Finite Group Databasebeta

← C2×#10590862 #11874253

Subgroups — C2×#10590862 #11874253

Order 1152.

1333 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic, complemented
2C22×C3×#204C211yesmaximal, characteristic, complemented
3C2×#63864C211yesmaximal, characteristic, complemented
4C2×#63860C211yesmaximal, characteristic, complemented
5C22×#3719C211yesmaximal, characteristic, complemented
6C22×#3714C211yesmaximal, characteristic
7C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
8#10590862C218yesmaximal, direct product factor
9C2×#5168—31nomaximal
10C2×#4696—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×#3744—24no—
17C2×#3744C2214yescomplemented
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×C3×#204—24no—
21C2×C3×#204C2214yescomplemented
22C2×#3722—22no—
23C2×(C2×D3)⋊Dic3—22no—
24#63864—22no—
25#63864C2214yescomplemented
26#63860—22no—
27#63860C2214yescomplemented
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C2×#3714—24no—
31C2×#3714C2214yes—
32C3×C8×Dic3C2214yescomplemented
33C22×C3×SD16—31no—
34C2×#947—31no—
35C22×#216—31no—
36C2×#936—31no—
37C22×#213—31no—
38C22×Dic12—31no—
39C22×D24—31no—
40C22×#204—31no—
41C22×#204—31no—
42C22×#204—61no—
43C22×#204D311yescharacteristic, complemented
44C2×#875—31no—
45C2×#875—31no—
46C2×C3×C4×C8—31no—
47#5168—38no—
48C2×C8×Dic3D311yescharacteristic, complemented
49#4696—38no—
50C23×C3⋊D3—21no—
51C23×C3×D3—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)C2312yes—
58C2×#634—22no—
59C2×#634—22no—
60C2×#634—21no—
61C2×#634C2312yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D412yes—
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—
72C2×C32×C8D414yes—
73C2×C32×C8C2312yes—
74#3744—28no—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8D414yes—
78C2×C3×C3⋊C8C2312yes—
79C3×#204—28no—
80#3722—28no—
81(C2×D3)⋊Dic3—28no—
82#3719—28no—
83#3714—28no—
84C2×#495—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C22×D12C2×D311yescharacteristic
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×Dic6C2×D311yescharacteristic
95C2×C3×SD16—34no—
96C2×C3×SD16—64no—
97C22×C3×C8—21no—
98C22×C3×C8—31no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C2×C3×C42—31no—
102C2×#217—62no—
103#947—34no—
104#947—62no—
105C2×#216—34no—
106C2×#216—64no—
107#936—34no—
108#936—62no—
109C2×#213—34no—
110C2×#213—64no—
111C2×(C2×D3)⋊C4—62no—
112C2×(C2×D3)⋊C4—62no—
113C2×(C2×D3)⋊C4—62no—
114C2×C4×Dic3C2×D311yescharacteristic
115C22×C3⋊C8C2×D311yescharacteristic
116C2×Dic12—34no—
117C2×Dic12—64no—
118C2×D24—34no—
119C2×D24—64no—
120C2×#204—24no—
121C2×#204—34no—
122C2×#204—34no—
123C2×#204—64no—
124C2×#204—68no—
125C2×#204—64no—
126C2×#204—64no—
127C2×#204C2×D314yescomplemented
128#875—34no—
129#875—34no—
130#875—62no—
131#875—62no—
132C3×C4×C8—34no—
133C8×Dic3C2×D314yescomplemented
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—22no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—44no—
138C22×C3×D3—22no—
139C22×C3×D3—42no—
140C22×C3×D3—44no—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D412yes—
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2411yescharacteristic
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—42no—
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—42no—
150#634—22no—
151#634—22no—
152#634—42no—
153C2×C3×Dic3—24no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3C2×D414yes—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—42no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163C32×C8C2×D414yes—
164C3×C3⋊C8C2×D414yes—
165C22×Q16—91no—
166C22×SD16—31no—
167C22×SD16—91no—
