Finite Group Databasebeta

← #11791497

Subgroups — #11791497

Order 1152.

853 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 853 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64156C211yesmaximal, characteristic
2C2×C3×#835C212yesmaximal, complemented
3#10591274C211yesmaximal, characteristic, complemented
4C2×#63572C211yesmaximal, characteristic, complemented
5C2×#63564C212yesmaximal
6#70230—32nomaximal
7C22×C32×Q8C2211yescharacteristic
8C22×C4⋊(C3⋊D3)C2211yescharacteristic
9#64156—22no—
10#64156C414yescomplemented
11C2×#3752—21no—
12C2×#3752—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×Dic32—21no—
17C3×#835—24no—
18#63579—21no—
19#63572—22no—
20#63564—24no—
21C2×#947—32no—
22C2×#947—61no—
23C2×C3×#103—32no—
24C2×#835D312yescomplemented
25C2×#821—32no—
26C2×Dic3⋊C8—32no—
27Dic3×C4⋊C4—32no—
28C2×#809—32no—
29C23×C3⋊D3—21no—
30C2×C32×Q8—21no—
31C2×C32×Q8—22no—
32C2×C32×Q8—22no—
33C2×C32×Q8C2×C412yes—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C2×C4⋊(C3⋊D3)—22no—
39C2×C4⋊(C3⋊D3)—22no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)C2×C412yes—
42C22×C3×Dic3—22no—
43#3752—24no—
44#3752—24no—
45C4×C3⋊Dic3C2×C412yes—
46C4×C3⋊Dic3D412yes—
47C3×C4⋊Dic3—22no—
48C3×C4⋊Dic3D414yes—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52Dic32—42no—
53#1983—91noSylow
54C22×C3×Q8—21no—
55C22×C3×Q8C2×D312yes—
56C22×D12—32no—
57C22×D12—61no—
58C22×C3×C8—32no—
59C2×C3×C4⋊C4—32no—
60#947—38no—
61#947—64no—
62#947—64no—
63#947—64no—
64C2×(C2×D3)⋊C4—62no—
65C2×(C2×D3)⋊C4—62no—
66C2×(C2×D3)⋊C4—62no—
67C2×(C2×D3)⋊C4—62no—
68C2×C4⋊Dic3C2×D312yes—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—61no—
71C2×C4×Dic3—62no—
72C22×C3⋊C8C2×D312yes—
73C3×#103—64no—
74#835—24no—
75C3⋊#95—62no—
76#821—64no—
77Dic3⋊C8—64no—
78#809—64no—
79C23×C32C2×D411yescharacteristic
80C22×C3⋊D3—22no—
81C22×C3⋊D3—42no—
82C22×C3⋊D3—42no—
83C22×C3⋊D3—41no—
84C22×C3⋊D3—41no—
85C32×Q8—24no—
86C32×Q8—41no—
87C32×Q8—41no—
88C2×C32×C4—22no—
89C2×C32×C4—42no—
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D412yes—
93C2×C32×C4#4112yes—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3C22⋊C412yes—
98C2×C3⋊Dic3C22⋊C412yes—
99C4⋊(C3⋊D3)—24no—
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—41no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—42no—
104C2×C3×Dic3—42no—
105C3×C3⋊C8—42no—
106C2×#124—91no—
107C2×C4⋊C8—91no—
108C2×#103—32no—
109C2×#102—92no—
110C4×C4⋊C4—91no—
111C23×D3—62no—
112C23×D3—62no—
113C2×C3×Q8—22no—
114C2×C3×Q8—22no—
115C2×C3×Q8—22no—
116C2×C3×Q8—22no—
117C2×C3×Q8—22no—
118C2×C3×Q8—22no—
119C2×C3×Q8—22no—
120C2×C3×Q8—42no—
121C2×C3×Q8—42no—
