Finite Group Databasebeta

← #49169376

Subgroups — #49169376

Order 37504.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036676C211yesmaximal, characteristic, complemented
2#34036666C211yesmaximal, characteristic, complemented
3#34036536C211yesmaximal, characteristic, complemented
4#34036515C211yesmaximal, characteristic, complemented
5#34036492C211yesmaximal, characteristic, complemented
6#34036490C211yesmaximal, characteristic, complemented
7#34036383C211yesmaximal, characteristic, complemented
8#34036381C211yesmaximal, characteristic, complemented
9#34036378C211yesmaximal, characteristic, complemented
10#34036372C211yesmaximal, characteristic, complemented
11C4×#17989789C211yesmaximal, characteristic, complemented
12C4×D2344C211yesmaximal, characteristic, complemented
13C4×#17989787C211yesmaximal, characteristic, complemented
14C4×#17989785C211yesmaximal, characteristic, complemented
15C4×SD16×C293C211yesmaximal, characteristic, complemented
16C2×#17989802—21no—
17C2×#17989789C2211yescharacteristic
18C2×D2344C2211yescharacteristic
19C2×#17989787C2211yescharacteristic
20C2×#17989785C2211yescharacteristic
21C2×#17989785C2211yescharacteristic
22#22627623C2211yescharacteristic
23#22627620C2211yescharacteristic
24#22627619—21no—
25#22627615C2211yescharacteristic
26#22627613C2211yescharacteristic
27#22627610—21no—
28#22627609—21no—
29#22627600C2211yescharacteristic
30#22627599C2211yescharacteristic
31#22627599C2211yescharacteristic
32#22627597—21no—
33#22627595C2211yescharacteristic
34C4×D1172—21no—
35C4×D1172C2211yescharacteristic
36C4×D1172C2211yescharacteristic
37C4×C22⋊D293—21no—
38#22627581—21no—
39C42×D293C2211yescharacteristic
40#22627558C2211yescharacteristic
41#22627557C2211yescharacteristic
42#22627555C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627546C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627534C2211yescharacteristic
50#22627534C2211yescharacteristic
51C4×#14556873C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59#17989802—44no—
60C2×Dic586—21no—
61C2×D1172—21no—
62C2×D1172—21no—
63C2×D1172C2311yescharacteristic
64C2×D1172C2311yescharacteristic
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C2×C22⋊D293—21no—
68C2×C4×D293—21no—
69C2×C4×D293—21no—
70C2×C4×D293D411yescharacteristic
71C2×C4×D293D411yescharacteristic
72C2×C4×D293C2311yescharacteristic
73#17989789—22no—
74D2344—22no—
75#17989787—22no—
76#17989785—22no—
77#17989785—22no—
78C2×#14556873C2311yescharacteristic
79C2×#14556873C2311yescharacteristic
80C4⋊Dic293—21no—
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86C22⋊Dic293—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—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×D293—21no—
111C22×D293C2×D411yescharacteristic
112Dic586—42no—
113D1172—21no—
114D1172—21no—
115D1172—21no—
116D1172—21no—
117D1172—42no—
118D1172—42no—
119C22⋊D293—42no—
120C22⋊D293—42no—
121C22⋊D293—42no—
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293C2×D411yescharacteristic
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C4×D293—22no—
128C4×D293—21no—
129C4×D293—21no—
130C4×D293—41no—
131C4×D293—42no—
132C4×D293—42no—
133#14556873—21no—
134#14556873#4112yescomplemented
135C23×C293—21no—
136Q8×C293—21no—
137Q8×C293—21no—
138D4×C293—21no—
139D4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—42no—
144C2×C4×C293C2×D411yescharacteristic
145C2×C4×C293C2×D411yescharacteristic
146C2×C4×C293C2411yescharacteristic
147C8×C293—21no—
148C8×C293#4112yescomplemented
149C22×C293—41no—
150C22×C293—41no—
151C22×C293—41no—
152C22×C293C22×D411yescharacteristic
153C2×D293—21no—
154C2×D293—21no—
155C2×D293—21no—
156C2×D293—41no—
157C2×D293—41no—
158C2×D293—41no—
159C2×D293—41no—
160C2×D293—41no—
161C2×D293—41no—
162C4×C293—21no—
163C4×C293—41no—
164C4×C293—41no—
165C4×C293—41no—
166C4×C293AGL(1,ℤ/8)12yes—
167C4×C293C2×#4111yescharacteristic
168C4×C293C2×#4111yescharacteristic
169Dic293—21no—
170Dic293—21no—
171Dic293—21no—
172Dic293—41no—
173Dic293—41no—
174C2×C293—81no—
175C2×C293#53211yescharacteristic
176C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C293#57511yescharacteristic
