Finite Group Databasebeta

← #34055597

Subgroups — #34055597

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#23750203C211yesmaximal, characteristic, complemented
2#23749955C211yesmaximal, characteristic, complemented
3#23749953C211yesmaximal, characteristic, complemented
4#23749943C211yesmaximal, characteristic, complemented
5#23749941C211yesmaximal, characteristic, complemented
6#23749881C211yesmaximal, characteristic, complemented
7#23749876C211yesmaximal, characteristic, complemented
8#23749856C211yesmaximal, characteristic, complemented
9#23749852C211yesmaximal, characteristic, complemented
10#23749787C211yesmaximal, characteristic, complemented
11#23749785C211yesmaximal, characteristic, complemented
12#23749770C211yesmaximal, characteristic, complemented
13#23749768C211yesmaximal, characteristic, complemented
14#23749592C211yesmaximal, characteristic, complemented
15#537×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21C2×#14558720C2211yescharacteristic
22C22×#11924746C2211yescharacteristic
23#18011890C2211yescharacteristic
24#18011890C2211yescharacteristic
25#18011887—21no—
26#18011885C2211yescharacteristic
27#18011885C2211yescharacteristic
28#18011883—21no—
29#18011883—21no—
30#18011882—21no—
31C2×C4⋊Dic149C2211yescharacteristic
32#18011842C2211yescharacteristic
33#18011842C2211yescharacteristic
34#18011842C2211yescharacteristic
35#18011842C2211yescharacteristic
36#18011835C2211yescharacteristic
37#18011835C2211yescharacteristic
38#18011834C2211yescharacteristic
39#18011834C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011831C2211yescharacteristic
43#18011831C2211yescharacteristic
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46C22⋊#11924746C2211yescharacteristic
47C22⋊#11924746C2211yescharacteristic
48C2×#41×C149C2211yescharacteristic
49C2×#41×C149C2211yescharacteristic
50C22⋊Q8×C149—21no—
51C22⋊Q8×C149C2211yescharacteristic
52C22⋊Q8×C149C2211yescharacteristic
53#121×C149—21no—
54#121×C149—21no—
55#121×C149—21no—
56#121×C149C2211yescharacteristic
57#121×C149C2211yescharacteristic
58C2×C4⋊C4×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C22×Dic149—21no—
67C2×C4×D149—21no—
68#14558726—41no—
69#14558724—41no—
70#14558723—41no—
71#14558721—41no—
72#14558720—41no—
73C2×#11924746—41no—
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C4⋊Dic149—21no—
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85#14558713—21no—
86#14558713—21no—
87#41×C149—41no—
88#41×C149—41no—
89#41×C149—41no—
90#41×C149—41no—
91C2×Q8×C149D411yescharacteristic
92C2×Q8×C149C2311yescharacteristic
93C2×D4×C149—21no—
94C2×D4×C149—21no—
95C2×D4×C149—21no—
96C2×D4×C149D411yescharacteristic
97C2×D4×C149D411yescharacteristic
98C2×D4×C149D411yescharacteristic
99C2×D4×C149C2311yescharacteristic
100C22×C4×C149—21no—
101C22×C4×C149—21no—
102C22×C4×C149C2311yescharacteristic
103C22×C4×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105C4⋊C4×C149—21no—
106C4⋊C4×C149—21no—
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C22⋊C4×C149—21no—
114C22×D149—21no—
115Dic298—21no—
116Dic298—21no—
117D596—21no—
118D596—21no—
119C22⋊D149—42no—
120C22⋊D149—81no—
121C22⋊D149—81no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—81no—
126C4×D149—42no—
127#11924746—21no—
128#11924746—21no—
129#11924746—21no—
130#11924746—21no—
131C23×C149—21no—
132C23×C149C2×D411yescharacteristic
133C23×C149C2×D411yescharacteristic
134C23×C149C2×D411yescharacteristic
135Q8×C149—21no—
136Q8×C149—21no—
137Q8×C149—41no—
138D4×C149—21no—
139D4×C149—21no—
140D4×C149—41no—
141D4×C149—41no—
142D4×C149—41no—
143D4×C149—42no—
144D4×C149—81no—
145D4×C149—81no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—42no—
156C2×C4×C149—81no—
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2×D411yescharacteristic
159C2×C4×C149C2×D411yescharacteristic
160C2×C4×C149C2411yescharacteristic
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149—21no—
165C22×C149—21no—
166C22×C149—21no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—21no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149C22×D411yescharacteristic
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C4×C149—21no—
178C4×C149—21no—
179C4×C149—21no—
180C4×C149—41no—
181C4×C149—41no—
182C4×C149—41no—
183C4×C149H(5,𝔽2)11yescharacteristic
