Finite Group Databasebeta

← C2×#10591187 #11866799

Subgroups — C2×#10591187 #11866799

Order 1152.

1185 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic
3C23×C3×C3⋊C8C211yesmaximal, characteristic
4C22×#3719C211yesmaximal, characteristic, complemented
5#10591187C218yesmaximal, direct product factor
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8C2×#63566C211yesmaximal, characteristic, complemented
9C2×#5116—31nomaximal
10C2×#5051—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×#3757—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16#64133—22no—
17#64133C2214yes—
18C2×#3750—21no—
19C2×C3×#217—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C3×#924—22no—
22C3×#924C2214yes—
23C2×C3×Dic3⋊C4—21no—
24C22×C3×C3⋊C8—24no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C22×C3×C3⋊C8C2214yes—
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30#63575C2214yescomplemented
31#63567C2214yescomplemented
32#63566C2214yescomplemented
33C23×C3×C8—31no—
34C2×C3×C22⋊Q8—31no—
35C22×#216—31no—
36C2×#924—31no—
37C2×#924—31no—
38C2×#924—61no—
39C2×#924D311yescharacteristic
40C23×C3⋊C8D311yescharacteristic
41C22×Dic12—31no—
42C2×#835—31no—
43#5116—38no—
44C2×#818—31no—
45C2×#816—31no—
46C2×#816—31no—
47#5051—38no—
48C2×#810—31no—
49C2×#807—31no—
50C24×C32D411yescharacteristic
51C22×C32×C4—22no—
52C22×C32×C4—22no—
53C22×C32×C4D411yescharacteristic
54C22×C32×C4D412yes—
55C22×C32×C4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C22×C3⋊Dic3—21no—
59C2×#634—22no—
60C2×#634—22no—
61C2×#634—21no—
62C2×#634C2312yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69#3757—24no—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)C2312yes—
72#3750—24no—
73C3×#217—24no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3C2312yes—
76C3×Dic3⋊C4—24no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8—28no—
79C2×C3×C3⋊C8D414yes—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82#3719—28no—
83C2×#467—91noSylow
84C22×C3×Q8—31no—
85C23×C3×C4—21no—
86C23×C3×C4C2×D311yescharacteristic
87C23×C3×C4C2×D311yescharacteristic
88C22×Dic6—31no—
89C22×Dic6—31no—
90C22×Dic6—61no—
91C22×Dic6C2×D311yescharacteristic
92C22×C3×C8—31no—
93C22×C3×C8—31no—
94C22×C3×C8—34no—
95C22×C3×C8—64no—
96C3×C22⋊Q8—34no—
97C3×C22⋊Q8—62no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—61no—
100C2×C3×C22⋊C4—61no—
101C2×#217—21no—
102C2×#217—62no—
103C2×#217—61no—
104C2×#217—61no—
105C2×#216—34no—
106C2×#216—64no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—61no—
110C2×C4⋊Dic3C2×D311yescharacteristic
111#924—22no—
112#924—34no—
113#924—34no—
114#924—64no—
115#924—64no—
116#924—62no—
117#924—62no—
118#924C2×D314yes—
119C2×Dic3⋊C4—21no—
120C2×Dic3⋊C4—62no—
121C2×Dic3⋊C4—61no—
122C2×Dic3⋊C4—61no—
123C22×C3⋊C8—24no—
124C22×C3⋊C8C2×D311yescharacteristic
125C22×C3⋊C8C2×D314yes—
126C22×C3⋊C8C2×D311yescharacteristic
127C2×Dic12—34no—
128C2×Dic12—64no—
129#835—34no—
130#818—34no—
131#816—34no—
132#816—34no—
133#810—34no—
134#807—34no—
135C23×C32—22no—
136C23×C32—22no—
137C23×C32Q1614yescomplemented
138C23×C32C2×D412yes—
139C23×C32C2×D411yescharacteristic
140C2×C32×C4—22no—
141C2×C32×C4—24no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—42no—
152C2×C3⋊Dic3—42no—
153#634—22no—
154#634—22no—
155#634—42no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3—42no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163C3×C3⋊C8—22no—
164C3×C3⋊C8C2×D414yes—
165C22×Q16—91no—
166C23×C8—31no—
167C2×C22⋊Q8—31no—
168C2×C22⋊Q8—91no—
169#467—98no—
170C2×#107—91no—
171C2×#103—91no—
172C2×#103—91no—
173C24×C3—21no—
174C24×C3D1211yescharacteristic
175C24×C3#6711yescharacteristic
176C2×C3×Q8—32no—
177C2×C3×Q8—61no—
178C2×C3×Q8—62no—
