Finite Group Databasebeta

← C2×#10590838 #11866918

Subgroups — C2×#10590838 #11866918

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic, complemented
2C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3C2×#63909C211yesmaximal, characteristic
4C2×#63857C211yesmaximal, characteristic, complemented
5C2×C3×#818C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590838C218yesmaximal, direct product factor
9C2×#5134—31nomaximal
10C2×#4886—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×#626—21no—
15C22×C32×C8C2211yescharacteristic
16C2×#3744—24no—
17C2×#3744C2214yescomplemented
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×C3×ΓL(1,𝔽25)—24no—
22C2×C3×ΓL(1,𝔽25)C2214yescomplemented
23C2×Dic3⋊Dic3—21no—
24C2×#3722—21no—
25C2×(C2×D3)⋊Dic3—21no—
26#63909—22no—
27#63909C2214yes—
28#63857—22no—
29#63857C2214yescomplemented
30C3×#818C2214yescomplemented
31#63567C2214yescomplemented
32#63564C2214yescomplemented
33C22×C3×M16—31no—
34C2×#930—31no—
35C2×#924—31no—
36C22×#204—31no—
37C22×#204—31no—
38C22×#204—61no—
39C22×ΓL(1,𝔽25)D311yescharacteristic, complemented
40C2×#897—31no—
41C2×#895—31no—
42C2×C3×#107—31no—
43#5134—38no—
44C2×#821—31no—
45C2×#818D311yescharacteristic, complemented
46C2×#816—31no—
47C2×#810—31no—
48C2×#809—31no—
49#4886—38no—
50C23×C3⋊D3—21no—
51C23×C3×D3D411yescharacteristic
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×Dic3—21no—
64C22×C3×Dic3D411yescharacteristic
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3—22no—
67C2×C3×C4×D3D412yes—
68C2×C3×C4×D3C2312yes—
69C2×#626—24no—
70C2×#626—44no—
71C2×C32×C8D414yescomplemented
72C2×C32×C8C2312yes—
73#3744—28no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3C2312yes—
77C3×C4⋊Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80C3×ΓL(1,𝔽25)—28no—
81Dic3⋊Dic3—24no—
82#3722—24no—
83(C2×D3)⋊Dic3—24no—
84C2×#468—91noSylow
85C23×C3×C4—31no—
86C22×#67—61no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C22×D12—61no—
91C22×C4×D3C2×D311yescharacteristic
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C2×C3×M16—34no—
96C2×C3×M16—64no—
97C22×C3×C8—21no—
98C22×C3×C8—31no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—31no—
103C2×#217—61no—
104#930—34no—
105#930—62no—
106C2×(C2×D3)⋊C4—61no—
107C2×(C2×D3)⋊C4—61no—
108C2×(C2×D3)⋊C4—61no—
109C2×C4⋊Dic3—61no—
110C2×C4⋊Dic3C2×D311yescharacteristic
111C2×C4⋊Dic3C2×D311yescharacteristic
112#924—34no—
113#924—62no—
114C2×Dic3⋊C4—61no—
115C22×C3⋊C8C2×D311yescharacteristic
116C2×#204—34no—
117C2×#204—34no—
118C2×#204—64no—
119C2×#204—68no—
120C2×#204—64no—
121C2×#204—64no—
122C2×ΓL(1,𝔽25)—24no—
123C2×ΓL(1,𝔽25)C2×D314yescomplemented
124#897—34no—
125#897—62no—
126#895—34no—
127#895—62no—
128C3×#107—34no—
129#821—34no—
130#818C2×D314yescomplemented
131#816—34no—
132#810—34no—
133#809—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—22no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3C2×D412yes—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D412yes—
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—42no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)—42no—
152#634—22no—
153#634—22no—
154#634—42no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3—42no—
160C2×C3×Dic3C2×D412yes—
161C3×C4×D3—24no—
162C3×C4×D3—22no—
163C3×C4×D3—22no—
164#626—48no—
165C32×C8C2×D414yescomplemented
166C3×C3⋊C8—22no—
167C22×SD16—91no—
168C22×M16—31no—
169C2×C22⋊Q8—91no—
170C2×#121—91no—
171#468—98no—
172C2×#107—31no—
173C2×#103—91no—
174C2×#102—91no—
175C24×C3—31no—
176C23×D3—61no—
177C23×D3—61no—
178C23×D3—121no—
179C23×D3D1211yescharacteristic
180C22×C3×C4—21no—
181C22×C3×C4—31no—
182C22×C3×C4—32no—
183C22×C3×C4—32no—
184C22×C3×C4—62no—
185C22×C3×C4—62no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—64no—
191C2×#67—124no—
192C22×Dic3—21no—
193C22×Dic3—21no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3—121no—
