Finite Group Databasebeta

← #34056100

Subgroups — #34056100

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#23750247C211yesmaximal, characteristic, complemented
2#23750229C211yesmaximal, characteristic, complemented
3#23749932C211yesmaximal, characteristic, complemented
4#23749926C211yesmaximal, characteristic, complemented
5#23749913C211yesmaximal, characteristic, complemented
6#23749903C211yesmaximal, characteristic, complemented
7#23749877C211yesmaximal, characteristic, complemented
8#23749868C211yesmaximal, characteristic, complemented
9#23749860C211yesmaximal, characteristic, complemented
10#23749851C211yesmaximal, characteristic, complemented
11#23749842C211yesmaximal, characteristic, complemented
12#23749842C211yesmaximal, characteristic, complemented
13#23749817C211yesmaximal, characteristic, complemented
14#23749650C211yesmaximal, characteristic, complemented
15#460×C149C211yesmaximal, characteristic, complemented
16C2×#14558721C2211yescharacteristic
17C2×#14558721C2211yescharacteristic
18C2×#14558719C2211yescharacteristic
19C2×C8×D149C2211yescharacteristic
20#18011910C2211yescharacteristic
21#18011905—21no—
22#18011903C2211yescharacteristic
23#18011900C2211yescharacteristic
24#18011899—21no—
25#18011896—21no—
26#18011892—21no—
27#18011892—21no—
28#18011889—21no—
29#18011887C2211yescharacteristic
30#18011886C2211yescharacteristic
31#18011883—21no—
32#18011883—21no—
33#18011882C2211yescharacteristic
34#18011882C2211yescharacteristic
35C4×D596C2211yescharacteristic
36D4×Dic149C2211yescharacteristic
37D4×Dic149C2211yescharacteristic
38#18011868C2211yescharacteristic
39#18011845C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011842C2211yescharacteristic
43C4⋊#11924746C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011835C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011832C2211yescharacteristic
51#18011832C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54#127×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×D596—21no—
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C22×Dic149—21no—
65C22×Dic149—21no—
66C2×C4×D149—21no—
67C2×C4×D149C2311yescharacteristic
68#14558721—41no—
69#14558721—41no—
70#14558719—41no—
71C2×#11924746C2311yescharacteristic
72C2×#11924746C2311yescharacteristic
73C8×D149—41no—
74C4⋊Dic149C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715D411yescharacteristic
82#14558715D411yescharacteristic
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713D411yescharacteristic
93#14558713D411yescharacteristic
94C4×Dic149C2311yescharacteristic
95C2×Q8×C149C2311yescharacteristic
96C2×D4×C149—21no—
97C2×D4×C149—21no—
98C2×D4×C149C2311yescharacteristic
99C2×D4×C149C2311yescharacteristic
100SD16×C149—41no—
101SD16×C149—41no—
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C4⋊C4×C149—21no—
105C4⋊C4×C149C2311yescharacteristic
106C42×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149C2×D411yescharacteristic
110Dic298—81no—
111D596—21no—
112D596—21no—
113D596—81no—
114C22⋊D149—81no—
115C22⋊D149—81no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—81no—
120C2×Dic149—81no—
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C4×D149—21no—
125C4×D149—21no—
126C4×D149—81no—
127#11924746—21no—
128#11924746—21no—
129C23×C149—21no—
130C23×C149—21no—
131Q8×C149—21no—
132Q8×C149—21no—
133D4×C149—21no—
134D4×C149—21no—
135D4×C149—21no—
136D4×C149—21no—
137D4×C149—81no—
138D4×C149—81no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2411yescharacteristic
144C8×C149—21no—
145C8×C149—21no—
146C22×C149—41no—
147C22×C149—41no—
148C22×C149—41no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149C22×D411yescharacteristic
153C2×D149—21no—
154C2×D149—21no—
155C2×D149—21no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C4×C149—21no—
