Finite Group Databasebeta

← C2×#10596133 #11901621

Subgroups — C2×#10596133 #11901621

Order 1152.

3396 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#123C211yesmaximal, characteristic, complemented
2C2×#64148C211yesmaximal, characteristic
3C2×#64145C211yesmaximal, characteristic, complemented
4C2×C4×#638C211yesmaximal, characteristic, complemented
5C2×#64133C211yesmaximal, characteristic, complemented
6#10596133C2116yesmaximal, direct product factor
7C2×#64107C211yesmaximal, characteristic, complemented
8C2×#64105C211yesmaximal, characteristic, complemented
9C2×#64097C211yesmaximal, characteristic, complemented
10C2×#64096C211yesmaximal, characteristic, complemented
11C2×#64094C211yesmaximal, characteristic, complemented
12C2×#64094C211yesmaximal, characteristic, complemented
13C2×#64092C211yesmaximal, characteristic, complemented
14C2×#64088C211yesmaximal, characteristic, complemented
15C2×#64087C211yesmaximal, characteristic, complemented
16C2×#64086C211yesmaximal, characteristic, complemented
17C2×#5662—34nomaximal
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic
24C22×#634C2211yescharacteristic
25C22×#634C2211yescharacteristic
26C22×#634C2211yescharacteristic
27C32×#123C2218yescomplemented
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×#3757C2211yescharacteristic
35C2×#3757C2211yescharacteristic
36C2×#3757C2211yescharacteristic
37C2×#3757C2211yescharacteristic
38#64148C2218yes—
39#64145C2218yescomplemented
40C4×#638C2218yescomplemented
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
46C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
47#64133C2218yescomplemented
48C2×#3750C2211yescharacteristic
49C2×#3750C2211yescharacteristic
50C2×#3750C2211yescharacteristic
51C2×#3750C2211yescharacteristic
52C2×#3750C2211yescharacteristic
53C2×#3750C2211yescharacteristic
54C2×C4×C3⋊Dic3C2211yescharacteristic
55C2×C4×C3⋊Dic3C2211yescharacteristic
56C2×C4×C3⋊Dic3C2211yescharacteristic
57C2×C4×C3⋊Dic3C2211yescharacteristic
58#64107C2218yescomplemented
59#64105C2218yescomplemented
60#64097C2218yescomplemented
61#64096C2218yescomplemented
62#64094C2218yescomplemented
63#64094C2218yescomplemented
64#64092C2218yescomplemented
65#64088C2218yescomplemented
66#64087C2218yescomplemented
67#64086C2218yescomplemented
68C2×C3×#123D314yescomplemented
69C2×#939—34no—
70C2×#936—34no—
71C2×C4×#67—34no—
72C2×#924—34no—
73#5662—364no—
74C2×#898—34no—
75C2×#896—34no—
76C2×#888—34no—
77C2×#887—34no—
78C2×#885—34no—
79C2×#885—34no—
80C2×#883—34no—
81C2×#879—34no—
82C2×#878—34no—
83C2×#877—34no—
84C24×C32C2311yescharacteristic
85C24×C32C2311yescharacteristic
86C23×C3⋊D3C2311yescharacteristic
87C2×C32×D4—42no—
88C2×C32×D4C2314yes—
89C22×C32×C4—42no—
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2314yes—
96C2×#638—24no—
97C2×#638—42no—
98C2×#638C2314yes—
99C2×#638C2314yes—
100C22×C3⋊Dic3—24no—
101C22×C3⋊Dic3C2314yes—
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C2×C4×C3⋊D3—42no—
110C2×C4×C3⋊D3C2314yes—
111C2×#634—24no—
112C2×#634—42no—
113C2×#634—42no—
114C2×#634C2314yes—
