Finite Group Databasebeta

← #34057014

Subgroups — #34057014

Order 19072.

430 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750294C211yesmaximal, characteristic, complemented
2#23750276C211yesmaximal, characteristic, complemented
3#23749970C211yesmaximal, characteristic, complemented
4#23749943C211yesmaximal, characteristic, complemented
5#23749942C211yesmaximal, characteristic, complemented
6#23749908C211yesmaximal, characteristic, complemented
7#23749878C211yesmaximal, characteristic, complemented
8#23749877C211yesmaximal, characteristic, complemented
9#23749819C211yesmaximal, characteristic, complemented
10#23749773C211yesmaximal, characteristic, complemented
11#23749770C211yesmaximal, characteristic, complemented
12#23749710C211yesmaximal, characteristic, complemented
13#23749701C211yesmaximal, characteristic, complemented
14#23749625C211yesmaximal, characteristic, complemented
15#417×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558736—21no—
18C2×#14558723C2211yescharacteristic
19C2×D1192C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21C2×#14558719C2211yescharacteristic
22#18011910C2211yescharacteristic
23#18011907—21no—
24#18011907C2211yescharacteristic
25#18011896—21no—
26#18011894—21no—
27#18011889—21no—
28#18011886C2211yescharacteristic
29#18011885—21no—
30#18011885C2211yescharacteristic
31#18011885C2211yescharacteristic
32#18011882—21no—
33#18011882C2211yescharacteristic
34Q8×Dic149C2211yescharacteristic
35#18011873C2211yescharacteristic
36C4×C22⋊D149—21no—
37C4×C22⋊D149C2211yescharacteristic
38C4⋊C4×D149C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×M16×C149C2211yescharacteristic
54C2×C4⋊C4×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558737—22no—
60#14558737—41no—
61#14558736—44no—
62C2×Dic298—21no—
63C2×D596—21no—
64C2×D596—21no—
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⋊D149D411yescharacteristic
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76C2×C4×D149C2311yescharacteristic
77#14558723—22no—
78D1192—41no—
79#14558721—41no—
80#14558719—41no—
81C2×#11924746C2311yescharacteristic
82C2×#11924746C2311yescharacteristic
83C4⋊Dic149—21no—
84C4⋊Dic149C2311yescharacteristic
85C4⋊Dic149C2311yescharacteristic
86#14558715—21no—
87#14558715—21no—
88#14558715D411yescharacteristic
89C22⋊Dic149—21no—
90C22⋊Dic149D411yescharacteristic
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713D411yescharacteristic
96C4×Dic149—21no—
97C4×Dic149C2311yescharacteristic
98#41×C149—22no—
99#41×C149—41no—
100C2×Q8×C149C2311yescharacteristic
101C2×D4×C149—21no—
102C2×D4×C149C2311yescharacteristic
103C22×C4×C149—21no—
104C22×C4×C149—21no—
105C22×C4×C149C2311yescharacteristic
106M16×C149—41no—
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C4⋊C4×C149—21no—
110C4⋊C4×C149C2311yescharacteristic
111C4⋊C4×C149C2311yescharacteristic
112C22×D149—21no—
113C22×D149—21no—
114C22×D149C2×D411yescharacteristic
115Dic298—42no—
116D596—21no—
117D596—21no—
118D596—21no—
119D596—21no—
120D596—42no—
121D596—42no—
122C22⋊D149—22no—
123C22⋊D149—42no—
124C22⋊D149—42no—
125C22⋊D149—81no—
126C22⋊D149—81no—
127C22⋊D149—81no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149C2×D411yescharacteristic
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C4×D149—21no—
134C4×D149—21no—
135C4×D149—42no—
136C4×D149—42no—
137C4×D149—42no—
138#11924746—21no—
139#11924746—21no—
140C23×C149—21no—
141C23×C149C2×D411yescharacteristic
142Q8×C149—21no—
143Q8×C149#4112yescomplemented
144D4×C149—21no—
145D4×C149—21no—
146D4×C149—42no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—42no—
153C2×C4×C149—42no—
154C2×C4×C149C2×D411yescharacteristic
155C2×C4×C149C2411yescharacteristic
156C8×C149—21no—
157C8×C149—21no—
158C22×C149—21no—
159C22×C149—21no—
160C22×C149—21no—
161C22×C149—41no—
162C22×C149—41no—
163C22×C149—41no—
164C22×C149C22×D411yescharacteristic
165C2×D149—21no—
166C2×D149—21no—
167C2×D149—21no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—41no—
171C2×D149—41no—
172C2×D149—41no—
173C2×D149—41no—
174C4×C149—21no—
175C4×C149—22no—
176C4×C149—41no—
177C4×C149—41no—
178C4×C149C2×#4111yescharacteristic
179C4×C149H(5,𝔽2)11yescharacteristic
180Dic149—21no—
181Dic149—21no—
182Dic149—41no—
183Dic149—41no—
184Dic149AGL(1,ℤ/8)12yes—
185C2×C149—41no—
186C2×C149—81no—
187C2×C149#54611yescharacteristic
188C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C149#57711yescharacteristic
