Finite Group Databasebeta

← #34055372

Subgroups — #34055372

Order 19072.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750247C211yesmaximal, characteristic, complemented
2#23750226C211yesmaximal, characteristic, complemented
3#23750033C211yesmaximal, characteristic, complemented
4#23750011C211yesmaximal, characteristic, complemented
5#23749981C211yesmaximal, characteristic, complemented
6#23749970C211yesmaximal, characteristic, complemented
7#23749877C211yesmaximal, characteristic, complemented
8#23749874C211yesmaximal, characteristic, complemented
9#23749862C211yesmaximal, characteristic, complemented
10#23749851C211yesmaximal, characteristic, complemented
11#23749738C211yesmaximal, characteristic, complemented
12C4×#14558723C211yesmaximal, characteristic, complemented
13C4×#14558721C211yesmaximal, characteristic, complemented
14#23749582C211yesmaximal, characteristic, complemented
15#440×C149C211yesmaximal, characteristic, complemented
16C2×#14558723C2211yescharacteristic
17C2×D1192C2211yescharacteristic
18C2×#14558721C2211yescharacteristic
19C2×#14558719C2211yescharacteristic
20C2×C8×D149C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011907C2211yescharacteristic
23#18011905—21no—
24#18011902C2211yescharacteristic
25#18011900C2211yescharacteristic
26#18011899—21no—
27#18011896—21no—
28#18011894—21no—
29#18011893—21no—
30#18011889—21no—
31#18011887C2211yescharacteristic
32#18011886C2211yescharacteristic
33#18011886C2211yescharacteristic
34#18011885—21no—
35#18011884—21no—
36#18011882C2211yescharacteristic
37C4×D596C2211yescharacteristic
38C4×D596C2211yescharacteristic
39#18011868C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011821C2211yescharacteristic
50C4×#11924746C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×D596—21no—
61C2×D596—21no—
62C2×D596C2311yescharacteristic
63C2×D596C2311yescharacteristic
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149C2311yescharacteristic
70#14558723—22no—
71D1192—22no—
72#14558721—22no—
73#14558719—22no—
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C8×D149—22no—
77C4⋊Dic149—21no—
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
94#14558713D411yescharacteristic
95C4×Dic149C2311yescharacteristic
96C2×Q8×C149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C22×C4×C149—21no—
99SD16×C149—22no—
100C2×C8×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C22⋊C4×C149—21no—
106C42×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—21no—
110C22×D149C2×D411yescharacteristic
111Dic298—81no—
112D596—21no—
113D596—21no—
114D596—21no—
115D596—21no—
116D596—81no—
117D596—81no—
118C22⋊D149—81no—
119C22⋊D149—81no—
120C22⋊D149—81no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C4×D149—21no—
127C4×D149—21no—
128C4×D149—81no—
129C4×D149—81no—
130#11924746—21no—
131#11924746#4112yes—
132C23×C149—21no—
133Q8×C149—21no—
134Q8×C149—21no—
135D4×C149—21no—
136D4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—81no—
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2411yescharacteristic
144C8×C149—21no—
145C8×C149#4112yes—
146C22×C149—41no—
147C22×C149—41no—
148C22×C149—41no—
149C22×C149C22×D411yescharacteristic
150C2×D149—21no—
151C2×D149—21no—
152C2×D149—21no—
153C2×D149—41no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C4×C149—21no—
160C4×C149—21no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149—41no—
164C4×C149C2×#4111yescharacteristic
165C4×C149C2×#4111yescharacteristic
166Dic149—21no—
167Dic149—21no—
168Dic149—21no—
169Dic149—41no—
170Dic149—41no—
171C2×C149—81no—
172C2×C149#53211yescharacteristic
173C2×C149#57611yescharacteristic
174C2×C149#57711yescharacteristic
175D149—41no—
176D149—81no—
177D149—81no—
178C149#317911yescharacteristic, complemented, Sylow
179#3179—1491nomaximal, Sylow
180#542—1491no—
181#540—1491no—
182#501—1491no—
183#496—1491no—
184#488—1491no—
185#486—1491no—
