Finite Group Databasebeta

← #49168905

Subgroups — #49168905

Order 37504.

424 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036676C211yesmaximal, characteristic
2C4×Q8×D293C211yesmaximal, characteristic, complemented
3#34036444C211yesmaximal, characteristic, complemented
4#34036441C211yesmaximal, characteristic, complemented
5#34036423C211yesmaximal, characteristic, complemented
6#34036422C211yesmaximal, characteristic, complemented
7#34036328C211yesmaximal, characteristic, complemented
8#34036327C211yesmaximal, characteristic, complemented
9#34036269C211yesmaximal, characteristic, complemented
10#34036266C211yesmaximal, characteristic, complemented
11#34036231C211yesmaximal, characteristic, complemented
12#34036229C211yesmaximal, characteristic, complemented
13#34036227C211yesmaximal, characteristic, complemented
14#34036184C211yesmaximal, characteristic, complemented
15#440×C293C211yesmaximal, characteristic, complemented
16C2×#17989802—21no—
17C2×Q8×D293C2211yescharacteristic
18C2×#17989791C2211yescharacteristic
19C2×#17989790C2211yescharacteristic
20C2×#17989789C2211yescharacteristic
21#22627623C2211yescharacteristic
22#22627620C2211yescharacteristic
23#22627610—21no—
24#22627599C2211yescharacteristic
25#22627597—21no—
26#22627595C2211yescharacteristic
27Q8×Dic293C2211yescharacteristic
28C4×Dic586—21no—
29C4×Dic586C2211yescharacteristic
30#22627589—21no—
31#22627589C2211yescharacteristic
32C4×D1172C2211yescharacteristic
33C4×C22⋊D293—21no—
34C4⋊C4×D293—21no—
35C4⋊C4×D293C2211yescharacteristic
36C42×D293—21no—
37C42×D293C2211yescharacteristic
38#22627558C2211yescharacteristic
39#22627557C2211yescharacteristic
40#22627557C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627547C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627536C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627535C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55#107×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic
59#17989802—44no—
60C2×Dic586—21no—
61C2×Dic586—21no—
62C2×Dic586C2311yescharacteristic
63Q8×D293—22no—
64Q8×D293—22no—
65C2×D1172—21no—
66C2×D1172C2311yescharacteristic
67C2×C22⋊D293—21no—
68C2×C22⋊D293—21no—
69C2×C22⋊D293—21no—
70C2×C4×D293—21no—
71C2×C4×D293—21no—
72C2×C4×D293—21no—
73C2×C4×D293D411yescharacteristic
74C2×C4×D293D411yescharacteristic
75C2×C4×D293C2311yescharacteristic
76#17989791—22no—
77#17989790—22no—
78#17989789—22no—
79C2×#14556873C2311yescharacteristic
80C2×#14556873C2311yescharacteristic
81C4⋊Dic293—21no—
82C4⋊Dic293C2311yescharacteristic
83C4⋊Dic293C2311yescharacteristic
84#17989781—21no—
85#17989781—21no—
86#17989781—21no—
87#17989781—21no—
88C22⋊Dic293—21no—
89#17989779—21no—
90#17989779—21no—
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293—21no—
94C4×Dic293D411yescharacteristic
95C4×Dic293D411yescharacteristic
96C4×Dic293C2311yescharacteristic
97C2×Q8×C293C2311yescharacteristic
98C2×D4×C293C2311yescharacteristic
99C22×C4×C293—21no—
100SD16×C293—22no—
101C2×C8×C293C2311yescharacteristic
102C2×C8×C293C2311yescharacteristic
103C4⋊C4×C293—21no—
104C4⋊C4×C293C2311yescharacteristic
105C4⋊C4×C293C2311yescharacteristic
106C22⋊C4×C293—21no—
107C42×C293—21no—
108C42×C293C2311yescharacteristic
109C22×D293—21no—
110C22×D293C2×D411yescharacteristic
111Dic586—24no—
112Dic586—21no—
113Dic586—42no—
114Dic586#4112yescomplemented
115D1172—21no—
116D1172—21no—
117D1172—42no—
118C22⋊D293—42no—
119C22⋊D293—42no—
120C22⋊D293—42no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293C2×D411yescharacteristic
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C4×D293—24no—
128C4×D293—22no—
129C4×D293—21no—
130C4×D293—21no—
131C4×D293—22no—
132C4×D293—42no—
133C4×D293—42no—
134#14556873—21no—
135#14556873—21no—
136C23×C293—21no—
137Q8×C293—21no—
138Q8×C293#4112yescomplemented
139D4×C293—21no—
140D4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—42no—
145C2×C4×C293C2×D411yescharacteristic
146C2×C4×C293C2×D411yescharacteristic
147C2×C4×C293C2411yescharacteristic
148C8×C293—21no—
149C8×C293—21no—
150C22×C293—41no—
151C22×C293—41no—
152C22×C293—41no—
153C22×C293C22×D411yescharacteristic
154C2×D293—21no—
155C2×D293—21no—
156C2×D293—41no—
157C2×D293—41no—
158C2×D293—41no—
159C2×D293AGL(1,ℤ/8)12yes—
160C4×C293—22no—
161C4×C293—21no—
162C4×C293—21no—
163C4×C293—41no—
164C4×C293—41no—
165C4×C293C2×#4111yescharacteristic
166C4×C293C2×#4111yescharacteristic
167Dic293—22no—
168Dic293—21no—
