Finite Group Databasebeta

← #34055599

Subgroups — #34055599

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#23750205C211yesmaximal, characteristic, complemented
2#23750203C211yesmaximal, characteristic, complemented
3#23749954C211yesmaximal, characteristic, complemented
4#23749953C211yesmaximal, characteristic, complemented
5#23749944C211yesmaximal, characteristic, complemented
6#23749942C211yesmaximal, characteristic, complemented
7#23749880C211yesmaximal, characteristic, complemented
8#23749877C211yesmaximal, characteristic, complemented
9#23749857C211yesmaximal, characteristic, complemented
10#23749851C211yesmaximal, characteristic, complemented
11#23749786C211yesmaximal, characteristic, complemented
12#23749770C211yesmaximal, characteristic, complemented
13#23749769C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic, complemented
15#452×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558736C2211yescharacteristic
18C2×#14558723C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×#14558719C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22#18011890—21no—
23#18011889—21no—
24#18011887C2211yescharacteristic
25#18011887C2211yescharacteristic
26#18011887C2211yescharacteristic
27#18011886—21no—
28#18011886C2211yescharacteristic
29#18011885—21no—
30#18011885C2211yescharacteristic
31#18011884—21no—
32#18011884—21no—
33#18011883—21no—
34#18011883—21no—
35#18011882C2211yescharacteristic
36#18011882C2211yescharacteristic
37C2×C4⋊Dic149C2211yescharacteristic
38C4⋊C4×D149C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×Q16×C149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C22⋊Q8×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558737—41no—
60#14558737—41no—
61#14558736—41no—
62#14558736—41no—
63C2×Dic298D411yescharacteristic
64C2×D596—21no—
65C2×D596—21no—
66C2×D596D411yescharacteristic
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149D411yescharacteristic
72C2×C22⋊D149D411yescharacteristic
73C22×Dic149—21no—
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76C2×C4×D149C2311yescharacteristic
77C2×C4×D149C2311yescharacteristic
78#14558723—41no—
79#14558721—41no—
80#14558719—41no—
81C2×#11924746C2311yescharacteristic
82C2×#11924746C2311yescharacteristic
83C8×D149—41no—
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—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#41×C149—41no—
100#41×C149—41no—
101C2×Q8×C149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103C2×D4×C149—21no—
104C2×D4×C149C2311yescharacteristic
105C22×C4×C149—21no—
106C22×C4×C149C2311yescharacteristic
107Q16×C149—41no—
108SD16×C149—41no—
109C2×C8×C149C2311yescharacteristic
110C2×C8×C149C2311yescharacteristic
111C4⋊C4×C149—21no—
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149—21no—
115C22×D149C2×D411yescharacteristic
116C22×D149C2×D411yescharacteristic
117Dic298—41no—
118D596—21no—
119D596—21no—
120D596—41no—
121D596—42no—
122D596—81no—
123C22⋊D149—41no—
124C22⋊D149—41no—
125C22⋊D149—81no—
126C22⋊D149—81no—
127C22⋊D149—81no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—81no—
132C2×Dic149C2×D411yescharacteristic
133C2×Dic149C2×D411yescharacteristic
134C4×D149—21no—
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—42no—
139C4×D149—81no—
140#11924746—21no—
141#11924746—21no—
142C23×C149—21no—
143C23×C149C2×D411yescharacteristic
144Q8×C149—21no—
145Q8×C149—21no—
146Q8×C149—21no—
147Q8×C149—21no—
148D4×C149—21no—
149D4×C149—21no—
150D4×C149—42no—
151C2×C4×C149—21no—
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×C149C22×D411yescharacteristic
168C2×D149—21no—
169C2×D149—21no—
170C2×D149—21no—
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C4×C149—21no—
178C4×C149—41no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149H(5,𝔽2)11yescharacteristic
182C4×C149H(5,𝔽2)11yescharacteristic
183Dic149—21no—
184Dic149—21no—
185Dic149—41no—
186Dic149—41no—
187Dic149—41no—
188C2×C149—41no—
189C2×C149—81no—
190C2×C149#53411yescharacteristic
191C2×C149#57711yescharacteristic
192C2×C149#57711yescharacteristic
193D149—41no—
194D149—41no—
195D149—81no—
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#452D14911yescharacteristic, complemented
210#449—1491no—
211#449—1491no—
212#408—1491no—
213C2×#41—1491no—
214C2×#41—1491no—
215C2×#41C2×D14911yescharacteristic
216C2×Q16C2×D14911yescharacteristic
217C2×SD16—1491no—
218C2×SD16C2×D14911yescharacteristic
219C2×D8—1491no—
220C2×M16—1491no—
221C22×C8—1491no—
222C22⋊Q8—2981no—
223C22⋊Q8—2981no—
224C22⋊Q8—1491no—
225C22⋊Q8—1491no—
226C22⋊Q8—1491no—
227C22⋊Q8C2×D14911yescharacteristic
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#121—1491no—
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×Q8C22×D14911yescharacteristic
264C2×Q8C22×D14911yescharacteristic
265C2×D4—21no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—2981no—
270C2×D4—2981no—
271C2×D4—1491no—
272C2×D4—1491no—
273C2×D4—1491no—
274C2×D4—1491no—
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—41no—
284SD16—41no—
285SD16—5961no—
286D8—5961no—
287M16—5961no—
288C2×C8—5961no—
289C2×C8—1491no—
290C2×C8—1491no—
291C2×C8C22×D14911yescharacteristic
292C2×C8C22×D14911yescharacteristic
293C4⋊C4—21no—
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—2981no—
313C23—1491no—
314C23—1491no—
315C23D4×D14911yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—5961no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—2981no—
325D4—2981no—
326D4—5961no—
327D4—5962no—
328D4—5961no—
329D4—5961no—
330D4—11921no—
331D4—11921no—
332D4—11921no—
333D4—11921no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
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—2981no—
365C22—2981no—
366C22—2981no—
367C22—2981no—
368C22—2981no—
369C22—2981no—
370C22—5961no—
371C22—5961no—
372C22—5961no—
373C22C2×D4×D14911yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—2981no—
379C4—2981no—
380C4—5961no—
381C4—5961no—
382C4—5961no—
383C4#1801195611yescharacteristic
384C4#1801195611yescharacteristic
385C2—41no—
386C2—81no—
387C2—5961no—
388C2—5961no—
389C2—11921no—
390C2#2375018511yescharacteristic
391C2#2375043211yescharacteristic
392C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#452×C149C2
socleC22×C149C22×D4
hypercenter#452D149
hypocenterC149#3204
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #23750205C2semidirect
2. #23750203C2semidirect
3. #23749954C2semidirect
4. #23749953C2semidirect
5. #23749944C2semidirect
6. #23749942C2semidirect
7. #23749880C2semidirect
8. #23749877C2semidirect
9. #23749857C2semidirect
10. #23749851C2semidirect
11. #23749786C2semidirect
12. #23749770C2semidirect
13. #23749769C2semidirect
14. #23749590C2semidirect
15. #452×C149C2semidirect
196. C149#3204semidirect
209. #452D149semidirect

Maximal subgroups

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

subgroupindex
#237502052
#237502032
#237499542
#237499532
#237499442
#237499422
#237498802
#237498772
#237498572
#237498512
#237497862
#237497702
#237497692
#237495902
#452×C1492
#3204149