Finite Group Databasebeta

← #11860572

Subgroups — #11860572

Order 1152.

1410 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64118C211yesmaximal, characteristic
2#10595987C211yesmaximal, characteristic, complemented
3#10595975C211yesmaximal, characteristic
4C32×#428C211yesmaximal, characteristic, complemented
5#10592821C211yesmaximal, characteristic, complemented
6#10592701C211yesmaximal, characteristic
7C2×#63637C211yesmaximal, characteristic, complemented
8#10592588C212yesmaximal, complemented
9#10592572C212yesmaximal, complemented
10#10592552C212yesmaximal, complemented
11#10592551C212yesmaximal, complemented
12#79202—34nomaximal
13C2×#3828C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C4×#638—22no—
19#64135C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21#64118C418yescomplemented
22C2×#3746C2212yes—
23C2×#3744C2212yes—
24#64102C2212yes—
25#64101—21no—
26C4⋊C4×C3⋊D3—21no—
27#64096C2212yes—
28#64096C2212yes—
29#64096C2212yes—
30#64086—22no—
31C4×#634—21no—
32C4×#634—21no—
33C32×#107C2212yes—
34C32×#106C2212yes—
35#63642C2212yes—
36C8×C3⋊Dic3C2212yes—
37#63637C2212yes—
38#63637C2211yescharacteristic
39#63637C2212yes—
40#63637C2211yescharacteristic
41#63636C2211yescharacteristic
42#63636C2211yescharacteristic
43C2×#909—34no—
44#5516—34no—
45#5504—34no—
46C3×#428D314yescomplemented
47#5122—34no—
48#5002—34no—
49C2×#810—34no—
50#4889—38no—
51#4873—38no—
52#4853—38no—
53#4852—38no—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—21no—
57C22×C3⋊Dic3—21no—
58#3828—22no—
59#3828C2×C414yes—
60C2×C4⋊(C3⋊D3)C2311yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×C4×C3⋊D3—22no—
63C2×#634—21no—
64C2×#634—22no—
65C2×#634C2×C414yescomplemented
66C2×#634C2312yes—
67C2×#634C2311yescharacteristic
68C32×M16C2×C414yescomplemented
69C2×C32×C8C2312yes—
70C32×C4⋊C4—21no—
71C32×C4⋊C4C2311yescharacteristic
72C32×C4⋊C4C2311yescharacteristic
73C32×C4⋊C4C2312yes—
74C32×C22⋊C4—21no—
75C32×C42—21no—
76#3757D412yes—
77#3752—22no—
78C4⋊(C3⋊Dic3)D411yescharacteristic
79C4⋊(C3⋊Dic3)D411yescharacteristic
80#3750—22no—
81#3750—22no—
82#3750—22no—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3—22no—
86C4×C3⋊Dic3C2312yes—
87C2×C3⋊(C3⋊C8)—22no—
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90#3746C2×C418yescomplemented
91#3744C2×C418yescomplemented
92#2947—91noSylow
93C2×#235—34no—
94C22×Dic6—34no—
95C2×C3×M16C2×D314yes—
96C3×#117C2×D314yes—
97C2×C3×C4⋊C4C2×D314yes—
98C4×#67—68no—
99#926—34no—
100C22×C3⋊C8—34no—
101#909—332no—
102C2×Dic12—38no—
103C2×#204—38no—
104#893—38no—
105#892—64no—
106D3×C4⋊C4—64no—
107#887—38no—
108#887—38no—
109#887—38no—
110#877—68no—
111C4×Dic6—64no—
112C4×Dic6—64no—
113C3×#107C2×D318yes—
114C3×#106C2×D318yes—
115#815—38no—
116C8×Dic3—38no—
117#810—34no—
118#810—38no—
119#810—38no—
120#810—34no—
121#809—34no—
122#809—34no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—21no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—22no—
