Finite Group Databasebeta

← C2×#10591474 #11874251

Subgroups — C2×#10591474 #11874251

Order 1152.

1349 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
1C2×#64145C211yesmaximal, characteristic, complemented
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C22×C3×#213C211yesmaximal, characteristic
4C2×#63863C211yesmaximal, characteristic, complemented
5C22×#3719C211yesmaximal, characteristic, complemented
6C22×#3716C211yesmaximal, characteristic, complemented
7#10591474C218yesmaximal, direct product factor
8C2×#63553C211yesmaximal, characteristic, complemented
9C2×#5168—31nomaximal
10C2×#5155—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×#3757—22no—
16#64145—22no—
17#64145C2214yescomplemented
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×#214—24no—
20C2×C3×#214C2214yescomplemented
21C2×C3×#213—24no—
22C2×C3×#213C2214yes—
23C22×C3×C3⋊C8C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—22no—
26#63863—22no—
27#63863C2214yescomplemented
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C2×#3716—24no—
31C2×#3716C2214yescomplemented
32#63553C2214yescomplemented
33C22×C3×SD16—31no—
34C22×C3×D8—31no—
35C2×#947—31no—
36C22×#216—31no—
37C2×#936—31no—
38C2×#936—31no—
39C2×#936—31no—
40C2×#936—61no—
41C22×#214—31no—
42C22×#214D311yescharacteristic, complemented
43C22×#213D311yescharacteristic
44C22×Dic12—31no—
45C22×#204—31no—
46#5168—38no—
47#5155—38no—
48C2×C8×Dic3—31no—
49C2×C8×Dic3—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
57C22×C3⋊Dic3—21no—
58C22×C3⋊Dic3D412yes—
59C2×#634—22no—
60C2×#634—22no—
61C2×#634—21no—
62C2×#634C2312yes—
63C22×C3×Dic3—21no—
64C2×C3×D12—22no—
65C2×C3×D12—22no—
66C2×C3×D12—21no—
67C2×C3×D12C2312yes—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72#3757—28no—
73C4×C3⋊Dic3D412yes—
74C4×C3⋊Dic3C2312yes—
75C3×#214—28no—
76C3×#213—28no—
77C2×C3×C3⋊C8D414yes—
78C2×C3×C3⋊C8D414yes—
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2312yes—
81(C2×D3)⋊Dic3—28no—
82#3719—28no—
83#3716—28no—
84C2×#495—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—21no—
87C22×C3×D4—31no—
88C22×C3×D4C2×D311yescharacteristic
89C22×C3×D4C2×D311yescharacteristic
90C22×D12C2×D311yescharacteristic
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×Dic6C2×D311yescharacteristic
95C2×C3×SD16—34no—
96C2×C3×SD16—64no—
97C2×C3×D8—34no—
98C2×C3×D8—64no—
99C22×C3×C8—31no—
100C22×C3×C8—31no—
101C2×#217—62no—
102C2×#217—62no—
103C2×#217—62no—
104C2×#217—64no—
105#947—34no—
106#947—62no—
107C2×#216—34no—
108C2×#216—64no—
109#936—34no—
110#936—34no—
111#936—34no—
112#936—64no—
113#936—62no—
114#936—62no—
115#936—62no—
116#936—64no—
117C2×#214—24no—
118C2×#214—34no—
119C2×#214—64no—
120C2×#214C2×D314yescomplemented
121C2×#213—24no—
122C2×#213C2×D314yes—
123C2×(C2×D3)⋊C4—62no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—61no—
127C22×C3⋊C8C2×D311yescharacteristic
128C22×C3⋊C8C2×D311yescharacteristic
129C2×Dic12—34no—
130C2×Dic12—64no—
131C2×#204—34no—
132C2×#204—64no—
133C8×Dic3—34no—
134C8×Dic3—34no—
135C23×C32—22no—
136C23×C32—42no—
137C23×C32—44no—
138C23×C32C2×D411yescharacteristic
139C22×C3×D3—22no—
140C22×C3×D3—42no—
141C22×C3×D3—44no—
142C32×D4—22no—
143C32×D4—22no—
144C32×D4—42no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—24no—
151C2×C3⋊Dic3—42no—
152C2×C3⋊Dic3C2×D414yes—
153#634—22no—
154#634—22no—
155#634—42no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—42no—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—42no—
161C3×Dic6—22no—
162C3×Dic6—22no—
163C3×Dic6—42no—
164C3×C3⋊C8C2×D414yes—
165C3×C3⋊C8C2×D414yes—
