Finite Group Databasebeta

← #34054883

Subgroups — #34054883

Order 19072.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750228C211yesmaximal, characteristic, complemented
2#23750108C211yesmaximal, characteristic, complemented
3#23749941C211yesmaximal, characteristic, complemented
4#23749939C211yesmaximal, characteristic, complemented
5#23749934C211yesmaximal, characteristic, complemented
6#23749923C211yesmaximal, characteristic, complemented
7#23749823C211yesmaximal, characteristic, complemented
8#23749818C211yesmaximal, characteristic, complemented
9#23749770C211yesmaximal, characteristic, complemented
10#23749734C211yesmaximal, characteristic, complemented
11#23749726C211yesmaximal, characteristic, complemented
12#23749710C211yesmaximal, characteristic, complemented
13D8×Dic149C211yesmaximal, characteristic, complemented
14#23749683C211yesmaximal, characteristic, complemented
15#449×C149C211yesmaximal, characteristic, complemented
16C2×#14558723C2211yescharacteristic
17C2×#14558721C2211yescharacteristic
18#18011907C2211yescharacteristic
19#18011902C2211yescharacteristic
20#18011895—21no—
21#18011893—21no—
22#18011885C2211yescharacteristic
23#18011883—21no—
24#18011882—21no—
25Q8×Dic149C2211yescharacteristic
26Q8×Dic149C2211yescharacteristic
27D4×Dic149—21no—
28D4×Dic149—21no—
29D4×Dic149C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31D4×Dic149C2211yescharacteristic
32#18011873C2211yescharacteristic
33#18011870—21no—
34#18011870C2211yescharacteristic
35C2×C4⋊Dic149—21no—
36C2×C4⋊Dic149C2211yescharacteristic
37#18011845C2211yescharacteristic
38#18011845C2211yescharacteristic
39#18011842C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C2×D8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59C2×D596C2311yescharacteristic
60C2×C22⋊D149—21no—
61C2×C22⋊D149—21no—
62C2×C22⋊D149—21no—
63C22×Dic149—21no—
64C22×Dic149—21no—
65C22×Dic149—21no—
66C22×Dic149—21no—
67C2×C4×D149—21no—
68#14558723—22no—
69#14558721—22no—
70C2×#11924746C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C4⋊Dic149—21no—
73C4⋊Dic149—21no—
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149D411yescharacteristic
77C4⋊Dic149D411yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149D411yescharacteristic
86C22⋊Dic149D411yescharacteristic
87#14558713—21no—
88#14558713—21no—
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149C2311yescharacteristic
92C4×Dic149C2311yescharacteristic
93#41×C149—22no—
94#41×C149—22no—
95C2×Q8×C149C2311yescharacteristic
96C2×D4×C149—21no—
97C2×D4×C149—21no—
98C2×D4×C149C2311yescharacteristic
99C2×D4×C149C2311yescharacteristic
100C22×C4×C149—21no—
101C22×C4×C149C2311yescharacteristic
102SD16×C149—22no—
103D8×C149—22no—
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C4⋊C4×C149C2311yescharacteristic
107C22⋊C4×C149—21no—
108C22×D149—21no—
109D596—21no—
110D596—21no—
111C22⋊D149—81no—
112C22⋊D149—81no—
113C22⋊D149—81no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—81no—
118C2×Dic149—81no—
119C2×Dic149—81no—
120C2×Dic149—81no—
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C4×D149—81no—
126#11924746—21no—
127#11924746—21no—
128C23×C149—21no—
129C23×C149—21no—
130C23×C149C2×D411yescharacteristic
131Q8×C149—21no—
132Q8×C149#4112yes—
133D4×C149—24no—
134D4×C149—21no—
135D4×C149—21no—
136D4×C149—21no—
137D4×C149—81no—
138D4×C149#4112yes—
139C2×C4×C149—24no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—21no—
147C8×C149—21no—
148C22×C149—21no—
149C22×C149—22no—
150C22×C149—21no—
151C22×C149—21no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149C22×D411yescharacteristic
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C4×C149—21no—
162C4×C149—22no—
163C4×C149—41no—
164C4×C149C2×#4111yescharacteristic
165C4×C149C2×#4111yescharacteristic
166Dic149—21no—
167Dic149—21no—
168Dic149—21no—
169Dic149—21no—
170Dic149—41no—
171Dic149—41no—
172Dic149—41no—
173C2×C149—41no—
174C2×C149—42no—
175C2×C149—81no—
176C2×C149#52511yescharacteristic
