Finite Group Databasebeta

← C2×#10591051 #11859288

Subgroups — C2×#10591051 #11859288

Order 1152.

1317 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×#638C211yesmaximal, characteristic
2C22×C3×#208C211yesmaximal, characteristic, complemented
3C22×#3712C211yesmaximal, characteristic, complemented
4C2×C3×#830C211yesmaximal, characteristic, complemented
5C2×#63572C211yesmaximal, characteristic, complemented
6C2×#63557C211yesmaximal, characteristic, complemented
7C2×#63553C211yesmaximal, characteristic, complemented
8#10591051C218yesmaximal, direct product factor
9C2×#5128—31nomaximal
10C2×#4729—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638C411yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×#3757C411yescharacteristic
15C4×#638C414yes—
16C4×#638C2214yes—
17C2×#3752C411yescharacteristic
18C2×#3750C411yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#208—24no—
21C2×C3×#208C2214yescomplemented
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×#3712—24no—
27C2×#3712C2214yescomplemented
28C3×#830C2214yescomplemented
29#63572C2214yescomplemented
30#63557C2214yescomplemented
31#63553C2214yescomplemented
32C22×C3×M16—31no—
33C2×C4×#67—31no—
34C2×C4×#67—31no—
35C2×C4×#67—61no—
36C22×#208D311yescharacteristic, complemented
37C22×ΓL(1,𝔽25)—31no—
38C22×ΓL(1,𝔽25)—31no—
39C2×C3×C22⋊C8—31no—
40C2×#830D311yescharacteristic, complemented
41#5128—38no—
42C2×(C2×D3)⋊C8—31no—
43C2×(C2×D3)⋊C8—31no—
44C2×Dic3⋊C8—31no—
45C2×Dic3⋊C8—31no—
46C2×C8×Dic3—31no—
47C2×C8×Dic3—31no—
48#4729—38no—
49C24×C32C2×C411yescharacteristic
50C23×C3⋊D3C2×C411yescharacteristic
51C22×C32×C4—22no—
52C22×C32×C4—22no—
53C22×C32×C4C2×C411yescharacteristic
54C22×C32×C4C2×C412yes—
55C22×C32×C4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C2×#638—24no—
58C2×#638C2×C414yes—
59C22×C3⋊Dic3C2×C411yescharacteristic
60C22×C3⋊Dic3C2×C411yescharacteristic
61C22×C3⋊Dic3C2×C411yescharacteristic
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3C2×C412yes—
65C2×C4×C3⋊D3C2312yes—
66#3757C2×C414yes—
67#3752C2×C414yes—
68#3750C2×C414yes—
69C4×C3⋊Dic3C2×C412yes—
70C4×C3⋊Dic3C2312yes—
71C3×#208—28no—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8D414yescomplemented
76C2×C3×C3⋊C8C2312yes—
77C2×C3×C3⋊C8C2312yes—
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80#3712—28no—
81C2×#436—91noSylow
82C23×C3×C4—21no—
83C23×C3×C4C2×D311yescharacteristic
84C23×C3×C4C2×D311yescharacteristic
85C22×#67—31no—
86C22×#67—31no—
87C22×#67—61no—
88C22×C4×D3—31no—
89C22×C4×D3—31no—
90C22×C4×D3—61no—
91C2×C3×M16—34no—
92C2×C3×M16—64no—
93C22×C3×C8—31no—
94C22×C3×C8—31no—
95C22×C3×C8—31no—
96C22×C3×C8—31no—
97C2×#217—31no—
98C2×#217—31no—
99C2×#217—61no—
100C4×#67—34no—
101C4×#67—34no—
102C4×#67—34no—
103C4×#67—34no—
104C4×#67—64no—
105C4×#67—64no—
106C2×(C2×D3)⋊C4—31no—
107C2×(C2×D3)⋊C4—31no—
108C2×(C2×D3)⋊C4—61no—
109C2×Dic3⋊C4—31no—
110C2×Dic3⋊C4—31no—
111C2×Dic3⋊C4—61no—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—61no—
115C2×#208—24no—
116C2×#208C2×D314yescomplemented
