Finite Group Databasebeta

← #11784047

Subgroups — #11784047

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C3×C4×C4⋊Dic3C211yesmaximal, characteristic
3C2×C3×#803C211yesmaximal, characteristic
4C2×#63567C212yesmaximal
5#10589164C212yesmaximal
6#69813—31nomaximal
7#69475—31nomaximal
8C22×#634C2211yescharacteristic
9C2×C32×C42C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×#3750—21no—
12C2×C4×C3⋊Dic3—21no—
13C4×#634—22no—
14C4×#634C414yescomplemented
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×C4×Dic3—21no—
17C22×C3×C3⋊C8C2212yes—
18C3×C3⋊#95—21no—
19C3×#803—22no—
20#63567C418yescomplemented
21C2×C4×Dic6—31no—
22C2×C4×Dic6—31no—
23C2×C4×Dic6—61no—
24C2×C3×#97—31no—
25C3×C4×C4⋊C4—31no—
26C2×#816—32no—
27C2×#810—32no—
28C4×C4⋊Dic3D311yescharacteristic
29C2×#803D311yescharacteristic
30#4551—32no—
31#4529—32no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C2×#634—21no—
38C2×#634—22no—
39C2×#634C2×C412yes—
40C2×#634C2×C414yes—
41C22×C3×Dic3—22no—
42C32×C42C2×C412yes—
43C32×C42D412yes—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)C2×C412yes—
46#3750—24no—
47C4×C3⋊Dic3—24no—
48C3×C4⋊Dic3—22no—
49C3×C4⋊Dic3C2×C414yes—
50C3×C4×Dic3—42no—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8C2×C414yes—
54#1763—91noSylow
55C22×Dic6—31no—
56C22×Dic6—31no—
57C22×Dic6—61no—
58C22×C3×C8—32no—
59C2×C3×C4⋊C4—32no—
60C2×C3×C42—21no—
61C2×C3×C42—61no—
62C2×C3×C42C2×D311yescharacteristic
63C2×C3×C42C2×D311yescharacteristic
64C2×C4⋊Dic3—31no—
65C2×C4⋊Dic3—31no—
66C2×C4⋊Dic3—61no—
67C2×C4⋊Dic3C2×D312yes—
68C2×Dic3⋊C4—62no—
69C2×Dic3⋊C4—61no—
70C2×Dic3⋊C4—61no—
71C2×C4×Dic3—21no—
72C2×C4×Dic3—62no—
73C2×C4×Dic3—61no—
74C2×C4×Dic3—61no—
75C22×C3⋊C8C2×D312yes—
76C4×Dic6—34no—
77C4×Dic6—34no—
78C4×Dic6—64no—
79C4×Dic6—64no—
80C4×Dic6—62no—
81C4×Dic6—62no—
82C3×#97—62no—
83C3×#95—61no—
84C3⋊#95—21no—
85#816—38no—
86#810—38no—
87#803—22no—
88C23×C32C2×D411yescharacteristic
89C2×C32×C4—22no—
90C2×C32×C4—21no—
91C2×C32×C4—21no—
92C2×C32×C4C22⋊C412yes—
93C2×C32×C4C22⋊C412yes—
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C22×C412yes—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4112yes—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—24no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103#634—22no—
104#634—24no—
105#634C4214yescomplemented
106C2×C3×Dic3—24no—
107C2×C3×Dic3—42no—
108C2×C3×Dic3—42no—
109C3×C3⋊C8—24no—
110C2×C4×Q8—91no—
111C2×#103—92no—
112C2×#97—31no—
113C4×C4⋊C4—31no—
114#340—92no—
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—
126C22×Dic3—62no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C22×Dic3—62no—
130C22×Dic3—61no—
131C22×Dic3—61no—
132C2×Dic6—34no—
