Finite Group Databasebeta

← C2×#10590519 #11869522

Subgroups — C2×#10590519 #11869522

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic
2C2×#63856C211yesmaximal, characteristic
3C2×#63635C211yesmaximal, characteristic, complemented
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
8#10590519C218yesmaximal, direct product factor
9C2×#4996—31nomaximal
10C2×#4814—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3—21no—
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#892—22no—
21C3×#892C2214yes—
22C2×#3724—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63856—22no—
25#63856C2214yes—
26#63635C2214yescomplemented
27C3×#810C2214yescomplemented
28#63575C2214yescomplemented
29#63565C2214yescomplemented
30(C2×D3)⋊(C3⋊C8)C2214yes—
31C2×C3×#117—31no—
32C2×#946—31no—
33C2×#924—31no—
34C2×#892D311yescharacteristic
35C2×C3×#103—31no—
36C2×#835—31no—
37C2×#830—31no—
38C2×(C2×D3)⋊C8—31no—
39C2×#818—31no—
40#4996—38no—
41C2×#810—31no—
42C2×#810D311yescharacteristic, complemented
43C2×#808—31no—
44C2×#808—31no—
45C2×#808—61no—
46C2×#807—31no—
47#4814—38no—
48C23×C3×D3D411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C2×C3×C4×D3—22no—
56C2×C3×C4×D3—22no—
57C2×C3×C4×D3D412yes—
58C2×C3×C4×D3C2312yes—
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×(C2×D3)⋊C4—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4×Dic3—24no—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75#3724—24no—
76(C2×D3)⋊Dic3—24no—
77C2×#485—91noSylow
78C22×C3×Q8—31no—
79C23×C3×C4—31no—
80C22×C4×D3C2×D311yescharacteristic
81C22×Dic6C2×D311yescharacteristic
82C22×C3×C8—31no—
83C3×#117—34no—
84C3×#117—62no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C4⋊C4C2×D311yescharacteristic
89C2×C3×C22⋊C4—61no—
90C2×C3×C42—61no—
91C2×#217—61no—
92#946—34no—
93#946—62no—
94C2×(C2×D3)⋊C4—21no—
95C2×(C2×D3)⋊C4—61no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3C2×D311yescharacteristic
100#924—34no—
101#924—62no—
102C2×Dic3⋊C4—61no—
103C2×Dic3⋊C4—61no—
104C2×C4×Dic3—21no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109#892—22no—
110#892C2×D314yes—
111C3×#103—34no—
112#835—34no—
113#830—34no—
114(C2×D3)⋊C8—34no—
115#818—34no—
116#810—34no—
117#810C2×D314yescomplemented
118#808—34no—
119#808—34no—
120#808—64no—
121#807—34no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3C2×D412yes—
127C2×C32×C4—22no—
128C2×C32×C4—42no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4112yes—
131C2×C32×C4#4112yes—
132C2×C32×C4C2411yescharacteristic
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—42no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—42no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3C2×D412yes—
141C3×C4×D3—24no—
142C3×C4×D3—22no—
143C3×C4×D3—22no—
144C3×Dic6—22no—
145C3×Dic6—22no—
146C3×Dic6—42no—
147C3⋊(C3⋊C8)—22no—
148C3×C3⋊C8—22no—
149C2×C22⋊Q8—91no—
150C2×#117—31no—
151#485—98no—
152C2×#107—91no—
153C2×#106—91no—
154C2×#103—31no—
155C2×#103—91no—
156C2×C22⋊C8—91no—
157C24×C3—31no—
158C23×D3#6711yescharacteristic
159C2×C3×Q8—32no—
160C2×C3×Q8—61no—
161C2×C3×Q8—62no—
162C2×C3×Q8—62no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—31no—
167C22×C3×C4—32no—
168C22×C3×C4—32no—
169C22×C3×C4—41no—
170C22×C3×C4—62no—
