Finite Group Databasebeta

← #31790990

Subgroups — #31790990

Order 17536.

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#22578008C211yesmaximal, characteristic, complemented
2#22577883C211yesmaximal, characteristic, complemented
3#22577722C211yesmaximal, characteristic, complemented
4#22577717C211yesmaximal, characteristic, complemented
5#22577711C211yesmaximal, characteristic, complemented
6#22577704C211yesmaximal, characteristic, complemented
7#22577604C211yesmaximal, characteristic, complemented
8#22577599C211yesmaximal, characteristic, complemented
9#22577550C211yesmaximal, characteristic, complemented
10#22577550C211yesmaximal, characteristic, complemented
11#22577516C211yesmaximal, characteristic, complemented
12#22577505C211yesmaximal, characteristic, complemented
13C4×#14555499C211yesmaximal, characteristic, complemented
14C4×D1096C211yesmaximal, characteristic, complemented
15#433×C137C211yesmaximal, characteristic, complemented
16C2×#14555510C2211yescharacteristic
17C2×#14555499C2211yescharacteristic
18C2×#14555499C2211yescharacteristic
19C2×D1096C2211yescharacteristic
20C2×D1096C2211yescharacteristic
21#17984085C2211yescharacteristic
22#17984080C2211yescharacteristic
23#17984073—21no—
24#17984073—21no—
25#17984062C2211yescharacteristic
26#17984062C2211yescharacteristic
27#17984061—21no—
28#17984061—21no—
29C4×Dic274C2211yescharacteristic
30C4×Dic274C2211yescharacteristic
31C4×D548C2211yescharacteristic
32C4×D548C2211yescharacteristic
33C4×D548C2211yescharacteristic
34C4×D548C2211yescharacteristic
35#17984048—21no—
36#17984048—21no—
37#17984046—21no—
38C2×C4⋊Dic137C2211yescharacteristic
39C4⋊C4×D137—21no—
40#17984022C2211yescharacteristic
41#17984022C2211yescharacteristic
42#17984020C2211yescharacteristic
43#17984020C2211yescharacteristic
44#17984013C2211yescharacteristic
45#17984013C2211yescharacteristic
46#17984010C2211yescharacteristic
47#17984010C2211yescharacteristic
48#17984010C2211yescharacteristic
49#17984010C2211yescharacteristic
50#17984010C2211yescharacteristic
51#17984010C2211yescharacteristic
52#117×C137C2211yescharacteristic
53C4⋊C8×C137C2211yescharacteristic
54C4⋊C8×C137C2211yescharacteristic
55C22⋊C8×C137C2211yescharacteristic
56C22⋊C8×C137C2211yescharacteristic
57#97×C137C2211yescharacteristic
58C4×C8×C137C2211yescharacteristic
59#14555510—22no—
60#14555510—22no—
61C2×Dic274C2311yescharacteristic
62C2×D548—21no—
63C2×D548—21no—
64C2×D548C2311yescharacteristic
65C2×D548C2311yescharacteristic
66C2×D548C2311yescharacteristic
67C2×C22⋊D137—21no—
68C2×C22⋊D137—21no—
69C2×C22⋊D137—21no—
70C22×Dic137—21no—
71C2×C4×D137—21no—
72C2×C4×D137—21no—
73C2×C4×D137—21no—
74C2×C4×D137—21no—
75C2×C4×D137—21no—
76#14555499—22no—
77#14555499—22no—
78D1096—22no—
79D1096—22no—
80C4⋊Dic137—21no—
81C4⋊Dic137C2311yescharacteristic
82C4⋊Dic137C2311yescharacteristic
83C4⋊Dic137C2311yescharacteristic
84C4⋊Dic137C2311yescharacteristic
85#14555489—21no—
86#14555489—21no—
87#14555489—21no—
88#14555489—21no—
89#14555487—21no—
90#14555487—21no—
91#14555487—21no—
92#14555487—21no—
93#14555487—21no—
94#14555487—21no—
95C4×Dic137—21no—
96C4×Dic137—21no—
