Finite Group Databasebeta

← #49171500

Subgroups — #49171500

Order 37504.

372 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036848C211yesmaximal, characteristic, complemented
2#34036794C211yesmaximal, characteristic, complemented
3#34036487C211yesmaximal, characteristic, complemented
4#34036478C211yesmaximal, characteristic, complemented
5#34036422C211yesmaximal, characteristic, complemented
6#34036421C211yesmaximal, characteristic, complemented
7#34036407C211yesmaximal, characteristic, complemented
8#34036343C211yesmaximal, characteristic
9#34036341C211yesmaximal, characteristic
10#34036333C211yesmaximal, characteristic, complemented
11#34036257C211yesmaximal, characteristic, complemented
12#34036232C211yesmaximal, characteristic, complemented
13#34036231C211yesmaximal, characteristic, complemented
14#34036209C211yesmaximal, characteristic
15#489×C293C211yesmaximal, characteristic, complemented
16C2×Q8×D293—21no—
17C2×#17989791C2211yescharacteristic
18C2×#17989789C2211yescharacteristic
19C2×#17989787C2211yescharacteristic
20#22627623C2211yescharacteristic
21#22627623C2211yescharacteristic
22#22627622C2211yescharacteristic
23#22627617—21no—
24#22627617—21no—
25#22627611C2211yescharacteristic
26#22627602—21no—
27#22627602—21no—
28#22627601—21no—
29#22627600—21no—
30Q8×Dic293C2211yescharacteristic
31C4×Dic586C2211yescharacteristic
32C4×Dic586C2211yescharacteristic
33C4×D1172C2211yescharacteristic
34D4×Dic293C2211yescharacteristic
35#22627586C2211yescharacteristic
36#22627586C2211yescharacteristic
37#22627580—21no—
38#22627558C2211yescharacteristic
39#22627557C2211yescharacteristic
40#22627557C2211yescharacteristic
41C4⋊#14556873C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627553C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627548C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627547C2211yescharacteristic
48#22627546C2211yescharacteristic
49#22627545C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C4⋊Q8×C293C2211yescharacteristic
53#124×C293C2211yescharacteristic
54#103×C293C2211yescharacteristic
55#103×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586—21no—
61C2×Dic586D411yescharacteristic
62C2×Dic586C2311yescharacteristic
63Q8×D293—44no—
64C2×D1172C2311yescharacteristic
65C22×Dic293—21no—
66C2×C4×D293—21no—
67C2×C4×D293—21no—
68C2×C4×D293—21no—
69#17989791—22no—
70#17989789—22no—
71#17989787—22no—
72C2×#14556873C2311yescharacteristic
73C2×#14556873C2311yescharacteristic
74C4⋊Dic293—21no—
75C4⋊Dic293D411yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77C4⋊Dic293C2311yescharacteristic
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781D411yescharacteristic
84#17989781D411yescharacteristic
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293C2311yescharacteristic
94C4×Dic293C2311yescharacteristic
95C2×Q8×C293—21no—
96C2×Q8×C293C2311yescharacteristic
97C2×D4×C293C2311yescharacteristic
98C2×C8×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C4⋊C4×C293—21no—
101C4⋊C4×C293C2311yescharacteristic
102C4⋊C4×C293C2311yescharacteristic
103C22⋊C4×C293—21no—
104C22⋊C4×C293—21no—
105C42×C293C2311yescharacteristic
106C22×D293—21no—
107Dic586—22no—
108Dic586—21no—
109Dic586—21no—
110Dic586—42no—
111Dic586—42no—
112D1172—21no—
113D1172#4112yes—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—42no—
118C2×Dic293C2×D411yescharacteristic
119C2×Dic293C2×D411yescharacteristic
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C4×D293—42no—
123C4×D293—42no—
124C4×D293—42no—
125#14556873—21no—
126#14556873—21no—
127C23×C293—21no—
128Q8×C293—21no—
129Q8×C293—21no—
130Q8×C293—42no—
131D4×C293—21no—
132D4×C293—21no—
133C2×C4×C293—21no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293C2×D411yescharacteristic
137C2×C4×C293C2×D411yescharacteristic
138C2×C4×C293C2411yescharacteristic
139C8×C293—21no—
140C8×C293—21no—
141C22×C293—41no—
142C22×C293—41no—
143C22×C293—41no—
144C22×C293C22×D411yescharacteristic
145C2×D293—22no—
146C2×D293—41no—
147C2×D293—41no—
148C4×C293—21no—
149C4×C293—21no—
150C4×C293—41no—
151C4×C293—41no—
152C4×C293—41no—
153C4×C293C2×#4111yescharacteristic
154C4×C2932−1+411yescharacteristic
155Dic293—21no—
156Dic293—21no—
157Dic293—21no—
158Dic293—41no—
