Finite Group Databasebeta

← C2×#10590957 #11857922

Subgroups — C2×#10590957 #11857922

Order 1152.

1781 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C22×#3743C211yesmaximal, characteristic, complemented
3C2×#63900C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590957C218yesmaximal, direct product factor
9C2×#4803—31nomaximal
10C2×#4771—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#626—21no—
15C22×#624—21no—
16C22×D3×Dic3—21no—
17C2×#3796—22no—
18C2×#3796—24no—
19C2×#3796C418yescomplemented
20C2×#3796C2214yes—
21C22×C32×C8C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×#3743—24no—
24C2×#3743C2214yescomplemented
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×#3724—21no—
28#63900—22no—
29#63900C2214yescomplemented
30C3×#821C2214yescomplemented
31C3×#816C2214yescomplemented
32#63565C2214yescomplemented
33#63562C2214yescomplemented
34C22×#239—31no—
35C22×#237—31no—
36C22×ΓL(1,𝔽25)—31no—
37C22×ΓL(1,𝔽25)—31no—
38C22×ΓL(1,𝔽25)—61no—
39C2×D3×C4⋊C4—31no—
40C2×D3×C4⋊C4—31no—
41C2×C3×#103—31no—
42C2×C3×#102—31no—
43C2×#835—31no—
44C2×#832—31no—
45C2×#821D311yescharacteristic, complemented
46C2×#816D311yescharacteristic, complemented
47C2×#810—31no—
48C2×#809—31no—
49#4803—38no—
50#4771—38no—
51C23×C3⋊D3D411yescharacteristic
52C23×C3×D3—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C2×C4×C3⋊D3C2×C414yes—
56C2×C4×C3⋊D3D412yes—
57C2×C4×C3⋊D3D414yes—
58C2×C4×C3⋊D3C2312yes—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C2×C3×D12—21no—
63C2×C3×D12—22no—
64C2×C3×D12C2×C414yescomplemented
65C2×C3×D12C2312yes—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6C2×C414yescomplemented
69C2×C3×Dic6C2312yes—
70C2×#626—28no—
71C2×#626—24no—
72C2×#624—24no—
73C2×#624—44no—
74C2×D3×Dic3—28no—
75C2×D3×Dic3—24no—
76#3796—216no—
77#3796—28no—
78#3796C2×C4116yescomplemented
79C2×C32×C8—22no—
80C2×C32×C8C2312yes—
81C2×C3⋊(C3⋊C8)—22no—
82C2×C3⋊(C3⋊C8)C2312yes—
83#3743—28no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2312yes—
88#3724—24no—
89C2×#417—91noSylow
90C22×C3×Q8—31no—
91C22×C3×D4—31no—
92C22×#67—61no—
93C23×Dic3—61no—
94C2×#239—38no—
95C2×#239—34no—
96C2×#239—62no—
97C2×#239—64no—
98C2×#237—38no—
99C2×#237—34no—
100C2×#237—62no—
101C2×#237—64no—
102C22×D12—61no—
103C22×D12C2×D311yescharacteristic
104C22×C4×D3—31no—
105C22×C4×D3—31no—
106C22×C4×D3—61no—
107C22×C4×D3—61no—
108C22×C4×D3—61no—
109C22×C4×D3—61no—
110C22×Dic6C2×D311yescharacteristic
111C22×C3×C8—21no—
112C22×C3×C8C2×D311yescharacteristic
113C22×C3×C8C2×D311yescharacteristic
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×Dic3⋊C4—61no—
119C2×Dic3⋊C4—61no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—61no—
123C2×ΓL(1,𝔽25)—34no—
124C2×ΓL(1,𝔽25)—34no—
125C2×ΓL(1,𝔽25)—64no—
126C2×ΓL(1,𝔽25)—64no—
127C2×ΓL(1,𝔽25)—64no—
128C2×ΓL(1,𝔽25)—68no—
129D3×C4⋊C4—34no—
130D3×C4⋊C4—34no—
131D3×C4⋊C4—62no—
132D3×C4⋊C4—62no—
133C3×#103—34no—
134C3×#102—34no—
135#835—34no—
136#832—34no—
137#821C2×D314yescomplemented
138#816C2×D314yescomplemented
139#810—34no—
140#809—34no—
141C23×C32C2×D411yescharacteristic
142C22×C3⋊D3—22no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3C22⋊C414yes—
