Finite Group Databasebeta

← #34056147

Subgroups — #34056147

Order 19072.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750246C211yesmaximal, characteristic, complemented
2#23749920C211yesmaximal, characteristic, complemented
3#23749917C211yesmaximal, characteristic, complemented
4#23749905C211yesmaximal, characteristic, complemented
5#23749902C211yesmaximal, characteristic, complemented
6#23749873C211yesmaximal, characteristic, complemented
7#23749869C211yesmaximal, characteristic, complemented
8#23749864C211yesmaximal, characteristic, complemented
9#23749859C211yesmaximal, characteristic
10#23749847C211yesmaximal, characteristic, complemented
11#23749844C211yesmaximal, characteristic, complemented
12#23749840C211yesmaximal, characteristic, complemented
13#23749837C211yesmaximal, characteristic, complemented
14#23749652C211yesmaximal, characteristic, complemented
15#542×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic
17C2×#14558724C2211yescharacteristic
18C2×#14558723C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×#14558720C2211yescharacteristic
21C22×#11924746C2211yescharacteristic
22#18011911C2211yescharacteristic
23#18011906—21no—
24#18011899C2211yescharacteristic
25#18011897—21no—
26#18011893—21no—
27#18011890C2211yescharacteristic
28#18011889—21no—
29#18011885C2211yescharacteristic
30C4×Dic298C2211yescharacteristic
31C4×D596C2211yescharacteristic
32#18011844C2211yescharacteristic
33#18011844C2211yescharacteristic
34#18011844C2211yescharacteristic
35#18011844C2211yescharacteristic
36C4⋊#11924746C2211yescharacteristic
37C4⋊#11924746C2211yescharacteristic
38C4⋊#11924746C2211yescharacteristic
39C4⋊#11924746C2211yescharacteristic
40#18011835C2211yescharacteristic
41#18011835C2211yescharacteristic
42#18011834C2211yescharacteristic
43#18011834C2211yescharacteristic
44#18011832C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48C4⋊Q8×C149C2211yescharacteristic
49#126×C149—21no—
50#124×C149—21no—
51#124×C149C2211yescharacteristic
52#123×C149—21no—
53C22⋊Q8×C149—21no—
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56C4×Q8×C149C2211yescharacteristic
57C4×D4×C149C2211yescharacteristic
58#117×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C4×D149—21no—
64#14558726—41no—
65#14558724—41no—
66#14558723—41no—
67#14558721—41no—
68#14558720—41no—
69C2×#11924746—41no—
70C2×#11924746C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C4⋊Dic149—21no—
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78#14558715—21no—
79C22⋊Dic149—21no—
80#14558713—21no—
81#14558713—21no—
82#14558713—21no—
83#14558713—21no—
84C4×Dic149—21no—
85C2×Q8×C149—21no—
86C2×Q8×C149C2311yescharacteristic
87C2×D4×C149—21no—
88C2×D4×C149C2311yescharacteristic
89C22×C4×C149—21no—
90C22×C4×C149C2311yescharacteristic
91C4⋊C4×C149—21no—
92C4⋊C4×C149—21no—
93C4⋊C4×C149—21no—
94C4⋊C4×C149D411yescharacteristic
95C4⋊C4×C149D411yescharacteristic
96C4⋊C4×C149C2311yescharacteristic
97C4⋊C4×C149C2311yescharacteristic
98C22⋊C4×C149—21no—
99C22⋊C4×C149—21no—
100C22⋊C4×C149—21no—
101C22⋊C4×C149—21no—
102C22⋊C4×C149—21no—
103C22⋊C4×C149D411yescharacteristic
104C22⋊C4×C149D411yescharacteristic
105C42×C149—21no—
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109Dic298—21no—
110Dic298—21no—
111Dic298—81no—
112D596—21no—
113D596—21no—
114C22⋊D149—81no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C4×D149—81no—
119#11924746—21no—
120#11924746—21no—
121#11924746—21no—
122#11924746—21no—
123C23×C149—21no—
124C23×C149C2×D411yescharacteristic
125Q8×C149—21no—
126Q8×C149—21no—
127Q8×C149—81no—
128D4×C149—21no—
129D4×C149—21no—
130D4×C149—81no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—81no—
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2411yescharacteristic
143C22×C149—21no—
144C22×C149—21no—
145C22×C149—21no—
146C22×C149—41no—
147C22×C149—41no—
148C22×C149—41no—
149C22×C149C22×D411yescharacteristic
150C2×D149—41no—
151C2×D149—41no—
152C2×D149—41no—
153C4×C149—21no—
154C4×C149—21no—
155C4×C149—21no—
156C4×C149—21no—
157C4×C149—21no—
158C4×C149—41no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149H(5,𝔽2)11yescharacteristic
