Finite Group Databasebeta

← C2×#88961 #11724433

Subgroups — C2×#88961 #11724433

Order 864.

818 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 156 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×#6294C211yesmaximal, characteristic, complemented
2C2×#6293C211yesmaximal, characteristic, complemented
3C2×#6290C211yesmaximal, characteristic, complemented
4C2×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C3×#626C211yesmaximal, characteristic, complemented
6C2×C3×#625C211yesmaximal, characteristic, complemented
7C2×C3×D3×Dic3C211yesmaximal, characteristic, complemented
8#88961C218yesmaximal, direct product factor
9C2×#3805—31nomaximal
10C2×#3804—31nomaximal
11C2×#3795—31nomaximal
12C22×C3×C3⋊D3C2211yescharacteristic
13C22×C32×D3C2211yescharacteristic
14C22×C32×D3C2211yescharacteristic
15C2×C3⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C3⋊Dic3C2211yescharacteristic
17C2×C3×C3⋊Dic3C2211yescharacteristic
18C2×C32×Dic3C2211yescharacteristic
19#6294C2214yescomplemented
20#6293C2214yescomplemented
21#6290C2214yescomplemented
22D3×C3⋊Dic3C2214yescomplemented
23C3×#626C2214yescomplemented
24C3×#625C2214yescomplemented
25C3×D3×Dic3C2214yescomplemented
26C2×#638—31no—
27C22×C3⋊Dic3—31no—
28C2×#634—31no—
29C2×C3×#67—31no—
30C2×C3×#67—31no—
31C2×C3×#67—31no—
32C22×C3×Dic3—31no—
33C2×C3×D12—31no—
34C2×C3×C4×D3—31no—
35C2×#627—31no—
36C2×#627—31no—
37C2×#627—61no—
38C2×#626D311yescharacteristic, complemented
39C2×#625—31no—
40C2×#625—31no—
41C2×#625—61no—
42C2×#625D311yescharacteristic, complemented
43C2×#624—31no—
44#3805—38no—
45#3804—38no—
46C2×D3×Dic3—31no—
47C2×D3×Dic3—31no—
48C2×D3×Dic3—31no—
49C2×D3×Dic3—31no—
50C2×D3×Dic3—61no—
51C2×D3×Dic3D311yescharacteristic, complemented
52#3795—38no—
53C22×C33C2311yescharacteristic
54C2×C3×C3⋊D3—22no—
55C2×C3×C3⋊D3C2312yes—
56C2×C32×D3—22no—
57C2×C32×D3—22no—
58C2×C32×D3C2312yes—
59C2×C32×D3C2312yes—
60C3⋊(C3⋊Dic3)C2312yes—
61C3×C3⋊Dic3C2312yes—
62C3×C3⋊Dic3C2312yes—
63C32×Dic3C2312yes—
64C2×#237—91no—
65C2×#237—91no—
66C2×#235—91no—
67C23×C32—31no—
68C23×C32—31no—
69C22×C3⋊D3C2×D311yescharacteristic
70C22×C3×D3—21no—
71C22×C3×D3—21no—
72C22×C3×D3—31no—
73C22×C3×D3—31no—
74C22×C3×D3—61no—
75C22×C3×D3C2×D311yescharacteristic
76C22×C3×D3C2×D311yescharacteristic
77C22×C3×D3C2×D311yescharacteristic
78C22×C3×D3C2×D311yescharacteristic
79C2×C32×C4—31no—
80#638—34no—
81C2×C3⋊Dic3—31no—
82C2×C3⋊Dic3—31no—
83C2×C3⋊Dic3—31no—
84C2×C3⋊Dic3—34no—
85C2×C3⋊Dic3—61no—
86C2×C3⋊Dic3—61no—
87C2×C3⋊Dic3—61no—
88C2×C3⋊Dic3—121no—
89C2×C3⋊Dic3C2×D311yescharacteristic
90C2×C3⋊Dic3C2×D311yescharacteristic
91#634—34no—
92C3×#67—34no—
93C3×#67—34no—
94C3×#67—34no—
95C2×C3×Dic3—21no—
96C2×C3×Dic3—31no—
97C2×C3×Dic3—31no—
98C2×C3×Dic3—31no—
99C2×C3×Dic3—31no—
100C2×C3×Dic3—34no—
101C2×C3×Dic3—61no—
102C2×C3×Dic3—61no—
103C2×C3×Dic3C2×D311yescharacteristic
104C2×C3×Dic3C2×D311yescharacteristic
105C3×D12—34no—
106C3×C4×D3—34no—
107#627—34no—
108#627—34no—
109#627—64no—
110#626C2×D314yescomplemented
111#625—34no—
112#625—34no—
113#625—64no—
114#625C2×D314yescomplemented
115#624—34no—
116D3×Dic3—34no—
117D3×Dic3—34no—
118D3×Dic3—34no—
119D3×Dic3—34no—
120D3×Dic3—64no—
121D3×Dic3C2×D314yescomplemented
122C2×C33#4112yescomplemented
123C2×C33C2411yescharacteristic
124C3×C3⋊D3—22no—
