Finite Group Databasebeta

← C2×#88962 #11724434

Subgroups — C2×#88962 #11724434

Order 864.

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

normal subgroups only

This group has 850 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×#6292C211yesmaximal, characteristic, complemented
3C2×#6291C211yesmaximal, characteristic, complemented
4C2×#6289C211yesmaximal, characteristic, complemented
5C2×C3×#627C211yesmaximal, characteristic, complemented
6C2×C3×#626C211yesmaximal, characteristic, complemented
7C2×C3×D3×Dic3C211yesmaximal, characteristic, complemented
8#88962C218yesmaximal, direct product factor
9C2×#3804—31nomaximal
10C2×#3799—31nomaximal
11C2×#3796—31nomaximal
12C22×C3⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×C3⋊D3C2211yescharacteristic
14C22×C32×D3C2211yescharacteristic
15C2×C3×C3⋊Dic3C2211yescharacteristic
16C2×C3×C3⋊Dic3C2211yescharacteristic
17C2×C32×Dic3C2211yescharacteristic
18C2×C32×Dic3C2211yescharacteristic
19#6294C2214yescomplemented
20#6292C2214yescomplemented
21#6291C2214yescomplemented
22#6289C2214yescomplemented
23C3×#627C2214yescomplemented
24C3×#626C2214yescomplemented
25C3×D3×Dic3C2214yescomplemented
26C2×#638—31no—
27C2×C4⋊(C3⋊D3)—31no—
28C2×C4×C3⋊D3—31no—
29C2×C3×#67—31no—
30C22×C3×Dic3—31no—
31C2×C3×D12—31no—
32C2×C3×C4×D3—31no—
33C2×C3×Dic6—31no—
34C2×C3×Dic6—31no—
35C2×#627D311yescharacteristic, complemented
36C2×#626—31no—
37C2×#626—31no—
38C2×#626—31no—
39C2×#626—31no—
40C2×#626—61no—
41C2×#626—61no—
42C2×#626D311yescharacteristic, complemented
43C2×#624—31no—
44C2×#624—31no—
45C2×#624—31no—
46C2×#624—61no—
47#3804—38no—
48C2×D3×Dic3—31no—
49C2×D3×Dic3—31no—
50C2×D3×Dic3D311yescharacteristic, complemented
51#3799—38no—
52#3796—38no—
53C22×C33C2311yescharacteristic
54C2×C3⋊(C3⋊D3)—22no—
55C2×C3⋊(C3⋊D3)C2312yes—
56C2×C3×C3⋊D3—22no—
57C2×C3×C3⋊D3C2312yes—
58C2×C32×D3—22no—
59C2×C32×D3C2312yes—
60C3×C3⋊Dic3C2312yes—
61C3×C3⋊Dic3C2312yes—
62C32×Dic3C2312yes—
63C32×Dic3C2312yes—
64C2×#239—91no—
65C2×#237—91no—
66C2×#235—91no—
67C23×C32—31no—
68C22×C3⋊D3—31no—
69C22×C3⋊D3—31no—
70C22×C3⋊D3—31no—
71C22×C3⋊D3—61no—
72C22×C3⋊D3—61no—
73C22×C3⋊D3—61no—
74C22×C3⋊D3—121no—
75C22×C3⋊D3C2×D311yescharacteristic
76C22×C3×D3—21no—
77C22×C3×D3—31no—
78C22×C3×D3—31no—
79C22×C3×D3—61no—
80C22×C3×D3C2×D311yescharacteristic
81C22×C3×D3C2×D311yescharacteristic
82C2×C32×C4—31no—
83C2×C32×C4—31no—
84#638—34no—
85C2×C3⋊Dic3C2×D311yescharacteristic
86C2×C3⋊Dic3C2×D311yescharacteristic
87C4⋊(C3⋊D3)—34no—
88C4×C3⋊D3—34no—
89C3×#67—34no—
90C2×C3×Dic3—21no—
91C2×C3×Dic3—21no—
92C2×C3×Dic3—31no—
93C2×C3×Dic3—31no—
94C2×C3×Dic3—31no—
95C2×C3×Dic3—31no—
96C2×C3×Dic3—34no—
97C2×C3×Dic3—61no—
98C2×C3×Dic3—61no—
99C2×C3×Dic3C2×D311yescharacteristic
100C2×C3×Dic3C2×D311yescharacteristic
101C2×C3×Dic3C2×D311yescharacteristic
102C2×C3×Dic3C2×D311yescharacteristic
103C3×D12—34no—
104C3×C4×D3—34no—
105C3×Dic6—34no—
106C3×Dic6—34no—
107#627C2×D314yescomplemented
108#626—34no—
109#626—34no—
110#626—34no—
111#626—34no—
112#626—64no—
113#626—64no—
114#626C2×D314yescomplemented
115#624—34no—
116#624—34no—
117#624—34no—
118#624—64no—
119D3×Dic3—34no—
120D3×Dic3—34no—
121D3×Dic3C2×D314yescomplemented
122C2×C33#4112yescomplemented
