Finite Group Databasebeta

← #34057312

Subgroups — #34057312

Order 19072.

354 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750339C211yesmaximal, characteristic
2#23750333C211yesmaximal, characteristic, complemented
3#23750029C211yesmaximal, characteristic, complemented
4#23749964C211yesmaximal, characteristic, complemented
5#23749963C211yesmaximal, characteristic, complemented
6#23749937C211yesmaximal, characteristic, complemented
7#23749936C211yesmaximal, characteristic, complemented
8#23749918C211yesmaximal, characteristic, complemented
9#23749913C211yesmaximal, characteristic, complemented
10#23749868C211yesmaximal, characteristic, complemented
11SD16×Dic149C211yesmaximal, characteristic, complemented
12#23749701C211yesmaximal, characteristic, complemented
13#23749667C211yesmaximal, characteristic, complemented
14#23749666C211yesmaximal, characteristic, complemented
15#468×C149C211yesmaximal, characteristic, complemented
16C2×#14558719C2211yescharacteristic
17#18011910C2211yescharacteristic
18#18011910C2211yescharacteristic
19#18011901—21no—
20#18011898—21no—
21#18011897—21no—
22#18011891—21no—
23#18011888—21no—
24#18011887C2211yescharacteristic
25#18011883—21no—
26#18011882C2211yescharacteristic
27Q8×Dic149C2211yescharacteristic
28D4×Dic149C2211yescharacteristic
29C4×C22⋊D149C2211yescharacteristic
30#18011871—21no—
31#18011870C2211yescharacteristic
32#18011869C2211yescharacteristic
33#18011867—21no—
34C2×C4⋊Dic149C2211yescharacteristic
35C4⋊C4×D149C2211yescharacteristic
36#18011845C2211yescharacteristic
37#18011845C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011843C2211yescharacteristic
43#18011842C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C2×M16×C149C2211yescharacteristic
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#107×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×C22⋊D149—21no—
62C2×C22⋊D149D411yescharacteristic
63C22×Dic149—21no—
64C22×Dic149—21no—
65C2×C4×D149—21no—
66C2×C4×D149C2311yescharacteristic
67#14558719—22no—
68C2×#11924746C2311yescharacteristic
69C2×#11924746C2311yescharacteristic
70C4⋊Dic149—21no—
71C4⋊Dic149—21no—
72C4⋊Dic149C2311yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715D411yescharacteristic
81C22⋊Dic149—21no—
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84C22⋊Dic149D411yescharacteristic
85#14558713—21no—
86#14558713—21no—
87#14558713D411yescharacteristic
88C4×Dic149—21no—
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149C2311yescharacteristic
92C2×Q8×C149C2311yescharacteristic
93C2×D4×C149—21no—
94C2×D4×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96SD16×C149—22no—
97M16×C149—22no—
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C4⋊C4×C149—21no—
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C22⋊C4×C149—21no—
104C22⋊C4×C149—21no—
105C22×D149C2×D411yescharacteristic
106Dic298—81no—
107Dic298—81no—
108C22⋊D149—22no—
109C22⋊D149—81no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—42no—
115C2×Dic149—81no—
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119C4×D149—21no—
120C4×D149—21no—
121C4×D149—81no—
122#11924746—21no—
123#11924746—21no—
124C23×C149—21no—
125C23×C149C2×D411yescharacteristic
126Q8×C149—21no—
127Q8×C149—21no—
128D4×C149—21no—
129D4×C149—21no—
130D4×C149—81no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2411yescharacteristic
138C8×C149—21no—
139C8×C149#4112yes—
140C22×C149—21no—
141C22×C149—21no—
142C22×C149—21no—
143C22×C149—41no—
144C22×C149—41no—
145C22×C149—41no—
146C22×C149C22×D411yescharacteristic
147C2×D149—21no—
148C2×D149—21no—
149C2×D149—21no—
150C4×C149—21no—
151C4×C149—41no—
152C4×C149—41no—
153C4×C149—41no—
154C4×C149C2×#4111yescharacteristic
155C4×C1492−1+411yescharacteristic
156Dic149—21no—
157Dic149—21no—
158Dic149—41no—
159Dic149—41no—
160Dic149—41no—
161Dic149—41no—
162Dic149#13712yes—
163C2×C149—41no—
164C2×C149—81no—
165C2×C149#54711yescharacteristic
166C2×C149C2×#13711yescharacteristic
167C2×C149#57611yescharacteristic
168D149—41no—
