Finite Group Databasebeta

← C2×#10591473 #11874252

Subgroups — C2×#10591473 #11874252

Order 1152.

1353 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic
2C2×C3×#936C211yesmaximal, characteristic, complemented
3C22×C3×#214C211yesmaximal, characteristic, complemented
4C2×#63864C211yesmaximal, characteristic, complemented
5C22×#3718C211yesmaximal, characteristic, complemented
6C22×#3717C211yesmaximal, characteristic, complemented
7#10591473C218yesmaximal, direct product factor
8C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
9C2×#5168—31nomaximal
10C2×#5059—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×#3753—24no—
16C2×#3753C2214yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—22no—
19C3×#936—22no—
20C3×#936C2214yescomplemented
21C2×C3×#214—24no—
22C2×C3×#214C2214yescomplemented
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×#3722—22no—
26#63864—22no—
27#63864C2214yescomplemented
28C2×#3718—24no—
29C2×#3718C2214yescomplemented
30C2×#3717—24no—
31C2×#3717C2214yescomplemented
32Dic3×C3⋊C8C2214yescomplemented
33C22×C3×SD16—31no—
34C2×C3×#124—31no—
35C2×#947—31no—
36C22×#216—31no—
37C22×#216—31no—
38C22×#215—31no—
39C2×#936D311yescharacteristic, complemented
40C22×#214D311yescharacteristic, complemented
41C22×#213—31no—
42C22×#213—31no—
43C22×#213—61no—
44C22×#204—31no—
45C2×#875—31no—
46#5168—38no—
47C2×C8×Dic3—31no—
48#5059—38no—
49C2×C4×C3⋊C8—31no—
50C24×C32—21no—
51C23×C3⋊D3—21no—
52C2×C32×D4—22no—
53C2×C32×D4—22no—
54C2×C32×D4—21no—
55C2×C32×D4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D412yes—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2312yes—
72#3753—28no—
73C2×C3⋊(C3⋊C8)D414yes—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#217—28no—
76C3×#214—28no—
77C3×C4×Dic3D412yes—
78C3×C4×Dic3C2312yes—
79C2×C3×C3⋊C8D414yes—
80C2×C3×C3⋊C8C2312yes—
81#3722—28no—
82#3718—28no—
83#3717—28no—
84C2×#495—91noSylow
85C22×C3×Q8—31no—
86C22×C3×Q8—31no—
87C22×C3×D4—21no—
88C22×C3×D4C2×D311yescharacteristic
89C22×C3×D4C2×D311yescharacteristic
90C22×D12—31no—
91C22×D12—31no—
92C22×D12—61no—
93C22×Dic6C2×D311yescharacteristic
94C22×Dic6C2×D311yescharacteristic
95C2×C3×SD16—34no—
96C2×C3×SD16—64no—
97C22×C3×C8—31no—
98C3×#124—34no—
99C3×#124—62no—
100C2×C3×C22⋊C4—62no—
101C2×C3×C42—31no—
102C2×#217—22no—
103#947—34no—
104#947—62no—
105C2×#216—34no—
106C2×#216—34no—
107C2×#216—64no—
108C2×#216—64no—
109C2×#215—34no—
110C2×#215—64no—
111#936—22no—
112#936C2×D314yescomplemented
113C2×#214—24no—
114C2×#214C2×D314yescomplemented
115C2×#213—34no—
116C2×#213—34no—
117C2×#213—64no—
118C2×#213—64no—
119C2×#213—64no—
120C2×#213—68no—
121C2×(C2×D3)⋊C4—62no—
122C2×(C2×D3)⋊C4—62no—
123C2×C4×Dic3C2×D311yescharacteristic
124C22×C3⋊C8—31no—
125C22×C3⋊C8—31no—
126C22×C3⋊C8—61no—
127C22×C3⋊C8C2×D311yescharacteristic
128C2×#204—34no—
129C2×#204—64no—
130#875—34no—
131#875—62no—
132C8×Dic3—34no—
133C4×C3⋊C8—34no—
134C23×C32—22no—
135C23×C32—42no—
136C23×C32—44no—
137C23×C32C2×D411yescharacteristic
138C22×C3⋊D3—22no—
139C22×C3⋊D3—42no—
140C22×C3⋊D3—44no—
141C32×D4—22no—
142C32×D4—22no—
143C32×D4—42no—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2411yescharacteristic
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—42no—
151C2×C3×Dic3—24no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3C2×D414yes—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—22no—
160C3×Dic6—22no—
161C3×Dic6—42no—
162C3×Dic6—42no—
163C3⋊(C3⋊C8)C2×D414yes—
164C3×C3⋊C8C2×D414yes—
165C22×Q16—91no—
166C22×SD16—31no—
167C22×SD16—91no—
168C22×D8—91no—
169C2×#124—31no—
170C2×#124—91no—
171#495—98no—
172C2×C4×C8—91no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—41no—