123C2×C33C2411yescharacteristic
124C3⋊(C3⋊D3)—22no—
125C3×C3⋊D3—22no—
126C32×D3—22no—
127C2×C3×Q8—91no—
128C2×C3×D4—91no—
129C22×C3×C4—91no—
130C2×#67—31no—
131C2×#67—91no—
132C2×#67—91no—
133C2×#67—91no—
134C2×#67—181no—
135C22×Dic3—31no—
136C22×Dic3—91no—
137#239—98no—
138#237—98no—
139#235—98no—
140C2×D12—31no—
141C2×D12—91no—
142C2×D12—91no—
143C2×D12—91no—
144C2×D12—181no—
145C2×C4×D3—31no—
146C2×C4×D3—91no—
147C2×C4×D3—91no—
148C2×C4×D3—91no—
149C2×C4×D3—91no—
150C2×C4×D3—91no—
151C2×C4×D3—181no—
152C2×Dic6—31no—
153C2×Dic6—31no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32—21no—
157C22×C32—32no—
158C22×C32—41no—
159C22×C32—62no—
160C22×C32C22×D311yescharacteristic
161C22×C32C22×D311yescharacteristic
162C22×C32C22×D311yescharacteristic
163C2×C3⋊D3—22no—
164C2×C3⋊D3—32no—
165C2×C3⋊D3—32no—
166C2×C3⋊D3—32no—
167C2×C3⋊D3—62no—
168C2×C3⋊D3—62no—
169C2×C3⋊D3—62no—
170C2×C3⋊D3—62no—
171C2×C3⋊D3—64no—
172C2×C3⋊D3—62no—
173C2×C3⋊D3—62no—
174C2×C3⋊D3—122no—
175C2×C3⋊D3—122no—
176C2×C3⋊D3—122no—
177C2×C3⋊D3—124no—
178C2×C3⋊D3C22×D312yes—
179C2×C3×D3—22no—
180C2×C3×D3—22no—
181C2×C3×D3—22no—
182C2×C3×D3—32no—
183C2×C3×D3—32no—
184C2×C3×D3—42no—
185C2×C3×D3—62no—
186C2×C3×D3—62no—
187C2×C3×D3—62no—
188C2×C3×D3—122no—
189C2×C3×D3C22×D312yes—
190C2×C3×D3C22×D312yes—
191C32×C4—32no—
192C32×C4—32no—
193C3⋊Dic3C22×D312yes—
194C3⋊Dic3C22×D312yes—
195C3×Dic3—22no—
196C3×Dic3—22no—
197C3×Dic3—32no—
198C3×Dic3—32no—
199C3×Dic3—32no—
200C3×Dic3—32no—
201C3×Dic3—62no—
202C3×Dic3—62no—
203C3×Dic3C22×D312yes—
204C3×Dic3C22×D312yes—
205C3×Dic3C22×D312yes—
206C3×Dic3C22×D312yes—
207C2×#41—271noSylow
208C33C2×#4111yescharacteristic, complemented, Sylow
209C23×C3—31no—
210C23×C3—31no—
211C23×C3—61no—
212C23×C3—91no—
213C22×D3—31no—
214C22×D3—31no—
215C22×D3—61no—
216C22×D3—91no—
217C22×D3—91no—
218C22×D3—91no—
219C22×D3—181no—
220C22×D3—181no—
221C22×D3—181no—
222C22×D3—361no—
223C22×D3D3211yescharacteristic
224C3×Q8—94no—
225C3×D4—94no—
226C2×C3×C4—31no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—31no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—94no—
233C2×C3×C4—91no—
234C2×C3×C4—91no—
235#67—34no—
236#67—94no—
237#67—94no—
238#67—94no—
239#67—184no—
240C2×Dic3—31no—
241C2×Dic3—31no—
242C2×Dic3—31no—
243C2×Dic3—31no—
244C2×Dic3—34no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—94no—
248C2×Dic3D3211yescharacteristic
249C2×Dic3D3211yescharacteristic
250D12—34no—
251D12—94no—
252D12—94no—
253D12—94no—
254D12—184no—
255C4×D3—34no—
256C4×D3—94no—
257C4×D3—94no—
258C4×D3—94no—
259C4×D3—94no—
260C4×D3—94no—
261C4×D3—184no—
262Dic6—34no—
263Dic6—34no—
264C2×C32—21no—
265C2×C32—21no—
266C2×C32—21no—
267C2×C32—22no—
268C2×C32—22no—
269C2×C32—22no—
270C2×C32—42no—
271C2×C32—41no—
272C2×C32—62no—
273C2×C32#23512yescomplemented
274C2×C32#23712yescomplemented
275C2×C32#23912yescomplemented
276C2×C32C23×D311yescharacteristic
277C2×C32C23×D311yescharacteristic
278C2×C32C23×D311yescharacteristic
279C3⋊D3—22no—
280C3⋊D3—62no—
281C3⋊D3—64no—
282C3⋊D3—62no—
283C3⋊D3—62no—
284C3⋊D3—122no—
285C3⋊D3—122no—
286C3⋊D3—124no—
287C3×D3—22no—
288C3×D3—22no—
289C3×D3—42no—
290C3×D3—62no—
291C3×D3—62no—
292C3×D3—122no—
293#41—278no—
294C2×Q8—91no—
295C2×D4—91no—
296C2×D4—271no—
