Finite Group Databasebeta

← #49170659

Subgroups — #49170659

Order 37504.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036834C211yesmaximal, characteristic
2#34036792C211yesmaximal, characteristic
3#34036478C211yesmaximal, characteristic, complemented
4#34036466C211yesmaximal, characteristic, complemented
5#34036423C211yesmaximal, characteristic, complemented
6#34036371C211yesmaximal, characteristic, complemented
7#34036368C211yesmaximal, characteristic, complemented
8#34036338C211yesmaximal, characteristic, complemented
9#34036287C211yesmaximal, characteristic, complemented
10#34036286C211yesmaximal, characteristic, complemented
11#34036223C211yesmaximal, characteristic, complemented
12#34036192C211yesmaximal, characteristic
13C2×#22627547C211yesmaximal, characteristic, complemented
14#103×D293C211yesmaximal, characteristic, complemented
15#484×C293C211yesmaximal, characteristic, complemented
16C22×Dic586C2211yescharacteristic
17C2×Q8×D293C2211yescharacteristic
18C2×Dic1172C2211yescharacteristic
19C2×Dic1172C2211yescharacteristic
20C2×#17989792C2211yescharacteristic
21C22×#14556873C2211yescharacteristic
22C2×C8×D293C2211yescharacteristic
23#22627623—21no—
24#22627623C2211yescharacteristic
25#22627622C2211yescharacteristic
26#22627614—21no—
27#22627604C2211yescharacteristic
28#22627604C2211yescharacteristic
29#22627603—21no—
30#22627603C2211yescharacteristic
31#22627602—21no—
32#22627602—21no—
33#22627601—21no—
34#22627589C2211yescharacteristic
35#22627589C2211yescharacteristic
36C4×C22⋊D293—21no—
37C4×C22⋊D293C2211yescharacteristic
38#22627584—21no—
39C4⋊C4×D293C2211yescharacteristic
40#22627557C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627547C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627547C2211yescharacteristic
48#22627547C2211yescharacteristic
49#22627547C2211yescharacteristic
50#22627536C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C22⋊Q8×C293C2211yescharacteristic
53C2×C4⋊C4×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic
55#107×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586—21no—
61C2×Dic586—22no—
62C2×Dic586—21no—
63C2×Dic586—41no—
64C2×Dic586C2311yescharacteristic
65C2×Dic586C2311yescharacteristic
66C2×Dic586C2311yescharacteristic
67Q8×D293—22no—
68Q8×D293—41no—
69C2×C22⋊D293D411yescharacteristic
70C22×Dic293—21no—
71C2×C4×D293—21no—
72C2×C4×D293—21no—
73C2×C4×D293C2311yescharacteristic
74Dic1172—22no—
75Dic1172—41no—
76#17989792—41no—
77C2×#14556873—41no—
78C2×#14556873C2311yescharacteristic
79C2×#14556873C2311yescharacteristic
80C8×D293—41no—
81C4⋊Dic293—21no—
82C4⋊Dic293—21no—
83C4⋊Dic293C2311yescharacteristic
84#17989781—21no—
85#17989781—21no—
86#17989781—21no—
87#17989781—21no—
88#17989781—21no—
89#17989781—21no—
90#17989781—21no—
91#17989781D411yescharacteristic
92C22⋊Dic293—21no—
93C22⋊Dic293D411yescharacteristic
94#17989779—21no—
95#17989779—21no—
96#17989779D411yescharacteristic
97C4×Dic293—21no—