145C22×C3⋊D3C2×D412yes—
146C22×C3×D3—24no—
147C22×C3×D3—22no—
148C22×C3×D3—42no—
149C22×C3×D3—42no—
150C2×C32×C4C22×C412yes—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3C22⋊C414yes—
155C2×C3⋊Dic3C2×D412yes—
156C4×C3⋊D3C22⋊C418yes—
157C4×C3⋊D3C22×C414yes—
158C4×C3⋊D3C2×D414yes—
159C2×C3×Dic3—24no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—42no—
164C2×C3×Dic3—42no—
165C3×D12—24no—
166C3×D12—22no—
167C3×D12C22×C414yescomplemented
168C3×Dic6—24no—
169C3×Dic6—22no—
170C3×Dic6C22×C414yescomplemented
171#626—216no—
172#624—48no—
173D3×Dic3—216no—
174C32×C8—22no—
175C3⋊(C3⋊C8)—22no—
176C22×#41—91no—
177C22×M16—91no—
178C22×C4⋊C4—91no—
179#417—98no—
180C2×#103—31no—
181C2×#103—91no—
182C2×#102—31no—
183C2×#102—91no—
184C24×C3—61no—
185C23×D3—21no—
186C23×D3—31no—
187C23×D3—31no—
188C23×D3—61no—
189C2×C3×Q8—34no—
190C2×C3×Q8—32no—
191C2×C3×Q8—61no—
192C2×C3×Q8—62no—
193C2×C3×D4—34no—
194C2×C3×D4—32no—
195C2×C3×D4—61no—
196C2×C3×D4—62no—
197C22×C3×C4—21no—
198C22×C3×C4—61no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C2×#67—68no—
204C2×#67—64no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—61no—
211C22×Dic3—68no—
212C22×Dic3—64no—
213#239—316no—
214#239—616no—
215#239—68no—
216#237—316no—
217#237—616no—
218#237—68no—
219C2×D12—21no—
220C2×D12—22no—
221C2×D12—68no—
222C2×D12—64no—
223C2×D12C4×D314yescomplemented
224C2×D12C22×D312yes—
225C2×C4×D3—34no—
226C2×C4×D3—34no—
227C2×C4×D3—32no—
228C2×C4×D3—32no—
229C2×C4×D3—34no—
230C2×C4×D3—34no—
231C2×C4×D3—32no—
232C2×C4×D3—32no—
233C2×C4×D3—64no—
234C2×C4×D3—62no—
235C2×C4×D3—64no—
236C2×C4×D3—62no—
237C2×C4×D3—68no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3—124no—
242C2×C4×D3—124no—
243C2×Dic6—21no—
244C2×Dic6—22no—
245C2×Dic6C4×D314yescomplemented
246C2×Dic6C22×D312yes—
247C2×C3×C8—24no—
248C2×C3×C8—22no—
249C2×C3×C8—22no—
250C2×C3×C8—22no—
251C2×C3×C8C22×D312yes—
252C2×C3×C8C22×D312yes—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—32no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257C4⋊Dic3—21no—
258C4⋊Dic3—21no—
259C4⋊Dic3C22×D312yes—
260C4⋊Dic3C22×D312yes—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263C2×C3⋊C8—32no—
264C2×C3⋊C8—32no—
265C2×C3⋊C8—62no—
266C2×C3⋊C8—64no—
267C2×C3⋊C8—62no—
268C2×C3⋊C8—62no—
269ΓL(1,𝔽25)—68no—
270ΓL(1,𝔽25)—68no—
271ΓL(1,𝔽25)—616no—
272C22×C32C2×C22⋊C412yes—
273C22×C32AGL(1,ℤ/8)12yes—
274C22×C32#13712yes—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—22no—
277C2×C3⋊D3—22no—
278C2×C3⋊D3—28no—
279C2×C3⋊D3C2×C22⋊C414yes—
280C2×C3×D3—24no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—48no—
284C32×C4C2×C22⋊C412yes—
285C32×C4C23×C411yescharacteristic
286C32×C4C22×D411yescharacteristic
287C3⋊Dic3C2×C22⋊C414yes—
288C3×Dic3—24no—
289C3×Dic3—42no—
290C3×Dic3—42no—
291C2×#41—94no—
292C2×#41—98no—
293C2×#41—182no—
294C2×#41—184no—
295C22×Q8—31no—
296C22×D4—31no—
297C22×D4—181no—
298C23×C4—91no—
299C23×C4—181no—
300C23×C4—181no—
301C2×M16—94no—
302C2×M16—184no—
303C22×C8—91no—
304C22×C8D3211yescharacteristic
305C2×C4⋊C4—31no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4—94no—
