Finite Group Databasebeta

← #49170762

Subgroups — #49170762

Order 37504.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036827C211yesmaximal, characteristic, complemented
2#34036778C211yesmaximal, characteristic, complemented
3#34036496C211yesmaximal, characteristic, complemented
4#34036469C211yesmaximal, characteristic, complemented
5#34036459C211yesmaximal, characteristic, complemented
6#34036427C211yesmaximal, characteristic, complemented
7#34036375C211yesmaximal, characteristic, complemented
8#34036361C211yesmaximal, characteristic, complemented
9#34036333C211yesmaximal, characteristic, complemented
10#34036275C211yesmaximal, characteristic, complemented
11#34036274C211yesmaximal, characteristic, complemented
12#34036238C211yesmaximal, characteristic, complemented
13#34036198C211yesmaximal, characteristic, complemented
14#34036122C211yesmaximal, characteristic, complemented
15#417×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C2×#17989791C2211yescharacteristic
18C2×#17989789C2211yescharacteristic
19C2×#17989787C2211yescharacteristic
20C2×C8×D293C2211yescharacteristic
21#22627622C2211yescharacteristic
22#22627619—21no—
23#22627615C2211yescharacteristic
24#22627609—21no—
25#22627607—21no—
26#22627605—21no—
27#22627603C2211yescharacteristic
28#22627600C2211yescharacteristic
29#22627599C2211yescharacteristic
30#22627598—21no—
31#22627598C2211yescharacteristic
32#22627596—21no—
33D4×Dic293C2211yescharacteristic
34#22627586C2211yescharacteristic
35C4×C22⋊D293—21no—
36C4×C22⋊D293C2211yescharacteristic
37#22627582C2211yescharacteristic
38C2×#17989781—21no—
39#22627558C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627555C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627547C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627546C2211yescharacteristic
48#22627545C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627534C2211yescharacteristic
52C2×#41×C293C2211yescharacteristic
53C2×M16×C293C2211yescharacteristic
54C2×C4⋊C4×C293C2211yescharacteristic
55#103×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59#17989801—22no—
60#17989801—41no—
61C2×Dic586C2311yescharacteristic
62C2×D1172—21no—
63C2×D1172C2311yescharacteristic
64C2×C22⋊D293—21no—
65C2×C22⋊D293—21no—
66C2×C22⋊D293D411yescharacteristic
67C22×Dic293—21no—
68C22×Dic293—21no—
69C2×C4×D293—21no—
70C2×C4×D293C2311yescharacteristic
71#17989791—41no—
72#17989789—41no—
73#17989787—22no—
74C2×#14556873C2311yescharacteristic
75C2×#14556873C2311yescharacteristic
76C8×D293—41no—
77C4⋊Dic293—21no—
78C4⋊Dic293C2311yescharacteristic
79C4⋊Dic293C2311yescharacteristic
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85#17989781D411yescharacteristic
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88C22⋊Dic293D411yescharacteristic
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779D411yescharacteristic
95C4×Dic293—21no—
96C4×Dic293C2311yescharacteristic
97#41×C293—22no—
98#41×C293—41no—
99C2×Q8×C293C2311yescharacteristic
100C2×D4×C293—21no—
101C2×D4×C293C2311yescharacteristic
102C22×C4×C293—21no—
103C22×C4×C293—21no—
104C22×C4×C293C2311yescharacteristic
105M16×C293—41no—
106C2×C8×C293C2311yescharacteristic
107C2×C8×C293C2311yescharacteristic
108C4⋊C4×C293—21no—
109C4⋊C4×C293C2311yescharacteristic
110C4⋊C4×C293C2311yescharacteristic
111C22×D293—21no—
112C22×D293C2×D411yescharacteristic
113Dic586—21no—
114Dic586—21no—
115D1172—21no—
116D1172—21no—
117D1172—81no—
118C22⋊D293—41no—
119C22⋊D293—42no—
120C22⋊D293—42no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293—42no—
125C2×Dic293—42no—
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C2×Dic293C2×D411yescharacteristic
129C4×D293—21no—
130C4×D293—21no—
131C4×D293—81no—
132#14556873—21no—
133#14556873—21no—
134C23×C293—21no—
135C23×C293C2×D411yescharacteristic
136Q8×C293—21no—
137Q8×C293—21no—
138D4×C293—21no—
139D4×C293—42no—
140D4×C293#4112yes—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—21no—
146C2×C4×C293—42no—
147C2×C4×C293—81no—
148C2×C4×C293C2×D411yescharacteristic
149C2×C4×C293C2411yescharacteristic
150C8×C293—21no—
151C8×C293—21no—
152C22×C293—21no—
153C22×C293—22no—
154C22×C293—21no—
155C22×C293—21no—
156C22×C293—41no—
157C22×C293—41no—
158C22×C293C22×D411yescharacteristic
159C2×D293—21no—
160C2×D293—21no—
161C2×D293—21no—
162C2×D293—41no—
163C2×D293—41no—
164C2×D293—41no—
165C4×C293—21no—
166C4×C293—41no—
167C4×C293—41no—
168C4×C293—41no—
169C4×C293C2×#4111yescharacteristic
170C4×C293H(5,𝔽2)11yescharacteristic
171Dic293—21no—