133C2×Dic6—34no—
134C2×Dic6—32no—
135C2×Dic6—32no—
136C2×Dic6—62no—
137C2×Dic6—64no—
138C2×Dic6—62no—
139C2×Dic6—64no—
140C2×Dic6—61no—
141C2×Dic6—62no—
142C2×Dic6—62no—
143C2×Dic6—61no—
144C2×C3×C8—34no—
145C2×C3×C8—62no—
146C2×C3×C8—62no—
147C3×C4⋊C4—34no—
148C3×C4⋊C4—62no—
149C3×C42—22no—
150C3×C42—22no—
151C3×C42—122no—
152C3×C42C4×D312yes—
153C3×C42C4×D312yes—
154C3×C42D1212yes—
155C3×C42#6712yes—
156C4⋊Dic3—22no—
157C4⋊Dic3—32no—
158C4⋊Dic3—32no—
159C4⋊Dic3—62no—
160C4⋊Dic3—62no—
161C4⋊Dic3—61no—
162C4⋊Dic3—61no—
163C4⋊Dic3C4×D314yes—
164Dic3⋊C4—68no—
165Dic3⋊C4—64no—
166Dic3⋊C4—64no—
167C4×Dic3—42no—
168C4×Dic3—68no—
169C4×Dic3—64no—
170C4×Dic3—64no—
171C2×C3⋊C8—22no—
172C2×C3⋊C8—22no—
173C2×C3⋊C8C4×D314yes—
174C22×C32C2×C22⋊C411yescharacteristic
175C22×C32C4×D412yes—
176C22×C32AGL(1,ℤ/8)11yescharacteristic
177C22×C32#13711yescharacteristic
178C22×C32#13712yes—
179C32×C4—22no—
180C32×C4—22no—
181C32×C4C2×C4211yescharacteristic
182C32×C4#11711yescharacteristic
183C32×C4C4×D412yes—
184C3⋊Dic3—24no—
185C3⋊Dic3—42no—
186C3×Dic3—44no—
187C22×Q8—91no—
188C22×C8—32no—
189C4×Q8—94no—
190C4×Q8—182no—
191C2×C4⋊C4—32no—
192C2×C4⋊C4—91no—
193C2×C4⋊C4—181no—
194C2×C42—61no—
195C2×C42—181no—
196C2×C42D3211yescharacteristic
197#103—98no—
198#97—62no—
199#95—61no—
200C23×C3—21no—
201C23×C3C2×D1211yescharacteristic
202C23×C3C2×#6711yescharacteristic
203C2×C3×C4—24no—
204C2×C3×C4—21no—
205C2×C3×C4—22no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—64no—
219C2×C3×C4—122no—
220C2×C3×C4—122no—
221C2×C3×C4(C2×D3)⋊C412yes—
222C2×C3×C4(C2×D3)⋊C412yes—
223C2×C3×C4(C2×D3)⋊C412yes—
224C2×C3×C4(C2×D3)⋊C412yes—
225C2×C3×C4C2×C4×D312yes—
226C2×C3×C4C2×C4×D312yes—
227C2×C3×C4C2×C4×D311yescharacteristic
228C2×C3×C4C2×C4×D311yescharacteristic
229C2×C3×C4C2×D1211yescharacteristic
230C2×C3×C4#23512yes—
231C2×C3×C4#23512yes—
232C2×C3×C4C2×#6711yescharacteristic
233C2×Dic3—24no—
234C2×Dic3—42no—
235C2×Dic3—42no—
236C2×Dic3—64no—
237C2×Dic3—68no—
238C2×Dic3—64no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—122no—
246C2×Dic3—122no—
247C2×Dic3—121no—
248C2×Dic3—121no—
249C2×Dic3—121no—
250C2×Dic3—121no—
251Dic6—34no—
252Dic6—34no—
253Dic6—64no—
254Dic6—64no—
255Dic6—68no—
256Dic6—62no—
257Dic6—62no—
258Dic6—64no—
259Dic6—64no—
260C3×C8—64no—
261C3⋊C8—24no—
262C2×C32C4×C22⋊C411yescharacteristic
263C2×C32#41711yescharacteristic
264C2×C32#41911yescharacteristic
265C2×C32#44012yes—
266C2×C32#44112yes—
267C2×Q8—94no—
268C2×Q8—92no—
269C2×Q8—182no—
270C2×Q8—181no—
271C22×C4—62no—
272C22×C4—181no—
273C22×C4—181no—
274C22×C4#62611yescharacteristic
275C22×C4#62611yescharacteristic
276C22×C4C2×D3211yescharacteristic
277C2×C8—34no—
278C2×C8—62no—
