Finite Group Databasebeta

← #11790793

Subgroups — #11790793

Order 1152.

875 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 875 conjugacy classes of subgroups — too many to draw. Only its 136 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
1#10596303C211yesmaximal, characteristic
2C2×C3×#837C212yesmaximal, complemented
3C4×Dic32C211yesmaximal, characteristic, complemented
4#10591120C211yesmaximal, characteristic, complemented
5C2×#63570C212yesmaximal, complemented
6#70356—32nomaximal
7C2×C32×#41C2211yescharacteristic
8C2×#3828C2211yescharacteristic
9#64156C411yescharacteristic, complemented
10#64153C411yescharacteristic, complemented
11#64149C411yescharacteristic, complemented
12#64148—22no—
13#64145C411yescharacteristic, complemented
14C4×#638—22no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2212yes—
17C2×C3×#208C2212yes—
18C2×Dic32—22no—
19C3×#837—24no—
20#63572—22no—
21#63570—24no—
22#5832—32no—
23#5832—61no—
24C2×C3×#104—32no—
25C2×#837D312yescomplemented
26C2×#825—32no—
27#5118—32no—
28C42×Dic3—32no—
29C2×#805—32no—
30C32×#41—22no—
31C32×#41—22no—
32C2×C32×Q8C2×C411yescharacteristic
33C2×C32×D4—21no—
34C2×C32×D4C2×C411yescharacteristic
35C22×C32×C4—21no—
36C22×C32×C4C2311yescharacteristic
37C2×#638—21no—
38C2×#638—22no—
39C22×C3⋊Dic3D412yes—
40#3828—22no—
41#3828—22no—
42C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×#634C2×C411yescharacteristic
45C22×C3×Dic3—22no—
46#3757—22no—
47#3752—22no—
48#3750—22no—
49C4×C3⋊Dic3C2×C411yescharacteristic
50C4×C3⋊Dic3C2×C411yescharacteristic
51C4×C3⋊Dic3D412yes—
52C3×C4×Dic3—22no—
53C3×C4×Dic3D414yescomplemented
54C3×#208—22no—
55C3×#208—22no—
56C2×C3×C3⋊C8—22no—
57Dic32—28no—
58#1962—91noSylow
59C2×C3×#41—21no—
60C2×C3×#41C2×D312yes—
61C2×#235—32no—
62C2×#235—61no—
63C2×C3×M16—32no—
64C2×C3×C42—32no—
65#947—32no—
66#947—61no—
67#944—32no—
68#944—61no—
69#940—32no—
70#940—61no—
71#939—64no—
72#939—64no—
73#936—32no—
74#936—61no—
75C4×#67—64no—
76C4×#67—64no—
77C2×C4×Dic3—32no—
78C2×C4×Dic3—61no—
79C2×C4×Dic3—64no—
80C2×C4×Dic3C2×D312yes—
81C2×#208C2×D312yes—
82C3×#104—64no—
83#837—24no—
84#825—64no—
85Dic3⋊C8—64no—
86#805—64no—
87C23×C32—21no—
88C23×C32C2×D411yescharacteristic
89C22×C3⋊D3—21no—
90C32×Q8—22no—
91C32×D4—22no—
92C32×D4—42no—
93C2×C32×C4—21no—
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D412yes—
99C2×C32×C4#4112yes—
100#638—42no—
101#638—44no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—24no—
104C2×C3⋊Dic3C22⋊C412yes—
105C2×C3⋊Dic3C22⋊C412yes—
106C4⋊(C3⋊D3)—22no—
107C4×C3⋊D3—41no—
108C4×C3⋊D3—41no—
109#634—22no—
110C2×C3×Dic3—28no—
111C2×C3×Dic3—24no—
112C3×C3⋊C8—42no—
113#532—91no—
114#423—91no—
115C2×#104—32no—
116C2×#104—92no—
117C43—91no—
118C3×#41—22no—