178D293—41no—
179D293—81no—
180D293—81no—
181C293#317111yescharacteristic, complemented, Sylow
182#3171—2931nomaximal, Sylow
183#532—2931no—
184#529—2931no—
185#501—2931no—
186#496—2931no—
187#490—2931no—
188#489—2931no—
189#469—2931no—
190#469—2931no—
191#468—2931no—
192#468—2931no—
193C4×SD16—2931no—
194C4×SD16D29311yescharacteristic, complemented
195C4×D8—2931no—
196C4×D8—2931no—
197C4×M16—2931no—
198C2×#41—5861no—
199C2×SD16—2931no—
200C2×SD16C2×D29311yescharacteristic
201C2×D8—2931no—
202C2×D8—2931no—
203C2×M16—2931no—
204C2×M16—2931no—
205C4⋊Q8—2931no—
206#127—2931no—
207#126—5861no—
208#125—2931no—
209#124—2931no—
210#124—5861no—
211#123—5861no—
212C22⋊Q8—2931no—
213#121—2931no—
214#121—2931no—
215#121—2931no—
216#121—5861no—
217C4×Q8C2×D29311yescharacteristic
218C4×D4—2931no—
219C4×D4—2931no—
220C4×D4—5861no—
221C4×D4—5861no—
222C4×D4C2×D29311yescharacteristic
223#117—5861no—
224C2×C42—2931no—
225#107—2931no—
226#107—2931no—
227#106—2931no—
228#106C2×D29311yescharacteristic
229#103—2931no—
230#103C2×D29311yescharacteristic
231#102—2931no—
232#102—2931no—
233#102—2931no—
234#102—2931no—
235#102—2931no—
236#102C2×D29311yescharacteristic
237#97—2931no—
238#97—2931no—
239C4×C8—2931no—
240C4×C8C2×D29311yescharacteristic
241#41—11724no—
242C2×Q8—5861no—
243C2×Q8C22×D29311yescharacteristic
244C2×D4—2931no—
245C2×D4—2931no—
246C2×D4—5861no—
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—
258SD16—22no—
259SD16—5862no—
260D8—5862no—
261D8—5862no—
262M16—5862no—
263M16—5862no—
264C2×C8—2931no—
265C2×C8—2931no—
266C2×C8C22×D29311yescharacteristic
267C2×C8C22×D29311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—2931no—
270C4⋊C4—2931no—
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—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C22⋊C4—5861no—
286C42—21no—
287C42—2931no—
288C42—2931no—
289C42—2931no—
290C42C22×D29311yescharacteristic
291C23—21no—
292C23—2931no—
293C23—5861no—
294C23—5861no—
295Q8—21no—
296Q8—21no—
297Q8—11722no—
298D4—21no—
299D4—21no—
300D4—5861no—
301D4—5861no—
302D4—5861no—
303D4—5861no—
304D4—11722no—
305D4—11722no—
306D4—11722no—
307D4—11722no—
308D4—11722no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—2931no—
314C2×C4—2931no—
315C2×C4—2931no—
316C2×C4—5862no—
317C2×C4—5861no—
318C2×C4—5861no—
319C2×C4—5861no—
320C2×C4—5861no—
321C2×C4—11721no—
322C2×C4—11722no—
323C2×C4—11722no—
324C2×C4D4×D29311yescharacteristic
325C2×C4D4×D29311yescharacteristic
326C2×C4C23×D29311yescharacteristic
327C8—21no—
328C8—2932no—
329C8—5861no—
330C8#1798980212yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—5861no—
335C22—5861no—
336C22—5861no—
337C22—11721no—
338C22—11721no—
339C22—11721no—
340C22—11721no—
341C22—11721no—
342C22—11721no—
343C22C2×D4×D29311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—5861no—
349C4—5861no—
350C4—5861no—
351C4—11721no—
352C4—11721no—
353C4#2262765112yes—
354C4#41×D29311yescharacteristic
355C4C2×#1798980211yescharacteristic
356C2—81no—
357C2—23441no—
358C2—23441no—
359C2—11721no—
360C2#3403667611yescharacteristic
361C2C2×#2262765111yescharacteristic
362C2#3403692611yescharacteristic
subgroupG/H
centerC2×C4D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC4×SD16×C293C2
socleC22×C293C22×D4
hypercenterC4×SD16D293
hypocenterC293#3171
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #34036676C2semidirect
2. #34036666C2semidirect
3. #34036536C2semidirect
4. #34036515C2semidirect
5. #34036492C2semidirect
6. #34036490C2semidirect
7. #34036383C2semidirect
8. #34036381C2semidirect
9. #34036378C2semidirect
10. #34036372C2semidirect
11. C4×#17989789C2semidirect
12. C4×D2344C2semidirect
13. C4×#17989787C2semidirect
14. C4×#17989785C2semidirect
15. C4×SD16×C293C2semidirect
134. #14556873#41semidirect
148. C8×C293#41semidirect
181. C293#3171semidirect
194. C4×SD16D293semidirect
330. C8#17989802semidirect

Maximal subgroups

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

subgroupindex
#340366762
#340366662
#340365362
#340365152
#340364922
#340364902
#340363832
#340363812
#340363782
#340363722
C4×#179897892
C4×D23442
C4×#179897872
C4×#179897852
C4×SD16×C2932
#3171293