Finite Group Databasebeta

← #49168985

Subgroups — #49168985

Order 37504.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036732C211yesmaximal, characteristic, complemented
2#34036612C211yesmaximal, characteristic, complemented
3#34036448C211yesmaximal, characteristic, complemented
4#34036440C211yesmaximal, characteristic, complemented
5#34036434C211yesmaximal, characteristic, complemented
6#34036431C211yesmaximal, characteristic, complemented
7#34036327C211yesmaximal, characteristic, complemented
8#34036322C211yesmaximal, characteristic, complemented
9#34036274C211yesmaximal, characteristic, complemented
10#34036241C211yesmaximal, characteristic, complemented
11#34036232C211yesmaximal, characteristic, complemented
12SD16×Dic293C211yesmaximal, characteristic, complemented
13#34036209C211yesmaximal, characteristic, complemented
14#34036187C211yesmaximal, characteristic, complemented
15#449×C293C211yesmaximal, characteristic, complemented
16C2×#17989789C2211yescharacteristic
17C2×#17989787C2211yescharacteristic
18#22627620C2211yescharacteristic
19#22627615C2211yescharacteristic
20#22627608—21no—
21#22627606—21no—
22#22627598C2211yescharacteristic
23#22627596—21no—
24#22627595—21no—
25Q8×Dic293C2211yescharacteristic
26Q8×Dic293C2211yescharacteristic
27D4×Dic293—21no—
28D4×Dic293—21no—
29D4×Dic293C2211yescharacteristic
30D4×Dic293C2211yescharacteristic
31D4×Dic293C2211yescharacteristic
32#22627586C2211yescharacteristic
33#22627583—21no—
34#22627583C2211yescharacteristic
35C2×C4⋊Dic293—21no—
36C2×C4⋊Dic293C2211yescharacteristic
37#22627557C2211yescharacteristic
38#22627557C2211yescharacteristic
39#22627556C2211yescharacteristic
40#22627556C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627546C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×#41×C293C2211yescharacteristic
53C2×SD16×C293C2211yescharacteristic
54C2×D8×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59C2×D1172C2311yescharacteristic
60C2×C22⋊D293—21no—
61C2×C22⋊D293—21no—
62C2×C22⋊D293—21no—
63C22×Dic293—21no—
64C22×Dic293—21no—
65C22×Dic293—21no—
66C22×Dic293—21no—
67C2×C4×D293—21no—
68#17989789—22no—
69#17989787—22no—
70C2×#14556873C2311yescharacteristic
71C2×#14556873C2311yescharacteristic
72C4⋊Dic293—21no—
73C4⋊Dic293—21no—
74C4⋊Dic293—21no—
75C4⋊Dic293—21no—
76C4⋊Dic293D411yescharacteristic
77C4⋊Dic293D411yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79C4⋊Dic293C2311yescharacteristic
80C4⋊Dic293C2311yescharacteristic
81#17989781—21no—
82C22⋊Dic293—21no—
83C22⋊Dic293—21no—
84C22⋊Dic293—21no—
85C22⋊Dic293D411yescharacteristic
86C22⋊Dic293D411yescharacteristic
87#17989779—21no—
88#17989779—21no—
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293C2311yescharacteristic
92C4×Dic293C2311yescharacteristic
93#41×C293—22no—
94#41×C293—22no—
95C2×Q8×C293C2311yescharacteristic
96C2×D4×C293—21no—
97C2×D4×C293—21no—
98C2×D4×C293C2311yescharacteristic
99C2×D4×C293C2311yescharacteristic
100C22×C4×C293—21no—
101C22×C4×C293C2311yescharacteristic
102SD16×C293—22no—
103D8×C293—22no—
104C2×C8×C293C2311yescharacteristic
105C2×C8×C293C2311yescharacteristic
106C4⋊C4×C293C2311yescharacteristic
107C22⋊C4×C293—21no—
108C22×D293—21no—
109D1172—21no—
110D1172—21no—
111C22⋊D293—81no—
112C22⋊D293—81no—
113C22⋊D293—81no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—81no—
118C2×Dic293—81no—
119C2×Dic293—81no—
120C2×Dic293—81no—
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C2×Dic293C2×D411yescharacteristic
125C4×D293—81no—
126#14556873—21no—
127#14556873—21no—
128C23×C293—21no—
129C23×C293—21no—
130C23×C293C2×D411yescharacteristic
131Q8×C293—21no—
132Q8×C293#4112yes—
133D4×C293—24no—
134D4×C293—21no—
135D4×C293—21no—
136D4×C293—21no—
137D4×C293—81no—
138D4×C293#4112yes—
139C2×C4×C293—24no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293C2×D411yescharacteristic
145C2×C4×C293C2411yescharacteristic
146C8×C293—21no—
147C8×C293—21no—
148C22×C293—21no—
149C22×C293—22no—
150C22×C293—21no—
151C22×C293—21no—
152C22×C293—41no—
153C22×C293—41no—
154C22×C293—41no—
155C22×C293—41no—
156C22×C293—41no—
157C22×C293C22×D411yescharacteristic
158C2×D293—41no—
159C2×D293—41no—
160C2×D293—41no—
161C4×C293—21no—
162C4×C293—22no—
163C4×C293—41no—
164C4×C293C2×#4111yescharacteristic
165C4×C293C2×#4111yescharacteristic
166Dic293—21no—
167Dic293—21no—
168Dic293—21no—
