Finite Group Databasebeta

← C2×#10590328 #11859245

Subgroups — C2×#10590328 #11859245

Order 1152.

1341 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C22×#3712C211yesmaximal, characteristic, complemented
3C22×#3710C211yesmaximal, characteristic, complemented
4C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C2×C3×#803C211yesmaximal, characteristic, complemented
6C2×#63557C211yesmaximal, characteristic, complemented
7C2×#63557C211yesmaximal, characteristic, complemented
8#10590328C218yesmaximal, direct product factor
9C2×#4836—31nomaximal
10C2×#4706—31nomaximal
11C22×C4⋊(C3⋊D3)C411yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×#3752C411yescharacteristic
16C2×#3752C411yescharacteristic
17C2×C4⋊(C3⋊Dic3)C411yescharacteristic
18C4×C4⋊(C3⋊D3)C414yes—
19C4×C4⋊(C3⋊D3)C2214yes—
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×#3712—24no—
25C2×#3712C2214yescomplemented
26C2×#3710—24no—
27C2×#3710C2214yescomplemented
28C3×C4⋊(C3⋊C8)C2214yescomplemented
29C3×#803C2214yescomplemented
30#63557C2214yescomplemented
31#63557C2214yescomplemented
32C22×ΓL(1,𝔽25)—31no—
33C22×ΓL(1,𝔽25)—31no—
34C22×D3×C8—31no—
35C22×D3×C8—31no—
36C2×C4×D12—31no—
37C2×C4×D12—31no—
38C2×C4×D12—61no—
39C2×C3×C4⋊C8—31no—
40C2×C3×#97—31no—
41C2×(C2×D3)⋊C8—31no—
42C2×(C2×D3)⋊C8—31no—
43C2×(C2×D3)⋊C8—31no—
44C2×(C2×D3)⋊C8—31no—
45C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
46C2×#803D311yescharacteristic, complemented
47#4836—38no—
48#4706—38no—
49C23×C3⋊D3C2×C411yescharacteristic
50C23×C3⋊D3C2×C411yescharacteristic
51C22×C32×C4C2×C411yescharacteristic
52C22×C32×C4C2×C411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2×C411yescharacteristic
55C22×C3⋊Dic3C2×C411yescharacteristic
56C2×C4⋊(C3⋊D3)—24no—
57C2×C4⋊(C3⋊D3)C2×C414yes—
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3C2×C412yes—
63C2×C4×C3⋊D3C2×C412yes—
64C2×C4×C3⋊D3C2312yes—
65C2×C4×C3⋊D3C2312yes—
66C32×C42C2×C412yes—
67C32×C42C2312yes—
68#3752C2×C414yes—
69#3752C2×C414yes—
70C4⋊(C3⋊Dic3)C2×C414yes—
71C2×C3×C3⋊C8—22no—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8D414yescomplemented
75C2×C3×C3⋊C8C2312yes—
76C2×C3×C3⋊C8C2312yes—
77C2×C3×C3⋊C8C2312yes—
78C2×C3×C3⋊C8C2312yes—
79#3712—28no—
80#3710—28no—
81C2×#435—91noSylow
82C22×D12—31no—
83C22×D12—31no—
84C22×D12—61no—
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—31no—
88C22×C4×D3—31no—
89C22×C4×D3—61no—
90C22×C4×D3—61no—
91C22×C3×C8—31no—
92C22×C3×C8—31no—
93C22×C3×C8—31no—
94C22×C3×C8—31no—
95C2×C3×C42—21no—
96C2×C3×C42C2×D311yescharacteristic
97C2×C3×C42C2×D311yescharacteristic
98C2×(C2×D3)⋊C4—31no—
99C2×(C2×D3)⋊C4—31no—
100C2×(C2×D3)⋊C4—31no—
101C2×(C2×D3)⋊C4—31no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108C22×C3⋊C8C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110C22×C3⋊C8C2×D311yescharacteristic
111C2×ΓL(1,𝔽25)—34no—
112C2×ΓL(1,𝔽25)—34no—
113C2×ΓL(1,𝔽25)—64no—
114C2×ΓL(1,𝔽25)—64no—
115C2×D3×C8—34no—
116C2×D3×C8—34no—
117C2×D3×C8—64no—
118C2×D3×C8—64no—
119C4×D12—34no—
120C4×D12—34no—
121C4×D12—34no—
122C4×D12—34no—
123C4×D12—64no—
124C4×D12—64no—