171C22×C3×C4—62no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×Dic3—21no—
177C22×Dic3—21no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C22×Dic3—121no—
181C22×Dic3#6711yescharacteristic
182C2×C4×D3—22no—
183C2×C4×D3—22no—
184C2×C4×D3#6712yes—
185C2×C4×D3C22×D312yes—
186C2×Dic6—22no—
187C2×Dic6—22no—
188C2×Dic6—21no—
189C2×Dic6C22×D312yes—
190C2×C3×C8—32no—
191C2×C3×C8—62no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4—32no—
196C3×C4⋊C4—41no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4C22×D312yes—
199C3×C4⋊C4C22×D312yes—
200C3×C22⋊C4—64no—
201C3×C42—64no—
202#217—64no—
203(C2×D3)⋊C4—24no—
204(C2×D3)⋊C4—64no—
205C4⋊Dic3—21no—
206C4⋊Dic3—32no—
207C4⋊Dic3—32no—
208C4⋊Dic3—62no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—121no—
212C4⋊Dic3C22×D312yes—
213Dic3⋊C4—64no—
214Dic3⋊C4—64no—
215C4×Dic3—24no—
216C2×C3⋊C8—22no—
217C2×C3⋊C8—32no—
218C2×C3⋊C8—32no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—64no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8C22×D312yes—
224C22×C32#12312yes—
225C22×C32#13512yes—
226C22×C32#13712yes—
227C22×C32C22×D411yescharacteristic
228C2×C3×D3—22no—
229C2×C3×D3—22no—
230C2×C3×D3—22no—
231C2×C3×D3—44no—
232C32×C4—42no—
233C32×C4#12312yes—
234C32×C4C2×#4111yescharacteristic
235C32×C4C2×#4111yescharacteristic
236C3⋊Dic3—42no—
237C3×Dic3—22no—
238C3×Dic3—42no—
239C3×Dic3—42no—
240C22×Q8—31no—
241C23×C4—31no—
242C22×C8—31no—
243C22×C8—91no—
244C22⋊Q8—94no—
245C22⋊Q8—182no—
246#117—34no—
247#117—62no—
248C2×C4⋊C4—31no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—181no—
251C2×C4⋊C4D3211yescharacteristic
252C2×C22⋊C4—61no—
253C2×C22⋊C4—181no—
254C2×C42—61no—
255#107—94no—
256#106—94no—
257#103—34no—
258#103—94no—
259C22⋊C8—94no—
260C23×C3—21no—
261C23×C3—32no—
262C23×C3—62no—
263C23×C3—62no—
264C23×C3—62no—
265C23×C3D3×D411yescharacteristic
266C23×C3C2×#6711yescharacteristic
267C22×D3—22no—
268C22×D3—22no—
269C22×D3—22no—
270C22×D3C2×#6712yes—
271C3×Q8—62no—
272C3×Q8—62no—
273C3×Q8—122no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—21no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—32no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—62no—
285C2×C3×C4—64no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—82no—
291C2×C3×C4—122no—
292C2×C3×C4—122no—
293C2×C3×C4#23512yes—
294C2×C3×C4#23512yes—
295C2×C3×C4#23512yes—
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4#23712yes—
298C2×C3×C4C2×#6711yescharacteristic
299C2×C3×C4C23×D311yescharacteristic
300C2×C3×C4C23×D311yescharacteristic
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—42no—
305C2×Dic3—42no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—122no—
309C2×Dic3—122no—
310C2×Dic3—122no—
311C2×Dic3—242no—
312C2×Dic3C2×#6712yes—
313C4×D3—24no—
314C4×D3—22no—
315C4×D3—22no—
316Dic6—22no—
317Dic6—22no—
318Dic6—42no—
319C3×C8—62no—
320C3⋊C8—22no—
321C3⋊C8—64no—
322C3⋊C8—62no—
323C3⋊C8—62no—
324C2×C32#48514yescomplemented
325C2×C32C2×#12311yescharacteristic
326C2×C32C2×#13511yescharacteristic
327C2×C32C2×#13711yescharacteristic
328C3×D3—42no—
329C24—31no—
330C2×Q8—32no—
331C2×Q8—61no—
332C2×Q8—62no—
333C2×Q8—62no—
334C22×C4—21no—
335C22×C4—31no—
336C22×C4—32no—
337C22×C4—32no—
338C22×C4—62no—
