Finite Group Databasebeta

← #49168990

Subgroups — #49168990

Order 37504.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036730C211yesmaximal, characteristic, complemented
2#34036611C211yesmaximal, characteristic, complemented
3#34036449C211yesmaximal, characteristic, complemented
4#34036441C211yesmaximal, characteristic, complemented
5#34036438C211yesmaximal, characteristic, complemented
6#34036428C211yesmaximal, characteristic, complemented
7#34036327C211yesmaximal, characteristic, complemented
8#34036323C211yesmaximal, characteristic, complemented
9#34036277C211yesmaximal, characteristic, complemented
10#34036273C211yesmaximal, characteristic, complemented
11#34036239C211yesmaximal, characteristic, complemented
12#34036227C211yesmaximal, characteristic, complemented
13C4×D2344C211yesmaximal, characteristic, complemented
14#34036188C211yesmaximal, characteristic, complemented
15C4×SD16×C293C211yesmaximal, characteristic, complemented
16C2×#17989803C2211yescharacteristic
17C2×#17989789C2211yescharacteristic
18C2×D2344C2211yescharacteristic
19C2×#17989787C2211yescharacteristic
20#22627620C2211yescharacteristic
21#22627615C2211yescharacteristic
22#22627607—21no—
23#22627606—21no—
24#22627599C2211yescharacteristic
25#22627598—21no—
26#22627597—21no—
27#22627595C2211yescharacteristic
28Q8×Dic293C2211yescharacteristic
29C4×D1172—21no—
30C4×D1172C2211yescharacteristic
31C4×D1172C2211yescharacteristic
32#22627586—21no—
33#22627586C2211yescharacteristic
34#22627581—21no—
35#22627581C2211yescharacteristic
36C4⋊C4×D293—21no—
37C4⋊C4×D293C2211yescharacteristic
38#22627558C2211yescharacteristic
39#22627557C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627546C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627536C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627535C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59#17989803—22no—
60#17989803—22no—
61C2×D1172—21no—
62C2×D1172—21no—
63C2×D1172C2311yescharacteristic
64C2×D1172C2311yescharacteristic
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C2×C22⋊D293—21no—
68C2×C4×D293—21no—
69C2×C4×D293—21no—
70C2×C4×D293—21no—
71C2×C4×D293—21no—
72C2×C4×D293—21no—
73C2×C4×D293C2311yescharacteristic
74#17989789—22no—
75D2344—22no—
76#17989787—22no—
77C2×#14556873C2311yescharacteristic
78C2×#14556873C2311yescharacteristic
79C4⋊Dic293—21no—
80C4⋊Dic293—21no—
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83#17989781—21no—
84#17989781—21no—
85#17989781D411yescharacteristic
86#17989781D411yescharacteristic
87C22⋊Dic293—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779D411yescharacteristic
93#17989779D411yescharacteristic
94C4×Dic293—21no—
95C4×Dic293C2311yescharacteristic
96C2×Q8×C293C2311yescharacteristic
97C2×D4×C293C2311yescharacteristic
98C22×C4×C293—21no—
99SD16×C293—22no—
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C4⋊C4×C293—21no—
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C22⋊C4×C293—21no—
106C42×C293—21no—
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109C22×D293—21no—
110C22×D293C2×D411yescharacteristic
111D1172—24no—
112D1172—21no—
113D1172—21no—
114D1172—21no—
115D1172—81no—
116D1172#4112yes—
117C22⋊D293—81no—
118C22⋊D293—81no—
119C22⋊D293—81no—
120C2×Dic293—21no—
121C2×Dic293—21no—
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C2×Dic293C2×D411yescharacteristic
125C4×D293—24no—
126C4×D293—21no—
127C4×D293—21no—
128C4×D293—81no—
129C4×D293—81no—
130C4×D293—81no—
131C4×D293—81no—
132#14556873—21no—
133#14556873—21no—
134C23×C293—21no—
135Q8×C293—21no—
136Q8×C293#4112yes—
137D4×C293—21no—
138D4×C293—21no—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—81no—
143C2×C4×C293C2×D411yescharacteristic
144C2×C4×C293C2×D411yescharacteristic
145C2×C4×C293C2411yescharacteristic
146C8×C293—21no—
147C8×C293—21no—
148C22×C293—41no—
149C22×C293—41no—
150C22×C293—41no—
151C22×C293C22×D411yescharacteristic
152C2×D293—21no—
153C2×D293—22no—
154C2×D293—21no—
155C2×D293—21no—
156C2×D293—41no—
157C2×D293—41no—
158C2×D293—41no—
159C2×D293—41no—
160C2×D293—41no—
161C4×C293—22no—
162C4×C293—21no—
163C4×C293—21no—
164C4×C293—41no—
165C4×C293—41no—
166C4×C293C2×#4111yescharacteristic
167C4×C293C2×#4111yescharacteristic
168Dic293—21no—
169Dic293—21no—
170Dic293—21no—
171Dic293—41no—
172Dic293—41no—
173C2×C293—81no—
174C2×C293#52511yescharacteristic