119C3×#41—22no—
120C3×#41—22no—
121C3×#41—22no—
122C3×#41—42no—
123C3×#41—42no—
124C2×C3×Q8—21no—
125C2×C3×Q8C4×D312yes—
126C2×C3×D4—22no—
127C2×C3×D4—22no—
128C2×C3×D4—21no—
129C2×C3×D4C4×D312yes—
130C22×C3×C4—22no—
131C22×C3×C4—22no—
132C22×C3×C4—21no—
133C22×C3×C4—62no—
134C22×C3×C4C22×D312yes—
135C2×#67—64no—
136C2×#67—64no—
137C2×#67—62no—
138C2×#67—62no—
139C22×Dic3—22no—
140C22×Dic3—34no—
141C22×Dic3—62no—
142#235—62no—
143#235—62no—
144#235—62no—
145#235—62no—
146#235—122no—
147#235—122no—
148C2×D12—32no—
149C2×D12—61no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×Dic6—32no—
153C2×Dic6—61no—
154C3×M16—62no—
155C3×M16—62no—
156C2×C3×C8—62no—
157C3×C42—34no—
158C3×C42—62no—
159#217—64no—
160#217—64no—
161(C2×D3)⋊C4—64no—
162(C2×D3)⋊C4—64no—
163Dic3⋊C4—64no—
164Dic3⋊C4—64no—
165C4×Dic3—22no—
166C4×Dic3—32no—
167C4×Dic3—32no—
168C4×Dic3—34no—
169C4×Dic3—62no—
170C4×Dic3—61no—
171C4×Dic3—61no—
172C4×Dic3—616no—
173C4×Dic3#6714yescomplemented
174#208—22no—
175#208—22no—
176C2×C3⋊C8—22no—
177C22×C32—22no—
178C22×C32—41no—
179C22×C32—42no—
180C22×C32C2×C22⋊C411yescharacteristic
181C22×C32#12112yes—
182C2×C3⋊D3—41no—
183C2×C3⋊D3—42no—
184C32×C4—41no—
185C32×C4C4×D412yes—
186C32×C4#12411yescharacteristic
187C32×C4#12711yescharacteristic
188C3⋊Dic3—22no—
189C3⋊Dic3—41no—
190C3⋊Dic3#10414yescomplemented
191C3×Dic3—28no—
192C2×#41—91no—
193C2×#41D3211yescharacteristic
194C2×M16—32no—
195C4⋊Q8—91no—
196#127—91no—
197#124—91no—
198#124—91no—
199#121—182no—
200C4×D4—182no—
201C2×C42—32no—
202C2×C42—91no—
203C2×C42—182no—
204C4⋊C8—182no—
205#104—64no—
206#104—184no—
207C23×C3—22no—
208C23×C3—22no—
209C23×C3—21no—
210C23×C3D3×D412yes—
211C22×D3—62no—
212C22×D3—62no—
213C3×Q8—22no—
214C3×Q8—22no—
215C3×Q8—42no—
216C3×D4—22no—
217C3×D4—22no—
218C3×D4—42no—
219C3×D4—44no—
220C3×D4—42no—
221C3×D4—42no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—21no—
226C2×C3×C4—22no—
227C2×C3×C4—21no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—42no—
231C2×C3×C4—42no—
232C2×C3×C4—68no—
233C2×C3×C4—64no—
234C2×C3×C4C2×C4×D312yes—
235C2×C3×C4#23512yes—
236C2×C3×C4D3×D412yes—
237C2×C3×C4D3×D412yes—
238C2×C3×C4#23712yes—
239C2×C3×C4C2×#6712yes—
240#67—128no—
241#67—128no—
242#67—124no—
243#67—122no—
244#67—122no—
245C2×Dic3—28no—
246C2×Dic3—24no—
247C2×Dic3—34no—
248C2×Dic3—34no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C2×Dic3—68no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—124no—
255D12—62no—
256D12—62no—
257D12—122no—
258C4×D3—122no—
259C4×D3—122no—
260C4×D3—122no—
261C4×D3—122no—
262Dic6—62no—
263Dic6—62no—
264Dic6—122no—
265C3×C8—122no—
266C3⋊C8—42no—
267C2×C32—22no—
268C2×C32—81no—
269C2×C32#39011yescharacteristic
270C2×C32C2×#10412yes—
271C3⋊D3—81no—
272#41—22no—
