Finite Group Databasebeta

← #34055600

Subgroups — #34055600

Order 19072.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750204C211yesmaximal, characteristic, complemented
2#23750203C211yesmaximal, characteristic, complemented
3#23749956C211yesmaximal, characteristic, complemented
4#23749954C211yesmaximal, characteristic, complemented
5#23749942C211yesmaximal, characteristic, complemented
6#23749941C211yesmaximal, characteristic, complemented
7#23749882C211yesmaximal, characteristic, complemented
8#23749875C211yesmaximal, characteristic, complemented
9#23749853C211yesmaximal, characteristic, complemented
10#23749851C211yesmaximal, characteristic, complemented
11#23749787C211yesmaximal, characteristic, complemented
12#23749784C211yesmaximal, characteristic, complemented
13#23749767C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic, complemented
15#449×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558719C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22#18011891C2211yescharacteristic
23#18011890—21no—
24#18011890C2211yescharacteristic
25#18011888—21no—
26#18011887C2211yescharacteristic
27#18011887C2211yescharacteristic
28#18011885—21no—
29#18011884—21no—
30#18011883—21no—
31#18011883—21no—
32#18011883—21no—
33#18011882—21no—
34#18011882C2211yescharacteristic
35#18011882C2211yescharacteristic
36#18011882C2211yescharacteristic
37C2×C4⋊Dic149C2211yescharacteristic
38C4⋊C4×D149C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C2×D8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61#14558735—41no—
62#14558735—41no—
63C2×Dic298D411yescharacteristic
64C2×Dic298C2311yescharacteristic
65C2×D596D411yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149D411yescharacteristic
71C2×C22⋊D149D411yescharacteristic
72C22×Dic149—21no—
73C22×Dic149—21no—
74C2×C4×D149—21no—
75C2×C4×D149C2311yescharacteristic
76C2×C4×D149C2311yescharacteristic
77#14558726—41no—
78#14558724—41no—
79#14558719—41no—
80C2×#11924746C2311yescharacteristic
81C2×#11924746C2311yescharacteristic
82C8×D149—41no—
83C4⋊Dic149—21no—
84C4⋊Dic149—21no—
85C4⋊Dic149C2311yescharacteristic
86C4⋊Dic149C2311yescharacteristic
87C4⋊Dic149C2311yescharacteristic
88#14558715—21no—
89#14558715—21no—
90#14558715—21no—
91#14558715—21no—
92C22⋊Dic149—21no—
93C22⋊Dic149—21no—
94C22⋊Dic149—21no—
95C22⋊Dic149—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#41×C149—41no—
100#41×C149—41no—
101C2×Q8×C149C2311yescharacteristic
102C2×D4×C149—21no—
103C2×D4×C149—21no—
104C2×D4×C149C2311yescharacteristic
105C2×D4×C149C2311yescharacteristic
106C22×C4×C149—21no—
107C22×C4×C149C2311yescharacteristic
108SD16×C149—41no—
109D8×C149—41no—
110C2×C8×C149C2311yescharacteristic
111C2×C8×C149C2311yescharacteristic
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149C2×D411yescharacteristic
115C22×D149C2×D411yescharacteristic
116Dic298—21no—
117Dic298—21no—
118Dic298—41no—
119D596—41no—
120C22⋊D149—41no—
121C22⋊D149—41no—
122C22⋊D149—42no—
123C22⋊D149—81no—
124C22⋊D149—81no—
125C22⋊D149—81no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—42no—
131C2×Dic149—81no—
132C2×Dic149C2×D411yescharacteristic
133C2×Dic149C2×D411yescharacteristic
134C4×D149—21no—
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—81no—
139#11924746—21no—
140#11924746—21no—
141C23×C149—21no—
142C23×C149—21no—
143C23×C149C2×D411yescharacteristic
144Q8×C149—21no—
145Q8×C149—21no—
146D4×C149—21no—
147D4×C149—21no—
148D4×C149—21no—
149D4×C149—21no—
150D4×C149—42no—
151D4×C149—81no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—42no—
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2411yescharacteristic
159C8×C149—21no—
160C8×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149—41no—
168C22×C149—41no—
169C22×C149—41no—
170C22×C149C22×D411yescharacteristic
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—21no—
177C4×C149—21no—
178C4×C149—41no—
179C4×C149—41no—
180C4×C149H(5,𝔽2)11yescharacteristic
181C4×C149H(5,𝔽2)11yescharacteristic
182Dic149—21no—
183Dic149—21no—
184Dic149—41no—
185Dic149—41no—
186Dic149—41no—
187Dic149—41no—
188C2×C149—41no—
189C2×C149—81no—
190C2×C149—81no—
191C2×C149#53411yescharacteristic
192C2×C149#57711yescharacteristic
193C2×C149#57711yescharacteristic
194D149—41no—
195D149—41no—