175C2×C293#57611yescharacteristic
176C2×C293#57711yescharacteristic
177D293—41no—
178D293—42no—
179D293—81no—
180C293#311911yescharacteristic, complemented, Sylow
181#3119—2931nomaximal, Sylow
182#540—2931no—
183#520—2931no—
184#481—2931no—
185#480—2931no—
186#479—2931no—
187#478—2931no—
188#460—2931no—
189#459—2931no—
190#449—2931no—
191#449—2931no—
192#442—2931no—
193#440—2931no—
194C4×SD16D29311yescharacteristic, complemented
195C4×D8—2931no—
196#433—2931no—
197C2×#41—2931no—
198C2×SD16—2931no—
199C2×SD16C2×D29311yescharacteristic
200C2×D8—2931no—
201C2×D8—2931no—
202#127—2931no—
203#125—2931no—
204#123—5861no—
205#123—5861no—
206#121—2931no—
207#121—2931no—
208#121—5861no—
209#121—5861no—
210C4×Q8—2931no—
211C4×Q8C2×D29311yescharacteristic
212C4×D4—2931no—
213C4×D4—2931no—
214C4×D4—2931no—
215C4×D4—5861no—
216C4×D4—5861no—
217C4×D4C2×D29311yescharacteristic
218#117—2931no—
219#117—5861no—
220C2×C4⋊C4—2931no—
221C2×C4⋊C4—5861no—
222#107—2931no—
223#107—2931no—
224#106—2931no—
225#106C2×D29311yescharacteristic
226C4⋊C8—2931no—
227C4⋊C8—2931no—
228#103—2931no—
229#103C2×D29311yescharacteristic
230#102—2931no—
231#102—2931no—
232#102—2931no—
233#102—2931no—
234#102—2931no—
235#102C2×D29311yescharacteristic
236C22⋊C8—2931no—
237C22⋊C8—2931no—
238#97—2931no—
239C4×C8C2×D29311yescharacteristic
240#41—5862no—
241#41—5862no—
242C2×Q8C22×D29311yescharacteristic
243C2×D4—2931no—
244C2×D4—2931no—
245C2×D4—5861no—
246C2×D4—5861no—
247C2×D4—5861no—
248C2×D4—5861no—
249C2×D4—5861no—
250C2×D4C22×D29311yescharacteristic
251C22×C4—21no—
252C22×C4—2931no—
253C22×C4—5861no—
254C22×C4—5861no—
255C22×C4—5861no—
256C22×C4—5861no—
257C22×C4—5861no—
258SD16—22no—
259SD16—5862no—
260D8—5862no—
261D8—5862no—
262C2×C8—2931no—
263C2×C8—2931no—
264C2×C8C22×D29311yescharacteristic
265C2×C8C22×D29311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—2931no—
268C4⋊C4—2931no—
269C4⋊C4—2931no—
270C4⋊C4—2931no—
271C4⋊C4—5861no—
272C4⋊C4—5861no—
273C4⋊C4—5861no—
274C4⋊C4—5861no—
275C4⋊C4C22×D29311yescharacteristic
276C4⋊C4C22×D29311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2931no—
279C22⋊C4—2931no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C42—21no—
286C42—2931no—
287C42—5861no—
288C42C22×D29311yescharacteristic
289C23—21no—
290C23—2931no—
291C23—5861no—
292C23—5861no—
293Q8—21no—
294Q8#1798980212yes—
295D4—21no—
296D4—21no—
297D4—2932no—
298D4—23441no—
299D4—23441no—
300D4—23441no—
301D4—23441no—
302D4—5864no—
303D4—5861no—
304D4—5861no—
305D4—5861no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—2931no—
311C2×C4—2931no—
312C2×C4—2931no—
313C2×C4—23441no—
314C2×C4—23441no—
315C2×C4—23441no—
316C2×C4—23441no—
317C2×C4—5864no—
318C2×C4—5861no—
319C2×C4—5861no—
320C2×C4—5861no—
321C2×C4—5861no—
322C2×C4D4×D29311yescharacteristic
323C2×C4D4×D29311yescharacteristic
324C2×C4C23×D29311yescharacteristic
325C8—21no—
326C8—21no—
327C8—5861no—
328C8—5861no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—5862no—
333C22—5861no—
334C22—5861no—
335C22—5861no—
336C22—11721no—
337C22—11721no—
338C22—11721no—
339C22—11721no—
340C22—11721no—
341C22C2×D4×D29311yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—5861no—
348C4—5861no—
349C4—5861no—
350C4—11721no—
351C4—11721no—
352C4#41×D29311yescharacteristic
353C4C2×#1798980211yescharacteristic
354C2—81no—
355C2—23441no—
356C2—11721no—
357C2—11722no—
358C2#3403663811yescharacteristic
359C2#3403693111yescharacteristic
360C2#3403693511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC4×SD16×C293C2
socleC22×C293C22×D4
hypercenterC4×SD16D293
hypocenterC293#3119
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #34036730C2semidirect
2. #34036611C2semidirect
3. #34036449C2semidirect
4. #34036441C2semidirect
5. #34036438C2semidirect
6. #34036428C2semidirect
7. #34036327C2semidirect
8. #34036323C2semidirect
9. #34036277C2semidirect
10. #34036273C2semidirect
11. #34036239C2semidirect
12. #34036227C2semidirect
13. C4×D2344C2semidirect
14. #34036188C2semidirect
15. C4×SD16×C293C2semidirect
180. C293#3119semidirect
194. C4×SD16D293semidirect

Maximal subgroups

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

subgroupindex
#340367302
#340366112
#340364492
#340364412
#340364382
#340364282
#340363272
#340363232
#340362772
#340362732
#340362392
#340362272
C4×D23442
#340361882
C4×SD16×C2932
#3119293