98C4×Dic293—21no—
99C4×Dic293C2311yescharacteristic
100C2×Q8×C293C2311yescharacteristic
101C22×C4×C293—21no—
102C22×C4×C293C2311yescharacteristic
103C2×C8×C293C2311yescharacteristic
104C2×C8×C293C2311yescharacteristic
105C4⋊C4×C293—21no—
106C4⋊C4×C293—21no—
107C4⋊C4×C293C2311yescharacteristic
108C4⋊C4×C293C2311yescharacteristic
109C4⋊C4×C293C2311yescharacteristic
110C22⋊C4×C293—21no—
111C22×D293C2×D411yescharacteristic
112Dic586—21no—
113Dic586—21no—
114Dic586—21no—
115Dic586—21no—
116Dic586—21no—
117Dic586—42no—
118Dic586—42no—
119Dic586—81no—
120Dic586#4112yes—
121C22⋊D293Q1614yescomplemented
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293—21no—
125C2×Dic293—21no—
126C2×Dic293—42no—
127C2×Dic293C2×D411yescharacteristic
128C2×Dic293C2×D411yescharacteristic
129C2×Dic293C2×D411yescharacteristic
130C4×D293—21no—
131C4×D293—21no—
132C4×D293—42no—
133C4×D293—81no—
134#14556873—21no—
135#14556873—21no—
136C23×C293C2×D411yescharacteristic
137Q8×C293—21no—
138Q8×C293—21no—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—81no—
146C2×C4×C293C2×D411yescharacteristic
147C2×C4×C293C2411yescharacteristic
148C8×C293—21no—
149C8×C293—21no—
150C22×C293—21no—
151C22×C293—21no—
152C22×C293C2×Q1612yes—
153C22×C293C22×D411yescharacteristic
154C2×D293—21no—
155C2×D293—21no—
156C2×D293C2×Q1612yes—
157C4×C293—21no—
158C4×C293—41no—
159C4×C293—41no—
160C4×C293—41no—
161C4×C293—41no—
162C4×C293C2×#4111yescharacteristic
163C4×C293H(5,𝔽2)11yescharacteristic
164Dic293—21no—
165Dic293—22no—
166Dic293—21no—
167Dic293—41no—
168Dic293—41no—
169Dic293—41no—
170Dic293C2×Q1612yes—
171C2×C293—22no—
172C2×C293#54611yescharacteristic
173C2×C293C22×Q1611yescharacteristic
174C2×C293#57711yescharacteristic
175D293—22no—
176C293#329911yescharacteristic, complemented, Sylow
177#3299—2931nomaximal, Sylow
178#554—2931no—
179D4×Q8—2931no—
180#487—2931no—
181#484—2931no—
182#484D29311yescharacteristic, complemented
183#477—2931no—
184#467—2931no—
185#467—2931no—
186#462—2931no—
187#451—2931no—
188#451—2931no—
189C4×Q16—2931no—
190C8×D4—2931no—
191C2×#103—2931no—
192C2×#103—2931no—
193C22×Q8—2931no—
194C22×Q8—2931no—
195C2×Q16—2931no—
196C2×Q16—2931no—
197C2×Q16—2931no—
198C22×C8—2931no—
199C22×C8—2931no—
200C4⋊Q8—2931no—
201C4⋊Q8—2931no—
202C4⋊Q8—5861no—
203#125—5861no—
204C22⋊Q8—2931no—
205C22⋊Q8—2931no—
206C22⋊Q8—2931no—
207C22⋊Q8—5861no—
208C22⋊Q8—5861no—
209C22⋊Q8—5861no—
210C22⋊Q8—5861no—
211C22⋊Q8C2×D29311yescharacteristic
212C4×Q8—2931no—
213C4×Q8—2931no—
214C4×D4—2931no—
215C4×D4—5861no—
216C4×D4—5861no—
217C2×C4⋊C4—2931no—
218C2×C4⋊C4C2×D29311yescharacteristic
219#107—2931no—
220#107C2×D29311yescharacteristic
221#107C2×D29311yescharacteristic
222C4⋊C8—2931no—
223#103—2931no—
224#103—2931no—
225#103—2931no—
226#103—2931no—
227#103—2931no—
228#103—2931no—
229#103—2931no—
230#103—2931no—
231#103C2×D29311yescharacteristic
232#103C2×D29311yescharacteristic
233C22⋊C8—2931no—
234C22⋊C8C2×D29311yescharacteristic
