Finite Group Databasebeta

← #11774403

Subgroups — #11774403

Order 1152.

543 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595941C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
4#10589085C214yesmaximal, complemented
5#70768—31nomaximal
6#70429—31nomaximal
7C2×C32×C42C2211yescharacteristic
8#64135—21no—
9#64133—21no—
10#64133C412yes—
11#64079—21no—
12#64078C411yescharacteristic
13#64078C411yescharacteristic
14C4×#634—21no—
15C4×#634C2212yes—
16C22×C3×C3⋊C8—21no—
17C3×#830—21no—
18C3×C4⋊(C3⋊C8)—21no—
19C3×C4⋊(C3⋊C8)—21no—
20C3×C4⋊(C3⋊C8)C2212yes—
21C3×C4×C3⋊C8C2212yes—
22#5470—31no—
23#5470—31no—
24#5470—61no—
25C3×#431—31no—
26C2×C3×C4⋊C8—31no—
27#4925D311yescharacteristic
28C2×C4⋊(C3⋊C8)D311yescharacteristic
29#4484—34no—
30#4456—34no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C2×#634—21no—
35C2×#634C2×C412yes—
36C32×C42C2×C411yescharacteristic
37C32×C42D411yescharacteristic
38C32×C42D411yescharacteristic
39C32×C42C2311yescharacteristic
40#3757—22no—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)C2×C412yes—
45#3750—22no—
46#3750—22no—
47C4×C3⋊Dic3—22no—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8—42no—
51#1481—91noSylow
52C22×C3×C8—61no—
53C2×C3×C42—21no—
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—
65C22×C3⋊C8—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—32no—
82C3×C4⋊C8—61no—
83C3×C4⋊C8—61no—
84C3×C22⋊C8—61no—
85C3×C4×C8—32no—
86#830—21no—
87C4⋊(C3⋊C8)—21no—
88C4⋊(C3⋊C8)—21no—
89C4⋊(C3⋊C8)C2×D312yes—
90C4×C3⋊C8C2×D312yes—
91C23×C32C22⋊C411yescharacteristic
92C2×C32×C4—22no—
93C2×C32×C4—41no—
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C22⋊C411yescharacteristic
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4SD1612yes—
98C2×C32×C4Q1612yes—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—22no—
104#634—24no—
105#634—42no—
106C3×C3⋊C8—42no—
107C3×C3⋊C8—42no—
108#533—91no—
109#431—31no—
110C2×C4⋊C8—31no—
111Q8⋊C8—94no—
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4C4×D311yescharacteristic
116C22×C3×C4C4×D311yescharacteristic
117C22×C3×C4D1211yescharacteristic
118C22×C3×C4D1211yescharacteristic
119C22×C3×C4#6711yescharacteristic
120C22×C3×C4#6711yescharacteristic
121C2×Dic6—32no—
122C2×Dic6—32no—
123C2×Dic6—62no—
124C2×Dic6—62no—
125C2×Dic6—61no—
126C2×Dic6—61no—
127C2×C3×C8—62no—
128C2×C3×C8—62no—
129C2×C3×C8—122no—
130C3×C42—21no—
131C3×C42—21no—
132C3×C42—21no—
133C3×C42—21no—
134C3×C42C4×D311yescharacteristic
135C3×C42C4×D311yescharacteristic
136C3×C42D1211yescharacteristic
137C3×C42D1211yescharacteristic
138C3×C42#6711yescharacteristic
139C3×C42#6711yescharacteristic
140C3×C42C22×D311yescharacteristic
141C3×C42C22×D311yescharacteristic
142#217—64no—
143#217—62no—
144#217—62no—
145C4⋊Dic3—32no—
146C4⋊Dic3—32no—
147C4⋊Dic3—62no—
148C4⋊Dic3—62no—
149C4⋊Dic3—62no—
150C4⋊Dic3—62no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157Dic3⋊C4—64no—
158Dic3⋊C4—64no—
159Dic3⋊C4—62no—
160Dic3⋊C4—62no—
161Dic3⋊C4—62no—
162Dic3⋊C4—62no—
163C4×Dic3—64no—
164C4×Dic3—62no—
165C4×Dic3—62no—
166C2×C3⋊C8—22no—
167C2×C3⋊C8—22no—
168C2×C3⋊C8—42no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32#10312yes—
172C22×C32C2×C22⋊C411yescharacteristic
173C32×C4—21no—
174C32×C4—21no—
175C32×C4—21no—
176C32×C4#10312yes—
177C32×C4#13112yes—
178C32×C4C2×SD1611yescharacteristic
179C32×C4C2×Q1611yescharacteristic
180C3⋊Dic3—42no—
181C3⋊Dic3—42no—
182C22×C8—61no—
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×C42D3211yescharacteristic
192C4⋊C8—32no—
193C4⋊C8—61no—
194C4⋊C8—61no—
195C22⋊C8—61no—
196C4×C8—32no—
197C23×C3—21no—
198C23×C3(C2×D3)⋊C411yescharacteristic
199C23×C3(C2×D3)⋊C411yescharacteristic