166C22×Q16—91no—
167C22×SD16—31no—
168C22×SD16—91no—
169C22×D8—31no—
170C2×#124—91no—
171C2×#124—91no—
172#495—98no—
173C2×C4×C8—91no—
174C24×C3—22no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—61no—
178C23×D3—21no—
179C2×C3×Q8—32no—
180C2×C3×Q8—61no—
181C2×C3×Q8—62no—
182C2×C3×Q8—62no—
183C2×C3×D4—22no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—32no—
192C2×C3×D4—42no—
193C2×C3×D4—42no—
194C2×C3×D4—62no—
195C2×C3×D4—61no—
196C2×C3×D4—62no—
197C2×C3×D4C22×D312yes—
198C2×C3×D4C22×D312yes—
199C22×C3×C4—21no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—62no—
207C22×Dic3—62no—
208C22×Dic3—61no—
209C22×Dic3—61no—
210C2×D12—22no—
211C2×D12—22no—
212C2×D12—21no—
213C2×D12C22×D312yes—
214C2×Dic6—22no—
215C2×Dic6—22no—
216C2×Dic6—21no—
217C2×Dic6—32no—
218C2×Dic6—32no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—61no—
226C2×Dic6—61no—
227C2×Dic6—122no—
228C2×Dic6—122no—
229C2×Dic6C22×D312yes—
230C3×SD16—68no—
231C3×D8—68no—
232C2×C3×C8—34no—
233C2×C3×C8—34no—
234C2×C3×C8—32no—
235C2×C3×C8—32no—
236#217—68no—
237#217—68no—
238#217—68no—
239#217—616no—
240#216—68no—
241#214—28no—
242#214—68no—
243#213—28no—
244(C2×D3)⋊C4—68no—
245C4×Dic3—32no—
246C4×Dic3—32no—
247C4×Dic3—32no—
248C4×Dic3—32no—
249C4×Dic3—62no—
250C4×Dic3—62no—
251C2×C3⋊C8#6714yes—
252C2×C3⋊C8#6714yes—
253C2×C3⋊C8C22×D312yes—
254C2×C3⋊C8C22×D312yes—
255Dic12—68no—
256#204—68no—
257C22×C32—42no—
258C22×C32—44no—
259C22×C32—84no—
260C22×C32#12712yes—
261C22×C32#13514yes—
262C22×C32C22×D411yescharacteristic
263C2×C3×D3—42no—
264C2×C3×D3—44no—
265C2×C3×D3—84no—
266C32×C4#12712yes—
267C32×C4C22×D411yescharacteristic
268C32×C4C22×D411yescharacteristic
269C3⋊Dic3—24no—
270C3⋊Dic3—42no—
271C3×Dic3—42no—
272C22×Q8—31no—
273C22×Q8—91no—
274C22×D4—31no—
275C22×D4D3211yescharacteristic
276C2×Q16—94no—
277C2×Q16—184no—
278C2×SD16—34no—
279C2×SD16—64no—
280C2×SD16—94no—
281C2×SD16—184no—
282C2×D8—34no—
283C2×D8—64no—
284C22×C8—31no—
285C22×C8—31no—
286#124—94no—
287#124—94no—
288#124—182no—
289#124—182no—
290C2×C22⋊C4—182no—
291C2×C22⋊C4—182no—
292C2×C42—91no—
293C4×C8—94no—
294C23×C3—24no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—21no—
298C23×C3—44no—
299C23×C3—48no—
300C23×C3—44no—
301C23×C3—44no—
302C23×C3—42no—
303C23×C3—42no—
304C23×C3—62no—
305C23×C3—124no—
306C23×C3—122no—
307C23×C3D3×D411yescharacteristic
308C23×C3D3×D411yescharacteristic
309C22×D3—22no—
310C22×D3—44no—
311C22×D3—42no—
312C3×Q8—62no—
313C3×Q8—62no—
314C3×Q8—122no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—22no—
319C3×D4—42no—
320C3×D4—42no—
321C3×D4—44no—
322C3×D4—42no—
323C3×D4—42no—
324C3×D4—62no—
325C3×D4—62no—
326C3×D4—122no—
327C2×C3×C4—21no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—62no—
332C2×C3×C4—122no—
333C2×C3×C4D3×D412yes—
334C2×C3×C4D3×D412yes—
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4C2×#6712yes—
338C2×C3×C4C2×#6712yes—
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×Dic3—22no—
342C2×Dic3—34no—
343C2×Dic3—34no—
344C2×Dic3—42no—
345C2×Dic3—64no—
346C2×Dic3—64no—
347C2×Dic3—64no—
348C2×Dic3—64no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—124no—
352C2×Dic3—124no—
353C2×Dic3—122no—
354C2×Dic3—122no—
355D12—22no—
356D12—22no—
357D12—42no—
358Dic6—22no—
359Dic6—22no—
360Dic6—42no—
361Dic6—62no—
362Dic6—62no—
363Dic6—62no—
364Dic6—62no—
365Dic6—122no—
366Dic6—122no—
367Dic6—124no—
368Dic6—122no—
369Dic6—122no—
370C3×C8—34no—
371C3×C8—34no—
372C3⋊C8C2×#6714yes—
373C3⋊C8C2×#6714yes—
374C2×C32—82no—
375C2×C32#49514yescomplemented
376C2×C32C2×#12711yescharacteristic
