Finite Group Databasebeta

← #34055595

Subgroups — #34055595

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#23750206C211yesmaximal, characteristic, complemented
2#23750205C211yesmaximal, characteristic, complemented
3#23749962C211yesmaximal, characteristic, complemented
4#23749940C211yesmaximal, characteristic, complemented
5#23749938C211yesmaximal, characteristic, complemented
6#23749874C211yesmaximal, characteristic, complemented
7#23749872C211yesmaximal, characteristic, complemented
8#23749865C211yesmaximal, characteristic, complemented
9#23749862C211yesmaximal, characteristic, complemented
10#23749790C211yesmaximal, characteristic, complemented
11#23749785C211yesmaximal, characteristic, complemented
12#23749773C211yesmaximal, characteristic, complemented
13#23749772C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic, complemented
15#484×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558736C2211yescharacteristic
18C2×#14558736C2211yescharacteristic
19C2×#14558726C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558723C2211yescharacteristic
22C2×D1192C2211yescharacteristic
23C2×#14558719C2211yescharacteristic
24C2×C8×D149C2211yescharacteristic
25#18011891—21no—
26#18011891C2211yescharacteristic
27#18011891C2211yescharacteristic
28#18011889—21no—
29#18011887C2211yescharacteristic
30#18011886—21no—
31#18011886—21no—
32#18011886C2211yescharacteristic
33#18011886C2211yescharacteristic
34#18011886C2211yescharacteristic
35#18011885—21no—
36#18011885—21no—
37#18011885C2211yescharacteristic
38#18011884—21no—
39#18011884—21no—
40C4⋊C4×D149C2211yescharacteristic
41#18011844C2211yescharacteristic
42#18011844C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C22⋊Q8×C149C2211yescharacteristic
53C2×C4⋊C4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558737—41no—
60#14558737—41no—
61#14558736—41no—
62#14558736—41no—
63#14558736—41no—
64#14558736—41no—
65C2×Dic298D411yescharacteristic
66C2×Dic298C2311yescharacteristic
67C2×D596—21no—
68C2×D596—21no—
69C2×D596—21no—
70C2×D596—21no—
71C2×D596D411yescharacteristic
72C2×D596C2311yescharacteristic
73C2×D596C2311yescharacteristic
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76C2×C22⋊D149D411yescharacteristic
77C2×C22⋊D149D411yescharacteristic
78C2×C4×D149—21no—
79C2×C4×D149—21no—
80C2×C4×D149—21no—
81C2×C4×D149C2311yescharacteristic
82C2×C4×D149C2311yescharacteristic
83#14558726—41no—
84#14558725—41no—
85#14558723—41no—
86D1192—41no—
87#14558719—41no—
88C2×#11924746C2311yescharacteristic
89C2×#11924746C2311yescharacteristic
90C8×D149—41no—
91C4⋊Dic149—21no—
92C4⋊Dic149—21no—
93C4⋊Dic149C2311yescharacteristic
94#14558715—21no—
95#14558715—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101#14558713—21no—
102#14558713—21no—
103C2×Q8×C149C2311yescharacteristic
104C22×C4×C149—21no—
105C22×C4×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149—21no—
109C4⋊C4×C149—21no—
110C4⋊C4×C149C2311yescharacteristic
111C4⋊C4×C149C2311yescharacteristic
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149—21no—
115C22×D149—21no—
116C22×D149C2×D411yescharacteristic
117C22×D149C2×D411yescharacteristic
118Dic298—21no—
119Dic298—21no—
120Dic298—41no—
121D596—21no—
122D596—21no—
123D596—21no—
124D596—21no—
125D596—41no—
126D596—42no—
127D596—81no—
128D596—81no—
129D596—81no—
130C22⋊D149—41no—
131C22⋊D149—41no—
132C22⋊D149—42no—
133C22⋊D149—81no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149C2×D411yescharacteristic
137C2×Dic149C2×D411yescharacteristic
138C4×D149—21no—
139C4×D149—21no—
140C4×D149—21no—
141C4×D149—21no—
142C4×D149—42no—
143C4×D149—42no—
144C4×D149—81no—
145#11924746—21no—
146#11924746—21no—
147C23×C149C2×D411yescharacteristic
148Q8×C149—21no—
149Q8×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—21no—
156C2×C4×C149—81no—
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2411yescharacteristic
159C8×C149—21no—
160C8×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149C22×D411yescharacteristic
165C2×D149—21no—
166C2×D149—21no—
167C2×D149—21no—
168C2×D149—21no—
169C2×D149—21no—
170C2×D149—21no—
171C2×D149—41no—