176C23×D3—61no—
177C23×D3—61no—
178C23×D3—121no—
179C2×C3×Q8—32no—
180C2×C3×Q8—32no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—62no—
184C2×C3×Q8—62no—
185C2×C3×Q8—62no—
186C2×C3×Q8—62no—
187C2×C3×D4—24no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—21no—
192C2×C3×D4—22no—
193C2×C3×D4—21no—
194C2×C3×D4—22no—
195C2×C3×D4—42no—
196C2×C3×D4—41no—
197C2×C3×D4C22×D312yes—
198C2×C3×D4C22×D312yes—
199C22×C3×C4—21no—
200C22×C3×C4—32no—
201C22×C3×C4—61no—
202C22×C3×C4—61no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3#6712yes—
208C2×D12—32no—
209C2×D12—32no—
210C2×D12—62no—
211C2×D12—64no—
212C2×D12—62no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—62no—
216C2×D12—61no—
217C2×D12—61no—
218C2×D12—122no—
219C2×D12—121no—
220C2×Dic6—22no—
221C2×Dic6—22no—
222C2×Dic6—22no—
223C2×Dic6—22no—
224C2×Dic6—21no—
225C2×Dic6—21no—
226C2×Dic6C22×D312yes—
227C2×Dic6C22×D312yes—
228C3×SD16—68no—
229C2×C3×C8—34no—
230C2×C3×C8—32no—
231C3×C22⋊C4—68no—
232C3×C42—32no—
233C3×C42—32no—
234#217—28no—
235#216—68no—
236#216—68no—
237#215—68no—
238#214—28no—
239#213—68no—
240#213—68no—
241#213—616no—
242(C2×D3)⋊C4—68no—
243(C2×D3)⋊C4—68no—
244C4×Dic3#6712yes—
245C4×Dic3C22×D312yes—
246C2×C3⋊C8—34no—
247C2×C3⋊C8—34no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—64no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8#6714yes—
253C2×C3⋊C8C22×D312yes—
254#204—68no—
255C22×C32—42no—
256C22×C32—44no—
257C22×C32—84no—
258C22×C32#12712yes—
259C22×C32#13514yes—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—42no—
262C2×C3⋊D3—44no—
263C2×C3⋊D3—84no—
264C32×C4#12712yes—
265C32×C4C22×D411yescharacteristic
266C32×C4C22×D411yescharacteristic
267C3×Dic3—24no—
268C3×Dic3—42no—
269C3×Dic3—42no—
270C22×Q8—31no—
271C22×Q8—31no—
272C22×D4—91no—
273C22×D4D3211yescharacteristic
274C2×Q16—94no—
275C2×Q16—184no—
276C2×SD16—34no—
277C2×SD16—64no—
278C2×SD16—94no—
279C2×SD16—184no—
280C2×D8—94no—
281C2×D8—184no—
282C22×C8—31no—
283C22×C8—91no—
284#124—34no—
285#124—62no—
286#124—94no—
287#124—182no—
288C2×C22⋊C4—62no—
289C2×C22⋊C4—182no—
290C2×C42—31no—
291C4×C8—94no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—21no—
295C23×C3—42no—
296C23×C3—44no—
297C23×C3—44no—
298C23×C3—42no—
299C23×C3—42no—
300C23×C3—44no—
301C23×C3—84no—
302C23×C3D3×D411yescharacteristic
303C23×C3C2×#6711yescharacteristic
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—122no—
307C22×D3—124no—
308C22×D3—124no—
309C22×D3—122no—
310C22×D3—122no—
311C22×D3—124no—
312C22×D3—244no—
313C3×Q8—62no—
314C3×Q8—62no—
315C3×Q8—62no—
316C3×Q8—62no—
317C3×Q8—122no—
318C3×Q8—122no—
319C3×D4—24no—
320C3×D4—22no—
321C3×D4—22no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—42no—
325C3×D4—44no—
326C3×D4—42no—
327C3×D4—42no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—34no—
333C2×C3×C4—64no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—122no—
337C2×C3×C4—122no—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D412yes—
340C2×C3×C4D3×D412yes—
341C2×C3×C4D3×D412yes—
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6712yes—
344C2×C3×C4C23×D311yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346C2×Dic3—24no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—42no—
350C2×Dic3—42no—
351C2×Dic3C2×#6714yes—
352D12—64no—
353D12—62no—
354D12—62no—
355D12—62no—
356D12—62no—
357D12—122no—
358D12—124no—
359D12—122no—
360D12—122no—
361Dic6—22no—
362Dic6—22no—
363Dic6—22no—
364Dic6—22no—
365Dic6—42no—
366Dic6—42no—
367C3×C8—34no—
368C3⋊C8—34no—
369C3⋊C8—34no—
370C3⋊C8—64no—
371C3⋊C8C2×#6714yes—
372C2×C32—82no—
373C2×C32#49514yescomplemented
374C2×C32C2×#12711yescharacteristic
375C2×C32C2×#13512yes—
376C3⋊D3—82no—