186#469—1491no—
187#468—1491no—
188#466—1491no—
189#465—1491no—
190#442—1491no—
191#440D14911yescharacteristic, complemented
192C4×SD16—1491no—
193C4×D8—1491no—
194#405—1491no—
195C2×SD16—1491no—
196C2×SD16C2×D14911yescharacteristic
197C2×D8—1491no—
198C2×D8—1491no—
199C2×M16—1491no—
200C22×C8—1491no—
201C4⋊Q8—1491no—
202#127—1491no—
203#126—2981no—
204#125—1491no—
205#124—2981no—
206#124—1491no—
207#123—2981no—
208#123—2981no—
209#123—2981no—
210C22⋊Q8—2981no—
211C22⋊Q8—1491no—
212#121—2981no—
213#121—2981no—
214#121—1491no—
215#121—1491no—
216#121—1491no—
217C4×Q8C2×D14911yescharacteristic
218C4×D4—1491no—
219C4×D4—1491no—
220C4×D4C2×D14911yescharacteristic
221#117—1491no—
222#107—1491no—
223#107C2×D14911yescharacteristic
224#106—1491no—
225#106—1491no—
226#103—1491no—
227#103C2×D14911yescharacteristic
228#102—1491no—
229#102—1491no—
230#102—1491no—
231#102—1491no—
232#102—1491no—
233#102C2×D14911yescharacteristic
234#97—1491no—
235#97C2×D14911yescharacteristic
236C4×C8—1491no—
237C4×C8—1491no—
238C2×Q8—2981no—
239C2×Q8C22×D14911yescharacteristic
240C2×D4—2981no—
241C2×D4—2981no—
242C2×D4—2981no—
243C2×D4—2981no—
244C2×D4—2981no—
245C2×D4—1491no—
246C2×D4—1491no—
247C2×D4C22×D14911yescharacteristic
248C22×C4—21no—
249C22×C4—2981no—
250C22×C4—2981no—
251C22×C4—1491no—
252SD16—22no—
253SD16—2982no—
254D8—2982no—
255D8—2982no—
256M16—2982no—
257C2×C8—2982no—
258C2×C8—1491no—
259C2×C8—1491no—
260C2×C8C22×D14911yescharacteristic
261C2×C8C22×D14911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—2981no—
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—1491no—
268C4⋊C4—1491no—
269C4⋊C4—1491no—
270C4⋊C4—1491no—
271C4⋊C4C22×D14911yescharacteristic
272C4⋊C4C22×D14911yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—1491no—
283C22⋊C4—1491no—
284C42—21no—
285C42—1491no—
286C42C22×D14911yescharacteristic
287C23—21no—
288C23—2981no—
289C23—2981no—
290C23—1491no—
291Q8—21no—
292Q8—21no—
293Q8—11921no—
294D4—21no—
295D4—21no—
296D4—2981no—
297D4—2981no—
298D4—2981no—
299D4—2981no—
300D4—11921no—
301D4—11921no—
302D4—11921no—
303D4—11921no—
304D4—11921no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—81no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—1491no—
314C2×C4—1491no—
315C2×C4—1491no—
316C2×C4—11921no—
317C2×C4—11921no—
318C2×C4D4×D14911yescharacteristic
319C2×C4D4×D14911yescharacteristic
320C2×C4C23×D14911yescharacteristic
321C8—21no—
322C8—2981no—
323C8—1492no—
324C8#1455873612yes—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—2981no—
329C22—2981no—
330C22—2981no—
331C22—5961no—
332C22—5961no—
333C22—5961no—
334C22—5961no—
335C22—5961no—
336C22—5961no—
337C22C2×D4×D14911yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2981no—
344C4—2981no—
345C4—2981no—
346C4—5961no—
347C4—5961no—
348C4#41×D14911yescharacteristic
349C4C2×#1455873611yescharacteristic
350C2—81no—
351C2—5961no—
352C2—11921no—
353C2—11921no—
354C2#2375017211yescharacteristic
355C2#2375042911yescharacteristic
356C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#440×C149C2
socleC22×C149C22×D4
hypercenter#440D149
hypocenterC149#3179
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #23750247C2semidirect
2. #23750226C2semidirect
3. #23750033C2semidirect
4. #23750011C2semidirect
5. #23749981C2semidirect
6. #23749970C2semidirect
7. #23749877C2semidirect
8. #23749874C2semidirect
9. #23749862C2semidirect
10. #23749851C2semidirect
11. #23749738C2semidirect
12. C4×#14558723C2semidirect
13. C4×#14558721C2semidirect
14. #23749582C2semidirect
15. #440×C149C2semidirect
178. C149#3179semidirect
191. #440D149semidirect

Maximal subgroups

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

subgroupindex
#237502472
#237502262
#237500332
#237500112
#237499812
#237499702
#237498772
#237498742
#237498622
#237498512
#237497382
C4×#145587232
C4×#145587212
#237495822
#440×C1492
#3179149