179C2×C3×Q8—62no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—22no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—42no—
189C22×C3×C4—42no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4D1211yescharacteristic
193C22×C3×C4D1212yes—
194C22×C3×C4#6711yescharacteristic
195C22×C3×C4#6712yes—
196C22×C3×C4C22×D312yes—
197C22×C3×C4C22×D312yes—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×Dic3—21no—
201C22×Dic3—21no—
202C22×Dic3—62no—
203C22×Dic3—62no—
204C22×Dic3—61no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—61no—
208C2×Dic6—22no—
209C2×Dic6—22no—
210C2×Dic6—21no—
211C2×Dic6—32no—
212C2×Dic6—32no—
213C2×Dic6—62no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—122no—
222C2×Dic6—122no—
223C2×Dic6C22×D312yes—
224C2×C3×C8—34no—
225C2×C3×C8—32no—
226C2×C3×C8—32no—
227C2×C3×C8—68no—
228C2×C3×C8—62no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—64no—
231C3×C4⋊C4—61no—
232C3×C22⋊C4—64no—
233#217—24no—
234#217—68no—
235#217—64no—
236#217—64no—
237#216—68no—
238C4⋊Dic3—21no—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—62no—
242C4⋊Dic3—62no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3C22×D312yes—
246Dic3⋊C4—24no—
247Dic3⋊C4—68no—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
250C2×C3⋊C8—22no—
251C2×C3⋊C8—28no—
252C2×C3⋊C8#6714yes—
253C2×C3⋊C8C22×D312yes—
254C2×C3⋊C8C22×D312yes—
255Dic12—68no—
256C22×C32—22no—
257C22×C32—22no—
258C22×C32—28no—
259C22×C32#12112yes—
260C22×C32C2×Q1612yes—
261C22×C32C2×Q1614yescomplemented
262C22×C32#13512yes—
263C22×C32C22×D411yescharacteristic
264C32×C4—22no—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3⋊Dic3—42no—
269C3⋊Dic3—42no—
270C3×Dic3—42no—
271C3×Dic3—42no—
272C22×Q8—31no—
273C22×Q8—91no—
274C23×C4D3211yescharacteristic
275C2×Q16—94no—
276C2×Q16—184no—
277C22×C8—31no—
278C22×C8—31no—
279C22×C8—34no—
280C22×C8—64no—
281C22⋊Q8—34no—
282C22⋊Q8—62no—
283C22⋊Q8—94no—
284C22⋊Q8—182no—
285C2×C4⋊C4—31no—
286C2×C4⋊C4—61no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—181no—
289C2×C22⋊C4—61no—
290C2×C22⋊C4—181no—
291#107—94no—
292#103—94no—
293#103—94no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—24no—
299C23×C3—22no—
300C23×C3—21no—
301C23×C3—42no—
302C23×C3—42no—
303C23×C3Dic1214yescomplemented
304C23×C3#21614yescomplemented
305C23×C3C2×D1212yes—
306C23×C3C2×D1211yescharacteristic
307C23×C3C2×#6712yes—
308C23×C3C2×#6711yescharacteristic
309C3×Q8—62no—
310C3×Q8—62no—
311C3×Q8—122no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—44no—
328C2×C3×C4—42no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—122no—
332C2×C3×C4—122no—
333C2×C3×C4C2×D1212yes—
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4#23512yes—
336C2×C3×C4D3×D412yes—
337C2×C3×C4#23712yes—
338C2×C3×C4C2×#6712yes—
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6712yes—
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—42no—
346C2×Dic3—42no—
347C2×Dic3—64no—
348C2×Dic3—64no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—124no—
354C2×Dic3—124no—
355C2×Dic3—122no—
356C2×Dic3—122no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359Dic6—22no—
360Dic6—22no—
361Dic6—42no—
362Dic6—62no—
363Dic6—62no—
364Dic6—62no—
365Dic6—62no—
366Dic6—122no—
367Dic6—122no—
368Dic6—124no—
369Dic6—122no—
370Dic6—122no—
371C3×C8—34no—
372C3×C8—62no—
373C3⋊C8—22no—
374C3⋊C8C2×#6714yes—
375C2×C32—24no—
376C2×C32#46714yescomplemented
377C2×C32C2×#12111yescharacteristic
378C2×C32C22×Q1611yescharacteristic
379C2×C32C2×#13511yescharacteristic
380C24#62611yescharacteristic
381C2×Q8—32no—
382C2×Q8—61no—
383C2×Q8—62no—
384C2×Q8—62no—
385C2×Q8—92no—
386C2×Q8—181no—
387C2×Q8—182no—
388C2×Q8—182no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—61no—