125C3×C4⋊C8—34no—
126C3×#97—34no—
127(C2×D3)⋊C8—34no—
128(C2×D3)⋊C8—34no—
129(C2×D3)⋊C8—34no—
130(C2×D3)⋊C8—34no—
131C4⋊(C3⋊C8)C2×D314yescomplemented
132#803C2×D314yescomplemented
133C23×C32C22×C411yescharacteristic
134C22×C3⋊D3—22no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3M1614yescomplemented
140C22×C3⋊D3C22×C412yes—
141C22×C3⋊D3C22×C412yes—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4C22×C412yes—
145C2×C32×C4C22×C412yes—
146C2×C32×C4C22×C411yescharacteristic
147C2×C32×C4C2×D412yes—
148C2×C32×C4#4112yes—
149C2×C32×C4C2411yescharacteristic
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3C22×C412yes—
153C2×C3⋊Dic3C22×C412yes—
154C4⋊(C3⋊D3)—28no—
155C4×C3⋊D3—24no—
156C4×C3⋊D3—24no—
157C4×C3⋊D3—22no—
158C4×C3⋊D3—22no—
159C4×C3⋊D3—22no—
160C4×C3⋊D3—22no—
161C3×C3⋊C8—22no—
162C3×C3⋊C8—22no—
163C3×C3⋊C8—22no—
164C3×C3⋊C8C2×D414yescomplemented
165C22×M16—91no—
166C23×C8—91no—
167C2×C4×D4—91no—
168#435—98no—
169C2×C4⋊C8—31no—
170C2×C22⋊C8—91no—
171C2×C22⋊C8—91no—
172C2×#97—31no—
173C23×D3—31no—
174C23×D3—31no—
175C23×D3—31no—
176C23×D3—31no—
177C23×D3—61no—
178C23×D3—61no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4C4×D311yescharacteristic
183C22×C3×C4C4×D311yescharacteristic
184C22×C3×C4C4×D311yescharacteristic
185C22×C3×C4C4×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×Dic3—31no—
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C2×D12—34no—
195C2×D12—34no—
196C2×D12—64no—
197C2×D12—64no—
198C2×D12—64no—
199C2×D12—68no—
200C2×C4×D3—32no—
201C2×C4×D3—32no—
202C2×C4×D3—32no—
203C2×C4×D3—32no—
204C2×C4×D3—32no—
205C2×C4×D3—32no—
206C2×C4×D3—32no—
207C2×C4×D3—32no—
208C2×C4×D3—62no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×C4×D3—122no—
221C2×C4×D3—122no—
222C2×C4×D3—122no—
223C2×C4×D3—122no—
224C2×C3×C8—34no—
225C2×C3×C8—32no—
226C2×C3×C8—32no—
227C2×C3×C8—32no—
228C2×C3×C8—32no—
229C2×C3×C8—62no—
230C2×C3×C8—62no—
231C2×C3×C8—62no—
232C3×C42—22no—
233C3×C42—22no—
234C3×C42C4×D312yes—
235C3×C42C4×D312yes—
236C3×C42C22×D312yes—
237C3×C42C22×D312yes—
238(C2×D3)⋊C4—34no—
239(C2×D3)⋊C4—34no—
240(C2×D3)⋊C4—34no—
241(C2×D3)⋊C4—34no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244C4⋊Dic3—34no—
245C4⋊Dic3—34no—
246C4⋊Dic3—64no—
247C2×C3⋊C8—22no—
248C2×C3⋊C8—22no—
249C2×C3⋊C8—22no—
250C2×C3⋊C8D1214yescomplemented
251C2×C3⋊C8C22×D312yes—
252C2×C3⋊C8C22×D312yes—
253C2×C3⋊C8C22×D312yes—
254C2×C3⋊C8C22×D312yes—
255ΓL(1,𝔽25)—68no—
256ΓL(1,𝔽25)—68no—
257D3×C8—68no—
258D3×C8—68no—
259C22×C32C4×D412yes—
260C22×C32C2×M1612yes—
261C22×C32#13112yes—
262C22×C32C23×C411yescharacteristic
263C2×C3⋊D3—22no—
264C2×C3⋊D3—22no—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—28no—
267C2×C3⋊D3—22no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—44no—
270C2×C3⋊D3C2×M1614yescomplemented
271C32×C4—22no—
272C32×C4—22no—
273C32×C4C4×D412yes—
274C32×C4C22×D411yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3⋊Dic3—22no—
277C3⋊Dic3—22no—
278C22×D4—91no—
279C23×C4—91no—
280C23×C4—91no—
281C2×M16—94no—
282C2×M16—184no—
283C22×C8—31no—
284C22×C8—31no—
285C22×C8—31no—
286C22×C8—31no—
