Finite Group Databasebeta

← #11775184

Subgroups — #11775184

Order 1152.

567 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#10595941C211yesmaximal, characteristic
2C3×#4932C211yesmaximal, characteristic
3C3×#4926C211yesmaximal, characteristic
4#10589154C214yesmaximal
5#70836—31nomaximal
6#69433—31nomaximal
7C2×C32×C42C2211yescharacteristic
8#64135—21no—
9#64133—21no—
10#64133C2212yes—
11#64079—21no—
12#64078C411yescharacteristic, complemented
13#64078C411yescharacteristic, complemented
14C4×#634—21no—
15C4×#634C412yescomplemented
16C2×C3×C4×Dic3—21no—
17C3×C3⋊#95—21no—
18C3×C3⋊#95C2212yes—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×#803—21no—
22#5470—31no—
23#5470—31no—
24#5470—61no—
25C3×#432—31no—
26C3×#376—31no—
27#4932D311yescharacteristic
28#4926D311yescharacteristic
29#4467—34no—
30#4452—34no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C2×#634—21no—
35C2×#634C2×C412yes—
36C22×C3×Dic3—22no—
37C32×C42C2×C411yescharacteristic
38C32×C42C2×C411yescharacteristic
39C32×C42D411yescharacteristic
40C32×C42D411yescharacteristic
41#3757—22no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)C2×C412yes—
46#3750—22no—
47#3750—22no—
48C4×C3⋊Dic3—22no—
49C3×C4×Dic3—24no—
50C2×C3×C3⋊C8—22no—
51#1506—91noSylow
52C2×C3×C42—21no—
53C2×C3×C42—61no—
54C2×C3×C42C2×D311yescharacteristic
55C2×C3×C42C2×D311yescharacteristic
56#926—62no—
57#926—61no—
58#926—61no—
59#924—32no—
60#924—32no—
61#924—62no—
62#924—62no—
63#924—61no—
64#924—61no—
65C2×C4×Dic3—21no—
66#870—62no—
67#870—61no—
68#870—61no—
69#869—31no—
70#869—31no—
71#869—31no—
72#869—31no—
73#869—61no—
74#869—61no—
75C4×Dic6—32no—
76C4×Dic6—32no—
77C4×Dic6—62no—
78C4×Dic6—62no—
79C4×Dic6—61no—
80C4×Dic6—61no—
81C3×C4⋊C8—61no—
82C3×C22⋊C8—32no—
83C3×#97—61no—
84C3×#95—32no—
85C3×#95—61no—
86C3⋊#95—21no—
87C3⋊#95C2×D312yes—
88#830C2×D312yes—
89C4⋊(C3⋊C8)—21no—
90#803—21no—
91C23×C32C2×D411yescharacteristic
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—41no—
95C2×C32×C4C22⋊C411yescharacteristic
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—22no—
103#634—42no—
104#634—42no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—42no—
107C2×C3×Dic3—42no—
108C3×C3⋊C8—42no—
109#533—91no—
110#432—31no—
111#376—31no—
112#328—94no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4—62no—
117C22×C3×C4D1211yescharacteristic
118C22×C3×C4D1211yescharacteristic
119C22×C3×C4#6711yescharacteristic
120C22×C3×C4#6711yescharacteristic
121C22×C3×C4C22×D311yescharacteristic
122C22×C3×C4C22×D311yescharacteristic
123C22×Dic3—22no—
124C2×Dic6—32no—
125C2×Dic6—32no—
126C2×Dic6—62no—
127C2×Dic6—62no—
128C2×Dic6—61no—
129C2×Dic6—61no—
130C2×C3×C8—62no—
131C3×C42—21no—
132C3×C42—21no—
133C3×C42—21no—
134C3×C42—21no—
135C3×C42—64no—
136C3×C42C4×D311yescharacteristic
137C3×C42C4×D311yescharacteristic
138C3×C42C4×D311yescharacteristic
139C3×C42C4×D311yescharacteristic
140C3×C42D1211yescharacteristic
141C3×C42D1211yescharacteristic
142C3×C42#6711yescharacteristic
143C3×C42#6711yescharacteristic
144#217—64no—
145#217—62no—
146#217—62no—
147C4⋊Dic3—32no—
148C4⋊Dic3—32no—
149C4⋊Dic3—62no—
150C4⋊Dic3—62no—
151C4⋊Dic3—62no—
152C4⋊Dic3—62no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157C4⋊Dic3—61no—
158C4⋊Dic3—61no—
159Dic3⋊C4—64no—
160Dic3⋊C4—64no—
161Dic3⋊C4—62no—
162Dic3⋊C4—62no—
163Dic3⋊C4—62no—
164Dic3⋊C4—62no—
165C4×Dic3—24no—
166C4×Dic3—64no—
167C4×Dic3—62no—
168C4×Dic3—62no—
169C2×C3⋊C8—22no—
170C22×C32—21no—
171C22×C32—21no—
172C22×C32C2×C22⋊C411yescharacteristic
173C22×C32#13712yes—
174C32×C4—21no—
175C32×C4—21no—
176C32×C4—21no—
177C32×C4—21no—
178C32×C4—21no—
179C32×C4#10412yes—
180C3⋊Dic3—42no—
181C3⋊Dic3—42no—
182C3×Dic3—44no—
183C4⋊Q8—91no—
184C4⋊Q8—91no—
185#125—181no—
186C22⋊Q8—92no—
187C22⋊Q8—181no—
