Finite Group Databasebeta

← C2×#10591638 #11867017

Subgroups — C2×#10591638 #11867017

Order 1152.

1065 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#946C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C2×#63856C211yesmaximal, characteristic
4C22×#3711C211yesmaximal, characteristic
5C2×#63662C211yesmaximal, characteristic, complemented
6#10591638C218yesmaximal, direct product factor
7C2×#63573C211yesmaximal, characteristic, complemented
8C2×#63565C211yesmaximal, characteristic, complemented
9C2×#5189—31nomaximal
10C2×#5052—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#946—22no—
17C3×#946C2214yes—
18C2×C3×#216—24no—
19C2×C3×#216C2214yescomplemented
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4—21no—
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×#3724—21no—
25C2×(C2×D3)⋊Dic3—21no—
26#63856—22no—
27#63856C2214yes—
28C2×#3711—24no—
29C2×#3711C2214yes—
30#63662C2214yescomplemented
31#63573C2214yescomplemented
32#63565C2214yescomplemented
33C22×C3×Q16—31no—
34C2×C3×C22⋊Q8—31no—
35C2×#946—31no—
36C2×#946D311yescharacteristic
37C22×#216D311yescharacteristic, complemented
38C2×#924—31no—
39C22×#208—31no—
40C22×ΓL(1,𝔽25)—31no—
41C2×#835—31no—
42C2×#835—31no—
43C2×#835—31no—
44C2×#835—61no—
45#5189—38no—
46C2×#817—31no—
47#5052—38no—
48C2×#810—31no—
49C2×#808—31no—
50C23×C3×D3D411yescharacteristic
51C2×C32×Q8—21no—
52C2×C32×Q8—22no—
53C2×C32×Q8—22no—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3D412yes—
64C2×C3×C4×D3C2312yes—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)C2312yes—
71C2×C3⋊(C3⋊C8)—22no—
72C2×C3⋊(C3⋊C8)C2312yes—
73C3×#216—28no—
74C3×(C2×D3)⋊C4—24no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3C2312yes—
77C3×Dic3⋊C4—24no—
78C2×C3×C3⋊C8D414yes—
79C2×C3×C3⋊C8C2312yes—
80#3724—24no—
81(C2×D3)⋊Dic3—24no—
82#3711—28no—
83C2×#470—91noSylow
84C22×C3×Q8—21no—
85C22×C3×Q8—31no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C2×D311yescharacteristic
88C23×C3×C4—31no—
89C22×C4×D3C2×D311yescharacteristic
90C22×Dic6C2×D311yescharacteristic
91C2×C3×Q16—34no—
92C2×C3×Q16—64no—
93C22×C3×C8—31no—
94C3×C22⋊Q8—34no—
95C3×C22⋊Q8—62no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—61no—
98C2×C3×C22⋊C4—61no—
99C2×#217—61no—
100#946—22no—
101#946—34no—
102#946—62no—
103#946C2×D314yes—
104C2×#216—24no—
105C2×#216C2×D314yescomplemented
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—61no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112#924—34no—
113#924—62no—
114C2×Dic3⋊C4—21no—
115C2×Dic3⋊C4—61no—
116C2×Dic3⋊C4—61no—
117C2×#208—34no—
118C2×#208—64no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—61no—
122C22×C3⋊C8C2×D311yescharacteristic
123C2×ΓL(1,𝔽25)—34no—
124C2×ΓL(1,𝔽25)—64no—
125#835—34no—
126#835—34no—
127#835—34no—
128#835—64no—
129#817—34no—
130#810—34no—
131#808—34no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3—22no—
136C22×C3×D3C2×D412yes—
137C32×Q8—22no—
138C32×Q8—22no—
139C32×Q8—42no—
140C2×C32×C4—22no—
141C2×C32×C4—42no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D412yes—
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—42no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3C2×D412yes—
154C3×C4×D3—24no—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—42no—
160C3⋊(C3⋊C8)—22no—
161C3×C3⋊C8C2×D414yes—
162C22×Q16—31no—
163C22×M16—91no—
164C2×C22⋊Q8—31no—
165C2×C22⋊Q8—91no—
166#470—98no—
167C2×#106—91no—
168C2×#103—91no—
169C2×#103—91no—
170C24×C3—31no—
