Finite Group Databasebeta

← C2×#10591134 #11869508

Subgroups — C2×#10591134 #11869508

Order 1152.

993 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4#10591134C218yesmaximal, direct product factor
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63573C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8C2×#63567C211yesmaximal, characteristic, complemented
9C2×#4996—31nomaximal
10C2×#4723—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C2×#3757—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15#64133—22no—
16#64133C2214yes—
17C2×#3750—21no—
18C2×C3×#217—21no—
19C3×#926—22no—
20C3×#926C2214yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3—21no—
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#830C2214yes—
27#63575C2214yescomplemented
28#63573C2214yescomplemented
29#63567C2214yescomplemented
30#63567C2214yescomplemented
31C2×C3×#117—31no—
32C2×#926D311yescharacteristic
33C2×#924—31no—
34C2×#924—31no—
35C2×#924—61no—
36C2×C3×C22⋊C8—31no—
37C2×#830D311yescharacteristic
38C2×#818—31no—
39C2×#817—31no—
40C2×#816—31no—
41C2×#816—31no—
42#4996—38no—
43C2×#810—31no—
44C2×#810—31no—
45C2×#808—31no—
46C2×#807—31no—
47#4723—38no—
48C24×C32D411yescharacteristic
49C22×C32×C4—22no—
50C22×C32×C4—22no—
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D412yes—
53C22×C32×C4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3—21no—
57C2×#634—22no—
58C2×#634—22no—
59C2×#634—21no—
60C2×#634C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63#3757—24no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)C2312yes—
66#3750—24no—
67C3×#217—24no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2312yes—
71C3×C4⋊Dic3C2312yes—
72C3×C4×Dic3—24no—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8C2312yes—
76C2×C3×C3⋊C8C2312yes—
77C2×#485—91noSylow
78C23×C3×C4—21no—
79C23×C3×C4C2×D311yescharacteristic
80C23×C3×C4C2×D311yescharacteristic
81C22×Dic6—31no—
82C22×Dic6—31no—
83C22×Dic6—61no—
84C22×C3×C8—31no—
85C22×C3×C8—31no—
86C3×#117—34no—
87C3×#117—62no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C22⋊C4—61no—
91C2×C3×C42—61no—
92C2×#217—21no—
93C2×#217—62no—
94C2×#217—61no—
95C2×#217—61no—
96#926—22no—
97#926C2×D314yes—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4⋊Dic3C2×D311yescharacteristic
103#924—34no—
104#924—34no—
105#924—64no—
106#924—64no—
107#924—62no—
108#924—62no—
109C2×Dic3⋊C4—62no—
110C2×Dic3⋊C4—61no—
111C2×Dic3⋊C4—61no—
112C2×C4×Dic3—21no—
113C22×C3⋊C8C2×D311yescharacteristic
114C22×C3⋊C8C2×D311yescharacteristic
115C3×C22⋊C8—34no—
116#830C2×D314yes—
117#818—34no—
118#817—34no—
119#816—34no—
120#816—34no—
121#810—34no—
122#810—34no—
123#808—34no—
124#807—34no—
125C23×C32—22no—
126C23×C32—22no—
127C23×C32—22no—
128C23×C32C2×D412yes—
129C23×C32C2×D411yescharacteristic
130C2×C32×C4—22no—
131C2×C32×C4—24no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4112yes—
137C2×C32×C4#4112yes—
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—42no—
142C2×C3⋊Dic3—42no—
143#634—22no—
144#634—22no—
145#634—42no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—42no—
149C2×C3×Dic3—42no—
150C3×C3⋊C8—22no—
151C3×C3⋊C8—22no—
152C2×C22⋊Q8—91no—
153C2×#117—31no—
154#485—98no—
155C2×#107—91no—
156C2×#106—91no—
157C2×#103—91no—
158C2×#103—91no—
159C2×C22⋊C8—31no—
160C24×C3—21no—
161C24×C3D1211yescharacteristic
162C24×C3#6711yescharacteristic
