Finite Group Databasebeta

← #11775091

Subgroups — #11775091

Order 1152.

591 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595941C211yesmaximal, characteristic
2C3×C4×C4⋊Dic3C211yesmaximal, characteristic
3C3×#4925C211yesmaximal, characteristic
4#10589154C214yesmaximal
5#70792—31nomaximal
6#69471—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—
17C2×C3×C4×Dic3—21no—
18C3×C3⋊#95C2212yes—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×C4×C3⋊C8—21no—
22#5470—31no—
23#5470—31no—
24#5470—61no—
25C3×#431—31no—
26C3×C4×C4⋊C4—31no—
27C4×C4⋊Dic3D311yescharacteristic
28#4925D311yescharacteristic
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—
50C3×C4×Dic3—42no—
51C2×C3×C3⋊C8—22no—
52#1503—91noSylow
53C2×C3×C4⋊C4—61no—
54C2×C3×C42—21no—
55C2×C3×C42—61no—
56C2×C3×C42C2×D311yescharacteristic
57C2×C3×C42C2×D311yescharacteristic
58#926—62no—
59#926—61no—
60#926—61no—
61C2×C4⋊Dic3—21no—
62#924—32no—
63#924—32no—
64#924—62no—
65#924—62no—
66#924—61no—
67#924—61no—
68C2×C4×Dic3—21no—
69#870—62no—
70#870—61no—
71#870—61no—
72#869—31no—
73#869—31no—
74#869—31no—
75#869—31no—
76#869—61no—
77#869—61no—
78C4×Dic6—32no—
79C4×Dic6—32no—
80C4×Dic6—62no—
81C4×Dic6—62no—
82C4×Dic6—61no—
83C4×Dic6—61no—
84C3×C4⋊C8—61no—
85C3×C22⋊C8—32no—
86C3×C4×C8—61no—
87C3×#95—32no—
88C3⋊#95C2×D312yes—
89#830C2×D312yes—
90C4⋊(C3⋊C8)—21no—
91C4×C3⋊C8—21no—
92C23×C32C2×D411yescharacteristic
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×C4SD1612yes—
100C2×C32×C4Q1612yes—
101C2×C32×C4C22×C411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105#634—42no—
106#634—42no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—42no—
109C2×C3×Dic3—42no—
110C3×C3⋊C8—42no—
111#533—91no—
112#431—31no—
113C4×C4⋊C4—31no—
114#328—94no—
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—62no—
119C22×C3×C4D1211yescharacteristic
120C22×C3×C4D1211yescharacteristic
121C22×C3×C4#6711yescharacteristic
122C22×C3×C4#6711yescharacteristic
123C22×C3×C4C22×D311yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C22×Dic3—22no—
126C2×Dic6—32no—
127C2×Dic6—32no—
128C2×Dic6—62no—
129C2×Dic6—62no—
130C2×Dic6—61no—
131C2×Dic6—61no—
132C2×C3×C8—62no—
133C3×C4⋊C4—64no—
134C3×C42—21no—
135C3×C42—21no—
136C3×C42—21no—
137C3×C42—21no—
138C3×C42—122no—
139C3×C42C4×D311yescharacteristic
140C3×C42C4×D311yescharacteristic
141C3×C42C4×D311yescharacteristic
142C3×C42C4×D311yescharacteristic
143C3×C42D1211yescharacteristic
144C3×C42D1211yescharacteristic
145C3×C42#6711yescharacteristic
146C3×C42#6711yescharacteristic
147#217—64no—
148#217—62no—
149#217—62no—
150C4⋊Dic3—24no—
151C4⋊Dic3—32no—
152C4⋊Dic3—32no—
153C4⋊Dic3—62no—
154C4⋊Dic3—62no—
155C4⋊Dic3—62no—
156C4⋊Dic3—62no—
157C4⋊Dic3—61no—
158C4⋊Dic3—61no—
159C4⋊Dic3—61no—
160C4⋊Dic3—61no—
161C4⋊Dic3—61no—
162C4⋊Dic3—61no—
163Dic3⋊C4—64no—
164Dic3⋊C4—64no—
165Dic3⋊C4—62no—
166Dic3⋊C4—62no—
167Dic3⋊C4—62no—
168Dic3⋊C4—62no—
169C4×Dic3—42no—
170C4×Dic3—64no—
171C4×Dic3—62no—
172C4×Dic3—62no—
173C2×C3⋊C8—22no—
174C22×C32—21no—
175C22×C32—21no—
176C22×C32C2×C22⋊C411yescharacteristic
177C22×C32C2×SD1611yescharacteristic
178C22×C32C2×Q1611yescharacteristic
179C32×C4—21no—
180C32×C4—21no—
181C32×C4—21no—
182C32×C4#10312yes—
183C32×C4#10312yes—
184C32×C4#10412yes—
185C3⋊Dic3—42no—
186C3⋊Dic3—42no—
187C3×Dic3—44no—
188C4⋊Q8—91no—
189C4⋊Q8—91no—
190#125—181no—
191C22⋊Q8—92no—
192C22⋊Q8—181no—
193C4×Q8—92no—
194C4×Q8—181no—
195#117—181no—
196C2×C4⋊C4—61no—
197C2×C42—61no—
198C2×C42D3211yescharacteristic
199C4⋊C8—61no—
200C22⋊C8—32no—
201C4×C8—61no—
202#95—32no—
203C23×C3—21no—
204C23×C3C2×D1211yescharacteristic
205C23×C3C2×#6711yescharacteristic
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—42no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—42no—
220C2×C3×C4—64no—
