Finite Group Databasebeta

← C2×#10590861 #11865715

Subgroups — C2×#10590861 #11865715

Order 1152.

1129 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3746C211yesmaximal, characteristic, complemented
2C2×#63860C211yesmaximal, characteristic
3C2×#63844C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic
5C2×C3×#821C211yesmaximal, characteristic
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590861C218yesmaximal, direct product factor
9C2×#4845—31nomaximal
10C2×#4767—31nomaximal
11C22×#634C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×#3746—24no—
16C2×#3746C2214yescomplemented
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×#3724—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×Dic32—21no—
24#63860—22no—
25#63860C2214yes—
26#63844—22no—
27#63844C2214yescomplemented
28C2×#3716—24no—
29C2×#3716C2214yes—
30C3×#821C2214yes—
31C3×Dic3⋊C8C2214yescomplemented
32#63567C2214yescomplemented
33C2×#936—31no—
34C22×#214—31no—
35C22×Dic12—31no—
36C22×Dic12—31no—
37C22×Dic12—61no—
38C22×#204—31no—
39C2×#887—31no—
40C2×#875—31no—
41C2×C4×Dic6—31no—
42C2×C3×C4⋊C8—31no—
43C2×C3×#102—31no—
44C2×#821D311yescharacteristic
45C2×#816—31no—
46C2×Dic3⋊C8D311yescharacteristic, complemented
47C2×#810—31no—
48#4845—38no—
49#4767—38no—
50C23×C3×D3—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3—21no—
54C2×#634—21no—
55C2×#634—22no—
56C2×#634—22no—
57C2×#634—22no—
58C2×#634—21no—
59C2×#634D414yes—
60C2×#634C2312yes—
61C2×#634C2312yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—21no—
68C2×C3×D12C2312yes—
69C2×C32×C8—22no—
70C2×C32×C8C2312yes—
71#3746—28no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3C2312yes—
74C3×C4×Dic3D412yes—
75C3×C4×Dic3C2312yes—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8C2312yes—
78#3724—24no—
79(C2×D3)⋊Dic3—24no—
80(C2×D3)⋊Dic3—24no—
81Dic32—24no—
82#3716—28no—
83C2×#464—91noSylow
84C22×C3×D4—31no—
85C22×D12C2×D311yescharacteristic
86C22×Dic6—31no—
87C22×Dic6—31no—
88C22×Dic6—31no—
89C22×Dic6—31no—
90C22×Dic6—61no—
91C22×Dic6—61no—
92C22×C3×C8—21no—
93C22×C3×C8—31no—
94C22×C3×C8C2×D311yescharacteristic
95C22×C3×C8C2×D311yescharacteristic
96C2×C3×C4⋊C4—31no—
97C2×C3×C42—31no—
98C2×#217—61no—
99C2×#217—61no—
100#936—34no—
101#936—62no—
102C2×#214—34no—
103C2×#214—64no—
104C2×(C2×D3)⋊C4—61no—
105C2×(C2×D3)⋊C4—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×Dic3⋊C4—61no—
108C2×Dic3⋊C4—61no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3—61no—
111C2×C4×Dic3C2×D311yescharacteristic
112C22×C3⋊C8C2×D311yescharacteristic
113C2×Dic12—34no—
114C2×Dic12—34no—
115C2×Dic12—64no—
116C2×Dic12—64no—
117C2×Dic12—64no—
118C2×Dic12—68no—
119C2×#204—34no—
120C2×#204—64no—
121#887—34no—
122#887—62no—
123#875—34no—
124#875—62no—
125C4×Dic6—34no—
126C4×Dic6—62no—
127C3×C4⋊C8—34no—
128C3×#102—34no—
129#821C2×D314yes—
130#816—34no—
131Dic3⋊C8C2×D314yescomplemented
132#810—34no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
137C22×C3×D3—42no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D412yes—
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3—24no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—42no—
146#634—22no—
147#634—24no—
148#634—22no—
149#634—22no—
150#634—42no—
151#634C2×D414yes—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3C2×D412yes—
157C2×C3×Dic3C2×D412yes—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—42no—
161C32×C8—22no—
162C3×C3⋊C8—22no—
163C22×Q16—91no—
164C22×SD16—91no—
165C2×#124—91no—
166C2×C4×Q8—91no—
167#464—98no—
168C2×C4⋊C8—31no—
169C2×#103—91no—
170C2×#102—31no—
171C24×C3—61no—
