Finite Group Databasebeta

← #49169048

Subgroups — #49169048

Order 37504.

384 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#34036752C211yesmaximal, characteristic, complemented
2#34036612C211yesmaximal, characteristic, complemented
3#34036462C211yesmaximal, characteristic, complemented
4#34036443C211yesmaximal, characteristic, complemented
5#34036422C211yesmaximal, characteristic, complemented
6#34036407C211yesmaximal, characteristic, complemented
7#34036353C211yesmaximal, characteristic, complemented
8#34036346C211yesmaximal, characteristic, complemented
9#34036274C211yesmaximal, characteristic
10#34036232C211yesmaximal, characteristic, complemented
11#34036230C211yesmaximal, characteristic, complemented
12Q16×Dic293C211yesmaximal, characteristic, complemented
13#34036209C211yesmaximal, characteristic, complemented
14#34036187C211yesmaximal, characteristic, complemented
15#452×C293C211yesmaximal, characteristic, complemented
16C2×#17989789C2211yescharacteristic
17C2×#17989787C2211yescharacteristic
18#22627623C2211yescharacteristic
19#22627619—21no—
20#22627613C2211yescharacteristic
21#22627610—21no—
22#22627606—21no—
23#22627604—21no—
24#22627598C2211yescharacteristic
25Q8×Dic293C2211yescharacteristic
26Q8×Dic293C2211yescharacteristic
27Q8×Dic293C2211yescharacteristic
28D4×Dic293—21no—
29D4×Dic293—21no—
30D4×Dic293C2211yescharacteristic
31D4×Dic293C2211yescharacteristic
32#22627586C2211yescharacteristic
33#22627583—21no—
34#22627583C2211yescharacteristic
35C2×C4⋊Dic293—21no—
36C2×C4⋊Dic293C2211yescharacteristic
37#22627558C2211yescharacteristic
38#22627558C2211yescharacteristic
39#22627557C2211yescharacteristic
40#22627557C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627548C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627546C2211yescharacteristic
48#22627545C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×#41×C293C2211yescharacteristic
53C2×Q16×C293C2211yescharacteristic
54C2×SD16×C293C2211yescharacteristic
55C22⋊Q8×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×D1172C2311yescharacteristic
61C2×C22⋊D293—21no—
62C22×Dic293—21no—
63C22×Dic293—21no—
64C22×Dic293—21no—
65C2×C4×D293—21no—
66#17989789—22no—
67#17989787—22no—
68C2×#14556873C2311yescharacteristic
69C2×#14556873C2311yescharacteristic
70C4⋊Dic293—21no—
71C4⋊Dic293—21no—
72C4⋊Dic293—21no—
73C4⋊Dic293—21no—
74C4⋊Dic293D411yescharacteristic
75C4⋊Dic293D411yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79#17989781—21no—
80C22⋊Dic293—21no—
81C22⋊Dic293—21no—
82C22⋊Dic293D411yescharacteristic
83C22⋊Dic293D411yescharacteristic
84#17989779—21no—
85#17989779—21no—
86#17989779—21no—
87#17989779—21no—
88C4×Dic293—21no—
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293C2311yescharacteristic
92C4×Dic293C2311yescharacteristic
93#41×C293—22no—
94#41×C293—22no—
95C2×Q8×C293C2311yescharacteristic
96C2×Q8×C293C2311yescharacteristic
97C2×D4×C293—21no—
98C2×D4×C293C2311yescharacteristic
99C22×C4×C293—21no—
100C22×C4×C293C2311yescharacteristic
101Q16×C293—22no—
102SD16×C293—22no—
103C2×C8×C293C2311yescharacteristic
104C2×C8×C293C2311yescharacteristic
105C4⋊C4×C293—21no—
106C4⋊C4×C293C2311yescharacteristic
107C22⋊C4×C293—21no—
108C22×D293—21no—
109Dic586—81no—
110D1172—21no—
111D1172—21no—
112C22⋊D293—81no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—81no—
117C2×Dic293—81no—
118C2×Dic293—81no—
119C2×Dic293C2×D411yescharacteristic
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C4×D293—81no—
124#14556873—21no—
125#14556873—21no—
126C23×C293—21no—
127C23×C293C2×D411yescharacteristic
128Q8×C293—21no—
129Q8×C293—21no—
130Q8×C293—21no—
131Q8×C293#4112yes—
132D4×C293—24no—
133D4×C293—21no—
134D4×C293#4112yes—
135C2×C4×C293—24no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—21no—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293C2×D411yescharacteristic
142C2×C4×C293C2411yescharacteristic
143C8×C293—21no—
144C8×C293—21no—
145C22×C293—21no—
146C22×C293—22no—
147C22×C293—21no—
148C22×C293—21no—
149C22×C293—41no—
150C22×C293—41no—
151C22×C293C22×D411yescharacteristic
152C2×D293—41no—
153C2×D293—41no—
154C2×D293—41no—
155C4×C293—21no—
156C4×C293—22no—
157C4×C293—41no—
158C4×C293—41no—
159C4×C293C2×#4111yescharacteristic
160C4×C293C2×#4111yescharacteristic
161Dic293—21no—
162Dic293—21no—
163Dic293—21no—