221C2×C3×C4—122no—
222C2×C3×C4—122no—
223C2×C3×C4#20412yes—
224C2×C3×C4Dic1212yes—
225C2×C3×C4(C2×D3)⋊C411yescharacteristic
226C2×C3×C4(C2×D3)⋊C411yescharacteristic
227C2×C3×C4(C2×D3)⋊C411yescharacteristic
228C2×C3×C4(C2×D3)⋊C411yescharacteristic
229C2×C3×C4(C2×D3)⋊C411yescharacteristic
230C2×C3×C4(C2×D3)⋊C411yescharacteristic
231C2×C3×C4(C2×D3)⋊C411yescharacteristic
232C2×C3×C4(C2×D3)⋊C411yescharacteristic
233C2×C3×C4#21412yes—
234C2×C3×C4#21612yes—
235C2×C3×C4C2×C4×D311yescharacteristic
236C2×C3×C4C2×C4×D311yescharacteristic
237C2×C3×C4C2×D1211yescharacteristic
238C2×C3×C4C2×#6711yescharacteristic
239C2×Dic3—24no—
240C2×Dic3—42no—
241C2×Dic3—42no—
242C2×Dic3—64no—
243C2×Dic3—64no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248Dic6—124no—
249Dic6—124no—
250Dic6—122no—
251Dic6—122no—
252Dic6—122no—
253Dic6—122no—
254C3×C8—122no—
255C3⋊C8—42no—
256C2×C32—21no—
257C2×C32—21no—
258C2×C32#41011yescharacteristic
259C2×C32C2×#10311yescharacteristic
260C2×C32C2×#10411yescharacteristic
261C2×Q8—92no—
262C2×Q8—181no—
263C22×C4—62no—
264C22×C4#62611yescharacteristic
265C22×C4#62611yescharacteristic
266C22×C4C2×D3211yescharacteristic
267C2×C8—62no—
268C4⋊C4—64no—
269C4⋊C4—92no—
270C4⋊C4—181no—
271C4⋊C4—181no—
272C4⋊C4—182no—
273C4⋊C4—181no—
274C4⋊C4—182no—
275C22⋊C4—182no—
276C42—122no—
277C42—182no—
278C42#62411yescharacteristic
279C42#62411yescharacteristic
280C42#62611yescharacteristic
281C42#62611yescharacteristic
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3C2×#20411yescharacteristic
292C22×C3C2×Dic1211yescharacteristic
293C22×C3C2×(C2×D3)⋊C411yescharacteristic
294C22×C3C2×(C2×D3)⋊C411yescharacteristic
295C22×C3C2×#21411yescharacteristic
296C22×C3C2×#21611yescharacteristic
297C3×C4—22no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—22no—
305C3×C4—22no—
306C3×C4—22no—
307C3×C4—41no—
308C3×C4—41no—
309C3×C4—124no—
310C3×C4#80512yes—
311C3×C4#81012yes—
312C3×C4#81012yes—
313C3×C4#81612yes—
314C3×C4#81612yes—
315C3×C4#82512yes—
316Dic3—44no—
317Dic3—124no—
318Dic3—124no—
319Dic3—122no—
320Dic3—122no—
321Dic3—122no—
322Dic3—122no—
323C32#150311yescharacteristic, complemented, Sylow
324C23C2×#62611yescharacteristic
325Q8—362no—
326Q8—362no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—64no—
330C2×C4—122no—
331C2×C4—122no—
332C2×C4—182no—
333C2×C4—182no—
334C2×C4#371612yes—
335C2×C4#371912yes—
336C2×C4#372211yescharacteristic
337C2×C4#372211yescharacteristic
338C2×C4#372211yescharacteristic
339C2×C4#372211yescharacteristic
340C2×C4C2×#62411yescharacteristic
341C2×C4C2×#62611yescharacteristic
342C8—122no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—41no—
351C2×C3—41no—
352C2×C3C2×#80511yescharacteristic
353C2×C3C2×#81011yescharacteristic
354C2×C3#500611yescharacteristic
355C2×C3#500611yescharacteristic
356C2×C3C2×#81611yescharacteristic
357C2×C3C2×#82511yescharacteristic
358C22—21no—
359C22—21no—
360C22C2×#371611yescharacteristic
361C22C2×#371911yescharacteristic
362C22C2×#372211yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—124no—
367C4—362no—
368C4—362no—
369C4#6356712yes—
370C4#6356712yes—
371C4#6357012yes—
372C3—21no—
373C3#6947111yescharacteristic, complemented
374C3#7079211yescharacteristic, complemented
375C2—21no—
376C2—21no—
377C2C2×#6356711yescharacteristic
378C2C2×#6357011yescharacteristic
379C2#1059123211yescharacteristic
subgroupG/H
centerC2×C4#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#1503
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
12. #64078C4semidirect
13. #64078C4semidirect
15. C4×#634C4semidirect
323. C32#1503semidirect
373. C3#69471semidirect
374. C3#70792semidirect

Maximal subgroups

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

subgroupindex
#105959412
C3×C4×C4⋊Dic32
C3×#49252
#105891542
#707923
#694713