235C4×C8—2931no—
236C2×Q8—2931no—
237C2×Q8—2931no—
238C2×Q8—2931no—
239C2×Q8—5861no—
240C2×Q8—5861no—
241C2×Q8—5862no—
242C2×Q8—5861no—
243C2×Q8—5862no—
244C2×Q8—11721no—
245C2×Q8—11721no—
246C2×Q8C22×D29311yescharacteristic
247C2×D4—2931no—
248C22×C4—21no—
249C22×C4—2931no—
250C22×C4—5861no—
251C22×C4—5861no—
252C22×C4—5861no—
253C22×C4C22×D29311yescharacteristic
254Q16—5862no—
255Q16—11721no—
256Q16—11721no—
257C2×C8—2931no—
258C2×C8—2931no—
259C2×C8—11721no—
260C2×C8—11721no—
261C2×C8C22×D29311yescharacteristic
262C2×C8C22×D29311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—2931no—
266C4⋊C4—2931no—
267C4⋊C4—5861no—
268C4⋊C4—5861no—
269C4⋊C4—5861no—
270C4⋊C4—5861no—
271C4⋊C4—5861no—
272C4⋊C4—5861no—
273C4⋊C4—5861no—
274C4⋊C4—5861no—
275C4⋊C4—5861no—
276C4⋊C4C22×D29311yescharacteristic
277C4⋊C4C22×D29311yescharacteristic
278C4⋊C4C22×D29311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—2931no—
281C22⋊C4—2931no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C42—2931no—
286C42—5861no—
287C42—5861no—
288C23—2931no—
289C23D4×D29311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—2932no—
293Q8—23441no—
294Q8—5861no—
295Q8—5861no—
296Q8—5861no—
297Q8—5861no—
298Q8—5861no—
299Q8—11722no—
300Q8—11722no—
301D4—2934no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—81no—
309C2×C4—2931no—
310C2×C4—2931no—
311C2×C4—2931no—
312C2×C4—23441no—
313C2×C4—5861no—
314C2×C4—5861no—
315C2×C4—5861no—
316C2×C4—5861no—
317C2×C4—5861no—
318C2×C4—5861no—
319C2×C4—11722no—
320C2×C4—11722no—
321C2×C4D4×D29311yescharacteristic
322C2×C4C23×D29311yescharacteristic
323C8—21no—
324C8—21no—
325C8—5861no—
326C8—5861no—
327C22—21no—
328C22—21no—
329C22—2932no—
330C22—5861no—
331C22—5861no—
332C22Q16×D29312yes—
333C22C2×D4×D29311yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—2932no—
340C4—5861no—
341C4—5862no—
342C4—5861no—
343C4—11721no—
344C4—11721no—
345C4—11721no—
346C4#41×D29311yescharacteristic
347C4#2262767011yescharacteristic
348C2—22no—
349C2—5862no—
350C2#3403677111yescharacteristic
351C2C2×Q16×D29311yescharacteristic
352C2#3403693911yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#484×C293C2
socleC22×C293C22×D4
prime radicalC2×C22⋊D293D4
hypercenter#484D293
hypocenterC293#3299
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #34036478C2semidirect
4. #34036466C2semidirect
5. #34036423C2semidirect
6. #34036371C2semidirect
7. #34036368C2semidirect
8. #34036338C2semidirect
9. #34036287C2semidirect
10. #34036286C2semidirect
11. #34036223C2semidirect
13. C2×#22627547C2semidirect
14. #103×D293C2semidirect
15. #484×C293C2semidirect
121. C22⋊D293Q16semidirect
176. C293#3299semidirect
182. #484D293semidirect

Maximal subgroups

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

subgroupindex
#340368342
#340367922
#340364782
#340364662
#340364232
#340363712
#340363682
#340363382
#340362872
#340362862
#340362232
#340361922
C2×#226275472
#103×D2932
#484×C2932
#3299293