Finite Group Databasebeta

← #11791472

Subgroups — #11791472

Order 1152.

1032 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64156C211yesmaximal, characteristic
2C2×C32×#103C211yesmaximal, characteristic, complemented
3C2×#63662C211yesmaximal, characteristic, complemented
4C2×#63648C211yesmaximal, characteristic
5C2×#63641C211yesmaximal, characteristic, complemented
6C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63636C211yesmaximal, characteristic
8#70230—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13#64156—22no—
14#64156C414yescomplemented
15C2×#3752—21no—
16C2×#3752—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3—21no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C32×#103—22no—
22#63662—22no—
23#63658—21no—
24#63648—22no—
25#63641—22no—
26#63636—22no—
27C2×#947—34no—
28C2×C3×#103D314yescomplemented
29C2×#835—34no—
30C2×#821—34no—
31C2×Dic3⋊C8—34no—
32Dic3×C4⋊C4—34no—
33C2×#809—34no—
34C23×C3⋊D3—21no—
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8—21no—
39C2×C32×Q8—21no—
40C2×C32×Q8C2×C412yes—
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)C2×C412yes—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4D412yes—
58#3752—24no—
59#3752—24no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)D412yes—
62C4×C3⋊Dic3—42no—
63C4×C3⋊Dic3C2×C412yes—
64C4×C3⋊Dic3D412yes—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68#1983—91noSylow
69C22×C3×Q8C2×D314yes—
70C22×D12—34no—
71C22×C3×C8C2×D314yes—
72C2×C3×C4⋊C4C2×D314yes—
73#947—316no—
74#947—68no—
75C2×(C2×D3)⋊C4—64no—
76C2×(C2×D3)⋊C4—64no—
77C2×C4⋊Dic3—34no—
78C2×C4×Dic3—34no—
79C2×C4×Dic3—64no—
80C22×C3⋊C8—34no—
81C3×#103—28no—
82#835—68no—
83C3⋊#95—64no—
84#821—68no—
85Dic3⋊C8—68no—
86#809—68no—
87C23×C32C2×D411yescharacteristic
88C22×C3⋊D3—22no—
89C22×C3⋊D3—41no—
90C22×C3⋊D3—41no—
91C22×C3⋊D3—41no—
92C22×C3⋊D3—41no—
93C22×C3⋊D3—41no—
94C22×C3⋊D3—41no—
95C32×Q8—22no—
96C32×Q8—22no—
97C32×Q8—41no—
98C32×Q8—41no—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4—41no—
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—41no—
117C2×C3⋊Dic3—41no—
118C2×C3⋊Dic3C22⋊C412yes—
119C2×C3⋊Dic3C22⋊C412yes—
120C4⋊(C3⋊D3)—22no—
121C4⋊(C3⋊D3)—22no—
122C4⋊(C3⋊D3)—41no—
123C4⋊(C3⋊D3)—41no—
124C32×C8—41no—
125C3⋊(C3⋊C8)—41no—
126C2×#124—91no—
127C2×C4⋊C8—91no—
128C2×#103—91no—
129C2×#103C3⋊D311yescharacteristic, complemented
130C2×#102—91no—
131C2×#102—91no—
132C4×C4⋊C4—91no—
133C23×D3—64no—
134C2×C3×Q8—24no—
135C2×C3×Q8—24no—
136C2×C3×Q8—24no—
137C2×C3×Q8—24no—
138C2×C3×Q8—24no—
139C2×C3×Q8C4×D318yes—
140C22×C3×C4—24no—
141C22×C3×C4—24no—
142C22×C3×C4C22×D314yes—
143C22×Dic3—34no—
144C22×Dic3—34no—
145C22×Dic3—64no—
146C2×D12—38no—
147C2×D12—64no—