159Dic293—41no—
160Dic293—41no—
161Dic293AGL(1,ℤ/8)12yes—
162C2×C293—81no—
163C2×C293#54811yescharacteristic
164C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
165C2×C293#57811yescharacteristic
166D293—42no—
167C293#336711yescharacteristic, complemented, Sylow
168#3367—2931nomaximal, Sylow
169#556—2931no—
170D4×Q8—2931no—
171#489—2931no—
172#489D29311yescharacteristic, complemented
173#487—2931no—
174#477—2931no—
175#477—2931no—
176#474—2931no—
177#463—2931no—
178#463—2931no—
179#461—2931no—
180#446—2931no—
181#440—2931no—
182#440—2931no—
183C4×D8—2931no—
184C22×Q8—5861no—
185C2×SD16—2931no—
186C2×SD16—2931no—
187C2×D8—2931no—
188C4⋊Q8—2931no—
189C4⋊Q8—2931no—
190C4⋊Q8—2931no—
191C4⋊Q8C2×D29311yescharacteristic
192#126—5861no—
193#126—5861no—
194#124—2931no—
195#124C2×D29311yescharacteristic
196C22⋊Q8—5861no—
197C22⋊Q8—5861no—
198C22⋊Q8—5861no—
199C22⋊Q8—5861no—
200C4×Q8—2931no—
201C4×Q8—2931no—
202C4×Q8—2931no—
203C4×D4—2931no—
204C4×D4—2931no—
205C4×D4—2931no—
206C4×D4—2931no—
207#117—5861no—
208#107—2931no—
209#107—2931no—
210#107—2931no—
211C4⋊C8—2931no—
212C4⋊C8—2931no—
213C4⋊C8—2931no—
214#103—2931no—
215#103—2931no—
216#103—2931no—
217#103—2931no—
218#103C2×D29311yescharacteristic
219#103C2×D29311yescharacteristic
220#102—2931no—
221#102—2931no—
222#102C2×D29311yescharacteristic
223#102C2×D29311yescharacteristic
224#97—2931no—
225#97C2×D29311yescharacteristic
226C4×C8—2931no—
227C2×Q8—21no—
228C2×Q8—2931no—
229C2×Q8—2931no—
230C2×Q8—5861no—
231C2×Q8—5861no—
232C2×Q8—11724no—
233C2×Q8C22×D29311yescharacteristic
234C2×D4—2931no—
235C2×D4C22×D29311yescharacteristic
236C22×C4—5861no—
237C22×C4—5861no—
238C22×C4—5861no—
239C22×C4—5861no—
240SD16—5862no—
241SD16—5862no—
242D8—5862no—
243C2×C8—2931no—
244C2×C8—2931no—
245C2×C8C22×D29311yescharacteristic
246C2×C8C22×D29311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—2931no—
249C4⋊C4—2931no—
250C4⋊C4—2931no—
251C4⋊C4—2931no—
252C4⋊C4—2931no—
253C4⋊C4—5861no—
254C4⋊C4—5861no—
255C4⋊C4—5861no—
256C4⋊C4—5861no—
257C4⋊C4—5861no—
258C4⋊C4—5861no—
259C4⋊C4C22×D29311yescharacteristic
260C4⋊C4C22×D29311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—5861no—
264C22⋊C4—5861no—
265C22⋊C4—5861no—
266C22⋊C4—5861no—
267C22⋊C4—5861no—
268C22⋊C4—5861no—
269C42—2931no—
270C42—2931no—
271C42—5861no—
272C42—5861no—
273C42C22×D29311yescharacteristic
274C23—21no—
275C23—5861no—
276Q8—21no—
277Q8—21no—
278Q8—42no—
279Q8—5862no—
280Q8—5861no—
281Q8—5861no—
282Q8—11722no—
283Q8—11722no—
284D4—21no—
285D4—21no—
286D4—2932no—
287D4—5861no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—2931no—
292C2×C4—2931no—
293C2×C4—2931no—
294C2×C4—2931no—
295C2×C4—5861no—
296C2×C4—5861no—
297C2×C4—5861no—
298C2×C4—11722no—
299C2×C4—11722no—
300C2×C4—11722no—
301C2×C4—11722no—
302C2×C4D4×D29311yescharacteristic
303C2×C4D4×D29311yescharacteristic
304C2×C4C23×D29311yescharacteristic
305C8—21no—
306C8—21no—
307C8—5861no—
308C8—5861no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—5862no—
313C22—11721no—
314C22—11721no—
315C22C2×D4×D29311yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—2932no—
322C4—5861no—
323C4—5861no—
324C4—5861no—
325C4—11721no—
326C4—11721no—
327C4—11721no—
328C4#41×D29311yescharacteristic
329C4#2262767111yescharacteristic
330C2—81no—
331C2—11722no—
332C2#3403678711yescharacteristic
333C2AGL(1,ℤ/8)×D29311yescharacteristic
334C2#3403694511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#489×C293C2
socleC22×C293C22×D4
prime radicalC2×#17989787C22
hypercenter#489D293
hypocenterC293#3367
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #34036848C2semidirect
2. #34036794C2semidirect
3. #34036487C2semidirect
4. #34036478C2semidirect
5. #34036422C2semidirect
6. #34036421C2semidirect
7. #34036407C2semidirect
10. #34036333C2semidirect
11. #34036257C2semidirect
12. #34036232C2semidirect
13. #34036231C2semidirect
15. #489×C293C2semidirect
167. C293#3367semidirect
172. #489D293semidirect

Maximal subgroups

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

subgroupindex
#340368482
#340367942
#340364872
#340364782
#340364222
#340364212
#340364072
#340363432
#340363412
#340363332
#340362572
#340362322
#340362312
#340362092
#489×C2932
#3367293