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4—22no—
169C22×C3×C4—21no—
170C22×C3×C4—22no—
171C22×C3×C4—42no—
172C22×C3×C4—42no—
173C22×C3×C4—61no—
174C22×C3×C4—61no—
175C22×C3×C4D1211yescharacteristic
176C22×C3×C4D1212yes—
177C22×C3×C4#6711yescharacteristic
178C22×C3×C4#6712yes—
179C22×C3×C4C22×D312yes—
180C22×C3×C4C22×D312yes—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3—62no—
186C22×Dic3—62no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C2×Dic6—32no—
192C2×Dic6—32no—
193C2×Dic6—62no—
194C2×Dic6—62no—
195C2×Dic6—62no—
196C2×Dic6—62no—
197C2×Dic6—62no—
198C2×Dic6—62no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—122no—
202C2×Dic6—122no—
203C2×C3×C8—32no—
204C2×C3×C8—32no—
205C2×C3×C8—62no—
206C2×C3×C8—62no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C22⋊C4—64no—
212C3×C42—64no—
213#217—24no—
214#217—68no—
215#217—64no—
216#217—64no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219C4⋊Dic3—32no—
220C4⋊Dic3—32no—
221C4⋊Dic3—62no—
222C4⋊Dic3—62no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225C4⋊Dic3C22×D312yes—
226C4⋊Dic3C22×D312yes—
227Dic3⋊C4—68no—
228Dic3⋊C4—64no—
229Dic3⋊C4—64no—
230C4×Dic3—24no—
231C2×C3⋊C8—22no—
232C2×C3⋊C8—22no—
233C2×C3⋊C8C22×D312yes—
234C2×C3⋊C8C22×D312yes—
235C22×C32—22no—
236C22×C32—22no—
237C22×C32—22no—
238C22×C32—44no—
239C22×C32#12312yes—
240C22×C32#13512yes—
241C22×C32#13712yes—
242C22×C32C22×D411yescharacteristic
243C32×C4—22no—
244C32×C4#12312yes—
245C32×C4C2×#4111yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3⋊Dic3—42no—
248C3⋊Dic3—42no—
249C3×Dic3—42no—
250C3×Dic3—42no—
251C22×Q8—91no—
252C23×C4D3211yescharacteristic
253C22×C8—31no—
254C22×C8—31no—
255C22⋊Q8—94no—
256C22⋊Q8—182no—
257#117—34no—
258#117—62no—
259C2×C4⋊C4—31no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—181no—
263C2×C22⋊C4—61no—
264C2×C22⋊C4—181no—
265C2×C42—61no—
266#107—94no—
267#106—94no—
268#103—94no—
269#103—94no—
270C22⋊C8—34no—
271C23×C3—24no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—22no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3—21no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3C2×D1212yes—
283C23×C3C2×D1211yescharacteristic
284C23×C3C2×#6712yes—
285C23×C3C2×#6711yescharacteristic
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—24no—
289C2×C3×C4—24no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—22no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—44no—
302C2×C3×C4—42no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—122no—
306C2×C3×C4—122no—
307C2×C3×C4C2×D1212yes—
308C2×C3×C4C2×D1211yescharacteristic
309C2×C3×C4#23512yes—
310C2×C3×C4#23512yes—
311C2×C3×C4#23712yes—
312C2×C3×C4#23712yes—
313C2×C3×C4C2×#6712yes—
314C2×C3×C4C2×#6711yescharacteristic
315C2×C3×C4C23×D311yescharacteristic
316C2×C3×C4C23×D311yescharacteristic
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—42no—
320C2×Dic3—42no—
321C2×Dic3—64no—
322C2×Dic3—64no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—124no—
328C2×Dic3—124no—
329C2×Dic3—122no—
330C2×Dic3—122no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333Dic6—62no—
334Dic6—62no—
335Dic6—62no—
336Dic6—62no—
337Dic6—122no—
338Dic6—122no—
339Dic6—124no—
340Dic6—122no—
341Dic6—122no—
342C3×C8—62no—
343C3×C8—62no—
344C3⋊C8—22no—
345C3⋊C8—22no—
346C2×C32—42no—
347C2×C32#48514yescomplemented
348C2×C32C2×#12311yescharacteristic
349C2×C32C2×#13511yescharacteristic