177C2×C149#57611yescharacteristic
178C2×C149#57711yescharacteristic
179D149—81no—
180C149#311911yescharacteristic, complemented, Sylow
181#3119—1491nomaximal, Sylow
182#540—1491no—
183#520—1491no—
184#481—1491no—
185#480—1491no—
186#479—1491no—
187#478—1491no—
188#460—1491no—
189#459—1491no—
190#449—1491no—
191#449D14911yescharacteristic, complemented
192#442—1491no—
193#440—1491no—
194C4×SD16—1491no—
195C4×D8—1491no—
196#433—1491no—
197C2×#41C2×D14911yescharacteristic
198C2×SD16—1491no—
199C2×SD16C2×D14911yescharacteristic
200C2×D8—1491no—
201C2×D8C2×D14911yescharacteristic
202#127—1491no—
203#125—1491no—
204#123—2981no—
205#123—2981no—
206#121—2981no—
207#121—2981no—
208#121—1491no—
209#121C2×D14911yescharacteristic
210C4×Q8—1491no—
211C4×Q8—1491no—
212C4×D4—2981no—
213C4×D4—2981no—
214C4×D4—1491no—
215C4×D4—1491no—
216C4×D4—1491no—
217C4×D4—1491no—
218#117—2981no—
219#117—1491no—
220C2×C4⋊C4—2981no—
221C2×C4⋊C4—1491no—
222#107—1491no—
223#107—1491no—
224#106—1491no—
225#106—1491no—
226C4⋊C8—1491no—
227C4⋊C8—1491no—
228#103—1491no—
229#103C2×D14911yescharacteristic
230#102—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102C2×D14911yescharacteristic
236C22⋊C8—1491no—
237C22⋊C8C2×D14911yescharacteristic
238#97—1491no—
239C4×C8—1491no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D14911yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—2981no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4C22×D14911yescharacteristic
250C2×D4C22×D14911yescharacteristic
251C22×C4—21no—
252C22×C4—2981no—
253C22×C4—2981no—
254C22×C4—2981no—
255C22×C4—2981no—
256C22×C4—2981no—
257C22×C4C22×D14911yescharacteristic
258SD16—22no—
259SD16—2982no—
260D8—22no—
261D8—2982no—
262C2×C8—1491no—
263C2×C8—1491no—
264C2×C8C22×D14911yescharacteristic
265C2×C8C22×D14911yescharacteristic
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—1491no—
272C4⋊C4—1491no—
273C4⋊C4—1491no—
274C4⋊C4—1491no—
275C4⋊C4—1491no—
276C4⋊C4C22×D14911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—1491no—
284C22⋊C4—1491no—
285C42—2981no—
286C42—2981no—
287C42—1491no—
288C42—1491no—
289C23—21no—
290C23—21no—
291C23—2981no—
292C23D4×D14911yescharacteristic
293Q8—21no—
294Q8#1455873512yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—2981no—
301D4—2981no—
302D4—11921no—
303D4—11921no—
304D4—11921no—
305D4#1455873512yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—1491no—
315C2×C4—1491no—
316C2×C4—1491no—
317C2×C4—1491no—
318C2×C4—11921no—
319C2×C4—11921no—
320C2×C4—11921no—
321C2×C4—11921no—
322C2×C4—11921no—
323C2×C4D4×D14911yescharacteristic
324C2×C4C23×D14911yescharacteristic
325C8—21no—
326C8—21no—
327C8—2981no—
328C8—2981no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—5961no—
339C22—5961no—
340C22—5961no—
341C22C2×D4×D14911yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—2981no—
346C4—2981no—
347C4—2981no—
348C4—2981no—
349C4—5961no—
350C4—5961no—
351C4—5961no—
352C4C2×#1455873511yescharacteristic
353C4C2×#1455873511yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—11921no—
358C2#2375013111yescharacteristic
359C2#2375042711yescharacteristic
360C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#449×C149C2
socleC22×C149C22×D4
hypercenter#449D149
hypocenterC149#3119
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23750228C2semidirect
2. #23750108C2semidirect
3. #23749941C2semidirect
4. #23749939C2semidirect
5. #23749934C2semidirect
6. #23749923C2semidirect
7. #23749823C2semidirect
8. #23749818C2semidirect
9. #23749770C2semidirect
10. #23749734C2semidirect
11. #23749726C2semidirect
12. #23749710C2semidirect
13. D8×Dic149C2semidirect
14. #23749683C2semidirect
15. #449×C149C2semidirect
180. C149#3119semidirect
191. #449D149semidirect

Maximal subgroups

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

subgroupindex
#237502282
#237501082
#237499412
#237499392
#237499342
#237499232
#237498232
#237498182
#237497702
#237497342
#237497262
#237497102
D8×Dic1492
#237496832
#449×C1492
#3119149