171C23×D3#6711yescharacteristic
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—24no—
175C2×C3×Q8—22no—
176C2×C3×Q8—22no—
177C2×C3×Q8—22no—
178C2×C3×Q8—22no—
179C2×C3×Q8—22no—
180C2×C3×Q8—32no—
181C2×C3×Q8—41no—
182C2×C3×Q8—42no—
183C2×C3×Q8—61no—
184C2×C3×Q8—62no—
185C2×C3×Q8—62no—
186C2×C3×Q8C22×D312yes—
187C2×C3×Q8C22×D312yes—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—31no—
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—41no—
195C22×C3×C4—62no—
196C22×C3×C4—62no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205C22×Dic3—121no—
206C22×Dic3#6711yescharacteristic
207C2×C4×D3—22no—
208C2×C4×D3—22no—
209C2×C4×D3#6712yes—
210C2×C4×D3C22×D312yes—
211C2×Dic6—22no—
212C2×Dic6—22no—
213C2×Dic6—21no—
214C2×Dic6C22×D312yes—
215C3×Q16—68no—
216C2×C3×C8—34no—
217C2×C3×C8—32no—
218C3×C4⋊C4—32no—
219C3×C4⋊C4—64no—
220C3×C4⋊C4—61no—
221C3×C22⋊C4—64no—
222#217—64no—
223#216—28no—
224(C2×D3)⋊C4—24no—
225(C2×D3)⋊C4—64no—
226C4⋊Dic3—21no—
227C4⋊Dic3—32no—
228C4⋊Dic3—32no—
229C4⋊Dic3—62no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—121no—
233C4⋊Dic3C22×D312yes—
234Dic3⋊C4—24no—
235Dic3⋊C4—64no—
236Dic3⋊C4—64no—
237#208—68no—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8—62no—
242C2×C3⋊C8—62no—
243C2×C3⋊C8—122no—
244C2×C3⋊C8#6714yes—
245C2×C3⋊C8C22×D312yes—
246ΓL(1,𝔽25)—68no—
247C22×C32#12112yes—
248C22×C32#13712yes—
249C22×C32#13712yes—
250C22×C32C22×D411yescharacteristic
251C2×C3×D3—22no—
252C2×C3×D3—22no—
253C2×C3×D3—22no—
254C2×C3×D3—44no—
255C32×C4—42no—
256C32×C4#12112yes—
257C32×C4C22×D411yescharacteristic
258C32×C4C2×#4111yescharacteristic
259C3⋊Dic3—42no—
260C3×Dic3—22no—
261C3×Dic3—42no—
262C3×Dic3—42no—
263C22×Q8—31no—
264C22×Q8D3211yescharacteristic
265C23×C4—31no—
266C2×Q16—34no—
267C2×Q16—64no—
268C2×M16—94no—
269C2×M16—184no—
270C22×C8—31no—
271C22×C8—91no—
272C22⋊Q8—34no—
273C22⋊Q8—62no—
274C22⋊Q8—94no—
275C22⋊Q8—182no—
276C2×C4⋊C4—31no—
277C2×C4⋊C4—61no—
278C2×C4⋊C4—91no—
279C2×C4⋊C4—181no—
280C2×C22⋊C4—61no—
281C2×C22⋊C4—181no—
282#106—94no—
283#103—94no—
284#103—94no—
285C23×C3—21no—
286C23×C3—32no—
287C23×C3—62no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3D3×D411yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C22×D3—22no—
293C22×D3—22no—
294C22×D3—22no—
295C22×D3C2×#6712yes—
296C3×Q8—24no—
297C3×Q8—22no—
298C3×Q8—22no—
299C3×Q8—22no—
300C3×Q8—22no—
301C3×Q8—42no—
302C3×Q8—44no—
303C3×Q8—42no—
304C3×Q8—42no—
305C3×Q8—62no—
306C3×Q8—62no—
307C3×Q8—122no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—21no—
314C2×C3×C4—32no—
315C2×C3×C4—42no—
316C2×C3×C4—44no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—62no—
320C2×C3×C4—64no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—122no—
326C2×C3×C4—122no—
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D412yes—
329C2×C3×C4#23712yes—
330C2×C3×C4#23712yes—
331C2×C3×C4C2×#6712yes—
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—42no—
339C2×Dic3—42no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344C2×Dic3—122no—
345C2×Dic3—242no—
346C2×Dic3C2×#6712yes—
347C4×D3—24no—
348C4×D3—22no—
349C4×D3—22no—
350Dic6—22no—
351Dic6—22no—
352Dic6—42no—
353C3×C8—34no—
354C3⋊C8—62no—
355C3⋊C8—62no—
356C3⋊C8—122no—
357C3⋊C8C2×#6714yes—
358C2×C32#47014yescomplemented
359C2×C32C2×#12111yescharacteristic
360C2×C32C2×#13711yescharacteristic
361C2×C32C2×#13711yescharacteristic
362C3×D3—42no—
363C24—31no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—32no—
