Finite Group Databasebeta

← C2×#10591442 #11865698

Subgroups — C2×#10591442 #11865698

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#936C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic
3C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
4C22×#3718C211yesmaximal, characteristic, complemented
5C2×#63659C211yesmaximal, characteristic
6#10591442C218yesmaximal, direct product factor
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63566C211yesmaximal, characteristic, complemented
9C2×#5166—31nomaximal
10C2×#5054—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×#217—21no—
17C2×C3×#217—21no—
18C3×#936—22no—
19C3×#936C2214yes—
20C2×C3×#214—24no—
21C2×C3×#214C2214yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×Dic3⋊Dic3—21no—
25C2×Dic32—21no—
26Dic3×Dic6—22no—
27Dic3×Dic6C2214yescomplemented
28C2×#3718—24no—
29C2×#3718C2214yescomplemented
30#63659C2214yes—
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63566C2214yescomplemented
33C22×C3×SD16—31no—
34C2×C3×#124—31no—
35C2×Q8×Dic3—31no—
36C22×#216—31no—
37C22×#216—31no—
38C2×#936D311yescharacteristic
39C22×#214D311yescharacteristic
40C2×C4×Dic6—31no—
41C2×#835—31no—
42C2×#832—31no—
43C2×#832—31no—
44C2×#832—61no—
45#5166—38no—
46C2×#816—31no—
47C2×Dic3⋊C8—31no—
48#5054—38no—
49C2×C4⋊(C3⋊C8)—31no—
50C24×C32—21no—
51C2×C32×D4—22no—
52C2×C32×D4—21no—
53C2×C32×D4—22no—
54C2×C32×D4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6D414yes—
67C2×C3×Dic6C2312yes—
68C2×C3×Dic6C2312yes—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)C2312yes—
71C2×C3⋊(C3⋊C8)—22no—
72C2×C3⋊(C3⋊C8)C2312yes—
73C3×#217—24no—
74C3×#217—24no—
75C3×#214—28no—
76C3×C4×Dic3D412yes—
77C3×C4×Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80Dic3⋊Dic3—24no—
81Dic32—24no—
82#3718—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×C3×Q8—31no—
86C22×C3×D4—21no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C22×Dic6C2×D311yescharacteristic
90C22×Dic6C2×D311yescharacteristic
91C2×C3×SD16—34no—
92C2×C3×SD16—64no—
93C22×C3×C8—31no—
94C3×#124—34no—
95C3×#124—62no—
96C2×C3×C22⋊C4—61no—
97C2×C3×C22⋊C4—61no—
98C2×C3×C42—31no—
99C2×#217—21no—
100C2×#217—21no—
101Q8×Dic3—34no—
102Q8×Dic3—62no—
103C2×#216—34no—
104C2×#216—34no—
105C2×#216—64no—
106C2×#216—64no—
107#936—22no—
108#936C2×D314yes—
109C2×#214—24no—
110C2×#214C2×D314yes—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—61no—
114C2×C4⋊Dic3—61no—
115C2×Dic3⋊C4—61no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3—61no—
118C2×C4×Dic3C2×D311yescharacteristic
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—61no—
122C22×C3⋊C8C2×D311yescharacteristic
123C4×Dic6—34no—
124C4×Dic6—62no—
125#835—34no—
126#832—34no—
127#832—34no—
128#832—64no—
129#816—34no—
130Dic3⋊C8—34no—
131C4⋊(C3⋊C8)—34no—
132C23×C32—22no—
133C23×C32—42no—
134C23×C32—42no—
135C23×C32—42no—
136C23×C32C2×D411yescharacteristic
137C32×D4—22no—
138C32×D4—22no—
139C32×D4—42no—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D412yes—
142C2×C32×C4#4112yes—
143C2×C32×C4C2411yescharacteristic
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—42no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3C2×D412yes—
153C2×C3×Dic3C2×D412yes—
154C3×Dic6—24no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—42no—
159C3×Dic6C2×D414yes—
160C3⋊(C3⋊C8)—22no—
161C3×C3⋊C8—22no—
162C22×Q16—91no—
163C22×SD16—31no—
164C2×#124—31no—
165C2×C4×Q8—91no—
166#464—98no—
167C2×C4⋊C8—91no—
168C2×#103—91no—
169C2×#102—91no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—41no—