169Dic293—21no—
170Dic293—41no—
171Dic293—41no—
172Dic293#13712yes—
173C2×C293—81no—
174C2×C293#52511yescharacteristic
175C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C293C2×#13711yescharacteristic
177D293—22no—
178D293—81no—
179C293#311211yescharacteristic, complemented, Sylow
180#3112—2931nomaximal, Sylow
181#532—2931no—
182C2×C4×Q8—2931no—
183#480—2931no—
184#480—2931no—
185#477—2931no—
186#477—2931no—
187#460—2931no—
188#460—2931no—
189#448—2931no—
190#448—2931no—
191#440—2931no—
192#440—2931no—
193#440—2931no—
194#440D29311yescharacteristic, complemented
195#432—2931no—
196C2×#41—5861no—
197C22×Q8—2931no—
198C2×SD16—2931no—
199C2×SD16—2931no—
200C2×SD16—2931no—
201C2×SD16C2×D29311yescharacteristic
202C4⋊Q8—2931no—
203#127—2931no—
204#124—5861no—
205#121—2931no—
206#121—2931no—
207#121—5861no—
208C4×Q8—2931no—
209C4×Q8—2931no—
210C4×Q8—2931no—
211C4×Q8—5861no—
212C4×Q8—5861no—
213C4×Q8C2×D29311yescharacteristic
214C4×D4—2931no—
215C4×D4—5861no—
216C4×D4C2×D29311yescharacteristic
217C2×C4⋊C4—2931no—
218C2×C4⋊C4—5861no—
219C2×C42—2931no—
220C2×C42—5861no—
221#107—2931no—
222#107—2931no—
223#107—2931no—
224#107C2×D29311yescharacteristic
225C4⋊C8—2931no—
226C4⋊C8—2931no—
227#103—2931no—
228#103—2931no—
229#103—2931no—
230#103C2×D29311yescharacteristic
231#102—2931no—
232#102—2931no—
233#102—2931no—
234#102C2×D29311yescharacteristic
235C22⋊C8—2931no—
236C22⋊C8—2931no—
237#97—2931no—
238#97C2×D29311yescharacteristic
239#41—11724no—
240C2×Q8—2931no—
241C2×Q8—5861no—
242C2×Q8—5861no—
243C2×Q8—5862no—
244C2×Q8—5862no—
245C2×Q8C22×D29311yescharacteristic
246C2×D4—2931no—
247C2×D4—5861no—
248C2×D4—5861no—
249C2×D4—5861no—
250C2×D4—5861no—
251C2×D4C22×D29311yescharacteristic
252C22×C4—21no—
253C22×C4—2931no—
254C22×C4—2931no—
255C22×C4—2931no—
256C22×C4—5861no—
257C22×C4—5861no—
258C22×C4—5861no—
259SD16—22no—
260SD16—5862no—
261SD16—5862no—
262SD16—5862no—
263C2×C8—2931no—
264C2×C8—2931no—
265C2×C8C22×D29311yescharacteristic
266C2×C8C22×D29311yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—2931no—
269C4⋊C4—2931no—
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—
280C22⋊C4—5861no—
281C42—21no—
282C42—2931no—
283C42—2931no—
284C42—2931no—
285C42—5861no—
286C42—5861no—
287C42—5861no—
288C42C22×D29311yescharacteristic
289C23—21no—
290C23—2931no—
291C23—5861no—
292Q8—21no—
293Q8—2932no—
294Q8—5864no—
295Q8—5861no—
296Q8—11722no—
297Q8#1798980212yescomplemented
298D4—21no—
299D4—21no—
300D4—5861no—
301D4—5861no—
302D4—11722no—
303D4—11722no—
304D4—11722no—
305D4—11722no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—2931no—
311C2×C4—2931no—
312C2×C4—2931no—
313C2×C4—5862no—
314C2×C4—5862no—
315C2×C4—5864no—
316C2×C4—5861no—
317C2×C4—5861no—
318C2×C4—5861no—
319C2×C4—5861no—
320C2×C4—5861no—
321C2×C4—11722no—
322C2×C4—11722no—
323C2×C4D4×D29311yescharacteristic
324C2×C4D4×D29311yescharacteristic
325C2×C4C23×D29311yescharacteristic
326C8—21no—
327C8—21no—
328C8—5861no—
329C8—5861no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—2932no—
334C22—5861no—
335C22—5861no—
336C22—11721no—
337C22—11721no—
338C22—11721no—
339C22C2×D4×D29311yescharacteristic
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—2932no—
346C4—5861no—
347C4—5862no—
348C4—5861no—
349C4—11721no—
350C4—11721no—
351C4#41×D29311yescharacteristic
352C4C2×#1798980211yescharacteristic
353C2—81no—
354C2—23441no—
355C2—5862no—
356C2#3403663811yescharacteristic
357C2AGL(1,ℤ/8)×D29311yescharacteristic
358C2#137×D29311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#440×C293C2
socleC22×C293C22×D4
prime radical#34036676C2
hypercenter#440D293
hypocenterC293#3112
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D293C2semidirect
3. #34036444C2semidirect
4. #34036441C2semidirect
5. #34036423C2semidirect
6. #34036422C2semidirect
7. #34036328C2semidirect
8. #34036327C2semidirect
9. #34036269C2semidirect
10. #34036266C2semidirect
11. #34036231C2semidirect
12. #34036229C2semidirect
13. #34036227C2semidirect
14. #34036184C2semidirect
15. #440×C293C2semidirect
114. Dic586#41semidirect
138. Q8×C293#41semidirect
179. C293#3112semidirect
194. #440D293semidirect
297. Q8#17989802semidirect

Maximal subgroups

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

subgroupindex
#340366762
C4×Q8×D2932
#340364442
#340364412
#340364232
#340364222
#340363282
#340363272
#340362692
#340362662
#340362312
#340362292
#340362272
#340361842
#440×C2932
#3112293