117C22×C3⋊C8C2×D311yescharacteristic
118C22×C3⋊C8C2×D311yescharacteristic
119C22×C3⋊C8C2×D311yescharacteristic
120C22×C3⋊C8C2×D311yescharacteristic
121C2×ΓL(1,𝔽25)—34no—
122C2×ΓL(1,𝔽25)—34no—
123C2×ΓL(1,𝔽25)—64no—
124C2×ΓL(1,𝔽25)—64no—
125C3×C22⋊C8—34no—
126#830C2×D314yescomplemented
127(C2×D3)⋊C8—34no—
128(C2×D3)⋊C8—34no—
129Dic3⋊C8—34no—
130Dic3⋊C8—34no—
131C8×Dic3—34no—
132C8×Dic3—34no—
133C23×C32—22no—
134C23×C32—22no—
135C23×C32—22no—
136C23×C32C22×C412yes—
137C23×C32C22×C411yescharacteristic
138C22×C3⋊D3—22no—
139C22×C3⋊D3—22no—
140C22×C3⋊D3—22no—
141C22×C3⋊D3C22×C412yes—
142C2×C32×C4—22no—
143C2×C32×C4—24no—
144C2×C32×C4—22no—
145C2×C32×C4—22no—
146C2×C32×C4C22×C412yes—
147C2×C32×C4C22×C411yescharacteristic
148C2×C32×C4C2×D412yes—
149C2×C32×C4#4112yes—
150C2×C32×C4C2411yescharacteristic
151#638—28no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3M1614yescomplemented
155C2×C3⋊Dic3C22×C412yes—
156C2×C3⋊Dic3C22×C412yes—
157C2×C3⋊Dic3C22×C412yes—
158C4×C3⋊D3—24no—
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—31no—
166C22×M16—91no—
167C2×C4×D4—91no—
168#436—98no—
169C2×C4⋊C8—91no—
170C2×C22⋊C8—31no—
171C2×C22⋊C8—91no—
172C2×C4×C8—91no—
173C24×C3—21no—
174C24×C3C4×D311yescharacteristic
175C24×C3C4×D311yescharacteristic
176C23×D3—31no—
177C23×D3—31no—
178C23×D3—61no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—21no—
187C22×C3×C4—42no—
188C22×C3×C4—42no—
189C22×C3×C4C4×D311yescharacteristic
190C22×C3×C4C4×D311yescharacteristic
191C22×C3×C4C4×D312yes—
192C22×C3×C4C4×D312yes—
193C22×C3×C4C22×D312yes—
194C22×C3×C4C22×D312yes—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C2×#67—34no—
198C2×#67—34no—
199C2×#67—64no—
200C2×#67—64no—
201C2×#67—64no—
202C2×#67—68no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—61no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C2×C4×D3—32no—
213C2×C4×D3—32no—
214C2×C4×D3—32no—
215C2×C4×D3—32no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×C4×D3—122no—
223C2×C4×D3—122no—
224C3×M16—68no—
225C2×C3×C8—34no—
226C2×C3×C8—32no—
227C2×C3×C8—32no—
228C2×C3×C8—32no—
229C2×C3×C8—32no—
230C2×C3×C8—62no—
231C2×C3×C8—62no—
232C2×C3×C8—62no—
233#217—34no—
234#217—34no—
235#217—64no—
236(C2×D3)⋊C4—34no—
237(C2×D3)⋊C4—34no—
238(C2×D3)⋊C4—64no—
239Dic3⋊C4—34no—
240Dic3⋊C4—34no—
241Dic3⋊C4—64no—
242C4×Dic3—32no—
243C4×Dic3—32no—
244C4×Dic3—32no—
245C4×Dic3—32no—
246C4×Dic3—62no—
247C4×Dic3—62no—
248#208—28no—
249C2×C3⋊C8—22no—
250C2×C3⋊C8—22no—
251C2×C3⋊C8—22no—
252C2×C3⋊C8#6714yescomplemented
253C2×C3⋊C8C22×D312yes—
254C2×C3⋊C8C22×D312yes—
255C2×C3⋊C8C22×D312yes—
256C2×C3⋊C8C22×D312yes—
257ΓL(1,𝔽25)—68no—
258ΓL(1,𝔽25)—68no—
259C22×C32—22no—
260C22×C32—22no—
261C22×C32—22no—
262C22×C32—44no—
263C22×C32C4×D412yes—
264C22×C32C2×M1612yes—
265C22×C32#13112yes—
266C22×C32C23×C411yescharacteristic
267C2×C3⋊D3—22no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—44no—
271C32×C4—22no—
272C32×C4C4×D412yes—
273C32×C4C22×D411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—22no—