377C24—21no—
378C24—181no—
379C2×Q8—32no—
380C2×Q8—32no—
381C2×Q8—61no—
382C2×Q8—61no—
383C2×Q8—62no—
384C2×Q8—62no—
385C2×Q8—62no—
386C2×Q8—62no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—92no—
391C2×D4—182no—
392C2×D4—181no—
393C2×D4—182no—
394C2×D4C2×D3212yes—
395C22×C4—32no—
396C22×C4—61no—
397C22×C4—61no—
398C22×C4C2×D3211yescharacteristic
399Q16—188no—
400SD16—68no—
401SD16—188no—
402D8—188no—
403C2×C8—32no—
404C2×C8—34no—
405C2×C8—92no—
406C2×C8—94no—
407C22⋊C4—68no—
408C22⋊C4—188no—
409C42—32no—
410C42—32no—
411C22×C3—21no—
412C22×C3—24no—
413C22×C3—22no—
414C22×C3—44no—
415C22×C3—44no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—44no—
419C22×C3—84no—
420C22×C3—88no—
421C22×C3—84no—
422C22×C3—84no—
423C22×C3#91614yes—
424C22×C3#94012yes—
425C22×C3#94012yes—
426C22×C3#95014yes—
427C22×C3C2×D3×D411yescharacteristic
428C22×C3C22×#6711yescharacteristic
429C2×D3—124no—
430C2×D3—124no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—124no—
434C2×D3—244no—
435C2×D3—248no—
436C2×D3—244no—
437C2×D3—244no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—64no—
442C3×C4—122no—
443C3×C4—122no—
444C3×C4#94012yes—
445C3×C4#94012yes—
446C3×C4C2×D3×D411yescharacteristic
447C3×C4C2×D3×D411yescharacteristic
448C3×C4C2×D3×D411yescharacteristic
449C3×C4C22×#6711yescharacteristic
450Dic3—24no—
451Dic3—42no—
452Dic3—42no—
453C32C2×#49511yescharacteristic, complemented, Sylow
454C23—22no—
455C23—44no—
456C23—42no—
457C23—182no—
458C23—364no—
459C23—362no—
460C23D3×#6711yescharacteristic
461Q8—62no—
462Q8—62no—
463Q8—62no—
464Q8—62no—
465Q8—122no—
466Q8—122no—
467D4—22no—
468D4—22no—
469D4—42no—
470D4—182no—
471D4—182no—
472D4—362no—
473C2×C4—34no—
474C2×C4—64no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—122no—
478C2×C4—122no—
479C2×C4D3×#6712yes—
480C2×C4D3×#6711yescharacteristic
481C2×C4#381112yes—
482C2×C4C22×D3211yescharacteristic
483C8—34no—
484C8—94no—
485C2×C3—22no—
486C2×C3—21no—
487C2×C3—24no—
488C2×C3—84no—
489C2×C3—82no—
490C2×C3—82no—
491C2×C3#505914yescomplemented
492C2×C3#516814yescomplemented
493C2×C3C2×#91612yes—
494C2×C3C2×#94011yescharacteristic
495C2×C3C2×#94011yescharacteristic
496C2×C3C2×#95012yes—
497D3—244no—
498D3—242no—
499D3—242no—
500C22—44no—
501C22—42no—
502C22—84no—
503C22—364no—
504C22—362no—
505C22—724no—
506C22#6393514yes—
507C22#6397912yes—
508C22C2×D3×#6711yescharacteristic
509C4—64no—
510C4—122no—
511C4—122no—
512C4#6397912yes—
513C4C2×D3×#6711yescharacteristic
514C4C2×#381111yescharacteristic
515C3—21no—
516C3C2×#505911yescharacteristic, complemented
517C3C2×#516811yescharacteristic, complemented
518C2—82no—
519C2—722no—
520C2#1059147314yesdirect product factor
521C2C2×#6393512yes—
522C2C2×#6397911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×#3753C2
hypercenterC22×D4D32
hypocenterC32C2×#495
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
2. C2×C3×#936C2semidirect
3. C22×C3×#214C2semidirect
4. C2×#63864C2semidirect
5. C22×#3718C2semidirect
6. C22×#3717C2semidirect
7. #10591473C2direct (N × H)
8. C2×Dic3×C3⋊C8C2semidirect
20. C3×#936C22semidirect
22. C2×C3×#214C22semidirect
27. #63864C22semidirect
29. C2×#3718C22semidirect
31. C2×#3717C22semidirect
32. Dic3×C3⋊C8C22semidirect
39. C2×#936D3semidirect
40. C22×#214D3semidirect
112. #936C2×D3semidirect
114. C2×#214C2×D3semidirect
373. C2×C32#495semidirect
453. C32C2×#495semidirect
491. C2×C3#5059semidirect
492. C2×C3#5168semidirect
516. C3C2×#5059semidirect
517. C3C2×#5168semidirect
520. C2#10591473direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37532
C2×C3×#9362
C22×C3×#2142
C2×#638642
C22×#37182
C22×#37172
#105914732
C2×Dic3×C3⋊C82
C2×#51683
C2×#50593