Finite Group Databasebeta

← #34056104

Subgroups — #34056104

Order 19072.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750246C211yesmaximal, characteristic, complemented
2#23750230C211yesmaximal, characteristic, complemented
3#23749933C211yesmaximal, characteristic, complemented
4#23749926C211yesmaximal, characteristic, complemented
5#23749916C211yesmaximal, characteristic, complemented
6#23749906C211yesmaximal, characteristic, complemented
7#23749878C211yesmaximal, characteristic, complemented
8#23749871C211yesmaximal, characteristic, complemented
9#23749861C211yesmaximal, characteristic, complemented
10#23749854C211yesmaximal, characteristic, complemented
11#23749841C211yesmaximal, characteristic, complemented
12#23749841C211yesmaximal, characteristic, complemented
13#23749826C211yesmaximal, characteristic, complemented
14#23749821C211yesmaximal, characteristic, complemented
15#424×C149C211yesmaximal, characteristic, complemented
16C2×#14558725C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×D1192C2211yescharacteristic
19C2×D1192C2211yescharacteristic
20#18011911C2211yescharacteristic
21#18011908C2211yescharacteristic
22#18011906—21no—
23#18011903C2211yescharacteristic
24#18011899C2211yescharacteristic
25#18011897—21no—
26#18011896—21no—
27#18011896—21no—
28#18011893—21no—
29#18011890C2211yescharacteristic
30#18011889—21no—
31#18011885C2211yescharacteristic
32#18011885C2211yescharacteristic
33#18011885C2211yescharacteristic
34#18011884—21no—
35#18011884—21no—
36C4×Dic298C2211yescharacteristic
37C4×D596C2211yescharacteristic
38C4×D596C2211yescharacteristic
39C4×D596C2211yescharacteristic
40#18011845C2211yescharacteristic
41#18011845C2211yescharacteristic
42#18011843C2211yescharacteristic
43#18011843C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011833C2211yescharacteristic
52C2×M16×C149C2211yescharacteristic
53C22×C8×C149C2211yescharacteristic
54#117×C149C2211yescharacteristic
55C4⋊C8×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57C4⋊C8×C149C2211yescharacteristic
58C4⋊C8×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61C2×D596—21no—
62C2×D596—21no—
63C2×D596C2311yescharacteristic
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72#14558725—41no—
73#14558725—41no—
74D1192—41no—
75D1192—41no—
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85C22⋊Dic149—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94C4×Dic149—21no—
95C22×C4×C149C2311yescharacteristic
96M16×C149—41no—
97C2×C8×C149—41no—
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C4⋊C4×C149D411yescharacteristic
103C4⋊C4×C149D411yescharacteristic
104C22⋊C4×C149D411yescharacteristic
105C22⋊C4×C149D411yescharacteristic
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—21no—
110C22×D149—21no—
111Dic298—21no—
112Dic298—21no—
113Dic298—81no—
114D596—21no—
115D596—21no—
116D596—21no—
117D596—21no—
118D596—21no—
119D596—21no—
120D596—81no—
121D596—81no—
122C22⋊D149—81no—
123C22⋊D149—81no—
124C22⋊D149—81no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C4×D149—81no—
131C4×D149—81no—
132C4×D149—81no—
133C23×C149C2×D411yescharacteristic
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2411yescharacteristic
142C8×C149—21no—
143C8×C149—21no—
144C8×C149—21no—
145C8×C149—21no—
146C22×C149—21no—
147C22×C149—21no—
148C22×C149—21no—
149C22×C149C22×D411yescharacteristic
150C2×D149—41no—
151C2×D149—41no—
152C2×D149—41no—
153C2×D149—41no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C4×C149—21no—
160C4×C149—21no—
161C4×C149—21no—
162C4×C149—21no—
163C4×C149—21no—
164C4×C149H(5,𝔽2)11yescharacteristic
165C4×C1492−1+411yescharacteristic
166Dic149—41no—
167Dic149—41no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171C2×C149—41no—
172C2×C149#53711yescharacteristic
173C2×C149#57611yescharacteristic
174C2×C149#57711yescharacteristic
175D149—81no—
176D149—81no—
177D149—81no—
178C149#325711yescharacteristic, complemented, Sylow
179#3257—1491nomaximal, Sylow
180#542—1491no—
