Finite Group Databasebeta

← #49168896

Subgroups — #49168896

Order 37504.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036663C211yesmaximal, characteristic, complemented
2C4×#17989802C211yesmaximal, characteristic, complemented
3#34036471C211yesmaximal, characteristic, complemented
4#34036454C211yesmaximal, characteristic, complemented
5#34036437C211yesmaximal, characteristic, complemented
6#34036430C211yesmaximal, characteristic, complemented
7#34036352C211yesmaximal, characteristic, complemented
8#34036345C211yesmaximal, characteristic, complemented
9#34036293C211yesmaximal, characteristic, complemented
10#34036276C211yesmaximal, characteristic
11#34036242C211yesmaximal, characteristic, complemented
12#34036237C211yesmaximal, characteristic, complemented
13#34036231C211yesmaximal, characteristic, complemented
14#34036231C211yesmaximal, characteristic, complemented
15#432×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic
17C2×Dic1172C2211yescharacteristic
18C2×#17989791C2211yescharacteristic
19C2×#17989791C2211yescharacteristic
20C2×D2344C2211yescharacteristic
21#22627618—21no—
22#22627616C2211yescharacteristic
23#22627612C2211yescharacteristic
24#22627607—21no—
25#22627603C2211yescharacteristic
26#22627598C2211yescharacteristic
27C4×Dic586C2211yescharacteristic
28C4×Dic586C2211yescharacteristic
29C4×Dic586C2211yescharacteristic
30C4×D1172C2211yescharacteristic
31C4×D1172C2211yescharacteristic
32C4×D1172C2211yescharacteristic
33C4×C22⋊D293—21no—
34C4×C22⋊D293—21no—
35C4×C22⋊D293—21no—
36#22627583C2211yescharacteristic
37#22627581—21no—
38#22627581—21no—
39C42×D293—21no—
40#22627558C2211yescharacteristic
41#22627558C2211yescharacteristic
42#22627556C2211yescharacteristic
43#22627556C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627549C2211yescharacteristic
46#22627549C2211yescharacteristic
47#22627549C2211yescharacteristic
48#22627546C2211yescharacteristic
49#22627546C2211yescharacteristic
50#22627546C2211yescharacteristic
51#22627546C2211yescharacteristic
52C2×C42×C293C2211yescharacteristic
53C4⋊C8×C293C2211yescharacteristic
54C4⋊C8×C293C2211yescharacteristic
55C22⋊C8×C293C2211yescharacteristic
56C22⋊C8×C293C2211yescharacteristic
57#97×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic
59#17989802—22no—
60#17989802—22no—
61C2×Dic586C2311yescharacteristic
62C2×Dic586C2311yescharacteristic
63C2×D1172C2311yescharacteristic
64C2×D1172C2311yescharacteristic
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C2×C4×D293—21no—
68C2×C4×D293—21no—
69C2×C4×D293—21no—
70C2×C4×D293—21no—
71Dic1172—22no—
72#17989791—22no—
73#17989791—22no—
74D2344—22no—
75C4⋊Dic293C2311yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93C4×Dic293—21no—
94C4×Dic293—21no—
95C4×Dic293—21no—
96C4×Dic293—21no—
97C22×C4×C293D411yescharacteristic
98C22×C4×C293D411yescharacteristic
99C22×C4×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C2×C8×C293C2311yescharacteristic
103C2×C8×C293C2311yescharacteristic
104C42×C293D411yescharacteristic
105C42×C293D411yescharacteristic
106C42×C293C2311yescharacteristic
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109C22×D293—21no—
110Dic586—21no—
111Dic586—21no—
112Dic586—21no—
113Dic586#4112yes—
114D1172—21no—
115D1172—21no—
116D1172—21no—
117D1172#4112yes—
118C22⋊D293—24no—
119C22⋊D293—42no—
120C2×Dic293—21no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293—21no—
125C2×Dic293—21no—
126C4×D293—24no—
127C4×D293—42no—
128C4×D293—42no—
129C4×D293—42no—
130C23×C293C2×D411yescharacteristic
131C2×C4×C293—21no—
132C2×C4×C293—21no—
133C2×C4×C293—41no—
134C2×C4×C293—41no—
135C2×C4×C293C2×D411yescharacteristic
136C2×C4×C293C2×D411yescharacteristic
137C2×C4×C293C2×D411yescharacteristic
138C2×C4×C293C2×D411yescharacteristic
139C2×C4×C293C2×D411yescharacteristic
140C2×C4×C293C2411yescharacteristic
141C8×C293—21no—
142C8×C293—21no—
143C8×C293—21no—
144C8×C293—21no—
145C22×C293—21no—
146C22×C293—21no—
147C22×C293—21no—
148C22×C293C22×D411yescharacteristic
149C2×D293—22no—
150C2×D293—41no—
151C2×D293—41no—
152C2×D293—41no—
153C2×D293—41no—
154C2×D293—41no—
155C4×C293—21no—
156C4×C293—21no—
157C4×C293—21no—
158C4×C293—21no—
159C4×C293—21no—
160C4×C293C2×#4111yescharacteristic
161C4×C293C2×#4111yescharacteristic
162Dic293—22no—
163Dic293—41no—
164Dic293—41no—
165Dic293—41no—
166Dic293—41no—
167Dic293—41no—