97C22×C4×C137C2311yescharacteristic
98C2×C8×C137C2311yescharacteristic
99C2×C8×C137C2311yescharacteristic
100C2×C8×C137C2311yescharacteristic
101C2×C8×C137C2311yescharacteristic
102C4⋊C4×C137D411yescharacteristic
103C4⋊C4×C137D411yescharacteristic
104C22⋊C4×C137D411yescharacteristic
105C22⋊C4×C137D411yescharacteristic
106C42×C137C2311yescharacteristic
107C42×C137C2311yescharacteristic
108C22×D137—21no—
109C22×D137—21no—
110C22×D137—21no—
111Dic274—21no—
112Dic274#4112yes—
113D548—21no—
114D548—21no—
115D548—21no—
116D548—21no—
117D548—21no—
118D548—81no—
119D548—81no—
120D548#4112yes—
121C22⋊D137—24no—
122C22⋊D137—81no—
123C22⋊D137—81no—
124C2×Dic137—21no—
125C2×Dic137—21no—
126C2×Dic137—21no—
127C2×Dic137—21no—
128C2×Dic137—21no—
129C2×Dic137—81no—
130C4×D137—24no—
131C4×D137—81no—
132C4×D137—81no—
133C4×D137—81no—
134C4×D137—81no—
135C23×C137C2×D411yescharacteristic
136C2×C4×C137—21no—
137C2×C4×C137—21no—
138C2×C4×C137C2×D411yescharacteristic
139C2×C4×C137C2×D411yescharacteristic
140C2×C4×C137C2×D411yescharacteristic
141C2×C4×C137C2×D411yescharacteristic
142C2×C4×C137C2×D411yescharacteristic
143C2×C4×C137C2411yescharacteristic
144C8×C137—21no—
145C8×C137—21no—
146C8×C137—21no—
147C8×C137—21no—
148C22×C137—21no—
149C22×C137—21no—
150C22×C137—21no—
151C22×C137C22×D411yescharacteristic
152C2×D137—22no—
153C2×D137—41no—
154C2×D137—41no—
155C2×D137—41no—
156C2×D137—41no—
157C2×D137—41no—
158C2×D137—41no—
159C2×D137—41no—
160C2×D137—41no—
161C4×C137—21no—
162C4×C137—21no—
163C4×C137—21no—
164C4×C137—21no—
165C4×C137—21no—
166C4×C137C2×#4111yescharacteristic
167C4×C137C2×#4111yescharacteristic
168Dic137—22no—
169Dic137—41no—
170Dic137—41no—
171Dic137—41no—
172Dic137—41no—
173C2×C137—41no—
174C2×C137#52511yescharacteristic
175C2×C137#57611yescharacteristic
176C2×C137#57711yescharacteristic
177D137—42no—
178D137—81no—
179D137—81no—
180C137#311911yescharacteristic, complemented, Sylow
181#3119—1371nomaximal, Sylow
182#540—1371no—
183#520—1371no—
184#481—1371no—
185#480—1371no—
186#479—1371no—
187#478—1371no—
188#460—1371no—
189#459—1371no—
190#449—1371no—
191#449—1371no—
192#442—1371no—
193#440—1371no—
194C4×SD16—1371no—
195C4×D8—1371no—
196#433D13711yescharacteristic, complemented
197C2×#41—1371no—
198C2×SD16—1371no—
199C2×SD16—1371no—
200C2×D8—1371no—
201C2×D8—1371no—
202#127—1371no—
203#125—1371no—
204#123—2741no—
205#123—2741no—
206#121—2741no—
207#121—2741no—
208#121—1371no—
209#121—1371no—
210C4×Q8—1371no—
211C4×Q8—1371no—
212C4×D4—2741no—
213C4×D4—2741no—
214C4×D4—1371no—
215C4×D4—1371no—
216C4×D4—1371no—
217C4×D4—1371no—
218#117—2741no—
219#117C2×D13711yescharacteristic
220C2×C4⋊C4—2741no—
221C2×C4⋊C4—1371no—
222#107—1371no—
223#107—1371no—
224#106—1371no—
225#106—1371no—
226C4⋊C8C2×D13711yescharacteristic
227C4⋊C8C2×D13711yescharacteristic
228#103—1371no—
229#103—1371no—
230#102—1371no—
231#102—1371no—
232#102—1371no—
233#102—1371no—
234#102—1371no—
235#102—1371no—
236C22⋊C8C2×D13711yescharacteristic
237C22⋊C8C2×D13711yescharacteristic
238#97C2×D13711yescharacteristic
239C4×C8C2×D13711yescharacteristic
240#41—2742no—
241#41—2742no—
242C2×Q8—1371no—