128C2×C32×C4—81no—
129C2×C32×C4C22×C412yes—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4112yes—
132C2×C32×C4C2411yescharacteristic
133#638—24no—
134C2×C3⋊Dic3—24no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3C2×D412yes—
138C2×C3⋊Dic3C2×D412yes—
139C4⋊(C3⋊D3)—21no—
140C4⋊(C3⋊D3)C22×C412yes—
141C4×C3⋊D3—24no—
142C4×C3⋊D3—82no—
143#634—24no—
144#634—22no—
145#634—21no—
146#634C22×C414yes—
147#634C22×C412yes—
148C32×C8C22×C414yes—
149C3⋊(C3⋊C8)—21no—
150C3⋊(C3⋊C8)—21no—
151C2×#137—91no—
152#520—91no—
153#519—91no—
154#441—92no—
155#440—92no—
156C4×Q16—92no—
157C4×SD16—92no—
158#428C3⋊D311yescharacteristic, complemented
159#416—91no—
160C2×#103—91no—
161#405—91no—
162C22×C3×C4—24no—
163C22×C3×C4C22×D314yes—
164C2×#67—64no—
165C22×Dic3—64no—
166#235—316no—
167#235—68no—
168C2×D12—34no—
169C2×C4×D3—64no—
170C2×C4×D3—68no—
171C2×Dic6—316no—
172C2×Dic6—38no—
173C2×Dic6—34no—
174C2×Dic6—64no—
175C2×Dic6—68no—
176C3×M16C4×D3116yescomplemented
177C2×C3×C8C22×D318yes—
178C3×C4⋊C4—24no—
179C3×C4⋊C4C22×D314yes—
180C3×C4⋊C4C22×D314yes—
181C3×C4⋊C4C22×D318yes—
182C3×C22⋊C4—24no—
183C3×C42—24no—
184#217—38no—
185(C2×D3)⋊C4—68no—
186C4⋊Dic3—34no—
187C4⋊Dic3—34no—
188Dic3⋊C4—68no—
189Dic3⋊C4—68no—
190Dic3⋊C4—68no—
191C4×Dic3—38no—
192C4×Dic3—68no—
193C4×Dic3—68no—
194C4×Dic3—68no—
195C2×C3⋊C8—34no—
196C2×C3⋊C8—34no—
197C2×C3⋊C8—68no—
198Dic12—332no—
199#204—332no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32C4×D412yes—
203C22×C32C22×D411yescharacteristic
204C2×C3⋊D3—22no—
205C2×C3⋊D3—41no—
206C2×C3⋊D3—41no—
207C32×C4—42no—
208C32×C4—41no—
209C32×C4—41no—
210C32×C4C4×D412yes—
211C32×C4C23×C411yescharacteristic
212C32×C4C2×#4111yescharacteristic
213C3⋊Dic3—24no—
214C3⋊Dic3—22no—
215C3⋊Dic3—22no—
216C3⋊Dic3—22no—
217C2×#41—91no—
218C22×Q8—91no—
219#137—98no—
220C2×Q16—92no—
221C2×SD16—92no—
222C2×M16C2×C3⋊D311yescharacteristic
223C22×C8—91no—
224C4×Q8—92no—
225C4×Q8—92no—
226C4×Q8—92no—
227C4×Q8—181no—
228C4×Q8—181no—
229C4×D4—92no—
230C4×D4—182no—
231#117—91no—
232#117—182no—
233#117—181no—
234#117C2×C3⋊D311yescharacteristic
235C2×C4⋊C4—181no—
236C2×C4⋊C4C2×C3⋊D311yescharacteristic
237#107C2×C3⋊D312yes—
238#106C2×C3⋊D312yes—
239#103—92no—
240#103—92no—
241#103—91no—
242#103—91no—
243#102—91no—
244#102—91no—
245#97—92no—
246C4×C8—92no—
247C23×C3D3×D414yes—
248C22×D3—64no—
249C2×C3×C4—24no—
250C2×C3×C4—24no—
251C2×C3×C4—28no—
252C2×C3×C4—84no—
253C2×C3×C4C2×C4×D318yes—
254C2×C3×C4D3×D414yes—
255C2×C3×C4#23918yes—
256C2×C3×C4C23×D314yes—
257#67—616no—
258C2×Dic3—38no—
259C2×Dic3—38no—
260C2×Dic3—616no—
261C2×Dic3—68no—
262C2×Dic3—64no—
263D12—38no—
264D12—64no—
265C4×D3—616no—
266C4×D3—248no—
267Dic6—316no—
268Dic6—38no—
269Dic6—616no—
270Dic6—68no—
271Dic6—64no—
272C3×C8C2×C4×D3116yes—
273C3⋊C8—64no—
274C3⋊C8—64no—
275C2×C32—22no—
276C2×C32C2×C4×D411yescharacteristic
277C2×C32#57711yescharacteristic