168C22×D8—91no—
169C2×#124—91no—
170C2×#124—91no—
171#495—98no—
172C2×C4×C8—31no—
173C24×C3—61no—
174C23×D3—21no—
175C23×D3—61no—
176C23×D3—61no—
177C23×D3—121no—
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C2×C3×Q8—62no—
181C2×C3×Q8—62no—
182C2×C3×D4—32no—
183C2×C3×D4—62no—
184C2×C3×D4—62no—
185C2×C3×D4—61no—
186C22×C3×C4—21no—
187C22×C3×C4—32no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×Dic3—21no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3—121no—
195C22×Dic3D1212yes—
196C2×D12—22no—
197C2×D12—22no—
198C2×D12—21no—
199C2×D12—32no—
200C2×D12—32no—
201C2×D12—62no—
202C2×D12—64no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—122no—
210C2×D12—121no—
211C2×D12C22×D312yes—
212C2×Dic6—22no—
213C2×Dic6—22no—
214C2×Dic6—21no—
215C2×Dic6—32no—
216C2×Dic6—32no—
217C2×Dic6—62no—
218C2×Dic6—64no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×Dic6—61no—
224C2×Dic6—61no—
225C2×Dic6—121no—
226C2×Dic6—122no—
227C2×Dic6C22×D312yes—
228C3×SD16—68no—
229C2×C3×C8—24no—
230C2×C3×C8—22no—
231C2×C3×C8—34no—
232C2×C3×C8—32no—
233C2×C3×C8D1214yes—
234C2×C3×C8#6714yes—
235C2×C3×C8C22×D312yes—
236C2×C3×C8C22×D312yes—
237C3×C42—32no—
238C3×C42—32no—
239#217—68no—
240#216—68no—
241#213—68no—
242(C2×D3)⋊C4—68no—
243(C2×D3)⋊C4—68no—
244(C2×D3)⋊C4—68no—
245C4×Dic3D1212yes—
246C4×Dic3C22×D312yes—
247C2×C3⋊C8D1214yes—
248C2×C3⋊C8C22×D312yes—
249Dic12—68no—
250D24—68no—
251#204—28no—
252#204—616no—
253#204—68no—
254#204—68no—
255C22×C32#12712yes—
256C22×C32#13514yes—
257C22×C32C22×D411yescharacteristic
258C2×C3⋊D3—42no—
259C2×C3⋊D3—44no—
260C2×C3⋊D3—84no—
261C2×C3×D3—42no—
262C2×C3×D3—44no—
263C2×C3×D3—84no—
264C32×C4#12712yes—
265C32×C4C22×D411yescharacteristic
266C32×C4C22×D411yescharacteristic
267C3⋊Dic3—42no—
268C3×Dic3—24no—
269C3×Dic3—42no—
270C22×Q8—31no—
271C22×Q8—91no—
272C22×D4—31no—
273C22×D4—91no—
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×C8D3211yescharacteristic
284#124—94no—
285#124—94no—
286#124—182no—
287#124—182no—
288C2×C22⋊C4—182no—
289C2×C22⋊C4—182no—
290C2×C42—31no—
291C4×C8—34no—
292C23×C3—21no—
293C23×C3—62no—
294C23×C3—122no—
295C23×C3—124no—
296C23×C3C2×D1211yescharacteristic
297C23×C3D3×D411yescharacteristic
298C22×D3—22no—
299C22×D3—44no—
300C22×D3—42no—
301C22×D3—62no—
302C22×D3—62no—
303C22×D3—122no—
304C22×D3—124no—
305C22×D3—122no—
306C22×D3—124no—
307C22×D3—124no—
308C22×D3—122no—
309C22×D3—244no—
310C3×Q8—62no—
311C3×Q8—62no—
312C3×Q8—122no—
313C3×D4—62no—
314C3×D4—62no—
315C3×D4—122no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—34no—
321C2×C3×C4—64no—
322C2×C3×C4—62no—
323C2×C3×C4—122no—
324C2×C3×C4C2×D1211yescharacteristic
325C2×C3×C4C2×D1212yes—
326C2×C3×C4C2×D1212yes—
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D412yes—
329C2×C3×C4C2×#6712yes—
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×Dic3—24no—
333C2×Dic3—22no—
334C2×Dic3—42no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—122no—
338C2×Dic3—124no—
339C2×Dic3—122no—
340C2×Dic3—122no—
341C2×Dic3C2×D1214yes—
342D12—22no—
343D12—22no—
344D12—42no—
345D12—64no—
346D12—62no—
347D12—62no—
348D12—62no—
349D12—62no—
350D12—122no—
351D12—124no—
352D12—122no—
353D12—122no—
354Dic6—22no—
355Dic6—22no—
356Dic6—42no—
357Dic6—64no—
358Dic6—62no—
359Dic6—62no—
360Dic6—62no—
361Dic6—62no—
362Dic6—122no—
363Dic6—124no—
364Dic6—122no—
365Dic6—122no—
366C3×C8—24no—
367C3×C8—34no—
368C3×C8C2×D1214yes—
369C3×C8C2×#6714yes—
370C3⋊C8C2×D1214yes—
371C2×C32#49514yescomplemented
372C2×C32C2×#12711yescharacteristic
373C2×C32C2×#13512yes—
374C3⋊D3—82no—
375C3×D3—82no—
376C24—61no—