125C32×D3—22no—
126C32×D3—22no—
127C2×C3×D4—91no—
128C2×C3×D4—91no—
129C22×C3×C4—91no—
130C2×#67—31no—
131C2×#67—31no—
132C2×#67—31no—
133C2×#67—91no—
134C2×#67—91no—
135C2×#67—91no—
136C2×#67—181no—
137C22×Dic3—31no—
138C22×Dic3—91no—
139C22×Dic3—91no—
140C22×Dic3—91no—
141C22×Dic3—181no—
142#237—98no—
143#237—98no—
144#235—98no—
145C2×D12—31no—
146C2×C4×D3—31no—
147C2×C4×D3—91no—
148C2×C4×D3—91no—
149C2×C4×D3—91no—
150C2×Dic6—91no—
151C2×Dic6—91no—
152C2×Dic6—91no—
153C2×Dic6—181no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32—21no—
157C22×C32—32no—
158C22×C32—32no—
159C22×C32—41no—
160C22×C32—62no—
161C22×C32—62no—
162C22×C32C22×D311yescharacteristic
163C22×C32C22×D311yescharacteristic
164C22×C32C22×D311yescharacteristic
165C2×C3⋊D3—22no—
166C2×C3⋊D3C22×D312yes—
167C2×C3×D3—24no—
168C2×C3×D3—22no—
169C2×C3×D3—22no—
170C2×C3×D3—22no—
171C2×C3×D3—22no—
172C2×C3×D3—22no—
173C2×C3×D3—22no—
174C2×C3×D3—32no—
175C2×C3×D3—32no—
176C2×C3×D3—42no—
177C2×C3×D3—62no—
178C2×C3×D3—62no—
179C2×C3×D3—62no—
180C2×C3×D3—122no—
181C2×C3×D3C22×D312yes—
182C2×C3×D3C22×D312yes—
183C2×C3×D3C22×D312yes—
184C2×C3×D3C22×D312yes—
185C32×C4—32no—
186C3⋊Dic3—32no—
187C3⋊Dic3—32no—
188C3⋊Dic3—32no—
189C3⋊Dic3—62no—
190C3⋊Dic3—62no—
191C3⋊Dic3—62no—
192C3⋊Dic3—122no—
193C3⋊Dic3C22×D312yes—
194C3⋊Dic3C22×D312yes—
195C3×Dic3—22no—
196C3×Dic3—32no—
197C3×Dic3—32no—
198C3×Dic3—32no—
199C3×Dic3—32no—
200C3×Dic3—62no—
201C3×Dic3—62no—
202C3×Dic3C22×D312yes—
203C3×Dic3C22×D312yes—
204C2×#41—271noSylow
205C33C2×#4111yescharacteristic, complemented, Sylow
206C23×C3—31no—
207C23×C3—31no—
208C23×C3—31no—
209C23×C3—31no—
210C23×C3—61no—
211C23×C3—61no—
212C23×C3—91no—
213C22×D3—31no—
214C22×D3—31no—
215C22×D3—61no—
216C22×D3D3211yescharacteristic
217C22×D3D3211yescharacteristic
218C3×D4—94no—
219C3×D4—94no—
220C2×C3×C4—31no—
221C2×C3×C4—31no—
222C2×C3×C4—61no—
223C2×C3×C4—94no—
224C2×C3×C4—91no—
225C2×C3×C4—91no—
226#67—34no—
227#67—34no—
228#67—34no—
229#67—94no—
230#67—94no—
231#67—94no—
232#67—184no—
233C2×Dic3—31no—
234C2×Dic3—31no—
235C2×Dic3—31no—
236C2×Dic3—31no—
237C2×Dic3—34no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—94no—
241C2×Dic3—94no—
242C2×Dic3—94no—
243C2×Dic3—91no—
244C2×Dic3—91no—
245C2×Dic3—91no—
246C2×Dic3—184no—
247C2×Dic3—181no—
248C2×Dic3—181no—
249C2×Dic3—181no—
250C2×Dic3—361no—
251C2×Dic3D3211yescharacteristic
252D12—34no—
253C4×D3—34no—
254C4×D3—94no—
255C4×D3—94no—
256C4×D3—94no—
257Dic6—94no—
258Dic6—94no—
259Dic6—94no—
260Dic6—184no—
261C2×C32—21no—
262C2×C32—21no—
263C2×C32—21no—
264C2×C32—22no—
265C2×C32—22no—
266C2×C32—22no—
267C2×C32—42no—
268C2×C32—41no—
269C2×C32—62no—
270C2×C32—62no—
271C2×C32#23512yescomplemented
272C2×C32#23712yescomplemented
273C2×C32#23712yescomplemented
274C2×C32C23×D311yescharacteristic
275C2×C32C23×D311yescharacteristic
276C2×C32C23×D311yescharacteristic
277C3⋊D3—22no—
278C3×D3—24no—
279C3×D3—22no—
280C3×D3—22no—
281C3×D3—22no—
282C3×D3—22no—
283C3×D3—42no—
284C3×D3—62no—
285C3×D3—62no—
286C3×D3—122no—
287#41—278no—
288C2×Q8—271no—
289C2×D4—91no—
290C2×D4—91no—
291C2×D4—271no—
292C22×C4—91no—
293C22×C4—271no—
294C22×C4—271no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—32no—
299C22×C3—32no—
300C22×C3—32no—
301C22×C3—32no—
302C22×C3—41no—
303C22×C3—62no—
