Finite Group Databasebeta

← #11794631

Subgroups — #11794631

Order 1152.

443 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#10592824C211yesmaximal, characteristic
2C2×C3×#824C211yesmaximal, characteristic
3C3×#5124C211yesmaximal, characteristic
4#10591143C211yesmaximal, characteristic
5C2×#63560C211yesmaximal, characteristic
6C2×#63560C211yesmaximal, characteristic
7#10589159C211yesmaximal, characteristic
8#70732—31nomaximal
9#70111—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63646—22no—
18C3×#824—22no—
19C3×#822—22no—
20#63578—22no—
21#63560—22no—
22#63560—22no—
23C3×#430—31no—
24C2×C3×#101—31no—
25C2×#836—31no—
26C2×#836—31no—
27C2×#824—31no—
28C2×#824—31no—
29C2×#824D311yescharacteristic
30#5125—31no—
31#5125—31no—
32#5125—61no—
33#5124—31no—
34#5124—31no—
35#5124D311yescharacteristic
36C3⋊#338—31no—
37C3⋊#338—31no—
38C22×C32×C4C2311yescharacteristic
39C22×C3×Dic3Q812yes—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C3×Dic6—21no—
45C2×C3×Dic6—21no—
46C32×M16—21no—
47C32×M16D412yes—
48C2×C32×C8—21no—
49#3748—21no—
50#3748—21no—
51#3748—21no—
52#3748D412yes—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×#208—21no—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208D412yes—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#2070—91noSylow
65C22×C3×Q8—31no—
66C22×Dic6C2×D311yescharacteristic
67C2×C3×M16—21no—
68C2×C3×M16—31no—
69C2×C3×M16—31no—
70C2×C3×M16—31no—
71C2×C3×M16C2×D311yescharacteristic
72C2×C3×M16C2×D311yescharacteristic
73C2×#208—31no—
74C2×#208—31no—
75C2×#208—31no—
76C2×#208—31no—
77C2×#208—61no—
78C2×#208—61no—
79C2×#208C2×D311yescharacteristic
80C2×#208C2×D311yescharacteristic
81C2×#208C2×D311yescharacteristic
82C3×#108—62no—
83C3×#101—62no—
84#836—62no—
85#836—62no—
86#824—22no—
87#824—62no—
88#824—62no—
89#822—22no—
90#822—62no—
91#822—62no—
92#819—62no—
93#819—62no—
94#819—64no—
95C23×C32C2×Q811yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—22no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3×Dic6—41no—
108C3×Dic6—41no—
109C32×C8—22no—
110C3⋊(C3⋊C8)—22no—
111C3⋊(C3⋊C8)—41no—
112C3×C3⋊C8—22no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115#430—31no—
116#430—91no—
117#430—91no—
118C2×#101—31no—
119C2×#101—91no—
120C2×#101—91no—
121#338—91no—
122C2×C3×Q8—61no—
123C2×C3×Q8—61no—
124C2×C3×Q8—61no—
125C2×C3×Q8—61no—
126C2×C3×Q8—61no—
127C2×C3×Q8—61no—
128C22×C3×C4—21no—
129C22×C3×C4—32no—
130C22×C3×C4C22×D311yescharacteristic
131C22×C3×C4C22×D311yescharacteristic
132C22×Dic3Dic612yes—
133C2×Dic6—21no—
134C2×Dic6—21no—
135C2×Dic6—21no—
136C2×Dic6—21no—
137C2×Dic6—21no—
138C2×Dic6—21no—
139C3×M16—22no—
140C3×M16—21no—
141C3×M16—21no—
142C3×M16—22no—
143C3×M16—32no—
144C3×M16—61no—
145C3×M16—61no—
146C3×M16—61no—
147C3×M16—61no—
148C3×M16—61no—
149C3×M16#6712yes—
150C3×M16#6712yes—
151C2×C3×C8—22no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—61no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157#208—21no—
158#208—21no—
159#208—21no—
160#208—21no—
161#208—21no—
162#208—32no—
163#208—32no—
164#208—62no—
165#208—61no—
166#208—61no—
167#208—62no—
168#208—61no—
169#208—61no—
170#208—61no—
171#208—61no—
172#208—121no—
173#208—121no—
174#208D1212yes—
175C2×C3⋊C8—21no—
176C2×C3⋊C8—21no—
177C2×C3⋊C8—21no—
178C2×C3⋊C8—61no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—121no—
183C2×C3⋊C8—121no—
184C22×C32—41no—
185C22×C32C22⋊Q811yescharacteristic
186C22×C32C22⋊Q811yescharacteristic
187C22×C32C22⋊Q811yescharacteristic
188C32×C4#12111yescharacteristic
189C32×C4#12111yescharacteristic
190C32×C4#12111yescharacteristic
191C32×C4#12611yescharacteristic
192C3×Dic3—42no—
193C22×Q8—31no—
194C2×M16—31no—
195C2×M16—31no—
196C2×M16—31no—
197C2×M16—91no—