172Dic293—21no—
173Dic293—21no—
174Dic293—41no—
175Dic293—41no—
176Dic293—41no—
177C2×C293—41no—
178C2×C293—42no—
179C2×C293#54611yescharacteristic
180C2×C293#57511yescharacteristic
181C2×C293#57711yescharacteristic
182D293—41no—
183D293—81no—
184C293#330711yescharacteristic, complemented, Sylow
185#3307—2931nomaximal, Sylow
186#553—2931no—
187#547—2931no—
188#491—2931no—
189#485—2931no—
190#483—2931no—
191#478—2931no—
192#468—2931no—
193#465—2931no—
194#461—2931no—
195#449—2931no—
196#449—2931no—
197#442—2931no—
198#435—2931no—
199#417D29311yescharacteristic, complemented
200#416—2931no—
201C2×#41—2931no—
202C2×#41C2×D29311yescharacteristic
203C2×SD16—2931no—
204C2×SD16—2931no—
205C2×D8—2931no—
206C2×M16C2×D29311yescharacteristic
207C22×C8—2931no—
208C4⋊Q8—2931no—
209#126—5861no—
210#125—2931no—
211#123—5861no—
212#123—5861no—
213#123—5861no—
214C22⋊Q8—2931no—
215C22⋊Q8—2931no—
216#121—2931no—
217#121—2931no—
218#121—5861no—
219#121—5861no—
220C4×D4—2931no—
221C4×D4—2931no—
222C4×D4—2931no—
223C4×D4—5861no—
224#117—2931no—
225C2×C4⋊C4—5861no—
226C2×C4⋊C4C2×D29311yescharacteristic
227#107—2931no—
228#106—2931no—
229#106—2931no—
230C4⋊C8—2931no—
231#103—2931no—
232#103—2931no—
233#103—2931no—
234#103—2931no—
235#103C2×D29311yescharacteristic
236#103C2×D29311yescharacteristic
237#102—2931no—
238#102—2931no—
239#102C2×D29311yescharacteristic
240#102C2×D29311yescharacteristic
241C22⋊C8—2931no—
242C22⋊C8—2931no—
243#97—2931no—
244#41—22no—
245#41—41no—
246#41—5862no—
247#41—11721no—
248C2×Q8—2931no—
249C2×Q8C22×D29311yescharacteristic
250C2×D4—21no—
251C2×D4—2931no—
252C2×D4—2931no—
253C2×D4—5861no—
254C2×D4—5861no—
255C2×D4—5861no—
256C2×D4C22×D29311yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—2931no—
260C22×C4—5861no—
261C22×C4—5861no—
262C22×C4—5861no—
263C22×C4C22×D29311yescharacteristic
264SD16—11721no—
265SD16—11721no—
266D8—5862no—
267M16—41no—
268C2×C8—2931no—
269C2×C8—2931no—
270C2×C8—11721no—
271C2×C8C22×D29311yescharacteristic
272C2×C8C22×D29311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—2931no—
275C4⋊C4—2931no—
276C4⋊C4—2931no—
277C4⋊C4—5861no—
278C4⋊C4—5861no—
279C4⋊C4—5861no—
280C4⋊C4—5861no—
281C4⋊C4—5861no—
282C4⋊C4—5861no—
283C4⋊C4C22×D29311yescharacteristic
284C4⋊C4C22×D29311yescharacteristic
285C22⋊C4—2931no—
286C22⋊C4—2931no—
287C22⋊C4—5861no—
288C22⋊C4—5861no—
289C22⋊C4—5861no—
290C22⋊C4—5861no—
291C22⋊C4—5861no—
292C22⋊C4—5861no—
293C22⋊C4—5861no—
294C42—2931no—
295C42—5861no—
296C23—21no—
297C23—2931no—
298C23—5861no—
299C23D4×D29311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—5861no—
303Q8—5861no—
304D4—21no—
305D4—42no—
306D4—23441no—
307D4—5861no—
308D4—5861no—
309D4—11721no—
310D4—11722no—
311D4—11722no—
312D4#1798980212yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—81no—
320C2×C4—2931no—
321C2×C4—2931no—
322C2×C4—2931no—
323C2×C4—23441no—
324C2×C4—5861no—
325C2×C4—5861no—
326C2×C4—5861no—
327C2×C4—5861no—
328C2×C4—5861no—
329C2×C4—11722no—
330C2×C4—11722no—
331C2×C4D4×D29311yescharacteristic
332C2×C4C23×D29311yescharacteristic
333C8—21no—
334C8—21no—
335C8—5861no—
336C8—5861no—
337C22—21no—
338C22—22no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—5861no—
344C22—5861no—
345C22—5861no—
346C22—11721no—
347C22—11721no—
348C22—11721no—
349C22C2×D4×D29311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—5861no—
355C4—5861no—
356C4—5861no—
357C4—11721no—
358C4—11721no—
359C4—11721no—
360C4C2×#1798980211yescharacteristic
361C4#2262766911yescharacteristic
362C2—41no—
363C2—42no—
364C2—23441no—
365C2—11721no—
366C2#3403676911yescharacteristic
367C2#3403692811yescharacteristic
368C2#3403693911yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#417×C293C2
socleC22×C293C22×D4
hypercenter#417D293
hypocenterC293#3307
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #34036827C2semidirect
2. #34036778C2semidirect
3. #34036496C2semidirect
4. #34036469C2semidirect
5. #34036459C2semidirect
6. #34036427C2semidirect
7. #34036375C2semidirect
8. #34036361C2semidirect
9. #34036333C2semidirect
10. #34036275C2semidirect
11. #34036274C2semidirect
12. #34036238C2semidirect
13. #34036198C2semidirect
14. #34036122C2semidirect
15. #417×C293C2semidirect
184. C293#3307semidirect
199. #417D293semidirect

Maximal subgroups

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

subgroupindex
#340368272
#340367782
#340364962
#340364692
#340364592
#340364272
#340363752
#340363612
#340363332
#340362752
#340362742
#340362382
#340361982
#340361222
#417×C2932
#3307293