297C2×D4—271no—
298C22×C4—91no—
299C22×C4—271no—
300C22×C4—271no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—32no—
305C22×C3—32no—
306C22×C3—41no—
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—32no—
318C2×D3—32no—
319C2×D3—62no—
320C2×D3—62no—
321C2×D3—62no—
322C2×D3—92no—
323C2×D3—92no—
324C2×D3—92no—
325C2×D3—122no—
326C2×D3—182no—
327C2×D3—182no—
328C2×D3—182no—
329C2×D3—184no—
330C2×D3—182no—
331C2×D3—182no—
332C2×D3—182no—
333C2×D3—362no—
334C2×D3—362no—
335C2×D3—362no—
336C2×D3—364no—
337C2×D3C2×D3212yes—
338C3×C4—32no—
339C3×C4—32no—
340C3×C4—32no—
341C3×C4—32no—
342C3×C4—62no—
343C3×C4—62no—
344C3×C4—92no—
345C3×C4—92no—
346Dic3—32no—
347Dic3—32no—
348Dic3—32no—
349Dic3—32no—
350Dic3—62no—
351Dic3—62no—
352Dic3C2×D3212yes—
353Dic3C2×D3212yes—
354C32—21no—
355C32—21no—
356C32—21no—
357C32—41no—
358C32C2×#23511yescharacteristic, complemented
359C32C2×#23711yescharacteristic, complemented
360C32C2×#23911yescharacteristic, complemented
361C23—31no—
362C23—91no—
363C23—271no—
364Q8—94no—
365D4—94no—
366D4—274no—
367D4—274no—
368C2×C4—31no—
369C2×C4—31no—
370C2×C4—94no—
371C2×C4—91no—
372C2×C4—91no—
373C2×C4—274no—
374C2×C4—274no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—22no—
379C2×C3—22no—
380C2×C3—22no—
381C2×C3—41no—
382C2×C3—42no—
383C2×C3—62no—
384C2×C3—62no—
385C2×C3—122no—
386C2×C3—182no—
387C2×C3#379612yescomplemented
388C2×C3#379912yescomplemented
389C2×C3#380412yescomplemented
390C2×C3C22×D3211yescharacteristic
391C2×C3C22×D3211yescharacteristic
392C2×C3C22×D3211yescharacteristic
393D3—22no—
394D3—62no—
395D3—62no—
396D3—122no—
397D3—184no—
398D3—182no—
399D3—182no—
400D3—182no—
401D3—362no—
402D3—362no—
403D3—364no—
404C22—32no—
405C22—62no—
406C22—92no—
407C22—182no—
408C22—272no—
409C22—542no—
410C22D3311yescharacteristic
411C4—32no—
412C4—32no—
413C4—92no—
414C4—92no—
415C3—21no—
416C3—21no—
417C3—21no—
418C3—41no—
419C3C2×#379611yescharacteristic, complemented
420C3C2×#379911yescharacteristic, complemented
421C3C2×#380411yescharacteristic, complemented
422C2—62no—
423C2—182no—
424C2—542no—
425C2#8896212yesdirect product factor
426C2C2×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×#6292C2semidirect
3. C2×#6291C2semidirect
4. C2×#6289C2semidirect
5. C2×C3×#627C2semidirect
6. C2×C3×#626C2semidirect
7. C2×C3×D3×Dic3C2semidirect
8. #88962C2direct (N × H)
19. #6294C22semidirect
20. #6292C22semidirect
21. #6291C22semidirect
22. #6289C22semidirect
23. C3×#627C22semidirect
24. C3×#626C22semidirect
25. C3×D3×Dic3C22semidirect
35. C2×#627D3semidirect
42. C2×#626D3semidirect
50. C2×D3×Dic3D3semidirect
107. #627C2×D3semidirect
114. #626C2×D3semidirect
121. D3×Dic3C2×D3semidirect
122. C2×C33#41semidirect
208. C33C2×#41semidirect
273. C2×C32#235semidirect
274. C2×C32#237semidirect
275. C2×C32#239semidirect
358. C32C2×#235semidirect
359. C32C2×#237semidirect
360. C32C2×#239semidirect
387. C2×C3#3796semidirect
388. C2×C3#3799semidirect
389. C2×C3#3804semidirect
419. C3C2×#3796semidirect
420. C3C2×#3799semidirect
421. C3C2×#3804semidirect
425. C2#88962direct (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×#62922
C2×#62912
C2×#62892
C2×C3×#6272
C2×C3×#6262
C2×C3×D3×Dic32
#889622
C2×#38043
C2×#37993
C2×#37963