13711yescharacteristic
183D149—41no—
184D149—81no—
185C149#321011yescharacteristic, complemented, Sylow
186#3210—1491nomaximal, Sylow
187#533—1491no—
188#532—1491no—
189#494—1491no—
190#492—1491no—
191#487—1491no—
192#486—1491no—
193#464—1491no—
194#464—1491no—
195#464—1491no—
196#464D14911yescharacteristic, complemented
197#452—1491no—
198#452—1491no—
199#452—1491no—
200#452—1491no—
201#431—1491no—
202C2×#41—1491no—
203C2×#41—1491no—
204C2×Q16—1491no—
205C2×Q16—1491no—
206C2×Q16—1491no—
207C2×Q16C2×D14911yescharacteristic
208C2×SD16—1491no—
209C2×SD16—1491no—
210C2×SD16—1491no—
211C2×SD16C2×D14911yescharacteristic
212C4⋊Q8—1491no—
213C4⋊Q8—1491no—
214C4⋊Q8—1491no—
215#127—1491no—
216#125—2981no—
217#124—1491no—
218#124C2×D14911yescharacteristic
219C22⋊Q8—2981no—
220C22⋊Q8—1491no—
221C22⋊Q8—1491no—
222#121—2981no—
223#121—2981no—
224C4×Q8—2981no—
225C4×Q8—1491no—
226C4×Q8C2×D14911yescharacteristic
227C4×D4—2981no—
228C4×D4—2981no—
229#117—2981no—
230C2×C42—1491no—
231C4⋊C8—1491no—
232C4⋊C8C2×D14911yescharacteristic
233#103—1491no—
234#103—1491no—
235#103—1491no—
236#103C2×D14911yescharacteristic
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102C2×D14911yescharacteristic
241C22⋊C8—1491no—
242C22⋊C8—1491no—
243C4×C8—1491no—
244C4×C8—1491no—
245#41—5961no—
246#41—5961no—
247#41—5961no—
248#41—5961no—
249C2×Q8—2981no—
250C2×Q8—1491no—
251C2×Q8—1491no—
252C2×Q8C22×D14911yescharacteristic
253C2×Q8C22×D14911yescharacteristic
254C2×D4—2981no—
255C2×D4—2981no—
256C2×D4—2981no—
257C2×D4—2981no—
258C2×D4—1491no—
259C2×D4C22×D14911yescharacteristic
260C22×C4—2981no—
261C22×C4—2981no—
262C22×C4—1491no—
263C22×C4—1491no—
264C22×C4—1491no—
265Q16—41no—
266Q16—5961no—
267Q16—5961no—
268Q16—5961no—
269SD16—41no—
270SD16—5961no—
271SD16—5961no—
272SD16—5961no—
273C2×C8—1491no—
274C2×C8—1491no—
275C2×C8C22×D14911yescharacteristic
276C2×C8C22×D14911yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—2981no—
279C4⋊C4—2981no—
280C4⋊C4—2981no—
281C4⋊C4—2981no—
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—2981no—
286C4⋊C4—1491no—
287C4⋊C4C22×D14911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C42—21no—
295C42—2981no—
296C42—1491no—
297C42—1491no—
298C42—1491no—
299C42C22×D14911yescharacteristic
300C23—21no—
301C23—2981no—
302C23—1491no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—2981no—
308Q8—2981no—
309Q8—2981no—
310Q8—2981no—
311Q8—5962no—
312D4—21no—
313D4—21no—
314D4—2981no—
315D4—2981no—
316D4—5962no—
317D4—5962no—
318D4—5962no—
319D4—5962no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—2982no—
324C2×C4—2982no—
325C2×C4—2981no—
326C2×C4—2981no—
327C2×C4—2981no—
328C2×C4—2981no—
329C2×C4—2981no—
330C2×C4—5962no—
331C2×C4—5962no—
332C2×C4—1491no—
333C2×C4—1491no—
334C2×C4—1491no—
335C2×C4D4×D14911yescharacteristic
336C2×C4D4×D14911yescharacteristic
337C2×C4C23×D14911yescharacteristic
338C8—21no—
339C8—21no—
340C8—2981no—
341C8—2981no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—2981no—
346C22—2981no—
347C22—2981no—
348C22—5961no—
349C22—5961no—
350C22—5961no—
351C22C2×D4×D14911yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—2981no—
358C4—5961no—
359C4—5961no—
360C4—5961no—
361C4—1492no—
362C4—1492no—
363C4#1801195611yescharacteristic
364C4#1801195711yescharacteristic
365C2—81no—
366C2—5961no—
367C2—11921no—
368C2#2375019111yescharacteristic
369C2#135×D14911yescharacteristic
370C2#137×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#464×C149C2
socleC22×C149C22×D4
prime radical#23750174C2
hypercenter#464D149
hypocenterC149#3210
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #23750179C2semidirect
3. #23750003C2semidirect
4. #23749996C2semidirect
5. #23749974C2semidirect
6. #23749970C2semidirect
7. #23749848C2semidirect
8. #23749847C2semidirect
9. #23749844C2semidirect
10. #23749790C2semidirect
11. #23749788C2semidirect
12. #23749786C2semidirect
13. #23749784C2semidirect
14. #23749677C2semidirect
15. #464×C149C2semidirect
185. C149#3210semidirect
196. #464D149semidirect

Maximal subgroups

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

subgroupindex
#237501792
#237501742
#237500032
#237499962
#237499742
#237499702
#237498482
#237498472
#237498442
#237497902
#237497882
#237497862
#237497842
#237496772
#464×C1492
#3210149