304C22×C3—62no—
305C22×C3—64no—
306C22×C3—62no—
307C22×C3—62no—
308C22×C3—62no—
309C22×C3—62no—
310C22×C3—92no—
311C22×C3—122no—
312C22×C3—182no—
313C22×C3C2×D3211yescharacteristic
314C22×C3C2×D3211yescharacteristic
315C22×C3C2×D3211yescharacteristic
316C2×D3—22no—
317C2×D3—22no—
318C2×D3—32no—
319C2×D3—32no—
320C2×D3—62no—
321C2×D3—62no—
322C2×D3—62no—
323C2×D3—122no—
324C2×D3C2×D3212yes—
325C2×D3C2×D3212yes—
326C3×C4—32no—
327C3×C4—32no—
328C3×C4—62no—
329C3×C4—92no—
330C3×C4—92no—
331Dic3—32no—
332Dic3—32no—
333Dic3—32no—
334Dic3—32no—
335Dic3—62no—
336Dic3—62no—
337Dic3—92no—
338Dic3—92no—
339Dic3—92no—
340Dic3—182no—
341Dic3—182no—
342Dic3—182no—
343Dic3—362no—
344Dic3C2×D3212yes—
345C32—21no—
346C32—21no—
347C32—21no—
348C32—41no—
349C32C2×#23511yescharacteristic, complemented
350C32C2×#23711yescharacteristic, complemented
351C32C2×#23711yescharacteristic, complemented
352C23—31no—
353C23—31no—
354C23—91no—
355Q8—274no—
356D4—94no—
357D4—94no—
358D4—274no—
359C2×C4—31no—
360C2×C4—94no—
361C2×C4—91no—
362C2×C4—91no—
363C2×C4—274no—
364C2×C4—274no—
365C2×C4—271no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—22no—
370C2×C3—22no—
371C2×C3—22no—
372C2×C3—41no—
373C2×C3—42no—
374C2×C3—64no—
375C2×C3—62no—
376C2×C3—62no—
377C2×C3—62no—
378C2×C3—62no—
379C2×C3—122no—
380C2×C3—182no—
381C2×C3#379512yescomplemented
382C2×C3#380412yescomplemented
383C2×C3#380512yescomplemented
384C2×C3C22×D3211yescharacteristic
385C2×C3C22×D3211yescharacteristic
386C2×C3C22×D3211yescharacteristic
387D3—22no—
388D3—22no—
389D3—62no—
390D3—62no—
391D3—122no—
392C22—32no—
393C22—32no—
394C22—62no—
395C22—62no—
396C22—92no—
397C22—182no—
398C22D3311yescharacteristic
399C4—32no—
400C4—92no—
401C4—92no—
402C4—272no—
403C3—21no—
404C3—21no—
405C3—21no—
406C3—41no—
407C3C2×#379511yescharacteristic, complemented
408C3C2×#380411yescharacteristic, complemented
409C3C2×#380511yescharacteristic, complemented
410C2—62no—
411C2—62no—
412C2—182no—
413C2#8896112yesdirect product factor
414C2C2×D3311yescharacteristic
subgroupG/H
center, hypercenterC22D33
commutator, cosocleC2×C33C24
FrattiniC2C2×D33
Fitting, socleC22×C33C23
hypocenterC33C2×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#6294C2semidirect
2. C2×#6293C2semidirect
3. C2×#6290C2semidirect
4. C2×D3×C3⋊Dic3C2semidirect
5. C2×C3×#626C2semidirect
6. C2×C3×#625C2semidirect
7. C2×C3×D3×Dic3C2semidirect
8. #88961C2direct (N × H)
19. #6294C22semidirect
20. #6293C22semidirect
21. #6290C22semidirect
22. D3×C3⋊Dic3C22semidirect
23. C3×#626C22semidirect
24. C3×#625C22semidirect
25. C3×D3×Dic3C22semidirect
38. C2×#626D3semidirect
42. C2×#625D3semidirect
51. C2×D3×Dic3D3semidirect
110. #626C2×D3semidirect
114. #625C2×D3semidirect
121. D3×Dic3C2×D3semidirect
122. C2×C33#41semidirect
205. C33C2×#41semidirect
271. C2×C32#235semidirect
272. C2×C32#237semidirect
273. C2×C32#237semidirect
349. C32C2×#235semidirect
350. C32C2×#237semidirect
351. C32C2×#237semidirect
381. C2×C3#3795semidirect
382. C2×C3#3804semidirect
383. C2×C3#3805semidirect
407. C3C2×#3795semidirect
408. C3C2×#3804semidirect
409. C3C2×#3805semidirect
413. C2#88961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#62942
C2×#62932
C2×#62902
C2×D3×C3⋊Dic32
C2×C3×#6262
C2×C3×#6252
C2×C3×D3×Dic32
#889612
C2×#38053
C2×#38043
C2×#37953