168C2×C293—41no—
169C2×C293#52511yescharacteristic
170C2×C293#57511yescharacteristic
171C2×C293#57511yescharacteristic
172D293—42no—
173D293—81no—
174C293#311111yescharacteristic, complemented, Sylow
175#3111—2931nomaximal, Sylow
176#529—2931no—
177C4×#41—2931no—
178#485—2931no—
179#482—2931no—
180#479—2931no—
181#478—2931no—
182#464—2931no—
183#463—2931no—
184#452—2931no—
185#449—2931no—
186#442—2931no—
187#441—2931no—
188#440—2931no—
189#440—2931no—
190#432D29311yescharacteristic, complemented
191C2×#41—2931no—
192C2×Q16—2931no—
193C2×SD16—2931no—
194C2×SD16—2931no—
195C2×D8—2931no—
196#126—5861no—
197#125—2931no—
198#124—2931no—
199#123—5861no—
200C22⋊Q8—2931no—
201#121—2931no—
202C4×Q8—2931no—
203C4×Q8—2931no—
204C4×Q8—2931no—
205C4×D4—2931no—
206C4×D4—2931no—
207C4×D4—2931no—
208C4×D4—5861no—
209C4×D4—5861no—
210C4×D4—5861no—
211#117—2931no—
212#117—5861no—
213#117—5861no—
214C2×C42—5861no—
215C2×C42C2×D29311yescharacteristic
216#107—2931no—
217#107—2931no—
218#106—2931no—
219#106—2931no—
220C4⋊C8C2×D29311yescharacteristic
221C4⋊C8C2×D29311yescharacteristic
222#103—2931no—
223#103—2931no—
224#103—2931no—
225#103—2931no—
226#102—2931no—
227#102—2931no—
228#102—2931no—
229#102—2931no—
230C22⋊C8C2×D29311yescharacteristic
231C22⋊C8C2×D29311yescharacteristic
232#97C2×D29311yescharacteristic
233#97C2×D29311yescharacteristic
234#41—5862no—
235#41—5862no—
236C2×Q8—2931no—
237C2×Q8—2931no—
238C2×D4—2931no—
239C2×D4—2931no—
240C2×D4—5861no—
241C2×D4—5861no—
242C22×C4—5861no—
243C22×C4—5861no—
244C22×C4—5861no—
245C22×C4—5861no—
246C22×C4D117211yescharacteristic
247C22×C4D117211yescharacteristic
248C22×C4C22×D29311yescharacteristic
249Q16—5862no—
250SD16—5862no—
251SD16—5862no—
252D8—5862no—
253C2×C8C22×D29311yescharacteristic
254C2×C8C22×D29311yescharacteristic
255C2×C8C22×D29311yescharacteristic
256C2×C8C22×D29311yescharacteristic
257C4⋊C4—2931no—
258C4⋊C4—2931no—
259C4⋊C4—2931no—
260C4⋊C4—2931no—
261C4⋊C4—5861no—
262C4⋊C4—5861no—
263C4⋊C4—5861no—
264C4⋊C4—5861no—
265C4⋊C4—5861no—
266C4⋊C4—5861no—
267C22⋊C4—5861no—
268C22⋊C4—5861no—
269C22⋊C4—5861no—
270C22⋊C4—5861no—
271C22⋊C4—5861no—
272C22⋊C4—5861no—
273C22⋊C4—5861no—
274C22⋊C4—5861no—
275C42—5861no—
276C42—5861no—
277C42—5861no—
278C42—5861no—
279C42D117211yescharacteristic
280C42D117211yescharacteristic
281C42C22×D29311yescharacteristic
282C42C22×D29311yescharacteristic
283C23—5861no—
284C23—5861no—
285C23C2×D117211yescharacteristic
286Q8—2932no—
287Q8—5861no—
288Q8—5861no—
289Q8—5861no—
290D4—2932no—
291D4—5864no—
292D4—5861no—
293D4—5861no—
294D4—5861no—
295D4—11722no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—5864no—
301C2×C4—5861no—
302C2×C4—5861no—
303C2×C4—5861no—
304C2×C4—5861no—
305C2×C4—5861no—
306C2×C4—5861no—
307C2×C4—11722no—
308C2×C4—11722no—
309C2×C4—11722no—
310C2×C4C2×D117211yescharacteristic
311C2×C4C2×D117211yescharacteristic
312C2×C4C2×D117211yescharacteristic
313C2×C4C2×D117211yescharacteristic
314C2×C4C2×D117211yescharacteristic
315C2×C4C23×D29311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—5862no—
324C22—11721no—
325C22—11721no—
326C22—11721no—
327C22—11721no—
328C22—11721no—
329C22C22×D117211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—5862no—
336C4—11721no—
337C4—11721no—
338C4—11721no—
339C4—11721no—
340C4—11721no—
341C4#41×D29311yescharacteristic
342C4#41×D29311yescharacteristic
343C2—41no—
344C2—23441no—
345C2—11722no—
346C2#3403664111yescharacteristic
347C2#3403692911yescharacteristic
348C2#3403692911yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#432×C293C2
socleC22×C293C22×D4
prime radical#34036276C2
hypercenter#432D293
hypocenterC293#3111
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #34036663C2semidirect
2. C4×#17989802C2semidirect
3. #34036471C2semidirect
4. #34036454C2semidirect
5. #34036437C2semidirect
6. #34036430C2semidirect
7. #34036352C2semidirect
8. #34036345C2semidirect
9. #34036293C2semidirect
11. #34036242C2semidirect
12. #34036237C2semidirect
13. #34036231C2semidirect
14. #34036231C2semidirect
15. #432×C293C2semidirect
174. C293#3111semidirect
190. #432D293semidirect

Maximal subgroups

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

subgroupindex
#340366632
C4×#179898022
#340364712
#340364542
#340364372
#340364302
#340363522
#340363452
#340362932
#340362762
#340362422
#340362372
#340362312
#432×C2932
#3111293