308C2×C4⋊C4—182no—
309C2×C4⋊C4—181no—
310#103—34no—
311#103—94no—
312#102—34no—
313#102—94no—
314C23×C3—21no—
315C23×C3—64no—
316C23×C3—62no—
317C23×C3—122no—
318C23×C3—122no—
319C23×C3D3×D411yescharacteristic
320C23×C3D3×D411yescharacteristic
321C22×D3—24no—
322C22×D3—22no—
323C22×D3—34no—
324C22×D3—34no—
325C22×D3—32no—
326C22×D3—32no—
327C22×D3—42no—
328C22×D3—42no—
329C22×D3—64no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—122no—
336C22×D3—122no—
337C3×Q8—34no—
338C3×Q8—64no—
339C3×Q8—62no—
340C3×D4—34no—
341C3×D4—64no—
342C3×D4—62no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—64no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—122no—
352C2×C3×C4—122no—
353C2×C3×C4C2×C4×D312yes—
354C2×C3×C4C2×C4×D312yes—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D412yes—
358C2×C3×C4D3×D412yes—
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—616no—
362C2×Dic3—24no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—34no—
367C2×Dic3—34no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—42no—
371C2×Dic3—42no—
372C2×Dic3—64no—
373C2×Dic3—62no—
374C2×Dic3—616no—
375D12—24no—
376D12—22no—
377D12—616no—
378D12C2×C4×D314yescomplemented
379C4×D3—38no—
380C4×D3—38no—
381C4×D3—34no—
382C4×D3—34no—
383C4×D3—34no—
384C4×D3—34no—
385C4×D3—68no—
386C4×D3—64no—
387C4×D3—64no—
388C4×D3—616no—
389C4×D3—128no—
390C4×D3—128no—
391Dic6—24no—
392Dic6—22no—
393Dic6C2×C4×D314yescomplemented
394C3×C8—24no—
395C3×C8—22no—
396C3×C8—22no—
397C3⋊C8—64no—
398C3⋊C8—62no—
399C3⋊C8—62no—
400C2×C32#41714yescomplemented
401C2×C32C22×C22⋊C411yescharacteristic
402C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
403C2×C32C2×#13711yescharacteristic
404C3⋊D3—24no—
405C3×D3—44no—
406C24—61no—
407C24—91no—
408#41—916no—
409#41—188no—
410#41—1816no—
411C2×Q8—32no—
412C2×Q8—34no—
413C2×Q8—61no—
414C2×Q8—62no—
415C2×D4—32no—
416C2×D4—34no—
417C2×D4—61no—
418C2×D4—62no—
419C2×D4—184no—
420C2×D4—188no—
421C22×C4—61no—
422C22×C4—61no—
423C22×C4—61no—
424C22×C4—91no—
425C22×C4—92no—
426C22×C4—94no—
427C22×C4—92no—
428C22×C4—94no—
429C22×C4—184no—
430C22×C4—184no—
431C22×C4—188no—
432C22×C4—364no—
433C22×C4C2×D3211yescharacteristic
434M16—188no—
435C2×C8—22no—
436C2×C8—92no—
437C2×C8—182no—
438C2×C8C2×D3212yes—
439C4⋊C4—32no—
440C4⋊C4—32no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C4⋊C4—184no—
444C22×C3—21no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—64no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3—128no—
452C22×C3D3×C22⋊C412yes—
453C22×C3D3×C22⋊C412yes—
454C22×C3#91112yes—
455C22×C3#91412yes—
456C22×C3#91512yes—
457C22×C3#91812yes—
458C22×C3C2×D3×D411yescharacteristic
459C22×C3C2×D3×D411yescharacteristic
460C2×D3—24no—
461C2×D3—34no—
462C2×D3—34no—
463C2×D3—42no—
464C2×D3—42no—
465C2×D3—48no—
466C2×D3—64no—
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—62no—
470C2×D3—62no—
471C2×D3—68no—
472C2×D3—68no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—128no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—22no—
479C3×C4—64no—
480C3×C4—122no—
481C3×C4—122no—
482C3×C4D3×C22⋊C412yes—
483C3×C4D3×C22⋊C412yes—