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—42no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—42no—
214C2×C3×C4#20412yes—
215C2×C3×C4Dic1212yes—
216C2×C3×C4(C2×D3)⋊C411yescharacteristic
217C2×C3×C4(C2×D3)⋊C411yescharacteristic
218C2×C3×C4(C2×D3)⋊C411yescharacteristic
219C2×C3×C4(C2×D3)⋊C411yescharacteristic
220C2×C3×C4(C2×D3)⋊C411yescharacteristic
221C2×C3×C4(C2×D3)⋊C411yescharacteristic
222C2×C3×C4#21412yes—
223C2×C3×C4#21612yes—
224C2×C3×C4C2×C4×D311yescharacteristic
225C2×C3×C4C2×C4×D311yescharacteristic
226C2×C3×C4C2×D1211yescharacteristic
227C2×C3×C4C2×D1211yescharacteristic
228C2×C3×C4C2×#6711yescharacteristic
229C2×C3×C4C2×#6711yescharacteristic
230C2×Dic3—64no—
231C2×Dic3—64no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236Dic6—64no—
237Dic6—64no—
238Dic6—124no—
239Dic6—124no—
240Dic6—122no—
241Dic6—122no—
242C3×C8—122no—
243C3×C8—122no—
244C3⋊C8—42no—
245C3⋊C8—42no—
246C2×C32—22no—
247C2×C32#40811yescharacteristic
248C2×C32C2×#10311yescharacteristic
249C2×C32#42111yescharacteristic
250C2×Q8—92no—
251C2×Q8—181no—
252C22×C4#62411yescharacteristic
253C22×C4#62611yescharacteristic
254C22×C4#62611yescharacteristic
255C2×C8—62no—
256C2×C8—62no—
257C2×C8—122no—
258C4⋊C4—92no—
259C4⋊C4—181no—
260C4⋊C4—181no—
261C4⋊C4—182no—
262C4⋊C4—181no—
263C4⋊C4—182no—
264C22⋊C4—182no—
265C42—182no—
266C42#62411yescharacteristic
267C42#62611yescharacteristic
268C42#62611yescharacteristic
269C42C2×D3211yescharacteristic
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—22no—
275C22×C3—21no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3#81012yes—
279C22×C3#81612yes—
280C22×C3C2×(C2×D3)⋊C411yescharacteristic
281C22×C3C2×(C2×D3)⋊C411yescharacteristic
282C3×C4—22no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4#81012yes—
296C3×C4#81612yes—
297C3×C4#90112yes—
298C3×C4C2×#20411yescharacteristic
299C3×C4C2×Dic1211yescharacteristic
300C3×C4#90712yes—
301C3×C4C2×#21411yescharacteristic
302C3×C4C2×#21611yescharacteristic
303Dic3—124no—
304Dic3—124no—
305Dic3—122no—
306Dic3—122no—
307Dic3—122no—
308Dic3—122no—
309C32#148111yescharacteristic, complemented, Sylow
310C23#372211yescharacteristic
311Q8—184no—
312Q8—362no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—182no—
316C2×C4—182no—
317C2×C4#371612yes—
318C2×C4#371912yes—
319C2×C4#372211yescharacteristic
320C2×C4#372211yescharacteristic
321C2×C4#372211yescharacteristic
322C2×C4C2×#62411yescharacteristic
323C2×C4C2×#62611yescharacteristic
324C2×C4C2×#62611yescharacteristic
325C8—122no—
326C8—122no—
327C2×C3—22no—
328C2×C3—22no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—42no—
333C2×C3C2×#81011yescharacteristic
334C2×C3#500511yescharacteristic
335C2×C3C2×#81611yescharacteristic
336C2×C3#511011yescharacteristic
337C2×C3#512911yescharacteristic
338C2×C3#513911yescharacteristic
339C22—21no—
340C22—21no—
341C22#6356712yes—
342C22C2×#372211yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—362no—
347C4—362no—
348C4#6356712yes—
349C4#6381712yes—
350C4C2×#371611yescharacteristic
351C4C2×#371911yescharacteristic
352C3—21no—
353C3#7042911yescharacteristic, complemented
354C3#7076811yescharacteristic, complemented
355C2—22no—
356C2#1059107311yescharacteristic
357C2C2×#6356711yescharacteristic
358C2#1059111311yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1481
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10589085C2semidirect
309. C32#1481semidirect
353. C3#70429semidirect
354. C3#70768semidirect

Maximal subgroups

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

subgroupindex
#105959412
C3×#49252
C2×C3×C4⋊(C3⋊C8)2
#105890852
#707683
#704293