Finite Group Databasebeta

← C2×#10591102 #11869510

Subgroups — C2×#10591102 #11869510

Order 1152.

933 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic
3C2×#63657C211yesmaximal, characteristic
4C2×#63576C211yesmaximal, characteristic, complemented
5C2×#63574C211yesmaximal, characteristic, complemented
6#10591102C218yesmaximal, direct product factor
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×#63565C211yesmaximal, characteristic, complemented
9C2×#5045—31nomaximal
10C2×#4996—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×#217—21no—
16C2×C3×#217—21no—
17C3×#926—22no—
18C3×#926C2214yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C3×#924—22no—
23C3×#924C2214yes—
24C2×C3×Dic3⋊C4—21no—
25C2×C3×C4×Dic3—21no—
26#63657C2214yes—
27#63576C2214yescomplemented
28#63574C2214yescomplemented
29#63565C2214yescomplemented
30#63565C2214yescomplemented
31C2×C3×C22⋊Q8—31no—
32C2×C3×#117—31no—
33C2×#926D311yescharacteristic
34C2×#924D311yescharacteristic
35C2×#835—31no—
36C2×#835—31no—
37C2×#830—31no—
38C2×#830—31no—
39C2×#830—61no—
40#5045—38no—
41#4996—38no—
42C2×#810—31no—
43C2×#810—31no—
44C2×#808—31no—
45C2×#808—31no—
46C2×#807—31no—
47C2×#807—31no—
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—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C2×C3⋊(C3⋊C8)—22no—
64C2×C3⋊(C3⋊C8)—22no—
65C2×C3⋊(C3⋊C8)C2312yes—
66C2×C3⋊(C3⋊C8)C2312yes—
67C3×#217—24no—
68C3×#217—24no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×C4⋊Dic3C2312yes—
74C3×C4⋊Dic3C2312yes—
75C3×Dic3⋊C4—24no—
76C3×C4×Dic3—24no—
77C2×#485—91noSylow
78C22×C3×Q8—31no—
79C23×C3×C4—21no—
80C23×C3×C4C2×D311yescharacteristic
81C23×C3×C4C2×D311yescharacteristic
82C22×Dic6C2×D311yescharacteristic
83C3×C22⋊Q8—34no—
84C3×C22⋊Q8—62no—
85C3×#117—34no—
86C3×#117—62no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—61no—
91C2×C3×C22⋊C4—61no—
92C2×C3×C22⋊C4—61no—
93C2×C3×C42—61no—
94C2×#217—21no—
95C2×#217—21no—
96#926—22no—
97#926C2×D314yes—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×C4⋊Dic3C2×D311yescharacteristic
101#924—22no—
102#924C2×D314yes—
103C2×Dic3⋊C4—21no—
104C2×C4×Dic3—21no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—31no—
109C22×C3⋊C8—61no—
110C22×C3⋊C8—61no—
111#835—34no—
112#835—34no—
113#830—34no—
114#830—34no—
115#830—64no—
116#810—34no—
117#810—34no—
118#808—34no—
119#808—34no—
120#807—34no—
121#807—34no—
122C23×C32—22no—
123C23×C32—22no—
124C23×C32—22no—
125C23×C32C2×D412yes—
126C23×C32C2×D411yescharacteristic
127C2×C32×C4—22no—
128C2×C32×C4—24no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4C2×D412yes—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4112yes—
134C2×C32×C4#4112yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3—42no—
144C3×Dic6—22no—
145C3×Dic6—22no—
146C3×Dic6—42no—
147C3⋊(C3⋊C8)—22no—
148C3⋊(C3⋊C8)—22no—
149C2×C22⋊Q8—31no—
150C2×#117—31no—
151#485—98no—
152C2×#107—91no—
153C2×#106—91no—
154C2×#103—91no—
155C2×#103—91no—
156C2×C22⋊C8—91no—
157C24×C3—21no—
158C24×C3#6711yescharacteristic
159C24×C3#6711yescharacteristic
160C2×C3×Q8—32no—
161C2×C3×Q8—61no—
162C2×C3×Q8—62no—