188C4×Q8—92no—
189C4×Q8—181no—
190#117—181no—
191C2×C42—61no—
192C2×C42D3211yescharacteristic
193C4⋊C8—61no—
194C22⋊C8—32no—
195#97—61no—
196#95—32no—
197#95—61no—
198C23×C3—21no—
199C23×C3C2×D1211yescharacteristic
200C23×C3C2×#6711yescharacteristic
201C2×C3×C4—24no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—42no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—42no—
216C2×C3×C4—64no—
217C2×C3×C4—122no—
218C2×C3×C4—122no—
219C2×C3×C4(C2×D3)⋊C411yescharacteristic
220C2×C3×C4(C2×D3)⋊C411yescharacteristic
221C2×C3×C4(C2×D3)⋊C411yescharacteristic
222C2×C3×C4(C2×D3)⋊C411yescharacteristic
223C2×C3×C4(C2×D3)⋊C411yescharacteristic
224C2×C3×C4(C2×D3)⋊C411yescharacteristic
225C2×C3×C4(C2×D3)⋊C411yescharacteristic
226C2×C3×C4(C2×D3)⋊C411yescharacteristic
227C2×C3×C4C2×C4×D311yescharacteristic
228C2×C3×C4C2×C4×D311yescharacteristic
229C2×C3×C4C2×D1211yescharacteristic
230C2×C3×C4C2×#6711yescharacteristic
231C2×Dic3—24no—
232C2×Dic3—42no—
233C2×Dic3—42no—
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240Dic6—124no—
241Dic6—124no—
242Dic6—122no—
243Dic6—122no—
244Dic6—122no—
245Dic6—122no—
246C3×C8—122no—
247C3⋊C8—42no—
248C2×C32—22no—
249C2×C32#41011yescharacteristic
250C2×C32#41911yescharacteristic
251C2×C32C2×#10411yescharacteristic
252C2×Q8—92no—
253C2×Q8—181no—
254C22×C4—62no—
255C22×C4#62611yescharacteristic
256C22×C4#62611yescharacteristic
257C22×C4C2×D3211yescharacteristic
258C2×C8—62no—
259C4⋊C4—92no—
260C4⋊C4—181no—
261C4⋊C4—181no—
262C4⋊C4—182no—
263C4⋊C4—181no—
264C4⋊C4—182no—
265C22⋊C4—182no—
266C42—64no—
267C42—182no—
268C42#62411yescharacteristic
269C42#62411yescharacteristic
270C42#62611yescharacteristic
271C42#62611yescharacteristic
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—22no—
277C22×C3—21no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3#90912yes—
281C22×C3C2×(C2×D3)⋊C411yescharacteristic
282C22×C3C2×(C2×D3)⋊C411yescharacteristic
283C22×C3#95112yes—
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—22no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—22no—
298C3×C4—41no—
299C3×C4—41no—
300C3×C4—124no—
301C3×C4#80512yes—
302C3×C4#82512yes—
303Dic3—44no—
304Dic3—124no—
305Dic3—124no—
306Dic3—122no—
307Dic3—122no—
308Dic3—122no—
309Dic3—122no—
310C32#150611yescharacteristic, complemented, Sylow
311C23C2×#62611yescharacteristic
312Q8—362no—
313Q8—362no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—64no—
318C2×C4—122no—
319C2×C4—122no—
320C2×C4—182no—
321C2×C4—182no—
322C2×C4#372211yescharacteristic
323C2×C4#372211yescharacteristic
324C2×C4#372211yescharacteristic
325C2×C4#372211yescharacteristic
326C2×C4C2×#62411yescharacteristic
327C2×C4C2×#62611yescharacteristic
328C8—122no—
329C2×C3—22no—
330C2×C3—22no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—42no—
335C2×C3C2×#80511yescharacteristic
336C2×C3#500411yescharacteristic
337C2×C3#500611yescharacteristic
338C2×C3#500611yescharacteristic
339C2×C3#512011yescharacteristic
340C2×C3C2×#82511yescharacteristic
341C22—21no—
342C22—21no—
343C22#6383112yes—
344C22C2×#372211yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—124no—
351C4—362no—
352C4—362no—
353C4#6357012yes—
354C3—21no—
355C3#6943311yescharacteristic, complemented
356C3#7083611yescharacteristic, complemented
357C2—22no—
358C2#1059110711yescharacteristic
359C2C2×#6357011yescharacteristic
360C2#1059123211yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1506
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
12. #64078C4semidirect
13. #64078C4semidirect
15. C4×#634C4semidirect
310. C32#1506semidirect
355. C3#69433semidirect
356. C3#70836semidirect

Maximal subgroups

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

subgroupindex
#105959412
C3×#49322
C3×#49262
#105891542
#708363
#694333