162C4×C1492−1+411yescharacteristic
163Dic149—41no—
164Dic149—41no—
165Dic149—41no—
166C2×C149—41no—
167C2×C149—81no—
168C2×C149#53711yescharacteristic
169C2×C149#57611yescharacteristic
170C2×C149#57811yescharacteristic
171D149—81no—
172C149#326211yescharacteristic, complemented, Sylow
173#3262—1491nomaximal, Sylow
174#542—1491no—
175#542D14911yescharacteristic, complemented
176#477—1491no—
177#477—1491no—
178#474—1491no—
179#474—1491no—
180#468—1491no—
181#468—1491no—
182#467—1491no—
183#466—1491no—
184#464—1491no—
185#464—1491no—
186#463—1491no—
187#463—1491no—
188#424—1491no—
189C2×Q16—1491no—
190C2×SD16—1491no—
191C2×SD16—1491no—
192C2×D8—1491no—
193C2×M16—1491no—
194C22×C8—1491no—
195C4⋊Q8—1491no—
196C4⋊Q8C2×D14911yescharacteristic
197#126—21no—
198#126—2981no—
199#124—21no—
200#124—2981no—
201#124—1491no—
202#124C2×D14911yescharacteristic
203#123—21no—
204#123—2981no—
205C22⋊Q8—21no—
206C22⋊Q8—2981no—
207C22⋊Q8—1491no—
208C22⋊Q8C2×D14911yescharacteristic
209#121—1491no—
210#121C2×D14911yescharacteristic
211C4×Q8—1491no—
212C4×Q8C2×D14911yescharacteristic
213C4×D4—1491no—
214C4×D4C2×D14911yescharacteristic
215#117C2×D14911yescharacteristic
216#107—1491no—
217#107—1491no—
218#107—1491no—
219#107—1491no—
220C4⋊C8—1491no—
221C4⋊C8—1491no—
222C4⋊C8—1491no—
223C4⋊C8—1491no—
224#103—1491no—
225#103—1491no—
226#103—1491no—
227#103—1491no—
228#102—1491no—
229#102—1491no—
230#102—1491no—
231#102—1491no—
232C2×Q8—21no—
233C2×Q8—2981no—
234C2×Q8—1491no—
235C2×Q8C22×D14911yescharacteristic
236C2×D4—21no—
237C2×D4—2981no—
238C2×D4—1491no—
239C2×D4C22×D14911yescharacteristic
240C22×C4—21no—
241C22×C4—2981no—
242C22×C4C22×D14911yescharacteristic
243Q16—5961no—
244SD16—5961no—
245SD16—5961no—
246D8—5961no—
247M16—5961no—
248C2×C8—5961no—
249C2×C8—1491no—
250C2×C8—1491no—
251C2×C8—1491no—
252C2×C8—1491no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—1491no—
260C4⋊C4—1491no—
261C4⋊C4C22⋊D14911yescharacteristic
262C4⋊C4C22⋊D14911yescharacteristic
263C4⋊C4C22×D14911yescharacteristic
264C4⋊C4C22×D14911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4C22⋊D14911yescharacteristic
276C22⋊C4C22⋊D14911yescharacteristic
277C42—21no—
278C42—2981no—
279C42C22×D14911yescharacteristic
280C42C22×D14911yescharacteristic
281C23—21no—
282C23—2981no—
283C23C2×C22⋊D14911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—2981no—
288Q8—2981no—
289Q8—11921no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—2981no—
294D4—2981no—
295D4—11921no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—11921no—
306C2×C4C2×C22⋊D14911yescharacteristic
307C2×C4C2×C22⋊D14911yescharacteristic
308C2×C4C2×C22⋊D14911yescharacteristic
309C2×C4C2×C22⋊D14911yescharacteristic
310C2×C4C2×C22⋊D14911yescharacteristic
311C2×C4C23×D14911yescharacteristic
312C8—2981no—
313C8—2981no—
314C8—2981no—
315C8—2981no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—5961no—
323C22—5961no—
324C22—5961no—
325C22C22×C22⋊D14911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—5961no—
335C4—5961no—
336C4—5961no—
337C4#1801195711yescharacteristic
338C4#1801195811yescharacteristic
339C2—41no—
340C2—81no—
341C2—11921no—
342C2#2375020311yescharacteristic
343C2#2375042811yescharacteristic
344C2#2375044011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#542×C149C2
socleC22×C149C22×D4
prime radical#23749859C2
hypercenter#542D149
hypocenterC149#3262
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #23750246C2semidirect
2. #23749920C2semidirect
3. #23749917C2semidirect
4. #23749905C2semidirect
5. #23749902C2semidirect
6. #23749873C2semidirect
7. #23749869C2semidirect
8. #23749864C2semidirect
10. #23749847C2semidirect
11. #23749844C2semidirect
12. #23749840C2semidirect
13. #23749837C2semidirect
14. #23749652C2semidirect
15. #542×C149C2semidirect
172. C149#3262semidirect
175. #542D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237499202
#237499172
#237499052
#237499022
#237498732
#237498692
#237498642
#237498592
#237498472
#237498442
#237498402
#237498372
#237496522
#542×C1492
#3262149