148C2×D12—64no—
149C2×D12—64no—
150C2×D12—64no—
151C2×D12—64no—
152C2×C3×C8—24no—
153C2×C3×C8—24no—
154C2×C3×C8—24no—
155C3×C4⋊C4—24no—
156C3×C4⋊C4#6718yes—
157(C2×D3)⋊C4—616no—
158(C2×D3)⋊C4—616no—
159C4⋊Dic3—38no—
160C4⋊Dic3—64no—
161C4×Dic3—38no—
162C4×Dic3—38no—
163C4×Dic3—128no—
164C2×C3⋊C8—64no—
165C2×C3⋊C8—64no—
166C2×C3⋊C8—64no—
167C22×C32C2×C22⋊C411yescharacteristic
168C22×C32#12111yescharacteristic
169C22×C32#12111yescharacteristic
170C22×C32#13511yescharacteristic
171C22×C32#13511yescharacteristic
172C22×C32AGL(1,ℤ/8)11yescharacteristic
173C22×C32#13711yescharacteristic
174C2×C3⋊D3—42no—
175C2×C3⋊D3—42no—
176C2×C3⋊D3—42no—
177C2×C3⋊D3—81no—
178C2×C3⋊D3—81no—
179C2×C3⋊D3—81no—
180C2×C3⋊D3—81no—
181C32×C4—42no—
182C32×C4—42no—
183C32×C4C4×D411yescharacteristic
184C32×C4C4×D411yescharacteristic
185C32×C4#12411yescharacteristic
186C32×C4#12711yescharacteristic
187C3⋊Dic3—22no—
188C3⋊Dic3—22no—
189C3⋊Dic3—42no—
190C22×Q8C2×C3⋊D311yescharacteristic
191C22×D4—91no—
192C22×C8—91no—
193C22×C8C2×C3⋊D311yescharacteristic
194#124—94no—
195#124—182no—
196C2×C4⋊C4—91no—
197C2×C4⋊C4C2×C3⋊D311yescharacteristic
198C2×C22⋊C4—181no—
199C2×C22⋊C4—181no—
200C2×C42—91no—
201C2×C42—181no—
202C4⋊C8—182no—
203#103—22no—
204#103—182no—
205#102—182no—
206#102—182no—
207#95—181no—
208C23×C3D3×D414yes—
209C22×D3—68no—
210C22×D3—124no—
211C22×D3—124no—
212C22×D3—124no—
213C22×D3—124no—
214C22×D3—124no—
215C22×D3—124no—
216C3×Q8—28no—
217C3×Q8—28no—
218C3×Q8—44no—
219C3×Q8—44no—
220C2×C3×C4—28no—
221C2×C3×C4—28no—
222C2×C3×C4—44no—
223C2×C3×C4—44no—
224C2×C3×C4—44no—
225C2×C3×C4—44no—
226C2×C3×C4C2×C4×D314yes—
227C2×C3×C4#23514yes—
228C2×C3×C4D3×D414yes—
229C2×C3×C4D3×D414yes—
230C2×C3×C4#23714yes—
231C2×C3×C4C2×#6714yes—
232C2×Dic3—38no—
233C2×Dic3—38no—
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—64no—
237C2×Dic3—64no—
238C2×Dic3—68no—
239C2×Dic3—124no—
240C2×Dic3—124no—
241D12—68no—
242D12—68no—
243D12—124no—
244D12—124no—
245C3×C8—44no—
246C3⋊C8—124no—
247C2×C32#39011yescharacteristic
248C2×C32#41611yescharacteristic
249C2×C32#41711yescharacteristic
250C2×C32#46311yescharacteristic
251C2×C32#46311yescharacteristic
252C2×C32#46411yescharacteristic
253C2×C32#46411yescharacteristic
254C3⋊D3—82no—
255C24—181no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8C4×C3⋊D312yes—
262C2×D4—92no—
263C2×D4—181no—
264C2×D4—181no—
265C2×D4—181no—
266C2×D4—181no—
267C2×D4—181no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—91no—
271C22×C4—91no—
272C22×C4—181no—
273C22×C4C22×C3⋊D311yescharacteristic
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—181no—
278C2×C8—181no—
279C2×C8—181no—
280C4⋊C4—21no—
281C4⋊C4—92no—
282C4⋊C4—181no—
