Finite Group Databasebeta

← #34055662

Subgroups — #34055662

Order 19072.

400 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750174C211yesmaximal, characteristic, complemented
2#23750154C211yesmaximal, characteristic, complemented
3#23750007C211yesmaximal, characteristic, complemented
4#23749980C211yesmaximal, characteristic, complemented
5#23749979C211yesmaximal, characteristic, complemented
6#23749833C211yesmaximal, characteristic, complemented
7#23749828C211yesmaximal, characteristic, complemented
8#23749823C211yesmaximal, characteristic, complemented
9#23749818C211yesmaximal, characteristic, complemented
10#23749786C211yesmaximal, characteristic, complemented
11#23749784C211yesmaximal, characteristic, complemented
12#23749769C211yesmaximal, characteristic, complemented
13#23749767C211yesmaximal, characteristic, complemented
14#23749676C211yesmaximal, characteristic, complemented
15#495×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21C2×#14558721C2211yescharacteristic
22#18011909C2211yescharacteristic
23#18011907C2211yescharacteristic
24#18011904—21no—
25#18011903C2211yescharacteristic
26#18011899C2211yescharacteristic
27#18011893—21no—
28#18011887C2211yescharacteristic
29#18011884—21no—
30#18011884—21no—
31#18011882C2211yescharacteristic
32Q8×Dic149C2211yescharacteristic
33D4×Dic149C2211yescharacteristic
34#18011871—21no—
35#18011871—21no—
36#18011871—21no—
37#18011867—21no—
38C42×D149C2211yescharacteristic
39#18011840C2211yescharacteristic
40#18011840C2211yescharacteristic
41#18011836C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51C4×#11924746C2211yescharacteristic
52C2×Q16×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C2×D8×C149C2211yescharacteristic
56#124×C149C2211yescharacteristic
57#124×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558737—41no—
60#14558737—41no—
61#14558735—41no—
62#14558735—41no—
63C2×Dic298C2311yescharacteristic
64C2×D596—21no—
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C22×Dic149—21no—
71C22×Dic149—21no—
72C2×C4×D149—21no—
73C2×C4×D149D411yescharacteristic
74C2×C4×D149D411yescharacteristic
75C2×C4×D149C2311yescharacteristic
76#14558726—41no—
77#14558724—41no—
78#14558723—41no—
79#14558721—41no—
80C2×#11924746C2311yescharacteristic
81C2×#11924746C2311yescharacteristic
82C4⋊Dic149—21no—
83C4⋊Dic149C2311yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89#14558715—21no—
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95C4×Dic149—21no—
96C4×Dic149D411yescharacteristic
97C4×Dic149D411yescharacteristic
98C4×Dic149C2311yescharacteristic
99C2×Q8×C149C2311yescharacteristic
100C2×Q8×C149C2311yescharacteristic
101C2×D4×C149C2311yescharacteristic
102C2×D4×C149C2311yescharacteristic
103Q16×C149—41no—
104SD16×C149—41no—
105SD16×C149—41no—
106D8×C149—41no—
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C22⋊C4×C149—21no—
110C22⋊C4×C149—21no—
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C42×C149C2311yescharacteristic
114C22×D149—21no—
115C22×D149C2×D411yescharacteristic
116Dic298—21no—
117Dic298—21no—
118D596—21no—
119D596—21no—
120D596—42no—
121C22⋊D149—42no—
122C22⋊D149—42no—
123C22⋊D149—42no—
124C22⋊D149—42no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—42no—
129C2×Dic149—42no—
130C2×Dic149C2×D411yescharacteristic
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C4×D149—21no—
134C4×D149—21no—
135C4×D149—22no—
136C4×D149—41no—
137C4×D149—42no—
138#11924746—21no—
139#11924746—21no—
140C23×C149—21no—
141C23×C149—21no—
142Q8×C149—21no—
143Q8×C149—21no—
144Q8×C149—21no—
145Q8×C149—21no—
146D4×C149—21no—
147D4×C149—21no—
148D4×C149—21no—
149D4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2×D411yescharacteristic
154C2×C4×C149C2411yescharacteristic
155C8×C149—21no—
156C8×C149—21no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149—41no—
163C22×C149C22×D411yescharacteristic
164C2×D149—21no—
165C2×D149—21no—
166C2×D149—21no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C4×C149—21no—
171C4×C149—21no—
172C4×C149—41no—
173C4×C149—41no—
174C4×C149H(5,𝔽2)11yescharacteristic
175C4×C149H(5,𝔽2)11yescharacteristic
176Dic149—21no—
177Dic149—21no—
178Dic149—41no—
179Dic149—41no—
180Dic149—41no—
181Dic149#13512yes—
182C2×C149—81no—
183C2×C149—81no—
184C2×C149#53511yescharacteristic