377C24—181no—
378C2×Q8—32no—
379C2×Q8—61no—
380C2×Q8—62no—
381C2×Q8—62no—
382C2×Q8—92no—
383C2×Q8—181no—
384C2×Q8—182no—
385C2×Q8—182no—
386C2×D4—32no—
387C2×D4—62no—
388C2×D4—61no—
389C2×D4—62no—
390C2×D4—92no—
391C2×D4—182no—
392C2×D4—181no—
393C2×D4—182no—
394C22×C4—32no—
395C22×C4—61no—
396C22×C4—181no—
397C22×C4C2×D3211yescharacteristic
398Q16—188no—
399SD16—68no—
400SD16—188no—
401D8—188no—
402C2×C8—32no—
403C2×C8—34no—
404C2×C8#62614yes—
405C2×C8C2×D3212yes—
406C22⋊C4—188no—
407C22⋊C4—188no—
408C42—32no—
409C42—32no—
410C22×C3—21no—
411C22×C3—24no—
412C22×C3—22no—
413C22×C3—122no—
414C22×C3—124no—
415C22×C3—244no—
416C22×C3#87412yes—
417C22×C3#90414yes—
418C22×C3#91614yes—
419C22×C3#94012yes—
420C22×C3C22×D1211yescharacteristic
421C22×C3C2×D3×D411yescharacteristic
422C2×D3—44no—
423C2×D3—42no—
424C2×D3—84no—
425C2×D3—124no—
426C2×D3—122no—
427C2×D3—124no—
428C2×D3—124no—
429C2×D3—122no—
430C2×D3—244no—
431C2×D3—248no—
432C2×D3—244no—
433C2×D3—244no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—64no—
438C3×C4—122no—
439C3×C4#87412yes—
440C3×C4#94012yes—
441C3×C4C22×D1211yescharacteristic
442C3×C4C22×D1211yescharacteristic
443C3×C4C2×D3×D411yescharacteristic
444C3×C4C22×#6711yescharacteristic
445Dic3—24no—
446Dic3—42no—
447Dic3—124no—
448Dic3—122no—
449Dic3—122no—
450C32C2×#49511yescharacteristic, complemented, Sylow
451C23—62no—
452C23—124no—
453C23—122no—
454C23—182no—
455C23—364no—
456C23—362no—
457C23D3×D1211yescharacteristic
458Q8—62no—
459Q8—62no—
460Q8—122no—
461Q8—182no—
462Q8—182no—
463Q8—362no—
464D4—62no—
465D4—62no—
466D4—122no—
467D4—182no—
468D4—182no—
469D4—362no—
470C2×C4—34no—
471C2×C4—64no—
472C2×C4—62no—
473C2×C4—122no—
474C2×C4—182no—
475C2×C4—362no—
476C2×C4D3×D1212yes—
477C2×C4D3×D1211yescharacteristic
478C2×C4C2×#62612yes—
479C2×C4C22×D3211yescharacteristic
480C8—34no—
481C8C2×#62614yes—
482C2×C3—22no—
483C2×C3—24no—
484C2×C3—21no—
485C2×C3—242no—
486C2×C3#469614yescomplemented
487C2×C3#516814yescomplemented
488C2×C3C2×#87411yescharacteristic
489C2×C3C2×#90412yes—
490C2×C3C2×#91612yes—
491C2×C3C2×#94011yescharacteristic
492D3—82no—
493D3—244no—
494D3—242no—
495D3—242no—
496C22—124no—
497C22—122no—
498C22—244no—
499C22—364no—
500C22—362no—
501C22—724no—
502C22#6380614yes—
503C22#6391112yes—
504C22C2×D3×D1211yescharacteristic
505C4—64no—
506C4—122no—
507C4—362no—
508C4#6391112yes—
509C4C2×D3×D1211yescharacteristic
510C4C22×#62611yescharacteristic
511C3—21no—
512C3C2×#469611yescharacteristic, complemented
513C3C2×#516811yescharacteristic, complemented
514C2—242no—
515C2—722no—
516C2#1059086214yesdirect product factor
517C2C2×#6380612yes—
518C2C2×#6391111yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
hypercenterC22×C8D32
hypocenterC32C2×#495
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×#3744C2semidirect
2. C22×C3×#204C2semidirect
3. C2×#63864C2semidirect
4. C2×#63860C2semidirect
5. C22×#3719C2semidirect
7. C2×C3×C8×Dic3C2semidirect
8. #10590862C2direct (N × H)
17. C2×#3744C22semidirect
21. C2×C3×#204C22semidirect
25. #63864C22semidirect
27. #63860C22semidirect
29. C2×#3719C22semidirect
32. C3×C8×Dic3C22semidirect
43. C22×#204D3semidirect
48. C2×C8×Dic3D3semidirect
127. C2×#204C2×D3semidirect
133. C8×Dic3C2×D3semidirect
371. C2×C32#495semidirect
450. C32C2×#495semidirect
486. C2×C3#4696semidirect
487. C2×C3#5168semidirect
512. C3C2×#4696semidirect
513. C3C2×#5168semidirect
516. C2#10590862direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37442
C22×C3×#2042
C2×#638642
C2×#638602
C22×#37192
C22×#37142
C2×C3×C8×Dic32
#105908622
C2×#51683
C2×#46963