273#41—22no—
274#41—182no—
275#41—182no—
276C2×Q8—91no—
277C2×Q8#62411yescharacteristic
278C2×D4—21no—
279C2×D4—91no—
280C2×D4—182no—
281C2×D4—181no—
282C2×D4#62411yescharacteristic
283C22×C4—21no—
284C22×C4—62no—
285C22×C4—92no—
286C22×C4—181no—
287C22×C4C2×D3211yescharacteristic
288M16—62no—
289M16—62no—
290C2×C8—62no—
291C4⋊C4—182no—
292C22⋊C4—182no—
293C22⋊C4—182no—
294C42—34no—
295C42—62no—
296C42—91no—
297C42—91no—
298C42—92no—
299C42—188no—
300C22×C3—24no—
301C22×C3—22no—
302C22×C3—21no—
303C22×C3—42no—
304C22×C3—44no—
305C22×C3—42no—
306C22×C3—42no—
307C22×C3—44no—
308C22×C3D3×C22⋊C412yes—
309C22×C3#88412yes—
310C22×C3#93912yes—
311C2×D3—122no—
312C2×D3—124no—
313C2×D3—122no—
314C2×D3—124no—
315C3×C4—22no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—42no—
319C3×C4—42no—
320C3×C4—68no—
321C3×C4#67⋊C412yes—
322C3×C4#88512yes—
323C3×C4C4×#6712yes—
324C3×C4#94012yes—
325Dic3—28no—
326Dic3—38no—
327Dic3—64no—
328Dic3—64no—
329Dic3—122no—
330Dic3—122no—
331Dic3—122no—
332C32#196211yescharacteristic, complemented, Sylow
333C23—21no—
334C23—181no—
335C23#381111yescharacteristic
336Q8—22no—
337Q8—182no—
338D4—22no—
339D4—42no—
340D4—182no—
341D4—364no—
342D4—362no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—68no—
347C2×C4—64no—
348C2×C4—92no—
349C2×C4—92no—
350C2×C4—184no—
351C2×C4—181no—
352C2×C4—361no—
353C2×C4—361no—
354C2×C4#380412yes—
355C2×C4C2×#62411yescharacteristic
356C2×C4D3×#6712yes—
357C2×C4#381111yescharacteristic
358C8—122no—
359C2×C3—22no—
360C2×C3—22no—
361C2×C3—22no—
362C2×C3—21no—
363C2×C3—42no—
364C2×C3—82no—
365C2×C3—82no—
366C2×C3D3×#10414yes—
367C2×C3#495712yes—
368D3—242no—
369D3—242no—
370C22—22no—
371C22—42no—
372C22—41no—
373C22—362no—
374C22—361no—
375C22#6397112yes—
376C22#6397411yescharacteristic
377C4—41no—
378C4—68no—
379C4—94no—
380C4—182no—
381C4—361no—
382C4#6395212yes—
383C4#6395311yescharacteristic
384C4#6397911yescharacteristic
385C3—21no—
386C3#7035612yescomplemented
387C2—22no—
388C2—81no—
389C2—721no—
390C2#1059167112yes—
391C2#1059170411yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32C2×C22⋊C4
prime radical#10596303C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1962
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#837C2semidirect
3. C4×Dic32C2semidirect
4. #10591120C2semidirect
5. C2×#63570C2semidirect
9. #64156C4semidirect
10. #64153C4semidirect
11. #64149C4semidirect
13. #64145C4semidirect
25. C2×#837D3semidirect
53. C3×C4×Dic3D4semidirect
173. C4×Dic3#67semidirect
190. C3⋊Dic3#104semidirect
332. C32#1962semidirect
386. C3#70356semidirect

Maximal subgroups

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

subgroupindex
#105963032
C2×C3×#8372
C4×Dic322
#105911202
C2×#635702
#703563