190D149—41no—
191D149—81no—
192D149—81no—
193C149#333211yescharacteristic, complemented, Sylow
194#3332—1491nomaximal, Sylow
195#550—1491no—
196#547—1491no—
197#486—1491no—
198#481—1491no—
199#481—1491no—
200#475—1491no—
201#469—1491no—
202#469—1491no—
203#459—1491no—
204#449—1491no—
205#449—1491no—
206C4×SD16—1491no—
207#436—1491no—
208#417—1491no—
209#417D14911yescharacteristic, complemented
210C2×#41—2981no—
211C2×#41—1491no—
212C2×#41C2×D14911yescharacteristic
213C2×SD16—1491no—
214C2×D8—1491no—
215C2×D8—1491no—
216C2×M16—1491no—
217C2×M16C2×D14911yescharacteristic
218C4⋊Q8—1491no—
219#127—2981no—
220#127—1491no—
221#123—2981no—
222#123—2981no—
223C22⋊Q8—2981no—
224#121—2981no—
225#121—2981no—
226#121—1491no—
227#121—1491no—
228#121—1491no—
229#121—1491no—
230C4×Q8—1491no—
231C4×D4—2981no—
232C4×D4—1491no—
233C4×D4—1491no—
234C2×C4⋊C4—1491no—
235C2×C4⋊C4C2×D14911yescharacteristic
236#106—1491no—
237#106—1491no—
238#106—1491no—
239C4⋊C8—1491no—
240#103—1491no—
241#103C2×D14911yescharacteristic
242#103C2×D14911yescharacteristic
243#102—1491no—
244#102—1491no—
245#102—1491no—
246#102—1491no—
247#102—1491no—
248#102C2×D14911yescharacteristic
249#102C2×D14911yescharacteristic
250C22⋊C8—1491no—
251C22⋊C8—1491no—
252C4×C8—1491no—
253#41—22no—
254#41—41no—
255#41—2982no—
256#41—5964no—
257#41—5961no—
258C2×Q8—2981no—
259C2×Q8C22×D14911yescharacteristic
260C2×D4—21no—
261C2×D4—2981no—
262C2×D4—2981no—
263C2×D4—2981no—
264C2×D4—2981no—
265C2×D4—2981no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—1491no—
269C2×D4—1491no—
270C2×D4—1491no—
271C2×D4C22×D14911yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—2981no—
275C22×C4—2981no—
276C22×C4—2981no—
277C22×C4—1491no—
278C22×C4C22×D14911yescharacteristic
279SD16—2982no—
280D8—5961no—
281D8—5961no—
282M16—41no—
283M16—5961no—
284C2×C8—1491no—
285C2×C8—1491no—
286C2×C8C22×D14911yescharacteristic
287C2×C8C22×D14911yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—2981no—
290C4⋊C4—2981no—
291C4⋊C4—2981no—
292C4⋊C4—1491no—
293C4⋊C4—1491no—
294C4⋊C4—1491no—
295C4⋊C4C22×D14911yescharacteristic
296C4⋊C4C22×D14911yescharacteristic
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4—2981no—
300C22⋊C4—2981no—
301C22⋊C4—2981no—
302C22⋊C4—1491no—
303C22⋊C4—1491no—
304C42—2981no—
305C42—1491no—
306C23—21no—
307C23—2981no—
308C23—2981no—
309C23—1491no—
310C23D4×D14911yescharacteristic
311Q8—21no—
312Q8—5962no—
313Q8#1455873612yescomplemented
314D4—21no—
315D4—21no—
316D4—42no—
317D4—2982no—
318D4—2981no—
319D4—2981no—
320D4—2981no—
321D4—2981no—
322D4—5962no—
323D4—5962no—
324D4—5962no—
325D4—5962no—
326D4—11921no—
327D4—11921no—
328D4—11921no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—2981no—
339C2×C4—2981no—
340C2×C4—5962no—
341C2×C4—5962no—
342C2×C4—5962no—
343C2×C4—1491no—
344C2×C4—1491no—
345C2×C4—1491no—
346C2×C4D4×D14911yescharacteristic
347C2×C4C23×D14911yescharacteristic
348C8—21no—
349C8—21no—
350C8—2981no—
351C8—2981no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—2981no—
359C22—2981no—
360C22—2981no—
361C22—5961no—
362C22—5961no—
363C22—5961no—
364C22—5961no—
365C22—5961no—
366C22—5961no—
367C22C2×D4×D14911yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—2981no—
373C4—2981no—
374C4—5961no—
375C4—5961no—
376C4—1492no—
377C4C2×#1455873611yescharacteristic
378C4#1801195611yescharacteristic
379C2—41no—
380C2—81no—
381C2—5961no—
382C2—11921no—
383C2—11921no—
384C2#2375026511yescharacteristic
385C2AGL(1,ℤ/8)×D14911yescharacteristic
386C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#417×C149C2
socleC22×C149C22×D4
hypercenter#417D149
hypocenterC149#3332
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #23750294C2semidirect
2. #23750276C2semidirect
3. #23749970C2semidirect
4. #23749943C2semidirect
5. #23749942C2semidirect
6. #23749908C2semidirect
7. #23749878C2semidirect
8. #23749877C2semidirect
9. #23749819C2semidirect
10. #23749773C2semidirect
11. #23749770C2semidirect
12. #23749710C2semidirect
13. #23749701C2semidirect
14. #23749625C2semidirect
15. #417×C149C2semidirect
143. Q8×C149#41semidirect
193. C149#3332semidirect
209. #417D149semidirect
313. Q8#14558736semidirect

Maximal subgroups

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

subgroupindex
#237502942
#237502762
#237499702
#237499432
#237499422
#237499082
#237498782
#237498772
#237498192
#237497732
#237497702
#237497102
#237497012
#237496252
#417×C1492
#3332149