276C3⋊Dic3—22no—
277C3⋊Dic3C2×M1614yescomplemented
278C22×D4—91no—
279C23×C4—91no—
280C23×C4D3211yescharacteristic
281C2×M16—34no—
282C2×M16—64no—
283C2×M16—94no—
284C2×M16—184no—
285C22×C8—31no—
286C22×C8—31no—
287C22×C8—31no—
288C22×C8—31no—
289C4×D4—94no—
290C4×D4—94no—
291C2×C4⋊C4—91no—
292C2×C22⋊C4—91no—
293C2×C22⋊C4—91no—
294C2×C42—91no—
295C4⋊C8—94no—
296C22⋊C8—34no—
297C22⋊C8—94no—
298C4×C8—94no—
299C23×C3—24no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—21no—
307C23×C3—22no—
308C23×C3—42no—
309C23×C3—42no—
310C23×C3C2×C4×D312yes—
311C23×C3C2×C4×D312yes—
312C23×C3C2×C4×D311yescharacteristic
313C23×C3C2×C4×D311yescharacteristic
314C22×D3—32no—
315C22×D3—32no—
316C22×D3—62no—
317C22×D3—64no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—122no—
325C22×D3—122no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—24no—
329C2×C3×C4—24no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—44no—
342C2×C3×C4—42no—
343C2×C3×C4C2×C4×D312yes—
344C2×C3×C4C2×C4×D312yes—
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4#23512yes—
348C2×C3×C4D3×D412yes—
349C2×C3×C4#23712yes—
350C2×C3×C4C2×#6712yes—
351C2×C3×C4C23×D311yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353#67—68no—
354#67—68no—
355#67—616no—
356C2×Dic3—34no—
357C2×Dic3—34no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—64no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374C4×D3—64no—
375C4×D3—64no—
376C4×D3—62no—
377C4×D3—62no—
378C4×D3—62no—
379C4×D3—62no—
380C4×D3—122no—
381C4×D3—122no—
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×#6714yescomplemented
391C2×C32—42no—
392C2×C32#43614yescomplemented
393C2×C32C2×C4×D411yescharacteristic
394C2×C32C22×M1611yescharacteristic
395C2×C32C2×#13111yescharacteristic
396C3⋊D3—42no—
397C24—91no—
398C24#62411yescharacteristic
399C2×D4—94no—
400C2×D4—184no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—91no—
404C22×C4—91no—
405C22×C4—91no—
406C22×C4—92no—
407C22×C4—92no—
408C22×C4—182no—
409C22×C4—182no—
410C22×C4#62411yescharacteristic
411C22×C4#62412yes—
412C22×C4C2×D3212yes—
413C22×C4C2×D3211yescharacteristic
414M16—68no—
415M16—188no—
416C2×C8—32no—
417C2×C8—34no—
418C2×C8—32no—
419C2×C8—32no—
420C2×C8—32no—
421C2×C8—62no—
422C2×C8—62no—
423C2×C8—62no—
424C4⋊C4—94no—
425C22⋊C4—94no—
426C22⋊C4—94no—
427C42—92no—
428C42—92no—
429C22×C3—24no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—21no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—48no—
443C22×C3—44no—
444C22×C3—44no—
445C22×C3#67⋊C412yes—
446C22×C3#90112yes—
447C22×C3D3×M1612yes—
448C22×C3D3×M1612yes—
449C22×C3#90712yes—
450C22×C3C4×#6712yes—
451C22×C3C22×C4×D311yescharacteristic
452C22×C3C22×C4×D311yescharacteristic
453C2×D3—64no—
454C2×D3—62no—
455C2×D3—62no—
456C2×D3—62no—
457C2×D3—62no—
458C2×D3—62no—
459C2×D3—62no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—128no—
463C2×D3—124no—
464C2×D3—124no—
465C3×C4—22no—
466C3×C4—22no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—22no—
470C3×C4—42no—