198C2×M16—91no—
199C2×M16D3211yescharacteristic
200#108—62no—
201#108—182no—
202#108—182no—
203#101—62no—
204#101—182no—
205#101—182no—
206C23×C3—21no—
207C23×C3C2×Dic611yescharacteristic
208C23×C3D3×Q811yescharacteristic
209C3×Q8—121no—
210C3×Q8—121no—
211C3×Q8—121no—
212C3×Q8—121no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—62no—
220C2×C3×C4—62no—
221C2×C3×C4—62no—
222C2×C3×C4C2×D1211yescharacteristic
223C2×C3×C4#23511yescharacteristic
224C2×C3×C4#23511yescharacteristic
225C2×C3×C4D3×D411yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4D3×D411yescharacteristic
228C2×C3×C4#23711yescharacteristic
229C2×C3×C4#23711yescharacteristic
230C2×C3×C4#23711yescharacteristic
231C2×C3×C4#23911yescharacteristic
232C2×C3×C4C2×#6711yescharacteristic
233C2×C3×C4C2×#6711yescharacteristic
234C2×Dic3—22no—
235C2×Dic3—22no—
236C2×Dic3—22no—
237Dic6—41no—
238Dic6—41no—
239Dic6—41no—
240Dic6—41no—
241C3×C8—24no—
242C3×C8—22no—
243C3×C8—22no—
244C3×C8—62no—
245C3×C8—121no—
246C3×C8—121no—
247C3⋊C8—22no—
248C3⋊C8—41no—
249C3⋊C8—41no—
250C3⋊C8—62no—
251C3⋊C8—62no—
252C3⋊C8—122no—
253C3⋊C8—122no—
254C3⋊C8—121no—
255C3⋊C8—121no—
256C2×C32—21no—
257C2×C32—21no—
258C2×C32—21no—
259C2×C32#39611yescharacteristic
260C2×Q8—61no—
261C2×Q8—61no—
262C2×Q8—61no—
263C2×Q8—61no—
264C2×Q8—61no—
265C2×Q8—61no—
266C22×C4—32no—
267C22×C4C2×D3211yescharacteristic
268M16—21no—
269M16—32no—
270M16—61no—
271M16—61no—
272M16—61no—
273M16—61no—
274M16—61no—
275M16—92no—
276M16—181no—
277M16—181no—
278M16—181no—
279M16#62512yes—
280C2×C8—21no—
281C2×C8—61no—
282C2×C8—61no—
283C2×C8—61no—
284C2×C8—181no—
285C2×C8—181no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3—81no—
292C22×C3#87811yescharacteristic
293C22×C3#87811yescharacteristic
294C22×C3#89611yescharacteristic
295C22×C3#89711yescharacteristic
296C22×C3#92411yescharacteristic
297C22×C3#94611yescharacteristic
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—122no—
303C3×C4#87911yescharacteristic
304C3×C4#88411yescharacteristic
305C3×C4#89511yescharacteristic
306C3×C4#89811yescharacteristic
307C3×C4#93011yescharacteristic
308C3×C4#93811yescharacteristic
309C3×C4#93911yescharacteristic
310C3×C4#93911yescharacteristic
311Dic3—42no—
312C32#207011yescharacteristic, complemented, Sylow
313C23D3×Dic611yescharacteristic
314Q8—121no—
315Q8—121no—
316Q8—121no—
317Q8—121no—
318C2×C4—62no—
319C2×C4—62no—
320C2×C4—62no—
321C2×C4#379511yescharacteristic
322C2×C4#379911yescharacteristic
323C2×C4D3×D1211yescharacteristic
324C2×C4#380511yescharacteristic
325C2×C4C2×#62511yescharacteristic
326C2×C4#381111yescharacteristic
327C8—22no—
328C8—62no—
329C8—121no—
330C8—121no—
331C8—182no—
332C8—361no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—41no—
341C2×C3—41no—
342C2×C3—41no—
343C2×C3#494811yescharacteristic
344C2×C3#499411yescharacteristic
345C22—41no—
346C22#6385611yescharacteristic
347C22#6389311yescharacteristic
348C22#6389611yescharacteristic
349C4—122no—
350C4#6386111yescharacteristic
351C4#6390811yescharacteristic
352C4#6391011yescharacteristic
353C4#6398011yescharacteristic
354C3—21no—
355C3#7011111yescharacteristic, complemented
356C3#7073211yescharacteristic, complemented
357C2—21no—
358C2—21no—
359C2—21no—
360C2#1059131911yescharacteristic
subgroupG/H
centerC2#10591319
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#396
prime radicalC23×C32C2×Q8
hypercenterC2×M16D32
hypocenterC32#2070
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
312. C32#2070semidirect
355. C3#70111semidirect
356. C3#70732semidirect

Maximal subgroups

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

subgroupindex
#105928242
C2×C3×#8242
C3×#51242
#105911432
C2×#635602
#105891592
#707323
#701113