122C2×C3×Q8C4×D314yes—
123C22×C3×C4—22no—
124C22×C3×C4—22no—
125C22×C3×C4—21no—
126C22×C3×C4—62no—
127C22×C3×C4C22×D312yes—
128C22×Dic3—22no—
129C22×Dic3—32no—
130C22×Dic3—32no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C2×D12—34no—
134C2×D12—62no—
135C2×D12—62no—
136C2×D12—62no—
137C2×D12—62no—
138C2×D12—62no—
139C2×D12—62no—
140C2×D12—62no—
141C2×D12—122no—
142C2×D12—122no—
143C2×C3×C8—62no—
144C2×C3×C8—62no—
145C2×C3×C8—62no—
146C3×C4⋊C4—34no—
147C3×C4⋊C4—62no—
148(C2×D3)⋊C4—68no—
149(C2×D3)⋊C4—68no—
150(C2×D3)⋊C4—68no—
151(C2×D3)⋊C4—68no—
152C4⋊Dic3—22no—
153C4⋊Dic3#6714yes—
154C4×Dic3—34no—
155C4×Dic3—34no—
156C4×Dic3—62no—
157C4×Dic3—62no—
158C4×Dic3—124no—
159C2×C3⋊C8—22no—
160C2×C3⋊C8—22no—
161C2×C3⋊C8—22no—
162C22×C32C2×C22⋊C411yescharacteristic
163C22×C32#12112yes—
164C22×C32#13512yes—
165C22×C32AGL(1,ℤ/8)11yescharacteristic
166C22×C32#13711yescharacteristic
167C2×C3⋊D3—42no—
168C2×C3⋊D3—42no—
169C2×C3⋊D3—42no—
170C2×C3⋊D3—82no—
171C2×C3⋊D3—82no—
172C32×C4—42no—
173C32×C4C4×D412yes—
174C32×C4#12411yescharacteristic
175C32×C4#12711yescharacteristic
176C3⋊Dic3—22no—
177C3⋊Dic3—22no—
178C3×Dic3—44no—
179C22×Q8D3211yescharacteristic
180C22×D4—91no—
181C22×C8—32no—
182#124—94no—
183#124—182no—
184C2×C4⋊C4—32no—
185C2×C22⋊C4—181no—
186C2×C22⋊C4—181no—
187C2×C42—91no—
188C2×C42—181no—
189C4⋊C8—182no—
190#103—64no—
191#102—184no—
192#95—181no—
193C23×C3—21no—
194C23×C3D3×D412yes—
195C22×D3—64no—
196C22×D3—64no—
197C22×D3—124no—
198C22×D3—122no—
199C22×D3—122no—
200C22×D3—124no—
201C22×D3—122no—
202C22×D3—122no—
203C22×D3—122no—
204C22×D3—122no—
205C22×D3—122no—
206C22×D3—122no—
207C3×Q8—24no—
208C3×Q8—24no—
209C3×Q8—44no—
210C3×Q8—42no—
211C3×Q8—42no—
212C3×Q8—42no—
213C3×Q8—42no—
214C2×C3×C4—24no—
215C2×C3×C4—24no—
216C2×C3×C4—22no—
217C2×C3×C4—21no—
218C2×C3×C4—22no—
219C2×C3×C4—21no—
220C2×C3×C4—44no—
221C2×C3×C4—42no—
222C2×C3×C4—42no—
223C2×C3×C4—64no—
224C2×C3×C4—122no—
225C2×C3×C4—122no—
226C2×C3×C4C2×C4×D312yes—
227C2×C3×C4#23512yes—
228C2×C3×C4D3×D412yes—
229C2×C3×C4D3×D412yes—
230C2×C3×C4#23712yes—
231C2×C3×C4C2×#6712yes—
232C2×Dic3—24no—
233C2×Dic3—34no—
234C2×Dic3—34no—
235C2×Dic3—42no—
236C2×Dic3—42no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—121no—
244C2×Dic3—121no—
245C2×Dic3—122no—
246D12—64no—
247D12—64no—
248D12—124no—
249D12—122no—
250D12—122no—
251D12—122no—
252D12—122no—
253C3×C8—122no—
254C3⋊C8—42no—
255C2×C32#39011yescharacteristic
256C2×C32#41611yescharacteristic
257C2×C32#41711yescharacteristic
258C2×C32#46312yes—
259C2×C32#46412yes—
260C3⋊D3—82no—
261C24—181no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8#62412yes—