278C2×C32#57811yescharacteristic
279C3⋊D3—42no—
280#41—94no—
281#41—182no—
282C2×Q8—92no—
283C2×Q8—91no—
284C2×Q8—94no—
285C2×Q8—181no—
286C2×Q8—182no—
287C2×D4—91no—
288C2×D4—181no—
289C22×C4—21no—
290C22×C4—182no—
291C22×C4—181no—
292C22×C4—181no—
293C22×C4C22×C3⋊D311yescharacteristic
294Q16—98no—
295SD16—98no—
296M16C4×C3⋊D314yescomplemented
297C2×C8—91no—
298C2×C8—91no—
299C2×C8—182no—
300C2×C8C22×C3⋊D312yes—
301C4⋊C4—21no—
302C4⋊C4—91no—
303C4⋊C4—91no—
304C4⋊C4—182no—
305C4⋊C4—182no—
306C4⋊C4—182no—
307C4⋊C4C22×C3⋊D311yescharacteristic
308C4⋊C4C22×C3⋊D311yescharacteristic
309C4⋊C4C22×C3⋊D312yes—
310C22⋊C4—21no—
311C22⋊C4—92no—
312C22⋊C4—182no—
313C42—21no—
314C42—92no—
315C42—182no—
316C42—182no—
317C42—182no—
318C22×C3—24no—
319C22×C3—24no—
320C22×C3#89318yes—
321C22×C3C2×D3×D414yes—
322C2×D3—68no—
323C2×D3—124no—
324C2×D3—124no—
325C3×C4—48no—
326C3×C4—44no—
327C3×C4—44no—
328C3×C4#89318yes—
329C3×C4C22×C4×D314yes—
330C3×C4C2×#23914yes—
331Dic3—616no—
332Dic3—68no—
333Dic3—68no—
334Dic3—68no—
335C32#294711yescharacteristic, complemented, Sylow
336C23—181no—
337C23D4×C3⋊D311yescharacteristic
338Q8—94no—
339Q8—92no—
340Q8—184no—
341Q8—182no—
342Q8—181no—
343D4—92no—
344D4—184no—
345D4—181no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—81no—
350C2×C4—92no—
351C2×C4—92no—
352C2×C4—184no—
353C2×C4—181no—
354C2×C4—182no—
355C2×C4—184no—
356C2×C4—722no—
357C2×C4C2×C4×C3⋊D312yes—
358C2×C4D4×C3⋊D311yescharacteristic
359C2×C4#383212yes—
360C2×C4C23×C3⋊D311yescharacteristic
361C8—181no—
362C8—181no—
363C8C2×C4×C3⋊D314yes—
364C2×C3—28no—
365C2×C3C2×#89314yes—
366C2×C3#577514yes—
367C2×C3#577914yes—
368D3—128no—
369C22—21no—
370C22—21no—
371C22—182no—
372C22—361no—
373C22—361no—
374C22#6410212yes—
375C22C2×D4×C3⋊D311yescharacteristic
376C4—42no—
377C4—41no—
378C4—41no—
379C4—182no—
380C4—184no—
381C4—182no—
382C4—182no—
383C4#6410212yes—
384C4C22×C4×C3⋊D311yescharacteristic
385C4C2×#383211yescharacteristic
386C3#7920214yescomplemented
387C2—22no—
388C2—362no—
389C2C2×#6410211yescharacteristic
390C2#1059624611yescharacteristic
391C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#428C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenter#428C3⋊D3
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #10595987C2semidirect
4. C32×#428C2semidirect
5. #10592821C2semidirect
7. C2×#63637C2semidirect
8. #10592588C2semidirect
9. #10592572C2semidirect
10. #10592552C2semidirect
11. #10592551C2semidirect
21. #64118C4semidirect
46. C3×#428D3semidirect
65. C2×#634C2×C4semidirect
68. C32×M16C2×C4semidirect
90. #3746C2×C4semidirect
91. #3744C2×C4semidirect
158. #428C3⋊D3semidirect
176. C3×M16C4×D3semidirect
296. M16C4×C3⋊D3semidirect
335. C32#2947semidirect
386. C3#79202semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
#105959872
#105959752
C32×#4282
#105928212
#105927012
C2×#636372
#105925882
#105925722
#105925522
#105925512
#792023