Finite Group Databasebeta

← #11791666

Subgroups — #11791666

Order 1152.

633 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64079C211yesmaximal, characteristic
2C3×C4×C4⋊Dic3C211yesmaximal, characteristic
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
4#10589164C212yesmaximal
5#10589164C212yesmaximal
6#70461—31nomaximal
7#69491—31nomaximal
8C2×C32×C42C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×#3750—21no—
12C2×#3750—21no—
13#64079—22no—
14#64079C414yescomplemented
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×C4×Dic3—21no—
17C22×C3×C3⋊C8C2212yes—
18C3×C3⋊#95—21no—
19C3×C4⋊(C3⋊C8)—22no—
20C2×#870—31no—
21C2×#870—31no—
22C2×#870—61no—
23C2×C3×C4⋊C8—31no—
24C3×C4×C4⋊C4—31no—
25C4×C4⋊Dic3D311yescharacteristic
26C2×C4⋊(C3⋊C8)D311yescharacteristic
27#4551—32no—
28#4551—32no—
29#4529—32no—
30#4529—32no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—21no—
36C22×C3×Dic3—22no—
37C32×C42C2×C412yes—
38C32×C42D412yes—
39C4⋊(C3⋊Dic3)—21no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)C2×C412yes—
42C4⋊(C3⋊Dic3)C2×C412yes—
43#3750—24no—
44#3750—24no—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3Q814yes—
47C3×C4×Dic3—42no—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—24no—
50#1989—91noSylow
51C22×C3×C8—32no—
52C2×C3×C4⋊C4—32no—
53C2×C3×C42—21no—
54C2×C3×C42—61no—
55C2×C3×C42C2×D311yescharacteristic
56C2×C3×C42C2×D311yescharacteristic
57C2×C4⋊Dic3—31no—
58C2×C4⋊Dic3—31no—
59C2×C4⋊Dic3—31no—
60C2×C4⋊Dic3—31no—
61C2×C4⋊Dic3—61no—
62C2×C4⋊Dic3—61no—
63C2×C4⋊Dic3C2×D312yes—
64C2×Dic3⋊C4—62no—
65C2×Dic3⋊C4—62no—
66C2×Dic3⋊C4—61no—
67C2×Dic3⋊C4—61no—
68C2×Dic3⋊C4—61no—
69C2×Dic3⋊C4—61no—
70C2×C4×Dic3—21no—
71C22×C3⋊C8C2×D312yes—
72#870—34no—
73#870—34no—
74#870—64no—
75#870—64no—
76#870—62no—
77#870—62no—
78C3×C4⋊C8—62no—
79C3×#95—61no—
80C3⋊#95—21no—
81C4⋊(C3⋊C8)—22no—
82C23×C32C2×D411yescharacteristic
83C2×C32×C4—22no—
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4C22⋊C412yes—
87C2×C32×C4C22⋊C412yes—
88C2×C32×C4C22×C411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×Q812yes—
91C2×C32×C4#4112yes—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—42no—
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3—41no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—42no—
99C2×C3×Dic3—42no—
100C3×C3⋊C8—42no—
101C2×#125—91no—
102C2×C4⋊C8—31no—
103C4×C4⋊C4—31no—
104#340—92no—
105#340—92no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4—21no—
109C22×C3×C4—62no—
110C22×C3×C4D1211yescharacteristic
111C22×C3×C4D1211yescharacteristic
112C22×C3×C4#6711yescharacteristic
113C22×C3×C4#6711yescharacteristic
114C22×C3×C4C22×D311yescharacteristic
115C22×C3×C4C22×D311yescharacteristic
116C22×Dic3—22no—
117C22×Dic3—62no—
118C22×Dic3—62no—
119C22×Dic3—61no—
120C22×Dic3—61no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C2×C3×C8—62no—
124C2×C3×C8—64no—
125C3×C4⋊C4—34no—
126C3×C4⋊C4—62no—
127C3×C42—22no—
128C3×C42—22no—
129C3×C42—122no—
130C3×C42C4×D312yes—
131C3×C42C4×D312yes—
132C3×C42D1212yes—
133C3×C42#6712yes—
134C4⋊Dic3—22no—
135C4⋊Dic3—32no—
136C4⋊Dic3—32no—
137C4⋊Dic3—32no—
138C4⋊Dic3—32no—
139C4⋊Dic3—62no—
140C4⋊Dic3—62no—
141C4⋊Dic3—62no—
142C4⋊Dic3—62no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3Dic614yes—
148Dic3⋊C4—68no—
149Dic3⋊C4—68no—
150Dic3⋊C4—64no—
151Dic3⋊C4—64no—
152Dic3⋊C4—64no—
153Dic3⋊C4—64no—
154C4×Dic3—42no—
155C2×C3⋊C8—24no—
156C2×C3⋊C8—22no—
157C22×C32C2×C22⋊C411yescharacteristic
158C22×C32C22⋊Q812yes—
159C22×C32#13512yes—
160C22×C32AGL(1,ℤ/8)11yescharacteristic
161C22×C32#13711yescharacteristic
162C32×C4—22no—
163C32×C4—22no—
164C32×C4C4×Q812yes—
165C32×C4#12411yescharacteristic
166C32×C4C4⋊Q811yescharacteristic
167C3⋊Dic3—42no—
168C3⋊Dic3—42no—
169C3×Dic3—44no—
170C22×C8—32no—
171#125—94no—
172#125—182no—
173C2×C4⋊C4—32no—
174C2×C4⋊C4—91no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—181no—
177C2×C4⋊C4—181no—