484C3×C4C22×C4×D311yescharacteristic
485C3×C4C22×C4×D311yescharacteristic
486C3×C4C2×D3×D411yescharacteristic
487C3×C4C2×D3×D411yescharacteristic
488Dic3—24no—
489Dic3—34no—
490Dic3—34no—
491Dic3—42no—
492Dic3—42no—
493Dic3—64no—
494C32C2×#41711yescharacteristic, complemented, Sylow
495C23—62no—
496C23—64no—
497C23—92no—
498C23—94no—
499C23—122no—
500C23—122no—
501C23—182no—
502C23—182no—
503C23#380211yescharacteristic
504Q8—34no—
505Q8—62no—
506Q8—64no—
507D4—34no—
508D4—62no—
509D4—64no—
510D4—1816no—
511C2×C4—62no—
512C2×C4—64no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—92no—
516C2×C4—94no—
517C2×C4—94no—
518C2×C4—94no—
519C2×C4—98no—
520C2×C4—122no—
521C2×C4—122no—
522C2×C4—1816no—
523C2×C4—368no—
524C2×C4C4×D3212yes—
525C2×C4#380211yescharacteristic
526C2×C4#381112yes—
527C2×C4C22×D3211yescharacteristic
528C8—22no—
529C8—182no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—24no—
533C2×C3—21no—
534C2×C3—124no—
535C2×C3#477114yescomplemented
536C2×C3#480314yescomplemented
537C2×C3C2×D3×C22⋊C411yescharacteristic
538C2×C3C2×D3×C22⋊C411yescharacteristic
539C2×C3C2×#91111yescharacteristic
540C2×C3C2×#91411yescharacteristic
541C2×C3C2×#91511yescharacteristic
542C2×C3C2×#91811yescharacteristic
543D3—44no—
544D3—64no—
545D3—64no—
546D3—124no—
547C22—64no—
548C22—94no—
549C22—122no—
550C22—122no—
551C22—128no—
552C22—182no—
553C22—182no—
554C22—188no—
555C22#6379812yes—
556C22#6381112yes—
557C22#6392112yes—
558C22C2×#380211yescharacteristic
559C4—64no—
560C4—94no—
561C4—122no—
562C4—122no—
563C4#6392112yes—
564C4C2×C4×D3211yescharacteristic
565C4C2×#381111yescharacteristic
566C3—21no—
567C3C2×#477111yescharacteristic, complemented
568C3C2×#480311yescharacteristic, complemented
569C2—124no—
570C2—184no—
571C2#1059095714yesdirect product factor
572C2C2×#6379811yescharacteristic
573C2C2×#6381111yescharacteristic
574C2C2×#6392111yescharacteristic
subgroupG/H
centerC23#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3796C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#417
LCSG ▷ 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
2. C22×#3743C2semidirect
3. C2×#63900C2semidirect
4. C2×C3×#821C2semidirect
5. C2×C3×#816C2semidirect
6. C2×#63565C2semidirect
7. C2×#63562C2semidirect
8. #10590957C2direct (N × H)
19. C2×#3796C4semidirect
24. C2×#3743C22semidirect
29. #63900C22semidirect
30. C3×#821C22semidirect
31. C3×#816C22semidirect
32. #63565C22semidirect
33. #63562C22semidirect
45. C2×#821D3semidirect
46. C2×#816D3semidirect
64. C2×C3×D12C2×C4semidirect
68. C2×C3×Dic6C2×C4semidirect
78. #3796C2×C4semidirect
137. #821C2×D3semidirect
138. #816C2×D3semidirect
167. C3×D12C22×C4semidirect
170. C3×Dic6C22×C4semidirect
223. C2×D12C4×D3semidirect
245. C2×Dic6C4×D3semidirect
378. D12C2×C4×D3semidirect
393. Dic6C2×C4×D3semidirect
400. C2×C32#417semidirect
494. C32C2×#417semidirect
535. C2×C3#4771semidirect
536. C2×C3#4803semidirect
567. C3C2×#4771semidirect
568. C3C2×#4803semidirect
571. C2#10590957direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C22×#37432
C2×#639002
C2×C3×#8212
C2×C3×#8162
C2×#635652
C2×#635622
#105909572
C2×#48033
C2×#47713