196C149#320411yescharacteristic, complemented, Sylow
197#3204—1491nomaximal, Sylow
198#537—1491no—
199#537—1491no—
200#483—1491no—
201#483—1491no—
202#481—1491no—
203#481—1491no—
204#470—1491no—
205#469—1491no—
206#465—1491no—
207#465—1491no—
208#452—1491no—
209#452—1491no—
210#449—1491no—
211#449D14911yescharacteristic, complemented
212#408—1491no—
213C2×#41—1491no—
214C2×#41—1491no—
215C2×#41C2×D14911yescharacteristic
216C2×Q16—1491no—
217C2×SD16—1491no—
218C2×SD16C2×D14911yescharacteristic
219C2×D8C2×D14911yescharacteristic
220C2×M16—1491no—
221C22×C8—1491no—
222C22⋊Q8—2981no—
223C22⋊Q8—2981no—
224C22⋊Q8—1491no—
225C22⋊Q8—1491no—
226C22⋊Q8—1491no—
227C22⋊Q8—1491no—
228#121—2981no—
229#121—2981no—
230#121—2981no—
231#121—2981no—
232#121—2981no—
233#121—2981no—
234#121—1491no—
235#121—1491no—
236#121—1491no—
237#121C2×D14911yescharacteristic
238C2×C4⋊C4—1491no—
239C2×C4⋊C4—1491no—
240#106—1491no—
241#106—1491no—
242#106—1491no—
243#106—1491no—
244#103—1491no—
245#103—1491no—
246#103—1491no—
247#103C2×D14911yescharacteristic
248#102—1491no—
249#102—1491no—
250#102—1491no—
251#102C2×D14911yescharacteristic
252C22⋊C8—1491no—
253C22⋊C8—1491no—
254C22⋊C8—1491no—
255C22⋊C8C2×D14911yescharacteristic
256#41—41no—
257#41—41no—
258#41—5961no—
259#41—5961no—
260#41—5961no—
261#41—5961no—
262C2×Q8—1491no—
263C2×Q8—1491no—
264C2×Q8C22×D14911yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—2981no—
270C2×D4—2981no—
271C2×D4—1491no—
272C2×D4—1491no—
273C2×D4—1491no—
274C2×D4C22×D14911yescharacteristic
275C2×D4C22×D14911yescharacteristic
276C22×C4—21no—
277C22×C4—2981no—
278C22×C4—2981no—
279C22×C4—2981no—
280C22×C4—1491no—
281C22×C4—1491no—
282C22×C4C22×D14911yescharacteristic
283Q16—5961no—
284SD16—41no—
285SD16—5961no—
286D8—41no—
287M16—5961no—
288C2×C8—5961no—
289C2×C8—1491no—
290C2×C8—1491no—
291C2×C8C22×D14911yescharacteristic
292C2×C8C22×D14911yescharacteristic
293C4⋊C4—2981no—
294C4⋊C4—2981no—
295C4⋊C4—2981no—
296C4⋊C4—2981no—
297C4⋊C4—2981no—
298C4⋊C4—2981no—
299C4⋊C4—1491no—
300C4⋊C4—1491no—
301C4⋊C4—1491no—
302C4⋊C4C22×D14911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—2981no—
307C22⋊C4—2981no—
308C22⋊C4—2981no—
309C22⋊C4—2981no—
310C22⋊C4—2981no—
311C23—21no—
312C23—21no—
313C23—1491no—
314C23—1491no—
315C23D4×D14911yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—2981no—
319Q8—2981no—
320Q8—5961no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—81no—
327D4—5961no—
328D4—5961no—
329D4—5961no—
330D4—5962no—
331D4—11921no—
332D4—11921no—
333D4—11921no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—2981no—
340C2×C4—2981no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—2981no—
347C2×C4—5962no—
348C2×C4—1491no—
349C2×C4—1491no—
350C2×C4—11921no—
351C2×C4—11921no—
352C2×C4D4×D14911yescharacteristic
353C2×C4C23×D14911yescharacteristic
354C8—21no—
355C8—21no—
356C8—2981no—
357C8—2981no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—2981no—
368C22—2981no—
369C22—2981no—
370C22—2981no—
371C22—2981no—
372C22—2981no—
373C22C2×D4×D14911yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—2981no—
378C4—2981no—
379C4—5961no—
380C4—5961no—
381C4—5961no—
382C4—5961no—
383C4#1801195611yescharacteristic
384C4#1801195611yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—5961no—
389C2—5961no—
390C2#2375018511yescharacteristic
391C2#2375043211yescharacteristic
392C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#449×C149C2
socleC22×C149C22×D4
hypercenter#449D149
hypocenterC149#3204
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. #23750204C2semidirect
2. #23750203C2semidirect
3. #23749956C2semidirect
4. #23749954C2semidirect
5. #23749942C2semidirect
6. #23749941C2semidirect
7. #23749882C2semidirect
8. #23749875C2semidirect
9. #23749853C2semidirect
10. #23749851C2semidirect
11. #23749787C2semidirect
12. #23749784C2semidirect
13. #23749767C2semidirect
14. #23749590C2semidirect
15. #449×C149C2semidirect
196. C149#3204semidirect
211. #449D149semidirect

Maximal subgroups

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

subgroupindex
#237502042
#237502032
#237499562
#237499542
#237499422
#237499412
#237498822
#237498752
#237498532
#237498512
#237497872
#237497842
#237497672
#237495902
#449×C1492
#3204149