287C22×C8—94no—
288C22×C8—184no—
289C4×D4—94no—
290C4×D4—94no—
291C2×C4⋊C4—91no—
292C2×C22⋊C4—91no—
293C2×C22⋊C4—91no—
294C2×C42D3211yescharacteristic
295C4⋊C8—34no—
296C22⋊C8—94no—
297C22⋊C8—94no—
298#97—34no—
299C23×C3—21no—
300C23×C3C2×C4×D311yescharacteristic
301C23×C3C2×C4×D311yescharacteristic
302C22×D3—34no—
303C22×D3—34no—
304C22×D3—32no—
305C22×D3—32no—
306C22×D3—32no—
307C22×D3—32no—
308C22×D3—64no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—64no—
316C22×D3—62no—
317C22×D3—62no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—122no—
323C22×D3—122no—
324C22×D3—122no—
325C22×D3—122no—
326C2×C3×C4—24no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—22no—
337C2×C3×C4—42no—
338C2×C3×C4C2×C4×D312yes—
339C2×C3×C4C2×C4×D312yes—
340C2×C3×C4C2×C4×D312yes—
341C2×C3×C4C2×C4×D312yes—
342C2×C3×C4C2×C4×D311yescharacteristic
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4C2×D1212yes—
345C2×C3×C4#23512yes—
346C2×C3×C4D3×D412yes—
347C2×C3×C4#23912yes—
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×Dic3—32no—
351C2×Dic3—32no—
352C2×Dic3—32no—
353C2×Dic3—32no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—122no—
361C2×Dic3—122no—
362D12—68no—
363D12—68no—
364D12—616no—
365C4×D3—64no—
366C4×D3—64no—
367C4×D3—64no—
368C4×D3—64no—
369C4×D3—62no—
370C4×D3—62no—
371C4×D3—62no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—62no—
375C4×D3—62no—
376C4×D3—62no—
377C4×D3—122no—
378C4×D3—122no—
379C4×D3—122no—
380C4×D3—122no—
381C4×D3—124no—
382C4×D3—124no—
383C3×C8—34no—
384C3×C8—62no—
385C3×C8—62no—
386C3×C8—62no—
387C3⋊C8—22no—
388C3⋊C8—22no—
389C3⋊C8—22no—
390C3⋊C8C2×D1214yescomplemented
391C2×C32#43514yescomplemented
392C2×C32C2×C4×D411yescharacteristic
393C2×C32C22×M1611yescharacteristic
394C2×C32C2×#13111yescharacteristic
395C3⋊D3—24no—
396C3⋊D3—42no—
397C24—91no—
398C24—91no—
399C2×D4—94no—
400C2×D4—184no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4—92no—
404C22×C4—92no—
405C22×C4—92no—
406C22×C4—92no—
407C22×C4—182no—
408C22×C4—182no—
409C22×C4—182no—
410C22×C4—182no—
411C22×C4#62411yescharacteristic
412C22×C4#62411yescharacteristic
413C22×C4C2×D3211yescharacteristic
414M16—188no—
415C2×C8—32no—
416C2×C8—34no—
417C2×C8—32no—
418C2×C8—32no—
419C2×C8—32no—
420C2×C8—62no—
421C2×C8—62no—
422C2×C8—62no—
423C2×C8—188no—
424C4⋊C4—94no—
425C22⋊C4—94no—
426C22⋊C4—94no—
427C42#62412yes—
428C42C2×D3212yes—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3C4×D1212yes—
434C22×C3#89312yes—
435C22×C3#90112yes—
436C22×C3D3×M1612yes—
437C22×C3D3×M1612yes—
438C22×C3#90712yes—
439C22×C3C22×C4×D311yescharacteristic
440C22×C3C22×C4×D311yescharacteristic
441C2×D3—34no—
442C2×D3—34no—
443C2×D3—64no—
444C2×D3—62no—
445C2×D3—68no—
446C2×D3—62no—
447C2×D3—62no—
448C2×D3—62no—
449C2×D3—68no—
450C2×D3—64no—
451C2×D3—62no—
452C2×D3—62no—
453C2×D3—62no—
454C2×D3—62no—
455C2×D3—62no—
456C2×D3—62no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—128no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—128no—
463C2×D3—124no—
464C2×D3—124no—
465C3×C4—24no—
466C3×C4—22no—
467C3×C4—22no—
