Finite Group Databasebeta

← #49170683

Subgroups — #49170683

Order 37504.

398 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#34036790C211yesmaximal, characteristic, complemented
3#34036485C211yesmaximal, characteristic, complemented
4#34036469C211yesmaximal, characteristic, complemented
5#34036447C211yesmaximal, characteristic, complemented
6#34036438C211yesmaximal, characteristic, complemented
7#34036365C211yesmaximal, characteristic, complemented
8#34036361C211yesmaximal, characteristic, complemented
9#34036347C211yesmaximal, characteristic, complemented
10#34036277C211yesmaximal, characteristic, complemented
11#34036268C211yesmaximal, characteristic, complemented
12#34036214C211yesmaximal, characteristic, complemented
13C8×C22⋊D293C211yesmaximal, characteristic, complemented
14#34036124C211yesmaximal, characteristic, complemented
15C2×#103×C293C211yesmaximal, characteristic, complemented
16C2×#17989803C2211yescharacteristic
17C2×#17989789C2211yescharacteristic
18C2×#17989789C2211yescharacteristic
19C2×D2344C2211yescharacteristic
20C2×C8×D293C2211yescharacteristic
21#22627619—21no—
22#22627615C2211yescharacteristic
23#22627613—21no—
24#22627613C2211yescharacteristic
25#22627609—21no—
26#22627600—21no—
27#22627600C2211yescharacteristic
28#22627599C2211yescharacteristic
29#22627598—21no—
30#22627598—21no—
31#22627598C2211yescharacteristic
32#22627598C2211yescharacteristic
33Q8×Dic293C2211yescharacteristic
34#22627586C2211yescharacteristic
35C4×C22⋊D293—21no—
36C4×C22⋊D293—21no—
37C4×C22⋊D293C2211yescharacteristic
38#22627582C2211yescharacteristic
39#22627558C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627555C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic
50#22627536C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C22×Q8×C293C2211yescharacteristic
53C22×C8×C293C2211yescharacteristic
54C2×C4⋊C4×C293C2211yescharacteristic
55#103×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58#103×C293C2211yescharacteristic
59#17989803—22no—
60#17989803—41no—
61C2×D1172—21no—
62C2×D1172—21no—
63C2×D1172C2311yescharacteristic
64C2×D1172C2311yescharacteristic
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C2×C22⋊D293D411yescharacteristic
68C2×C4×D293—21no—
69C2×C4×D293—21no—
70C2×C4×D293C2311yescharacteristic
71#17989789—22no—
72#17989789—41no—
73D2344—41no—
74C2×#14556873C2311yescharacteristic
75C2×#14556873C2311yescharacteristic
76C8×D293—41no—
77C4⋊Dic293—21no—
78C4⋊Dic293—21no—
79C4⋊Dic293C2311yescharacteristic
80C4⋊Dic293C2311yescharacteristic
81#17989781—21no—
82#17989781—21no—
83#17989781D411yescharacteristic
84C22⋊Dic293D411yescharacteristic
85#17989779—21no—
86#17989779—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779D411yescharacteristic
94C4×Dic293—21no—
95C4×Dic293—21no—
96C4×Dic293C2311yescharacteristic
97C2×Q8×C293—21no—
98C2×Q8×C293—22no—
99C2×Q8×C293—41no—
100C2×Q8×C293C2311yescharacteristic
101C2×Q8×C293C2311yescharacteristic
102C22×C4×C293—21no—
103C22×C4×C293—21no—
104C22×C4×C293C2311yescharacteristic
105C2×C8×C293—41no—
106C2×C8×C293C2311yescharacteristic
107C2×C8×C293C2311yescharacteristic
108C4⋊C4×C293—21no—
109C4⋊C4×C293C2311yescharacteristic
110C4⋊C4×C293C2311yescharacteristic
111C22×D293—21no—
112C22×D293—21no—
113C22×D293C2×D411yescharacteristic
114D1172—21no—
115D1172—21no—
116D1172—21no—
117D1172—21no—
118D1172—42no—
119D1172—81no—
120C22⋊D293—22no—
121C22⋊D293—42no—
122C22⋊D293—42no—
123C2×Dic293—21no—
124C2×Dic293—21no—
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C4×D293—21no—
129C4×D293—21no—
130C4×D293—42no—
131C4×D293—81no—
132#14556873—21no—
133#14556873—21no—
134C23×C293C2×D411yescharacteristic
135Q8×C293—21no—
136Q8×C293—21no—
137Q8×C293—21no—
138Q8×C293—42no—
139Q8×C293#4112yes—
140C2×C4×C293—21no—
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—21no—
154C22×C293#13512yes—
155C22×C293C22×D411yescharacteristic
156C2×D293—21no—
157C2×D293—21no—
158C2×D293—21no—
159C2×D293—41no—
160C2×D293—41no—
161C2×D293—41no—
162C2×D293—41no—
163C2×D293—41no—
164C2×D293—41no—
165C4×C293—21no—
166C4×C293—22no—
167C4×C293—41no—
168C4×C293—41no—
169C4×C293—41no—
170C4×C293C2×#4111yescharacteristic
171C4×C293H(5,𝔽2)11yescharacteristic
172Dic293—21no—
173Dic293—21no—