163C2×C3×Q8—62no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—22no—
172C22×C3×C4—42no—
173C22×C3×C4—42no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4#6711yescharacteristic
179C22×C3×C4#6711yescharacteristic
180C22×C3×C4#6712yes—
181C22×C3×C4#6712yes—
182C22×C3×C4C22×D312yes—
183C22×C3×C4C22×D312yes—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—21no—
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—21no—
190C2×Dic6—22no—
191C2×Dic6—22no—
192C2×Dic6—21no—
193C2×Dic6C22×D312yes—
194C3×C4⋊C4—32no—
195C3×C4⋊C4—32no—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—64no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C22⋊C4—64no—
202C3×C22⋊C4—64no—
203C3×C42—64no—
204#217—24no—
205#217—24no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3C22×D312yes—
210C4⋊Dic3C22×D312yes—
211C4⋊Dic3C22×D312yes—
212Dic3⋊C4—24no—
213C4×Dic3—24no—
214C2×C3⋊C8—32no—
215C2×C3⋊C8—32no—
216C2×C3⋊C8—32no—
217C2×C3⋊C8—32no—
218C2×C3⋊C8—62no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—62no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8—62no—
224C2×C3⋊C8—122no—
225C2×C3⋊C8—122no—
226C22×C32—22no—
227C22×C32—22no—
228C22×C32—22no—
229C22×C32—44no—
230C22×C32#12312yes—
231C22×C32#13512yes—
232C22×C32#13712yes—
233C22×C32C22×D411yescharacteristic
234C32×C4—22no—
235C32×C4#12312yes—
236C32×C4C2×#4111yescharacteristic
237C32×C4C2×#4111yescharacteristic
238C3×Dic3—42no—
239C3×Dic3—42no—
240C3×Dic3—42no—
241C3×Dic3—42no—
242C22×Q8—31no—
243C23×C4D3211yescharacteristic
244C22×C8—91no—
245C22×C8—91no—
246C22⋊Q8—34no—
247C22⋊Q8—62no—
248#117—34no—
249#117—62no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—31no—
253C2×C4⋊C4—61no—
254C2×C22⋊C4—61no—
255C2×C22⋊C4—61no—
256C2×C42—61no—
257#107—94no—
258#106—94no—
259#103—94no—
260#103—94no—
261C22⋊C8—94no—
262C23×C3—24no—
263C23×C3—22no—
264C23×C3—22no—
265C23×C3—22no—
266C23×C3—22no—
267C23×C3—22no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—21no—
271C23×C3—42no—
272C23×C3—42no—
273C23×C3C2×#6712yes—
274C23×C3C2×#6712yes—
275C23×C3C2×#6711yescharacteristic
276C23×C3C2×#6711yescharacteristic
277C3×Q8—62no—
278C3×Q8—62no—
279C3×Q8—122no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—24no—
283C2×C3×C4—24no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—44no—
296C2×C3×C4—42no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—122no—
302C2×C3×C4—122no—
303C2×C3×C4—122no—
304C2×C3×C4—122no—
305C2×C3×C4#23512yes—
306C2×C3×C4#23512yes—
307C2×C3×C4#23712yes—
308C2×C3×C4#23712yes—
309C2×C3×C4C2×#6712yes—
310C2×C3×C4C2×#6712yes—
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—42no—
320C2×Dic3—42no—
321C2×Dic3—42no—
322C2×Dic3—42no—
323Dic6—22no—
324Dic6—22no—
325Dic6—42no—
326C3⋊C8—62no—
327C3⋊C8—62no—
328C3⋊C8—62no—
329C3⋊C8—62no—
330C3⋊C8—122no—
331C3⋊C8—122no—
332C2×C32—42no—
333C2×C32#48514yescomplemented
334C2×C32C2×#12311yescharacteristic
335C2×C32C2×#13511yescharacteristic
336C2×C32C2×#13711yescharacteristic
337C24#62511yescharacteristic
338C2×Q8—32no—
339C2×Q8—61no—
340C2×Q8—62no—
341C2×Q8—62no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—61no—
345C22×C4—61no—
