Finite Group Databasebeta

← #34055806

Subgroups — #34055806

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#23750248C211yesmaximal, characteristic, complemented
2#23750199C211yesmaximal, characteristic, complemented
3#23750018C211yesmaximal, characteristic, complemented
4#23750010C211yesmaximal, characteristic, complemented
5#23749986C211yesmaximal, characteristic, complemented
6#23749974C211yesmaximal, characteristic, complemented
7#23749849C211yesmaximal, characteristic, complemented
8#23749843C211yesmaximal, characteristic, complemented
9#23749833C211yesmaximal, characteristic, complemented
10#23749829C211yesmaximal, characteristic, complemented
11#23749785C211yesmaximal, characteristic, complemented
12#23749772C211yesmaximal, characteristic
13#23749764C211yesmaximal, characteristic, complemented
14#23749683C211yesmaximal, characteristic, complemented
15#451×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21C2×#14558723C2211yescharacteristic
22C2×D1192C2211yescharacteristic
23#18011910C2211yescharacteristic
24#18011909C2211yescharacteristic
25#18011909C2211yescharacteristic
26#18011906—21no—
27#18011900C2211yescharacteristic
28#18011900C2211yescharacteristic
29#18011900C2211yescharacteristic
30#18011897—21no—
31#18011894—21no—
32#18011894—21no—
33#18011893—21no—
34#18011891—21no—
35#18011887—21no—
36#18011887—21no—
37#18011885C2211yescharacteristic
38Q8×Dic149C2211yescharacteristic
39#18011873C2211yescharacteristic
40#18011870C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C22×Q8×C149C2211yescharacteristic
53C2×Q16×C149C2211yescharacteristic
54C2×Q16×C149C2211yescharacteristic
55C22⋊Q8×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×D596C2311yescharacteristic
64C2×D596C2311yescharacteristic
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69#14558726—41no—
70#14558725—41no—
71#14558723—41no—
72#14558723—41no—
73#14558723—41no—
74D1192—41no—
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C4⋊Dic149—21no—
78C4⋊Dic149D411yescharacteristic
79C4⋊Dic149D411yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149D411yescharacteristic
87C22⋊Dic149D411yescharacteristic
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96C4×Dic149—21no—
97C4×Dic149C2311yescharacteristic
98C4×Dic149C2311yescharacteristic
99C2×Q8×C149—21no—
100C2×Q8×C149—41no—
101C2×Q8×C149—41no—
102C2×Q8×C149C2311yescharacteristic
103C2×Q8×C149C2311yescharacteristic
104C2×Q8×C149C2311yescharacteristic
105C22×C4×C149—21no—
106C22×C4×C149C2311yescharacteristic
107Q16×C149—41no—
108Q16×C149—41no—
109C2×C8×C149C2311yescharacteristic
110C2×C8×C149C2311yescharacteristic
111C4⋊C4×C149—21no—
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149—21no—
115C22×D149—21no—
116Dic298—21no—
117Dic298—21no—
118Dic298—81no—
119D596—21no—
120D596—21no—
121D596—21no—
122D596—21no—
123C22⋊D149—42no—
124C22⋊D149—81no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C2×Dic149C2×D411yescharacteristic
131C4×D149—42no—
132C4×D149—81no—
133#11924746—21no—
134#11924746—21no—
135C23×C149C2×D411yescharacteristic
136Q8×C149—21no—
137Q8×C149—21no—
138Q8×C149—21no—
139Q8×C149—21no—
140Q8×C149—21no—
141Q8×C149—21no—
142Q8×C149—42no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—42no—
150C2×C4×C149C2×D411yescharacteristic
151C2×C4×C149C2411yescharacteristic
152C8×C149—21no—
153C8×C149—21no—
154C22×C149—21no—
155C22×C149—21no—
156C22×C149—21no—
157C22×C149C22×D411yescharacteristic
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C4×C149—21no—
165C4×C149—41no—
166C4×C149—41no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149H(5,𝔽2)11yescharacteristic
170C4×C149H(5,𝔽2)11yescharacteristic
171Dic149—21no—
172Dic149—21no—
173Dic149—21no—
174Dic149—21no—
175Dic149—41no—
176Dic149—41no—
177C2×C149—41no—
178C2×C149#53511yescharacteristic