243C2×D4—2741no—
244C2×D4—2741no—
245C2×D4—2741no—
246C2×D4—2741no—
247C2×D4—2741no—
248C2×D4—1371no—
249C2×D4—1371no—
250C2×D4—1371no—
251C22×C4—2741no—
252C22×C4—2741no—
253C22×C4—2741no—
254C22×C4—2741no—
255C22×C4—2741no—
256C22×C4—2741no—
257C22×C4C22×D13711yescharacteristic
258SD16—2742no—
259SD16—2742no—
260D8—2742no—
261D8—2742no—
262C2×C8C22×D13711yescharacteristic
263C2×C8C22×D13711yescharacteristic
264C2×C8C22×D13711yescharacteristic
265C2×C8C22×D13711yescharacteristic
266C4⋊C4—2741no—
267C4⋊C4—2741no—
268C4⋊C4—2741no—
269C4⋊C4—2741no—
270C4⋊C4—2741no—
271C4⋊C4—1371no—
272C4⋊C4—1371no—
273C4⋊C4—1371no—
274C4⋊C4—1371no—
275C4⋊C4D54811yescharacteristic
276C4⋊C4D54811yescharacteristic
277C22⋊C4—2741no—
278C22⋊C4—2741no—
279C22⋊C4—2741no—
280C22⋊C4—2741no—
281C22⋊C4—2741no—
282C22⋊C4—2741no—
283C22⋊C4D54811yescharacteristic
284C22⋊C4D54811yescharacteristic
285C42—2741no—
286C42—2741no—
287C42C22×D13711yescharacteristic
288C42C22×D13711yescharacteristic
289C23—2741no—
290C23—2741no—
291C23—2741no—
292C23C2×D54811yescharacteristic
293Q8—2741no—
294Q8—1372no—
295D4—2744no—
296D4—2741no—
297D4—2741no—
298D4—2741no—
299D4—2741no—
300D4—2741no—
301D4—10961no—
302D4—10961no—
303D4—10961no—
304D4—10961no—
305D4—1372no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—2744no—
309C2×C4—2741no—
310C2×C4—2741no—
311C2×C4—2741no—
312C2×C4—2741no—
313C2×C4—2741no—
314C2×C4—10961no—
315C2×C4—10961no—
316C2×C4—10961no—
317C2×C4—10961no—
318C2×C4—10961no—
319C2×C4C2×D54811yescharacteristic
320C2×C4C2×D54811yescharacteristic
321C2×C4C2×D54811yescharacteristic
322C2×C4C2×D54811yescharacteristic
323C2×C4C2×D54811yescharacteristic
324C2×C4C23×D13711yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—2742no—
333C22—5481no—
334C22—5481no—
335C22—5481no—
336C22—5481no—
337C22—5481no—
338C22—5481no—
339C22—5481no—
340C22—5481no—
341C22C22×D54811yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—2742no—
348C4—5481no—
349C4—5481no—
350C4—5481no—
351C4—5481no—
352C4#41×D13711yescharacteristic
353C4#41×D13711yescharacteristic
354C2—41no—
355C2—5482no—
356C2—10961no—
357C2—10961no—
358C2#2257791511yescharacteristic
359C2#2257820811yescharacteristic
360C2#2257821511yescharacteristic
subgroupG/H
centerC22C22×D548
commutator, cosocleC2×C4×C137C24
FrattiniC2×C4C23×D137
Fitting#433×C137C2
socleC22×C137C22×D4
hypercenter#433D137
hypocenterC137#3119
LCSG ▷ C2×C4×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #22578008C2semidirect
2. #22577883C2semidirect
3. #22577722C2semidirect
4. #22577717C2semidirect
5. #22577711C2semidirect
6. #22577704C2semidirect
7. #22577604C2semidirect
8. #22577599C2semidirect
9. #22577550C2semidirect
10. #22577550C2semidirect
11. #22577516C2semidirect
12. #22577505C2semidirect
13. C4×#14555499C2semidirect
14. C4×D1096C2semidirect
15. #433×C137C2semidirect
180. C137#3119semidirect
196. #433D137semidirect

Maximal subgroups

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

subgroupindex
#225780082
#225778832
#225777222
#225777172
#225777112
#225777042
#225776042
#225775992
#225775502
#225775162
#225775052
C4×#145554992
C4×D10962
#433×C1372
#3119137