Finite Group Databasebeta

← #34057734

Subgroups — #34057734

Order 19072.

418 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750358C211yesmaximal, characteristic, complemented
2#23750296C211yesmaximal, characteristic, complemented
3#23750014C211yesmaximal, characteristic, complemented
4#23750013C211yesmaximal, characteristic, complemented
5#23750000C211yesmaximal, characteristic, complemented
6#23749840C211yesmaximal, characteristic, complemented
7#23749839C211yesmaximal, characteristic, complemented
8#23749824C211yesmaximal, characteristic, complemented
9#23749820C211yesmaximal, characteristic, complemented
10#23749819C211yesmaximal, characteristic, complemented
11#23749819C211yesmaximal, characteristic, complemented
12#23749753C211yesmaximal, characteristic, complemented
13#23749736C211yesmaximal, characteristic, complemented
14#23749712C211yesmaximal, characteristic, complemented
15#442×C149C211yesmaximal, characteristic, complemented
16C2×#14558736—21no—
17C2×#14558725C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×D1192C2211yescharacteristic
21C2×D1192C2211yescharacteristic
22C2×#14558721C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24C2×#14558721C2211yescharacteristic
25#18011908C2211yescharacteristic
26#18011907C2211yescharacteristic
27#18011907C2211yescharacteristic
28#18011907C2211yescharacteristic
29#18011899C2211yescharacteristic
30#18011898C2211yescharacteristic
31#18011897—21no—
32#18011894—21no—
33#18011893—21no—
34#18011885—21no—
35#18011884—21no—
36#18011884—21no—
37C4×Dic298C2211yescharacteristic
38#18011876C2211yescharacteristic
39#18011873C2211yescharacteristic
40#18011873C2211yescharacteristic
41#18011873C2211yescharacteristic
42C4×C22⋊D149—21no—
43C4⋊#11924746C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×D8×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59#14558736—44no—
60C2×Dic298D411yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×D596—21no—
63C2×D596—21no—
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76#14558725—22no—
77#14558725—41no—
78#14558724—41no—
79D1192—22no—
80D1192—41no—
81#14558721—41no—
82#14558721—41no—
83#14558721—41no—
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C4⋊Dic149D411yescharacteristic
87#14558715—21no—
88#14558715D411yescharacteristic
89#14558715D411yescharacteristic
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97C4×Dic149—21no—
98C4×Dic149C2311yescharacteristic
99C4×Dic149C2311yescharacteristic
100C2×D4×C149C2311yescharacteristic
101C2×D4×C149C2311yescharacteristic
102C22×C4×C149—21no—
103C22×C4×C149—21no—
104D8×C149—22no—
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C4⋊C4×C149C2311yescharacteristic
109C22⋊C4×C149—21no—
110C22⋊C4×C149—21no—
111C42×C149C2311yescharacteristic
112C22×D149—21no—
113C22×D149—21no—
114C22×D149—21no—
115Dic298—22no—
116Dic298—21no—
117Dic298—21no—
118D596—21no—
119D596—21no—
120D596—21no—
121D596—21no—
122D596—21no—
123D596—21no—
124D596—42no—
125D596—81no—
126C22⋊D149—42no—
127C22⋊D149—42no—
128C22⋊D149—42no—
129C22⋊D149—81no—
130C22⋊D149—81no—
131C22⋊D149—81no—
132C2×Dic149—21no—
133C2×Dic149C2×D411yescharacteristic
134C2×Dic149C2×D411yescharacteristic
135C2×Dic149C2×D411yescharacteristic
136C2×Dic149C2×D411yescharacteristic
137C4×D149—42no—
138C4×D149—42no—
139C4×D149—81no—
140#11924746—21no—
141#11924746—21no—
142C23×C149—21no—
143C23×C149—21no—
144D4×C149—21no—
145D4×C149—21no—
146D4×C149—21no—
147D4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—42no—
151C2×C4×C149—81no—
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2×D411yescharacteristic
154C2×C4×C149C2411yescharacteristic
155C8×C149—21no—
156C8×C149#4112yescomplemented
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149—41no—
163C22×C149C22×D411yescharacteristic
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—41no—
171C2×D149—41no—
172C2×D149—41no—
173C4×C149—21no—
174C4×C149—21no—
175C4×C149—41no—
176C4×C149—41no—
177C4×C149C2×#4111yescharacteristic
178C4×C149H(5,𝔽2)11yescharacteristic
179Dic149—21no—
180Dic149—21no—
181Dic149—21no—
182Dic149—41no—
183Dic149AGL(1,ℤ/8)12yes—
184C2×C149—81no—
185C2×C149—81no—
186C2×C149#55011yescharacteristic
187C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C149#57611yescharacteristic
189D149—81no—
190D149—81no—
191D149—81no—