173C2×C3×Q8—34no—
174C2×C3×Q8—32no—
175C2×C3×Q8—32no—
176C2×C3×Q8—61no—
177C2×C3×Q8—62no—
178C2×C3×Q8—61no—
179C2×C3×Q8—62no—
180C2×C3×Q8—62no—
181C2×C3×D4—24no—
182C2×C3×D4—22no—
183C2×C3×D4—21no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—21no—
188C2×C3×D4—22no—
189C2×C3×D4—42no—
190C2×C3×D4—41no—
191C2×C3×D4C22×D312yes—
192C2×C3×D4C22×D312yes—
193C22×C3×C4—21no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×Dic3—21no—
201C22×Dic3—21no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3—121no—
205C22×Dic3#6711yescharacteristic
206C22×Dic3#6711yescharacteristic
207C2×Dic6—21no—
208C2×Dic6—22no—
209C2×Dic6—22no—
210C2×Dic6—22no—
211C2×Dic6—21no—
212C2×Dic6#6714yes—
213C2×Dic6C22×D312yes—
214C2×Dic6C22×D312yes—
215C3×SD16—68no—
216C2×C3×C8—32no—
217C2×C3×C8—62no—
218C3×C22⋊C4—64no—
219C3×C22⋊C4—64no—
220C3×C42—32no—
221C3×C42—32no—
222#217—24no—
223#217—24no—
224#216—68no—
225#216—68no—
226#214—28no—
227C4⋊Dic3—32no—
228C4⋊Dic3—32no—
229C4⋊Dic3—62no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—64no—
233C4⋊Dic3—121no—
234Dic3⋊C4—64no—
235C4×Dic3—64no—
236C4×Dic3—64no—
237C4×Dic3#6712yes—
238C4×Dic3C22×D312yes—
239C2×C3⋊C8—22no—
240C2×C3⋊C8—32no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—62no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—122no—
246C2×C3⋊C8C22×D312yes—
247C22×C32—42no—
248C22×C32—42no—
249C22×C32—42no—
250C22×C32—84no—
251C22×C32#12112yes—
252C22×C32#13512yes—
253C22×C32#13712yes—
254C22×C32C22×D411yescharacteristic
255C32×C4#12112yes—
256C32×C4C22×D411yescharacteristic
257C32×C4C2×#4111yescharacteristic
258C3⋊Dic3—42no—
259C3×Dic3—24no—
260C3×Dic3—22no—
261C3×Dic3—22no—
262C3×Dic3—42no—
263C22×Q8—31no—
264C22×Q8—31no—
265C22×D4D3211yescharacteristic
266C2×Q16—94no—
267C2×Q16—184no—
268C2×SD16—34no—
269C2×SD16—64no—
270C22×C8—31no—
271C22×C8—91no—
272#124—34no—
273#124—62no—
274C4×Q8—94no—
275C4×Q8—182no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—181no—
278C2×C22⋊C4—61no—
279C2×C22⋊C4—61no—
280C2×C42—31no—
281C2×C42—181no—
282C4⋊C8—94no—
283#103—94no—
284#102—94no—
285C23×C3—22no—
286C23×C3—22no—
287C23×C3—21no—
288C23×C3—42no—
289C23×C3—44no—
290C23×C3—42no—
291C23×C3—42no—
292C23×C3—42no—
293C23×C3—42no—
294C23×C3—42no—
295C23×C3—42no—
296C23×C3—82no—
297C23×C3—82no—
298C23×C3D3×D411yescharacteristic
299C23×C3C2×#6711yescharacteristic
300C3×Q8—34no—
301C3×Q8—64no—
302C3×Q8—62no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—122no—
306C3×D4—24no—
307C3×D4—22no—
308C3×D4—22no—
309C3×D4—22no—
310C3×D4—22no—
311C3×D4—42no—
312C3×D4—44no—
313C3×D4—42no—
314C3×D4—42no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—64no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—122no—
327C2×C3×C4D3×D412yes—
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4#23712yes—
330C2×C3×C4#23712yes—
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C2×#6712yes—
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×Dic3—24no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—42no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—122no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C2×Dic3—242no—
347C2×Dic3C2×#6712yes—
348C2×Dic3C2×#6712yes—
349Dic6—24no—
350Dic6—22no—
351Dic6—22no—
352Dic6—22no—
353Dic6—42no—
354Dic6C2×#6714yes—
355C3×C8—62no—
356C3⋊C8—22no—
357C3⋊C8—62no—
358C3⋊C8—62no—
359C3⋊C8—122no—
360C2×C32—82no—
361C2×C32#46414yescomplemented
362C2×C32C2×#12111yescharacteristic
363C2×C32C2×#13511yescharacteristic