184C4×C149H(5,𝔽2)11yescharacteristic
185Dic149—41no—
186Dic149—41no—
187Dic149—41no—
188C2×C149—41no—
189C2×C149—41no—
190C2×C149—41no—
191C2×C149—81no—
192C2×C149#53411yescharacteristic
193C2×C149#57711yescharacteristic
194C2×C149#57711yescharacteristic
195D149—81no—
196C149#320411yescharacteristic, complemented, Sylow
197#3204—1491nomaximal, Sylow
198#537—1491no—
199#537D14911yescharacteristic, complemented
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#449—1491no—
212#408—1491no—
213C2×#41—1491no—
214C2×#41C2×D14911yescharacteristic
215C2×#41C2×D14911yescharacteristic
216C2×Q16—1491no—
217C2×SD16—1491no—
218C2×SD16—1491no—
219C2×D8—1491no—
220C2×M16—1491no—
221C22×C8—1491no—
222C22⋊Q8—21no—
223C22⋊Q8—2981no—
224C22⋊Q8—1491no—
225C22⋊Q8—1491no—
226C22⋊Q8C2×D14911yescharacteristic
227C22⋊Q8C2×D14911yescharacteristic
228#121—21no—
229#121—21no—
230#121—21no—
231#121—2981no—
232#121—2981no—
233#121—2981no—
234#121—1491no—
235#121—1491no—
236#121C2×D14911yescharacteristic
237#121C2×D14911yescharacteristic
238C2×C4⋊C4—1491no—
239C2×C4⋊C4C2×D14911yescharacteristic
240#106—1491no—
241#106—1491no—
242#106—1491no—
243#106—1491no—
244#103—1491no—
245#103—1491no—
246#103—1491no—
247#103—1491no—
248#102—1491no—
249#102—1491no—
250#102—1491no—
251#102—1491no—
252C22⋊C8—1491no—
253C22⋊C8—1491no—
254C22⋊C8—1491no—
255C22⋊C8—1491no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—5961no—
261#41—5961no—
262C2×Q8—1491no—
263C2×Q8C22⋊D14911yescharacteristic
264C2×Q8C22×D14911yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—2981no—
269C2×D4—2981no—
270C2×D4—2981no—
271C2×D4—1491no—
272C2×D4C22⋊D14911yescharacteristic
273C2×D4C22⋊D14911yescharacteristic
274C2×D4C22⋊D14911yescharacteristic
275C2×D4C22×D14911yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—2981no—
279C22×C4—2981no—
280C22×C4C22×D14911yescharacteristic
281C22×C4C22×D14911yescharacteristic
282C22×C4C22×D14911yescharacteristic
283Q16—5961no—
284SD16—5961no—
285SD16—5961no—
286D8—5961no—
287M16—5961no—
288C2×C8—5961no—
289C2×C8—1491no—
290C2×C8—1491no—
291C2×C8—1491no—
292C2×C8—1491no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—2981no—
297C4⋊C4—2981no—
298C4⋊C4—2981no—
299C4⋊C4—1491no—
300C4⋊C4—1491no—
301C4⋊C4C22×D14911yescharacteristic
302C4⋊C4C22×D14911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—2981no—
308C22⋊C4—2981no—
309C22⋊C4—2981no—
310C22⋊C4—2981no—
311C23—21no—
312C23—2981no—
313C23C2×C22⋊D14911yescharacteristic
314C23C2×C22⋊D14911yescharacteristic
315C23C2×C22⋊D14911yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—2981no—
320Q8—2981no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—2981no—
330D4—2981no—
331D4—5962no—
332D4—11921no—
333D4—11921no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—2981no—
346C2×C4—2981no—
347C2×C4—2981no—
348C2×C4—5962no—
349C2×C4—11921no—
350C2×C4C2×C22⋊D14911yescharacteristic
351C2×C4C2×C22⋊D14911yescharacteristic
352C2×C4C2×C22⋊D14911yescharacteristic
353C2×C4C23×D14911yescharacteristic
354C8—2981no—
355C8—2981no—
356C8—2981no—
357C8—2981no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—5961no—
371C22—5961no—
372C22—5961no—
373C22C22×C22⋊D14911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—5961no—
381C4—5961no—
382C4—5961no—
383C4#1801195611yescharacteristic
384C4#1801195611yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—11921no—
390C2#2375018411yescharacteristic
391C2#2375043311yescharacteristic
392C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#537×C149C2
socleC22×C149C22×D4
hypercenter#537D149
hypocenterC149#3204
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #23750203C2semidirect
2. #23749955C2semidirect
3. #23749953C2semidirect
4. #23749943C2semidirect
5. #23749941C2semidirect
6. #23749881C2semidirect
7. #23749876C2semidirect
8. #23749856C2semidirect
9. #23749852C2semidirect
10. #23749787C2semidirect
11. #23749785C2semidirect
12. #23749770C2semidirect
13. #23749768C2semidirect
14. #23749592C2semidirect
15. #537×C149C2semidirect
196. C149#3204semidirect
199. #537D149semidirect

Maximal subgroups

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

subgroupindex
#237502032
#237499552
#237499532
#237499432
#237499412
#237498812
#237498762
#237498562
#237498522
#237497872
#237497852
#237497702
#237497682
#237495922
#537×C1492
#3204149