346C22×C4—61no—
347C22×C4—61no—
348C22×C4#62512yes—
349C22×C4#62511yescharacteristic
350C22×C4C2×D3212yes—
351C22×C4C2×D3211yescharacteristic
352C2×C8—92no—
353C2×C8—92no—
354C2×C8—182no—
355C2×C8—182no—
356C4⋊C4—32no—
357C4⋊C4—32no—
358C4⋊C4—32no—
359C4⋊C4—61no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—64no—
363C22⋊C4—64no—
364C22⋊C4—64no—
365C42—64no—
366C22×C3—24no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—42no—
378C22×C3—42no—
379C22×C3—48no—
380C22×C3—44no—
381C22×C3—44no—
382C22×C3#92912yes—
383C22×C3#93512yes—
384C22×C3#94212yes—
385C22×C3#95012yes—
386C22×C3#95012yes—
387C22×C3#95112yes—
388C22×C3C22×#6711yescharacteristic
389C22×C3C22×#6711yescharacteristic
390C3×C4—22no—
391C3×C4—22no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—22no—
395C3×C4—42no—
396C3×C4—122no—
397C3×C4—122no—
398C3×C4—122no—
399C3×C4—122no—
400C3×C4#92912yes—
401C3×C4#93512yes—
402C3×C4C2×#23511yescharacteristic
403C3×C4C2×#23511yescharacteristic
404C3×C4C2×#23711yescharacteristic
405C3×C4C2×#23711yescharacteristic
406Dic3—42no—
407Dic3—42no—
408Dic3—42no—
409Dic3—42no—
410C32C2×#48511yescharacteristic, complemented, Sylow
411C23—22no—
412C23—22no—
413C23—22no—
414C23C2×#62512yes—
415C23C2×#62511yescharacteristic
416Q8—62no—
417Q8—62no—
418Q8—122no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—122no—
428C2×C4—122no—
429C2×C4—122no—
430C2×C4—122no—
431C2×C4#380412yes—
432C2×C4#380412yes—
433C2×C4C2×#62512yes—
434C2×C4C2×#62511yescharacteristic
435C2×C4C22×D3211yescharacteristic
436C8—182no—
437C8—182no—
438C2×C3—24no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—44no—
443C2×C3—42no—
444C2×C3—42no—
445C2×C3#499614yescomplemented
446C2×C3#504514yescomplemented
447C2×C3C2×#92911yescharacteristic
448C2×C3C2×#93511yescharacteristic
449C2×C3C2×#94211yescharacteristic
450C2×C3C2×#95011yescharacteristic
451C2×C3C2×#95011yescharacteristic
452C2×C3C2×#95111yescharacteristic
453C22—22no—
454C22—22no—
455C22—22no—
456C22—44no—
457C22#6382212yes—
458C22#6382712yes—
459C22#6396112yes—
460C22C22×#62511yescharacteristic
461C4—22no—
462C4—122no—
463C4—122no—
464C4—122no—
465C4—122no—
466C4#6396112yes—
467C4C2×#380411yescharacteristic
468C4C2×#380411yescharacteristic
469C3—21no—
470C3C2×#499611yescharacteristic, complemented
471C3C2×#504511yescharacteristic, complemented
472C2—42no—
473C2#1059110214yesdirect product factor
474C2C2×#6382211yescharacteristic
475C2C2×#6382711yescharacteristic
476C2C2×#6396111yescharacteristic
subgroupG/H
centerC23C2×#625
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. C2×#63576C2semidirect
5. C2×#63574C2semidirect
6. #10591102C2direct (N × H)
7. C2×#63565C2semidirect
8. C2×#63565C2semidirect
27. #63576C22semidirect
28. #63574C22semidirect
29. #63565C22semidirect
30. #63565C22semidirect
333. C2×C32#485semidirect
410. C32C2×#485semidirect
445. C2×C3#4996semidirect
446. C2×C3#5045semidirect
470. C3C2×#4996semidirect
471. C3C2×#5045semidirect
473. C2#10591102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9262
C2×C3×#9242
C2×#636572
C2×#635762
C2×#635742
#105911022
C2×#635652
C2×#50453
C2×#49963