197C22×Dic3D1211yescharacteristic
198C2×D12—32no—
199C2×D12—32no—
200C2×D12—62no—
201C2×D12—64no—
202C2×D12—62no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—64no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—122no—
210C2×D12—121no—
211C2×D12—124no—
212C2×C4×D3—22no—
213C2×C4×D3—22no—
214C2×C4×D3D1212yes—
215C2×C4×D3C22×D312yes—
216C2×Dic6—32no—
217C2×Dic6—32no—
218C2×Dic6—62no—
219C2×Dic6—64no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—121no—
227C2×Dic6—122no—
228C3×M16—68no—
229C2×C3×C8—24no—
230C2×C3×C8—22no—
231C2×C3×C8—32no—
232C2×C3×C8—62no—
233C2×C3×C8D1214yescomplemented
234C2×C3×C8#6714yescomplemented
235C2×C3×C8C22×D312yes—
236C2×C3×C8C22×D312yes—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—61no—
241#217—64no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245C4⋊Dic3—21no—
246C4⋊Dic3—21no—
247C4⋊Dic3—64no—
248C4⋊Dic3C22×D312yes—
249C4⋊Dic3C22×D312yes—
250Dic3⋊C4—64no—
251C2×C3⋊C8—22no—
252C2×C3⋊C8C22×D312yes—
253#204—616no—
254#204—68no—
255#204—68no—
256ΓL(1,𝔽25)—28no—
257C22×C32#12112yes—
258C22×C32AGL(1,ℤ/8)12yes—
259C22×C32#13712yes—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—42no—
264C2×C3⋊D3—84no—
265C2×C3×D3—22no—
266C2×C3×D3—22no—
267C2×C3×D3—22no—
268C2×C3×D3—44no—
269C32×C4#12112yes—
270C32×C4C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3⋊Dic3—42no—
273C3×Dic3—22no—
274C3×Dic3—42no—
275C3×Dic3—42no—
276C22×Q8—91no—
277C22×D4—91no—
278C22×D4—181no—
279C23×C4—31no—
280C2×SD16—94no—
281C2×SD16—184no—
282C2×M16—34no—
283C2×M16—64no—
284C22×C8—31no—
285C22×C8D3211yescharacteristic
286C22⋊Q8—94no—
287C22⋊Q8—182no—
288#121—94no—
289#121—182no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—181no—
293C2×C22⋊C4—181no—
294C2×C22⋊C4—181no—
295#107—34no—
296#103—94no—
297#102—94no—
298C23×C3—21no—
299C23×C3—32no—
300C23×C3—62no—
301C23×C3—62no—
302C23×C3—62no—
303C23×C3C2×D1211yescharacteristic
304C23×C3D3×D411yescharacteristic
305C22×D3—22no—
306C22×D3—22no—
307C22×D3—22no—
308C22×D3—62no—
309C22×D3—62no—
310C22×D3—122no—
311C22×D3—124no—
312C22×D3—122no—
313C22×D3—122no—
314C22×D3—122no—
315C22×D3—122no—
316C22×D3—122no—
317C22×D3—122no—
318C22×D3—242no—
319C22×D3—242no—
320C22×D3C2×D1212yes—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—32no—
326C2×C3×C4—62no—
327C2×C3×C4—64no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—122no—
333C2×C3×C4—122no—
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4C2×D1212yes—
336C2×C3×C4#23512yes—
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4#23912yes—
339C2×C3×C4C2×#6712yes—
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342#67—128no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—42no—
347C2×Dic3—42no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—122no—
351C2×Dic3—124no—
352C2×Dic3—122no—
353C2×Dic3—122no—
354C2×Dic3C2×D1212yes—
355D12—64no—
356D12—62no—
357D12—62no—
358D12—62no—
359D12—62no—
360D12—122no—
361D12—124no—
362D12—128no—
363D12—122no—
364D12—122no—
365C4×D3—24no—
366C4×D3—22no—
367C4×D3—22no—
368Dic6—64no—
369Dic6—62no—
370Dic6—62no—
371Dic6—62no—
372Dic6—62no—
373Dic6—122no—
374Dic6—124no—
375Dic6—122no—
376Dic6—122no—
377C3×C8—24no—
378C3×C8—62no—
379C3×C8C2×D1214yescomplemented
380C3×C8C2×#6714yescomplemented
381C3⋊C8—22no—
382C2×C32#46814yescomplemented
383C2×C32C2×#12111yescharacteristic
384C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
385C2×C32C2×#13711yescharacteristic
386C3⋊D3—82no—
387C3×D3—42no—
388C24—31no—
389C24—181no—
390C2×Q8—92no—
391C2×Q8—181no—
392C2×Q8—182no—
393C2×Q8—182no—
394C2×D4—92no—
395C2×D4—184no—
396C2×D4—182no—
397C2×D4—181no—
398C2×D4—182no—
399C2×D4—364no—
400C22×C4—31no—
401C22×C4—32no—
402C22×C4—32no—
403C22×C4—62no—
404C22×C4—62no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—181no—
408C22×C4C2×D3211yescharacteristic