178C2×C42—61no—
179C2×C42D3211yescharacteristic
180C4⋊C8—62no—
181#95—61no—
182C23×C3—21no—
183C23×C3C2×D1211yescharacteristic
184C23×C3C2×#6711yescharacteristic
185C2×C3×C4—22no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—42no—
198C2×C3×C4—41no—
199C2×C3×C4—41no—
200C2×C3×C4—64no—
201C2×C3×C4—122no—
202C2×C3×C4—122no—
203C2×C3×C4(C2×D3)⋊C412yes—
204C2×C3×C4(C2×D3)⋊C412yes—
205C2×C3×C4(C2×D3)⋊C412yes—
206C2×C3×C4(C2×D3)⋊C412yes—
207C2×C3×C4C2×Dic612yes—
208C2×C3×C4C2×C4×D311yescharacteristic
209C2×C3×C4C2×C4×D311yescharacteristic
210C2×C3×C4C2×D1211yescharacteristic
211C2×C3×C4#23512yes—
212C2×C3×C4#23712yes—
213C2×C3×C4D3×Q812yes—
214C2×C3×C4C2×#6711yescharacteristic
215C2×Dic3—24no—
216C2×Dic3—42no—
217C2×Dic3—42no—
218C2×Dic3—64no—
219C2×Dic3—64no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—124no—
225C2×Dic3—122no—
226C2×Dic3—122no—
227C2×Dic3—122no—
228C2×Dic3—121no—
229C2×Dic3—121no—
230C2×Dic3—121no—
231C2×Dic3—121no—
232C2×Dic3—122no—
233C3×C8—122no—
234C3⋊C8—42no—
235C2×C32#39111yescharacteristic
236C2×C32#41611yescharacteristic
237C2×C32#41711yescharacteristic
238C2×C32#47812yes—
239C2×C32#47912yes—
240C22×C4—62no—
241C22×C4—181no—
242C22×C4—181no—
243C22×C4#62611yescharacteristic
244C22×C4#62611yescharacteristic
245C22×C4C2×D3211yescharacteristic
246C2×C8—64no—
247C2×C8—62no—
248C4⋊C4—34no—
249C4⋊C4—62no—
250C4⋊C4—92no—
251C4⋊C4—92no—
252C4⋊C4—184no—
253C4⋊C4—184no—
254C4⋊C4—181no—
255C4⋊C4—181no—
256C42—122no—
257C42#62412yes—
258C42#62612yes—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—21no—
264C22×C3#89712yes—
265C22×C3#90412yes—
266C22×C3#90811yescharacteristic
267C22×C3#90911yescharacteristic
268C22×C3#92412yes—
269C22×C3C2×(C2×D3)⋊C411yescharacteristic
270C22×C3C2×(C2×D3)⋊C411yescharacteristic
271C22×C3#93211yescharacteristic
272C22×C3#94211yescharacteristic
273C22×C3#95012yes—
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—42no—
282C3×C4—42no—
283C3×C4—124no—
284C3×C4C4×Dic612yes—
285C3×C4#86911yescharacteristic
286C3×C4#87511yescharacteristic
287C3×C4#88712yes—
288C3×C4#93611yescharacteristic
289C3×C4#94411yescharacteristic
290Dic3—44no—
291Dic3—124no—
292Dic3—124no—
293Dic3—122no—
294Dic3—122no—
295Dic3—122no—
296Dic3—122no—
297C32#198911yescharacteristic, complemented, Sylow
298C23C2×#62611yescharacteristic
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—64no—
303C2×C4—122no—
304C2×C4—122no—
305C2×C4—182no—
306C2×C4—182no—
307C2×C4—362no—
308C2×C4—361no—
309C2×C4—361no—
310C2×C4#372212yes—
311C2×C4#372212yes—
312C2×C4D3×Dic612yes—
313C2×C4#379512yes—
314C2×C4C2×#62411yescharacteristic
315C2×C4C2×#62611yescharacteristic
316C8—122no—
317C2×C3—22no—
318C2×C3—22no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3#482912yes—
323C2×C3#484712yes—
324C2×C3#492911yescharacteristic
325C2×C3#496611yescharacteristic
326C2×C3#497311yescharacteristic
327C2×C3#500211yescharacteristic
328C2×C3#500912yes—
329C2×C3#502212yes—
330C2×C3#511311yescharacteristic
331C2×C3#513311yescharacteristic
332C22#6382912yes—
333C22#6383011yescharacteristic
334C22#6383311yescharacteristic
335C22#6385712yes—
336C22C2×#372211yescharacteristic
337C4—22no—
338C4—22no—
339C4—124no—
340C4—362no—
341C4—362no—
342C4#6384412yes—
343C4#6386011yescharacteristic
344C4#6386611yescharacteristic
345C3—21no—
346C3#6949111yescharacteristic, complemented
347C3#7046111yescharacteristic, complemented
348C2#1059027112yes—
349C2#1059030212yes—
350C2#1059110511yescharacteristic
351C2#1059110611yescharacteristic
352C2#1059121311yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1989
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
14. #64079C4semidirect
297. C32#1989semidirect
346. C3#69491semidirect
347. C3#70461semidirect

Maximal subgroups

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

subgroupindex
C2×#640792
C3×C4×C4⋊Dic32
C2×C3×C4⋊(C3⋊C8)2
#105891642
#704613
#694913