169Dic293—21no—
170Dic293—41no—
171Dic293—41no—
172Dic293—41no—
173C2×C293—41no—
174C2×C293—42no—
175C2×C293—81no—
176C2×C293#52511yescharacteristic
177C2×C293#57611yescharacteristic
178C2×C293#57711yescharacteristic
179D293—81no—
180C293#311911yescharacteristic, complemented, Sylow
181#3119—2931nomaximal, Sylow
182#540—2931no—
183#520—2931no—
184#481—2931no—
185#480—2931no—
186#479—2931no—
187#478—2931no—
188#460—2931no—
189#459—2931no—
190#449—2931no—
191#449D29311yescharacteristic, complemented
192#442—2931no—
193#440—2931no—
194C4×SD16—2931no—
195C4×D8—2931no—
196#433—2931no—
197C2×#41C2×D29311yescharacteristic
198C2×SD16—2931no—
199C2×SD16C2×D29311yescharacteristic
200C2×D8—2931no—
201C2×D8C2×D29311yescharacteristic
202#127—2931no—
203#125—2931no—
204#123—5861no—
205#123—5861no—
206#121—2931no—
207#121—5861no—
208#121—5861no—
209#121C2×D29311yescharacteristic
210C4×Q8—2931no—
211C4×Q8—2931no—
212C4×D4—2931no—
213C4×D4—2931no—
214C4×D4—2931no—
215C4×D4—2931no—
216C4×D4—5861no—
217C4×D4—5861no—
218#117—2931no—
219#117—5861no—
220C2×C4⋊C4—2931no—
221C2×C4⋊C4—5861no—
222#107—2931no—
223#107—2931no—
224#106—2931no—
225#106—2931no—
226C4⋊C8—2931no—
227C4⋊C8—2931no—
228#103—2931no—
229#103C2×D29311yescharacteristic
230#102—2931no—
231#102—2931no—
232#102—2931no—
233#102—2931no—
234#102—2931no—
235#102C2×D29311yescharacteristic
236C22⋊C8—2931no—
237C22⋊C8C2×D29311yescharacteristic
238#97—2931no—
239C4×C8—2931no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D29311yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—2931no—
246C2×D4—5861no—
247C2×D4—5861no—
248C2×D4—5861no—
249C2×D4C22×D29311yescharacteristic
250C2×D4C22×D29311yescharacteristic
251C22×C4—21no—
252C22×C4—5861no—
253C22×C4—5861no—
254C22×C4—5861no—
255C22×C4—5861no—
256C22×C4—5861no—
257C22×C4C22×D29311yescharacteristic
258SD16—22no—
259SD16—5862no—
260D8—22no—
261D8—5862no—
262C2×C8—2931no—
263C2×C8—2931no—
264C2×C8C22×D29311yescharacteristic
265C2×C8C22×D29311yescharacteristic
266C4⋊C4—2931no—
267C4⋊C4—2931no—
268C4⋊C4—2931no—
269C4⋊C4—2931no—
270C4⋊C4—2931no—
271C4⋊C4—5861no—
272C4⋊C4—5861no—
273C4⋊C4—5861no—
274C4⋊C4—5861no—
275C4⋊C4—5861no—
276C4⋊C4C22×D29311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2931no—
279C22⋊C4—2931no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C42—2931no—
286C42—2931no—
287C42—5861no—
288C42—5861no—
289C23—21no—
290C23—21no—
291C23—5861no—
292C23D4×D29311yescharacteristic
293Q8—21no—
294Q8#1798980112yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—23441no—
301D4—23441no—
302D4—23441no—
303D4—5861no—
304D4—5861no—
305D4#1798980112yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—2931no—
312C2×C4—2931no—
313C2×C4—2931no—
314C2×C4—2931no—
315C2×C4—23441no—
316C2×C4—23441no—
317C2×C4—23441no—
318C2×C4—23441no—
319C2×C4—23441no—
320C2×C4—5861no—
321C2×C4—5861no—
322C2×C4—5861no—
323C2×C4D4×D29311yescharacteristic
324C2×C4C23×D29311yescharacteristic
325C8—21no—
326C8—21no—
327C8—5861no—
328C8—5861no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—11721no—
339C22—11721no—
340C22—11721no—
341C22C2×D4×D29311yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—5861no—
346C4—5861no—
347C4—5861no—
348C4—5861no—
349C4—11721no—
350C4—11721no—
351C4—11721no—
352C4C2×#1798980111yescharacteristic
353C4C2×#1798980111yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—23441no—
358C2#3403663511yescharacteristic
359C2#3403693311yescharacteristic
360C2#3403693611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#449×C293C2
socleC22×C293C22×D4
hypercenter#449D293
hypocenterC293#3119
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #34036732C2semidirect
2. #34036612C2semidirect
3. #34036448C2semidirect
4. #34036440C2semidirect
5. #34036434C2semidirect
6. #34036431C2semidirect
7. #34036327C2semidirect
8. #34036322C2semidirect
9. #34036274C2semidirect
10. #34036241C2semidirect
11. #34036232C2semidirect
12. SD16×Dic293C2semidirect
13. #34036209C2semidirect
14. #34036187C2semidirect
15. #449×C293C2semidirect
180. C293#3119semidirect
191. #449D293semidirect

Maximal subgroups

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

subgroupindex
#340367322
#340366122
#340364482
#340364402
#340364342
#340364312
#340363272
#340363222
#340362742
#340362412
#340362322
SD16×Dic2932
#340362092
#340361872
#449×C2932
#3119293