172C23×D3—21no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—62no—
176C2×C3×D4—62no—
177C22×C3×C4—21no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×Dic3—21no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—121no—
189C22×Dic3—121no—
190C22×Dic3D1211yescharacteristic
191C22×Dic3D1211yescharacteristic
192C2×D12—22no—
193C2×D12—22no—
194C2×D12—21no—
195C2×D12C22×D312yes—
196C2×Dic6—34no—
197C2×Dic6—34no—
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—32no—
201C2×Dic6—32no—
202C2×Dic6—64no—
203C2×Dic6—62no—
204C2×Dic6—62no—
205C2×Dic6—61no—
206C2×Dic6—62no—
207C2×Dic6—61no—
208C2×Dic6—62no—
209C2×Dic6—64no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×Dic6—62no—
213C2×Dic6—62no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—122no—
217C2×Dic6—121no—
218C2×Dic6—121no—
219C2×Dic6—122no—
220C2×C3×C8—24no—
221C2×C3×C8—22no—
222C2×C3×C8—22no—
223C2×C3×C8—22no—
224C2×C3×C8—32no—
225C2×C3×C8—62no—
226C2×C3×C8C22×D312yes—
227C2×C3×C8C22×D312yes—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—61no—
230C3×C42—32no—
231C3×C42—32no—
232#217—64no—
233#217—64no—
234#214—68no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237C4⋊Dic3—21no—
238C4⋊Dic3C22×D312yes—
239Dic3⋊C4—64no—
240Dic3⋊C4—64no—
241C4×Dic3—64no—
242C4×Dic3—64no—
243C4×Dic3D1212yes—
244C4×Dic3C22×D312yes—
245C2×C3⋊C8—22no—
246C2×C3⋊C8C22×D312yes—
247Dic12—68no—
248Dic12—68no—
249Dic12—616no—
250#204—68no—
251C22×C32#12112yes—
252C22×C32#13512yes—
253C22×C32#13712yes—
254C22×C32C22×D411yescharacteristic
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C2×C3×D3—42no—
258C2×C3×D3—84no—
259C32×C4#12112yes—
260C32×C4C22×D411yescharacteristic
261C32×C4C2×#4111yescharacteristic
262C3⋊Dic3—24no—
263C3⋊Dic3—42no—
264C3×Dic3—22no—
265C3×Dic3—22no—
266C3×Dic3—42no—
267C22×Q8—91no—
268C22×Q8—91no—
269C22×D4—31no—
270C2×Q16—94no—
271C2×Q16—184no—
272C2×SD16—94no—
273C2×SD16—184no—
274C22×C8—31no—
275C22×C8D3211yescharacteristic
276#124—94no—
277#124—182no—
278C4×Q8—94no—
279C4×Q8—182no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—181no—
282C2×C22⋊C4—181no—
283C2×C22⋊C4—181no—
284C2×C42—31no—
285C2×C42—181no—
286C4⋊C8—34no—
287#103—94no—
288#102—34no—
289C23×C3—21no—
290C23×C3—62no—
291C23×C3—122no—
292C23×C3—122no—
293C23×C3—122no—
294C23×C3C2×D1211yescharacteristic
295C23×C3D3×D411yescharacteristic
296C22×D3—22no—
297C22×D3—42no—
298C22×D3—42no—
299C22×D3—42no—
300C3×D4—62no—
301C3×D4—62no—
302C3×D4—122no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—22no—
307C2×C3×C4—32no—
308C2×C3×C4—32no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—122no—
313C2×C3×C4C2×D1211yescharacteristic
314C2×C3×C4#23512yes—
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D412yes—
317C2×C3×C4D3×D412yes—
318C2×C3×C4#23912yes—
319C2×C3×C4C23×D311yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—42no—
325C2×Dic3—64no—
326C2×Dic3—64no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—122no—
332C2×Dic3—124no—
333C2×Dic3—122no—
334C2×Dic3—124no—
335C2×Dic3—122no—
336C2×Dic3—122no—
337C2×Dic3C2×D1212yes—
338C2×Dic3C2×D1212yes—
339D12—22no—
340D12—22no—
341D12—42no—
342Dic6—34no—
343Dic6—34no—
344Dic6—64no—
345Dic6—64no—
346Dic6—64no—
347Dic6—62no—
348Dic6—62no—
349Dic6—64no—
350Dic6—62no—
351Dic6—62no—
352Dic6—62no—
353Dic6—62no—
354Dic6—122no—
355Dic6—124no—
356Dic6—122no—
357Dic6—124no—
358Dic6—122no—
359Dic6—122no—
360C3×C8—24no—
361C3×C8—22no—
362C3×C8—22no—
363C3×C8—62no—
364C3⋊C8—22no—
365C2×C32#46414yescomplemented
366C2×C32C2×#12111yescharacteristic
367C2×C32C2×#13511yescharacteristic
368C2×C32C2×#13711yescharacteristic