339C22×C4—62no—
340C22×C4—61no—
341C22×C4—61no—
342C22×C4—181no—
343C22×C4C2×D3211yescharacteristic
344C2×C8—32no—
345C2×C8—62no—
346C2×C8—92no—
347C2×C8—182no—
348C4⋊C4—21no—
349C4⋊C4—32no—
350C4⋊C4—61no—
351C4⋊C4—92no—
352C4⋊C4—184no—
353C4⋊C4—181no—
354C4⋊C4C2×D3212yes—
355C22⋊C4—64no—
356C22⋊C4—184no—
357C42—64no—
358C22×C3—21no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—62no—
363C22×C3—62no—
364C22×C3—62no—
365C22×C3—124no—
366C22×C3#88312yes—
367C22×C3#91512yes—
368C22×C3#91912yes—
369C22×C3#92912yes—
370C22×C3#95012yes—
371C22×C3#95112yes—
372C22×C3C2×D3×D411yescharacteristic
373C22×C3C22×#6711yescharacteristic
374C2×D3—22no—
375C2×D3—22no—
376C2×D3—22no—
377C2×D3—44no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—22no—
381C3×C4—42no—
382C3×C4—42no—
383C3×C4—62no—
384C3×C4—82no—
385C3×C4—122no—
386C3×C4—122no—
387C3×C4#88312yes—
388C3×C4#92912yes—
389C3×C4C2×#23511yescharacteristic
390C3×C4C2×#23511yescharacteristic
391C3×C4C2×#23511yescharacteristic
392C3×C4C2×#23711yescharacteristic
393Dic3—22no—
394Dic3—42no—
395Dic3—42no—
396Dic3—122no—
397Dic3—122no—
398Dic3—242no—
399C32C2×#48511yescharacteristic, complemented, Sylow
400C23—32no—
401C23—62no—
402C23—62no—
403C23—62no—
404C23D3×#6711yescharacteristic
405Q8—62no—
406Q8—62no—
407Q8—122no—
408C2×C4—22no—
409C2×C4—32no—
410C2×C4—42no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—64no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—122no—
418C2×C4—122no—
419C2×C4—182no—
420C2×C4—362no—
421C2×C4#379512yes—
422C2×C4#379812yes—
423C2×C4D3×#6711yescharacteristic
424C2×C4C22×D3211yescharacteristic
425C8—62no—
426C8—182no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—24no—
430C2×C3—21no—
431C2×C3—122no—
432C2×C3#481414yescomplemented
433C2×C3#499614yescomplemented
434C2×C3C2×#88311yescharacteristic
435C2×C3C2×#91511yescharacteristic
436C2×C3C2×#91911yescharacteristic
437C2×C3C2×#92911yescharacteristic
438C2×C3C2×#95011yescharacteristic
439C2×C3C2×#95111yescharacteristic
440D3—42no—
441C22—62no—
442C22—62no—
443C22—62no—
444C22—124no—
445C22#6390512yes—
446C22#6392912yes—
447C22#6394912yes—
448C22C2×D3×#6711yescharacteristic
449C4—42no—
450C4—62no—
451C4—122no—
452C4—122no—
453C4—362no—
454C4#6390512yes—
455C4C2×#379511yescharacteristic
456C4C2×#379811yescharacteristic
457C3—21no—
458C3C2×#481411yescharacteristic, complemented
459C3C2×#499611yescharacteristic, complemented
460C2—122no—
461C2#1059051914yesdirect product factor
462C2C2×#6390511yescharacteristic
463C2C2×#6392911yescharacteristic
464C2C2×#6394911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63635C2semidirect
4. C2×C3×#810C2semidirect
5. C2×#63575C2semidirect
6. C2×#63565C2semidirect
8. #10590519C2direct (N × H)
26. #63635C22semidirect
27. C3×#810C22semidirect
28. #63575C22semidirect
29. #63565C22semidirect
42. C2×#810D3semidirect
117. #810C2×D3semidirect
324. C2×C32#485semidirect
399. C32C2×#485semidirect
432. C2×C3#4814semidirect
433. C2×C3#4996semidirect
458. C3C2×#4814semidirect
459. C3C2×#4996semidirect
461. C2#10590519direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×#638562
C2×#636352
C2×C3×#8102
C2×#635752
C2×#635652
C2×(C2×D3)⋊(C3⋊C8)2
#105905192
C2×#49963
C2×#48143