164Dic293—21no—
165Dic293—41no—
166Dic293—41no—
167Dic293—41no—
168C2×C293—41no—
169C2×C293—42no—
170C2×C293#52511yescharacteristic
171C2×C293#57611yescharacteristic
172C2×C293#57811yescharacteristic
173D293—81no—
174C293#312411yescharacteristic, complemented, Sylow
175#3124—2931nomaximal, Sylow
176#542—2931no—
177#520—2931no—
178#484—2931no—
179#480—2931no—
180#477—2931no—
181#474—2931no—
182#464—2931no—
183#463—2931no—
184#452D29311yescharacteristic, complemented
185#449—2931no—
186#440—2931no—
187#440—2931no—
188C4×Q16—2931no—
189C4×D8—2931no—
190#433—2931no—
191C2×#41C2×D29311yescharacteristic
192C2×Q16C2×D29311yescharacteristic
193C2×SD16—2931no—
194C2×SD16C2×D29311yescharacteristic
195C2×D8—2931no—
196C4⋊Q8—2931no—
197#126—5861no—
198#124—2931no—
199#124—5861no—
200#123—5861no—
201C22⋊Q8—5861no—
202C22⋊Q8C2×D29311yescharacteristic
203#121—2931no—
204C4×Q8—2931no—
205C4×Q8—2931no—
206C4×Q8—2931no—
207C4×D4—2931no—
208C4×D4—2931no—
209C4×D4—2931no—
210C4×D4—5861no—
211C4×D4—5861no—
212#117—2931no—
213#117—5861no—
214C2×C4⋊C4—2931no—
215C2×C4⋊C4—5861no—
216#107—2931no—
217#107—2931no—
218#107—2931no—
219#107—2931no—
220C4⋊C8—2931no—
221C4⋊C8—2931no—
222#103—2931no—
223#103—2931no—
224#103—2931no—
225#103C2×D29311yescharacteristic
226#102—2931no—
227#102—2931no—
228#102—2931no—
229#102C2×D29311yescharacteristic
230C22⋊C8—2931no—
231C22⋊C8C2×D29311yescharacteristic
232#97—2931no—
233C4×C8—2931no—
234#41—22no—
235#41—22no—
236C2×Q8—5861no—
237C2×Q8C22×D29311yescharacteristic
238C2×Q8C22×D29311yescharacteristic
239C2×D4—21no—
240C2×D4—2931no—
241C2×D4—5861no—
242C2×D4C22×D29311yescharacteristic
243C22×C4—21no—
244C22×C4—5861no—
245C22×C4—5861no—
246C22×C4—5861no—
247C22×C4—5861no—
248C22×C4C22×D29311yescharacteristic
249Q16—22no—
250SD16—22no—
251SD16—5862no—
252D8—5862no—
253C2×C8—2931no—
254C2×C8—2931no—
255C2×C8C22×D29311yescharacteristic
256C2×C8C22×D29311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—2931no—
259C4⋊C4—2931no—
260C4⋊C4—2931no—
261C4⋊C4—2931no—
262C4⋊C4—2931no—
263C4⋊C4—5861no—
264C4⋊C4—5861no—
265C4⋊C4—5861no—
266C4⋊C4—5861no—
267C4⋊C4—5861no—
268C4⋊C4C22×D29311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—2931no—
271C22⋊C4—2931no—
272C22⋊C4—5861no—
273C22⋊C4—5861no—
274C22⋊C4—5861no—
275C22⋊C4—5861no—
276C22⋊C4—5861no—
277C22⋊C4—5861no—
278C42—2931no—
279C42—2931no—
280C42—5861no—
281C42—5861no—
282C42—5861no—
283C23—21no—
284C23—5861no—
285C23D4×D29311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—23441no—
290Q8#1798980112yes—
291D4—24no—
292D4—21no—
293D4—23441no—
294D4—5861no—
295D4—5861no—
296D4#1798980112yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—2931no—
304C2×C4—2931no—
305C2×C4—2931no—
306C2×C4—2931no—
307C2×C4—23441no—
308C2×C4—23441no—
309C2×C4—23441no—
310C2×C4—23441no—
311C2×C4—5861no—
312C2×C4—5861no—
313C2×C4—5861no—
314C2×C4D4×D29311yescharacteristic
315C2×C4C23×D29311yescharacteristic
316C8—21no—
317C8—21no—
318C8—5861no—
319C8—5861no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—11721no—
327C22—11721no—
328C22—11721no—
329C22C2×D4×D29311yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—5861no—
335C4—5861no—
336C4—5861no—
337C4—5861no—
338C4—11721no—
339C4—11721no—
340C4—11721no—
341C4C2×#1798980111yescharacteristic
342C4C2×#1798980111yescharacteristic
343C2—41no—
344C2—42no—
345C2—23441no—
346C2#3403663511yescharacteristic
347C2#3403693111yescharacteristic
348C2#3403694511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#452×C293C2
socleC22×C293C22×D4
prime radical#34036274C2
hypercenter#452D293
hypocenterC293#3124
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #34036752C2semidirect
2. #34036612C2semidirect
3. #34036462C2semidirect
4. #34036443C2semidirect
5. #34036422C2semidirect
6. #34036407C2semidirect
7. #34036353C2semidirect
8. #34036346C2semidirect
10. #34036232C2semidirect
11. #34036230C2semidirect
12. Q16×Dic293C2semidirect
13. #34036209C2semidirect
14. #34036187C2semidirect
15. #452×C293C2semidirect
174. C293#3124semidirect
184. #452D293semidirect

Maximal subgroups

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

subgroupindex
#340367522
#340366122
#340364622
#340364432
#340364222
#340364072
#340363532
#340363462
#340362742
#340362322
#340362302
Q16×Dic2932
#340362092
#340361872
#452×C2932
#3124293