Finite Group Databasebeta

← #49169053

Subgroups — #49169053

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#34036751C211yesmaximal, characteristic, complemented
2#34036611C211yesmaximal, characteristic, complemented
3#34036463C211yesmaximal, characteristic, complemented
4#34036444C211yesmaximal, characteristic, complemented
5#34036422C211yesmaximal, characteristic, complemented
6#34036408C211yesmaximal, characteristic, complemented
7#34036353C211yesmaximal, characteristic, complemented
8#34036347C211yesmaximal, characteristic, complemented
9#34036290C211yesmaximal, characteristic, complemented
10#34036277C211yesmaximal, characteristic
11#34036227C211yesmaximal, characteristic, complemented
12#34036227C211yesmaximal, characteristic, complemented
13C4×D2344C211yesmaximal, characteristic, complemented
14#34036188C211yesmaximal, characteristic, complemented
15C4×Q16×C293C211yesmaximal, characteristic, complemented
16C2×#17989803C2211yescharacteristic
17C2×#17989789C2211yescharacteristic
18C2×#17989789C2211yescharacteristic
19C2×D2344C2211yescharacteristic
20#22627623C2211yescharacteristic
21#22627618—21no—
22#22627613C2211yescharacteristic
23#22627612—21no—
24#22627609—21no—
25#22627602—21no—
26#22627600C2211yescharacteristic
27#22627599C2211yescharacteristic
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#22627557C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627536C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627535C2211yescharacteristic
52C2×Q16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54C4×Q8×C293C2211yescharacteristic
55#107×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59#17989803—22no—
60#17989803—22no—
61C2×Dic586—21no—
62C2×D1172—21no—
63C2×D1172—21no—
64C2×D1172C2311yescharacteristic
65C2×D1172C2311yescharacteristic
66C2×C4×D293—21no—
67C2×C4×D293—21no—
68C2×C4×D293—21no—
69C2×C4×D293—21no—
70C2×C4×D293—21no—
71C2×C4×D293C2311yescharacteristic
72#17989789—22no—
73#17989789—22no—
74D2344—22no—
75C2×#14556873C2311yescharacteristic
76C2×#14556873C2311yescharacteristic
77C4⋊Dic293—21no—
78C4⋊Dic293C2311yescharacteristic
79C4⋊Dic293C2311yescharacteristic
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781D411yescharacteristic
84#17989781D411yescharacteristic
85#17989779—21no—
86#17989779—21no—
87#17989779—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×Q8×C293C2311yescharacteristic
98Q16×C293—22no—
99C2×C8×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C4⋊C4×C293—21no—
102C4⋊C4×C293—21no—
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C42×C293—21no—
106C42×C293—21no—
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109C22×D293—21no—
110C22×D293C2×D411yescharacteristic
111Dic586—81no—
112D1172—24no—
113D1172—21no—
114D1172—21no—
115D1172—21no—
116D1172—81no—
117D1172#4112yes—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C4×D293—24no—
124C4×D293—21no—
125C4×D293—21no—
126C4×D293—81no—
127C4×D293—81no—
128C4×D293—81no—
129C4×D293—81no—
130#14556873—21no—
131#14556873—21no—
132Q8×C293—21no—
133Q8×C293—21no—
134Q8×C293—21no—
135Q8×C293#4112yes—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—21no—
139C2×C4×C293—21no—
140C2×C4×C293C2×D411yescharacteristic
141C2×C4×C293C2×D411yescharacteristic
142C2×C4×C293C2411yescharacteristic
143C8×C293—21no—
144C8×C293—21no—
145C22×C293C22×D411yescharacteristic
146C2×D293—21no—
147C2×D293—22no—
148C2×D293—21no—
149C2×D293—21no—
150C2×D293—41no—
151C2×D293—41no—
152C2×D293—41no—
153C2×D293—41no—
154C2×D293—41no—
155C4×C293—22no—
156C4×C293—21no—
157C4×C293—21no—
158C4×C293—41no—
159C4×C293—41no—
160C4×C293—41no—
161C4×C293C2×#4111yescharacteristic
162C4×C293C2×#4111yescharacteristic
163Dic293—21no—
164Dic293—21no—
165Dic293—21no—
166Dic293—41no—
167Dic293—41no—
168C2×C293#52511yescharacteristic
169C2×C293#57611yescharacteristic