160C4×C149—21no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149H(5,𝔽2)11yescharacteristic
164C4×C1492−1+411yescharacteristic
165Dic149—21no—
166Dic149—21no—
167Dic149—21no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171C2×C149—81no—
172C2×C149—81no—
173C2×C149#53711yescharacteristic
174C2×C149#57611yescharacteristic
175C2×C149#57711yescharacteristic
176D149—41no—
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#460D14911yescharacteristic, complemented
193#459—1491no—
194#424—1491no—
195C2×SD16C2×D14911yescharacteristic
196C2×SD16C2×D14911yescharacteristic
197C2×D8—1491no—
198C2×D8—1491no—
199C2×M16—1491no—
200C22×C8—1491no—
201C4⋊Q8—1491no—
202#127C2×D14911yescharacteristic
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×Q8C2×D14911yescharacteristic
218C4×D4—1491no—
219C4×D4—1491no—
220C4×D4—1491no—
221#117—1491no—
222#107—1491no—
223#107—1491no—
224#106—1491no—
225#106—1491no—
226C4⋊C8—1491no—
227C4⋊C8—1491no—
228C4⋊C8—1491no—
229C4⋊C8C2×D14911yescharacteristic
230#103—1491no—
231#103—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102—1491no—
236#102C2×D14911yescharacteristic
237#102C2×D14911yescharacteristic
238C2×Q8—2981no—
239C2×Q8C22×D14911yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—2981no—
243C2×D4—2981no—
244C2×D4—2981no—
245C2×D4—1491no—
246C2×D4C22×D14911yescharacteristic
247C2×D4C22×D14911yescharacteristic
248C22×C4—2981no—
249C22×C4—2981no—
250C22×C4—2981no—
251C22×C4—1491no—
252SD16—41no—
253SD16—41no—
254D8—5961no—
255D8—5961no—
256M16—5961no—
257C2×C8—5961no—
258C2×C8—1491no—
259C2×C8—1491no—
260C2×C8C22×D14911yescharacteristic
261C2×C8C22×D14911yescharacteristic
262C4⋊C4—21no—
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⋊C4—1491no—
272C4⋊C4C22×D14911yescharacteristic
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⋊C4—1491no—
283C22⋊C4—1491no—
284C42—21no—
285C42—1491no—
286C42C22×D14911yescharacteristic
287C23—21no—
288C23—21no—
289C23—2981no—
290C23—1491no—
291Q8—21no—
292Q8—21no—
293Q8—11921no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—2981no—
301D4—2981no—
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—1491no—
313C2×C4—1491no—
314C2×C4—1491no—
315C2×C4—11921no—
316C2×C4—11921no—
317C2×C4—11921no—
318C2×C4D4×D14911yescharacteristic
319C2×C4D4×D14911yescharacteristic
320C2×C4C23×D14911yescharacteristic
321C8—21no—
322C8—21no—
323C8—2981no—
324C8—2981no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—2981no—
332C22—2981no—
333C22—2981no—
334C22—5961no—
335C22—5961no—
336C22—5961no—
337C22C2×D4×D14911yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—2981no—
343C4—2981no—
344C4—2981no—
345C4—5961no—
346C4—5961no—
347C4—5961no—
348C4#1801195611yescharacteristic
349C4#1801195811yescharacteristic
350C2—81no—
351C2—81no—
352C2—5961no—
353C2—11921no—
354C2#2375020411yescharacteristic
355C2#2375042911yescharacteristic
356C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#460×C149C2
socleC22×C149C22×D4
hypercenter#460D149
hypocenterC149#3257
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #23750247C2semidirect
2. #23750229C2semidirect
3. #23749932C2semidirect
4. #23749926C2semidirect
5. #23749913C2semidirect
6. #23749903C2semidirect
7. #23749877C2semidirect
8. #23749868C2semidirect
9. #23749860C2semidirect
10. #23749851C2semidirect
11. #23749842C2semidirect
12. #23749842C2semidirect
13. #23749817C2semidirect
14. #23749650C2semidirect
15. #460×C149C2semidirect
178. C149#3257semidirect
192. #460D149semidirect

Maximal subgroups

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

subgroupindex
#237502472
#237502292
#237499322
#237499262
#237499132
#237499032
#237498772
#237498682
#237498602
#237498512
#237498422
#237498172
#237496502
#460×C1492
#3257149