369C3×D3—82no—
370C24—61no—
371C2×Q8—92no—
372C2×Q8—92no—
373C2×Q8—94no—
374C2×Q8—182no—
375C2×Q8—181no—
376C2×Q8—181no—
377C2×Q8—182no—
378C2×Q8—182no—
379C2×D4—32no—
380C2×D4—62no—
381C2×D4—61no—
382C2×D4—62no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—61no—
386C22×C4—181no—
387C22×C4—181no—
388C22×C4C2×D3211yescharacteristic
389Q16—188no—
390SD16—188no—
391C2×C8—22no—
392C2×C8—32no—
393C2×C8—62no—
394C2×C8C2×D3212yes—
395C4⋊C4—32no—
396C4⋊C4—61no—
397C4⋊C4—184no—
398C22⋊C4—184no—
399C22⋊C4—184no—
400C42—32no—
401C42—32no—
402C42—184no—
403C22×C3—21no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—122no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—244no—
411C22×C3#88412yes—
412C22×C3#89512yes—
413C22×C3#90412yes—
414C22×C3#90912yes—
415C22×C3#91212yes—
416C22×C3#91512yes—
417C22×C3C22×D1211yescharacteristic
418C22×C3C2×D3×D411yescharacteristic
419C2×D3—42no—
420C2×D3—42no—
421C2×D3—42no—
422C2×D3—84no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—22no—
426C3×C4—62no—
427C3×C4—62no—
428C3×C4—122no—
429C3×C4#88412yes—
430C3×C4#89512yes—
431C3×C4C2×#23511yescharacteristic
432C3×C4C2×D3×D411yescharacteristic
433C3×C4C2×D3×D411yescharacteristic
434C3×C4C2×#23911yescharacteristic
435Dic3—22no—
436Dic3—22no—
437Dic3—42no—
438Dic3—64no—
439Dic3—64no—
440Dic3—124no—
441Dic3—124no—
442Dic3—122no—
443Dic3—122no—
444C32C2×#46411yescharacteristic, complemented, Sylow
445C23—62no—
446C23—122no—
447C23—122no—
448C23—122no—
449C23D3×D1211yescharacteristic
450Q8—94no—
451Q8—182no—
452Q8—184no—
453Q8—182no—
454Q8—182no—
455Q8—362no—
456D4—62no—
457D4—62no—
458D4—122no—
459C2×C4—32no—
460C2×C4—32no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—122no—
465C2×C4—182no—
466C2×C4—184no—
467C2×C4—182no—
468C2×C4—362no—
469C2×C4#379912yes—
470C2×C4D3×D1211yescharacteristic
471C2×C4#381112yes—
472C2×C4C22×D3211yescharacteristic
473C8—22no—
474C8—62no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—24no—
478C2×C3—21no—
479C2×C3—242no—
480C2×C3#476714yescomplemented
481C2×C3#484514yescomplemented
482C2×C3C2×#88411yescharacteristic
483C2×C3C2×#89511yescharacteristic
484C2×C3C2×#90411yescharacteristic
485C2×C3C2×#90911yescharacteristic
486C2×C3C2×#91211yescharacteristic
487C2×C3C2×#91511yescharacteristic
488D3—82no—
489C22—122no—
490C22—122no—
491C22—122no—
492C22—244no—
493C22#6380012yes—
494C22#6380712yes—
495C22#6391012yes—
496C22C2×D3×D1211yescharacteristic
497C4—62no—
498C4—62no—
499C4—122no—
500C4—184no—
501C4—362no—
502C4#6391012yes—
503C4C2×#379911yescharacteristic
504C4C2×#381111yescharacteristic
505C3—21no—
506C3C2×#476711yescharacteristic, complemented
507C3C2×#484511yescharacteristic, complemented
508C2—242no—
509C2#1059086114yesdirect product factor
510C2C2×#6380011yescharacteristic
511C2C2×#6380711yescharacteristic
512C2C2×#6391011yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32C2×#464
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×#3746C2semidirect
3. C2×#63844C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
7. C2×#63567C2semidirect
8. #10590861C2direct (N × H)
16. C2×#3746C22semidirect
27. #63844C22semidirect
31. C3×Dic3⋊C8C22semidirect
32. #63567C22semidirect
46. C2×Dic3⋊C8D3semidirect
131. Dic3⋊C8C2×D3semidirect
365. C2×C32#464semidirect
444. C32C2×#464semidirect
480. C2×C3#4767semidirect
481. C2×C3#4845semidirect
506. C3C2×#4767semidirect
507. C3C2×#4845semidirect
509. C2#10590861direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37462
C2×#638602
C2×#638442
C22×#37162
C2×C3×#8212
C2×C3×Dic3⋊C82
C2×#635672
#105908612
C2×#48453
C2×#47673