Finite Group Databasebeta

← #49169015

Subgroups — #49169015

Order 37504.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036752C211yesmaximal, characteristic
2#34036607C211yesmaximal, characteristic, complemented
3#34036467C211yesmaximal, characteristic, complemented
4#34036454C211yesmaximal, characteristic
5#34036422C211yesmaximal, characteristic, complemented
6#34036412C211yesmaximal, characteristic, complemented
7#34036353C211yesmaximal, characteristic, complemented
8#34036353C211yesmaximal, characteristic, complemented
9#34036268C211yesmaximal, characteristic
10#34036236C211yesmaximal, characteristic, complemented
11#34036232C211yesmaximal, characteristic, complemented
12Q16×Dic293C211yesmaximal, characteristic, complemented
13#34036214C211yesmaximal, characteristic, complemented
14#34036187C211yesmaximal, characteristic, complemented
15#451×C293C211yesmaximal, characteristic, complemented
16C2×#17989789C2211yescharacteristic
17C2×#17989789C2211yescharacteristic
18#22627623C2211yescharacteristic
19#22627619—21no—
20#22627613C2211yescharacteristic
21#22627610—21no—
22#22627606—21no—
23#22627604—21no—
24#22627598C2211yescharacteristic
25Q8×Dic293—21no—
26Q8×Dic293—21no—
27Q8×Dic293C2211yescharacteristic
28Q8×Dic293C2211yescharacteristic
29Q8×Dic293C2211yescharacteristic
30Q8×Dic293C2211yescharacteristic
31Q8×Dic293C2211yescharacteristic
32#22627586C2211yescharacteristic
33#22627583—21no—
34#22627583—21no—
35#22627583C2211yescharacteristic
36#22627583C2211yescharacteristic
37#22627558C2211yescharacteristic
38#22627557C2211yescharacteristic
39#22627556C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627548C2211yescharacteristic
46#22627548C2211yescharacteristic
47#22627546C2211yescharacteristic
48#22627546C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C22×Q8×C293C2211yescharacteristic
53C2×Q16×C293C2211yescharacteristic
54C2×Q16×C293C2211yescharacteristic
55C22⋊Q8×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×D1172C2311yescharacteristic
61C2×C22⋊D293—21no—
62C2×C4×D293—21no—
63#17989789—22no—
64#17989789—22no—
65C2×#14556873C2311yescharacteristic
66C2×#14556873C2311yescharacteristic
67C4⋊Dic293—21no—
68C4⋊Dic293—21no—
69C4⋊Dic293—21no—
70C4⋊Dic293—21no—
71C4⋊Dic293—21no—
72C4⋊Dic293D411yescharacteristic
73C4⋊Dic293D411yescharacteristic
74C4⋊Dic293C2311yescharacteristic
75C4⋊Dic293C2311yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77#17989781—21no—
78C22⋊Dic293—21no—
79C22⋊Dic293D411yescharacteristic
80C22⋊Dic293D411yescharacteristic
81#17989779—21no—
82#17989779—21no—
83#17989779—21no—
84#17989779—21no—
85C4×Dic293—21no—
86C4×Dic293—21no—
87C4×Dic293—21no—
88C4×Dic293—21no—
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293C2311yescharacteristic
92C4×Dic293C2311yescharacteristic
93C2×Q8×C293—22no—
94C2×Q8×C293—22no—
95C2×Q8×C293—21no—
96C2×Q8×C293C2311yescharacteristic
97C2×Q8×C293C2311yescharacteristic
98C2×Q8×C293C2311yescharacteristic
99C22×C4×C293—21no—
100C22×C4×C293C2311yescharacteristic
101Q16×C293—22no—
102Q16×C293—22no—
103C2×C8×C293C2311yescharacteristic
104C2×C8×C293C2311yescharacteristic
105C4⋊C4×C293—21no—
106C4⋊C4×C293C2311yescharacteristic
107C22⋊C4×C293—21no—
108C22×D293—21no—
109Dic586—81no—
110D1172—21no—
111D1172—21no—
112C22⋊D293—81no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293C2×D411yescharacteristic
117C2×Dic293C2×D411yescharacteristic
118C2×Dic293C2×D411yescharacteristic
119C2×Dic293C2×D411yescharacteristic
120C4×D293—81no—
121#14556873—21no—
122#14556873—21no—
123C23×C293C2×D411yescharacteristic
124Q8×C293—24no—
125Q8×C293—21no—
126Q8×C293—21no—
127Q8×C293—21no—
128Q8×C293—21no—
129Q8×C293#4112yes—
130Q8×C293#4112yes—
131C2×C4×C293—24no—
132C2×C4×C293—21no—
133C2×C4×C293—21no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293C2×D411yescharacteristic
139C2×C4×C293C2411yescharacteristic
140C8×C293—21no—
141C8×C293—21no—
142C22×C293—21no—
143C22×C293—21no—
144C22×C293—21no—
145C22×C293C22×D411yescharacteristic
146C2×D293—41no—
147C2×D293—41no—
148C2×D293—41no—
149C4×C293—22no—
150C4×C293—22no—
151C4×C293—21no—
152C4×C293—41no—
153C4×C293—41no—
154C4×C293C2×#4111yescharacteristic
155C4×C293C2×#4111yescharacteristic
