Finite Group Databasebeta

← #49167607

Subgroups — #49167607

Order 37504.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627653C211yesmaximal, characteristic
2C4×#17989801C211yesmaximal, characteristic
3C4×Q8×D293C211yesmaximal, characteristic, complemented
4#34036237C211yesmaximal, characteristic, complemented
5#34036234C211yesmaximal, characteristic, complemented
6#34036229C211yesmaximal, characteristic, complemented
7#34036223C211yesmaximal, characteristic, complemented
8#34036221C211yesmaximal, characteristic, complemented
9#34036220C211yesmaximal, characteristic, complemented
10SD16×Dic293C211yesmaximal, characteristic, complemented
11#34036170C211yesmaximal, characteristic, complemented
12#34036136C211yesmaximal, characteristic, complemented
13#34036127C211yesmaximal, characteristic
14#34036081C211yesmaximal, characteristic, complemented
15#440×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C2×Q8×D293C2211yescharacteristic
18#22627653C418yescomplemented
19C2×Dic1172C2211yescharacteristic
20C2×#17989792C2211yescharacteristic
21C2×#17989790C2211yescharacteristic
22C2×#17989785C2211yescharacteristic
23C2×#17989785C2211yescharacteristic
24Q8×Dic293C2211yescharacteristic
25C4×Dic586—21no—
26C4×Dic586C2211yescharacteristic
27C4×Dic586C2211yescharacteristic
28#22627589—21no—
29#22627589C2211yescharacteristic
30#22627589C2211yescharacteristic
31D4×Dic293C2211yescharacteristic
32C4×C22⋊D293—21no—
33#22627584—21no—
34#22627582C2211yescharacteristic
35#22627580—21no—
36C4⋊C4×D293—21no—
37C4⋊C4×D293C2211yescharacteristic
38C2×C4×Dic293—21no—
39C42×D293—21no—
40C42×D293C2211yescharacteristic
41#22627557C2211yescharacteristic
42#22627556C2211yescharacteristic
43#22627555C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627549C2211yescharacteristic
46#22627548C2211yescharacteristic
47#22627547C2211yescharacteristic
48#22627547C2211yescharacteristic
49#22627545C2211yescharacteristic
50#22627535C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C8×Dic293C2211yescharacteristic
53C2×SD16×C293C2211yescharacteristic
54C4×Q8×C293C2211yescharacteristic
55C4×D4×C293C2211yescharacteristic
56#107×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59#97×C293C2211yescharacteristic
60#17989801—22no—
61#17989801C2×C414yes—
62C2×Dic586—21no—
63C2×Dic586C2311yescharacteristic
64C2×Dic586C2311yescharacteristic
65Q8×D293—22no—
66Q8×D293C2×C414yescomplemented
67C2×C22⋊D293—21no—
68C22×Dic293—21no—
69C22×Dic293—21no—
70C2×C4×D293—21no—
71C2×C4×D293—21no—
72C2×C4×D293D411yescharacteristic
73C2×C4×D293D411yescharacteristic
74C2×C4×D293C2311yescharacteristic
75Dic1172C2×C414yescomplemented
76#17989792C2×C414yescomplemented
77#17989790C2×C414yescomplemented
78#17989785—22no—
79#17989785C2×C414yescomplemented
80C2×#14556873C2311yescharacteristic
81C2×#14556873C2311yescharacteristic
82C4⋊Dic293—21no—
83C4⋊Dic293C2311yescharacteristic
84C4⋊Dic293C2311yescharacteristic
85#17989781—21no—
86#17989781—21no—
87#17989781—21no—
88#17989781—21no—
89#17989781—21no—
90C22⋊Dic293—21no—
91#17989779—21no—
92C4×Dic293—21no—
93C4×Dic293—21no—
94C4×Dic293—21no—
95C4×Dic293—21no—
96C4×Dic293—21no—
97C4×Dic293—21no—