364C2×C32C2×#13711yescharacteristic
365C24—21no—
366C2×Q8—32no—
367C2×Q8—32no—
368C2×Q8—34no—
369C2×Q8—62no—
370C2×Q8—61no—
371C2×Q8—61no—
372C2×Q8—62no—
373C2×Q8—62no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4C2×D3212yes—
378C22×C4—31no—
379C22×C4—31no—
380C22×C4—61no—
381C22×C4—61no—
382C22×C4—181no—
383C22×C4C2×D3211yescharacteristic
384Q16—188no—
385SD16—68no—
386C2×C8—32no—
387C2×C8—62no—
388C2×C8—92no—
389C2×C8—182no—
390C4⋊C4—92no—
391C4⋊C4—184no—
392C4⋊C4—181no—
393C22⋊C4—64no—
394C22⋊C4—64no—
395C42—32no—
396C42—32no—
397C42—184no—
398C22×C3—21no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—44no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—82no—
410C22×C3—82no—
411C22×C3—88no—
412C22×C3—84no—
413C22×C3—84no—
414C22×C3#91512yes—
415C22×C3#91612yes—
416C22×C3#93812yes—
417C22×C3#93912yes—
418C22×C3#95012yes—
419C22×C3#95112yes—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C22×#6711yescharacteristic
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—62no—
426C3×C4—62no—
427C3×C4—64no—
428C3×C4—122no—
429C3×C4#93812yes—
430C3×C4#93912yes—
431C3×C4C2×D3×D411yescharacteristic
432C3×C4C2×#23711yescharacteristic
433C3×C4C2×#23711yescharacteristic
434C3×C4C22×#6711yescharacteristic
435Dic3—24no—
436Dic3—22no—
437Dic3—22no—
438Dic3—42no—
439Dic3—122no—
440Dic3—122no—
441Dic3—242no—
442C32C2×#46411yescharacteristic, complemented, Sylow
443C23—22no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23D3×#6711yescharacteristic
448Q8—34no—
449Q8—62no—
450Q8—64no—
451Q8—62no—
452Q8—62no—
453Q8—122no—
454D4—22no—
455D4—22no—
456D4—42no—
457C2×C4—32no—
458C2×C4—32no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—64no—
463C2×C4—62no—
464C2×C4—122no—
465C2×C4—182no—
466C2×C4—362no—
467C2×C4#380512yes—
468C2×C4D3×#6712yes—
469C2×C4D3×#6711yescharacteristic
470C2×C4C22×D3211yescharacteristic
471C8—62no—
472C8—182no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—24no—
477C2×C3—84no—
478C2×C3—82no—
479C2×C3—82no—
480C2×C3#505414yescomplemented
481C2×C3#516614yescomplemented
482C2×C3C2×#91511yescharacteristic
483C2×C3C2×#91611yescharacteristic
484C2×C3C2×#93811yescharacteristic
485C2×C3C2×#93911yescharacteristic
486C2×C3C2×#95011yescharacteristic
487C2×C3C2×#95111yescharacteristic
488C22—42no—
489C22—42no—
490C22—42no—
491C22—84no—
492C22#6392912yes—
493C22#6393512yes—
494C22#6397012yes—
495C22C2×D3×#6711yescharacteristic
496C4—62no—
497C4—62no—
498C4—64no—
499C4—122no—
500C4—362no—
501C4#6397012yes—
502C4C2×#380511yescharacteristic
503C4C2×D3×#6711yescharacteristic
504C3—21no—
505C3C2×#505411yescharacteristic, complemented
506C3C2×#516611yescharacteristic, complemented
507C2—82no—
508C2#1059144214yesdirect product factor
509C2C2×#6392911yescharacteristic
510C2C2×#6393511yescharacteristic
511C2C2×#6397011yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. C2×Dic3×Dic6C2semidirect
4. C22×#3718C2semidirect
6. #10591442C2direct (N × H)
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. C2×#63566C2semidirect
27. Dic3×Dic6C22semidirect
29. C2×#3718C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63566C22semidirect
361. C2×C32#464semidirect
442. C32C2×#464semidirect
480. C2×C3#5054semidirect
481. C2×C3#5166semidirect
505. C3C2×#5054semidirect
506. C3C2×#5166semidirect
508. C2#10591442direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9362
C22×C3×#2142
C2×Dic3×Dic62
C22×#37182
C2×#636592
#105914422
C2×Dic3⋊(C3⋊C8)2
C2×#635662
C2×#51663
C2×#50543