409SD16—188no—
410M16—68no—
411C2×C8—32no—
412C2×C8—62no—
413C2×C8#62614yescomplemented
414C2×C8C2×D3212yes—
415C4⋊C4—32no—
416C4⋊C4—32no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—184no—
420C22⋊C4—184no—
421C22⋊C4—184no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—62no—
427C22×C3—62no—
428C22×C3—62no—
429C22×C3—124no—
430C22×C3#89512yes—
431C22×C3#90812yes—
432C22×C3#90912yes—
433C22×C3#91112yes—
434C22×C3#91812yes—
435C22×C3#93012yes—
436C22×C3C22×D1211yescharacteristic
437C22×C3C2×D3×D411yescharacteristic
438C2×D3—22no—
439C2×D3—22no—
440C2×D3—22no—
441C2×D3—44no—
442C2×D3—124no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—242no—
450C2×D3—242no—
451C2×D3—248no—
452C2×D3—244no—
453C2×D3—244no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—62no—
458C3×C4—122no—
459C3×C4—122no—
460C3×C4#89512yes—
461C3×C4#93012yes—
462C3×C4C22×D1211yescharacteristic
463C3×C4C2×#23511yescharacteristic
464C3×C4C2×#23911yescharacteristic
465C3×C4C22×#6711yescharacteristic
466Dic3—22no—
467Dic3—42no—
468Dic3—42no—
469Dic3—124no—
470Dic3—122no—
471Dic3—122no—
472C32C2×#46811yescharacteristic, complemented, Sylow
473C23—32no—
474C23—62no—
475C23—62no—
476C23—62no—
477C23—182no—
478C23—362no—
479C23—362no—
480C23—362no—
481C23D3×D1211yescharacteristic
482Q8—182no—
483Q8—182no—
484Q8—362no—
485D4—182no—
486D4—182no—
487D4—368no—
488D4—362no—
489C2×C4—32no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—64no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—122no—
497C2×C4—122no—
498C2×C4—182no—
499C2×C4—362no—
500C2×C4#379912yes—
501C2×C4D3×D1211yescharacteristic
502C2×C4C2×#62612yes—
503C2×C4C22×D3211yescharacteristic
504C8—62no—
505C8C2×#62614yescomplemented
506C2×C3—21no—
507C2×C3—24no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—122no—
511C2×C3#488614yescomplemented
512C2×C3#513414yescomplemented
513C2×C3C2×#89511yescharacteristic
514C2×C3C2×#90811yescharacteristic
515C2×C3C2×#90911yescharacteristic
516C2×C3C2×#91111yescharacteristic
517C2×C3C2×#91811yescharacteristic
518C2×C3C2×#93011yescharacteristic
519D3—42no—
520D3—244no—
521D3—242no—
522D3—242no—
523C22—62no—
524C22—62no—
525C22—62no—
526C22—124no—
527C22—362no—
528C22—362no—
529C22—362no—
530C22—724no—
531C22#6379512yes—
532C22#6380112yes—
533C22#6390912yes—
534C22C2×D3×D1211yescharacteristic
535C4—62no—
536C4—122no—
537C4—122no—
538C4—362no—
539C4#6390912yes—
540C4C2×#379911yescharacteristic
541C4C22×#62611yescharacteristic
542C3—21no—
543C3C2×#488611yescharacteristic, complemented
544C3C2×#513411yescharacteristic, complemented
545C2—122no—
546C2—722no—
547C2#1059083814yesdirect product factor
548C2C2×#6379511yescharacteristic
549C2C2×#6380111yescharacteristic
550C2C2×#6390911yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63909C2
hypercenterC22×C8D32
hypocenterC32C2×#468
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×ΓL(1,𝔽25)C2semidirect
4. C2×#63857C2semidirect
5. C2×C3×#818C2semidirect
6. C2×#63567C2semidirect
7. C2×#63564C2semidirect
8. #10590838C2direct (N × H)
17. C2×#3744C22semidirect
22. C2×C3×ΓL(1,𝔽25)C22semidirect
29. #63857C22semidirect
30. C3×#818C22semidirect
31. #63567C22semidirect
32. #63564C22semidirect
39. C22×ΓL(1,𝔽25)D3semidirect
45. C2×#818D3semidirect
71. C2×C32×C8D4semidirect
123. C2×ΓL(1,𝔽25)C2×D3semidirect
130. #818C2×D3semidirect
165. C32×C8C2×D4semidirect
233. C2×C3×C8D12semidirect
234. C2×C3×C8#67semidirect
379. C3×C8C2×D12semidirect
380. C3×C8C2×#67semidirect
382. C2×C32#468semidirect
413. C2×C8#626semidirect
472. C32C2×#468semidirect
505. C8C2×#626semidirect
511. C2×C3#4886semidirect
512. C2×C3#5134semidirect
543. C3C2×#4886semidirect
544. C3C2×#5134semidirect
547. C2#10590838direct (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×ΓL(1,𝔽25)2
C2×#639092
C2×#638572
C2×C3×#8182
C2×#635672
C2×#635642
#105908382
C2×#51343
C2×#48863