98C4×Dic293D411yescharacteristic
99C4×Dic293D411yescharacteristic
100C4×Dic293C2311yescharacteristic
101C2×Q8×C293C2311yescharacteristic
102C2×D4×C293C2311yescharacteristic
103C22×C4×C293—21no—
104SD16×C293C2×C414yescomplemented
105C2×C8×C293C2311yescharacteristic
106C2×C8×C293C2311yescharacteristic
107C4⋊C4×C293—21no—
108C4⋊C4×C293C2311yescharacteristic
109C4⋊C4×C293C2311yescharacteristic
110C22⋊C4×C293—21no—
111C42×C293—21no—
112C42×C293C2311yescharacteristic
113C22×D293C2×D411yescharacteristic
114Dic586—21no—
115Dic586—21no—
116Dic586—24no—
117Dic586C22×C412yes—
118Dic586C22×C412yes—
119C22⋊D293—24no—
120C2×Dic293—21no—
121C2×Dic293—21no—
122C2×Dic293—24no—
123C2×Dic293—21no—
124C2×Dic293—21no—
125C2×Dic293—42no—
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C2×Dic293C2×D411yescharacteristic
129C4×D293—24no—
130C4×D293—22no—
131C4×D293—41no—
132C4×D293—42no—
133C4×D293C22×C412yes—
134C4×D293#4112yes—
135#14556873—21no—
136#14556873C22×C412yes—
137C23×C293—21no—
138Q8×C293—21no—
139Q8×C293C22×C412yes—
140D4×C293—21no—
141D4×C293C22×C412yes—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—42no—
146C2×C4×C293C2×D411yescharacteristic
147C2×C4×C293C2×D411yescharacteristic
148C2×C4×C293C2411yescharacteristic
149C8×C293—21no—
150C8×C293C22×C412yes—
151C22×C293—22no—
152C22×C293—41no—
153C22×C293—41no—
154C22×C293C22×D411yescharacteristic
155C2×D293—21no—
156C2×D293—21no—
157C2×D293C4×D412yes—
158C4×C293—22no—
159C4×C293—21no—
160C4×C293—21no—
161C4×C293—41no—
162C4×C293—41no—
163C4×C293C23×C411yescharacteristic
164C4×C293C2×#4111yescharacteristic
165Dic293—22no—
166Dic293—22no—
167Dic293—21no—
168Dic293—41no—
169Dic293—41no—
170Dic293C4×D412yes—
171Dic293#13712yescomplemented
172C2×C293—42no—
173C2×C293C2×C4×D411yescharacteristic
174C2×C293C2×#13711yescharacteristic
175C2×C293#57511yescharacteristic
176D293—22no—
177C293C4×#13711yescharacteristic, complemented, Sylow
178C4×#137—2931nomaximal, Sylow
179C2×#137—2931no—
180C4×#41—2931no—
181C2×C4×Q8—2931no—
182#441—2931no—
183#441—2931no—
184#440—2931no—
185#440D29311yescharacteristic, complemented
186C4×Q16—2931no—
187C4×Q16—2931no—
188C4×SD16—2931no—
189C4×SD16—2931no—
190#428—2931no—
191#419—2931no—
192#417—2931no—
193C4×M16—2931no—
194C2×#41—2931no—
195C22×Q8—2931no—
196#137—2938no—
197C2×Q16—2931no—
198C2×Q16—2931no—
199C2×SD16—2931no—
200C2×SD16C2×D29311yescharacteristic
201C2×M16—2931no—
202C2×M16—2931no—
203C4×Q8—2931no—
204C4×Q8—2931no—
205C4×Q8—2931no—
206C4×Q8—2931no—
207C4×Q8—2931no—
208C4×Q8—5861no—
209C4×Q8—5861no—
210C4×Q8C2×D29311yescharacteristic
211C4×D4—2931no—
212C4×D4—5861no—
213C4×D4—5861no—
214C4×D4C2×D29311yescharacteristic
215#117—2931no—
216#117—5861no—
217C2×C4⋊C4—2931no—
218C2×C4⋊C4—5861no—
219C2×C42—2931no—
220C2×C42—5861no—
221C2×C42—5861no—
222#107—2931no—
223#107C2×D29311yescharacteristic
224#106—2931no—
225#106—2931no—
226#103—2931no—
227#103—2931no—
228#103—2931no—
229#103—2931no—
230#103—2931no—
231#103C2×D29311yescharacteristic
232#102—2931no—
233#102C2×D29311yescharacteristic
234#97—2931no—
235#97C2×D29311yescharacteristic
236C4×C8—2931no—
237C4×C8—2931no—
238#41—2934no—
239#41—5862no—
240C2×Q8—2934no—
241C2×Q8—2931no—