377C2×C32C2×#13512yes—
378C3×D3—82no—
379C24—21no—
380C24—61no—
381C2×Q8—32no—
382C2×Q8—61no—
383C2×Q8—62no—
384C2×Q8—62no—
385C2×Q8—92no—
386C2×Q8—181no—
387C2×Q8—182no—
388C2×Q8—182no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—32no—
393C2×D4—62no—
394C2×D4—62no—
395C2×D4—61no—
396C2×D4C2×D3212yes—
397C22×C4—61no—
398C22×C4—92no—
399C22×C4—181no—
400C22×C4C2×D3211yescharacteristic
401Q16—188no—
402SD16—68no—
403SD16—188no—
404D8—68no—
405C2×C8—32no—
406C2×C8—32no—
407C2×C8—34no—
408C2×C8—34no—
409C22⋊C4—188no—
410C22⋊C4—188no—
411C42—92no—
412C42—92no—
413C22×C3—21no—
414C22×C3—24no—
415C22×C3—22no—
416C22×C3—44no—
417C22×C3—48no—
418C22×C3—44no—
419C22×C3—44no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—88no—
423C22×C3—84no—
424C22×C3—84no—
425C22×C3—124no—
426C22×C3—122no—
427C22×C3—244no—
428C22×C3#91214yes—
429C22×C3#91614yes—
430C22×C3#94012yes—
431C22×C3#94012yes—
432C22×C3C2×D3×D411yescharacteristic
433C22×C3C2×D3×D411yescharacteristic
434C2×D3—44no—
435C2×D3—42no—
436C2×D3—84no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—122no—
441C3×C4#94012yes—
442C3×C4#94012yes—
443C3×C4C2×D3×D411yescharacteristic
444C3×C4C2×D3×D411yescharacteristic
445C3×C4C22×#6711yescharacteristic
446C3×C4C22×#6711yescharacteristic
447Dic3—42no—
448Dic3—64no—
449Dic3—64no—
450Dic3—124no—
451Dic3—124no—
452Dic3—122no—
453Dic3—122no—
454C32C2×#49511yescharacteristic, complemented, Sylow
455C23—22no—
456C23—44no—
457C23—42no—
458C23—62no—
459C23—124no—
460C23—122no—
461C23#381111yescharacteristic
462Q8—62no—
463Q8—62no—
464Q8—122no—
465Q8—182no—
466Q8—182no—
467Q8—362no—
468D4—22no—
469D4—22no—
470D4—42no—
471D4—62no—
472D4—62no—
473D4—122no—
474C2×C4—62no—
475C2×C4—94no—
476C2×C4—122no—
477C2×C4—184no—
478C2×C4—182no—
479C2×C4—362no—
480C2×C4D3×#6712yes—
481C2×C4D3×#6712yes—
482C2×C4#381111yescharacteristic
483C2×C4C22×D3211yescharacteristic
484C8—34no—
485C8—34no—
486C2×C3—22no—
487C2×C3—21no—
488C2×C3—24no—
489C2×C3—84no—
490C2×C3—82no—
491C2×C3—82no—
492C2×C3—242no—
493C2×C3#515514yescomplemented
494C2×C3#516814yescomplemented
495C2×C3C2×#91212yes—
496C2×C3C2×#91612yes—
497C2×C3C2×#94011yescharacteristic
498C2×C3C2×#94011yescharacteristic
499D3—82no—
500C22—44no—
501C22—42no—
502C22—84no—
503C22—124no—
504C22—122no—
505C22—244no—
506C22#6393614yes—
507C22#6397912yes—
508C22C2×#381111yescharacteristic
509C4—122no—
510C4—184no—
511C4—362no—
512C4#6397912yes—
513C4C2×D3×#6711yescharacteristic
514C4C2×D3×#6711yescharacteristic
515C3—21no—
516C3C2×#515511yescharacteristic, complemented
517C3C2×#516811yescharacteristic, complemented
518C2—82no—
519C2—242no—
520C2#1059147414yesdirect product factor
521C2C2×#6393612yes—
522C2C2×#6397911yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×C3×#213C2
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
1. C2×#64145C2semidirect
2. C22×C3×#214C2semidirect
4. C2×#63863C2semidirect
5. C22×#3719C2semidirect
6. C22×#3716C2semidirect
7. #10591474C2direct (N × H)
8. C2×#63553C2semidirect
17. #64145C22semidirect
20. C2×C3×#214C22semidirect
27. #63863C22semidirect
29. C2×#3719C22semidirect
31. C2×#3716C22semidirect
32. #63553C22semidirect
42. C22×#214D3semidirect
120. C2×#214C2×D3semidirect
375. C2×C32#495semidirect
454. C32C2×#495semidirect
493. C2×C3#5155semidirect
494. C2×C3#5168semidirect
516. C3C2×#5155semidirect
517. C3C2×#5168semidirect
520. C2#10591474direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641452
C22×C3×#2142
C22×C3×#2132
C2×#638632
C22×#37192
C22×#37162
#105914742
C2×#635532
C2×#51683
C2×#51553