172C2×D149—41no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C4×C149—21no—
178C4×C149—41no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149—41no—
182C4×C149H(5,𝔽2)11yescharacteristic
183C4×C149H(5,𝔽2)11yescharacteristic
184Dic149—21no—
185Dic149—21no—
186Dic149—41no—
187Dic149—41no—
188C2×C149—41no—
189C2×C149#53411yescharacteristic
190C2×C149#57611yescharacteristic
191C2×C149#57811yescharacteristic
192D149—41no—
193D149—41no—
194D149—81no—
195D149—81no—
196C149#320311yescharacteristic, complemented, Sylow
197#3203—1491nomaximal, Sylow
198#537—1491no—
199#537—1491no—
200#484—1491no—
201#484D14911yescharacteristic, complemented
202#480—1491no—
203#480—1491no—
204#468—1491no—
205#468—1491no—
206#467—1491no—
207#466—1491no—
208#452—1491no—
209#452—1491no—
210#449—1491no—
211#449—1491no—
212#408—1491no—
213C2×#41—1491no—
214C2×#41—1491no—
215C2×#41—1491no—
216C2×Q16—1491no—
217C2×SD16—1491no—
218C2×SD16—1491no—
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⋊C4C2×D14911yescharacteristic
240#107—1491no—
241#107—1491no—
242#107C2×D14911yescharacteristic
243#107C2×D14911yescharacteristic
244#103—1491no—
245#103—1491no—
246#103C2×D14911yescharacteristic
247#103C2×D14911yescharacteristic
248#102—1491no—
249#102—1491no—
250#102—1491no—
251#102—1491no—
252C22⋊C8—1491no—
253C22⋊C8—1491no—
254C22⋊C8—1491no—
255C22⋊C8C2×D14911yescharacteristic
256#41—5961no—
257#41—5961no—
258#41—5961no—
259#41—5961no—
260#41—5961no—
261#41—5961no—
262C2×Q8—1491no—
263C2×Q8—1491no—
264C2×Q8C22×D14911yescharacteristic
265C2×D4—2981no—
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×D4—1491no—
276C22×C4—21no—
277C22×C4—2981no—
278C22×C4—2981no—
279C22×C4—2981no—
280C22×C4—1491no—
281C22×C4—1491no—
282C22×C4C22×D14911yescharacteristic
283Q16—5961no—
284SD16—5961no—
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—21no—
295C4⋊C4—2981no—
296C4⋊C4—2981no—
297C4⋊C4—2981no—
298C4⋊C4—2981no—
299C4⋊C4—1491no—
300C4⋊C4C22×D14911yescharacteristic
301C4⋊C4C22×D14911yescharacteristic
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—2981no—
312C23—2981no—
313C23—1491no—
314C23—1491no—
315C23D4×D14911yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—2981no—
319Q8—2981no—
320Q8—5961no—
321D4—2981no—
322D4—2981no—
323D4—2981no—
324D4—2981no—
325D4—5961no—
326D4—5962no—
327D4—5961no—
328D4—5961no—
329D4—5962no—
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—21no—
340C2×C4—81no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—2981no—
347C2×C4—5962no—
348C2×C4—5962no—
349C2×C4—1491no—
350C2×C4—1491no—
351C2×C4—11921no—
352C2×C4D4×D14911yescharacteristic
353C2×C4C23×D14911yescharacteristic
354C8—21no—
355C8—21no—
356C8—2981no—
357C8—2981no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—2981no—
362C22—2981no—
363C22—2981no—
364C22—2981no—
365C22—2981no—
366C22—2981no—
367C22—5961no—
368C22—5961no—
369C22—5961no—
370C22—5961no—
371C22—5961no—
372C22—5961no—
373C22C2×D4×D14911yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—2981no—
380C4—2981no—
381C4—5961no—
382C4—5961no—
383C4#1801195711yescharacteristic
384C4#1801195711yescharacteristic
385C2—41no—
386C2—5961no—
387C2—5961no—
388C2—11921no—
389C2—11921no—
390C2#2375018611yescharacteristic
391C2#2375042911yescharacteristic
392C2#2375043811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#484×C149C2
socleC22×C149C22×D4
hypercenter#484D149
hypocenterC149#3203
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #23750206C2semidirect
2. #23750205C2semidirect
3. #23749962C2semidirect
4. #23749940C2semidirect
5. #23749938C2semidirect
6. #23749874C2semidirect
7. #23749872C2semidirect
8. #23749865C2semidirect
9. #23749862C2semidirect
10. #23749790C2semidirect
11. #23749785C2semidirect
12. #23749773C2semidirect
13. #23749772C2semidirect
14. #23749590C2semidirect
15. #484×C149C2semidirect
196. C149#3203semidirect
201. #484D149semidirect

Maximal subgroups

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

subgroupindex
#237502062
#237502052
#237499622
#237499402
#237499382
#237498742
#237498722
#237498652
#237498622
#237497902
#237497852
#237497732
#237497722
#237495902
#484×C1492
#3203149