242C2×Q8—2931no—
243C2×Q8—5861no—
244C2×Q8—5862no—
245C2×Q8C22×D29311yescharacteristic
246C2×D4—5861no—
247C2×D4C22×D29311yescharacteristic
248C22×C4—21no—
249C22×C4—2931no—
250C22×C4—2931no—
251C22×C4—2931no—
252C22×C4—5861no—
253C22×C4—5861no—
254C22×C4—5861no—
255C22×C4—5861no—
256Q16—2934no—
257Q16—2934no—
258SD16—2934no—
259SD16C4×D29314yescomplemented
260M16—2934no—
261M16—5862no—
262C2×C8—2931no—
263C2×C8—2931no—
264C2×C8C22×D29311yescharacteristic
265C2×C8C22×D29311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—2931no—
268C4⋊C4—2931no—
269C4⋊C4—5861no—
270C4⋊C4—5861no—
271C4⋊C4—5861no—
272C4⋊C4—5861no—
273C4⋊C4—5861no—
274C4⋊C4—5861no—
275C4⋊C4C22×D29311yescharacteristic
276C4⋊C4C22×D29311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—5861no—
279C22⋊C4—5861no—
280C42—21no—
281C42—2931no—
282C42—2931no—
283C42—2931no—
284C42—5861no—
285C42—5861no—
286C42—5861no—
287C42—5861no—
288C42—5861no—
289C42—5861no—
290C42C22×D29311yescharacteristic
291C23—21no—
292C23—2931no—
293Q8—21no—
294Q8—2932no—
295Q8—2932no—
296Q8—5864no—
297Q8—5861no—
298Q8—5861no—
299Q8C2×C4×D29312yes—
300D4—21no—
301D4—5864no—
302D4C2×C4×D29312yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—2931no—
308C2×C4—2931no—
309C2×C4—2932no—
310C2×C4—2932no—
311C2×C4—2931no—
312C2×C4—5862no—
313C2×C4—5864no—
314C2×C4—5864no—
315C2×C4—5861no—
316C2×C4—5861no—
317C2×C4—5861no—
318C2×C4—5861no—
319C2×C4—11721no—
320C2×C4—11722no—
321C2×C4—11722no—
322C2×C4D4×D29311yescharacteristic
323C2×C4D4×D29311yescharacteristic
324C2×C4C23×D29311yescharacteristic
325C8—21no—
326C8—2932no—
327C8—5861no—
328C8C2×C4×D29312yes—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—2932no—
333C22—5861no—
334C22—5861no—
335C22C2×D4×D29311yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—2932no—
342C4—2932no—
343C4—5862no—
344C4—5862no—
345C4—5861no—
346C4—11721no—
347C4—11721no—
348C4C22×C4×D29311yescharacteristic
349C4#41×D29311yescharacteristic
350C2—42no—
351C2—5862no—
352C2C4×D4×D29311yescharacteristic
353C2#137×D29311yescharacteristic
354C2#3403692511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutatorC4×C293C23×C4
FrattiniC2×C4C23×D293
Fitting#440×C293C2
socleC22×C293C22×D4
prime radicalC2×#17989801C22
cosocleC2×C4×C293C24
hypercenter#440D293
hypocenterC293C4×#137
LCSG ▷ C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D293C2semidirect
4. #34036237C2semidirect
5. #34036234C2semidirect
6. #34036229C2semidirect
7. #34036223C2semidirect
8. #34036221C2semidirect
9. #34036220C2semidirect
10. SD16×Dic293C2semidirect
11. #34036170C2semidirect
12. #34036136C2semidirect
14. #34036081C2semidirect
15. #440×C293C2semidirect
18. #22627653C4semidirect
66. Q8×D293C2×C4semidirect
75. Dic1172C2×C4semidirect
76. #17989792C2×C4semidirect
77. #17989790C2×C4semidirect
79. #17989785C2×C4semidirect
104. SD16×C293C2×C4semidirect
171. Dic293#137semidirect
177. C293C4×#137semidirect
185. #440D293semidirect
259. SD16C4×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276532
C4×#179898012
C4×Q8×D2932
#340362372
#340362342
#340362292
#340362232
#340362212
#340362202
SD16×Dic2932
#340361702
#340361362
#340361272
#340360812
#440×C2932
C4×#137293