156Dic293—21no—
157Dic293—21no—
158Dic293—21no—
159Dic293—21no—
160Dic293—41no—
161Dic293—41no—
162Dic293—41no—
163C2×C293—41no—
164C2×C293#52511yescharacteristic
165C2×C293#57711yescharacteristic
166C2×C293#57811yescharacteristic
167D293—81no—
168C293#312111yescharacteristic, complemented, Sylow
169#3121—2931nomaximal, Sylow
170#542—2931no—
171#519—2931no—
172#485—2931no—
173#482—2931no—
174#477—2931no—
175#475—2931no—
176#464—2931no—
177#464—2931no—
178#451D29311yescharacteristic, complemented
179#448—2931no—
180#441—2931no—
181#440—2931no—
182C4×Q16—2931no—
183C4×SD16—2931no—
184#433—2931no—
185C22×Q8C2×D29311yescharacteristic
186C2×Q16C2×D29311yescharacteristic
187C2×Q16C2×D29311yescharacteristic
188C2×SD16—2931no—
189C2×SD16—2931no—
190C4⋊Q8—2931no—
191#126—5861no—
192#124—2931no—
193#124—5861no—
194#123—5861no—
195C22⋊Q8—5861no—
196C22⋊Q8C2×D29311yescharacteristic
197#121—2931no—
198C4×Q8—2931no—
199C4×Q8—2931no—
200C4×Q8—2931no—
201C4×Q8—2931no—
202C4×Q8—2931no—
203C4×Q8—5861no—
204C4×Q8—5861no—
205C4×D4—2931no—
206#117—2931no—
207#117—2931no—
208#117—5861no—
209#117—5861no—
210#107—2931no—
211#107—2931no—
212#106—2931no—
213#106—2931no—
214C4⋊C8—2931no—
215C4⋊C8—2931no—
216#103—2931no—
217#103—2931no—
218#103—2931no—
219#103—2931no—
220#103C2×D29311yescharacteristic
221#103C2×D29311yescharacteristic
222#102—2931no—
223#102—2931no—
224C22⋊C8—2931no—
225C22⋊C8C2×D29311yescharacteristic
226#97—2931no—
227C4×C8—2931no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—5861no—
232C2×Q8C22×D29311yescharacteristic
233C2×Q8C22×D29311yescharacteristic
234C2×Q8C22×D29311yescharacteristic
235C2×D4—2931no—
236C2×D4—5861no—
237C22×C4—21no—
238C22×C4—5861no—
239C22×C4C22×D29311yescharacteristic
240Q16—22no—
241Q16—22no—
242SD16—5862no—
243SD16—5862no—
244C2×C8—2931no—
245C2×C8—2931no—
246C2×C8C22×D29311yescharacteristic
247C2×C8C22×D29311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—2931no—
250C4⋊C4—2931no—
251C4⋊C4—2931no—
252C4⋊C4—2931no—
253C4⋊C4—2931no—
254C4⋊C4—5861no—
255C4⋊C4—5861no—
256C4⋊C4—5861no—
257C4⋊C4—5861no—
258C4⋊C4—5861no—
259C4⋊C4—5861no—
260C4⋊C4C22×D29311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—2931no—
263C22⋊C4—2931no—
264C22⋊C4—5861no—
265C22⋊C4—5861no—
266C22⋊C4—5861no—
267C22⋊C4—5861no—
268C22⋊C4—5861no—
269C42—2931no—
270C42—2931no—
271C42—5861no—
272C42—5861no—
273C42—5861no—
274C42—5861no—
275C42—5861no—
276C42—5861no—
277C23—5861no—
278C23D4×D29311yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—23441no—
285Q8#1798980112yes—
286Q8#1798980112yes—
287D4—23441no—
288D4—5861no—
289D4—5861no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—2931no—
298C2×C4—2931no—
299C2×C4—2931no—
300C2×C4—2931no—
301C2×C4—23441no—
302C2×C4—5861no—
303C2×C4—5861no—
304C2×C4—5861no—
305C2×C4D4×D29311yescharacteristic
306C2×C4C23×D29311yescharacteristic
307C8—21no—
308C8—21no—
309C8—5861no—
310C8—5861no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—11721no—
315C22—11721no—
316C22—11721no—
317C22C2×D4×D29311yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—5861no—
324C4—5861no—
325C4—5861no—
326C4—5861no—
327C4—11721no—
328C4—11721no—
329C4—11721no—
330C4C2×#1798980111yescharacteristic
331C4C2×#1798980111yescharacteristic
332C2—41no—
333C2—23441no—
334C2#3403663511yescharacteristic
335C2#3403693811yescharacteristic
336C2#3403694211yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#451×C293C2
socleC22×C293C22×D4
prime radical#22627598C22
hypercenter#451D293
hypocenterC293#3121
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #34036607C2semidirect
3. #34036467C2semidirect
5. #34036422C2semidirect
6. #34036412C2semidirect
7. #34036353C2semidirect
8. #34036353C2semidirect
10. #34036236C2semidirect
11. #34036232C2semidirect
12. Q16×Dic293C2semidirect
13. #34036214C2semidirect
14. #34036187C2semidirect
15. #451×C293C2semidirect
168. C293#3121semidirect
178. #451D293semidirect

Maximal subgroups

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

subgroupindex
#340367522
#340366072
#340364672
#340364542
#340364222
#340364122
#340363532
#340362682
#340362362
#340362322
Q16×Dic2932
#340362142
#340361872
#451×C2932
#3121293