471C3×C4#67⋊C412yes—
472C3×C4C4×#6712yes—
473C3×C4C2×#23511yescharacteristic
474C3×C4C2×D3×D411yescharacteristic
475C3×C4C2×#23711yescharacteristic
476C3×C4C22×#6711yescharacteristic
477Dic3—34no—
478Dic3—34no—
479Dic3—64no—
480Dic3—62no—
481Dic3—62no—
482Dic3—62no—
483Dic3—62no—
484Dic3—122no—
485Dic3—122no—
486C32C2×#43611yescharacteristic, complemented, Sylow
487C23—22no—
488C23—22no—
489C23—22no—
490C23—92no—
491C23—182no—
492C23—182no—
493C23—182no—
494C23C2×#62412yes—
495C23C2×#62411yescharacteristic
496D4—188no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—92no—
502C2×C4—94no—
503C2×C4—92no—
504C2×C4—92no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4—184no—
510C2×C4#380412yes—
511C2×C4C2×#62412yes—
512C2×C4C2×#62411yescharacteristic
513C2×C4D3×#6712yes—
514C2×C4C22×D3211yescharacteristic
515C8—34no—
516C8—62no—
517C8—62no—
518C8—62no—
519C2×C3—24no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—44no—
524C2×C3—42no—
525C2×C3—42no—
526C2×C3#472914yescomplemented
527C2×C3#512814yescomplemented
528C2×C3C2×#67⋊C411yescharacteristic
529C2×C3C2×#90111yescharacteristic
530C2×C3C2×D3×M1611yescharacteristic
531C2×C3C2×D3×M1611yescharacteristic
532C2×C3C2×#90711yescharacteristic
533C2×C3C2×C4×#6711yescharacteristic
534D3—124no—
535D3—122no—
536D3—122no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—44no—
541C22—182no—
542C22—182no—
543C22—182no—
544C22—364no—
545C22#6381712yes—
546C22#6381812yes—
547C22#6395212yes—
548C22C22×#62411yescharacteristic
549C4—22no—
550C4—94no—
551C4—182no—
552C4—182no—
553C4#6395212yes—
554C4C2×#380411yescharacteristic
555C4C2×D3×#6711yescharacteristic
556C3—21no—
557C3C2×#472911yescharacteristic, complemented
558C3C2×#512811yescharacteristic, complemented
559C2—42no—
560C2—362no—
561C2#1059105114yesdirect product factor
562C2C2×#6381711yescharacteristic
563C2C2×#6381811yescharacteristic
564C2C2×#6395211yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC22×#638C4
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#436
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#208C2semidirect
3. C22×#3712C2semidirect
4. C2×C3×#830C2semidirect
5. C2×#63572C2semidirect
6. C2×#63557C2semidirect
7. C2×#63553C2semidirect
8. #10591051C2direct (N × H)
21. C2×C3×#208C22semidirect
27. C2×#3712C22semidirect
28. C3×#830C22semidirect
29. #63572C22semidirect
30. #63557C22semidirect
31. #63553C22semidirect
36. C22×#208D3semidirect
40. C2×#830D3semidirect
75. C2×C3×C3⋊C8D4semidirect
116. C2×#208C2×D3semidirect
126. #830C2×D3semidirect
154. C2×C3⋊Dic3M16semidirect
164. C3×C3⋊C8C2×D4semidirect
252. C2×C3⋊C8#67semidirect
277. C3⋊Dic3C2×M16semidirect
390. C3⋊C8C2×#67semidirect
392. C2×C32#436semidirect
486. C32C2×#436semidirect
526. C2×C3#4729semidirect
527. C2×C3#5128semidirect
557. C3C2×#4729semidirect
558. C3C2×#5128semidirect
561. C2#10591051direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C22×C3×#2082
C22×#37122
C2×C3×#8302
C2×#635722
C2×#635572
C2×#635532
#105910512
C2×#51283
C2×#47293