181#540—1491no—
182#479—1491no—
183#478—1491no—
184#476—1491no—
185#474—1491no—
186#469—1491no—
187#468—1491no—
188#466—1491no—
189#465—1491no—
190#463—1491no—
191#463—1491no—
192#460—1491no—
193#459—1491no—
194#424D14911yescharacteristic, complemented
195C2×SD16—1491no—
196C2×SD16—1491no—
197C2×D8—1491no—
198C2×D8—1491no—
199C2×M16C2×D14911yescharacteristic
200C22×C8C2×D14911yescharacteristic
201C4⋊Q8—1491no—
202#127—1491no—
203#126—2981no—
204#125—1491no—
205#124—2981no—
206#124—1491no—
207#123—2981no—
208#123—2981no—
209#123—2981no—
210C22⋊Q8—2981no—
211C22⋊Q8—1491no—
212#121—2981no—
213#121—2981no—
214#121—1491no—
215#121—1491no—
216#121—1491no—
217C4×Q8—1491no—
218C4×D4—1491no—
219C4×D4—1491no—
220C4×D4—1491no—
221#117C2×D14911yescharacteristic
222#107—1491no—
223#107—1491no—
224#106—1491no—
225#106—1491no—
226C4⋊C8C2×D14911yescharacteristic
227C4⋊C8C2×D14911yescharacteristic
228C4⋊C8C2×D14911yescharacteristic
229C4⋊C8C2×D14911yescharacteristic
230#103—1491no—
231#103—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102—1491no—
236#102—1491no—
237#102—1491no—
238C2×Q8—2981no—
239C2×Q8—1491no—
240C2×D4—2981no—
241C2×D4—2981no—
242C2×D4—2981no—
243C2×D4—2981no—
244C2×D4—2981no—
245C2×D4—1491no—
246C2×D4—1491no—
247C2×D4—1491no—
248C22×C4—2981no—
249C22×C4—2981no—
250C22×C4—2981no—
251C22×C4C22×D14911yescharacteristic
252SD16—5961no—
253SD16—5961no—
254D8—5961no—
255D8—5961no—
256M16—41no—
257C2×C8—41no—
258C2×C8C22×D14911yescharacteristic
259C2×C8C22×D14911yescharacteristic
260C2×C8C22×D14911yescharacteristic
261C2×C8C22×D14911yescharacteristic
262C4⋊C4—2981no—
263C4⋊C4—2981no—
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—1491no—
268C4⋊C4—1491no—
269C4⋊C4—1491no—
270C4⋊C4—1491no—
271C4⋊C4D59611yescharacteristic
272C4⋊C4D59611yescharacteristic
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4D59611yescharacteristic
283C22⋊C4D59611yescharacteristic
284C42—2981no—
285C42C22×D14911yescharacteristic
286C42C22×D14911yescharacteristic
287C23—2981no—
288C23—2981no—
289C23—2981no—
290C23C2×D59611yescharacteristic
291Q8—2981no—
292Q8—2981no—
293Q8—11921no—
294D4—2981no—
295D4—2981no—
296D4—2981no—
297D4—2981no—
298D4—2981no—
299D4—2981no—
300D4—11921no—
301D4—11921no—
302D4—11921no—
303D4—11921no—
304D4—11921no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—2981no—
308C2×C4—2981no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—11921no—
313C2×C4—11921no—
314C2×C4—11921no—
315C2×C4C2×D59611yescharacteristic
316C2×C4C2×D59611yescharacteristic
317C2×C4C2×D59611yescharacteristic
318C2×C4C2×D59611yescharacteristic
319C2×C4C2×D59611yescharacteristic
320C2×C4C23×D14911yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—5961no—
329C22—5961no—
330C22—5961no—
331C22—5961no—
332C22—5961no—
333C22—5961no—
334C22—5961no—
335C22—5961no—
336C22—5961no—
337C22C22×D59611yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—5961no—
344C4—5961no—
345C4—5961no—
346C4—5961no—
347C4—5961no—
348C4#1801195611yescharacteristic
349C4#1801195911yescharacteristic
350C2—41no—
351C2—11921no—
352C2—11921no—
353C2—11921no—
354C2#2375020611yescharacteristic
355C2#2375043011yescharacteristic
356C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#424×C149C2
socleC22×C149C22×D4
hypercenter#424D149
hypocenterC149#3257
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #23750246C2semidirect
2. #23750230C2semidirect
3. #23749933C2semidirect
4. #23749926C2semidirect
5. #23749916C2semidirect
6. #23749906C2semidirect
7. #23749878C2semidirect
8. #23749871C2semidirect
9. #23749861C2semidirect
10. #23749854C2semidirect
11. #23749841C2semidirect
12. #23749841C2semidirect
13. #23749826C2semidirect
14. #23749821C2semidirect
15. #424×C149C2semidirect
178. C149#3257semidirect
194. #424D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237502302
#237499332
#237499262
#237499162
#237499062
#237498782
#237498712
#237498612
#237498542
#237498412
#237498262
#237498212
#424×C1492
#3257149