170C2×C293#57811yescharacteristic
171D293—41no—
172D293—42no—
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#452—2931no—
185#449—2931no—
186#440—2931no—
187#440—2931no—
188C4×Q16D29311yescharacteristic, complemented
189C4×D8—2931no—
190#433—2931no—
191C2×#41—2931no—
192C2×Q16C2×D29311yescharacteristic
193C2×SD16—2931no—
194C2×SD16—2931no—
195C2×D8—2931no—
196C4⋊Q8—2931no—
197#126—5861no—
198#124—2931no—
199#124—5861no—
200#123—5861no—
201C22⋊Q8—2931no—
202C22⋊Q8—5861no—
203#121—2931no—
204C4×Q8—2931no—
205C4×Q8C2×D29311yescharacteristic
206C4×Q8C2×D29311yescharacteristic
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#107C2×D29311yescharacteristic
220C4⋊C8—2931no—
221C4⋊C8—2931no—
222#103—2931no—
223#103—2931no—
224#103C2×D29311yescharacteristic
225#103C2×D29311yescharacteristic
226#102—2931no—
227#102—2931no—
228#102—2931no—
229#102—2931no—
230C22⋊C8—2931no—
231C22⋊C8—2931no—
232#97—2931no—
233C4×C8C2×D29311yescharacteristic
234#41—5862no—
235#41—5862no—
236C2×Q8—5861no—
237C2×Q8C22×D29311yescharacteristic
238C2×Q8C22×D29311yescharacteristic
239C2×D4—2931no—
240C2×D4—2931no—
241C2×D4—5861no—
242C2×D4—5861no—
243C22×C4—2931no—
244C22×C4—5861no—
245C22×C4—5861no—
246C22×C4—5861no—
247C22×C4—5861no—
248C22×C4—5861no—
249Q16—22no—
250SD16—5862no—
251SD16—5862no—
252D8—5862no—
253C2×C8—2931no—
254C2×C8—2931no—
255C2×C8C22×D29311yescharacteristic
256C2×C8C22×D29311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
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⋊C4C22×D29311yescharacteristic
268C4⋊C4C22×D29311yescharacteristic
269C22⋊C4—2931no—
270C22⋊C4—2931no—
271C22⋊C4—5861no—
272C22⋊C4—5861no—
273C22⋊C4—5861no—
274C22⋊C4—5861no—
275C22⋊C4—5861no—
276C22⋊C4—5861no—
277C22⋊C4—5861no—
278C42—21no—
279C42—21no—
280C42—2931no—
281C42—5861no—
282C42C22×D29311yescharacteristic
283C23—2931no—
284C23—5861no—
285C23—5861no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—23441no—
290Q8#1798980212yes—
291D4—2932no—
292D4—23441no—
293D4—5864no—
294D4—5861no—
295D4—5861no—
296D4—5861no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—2931no—
302C2×C4—2931no—
303C2×C4—2931no—
304C2×C4—23441no—
305C2×C4—23441no—
306C2×C4—23441no—
307C2×C4—23441no—
308C2×C4—5864no—
309C2×C4—5861no—
310C2×C4—5861no—
311C2×C4—5861no—
312C2×C4—5861no—
313C2×C4D4×D29311yescharacteristic
314C2×C4D4×D29311yescharacteristic
315C2×C4C23×D29311yescharacteristic
316C8—21no—
317C8—21no—
318C8—5861no—
319C8—5861no—
320C22—5862no—
321C22—5861no—
322C22—5861no—
323C22—5861no—
324C22—11721no—
325C22—11721no—
326C22—11721no—
327C22—11721no—
328C22—11721no—
329C22C2×D4×D29311yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—5861no—
337C4—5861no—
338C4—5861no—
339C4—11721no—
340C4—11721no—
341C4#41×D29311yescharacteristic
342C4C2×#1798980211yescharacteristic
343C2—23441no—
344C2—11721no—
345C2—11722no—
346C2#3403663811yescharacteristic
347C2#3403693111yescharacteristic
348C2#3403694211yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC4×Q16×C293C2
socleC22×C293C22×D4
prime radical#34036277C2
hypercenterC4×Q16D293
hypocenterC293#3124
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #34036751C2semidirect
2. #34036611C2semidirect
3. #34036463C2semidirect
4. #34036444C2semidirect
5. #34036422C2semidirect
6. #34036408C2semidirect
7. #34036353C2semidirect
8. #34036347C2semidirect
9. #34036290C2semidirect
11. #34036227C2semidirect
12. #34036227C2semidirect
13. C4×D2344C2semidirect
14. #34036188C2semidirect
15. C4×Q16×C293C2semidirect
174. C293#3124semidirect
188. C4×Q16D293semidirect

Maximal subgroups

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

subgroupindex
#340367512
#340366112
#340364632
#340364442
#340364222
#340364082
#340363532
#340363472
#340362902
#340362772
#340362272
C4×D23442
#340361882
C4×Q16×C2932
#3124293