279C2×C8—62no—
280C4⋊C4—34no—
281C4⋊C4—62no—
282C4⋊C4—92no—
283C4⋊C4—184no—
284C4⋊C4—181no—
285C42—122no—
286C42—184no—
287C42#62412yes—
288C42#62612yes—
289C22×C3—21no—
290C22×C3—22no—
291C22×C3—21no—
292C22×C3—22no—
293C22×C3—21no—
294C22×C3C4×D1212yes—
295C22×C3#90811yescharacteristic
296C22×C3#90912yes—
297C22×C3#90911yescharacteristic
298C22×C3C2×(C2×D3)⋊C411yescharacteristic
299C22×C3C2×(C2×D3)⋊C411yescharacteristic
300C22×C3C4×#6712yes—
301C22×C3#93211yescharacteristic
302C22×C3#94211yescharacteristic
303C22×C3#95112yes—
304C3×C4—24no—
305C3×C4—22no—
306C3×C4—22no—
307C3×C4—22no—
308C3×C4—22no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—22no—
312C3×C4—42no—
313C3×C4—124no—
314C3×C4C42×D311yescharacteristic
315C3×C4C42×D311yescharacteristic
316C3×C4#87211yescharacteristic
317C3×C4#87211yescharacteristic
318C3×C4C4×D1212yes—
319C3×C4C4×#6712yes—
320Dic3—44no—
321Dic3—68no—
322Dic3—64no—
323Dic3—64no—
324Dic3—124no—
325Dic3—122no—
326Dic3—122no—
327C32#176311yescharacteristic, complemented, Sylow
328C23C2×#62611yescharacteristic
329Q8—94no—
330Q8—182no—
331Q8—184no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—64no—
336C2×C4—122no—
337C2×C4—122no—
338C2×C4—184no—
339C2×C4—182no—
340C2×C4—182no—
341C2×C4—361no—
342C2×C4—361no—
343C2×C4#372212yes—
344C2×C4#372212yes—
345C2×C4#379812yes—
346C2×C4C4×D3212yes—
347C2×C4C2×#62411yescharacteristic
348C2×C4C2×#62611yescharacteristic
349C8—64no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—22no—
354C2×C3—22no—
355C2×C3#471012yes—
356C2×C3#471612yes—
357C2×C3C4×(C2×D3)⋊C411yescharacteristic
358C2×C3C4×(C2×D3)⋊C411yescharacteristic
359C2×C3#496611yescharacteristic
360C2×C3#500411yescharacteristic
361C2×C3#501812yes—
362C2×C3#503012yes—
363C2×C3#512011yescharacteristic
364C2×C3#513311yescharacteristic
365C22#6383011yescharacteristic
366C22#6383112yes—
367C22#6383311yescharacteristic
368C22C4×#62612yes—
369C22C2×#372211yescharacteristic
370C4—22no—
371C4—22no—
372C4—124no—
373C4—184no—
374C4—362no—
375C4#6387411yescharacteristic
376C4C4×#62411yescharacteristic
377C4C4×#62612yes—
378C3—21no—
379C3#6947511yescharacteristic, complemented
380C3#6981311yescharacteristic, complemented
381C2#1059036012yes—
382C2#1059038312yes—
383C2#1059110611yescharacteristic
384C2#1059110711yescharacteristic
385C2C4×#372211yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1763
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
14. C4×#634C4semidirect
20. #63567C4semidirect
105. #634C42semidirect
327. C32#1763semidirect
379. C3#69475semidirect
380. C3#69813semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C3×C4×C4⋊Dic32
C2×C3×#8032
C2×#635672
#105891642
#698133
#694753