Finite Group Databasebeta

← #34055800

Subgroups — #34055800

Order 19072.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750246C211yesmaximal, characteristic, complemented
2#23750017C211yesmaximal, characteristic, complemented
3#23750007C211yesmaximal, characteristic, complemented
4#23749984C211yesmaximal, characteristic, complemented
5#23749975C211yesmaximal, characteristic, complemented
6#23749844C211yesmaximal, characteristic, complemented
7#23749837C211yesmaximal, characteristic, complemented
8#23749832C211yesmaximal, characteristic, complemented
9#23749827C211yesmaximal, characteristic, complemented
10#23749787C211yesmaximal, characteristic, complemented
11#23749781C211yesmaximal, characteristic, complemented
12#23749770C211yesmaximal, characteristic
13#23749764C211yesmaximal, characteristic, complemented
14#23749686C211yesmaximal, characteristic, complemented
15#536×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21C2×#14558723C2211yescharacteristic
22C2×#14558723C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24#18011911C2211yescharacteristic
25#18011906—21no—
26#18011899C2211yescharacteristic
27#18011897—21no—
28#18011893—21no—
29#18011890C2211yescharacteristic
30#18011889—21no—
31#18011885C2211yescharacteristic
32C4×Dic298C2211yescharacteristic
33C4×D596C2211yescharacteristic
34C4⋊#11924746C2211yescharacteristic
35C4⋊#11924746C2211yescharacteristic
36#18011835C2211yescharacteristic
37#18011835C2211yescharacteristic
38#18011835C2211yescharacteristic
39#18011835C2211yescharacteristic
40#18011835C2211yescharacteristic
41#18011835C2211yescharacteristic
42#18011832C2211yescharacteristic
43#18011832C2211yescharacteristic
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46#18011822C2211yescharacteristic
47C4×#11924746C2211yescharacteristic
48C2×#41×C149C2211yescharacteristic
49C22×Q8×C149C2211yescharacteristic
50C4⋊Q8×C149C2211yescharacteristic
51C4⋊Q8×C149C2211yescharacteristic
52#124×C149C2211yescharacteristic
53#124×C149C2211yescharacteristic
54#123×C149—21no—
55#123×C149—21no—
56C22⋊Q8×C149—21no—
57C22⋊Q8×C149—21no—
58#117×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C4×D149—21no—
64#14558726—41no—
65#14558726—41no—
66#14558726—41no—
67#14558724—41no—
68#14558723—41no—
69#14558723—41no—
70#14558723—41no—
71#14558721—41no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81C22⋊Dic149—21no—
82#14558713—21no—
83#14558713—21no—
84#14558713—21no—
85#14558713—21no—
86C4×Dic149—21no—
87#41×C149—41no—
88#41×C149—41no—
89C2×Q8×C149—21no—
90C2×Q8×C149—41no—
91C2×Q8×C149—41no—
92C2×Q8×C149C2311yescharacteristic
93C2×Q8×C149C2311yescharacteristic
94C2×Q8×C149C2311yescharacteristic
95C2×D4×C149—21no—
96C2×D4×C149C2311yescharacteristic
97C22×C4×C149—21no—
98C22×C4×C149—21no—
99C22×C4×C149C2311yescharacteristic
100C4⋊C4×C149—21no—
101C4⋊C4×C149—21no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149—21no—
104C4⋊C4×C149D411yescharacteristic
105C4⋊C4×C149D411yescharacteristic
106C22⋊C4×C149—21no—
107C22⋊C4×C149—21no—
108C22⋊C4×C149—21no—
109C22⋊C4×C149—21no—
110C22⋊C4×C149D411yescharacteristic
111C22⋊C4×C149D411yescharacteristic
112C42×C149C2311yescharacteristic
113C42×C149C2311yescharacteristic
114C22×D149—21no—
115Dic298—21no—
116Dic298—21no—
117Dic298—81no—
118D596—21no—
119D596—21no—
120C22⋊D149—81no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C4×D149—81no—
125#11924746—21no—
126#11924746—21no—
127#11924746—21no—
128#11924746—21no—
129C23×C149—21no—
130C23×C149C2×D411yescharacteristic
131Q8×C149—21no—
132Q8×C149—21no—
133Q8×C149—21no—
134Q8×C149—21no—
135Q8×C149—21no—
136Q8×C149—21no—
137Q8×C149—42no—
138D4×C149—21no—
139D4×C149—21no—
140D4×C149—42no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—42no—
147C2×C4×C149—42no—
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2×D411yescharacteristic
150C2×C4×C149C2×D411yescharacteristic
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2411yescharacteristic
154C22×C149—21no—
155C22×C149—21no—
156C22×C149—21no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149C22×D411yescharacteristic
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—21no—
167C4×C149—21no—
168C4×C149—21no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149—41no—