468C3×C4—22no—
469C3×C4—22no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—42no—
474C3×C4C4×D1212yes—
475C3×C4#89312yes—
476C3×C4C22×D1211yescharacteristic
477C3×C4C2×#23511yescharacteristic
478C3×C4C2×D3×D411yescharacteristic
479C3×C4C2×#23911yescharacteristic
480Dic3—62no—
481Dic3—62no—
482Dic3—62no—
483Dic3—62no—
484Dic3—122no—
485Dic3—122no—
486C32C2×#43511yescharacteristic, complemented, Sylow
487C23—92no—
488C23—94no—
489C23—92no—
490C23—182no—
491C23—182no—
492C23—182no—
493C23—182no—
494C23—182no—
495C23C2×#62411yescharacteristic
496D4—188no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—92no—
500C2×C4—92no—
501C2×C4—182no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—184no—
508C2×C4—184no—
509C2×C4#379912yes—
510C2×C4D3×D1212yes—
511C2×C4C2×#62412yes—
512C2×C4C2×#62412yes—
513C2×C4C2×#62411yescharacteristic
514C2×C4C22×D3211yescharacteristic
515C8—34no—
516C8—62no—
517C8—62no—
518C8—62no—
519C2×C3—21no—
520C2×C3—24no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3#470614yescomplemented
524C2×C3#483614yescomplemented
525C2×C3C2×C4×D1211yescharacteristic
526C2×C3C2×#89311yescharacteristic
527C2×C3C2×#90111yescharacteristic
528C2×C3C2×D3×M1611yescharacteristic
529C2×C3C2×D3×M1611yescharacteristic
530C2×C3C2×#90711yescharacteristic
531D3—64no—
532D3—64no—
533D3—124no—
534D3—124no—
535D3—122no—
536D3—122no—
537C22—94no—
538C22—182no—
539C22—188no—
540C22—182no—
541C22—182no—
542C22—182no—
543C22—182no—
544C22—364no—
545C22#6381712yes—
546C22#6381812yes—
547C22#6389412yes—
548C22C22×#62411yescharacteristic
549C4—22no—
550C4—22no—
551C4—182no—
552C4—182no—
553C4#6389412yes—
554C4C2×#379911yescharacteristic
555C4C2×D3×D1211yescharacteristic
556C3—21no—
557C3C2×#470611yescharacteristic, complemented
558C3C2×#483611yescharacteristic, complemented
559C2—184no—
560C2—362no—
561C2#1059032814yesdirect product factor
562C2C2×#6381711yescharacteristic
563C2C2×#6381811yescharacteristic
564C2C2×#6389411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C22×C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#435
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C22×#3712C2semidirect
3. C22×#3710C2semidirect
4. C2×C3×C4⋊(C3⋊C8)C2semidirect
5. C2×C3×#803C2semidirect
6. C2×#63557C2semidirect
7. C2×#63557C2semidirect
8. #10590328C2direct (N × H)
25. C2×#3712C22semidirect
27. C2×#3710C22semidirect
28. C3×C4⋊(C3⋊C8)C22semidirect
29. C3×#803C22semidirect
30. #63557C22semidirect
31. #63557C22semidirect
45. C2×C4⋊(C3⋊C8)D3semidirect
46. C2×#803D3semidirect
74. C2×C3×C3⋊C8D4semidirect
131. C4⋊(C3⋊C8)C2×D3semidirect
132. #803C2×D3semidirect
139. C22×C3⋊D3M16semidirect
164. C3×C3⋊C8C2×D4semidirect
250. C2×C3⋊C8D12semidirect
270. C2×C3⋊D3C2×M16semidirect
390. C3⋊C8C2×D12semidirect
391. C2×C32#435semidirect
486. C32C2×#435semidirect
523. C2×C3#4706semidirect
524. C2×C3#4836semidirect
557. C3C2×#4706semidirect
558. C3C2×#4836semidirect
561. C2#10590328direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C22×#37122
C22×#37102
C2×C3×C4⋊(C3⋊C8)2
C2×C3×#8032
C2×#635572
#105903282
C2×#48363
C2×#47063