169C149#335711yescharacteristic, complemented, Sylow
170#3357—1491nomaximal, Sylow
171#555—1491no—
172#554—1491no—
173#500—1491no—
174#485—1491no—
175#485—1491no—
176#480—1491no—
177#480—1491no—
178#477—1491no—
179#476—1491no—
180#468—1491no—
181#468D14911yescharacteristic, complemented
182C4×SD16—1491no—
183#436—1491no—
184#428—1491no—
185#428—1491no—
186C2×SD16C2×D14911yescharacteristic
187C2×M16—1491no—
188C2×M16C2×D14911yescharacteristic
189C4⋊Q8—1491no—
190C4⋊Q8—1491no—
191#125—2981no—
192#124—2981no—
193#124—2981no—
194C22⋊Q8—2981no—
195C22⋊Q8—2981no—
196C22⋊Q8—1491no—
197C22⋊Q8C2×D14911yescharacteristic
198#121—2981no—
199#121—1491no—
200#121C2×D14911yescharacteristic
201C4×Q8—1491no—
202C4×D4—2981no—
203C4×D4—1491no—
204C4×D4—1491no—
205#117—2981no—
206#117—1491no—
207#117—1491no—
208C2×C4⋊C4—1491no—
209C2×C4⋊C4—1491no—
210#107—1491no—
211#107—1491no—
212#107—1491no—
213#107—1491no—
214#107—1491no—
215#107C2×D14911yescharacteristic
216#106—1491no—
217#106—1491no—
218#106—1491no—
219C4⋊C8—1491no—
220#103—1491no—
221#103—1491no—
222#103C2×D14911yescharacteristic
223#102—1491no—
224#102—1491no—
225#102C2×D14911yescharacteristic
226C22⋊C8—1491no—
227C22⋊C8—1491no—
228C4×C8—1491no—
229C2×Q8—2981no—
230C2×Q8—2981no—
231C2×Q8C22×D14911yescharacteristic
232C2×D4—21no—
233C2×D4—2981no—
234C2×D4—1491no—
235C2×D4C22×D14911yescharacteristic
236C22×C4—2981no—
237C22×C4—2981no—
238C22×C4—2981no—
239C22×C4—1491no—
240C22×C4C22×D14911yescharacteristic
241SD16—22no—
242M16—22no—
243M16—2982no—
244C2×C8—1491no—
245C2×C8—1491no—
246C2×C8C22×D14911yescharacteristic
247C2×C8C22×D14911yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—2981no—
250C4⋊C4—2981no—
251C4⋊C4—2981no—
252C4⋊C4—2981no—
253C4⋊C4—2981no—
254C4⋊C4—2981no—
255C4⋊C4—1491no—
256C4⋊C4—1491no—
257C4⋊C4—1491no—
258C4⋊C4—1491no—
259C4⋊C4—1491no—
260C4⋊C4C22×D14911yescharacteristic
261C4⋊C4C22×D14911yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—2981no—
265C22⋊C4—2981no—
266C22⋊C4—2981no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4—1491no—
270C22⋊C4—1491no—
271C42—2981no—
272C42—2981no—
273C42—2981no—
274C42—1491no—
275C23—21no—
276C23—1491no—
277C23D4×D14911yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—11921no—
281Q8—11921no—
282D4—21no—
283D4—21no—
284D4—81no—
285D4—2982no—
286D4—11921no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—2981no—
293C2×C4—2981no—
294C2×C4—2981no—
295C2×C4—2981no—
296C2×C4—2981no—
297C2×C4—2981no—
298C2×C4—5962no—
299C2×C4—1491no—
300C2×C4—1491no—
301C2×C4—1491no—
302C2×C4—11921no—
303C2×C4—11921no—
304C2×C4D4×D14911yescharacteristic
305C2×C4C23×D14911yescharacteristic
306C8—21no—
307C8—2981no—
308C8—2981no—
309C8#1455873512yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—2981no—
317C22—2981no—
318C22—2981no—
319C22C2×D4×D14911yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—2981no—
325C4—2981no—
326C4—5961no—
327C4—5961no—
328C4—5961no—
329C4—5961no—
330C4—1492no—
331C4C2×#1455873511yescharacteristic
332C4#1801195811yescharacteristic
333C2—41no—
334C2—81no—
335C2—5961no—
336C2#2375027511yescharacteristic
337C2#137×D14911yescharacteristic
338C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#468×C149C2
socleC22×C149C22×D4
prime radical#23750339C2
hypercenter#468D149
hypocenterC149#3357
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #23750333C2semidirect
3. #23750029C2semidirect
4. #23749964C2semidirect
5. #23749963C2semidirect
6. #23749937C2semidirect
7. #23749936C2semidirect
8. #23749918C2semidirect
9. #23749913C2semidirect
10. #23749868C2semidirect
11. SD16×Dic149C2semidirect
12. #23749701C2semidirect
13. #23749667C2semidirect
14. #23749666C2semidirect
15. #468×C149C2semidirect
169. C149#3357semidirect
181. #468D149semidirect

Maximal subgroups

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

subgroupindex
#237503392
#237503332
#237500292
#237499642
#237499632
#237499372
#237499362
#237499182
#237499132
#237498682
SD16×Dic1492
#237497012
#237496672
#237496662
#468×C1492
#3357149