Finite Group Databasebeta

← #34056096

Subgroups — #34056096

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#23749929C211yesmaximal, characteristic, complemented
3#23749922C211yesmaximal, characteristic, complemented
4#23749915C211yesmaximal, characteristic, complemented
5#23749905C211yesmaximal, characteristic, complemented
6#23749876C211yesmaximal, characteristic, complemented
7#23749869C211yesmaximal, characteristic, complemented
8#23749859C211yesmaximal, characteristic, complemented
9#23749852C211yesmaximal, characteristic, complemented
10#23749840C211yesmaximal, characteristic, complemented
11#23749840C211yesmaximal, characteristic, complemented
12#23749822C211yesmaximal, characteristic, complemented
13#23749817C211yesmaximal, characteristic, complemented
14#23749652C211yesmaximal, characteristic, complemented
15#540×C149C211yesmaximal, characteristic, complemented
16C2×#14558724C2211yescharacteristic
17C2×#14558724C2211yescharacteristic
18C2×#14558721C2211yescharacteristic
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#18011842C2211yescharacteristic
35#18011842C2211yescharacteristic
36C4⋊#11924746C2211yescharacteristic
37C4⋊#11924746C2211yescharacteristic
38C4⋊#11924746C2211yescharacteristic
39C4⋊#11924746C2211yescharacteristic
40#18011834C2211yescharacteristic
41#18011834C2211yescharacteristic
42#18011832C2211yescharacteristic
43#18011832C2211yescharacteristic
44#18011832C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#127×C149C2211yescharacteristic
49#125×C149C2211yescharacteristic
50#123×C149—21no—
51#123×C149—21no—
52#121×C149—21no—
53#121×C149—21no—
54#121×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56C4×D4×C149C2211yescharacteristic
57C4×D4×C149C2211yescharacteristic
58#117×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C4×D149—21no—
64#14558724—41no—
65#14558724—41no—
66#14558721—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×D4×C149—21no—
86C2×D4×C149—21no—
87C2×D4×C149—21no—
88C2×D4×C149—21no—
89C2×D4×C149C2311yescharacteristic
90C2×D4×C149C2311yescharacteristic
91C22×C4×C149—21no—
92C22×C4×C149—21no—
93C22×C4×C149C2311yescharacteristic
94C4⋊C4×C149—21no—
95C4⋊C4×C149—21no—
96C4⋊C4×C149D411yescharacteristic
97C4⋊C4×C149D411yescharacteristic
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C22⋊C4×C149—21no—
101C22⋊C4×C149—21no—
102C22⋊C4×C149—21no—
103C22⋊C4×C149—21no—
104C22⋊C4×C149D411yescharacteristic
105C22⋊C4×C149D411yescharacteristic
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×C149—21no—
125C23×C149C2×D411yescharacteristic
126D4×C149—21no—
127D4×C149—21no—
128D4×C149—21no—
129D4×C149—21no—
130D4×C149—81no—
131D4×C149—81no—
132D4×C149—81no—
133D4×C149—81no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—81no—
139C2×C4×C149—81no—
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C22×C149—21no—
147C22×C149—21no—
148C22×C149—21no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149C22×D411yescharacteristic
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×C149—41no—
165C4×C149—41no—
166C4×C149H(5,𝔽2)11yescharacteristic
167C4×C1492−1+411yescharacteristic
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171C2×C149—41no—
172C2×C149—81no—
173C2×C149—81no—
174C2×C149#53711yescharacteristic
175C2×C149#57611yescharacteristic
176C2×C149#57711yescharacteristic
177D149—81no—
178C149#325711yescharacteristic, complemented, Sylow
179#3257—1491nomaximal, Sylow
180#542—1491no—
181#540D14911yescharacteristic, complemented
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#424—1491no—
195C2×SD16—1491no—
196C2×SD16—1491no—
197C2×D8—1491no—
198C2×D8—1491no—
199C2×M16—1491no—
200C22×C8—1491no—
201C4⋊Q8—1491no—
202#127C2×D14911yescharacteristic
203#126—2981no—
204#125C2×D14911yescharacteristic
205#124—2981no—
206#124—1491no—
207#123—21no—
208#123—21no—
209#123—2981no—
210C22⋊Q8—2981no—
211C22⋊Q8—1491no—
212#121—21no—
213#121—21no—
214#121—1491no—
215#121C2×D14911yescharacteristic
216#121C2×D14911yescharacteristic
217C4×Q8—1491no—
218C4×D4—1491no—
219C4×D4C2×D14911yescharacteristic
220C4×D4C2×D14911yescharacteristic
221#117C2×D14911yescharacteristic
222#107—1491no—
223#107—1491no—
224#106—1491no—
225#106—1491no—
226C4⋊C8—1491no—
227C4⋊C8—1491no—
228C4⋊C8—1491no—
229C4⋊C8—1491no—
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—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—2981no—
245C2×D4—1491no—
246C2×D4C22×D14911yescharacteristic
247C2×D4C22×D14911yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—2981no—
251C22×C4C22×D14911yescharacteristic
252SD16—5961no—
253SD16—5961no—
254D8—5961no—
255D8—5961no—
256M16—5961no—
257C2×C8—5961no—
258C2×C8—1491no—
259C2×C8—1491no—
260C2×C8—1491no—
261C2×C8—1491no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—1491no—
268C4⋊C4—1491no—
269C4⋊C4C22⋊D14911yescharacteristic
270C4⋊C4C22⋊D14911yescharacteristic
271C4⋊C4C22×D14911yescharacteristic
272C4⋊C4C22×D14911yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4C22⋊D14911yescharacteristic
283C22⋊C4C22⋊D14911yescharacteristic
284C42—2981no—
285C42C22×D14911yescharacteristic
286C42C22×D14911yescharacteristic
287C23—21no—
288C23—21no—
289C23—2981no—
290C23C2×C22⋊D14911yescharacteristic
291Q8—2981no—
292Q8—2981no—
293Q8—11921no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—2981no—
303D4—2981no—
304D4—11921no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—11921no—
315C2×C4C2×C22⋊D14911yescharacteristic
316C2×C4C2×C22⋊D14911yescharacteristic
317C2×C4C2×C22⋊D14911yescharacteristic
318C2×C4C2×C22⋊D14911yescharacteristic
319C2×C4C2×C22⋊D14911yescharacteristic
320C2×C4C23×D14911yescharacteristic
321C8—2981no—
322C8—2981no—
323C8—2981no—
324C8—2981no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—5961no—
335C22—5961no—
336C22—5961no—
337C22C22×C22⋊D14911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—5961no—
346C4—5961no—
347C4—5961no—
348C4#1801195711yescharacteristic
349C4#1801195811yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—11921no—
354C2#2375020311yescharacteristic
355C2#2375042811yescharacteristic
356C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#540×C149C2
socleC22×C149C22×D4
hypercenter#540D149
hypocenterC149#3257
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #23750246C2semidirect
2. #23749929C2semidirect
3. #23749922C2semidirect
4. #23749915C2semidirect
5. #23749905C2semidirect
6. #23749876C2semidirect
7. #23749869C2semidirect
8. #23749859C2semidirect
9. #23749852C2semidirect
10. #23749840C2semidirect
11. #23749840C2semidirect
12. #23749822C2semidirect
13. #23749817C2semidirect
14. #23749652C2semidirect
15. #540×C149C2semidirect
178. C149#3257semidirect
181. #540D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237499292
#237499222
#237499152
#237499052
#237498762
#237498692
#237498592
#237498522
#237498402
#237498222
#237498172
#237496522
#540×C1492
#3257149