172C4×C149H(5,𝔽2)11yescharacteristic
173C4×C149H(5,𝔽2)11yescharacteristic
174Dic149—41no—
175Dic149—41no—
176Dic149—41no—
177C2×C149—41no—
178C2×C149—81no—
179C2×C149#53511yescharacteristic
180C2×C149#57711yescharacteristic
181C2×C149#57811yescharacteristic
182D149—81no—
183C149#322511yescharacteristic, complemented, Sylow
184#3225—1491nomaximal, Sylow
185#542—1491no—
186#536D14911yescharacteristic, complemented
187#497—1491no—
188#495—1491no—
189#489—1491no—
190#487—1491no—
191#464—1491no—
192#463—1491no—
193#462—1491no—
194#461—1491no—
195#452—1491no—
196#451—1491no—
197#449—1491no—
198#448—1491no—
199#433—1491no—
200C2×#41C2×D14911yescharacteristic
201C22×Q8C2×D14911yescharacteristic
202C2×Q16—1491no—
203C2×Q16—1491no—
204C2×Q16—1491no—
205C2×SD16—1491no—
206C2×SD16—1491no—
207C2×SD16—1491no—
208C2×SD16—1491no—
209C2×D8—1491no—
210C4⋊Q8—1491no—
211C4⋊Q8C2×D14911yescharacteristic
212C4⋊Q8C2×D14911yescharacteristic
213#126—2981no—
214#124—2981no—
215#124—1491no—
216#124C2×D14911yescharacteristic
217#124C2×D14911yescharacteristic
218#123—21no—
219#123—21no—
220#123—2981no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—2981no—
224C22⋊Q8—1491no—
225#121—1491no—
226C4×Q8—1491no—
227C4×D4—1491no—
228#117C2×D14911yescharacteristic
229C4⋊C8—1491no—
230C4⋊C8—1491no—
231#103—1491no—
232#103—1491no—
233#103—1491no—
234#103—1491no—
235#103—1491no—
236#103—1491no—
237#102—1491no—
238#102—1491no—
239C22⋊C8—1491no—
240C22⋊C8—1491no—
241#97—1491no—
242C4×C8—1491no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—2981no—
249C2×Q8—1491no—
250C2×Q8C22×D14911yescharacteristic
251C2×Q8C22×D14911yescharacteristic
252C2×Q8C22×D14911yescharacteristic
253C2×D4—21no—
254C2×D4—2981no—
255C2×D4—1491no—
256C2×D4C22×D14911yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—2981no—
260C22×C4C22×D14911yescharacteristic
261Q16—5961no—
262Q16—5961no—
263Q16—5961no—
264SD16—5961no—
265SD16—5961no—
266SD16—5961no—
267SD16—5961no—
268D8—5961no—
269C2×C8—1491no—
270C2×C8—1491no—
271C2×C8—1491no—
272C2×C8—1491no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—2981no—
278C4⋊C4—2981no—
279C4⋊C4—2981no—
280C4⋊C4—1491no—
281C4⋊C4—1491no—
282C4⋊C4C22⋊D14911yescharacteristic
283C4⋊C4C22⋊D14911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4C22⋊D14911yescharacteristic
294C22⋊C4C22⋊D14911yescharacteristic
295C42—2981no—
296C42C22×D14911yescharacteristic
297C42C22×D14911yescharacteristic
298C23—21no—
299C23—2981no—
300C23C2×C22⋊D14911yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—2981no—
309Q8—2981no—
310Q8—11921no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—2981no—
315D4—2981no—
316D4—11921no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—2981no—
325C2×C4—2981no—
326C2×C4—2981no—
327C2×C4—11921no—
328C2×C4C2×C22⋊D14911yescharacteristic
329C2×C4C2×C22⋊D14911yescharacteristic
330C2×C4C2×C22⋊D14911yescharacteristic
331C2×C4C2×C22⋊D14911yescharacteristic
332C2×C4C2×C22⋊D14911yescharacteristic
333C2×C4C23×D14911yescharacteristic
334C8—2981no—
335C8—2981no—
336C8—2981no—
337C8—2981no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22C22×C22⋊D14911yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—5961no—
357C4—5961no—
358C4—5961no—
359C4#1801195611yescharacteristic
360C4#1801195611yescharacteristic
361C2—41no—
362C2—81no—
363C2—11921no—
364C2#2375019211yescharacteristic
365C2#2375043311yescharacteristic
366C2#2375044011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#536×C149C2
socleC22×C149C22×D4
prime radical#23749770C2
hypercenter#536D149
hypocenterC149#3225
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #23750246C2semidirect
2. #23750017C2semidirect
3. #23750007C2semidirect
4. #23749984C2semidirect
5. #23749975C2semidirect
6. #23749844C2semidirect
7. #23749837C2semidirect
8. #23749832C2semidirect
9. #23749827C2semidirect
10. #23749787C2semidirect
11. #23749781C2semidirect
13. #23749764C2semidirect
14. #23749686C2semidirect
15. #536×C149C2semidirect
183. C149#3225semidirect
186. #536D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237500172
#237500072
#237499842
#237499752
#237498442
#237498372
#237498322
#237498272
#237497872
#237497812
#237497702
#237497642
#237496862
#536×C1492
#3225149