392C22×C4—61no—
393C22×C4—181no—
394C22×C4—181no—
395C22×C4#62612yes—
396C22×C4#62611yescharacteristic
397C22×C4C2×D3212yes—
398C22×C4C2×D3211yescharacteristic
399Q16—188no—
400C2×C8—32no—
401C2×C8—34no—
402C2×C8—32no—
403C2×C8—68no—
404C2×C8—62no—
405C4⋊C4—32no—
406C4⋊C4—61no—
407C4⋊C4—64no—
408C4⋊C4—92no—
409C4⋊C4—181no—
410C4⋊C4—184no—
411C22⋊C4—64no—
412C22⋊C4—184no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—28no—
417C22×C3—22no—
418C22×C3—28no—
419C22×C3—21no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—24no—
423C22×C3—22no—
424C22×C3—42no—
425C22×C3—48no—
426C22×C3—42no—
427C22×C3#90412yes—
428C22×C3C2×Dic1212yes—
429C22×C3C2×Dic1214yescomplemented
430C22×C3#93012yes—
431C22×C3#93912yes—
432C22×C3C2×#21612yes—
433C22×C3C2×#21614yescomplemented
434C22×C3#95012yes—
435C22×C3C22×D1211yescharacteristic
436C22×C3C22×#6711yescharacteristic
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—22no—
442C3×C4—42no—
443C3×C4—122no—
444C3×C4—122no—
445C3×C4#93012yes—
446C3×C4#93912yes—
447C3×C4C2×#23511yescharacteristic
448C3×C4C2×D3×D411yescharacteristic
449C3×C4C2×#23711yescharacteristic
450C3×C4C22×#6711yescharacteristic
451Dic3—42no—
452Dic3—42no—
453Dic3—124no—
454Dic3—124no—
455Dic3—122no—
456Dic3—122no—
457Dic3—122no—
458Dic3—122no—
459C32C2×#46711yescharacteristic, complemented, Sylow
460C23—22no—
461C23—22no—
462C23#371914yescomplemented
463C23C2×#62612yes—
464C23C2×#62611yescharacteristic
465Q8—62no—
466Q8—62no—
467Q8—122no—
468Q8—182no—
469Q8—182no—
470Q8—362no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—122no—
478C2×C4—122no—
479C2×C4—182no—
480C2×C4—182no—
481C2×C4—362no—
482C2×C4—362no—
483C2×C4#380412yes—
484C2×C4C2×#62612yes—
485C2×C4C2×#62611yescharacteristic
486C2×C4D3×#6712yes—
487C2×C4C22×D3211yescharacteristic
488C8—34no—
489C8—62no—
490C2×C3—24no—
491C2×C3—24no—
492C2×C3—21no—
493C2×C3—24no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—44no—
497C2×C3#505114yescomplemented
498C2×C3#511614yescomplemented
499C2×C3C2×#90411yescharacteristic
500C2×C3C22×Dic1211yescharacteristic
501C2×C3C2×#93011yescharacteristic
502C2×C3C2×#93911yescharacteristic
503C2×C3C22×#21611yescharacteristic
504C2×C3C2×#95011yescharacteristic
505C22—22no—
506C22—28no—
507C22—22no—
508C22#6382912yes—
509C22C2×#371912yes—
510C22C2×#371914yescomplemented
511C22#6397812yes—
512C22C22×#62611yescharacteristic
513C4—22no—
514C4—122no—
515C4—122no—
516C4—362no—
517C4—362no—
518C4#6397812yes—
519C4C2×#380411yescharacteristic
520C4C2×D3×#6711yescharacteristic
521C3—21no—
522C3C2×#505111yescharacteristic, complemented
523C3C2×#511611yescharacteristic, complemented
524C2—24no—
525C2#1059118714yesdirect product factor
526C2C2×#6382911yescharacteristic
527C2C22×#371911yescharacteristic
528C2C2×#6397811yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC23×C4D32
hypocenterC32C2×#467
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. C22×#3719C2semidirect
5. #10591187C2direct (N × H)
6. C2×#63575C2semidirect
7. C2×#63567C2semidirect
8. C2×#63566C2semidirect
29. C2×#3719C22semidirect
30. #63575C22semidirect
31. #63567C22semidirect
32. #63566C22semidirect
137. C23×C32Q16semidirect
261. C22×C32C2×Q16semidirect
303. C23×C3Dic12semidirect
304. C23×C3#216semidirect
376. C2×C32#467semidirect
429. C22×C3C2×Dic12semidirect
433. C22×C3C2×#216semidirect
459. C32C2×#467semidirect
462. C23#3719semidirect
497. C2×C3#5051semidirect
498. C2×C3#5116semidirect
510. C22C2×#3719semidirect
522. C3C2×#5051semidirect
523. C3C2×#5116semidirect
525. C2#10591187direct (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×#9242
C23×C3×C3⋊C82
C22×#37192
#105911872
C2×#635752
C2×#635672
C2×#635662
C2×#51163
C2×#50513