266C2×D4—92no—
267C2×D4—182no—
268C2×D4—182no—
269C2×D4—181no—
270C22×C4—21no—
271C22×C4—62no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4C2×D3211yescharacteristic
275C2×C8—62no—
276C2×C8—62no—
277C2×C8—62no—
278C4⋊C4—34no—
279C4⋊C4—62no—
280C22⋊C4—184no—
281C22⋊C4—184no—
282C42—92no—
283C42—92no—
284C42—362no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—21no—
290C22×C3D3×C22⋊C412yes—
291C22×C3#88412yes—
292C22×C3#91412yes—
293C22×C3#91612yes—
294C22×C3#91812yes—
295C22×C3#91912yes—
296C22×C3#93912yes—
297C2×D3—124no—
298C2×D3—124no—
299C2×D3—124no—
300C2×D3—124no—
301C2×D3—124no—
302C2×D3—124no—
303C2×D3—244no—
304C2×D3—244no—
305C2×D3—242no—
306C2×D3—242no—
307C2×D3—242no—
308C2×D3—242no—
309C3×C4—22no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—44no—
313C3×C4—44no—
314C3×C4—124no—
315C3×C4#67⋊C412yes—
316C3×C4#88512yes—
317C3×C4C4×#6712yes—
318C3×C4#94012yes—
319Dic3—44no—
320Dic3—64no—
321Dic3—64no—
322Dic3—122no—
323Dic3—122no—
324C32#198311yescharacteristic, complemented, Sylow
325C23—182no—
326C23—361no—
327C23—361no—
328C23—362no—
329C23—362no—
330C23#381111yescharacteristic
331Q8—24no—
332Q8—41no—
333Q8—41no—
334D4—184no—
335D4—361no—
336D4—361no—
337C2×C4—22no—
338C2×C4—42no—
339C2×C4—64no—
340C2×C4—92no—
341C2×C4—92no—
342C2×C4—122no—
343C2×C4—122no—
344C2×C4—181no—
345C2×C4—181no—
346C2×C4—182no—
347C2×C4#380412yes—
348C2×C4C2×#62411yescharacteristic
349C2×C4D3×#6712yes—
350C2×C4#381111yescharacteristic
351C8—122no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—22no—
355C2×C3—22no—
356C2×C3—21no—
357C2×C3#479812yes—
358C2×C3#480312yes—
359C2×C3#480412yes—
360C2×C3#481912yes—
361C2×C3#495712yes—
362C2×C3#516512yes—
363C2×C3#518512yes—
364D3—244no—
365D3—244no—
366C22—362no—
367C22—362no—
368C22—362no—
369C22—722no—
370C22—722no—
371C22#6394111yescharacteristic
372C22#6394511yescharacteristic
373C22#6395012yes—
374C22#6397112yes—
375C22#6397411yescharacteristic
376C4—42no—
377C4—124no—
378C4—182no—
379C4—182no—
380C4#6395212yes—
381C4#6395311yescharacteristic
382C4#6397911yescharacteristic
383C3—21no—
384C3#7023012yescomplemented
385C2—722no—
386C2#1059155411yescharacteristic
387C2#1059156011yescharacteristic
388C2#1059157012yes—
389C2#1059157912yes—
390C2#1059170411yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1983
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#835C2semidirect
3. #10591274C2semidirect
4. C2×#63572C2semidirect
10. #64156C4semidirect
24. C2×#835D3semidirect
324. C32#1983semidirect
384. 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×C3×#8352
#105912742
C2×#635722
C2×#635642
#702303