283C4⋊C4#63812yes—
284C22⋊C4—184no—
285C22⋊C4—184no—
286C42—92no—
287C42—92no—
288C42—362no—
289C22×C3D3×C22⋊C414yes—
290C22×C3#88414yes—
291C22×C3#91414yes—
292C22×C3#91614yes—
293C22×C3#91814yes—
294C22×C3#91914yes—
295C22×C3#93914yes—
296C2×D3—128no—
297C2×D3—128no—
298C2×D3—128no—
299C2×D3—244no—
300C2×D3—244no—
301C2×D3—244no—
302C2×D3—244no—
303C3×C4—48no—
304C3×C4—48no—
305C3×C4#67⋊C414yes—
306C3×C4#88514yes—
307C3×C4C4×#6714yes—
308C3×C4#94014yes—
309Dic3—68no—
310Dic3—68no—
311Dic3—128no—
312C32#198311yescharacteristic, complemented, Sylow
313C23—182no—
314C23—361no—
315C23—361no—
316C23—361no—
317C23—361no—
318C23—361no—
319C23—361no—
320C23D4×C3⋊D311yescharacteristic
321Q8—22no—
322Q8—22no—
323Q8—41no—
324Q8—41no—
325D4—182no—
326D4—182no—
327D4—361no—
328D4—361no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—92no—
336C2×C4—92no—
337C2×C4—181no—
338C2×C4—181no—
339C2×C4—181no—
340C2×C4—181no—
341C2×C4—182no—
342C2×C4—361no—
343C2×C4—361no—
344C2×C4C2×C4×C3⋊D311yescharacteristic
345C2×C4#382811yescharacteristic
346C2×C4D4×C3⋊D311yescharacteristic
347C2×C4D4×C3⋊D311yescharacteristic
348C2×C4#383011yescharacteristic
349C2×C4C2×#63811yescharacteristic
350C8—41no—
351C8—361no—
352C2×C3#479814yes—
353C2×C3#480314yes—
354C2×C3#480414yes—
355C2×C3#481914yes—
356C2×C3#495714yes—
357C2×C3#516514yes—
358C2×C3#518514yes—
359D3—248no—
360C22—362no—
361C22—362no—
362C22—362no—
363C22—721no—
364C22—721no—
365C22—721no—
366C22—721no—
367C22C22⋊C4×C3⋊D311yescharacteristic
368C22#6409311yescharacteristic
369C22#6412311yescharacteristic
370C22#6412511yescharacteristic
371C22#6412711yescharacteristic
372C22#6412811yescharacteristic
373C22#6414811yescharacteristic
374C4—42no—
375C4—42no—
376C4—182no—
377C4—182no—
378C4—362no—
379C4#6409011yescharacteristic
380C4#6409411yescharacteristic
381C4C4×#63811yescharacteristic
382C4#6414911yescharacteristic
383C3#7023014yescomplemented
384C2—722no—
385C2#1059249711yescharacteristic
386C2#1059250211yescharacteristic
387C2#1059250311yescharacteristic
388C2#1059251811yescharacteristic
389C2#1059265611yescharacteristic
390C2#1059286411yescharacteristic
391C2#1059288411yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×#103C3⋊D3
hypocenterC32#1983
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×C32×#103C2semidirect
3. C2×#63662C2semidirect
5. C2×#63641C2semidirect
6. C4⋊C4×C3⋊Dic3C2semidirect
14. #64156C4semidirect
28. C2×C3×#103D3semidirect
129. C2×#103C3⋊D3semidirect
312. C32#1983semidirect
383. C3#70230semidirect

Maximal subgroups

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

subgroupindex
C2×#641562
C2×C32×#1032
C2×#636622
C2×#636482
C2×#636412
C4⋊C4×C3⋊Dic32
C2×#636362
#702303