174Dic293—21no—
175Dic293—41no—
176Dic293—41no—
177C2×C293—22no—
178C2×C293#54611yescharacteristic
179C2×C293C2×#13511yescharacteristic
180C2×C293#57711yescharacteristic
181D293—41no—
182D293—81no—
183D293—81no—
184C293#330111yescharacteristic, complemented, Sylow
185#3301—2931nomaximal, Sylow
186#553—2931no—
187#548—2931no—
188#488—2931no—
189#485—2931no—
190#481—2931no—
191#479—2931no—
192#466—2931no—
193#465—2931no—
194#463—2931no—
195#449—2931no—
196#448—2931no—
197C4×SD16—2931no—
198C8×D4—2931no—
199#416—2931no—
200C2×#103D29311yescharacteristic, complemented
201C2×#41—2931no—
202C22×Q8C2×D29311yescharacteristic
203C2×SD16—2931no—
204C2×SD16—2931no—
205C2×D8—2931no—
206C22×C8—2931no—
207C22×C8C2×D29311yescharacteristic
208#126—5861no—
209#125—2931no—
210#124—2931no—
211#124—5861no—
212#123—5861no—
213C22⋊Q8—2931no—
214C22⋊Q8—5861no—
215#121—2931no—
216#121—2931no—
217#121—2931no—
218#121—5861no—
219#121—5861no—
220C4×Q8—2931no—
221C4×D4—2931no—
222C4×D4—2931no—
223C4×D4—5861no—
224C4×D4—5861no—
225#117—2931no—
226C2×C4⋊C4C2×D29311yescharacteristic
227#107—2931no—
228#106—2931no—
229#106—2931no—
230C4⋊C8—2931no—
231#103—2931no—
232#103—2931no—
233#103C2×D29311yescharacteristic
234#103C2×D29311yescharacteristic
235#103C2×D29311yescharacteristic
236#103C2×D29311yescharacteristic
237#102—2931no—
238#102—2931no—
239#102—2931no—
240#102—2931no—
241C22⋊C8—2931no—
242C22⋊C8—2931no—
243C4×C8—2931no—
244#41—5862no—
245#41—11721no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D29311yescharacteristic
250C2×Q8C22×D29311yescharacteristic
251C2×D4—2931no—
252C2×D4—2931no—
253C2×D4—2931no—
254C2×D4—5861no—
255C2×D4—5861no—
256C2×D4—5861no—
257C2×D4—5861no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—2931no—
261C22×C4—5861no—
262C22×C4—5861no—
263C22×C4C22×D29311yescharacteristic
264SD16—5862no—
265SD16—11721no—
266D8—11721no—
267C2×C8—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⋊C4C22×D29311yescharacteristic
282C4⋊C4C22×D29311yescharacteristic
283C22⋊C4—2931no—
284C22⋊C4—2931no—
285C22⋊C4—5861no—
286C22⋊C4—5861no—
287C22⋊C4—5861no—
288C22⋊C4—5861no—
289C22⋊C4—5861no—
290C22⋊C4—5861no—
291C22⋊C4—5861no—
292C22⋊C4—5861no—
293C42—2931no—
294C42—5861no—
295C42—5861no—
296C23—2931no—
297C23—5861no—
298C23—5861no—
299C23D4×D29311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1798980212yes—
305D4—23441no—
306D4—5862no—
307D4—5861no—
308D4—5861no—
309D4—5861no—
310D4—5861no—
311D4—11722no—
312D4—11722no—
313D4—11722no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—2931no—
323C2×C4—2931no—
324C2×C4—2931no—
325C2×C4—23441no—
326C2×C4—5861no—
327C2×C4—5861no—
328C2×C4—5861no—
329C2×C4—5861no—
330C2×C4—11722no—
331C2×C4D4×D29311yescharacteristic
332C2×C4C23×D29311yescharacteristic
333C8—21no—
334C8—21no—
335C8—5861no—
336C8—5861no—
337C22—21no—
338C22—21no—
339C22—5861no—
340C22—5861no—
341C22—5861no—
342C22—11721no—
343C22—11721no—
344C22—11721no—
345C22—11721no—
346C22—11721no—
347C22—11721no—
348C22#2262764712yes—
349C22C2×D4×D29311yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—5861no—
356C4—5861no—
357C4—5861no—
358C4—11721no—
359C4—11721no—
360C4C2×#1798980211yescharacteristic
361C4#2262766911yescharacteristic
362C2—22no—
363C2—23441no—
364C2—23441no—
365C2—11721no—
366C2#3403676911yescharacteristic
367C2C2×#2262764711yescharacteristic
368C2#3403693511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×#103×C293C2
socleC22×C293C22×D4
hypercenterC2×#103D293
hypocenterC293#3301
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #34036827C2semidirect
2. #34036790C2semidirect
3. #34036485C2semidirect
4. #34036469C2semidirect
5. #34036447C2semidirect
6. #34036438C2semidirect
7. #34036365C2semidirect
8. #34036361C2semidirect
9. #34036347C2semidirect
10. #34036277C2semidirect
11. #34036268C2semidirect
12. #34036214C2semidirect
13. C8×C22⋊D293C2semidirect
14. #34036124C2semidirect
15. C2×#103×C293C2semidirect
184. C293#3301semidirect
200. C2×#103D293semidirect

Maximal subgroups

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

subgroupindex
#340368272
#340367902
#340364852
#340364692
#340364472
#340364382
#340363652
#340363612
#340363472
#340362772
#340362682
#340362142
C8×C22⋊D2932
#340361242
C2×#103×C2932
#3301293