192C149#339911yescharacteristic, complemented, Sylow
193#3399—1491nomaximal, Sylow
194#559—1491no—
195#550—1491no—
196#496—1491no—
197#496—1491no—
198#493—1491no—
199#463—1491no—
200#463—1491no—
201#460—1491no—
202#459—1491no—
203#459—1491no—
204#459—1491no—
205#446—1491no—
206#442—1491no—
207#442D14911yescharacteristic, complemented
208C4×SD16—1491no—
209C2×#41—2981no—
210C2×SD16—1491no—
211C2×SD16—1491no—
212C2×SD16—1491no—
213C2×D8—1491no—
214C2×D8—1491no—
215C2×D8—1491no—
216C2×D8—1491no—
217C2×D8—1491no—
218C2×D8C2×D14911yescharacteristic
219#127—1491no—
220#127—1491no—
221#127—1491no—
222#127—1491no—
223#124—2981no—
224#124—1491no—
225#124—1491no—
226#123—2981no—
227#123—2981no—
228#121—2981no—
229#121—2981no—
230#121—2981no—
231C4×Q8—1491no—
232C4×Q8—1491no—
233C4×D4—2981no—
234C4×D4—1491no—
235C4×D4—1491no—
236C4×D4—1491no—
237C4×D4C2×D14911yescharacteristic
238C4×D4C2×D14911yescharacteristic
239#106C2×D14911yescharacteristic
240C4⋊C8—1491no—
241C4⋊C8—1491no—
242C4⋊C8—1491no—
243#103—1491no—
244#102—1491no—
245#102—1491no—
246#102—1491no—
247#102C2×D14911yescharacteristic
248#102C2×D14911yescharacteristic
249#97—1491no—
250#97C2×D14911yescharacteristic
251C4×C8—1491no—
252#41—5964no—
253C2×Q8—1491no—
254C2×Q8—1491no—
255C2×D4—2981no—
256C2×D4—2981no—
257C2×D4—2981no—
258C2×D4—2981no—
259C2×D4—2981no—
260C2×D4—2981no—
261C2×D4—2981no—
262C2×D4—2981no—
263C2×D4—1491no—
264C2×D4—1491no—
265C2×D4—1491no—
266C2×D4C22×D14911yescharacteristic
267C2×D4C22×D14911yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—2981no—
271C22×C4—2981no—
272C22×C4—2981no—
273SD16—2982no—
274SD16—5961no—
275SD16—5961no—
276D8—22no—
277D8—2982no—
278D8—5961no—
279D8—5961no—
280D8—5961no—
281D8—5961no—
282C2×C8—1491no—
283C2×C8—1491no—
284C2×C8C22×D14911yescharacteristic
285C2×C8C22×D14911yescharacteristic
286C4⋊C4—2981no—
287C4⋊C4—1491no—
288C4⋊C4—1491no—
289C4⋊C4—1491no—
290C4⋊C4C22×D14911yescharacteristic
291C4⋊C4C22×D14911yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4—2981no—
300C22⋊C4—2981no—
301C42—2981no—
302C42—1491no—
303C42—1491no—
304C42C22×D14911yescharacteristic
305C23—21no—
306C23—21no—
307C23—2981no—
308C23—2981no—
309C23—2981no—
310Q8—2982no—
311Q8—2981no—
312Q8—2981no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—2981no—
318D4—2981no—
319D4—2981no—
320D4—2981no—
321D4—2981no—
322D4—2981no—
323D4—5962no—
324D4—5962no—
325D4—5962no—
326D4—5962no—
327D4—11921no—
328D4—11921no—
329D4—11921no—
330D4—11921no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—81no—
335C2×C4—2981no—
336C2×C4—5962no—
337C2×C4—5962no—
338C2×C4—1491no—
339C2×C4—1491no—
340C2×C4—1491no—
341C2×C4—1491no—
342C2×C4—11921no—
343C2×C4D4×D14911yescharacteristic
344C2×C4D4×D14911yescharacteristic
345C2×C4C23×D14911yescharacteristic
346C8—21no—
347C8—2981no—
348C8—2981no—
349C8#1455873612yescomplemented
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—5961no—
357C22—5961no—
358C22—5961no—
359C22—5961no—
360C22—5961no—
361C22—5961no—
362C22—5961no—
363C22—5961no—
364C22—5961no—
365C22C2×D4×D14911yescharacteristic
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—2981no—
371C4—2981no—
372C4—2981no—
373C4—5961no—
374C4—1492no—
375C4C2×#1455873611yescharacteristic
376C4#1801195711yescharacteristic
377C2—81no—
378C2—81no—
379C2—11921no—
380C2—11921no—
381C2—11921no—
382C2#2375029611yescharacteristic
383C2AGL(1,ℤ/8)×D14911yescharacteristic
384C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#442×C149C2
socleC22×C149C22×D4
hypercenter#442D149
hypocenterC149#3399
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #23750358C2semidirect
2. #23750296C2semidirect
3. #23750014C2semidirect
4. #23750013C2semidirect
5. #23750000C2semidirect
6. #23749840C2semidirect
7. #23749839C2semidirect
8. #23749824C2semidirect
9. #23749820C2semidirect
10. #23749819C2semidirect
11. #23749819C2semidirect
12. #23749753C2semidirect
13. #23749736C2semidirect
14. #23749712C2semidirect
15. #442×C149C2semidirect
156. C8×C149#41semidirect
192. C149#3399semidirect
207. #442D149semidirect
349. C8#14558736semidirect

Maximal subgroups

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

subgroupindex
#237503582
#237502962
#237500142
#237500132
#237500002
#237498402
#237498392
#237498242
#237498202
#237498192
#237497532
#237497362
#237497122
#442×C1492
#3399149