185C2×C149C2×#13511yescharacteristic
186C2×C149#57511yescharacteristic
187D149—41no—
188D149—81no—
189C149#321211yescharacteristic, complemented, Sylow
190#3212—1491nomaximal, Sylow
191#532—1491no—
192#529—1491no—
193#495—1491no—
194#495D14911yescharacteristic, complemented
195#488—1491no—
196#488—1491no—
197#462—1491no—
198#461—1491no—
199#460—1491no—
200#459—1491no—
201#452—1491no—
202#452—1491no—
203#449—1491no—
204#449—1491no—
205#431—1491no—
206C2×#41—1491no—
207C2×#41—1491no—
208C2×Q16—1491no—
209C2×Q16C2×D14911yescharacteristic
210C2×SD16—1491no—
211C2×SD16—1491no—
212C2×SD16C2×D14911yescharacteristic
213C2×SD16C2×D14911yescharacteristic
214C2×D8—1491no—
215C2×D8C2×D14911yescharacteristic
216C4⋊Q8—1491no—
217#127—1491no—
218#126—2981no—
219#125—1491no—
220#124—1491no—
221#124C2×D14911yescharacteristic
222#124C2×D14911yescharacteristic
223#123—2981no—
224C22⋊Q8—1491no—
225#121—2981no—
226#121—2981no—
227#121—1491no—
228C4×Q8—1491no—
229C4×D4—2981no—
230C4×D4—2981no—
231C4×D4—2981no—
232C4×D4—1491no—
233#117—2981no—
234C2×C42—1491no—
235C4⋊C8—1491no—
236C4⋊C8—1491no—
237#103—1491no—
238#103—1491no—
239#103—1491no—
240#103—1491no—
241#102—1491no—
242#102—1491no—
243#102—1491no—
244#102—1491no—
245C22⋊C8—1491no—
246C22⋊C8—1491no—
247C4×C8—1491no—
248C4×C8C2×D14911yescharacteristic
249#41—5961no—
250#41—5961no—
251#41—5961no—
252#41—5961no—
253C2×Q8—1491no—
254C2×Q8C22×D14911yescharacteristic
255C2×Q8C22×D14911yescharacteristic
256C2×D4—2981no—
257C2×D4—2981no—
258C2×D4—2981no—
259C2×D4—2981no—
260C2×D4—2981no—
261C2×D4—1491no—
262C2×D4C22×D14911yescharacteristic
263C2×D4C22×D14911yescharacteristic
264C22×C4—2981no—
265C22×C4—2981no—
266C22×C4—2981no—
267C22×C4—1491no—
268C22×C4—1491no—
269C22×C4—1491no—
270Q16—41no—
271Q16—5961no—
272SD16—41no—
273SD16—41no—
274SD16—5961no—
275SD16—5961no—
276D8—41no—
277D8—5961no—
278C2×C8—1491no—
279C2×C8—1491no—
280C2×C8C22×D14911yescharacteristic
281C2×C8C22×D14911yescharacteristic
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—2981no—
286C4⋊C4—2981no—
287C4⋊C4—2981no—
288C4⋊C4—1491no—
289C4⋊C4—1491no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C42—2981no—
300C42—1491no—
301C42—1491no—
302C42—1491no—
303C42C22×D14911yescharacteristic
304C23—21no—
305C23—21no—
306C23—2981no—
307C23—1491no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—2981no—
313Q8—2981no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—2981no—
319D4—2981no—
320D4—5962no—
321D4—5962no—
322D4—5962no—
323D4—5962no—
324D4—5962no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—2982no—
328C2×C4—2981no—
329C2×C4—2981no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—5961no—
334C2×C4—5962no—
335C2×C4—5962no—
336C2×C4—5962no—
337C2×C4—1491no—
338C2×C4—1491no—
339C2×C4—1491no—
340C2×C4D4×D14911yescharacteristic
341C2×C4D4×D14911yescharacteristic
342C2×C4C23×D14911yescharacteristic
343C8—21no—
344C8—21no—
345C8—2981no—
346C8—2981no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—2981no—
354C22—2981no—
355C22—2981no—
356C22—5961no—
357C22—5961no—
358C22—5961no—
359C22C2×D4×D14911yescharacteristic
360C4—21no—
361C4—21no—
362C4—41no—
363C4—41no—
364C4—2981no—
365C4—2981no—
366C4—5961no—
367C4—5961no—
368C4—5961no—
369C4—1492no—
370C4#1801195611yescharacteristic
371C4#1801195611yescharacteristic
372C2—81no—
373C2—81no—
374C2—5961no—
375C2—11921no—
376C2#2375018811yescharacteristic
377C2#135×D14911yescharacteristic
378C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#495×C149C2
socleC22×C149C22×D4
hypercenter#495D149
hypocenterC149#3212
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #23750174C2semidirect
2. #23750154C2semidirect
3. #23750007C2semidirect
4. #23749980C2semidirect
5. #23749979C2semidirect
6. #23749833C2semidirect
7. #23749828C2semidirect
8. #23749823C2semidirect
9. #23749818C2semidirect
10. #23749786C2semidirect
11. #23749784C2semidirect
12. #23749769C2semidirect
13. #23749767C2semidirect
14. #23749676C2semidirect
15. #495×C149C2semidirect
189. C149#3212semidirect
194. #495D149semidirect

Maximal subgroups

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

subgroupindex
#237501742
#237501542
#237500072
#237499802
#237499792
#237498332
#237498282
#237498232
#237498182
#237497862
#237497842
#237497692
#237497672
#237496762
#495×C1492
#3212149