179C2×C149#57711yescharacteristic
180C2×C149#57811yescharacteristic
181D149—81no—
182D149—81no—
183C149#322511yescharacteristic, complemented, Sylow
184#3225—1491nomaximal, Sylow
185#542—1491no—
186#536—1491no—
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#451D14911yescharacteristic, complemented
197#449—1491no—
198#448—1491no—
199#433—1491no—
200C2×#41—1491no—
201C22×Q8C2×D14911yescharacteristic
202C2×Q16—1491no—
203C2×Q16C2×D14911yescharacteristic
204C2×Q16C2×D14911yescharacteristic
205C2×SD16—1491no—
206C2×SD16—1491no—
207C2×SD16—1491no—
208C2×SD16—1491no—
209C2×D8—1491no—
210C4⋊Q8—1491no—
211C4⋊Q8—1491no—
212C4⋊Q8—1491no—
213#126—2981no—
214#124—2981no—
215#124—1491no—
216#124—1491no—
217#124—1491no—
218#123—2981no—
219#123—2981no—
220#123—2981no—
221C22⋊Q8—2981no—
222C22⋊Q8—2981no—
223C22⋊Q8—2981no—
224C22⋊Q8C2×D14911yescharacteristic
225#121—1491no—
226C4×Q8—1491no—
227C4×D4—1491no—
228#117—1491no—
229C4⋊C8—1491no—
230C4⋊C8—1491no—
231#103—1491no—
232#103—1491no—
233#103—1491no—
234#103—1491no—
235#103C2×D14911yescharacteristic
236#103C2×D14911yescharacteristic
237#102—1491no—
238#102—1491no—
239C22⋊C8—1491no—
240C22⋊C8C2×D14911yescharacteristic
241#97—1491no—
242C4×C8—1491no—
243#41—5961no—
244#41—5961no—
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—2981no—
254C2×D4—2981no—
255C2×D4—1491no—
256C2×D4—1491no—
257C22×C4—21no—
258C22×C4—2981no—
259C22×C4—2981no—
260C22×C4C22×D14911yescharacteristic
261Q16—41no—
262Q16—41no—
263Q16—5961no—
264SD16—5961no—
265SD16—5961no—
266SD16—5961no—
267SD16—5961no—
268D8—5961no—
269C2×C8—1491no—
270C2×C8—1491no—
271C2×C8C22×D14911yescharacteristic
272C2×C8C22×D14911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—2981no—
279C4⋊C4—2981no—
280C4⋊C4—1491no—
281C4⋊C4—1491no—
282C4⋊C4—1491no—
283C4⋊C4C22×D14911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—1491no—
294C22⋊C4—1491no—
295C42—2981no—
296C42—1491no—
297C42—1491no—
298C23—2981no—
299C23—2981no—
300C23D4×D14911yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—2981no—
309Q8—2981no—
310Q8—11921no—
311D4—2981no—
312D4—2981no—
313D4—2981no—
314D4—2981no—
315D4—5962no—
316D4—11921no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—2981no—
325C2×C4—2981no—
326C2×C4—5962no—
327C2×C4—1491no—
328C2×C4—1491no—
329C2×C4—1491no—
330C2×C4—1491no—
331C2×C4—11921no—
332C2×C4D4×D14911yescharacteristic
333C2×C4C23×D14911yescharacteristic
334C8—21no—
335C8—21no—
336C8—2981no—
337C8—2981no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—5961no—
342C22—5961no—
343C22—5961no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22C2×D4×D14911yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—2981no—
354C4—2981no—
355C4—2981no—
356C4—2981no—
357C4—5961no—
358C4—5961no—
359C4#1801195611yescharacteristic
360C4#1801195611yescharacteristic
361C2—41no—
362C2—11921no—
363C2—11921no—
364C2#2375019011yescharacteristic
365C2#2375043411yescharacteristic
366C2#2375043811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#451×C149C2
socleC22×C149C22×D4
prime radical#23749772C2
hypercenter#451D149
hypocenterC149#3225
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #23750248C2semidirect
2. #23750199C2semidirect
3. #23750018C2semidirect
4. #23750010C2semidirect
5. #23749986C2semidirect
6. #23749974C2semidirect
7. #23749849C2semidirect
8. #23749843C2semidirect
9. #23749833C2semidirect
10. #23749829C2semidirect
11. #23749785C2semidirect
13. #23749764C2semidirect
14. #23749683C2semidirect
15. #451×C149C2semidirect
183. C149#3225semidirect
196. #451D149semidirect

Maximal subgroups

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

subgroupindex
#237502482
#237501992
#237500182
#237500102
#237499862
#237499742
#237498492
#237498432
#237498332
#237498292
#237497852
#237497722
#237497642
#237496832
#451×C1492
#3225149