368C2×Q8—61no—
369C2×Q8—62no—
370C2×Q8—62no—
371C2×Q8C2×D3212yes—
372C22×C4—21no—
373C22×C4—31no—
374C22×C4—32no—
375C22×C4—32no—
376C22×C4—62no—
377C22×C4—62no—
378C22×C4—61no—
379C22×C4—61no—
380C22×C4—181no—
381C22×C4C2×D3211yescharacteristic
382Q16—68no—
383M16—188no—
384C2×C8—32no—
385C2×C8—34no—
386C2×C8—92no—
387C2×C8—182no—
388C4⋊C4—32no—
389C4⋊C4—64no—
390C4⋊C4—61no—
391C4⋊C4—92no—
392C4⋊C4—184no—
393C4⋊C4—181no—
394C22⋊C4—64no—
395C22⋊C4—184no—
396C22×C3—21no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—62no—
401C22×C3—62no—
402C22×C3—62no—
403C22×C3—124no—
404C22×C3#91812yes—
405C22×C3#91812yes—
406C22×C3#93812yes—
407C22×C3#93912yes—
408C22×C3#94212yes—
409C22×C3#95112yes—
410C22×C3C2×D3×D411yescharacteristic
411C22×C3C22×#6711yescharacteristic
412C2×D3—22no—
413C2×D3—22no—
414C2×D3—22no—
415C2×D3—44no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—44no—
420C3×C4—42no—
421C3×C4—42no—
422C3×C4—62no—
423C3×C4—122no—
424C3×C4—122no—
425C3×C4#93812yes—
426C3×C4#93912yes—
427C3×C4C2×D3×D411yescharacteristic
428C3×C4C2×#23711yescharacteristic
429C3×C4C2×#23711yescharacteristic
430C3×C4C22×#6711yescharacteristic
431Dic3—22no—
432Dic3—42no—
433Dic3—42no—
434Dic3—122no—
435Dic3—122no—
436Dic3—242no—
437C32C2×#47011yescharacteristic, complemented, Sylow
438C23—32no—
439C23—62no—
440C23—62no—
441C23—62no—
442C23D3×#6711yescharacteristic
443Q8—22no—
444Q8—22no—
445Q8—42no—
446Q8—62no—
447Q8—62no—
448Q8—122no—
449C2×C4—22no—
450C2×C4—32no—
451C2×C4—42no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—64no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—122no—
459C2×C4—122no—
460C2×C4—182no—
461C2×C4—362no—
462C2×C4#380512yes—
463C2×C4D3×#6712yes—
464C2×C4D3×#6711yescharacteristic
465C2×C4C22×D3211yescharacteristic
466C8—34no—
467C8—182no—
468C2×C3—21no—
469C2×C3—24no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—122no—
473C2×C3#505214yescomplemented
474C2×C3#518914yescomplemented
475C2×C3C2×#91811yescharacteristic
476C2×C3C2×#91811yescharacteristic
477C2×C3C2×#93811yescharacteristic
478C2×C3C2×#93911yescharacteristic
479C2×C3C2×#94211yescharacteristic
480C2×C3C2×#95111yescharacteristic
481D3—42no—
482C22—62no—
483C22—62no—
484C22—62no—
485C22—124no—
486C22#6394312yes—
487C22#6394812yes—
488C22#6397012yes—
489C22C2×D3×#6711yescharacteristic
490C4—42no—
491C4—62no—
492C4—122no—
493C4—122no—
494C4—362no—
495C4#6397012yes—
496C4C2×#380511yescharacteristic
497C4C2×D3×#6711yescharacteristic
498C3—21no—
499C3C2×#505211yescharacteristic, complemented
500C3C2×#518911yescharacteristic, complemented
501C2—122no—
502C2#1059163814yesdirect product factor
503C2C2×#6394311yescharacteristic
504C2C2×#6394811yescharacteristic
505C2C2×#6397011yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC22×Q8D32
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×C3×#216C2semidirect
5. C2×#63662C2semidirect
6. #10591638C2direct (N × H)
7. C2×#63573C2semidirect
8. C2×#63565C2semidirect
19. C2×C3×#216C22semidirect
30. #63662C22semidirect
31. #63573C22semidirect
32. #63565C22semidirect
37. C22×#216D3semidirect
105. C2×#216C2×D3semidirect
358. C2×C32#470semidirect
437. C32C2×#470semidirect
473. C2×C3#5052semidirect
474. C2×C3#5189semidirect
499. C3C2×#5052semidirect
500. C3C2×#5189semidirect
502. C2#10591638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9462
C22×C3×#2162
C2×#638562
C22×#37112
C2×#636622
#105916382
C2×#635732
C2×#635652
C2×#51893
C2×#50523