350C2×C32C2×#13711yescharacteristic
351C24#62611yescharacteristic
352C2×Q8—92no—
353C2×Q8—181no—
354C2×Q8—182no—
355C2×Q8—182no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—61no—
359C22×C4—61no—
360C22×C4—181no—
361C22×C4—181no—
362C22×C4#62612yes—
363C22×C4#62611yescharacteristic
364C22×C4C2×D3212yes—
365C22×C4C2×D3211yescharacteristic
366C2×C8—32no—
367C2×C8—32no—
368C2×C8—62no—
369C2×C8—62no—
370C4⋊C4—32no—
371C4⋊C4—32no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—92no—
375C4⋊C4—181no—
376C4⋊C4—184no—
377C22⋊C4—64no—
378C22⋊C4—184no—
379C42—64no—
380C22×C3—24no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—48no—
394C22×C3—44no—
395C22×C3—44no—
396C22×C3#88612yes—
397C22×C3#90412yes—
398C22×C3#90912yes—
399C22×C3#92912yes—
400C22×C3#95012yes—
401C22×C3#95112yes—
402C22×C3C22×D1211yescharacteristic
403C22×C3C22×#6711yescharacteristic
404C3×C4—22no—
405C3×C4—22no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—22no—
409C3×C4—42no—
410C3×C4—122no—
411C3×C4—122no—
412C3×C4#88612yes—
413C3×C4#92912yes—
414C3×C4C2×#23511yescharacteristic
415C3×C4C2×#23511yescharacteristic
416C3×C4C2×#23711yescharacteristic
417C3×C4C2×#23711yescharacteristic
418Dic3—42no—
419Dic3—42no—
420Dic3—124no—
421Dic3—124no—
422Dic3—122no—
423Dic3—122no—
424Dic3—122no—
425Dic3—122no—
426C32C2×#48511yescharacteristic, complemented, Sylow
427C23—22no—
428C23—22no—
429C23—22no—
430C23C2×#62612yes—
431C23C2×#62611yescharacteristic
432Q8—182no—
433Q8—182no—
434Q8—362no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—122no—
442C2×C4—122no—
443C2×C4—182no—
444C2×C4—182no—
445C2×C4—362no—
446C2×C4—362no—
447C2×C4#380412yes—
448C2×C4#380412yes—
449C2×C4C2×#62612yes—
450C2×C4C2×#62611yescharacteristic
451C2×C4C22×D3211yescharacteristic
452C8—62no—
453C8—62no—
454C2×C3—24no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—44no—
459C2×C3—42no—
460C2×C3—42no—
461C2×C3#472314yescomplemented
462C2×C3#499614yescomplemented
463C2×C3C2×#88611yescharacteristic
464C2×C3C2×#90411yescharacteristic
465C2×C3C2×#90911yescharacteristic
466C2×C3C2×#92911yescharacteristic
467C2×C3C2×#95011yescharacteristic
468C2×C3C2×#95111yescharacteristic
469C22—22no—
470C22—22no—
471C22—22no—
472C22—44no—
473C22#6382912yes—
474C22#6383112yes—
475C22#6396612yes—
476C22C22×#62611yescharacteristic
477C4—22no—
478C4—122no—
479C4—122no—
480C4—362no—
481C4—362no—
482C4#6396612yes—
483C4C2×#380411yescharacteristic
484C4C2×#380411yescharacteristic
485C3—21no—
486C3C2×#472311yescharacteristic, complemented
487C3C2×#499611yescharacteristic, complemented
488C2—42no—
489C2#1059113414yesdirect product factor
490C2C2×#6382911yescharacteristic
491C2C2×#6383111yescharacteristic
492C2C2×#6396611yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC23×C4D32
hypocenterC32C2×#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #10591134C2direct (N × H)
5. C2×#63575C2semidirect
6. C2×#63573C2semidirect
7. C2×#63567C2semidirect
8. C2×#63567C2semidirect
27. #63575C22semidirect
28. #63573C22semidirect
29. #63567C22semidirect
30. #63567C22semidirect
347. C2×C32#485semidirect
426. C32C2×#485semidirect
461. C2×C3#4723semidirect
462. C2×C3#4996semidirect
486. C3C2×#4723semidirect
487. C3C2×#4996semidirect
489. C2#10591134direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×#9262
C2×C3×#8302
#105911342
C2×#635752
C2×#635732
C2×#635672
C2×#49963
C2×#47233