115C2×#634C2314yes—
116C2×#634C2314yes—
117C32×C4⋊C4C2314yes—
118C32×C4⋊C4C2314yes—
119C32×C22⋊C4C2314yes—
120C32×C22⋊C4C2314yes—
121C32×C22⋊C4C2314yes—
122#3757C2314yes—
123#3757C2314yes—
124#3757C2314yes—
125#3757C2314yes—
126#3757C2314yes—
127#3752C2314yes—
128#3752C2314yes—
129#3752C2314yes—
130#3752C2314yes—
131C4⋊(C3⋊Dic3)C2314yes—
132C4⋊(C3⋊Dic3)C2314yes—
133#3750C2314yes—
134#3750C2314yes—
135#3750C2314yes—
136#3750C2314yes—
137#3750C2314yes—
138#3750C2314yes—
139C4×C3⋊Dic3C2314yes—
140C4×C3⋊Dic3C2314yes—
141C4×C3⋊Dic3C2314yes—
142C4×C3⋊Dic3C2314yes—
143C2×#542—91noSylow
144C22×C3×D4C2×D314yes—
145C23×C3×C4C2×D314yes—
146C22×#67—34no—
147C22×#67—34no—
148C23×Dic3—34no—
149C22×C4×D3—34no—
150C22×Dic6—34no—
151C22×Dic6—34no—
152C22×Dic6—34no—
153C3×#123C2×D3132yescomplemented
154C2×C3×C4⋊C4C2×D314yes—
155C2×C3×C4⋊C4C2×D314yes—
156C2×C3×C22⋊C4C2×D314yes—
157C2×C3×C22⋊C4C2×D314yes—
158C2×C3×C22⋊C4C2×D314yes—
159C2×#217—34no—
160C2×#217—34no—
161C2×#217—34no—
162C2×#217—34no—
163C2×#217—34no—
164#939—332no—
165#936—332no—
166C4×#67—332no—
167C2×(C2×D3)⋊C4—34no—
168C2×(C2×D3)⋊C4—34no—
169C2×(C2×D3)⋊C4—34no—
170C2×(C2×D3)⋊C4—34no—
171C2×C4⋊Dic3—34no—
172C2×C4⋊Dic3—34no—
173#924—332no—
174C2×Dic3⋊C4—34no—
175C2×Dic3⋊C4—34no—
176C2×Dic3⋊C4—34no—
177C2×Dic3⋊C4—34no—
178C2×Dic3⋊C4—34no—
179C2×Dic3⋊C4—34no—
180C2×C4×Dic3—34no—
181C2×C4×Dic3—34no—
182C2×C4×Dic3—34no—
183C2×C4×Dic3—34no—
184#898—332no—
185#896—332no—
186#888—332no—
187#887—332no—
188#885—332no—
189#885—332no—
190#883—332no—
191#879—332no—
192#878—332no—
193#877—332no—
194C23×C32—22no—
195C23×C32—22no—
196C23×C32—22no—
197C23×C32—22no—
198C23×C32—22no—
199C23×C32—22no—
200C23×C32C2412yes—
201C23×C32C2412yes—
202C23×C32C2411yescharacteristic
203C22×C3⋊D3—22no—
204C22×C3⋊D3—22no—
205C22×C3⋊D3—22no—
206C22×C3⋊D3C2412yes—
207C32×D4—44no—
208C2×C32×C4—22no—
209C2×C32×C4—22no—
210C2×C32×C4—22no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—44no—
214C2×C32×C4C2412yes—
215C2×C32×C4C2412yes—
216C2×C32×C4C2412yes—
217C2×C32×C4C2412yes—
218C2×C32×C4C2412yes—
219#638—28no—
220#638—44no—
221C2×C3⋊Dic3—22no—
222C2×C3⋊Dic3—22no—
223C2×C3⋊Dic3—22no—
224C2×C3⋊Dic3—22no—
225C2×C3⋊Dic3—22no—
226C2×C3⋊Dic3—22no—
227C2×C3⋊Dic3—28no—
228C2×C3⋊Dic3#4114yes—
229C2×C3⋊Dic3C2412yes—
230C2×C3⋊Dic3C2412yes—
231C2×C3⋊Dic3C2412yes—
232C2×C3⋊Dic3C2412yes—
233C2×C3⋊Dic3C2412yes—
234C2×C3⋊Dic3C2412yes—
235C2×C3⋊Dic3C2412yes—
236C4×C3⋊D3—44no—
237#634—28no—
238#634—44no—
239#634—44no—
240#542—916no—
241C2×C4⋊Q8—91no—
242C2×#126—91no—
243C2×#126—91no—
244C2×#124—91no—
245C2×#124—91no—
246C2×#124—91no—
247C2×#123—91no—
248C2×#123C3⋊D311yescharacteristic, complemented
249C2×C22⋊Q8—91no—
250C2×C22⋊Q8—91no—
251C2×C22⋊Q8—91no—
252C2×#121—91no—
253C2×C4×Q8—91no—
254C2×C4×D4—91no—
255C2×#117—91no—
256C24×C3C22×D314yes—
257C24×C3C22×D314yes—
258C23×D3—34no—
259C2×C3×D4—48no—
260C2×C3×D4C22×D3116yes—
261C22×C3×C4—48no—
262C22×C3×C4C22×D314yes—
263C22×C3×C4C22×D314yes—
264C22×C3×C4C22×D314yes—
265C22×C3×C4C22×D314yes—
266C22×C3×C4C22×D314yes—
267C22×C3×C4C22×D3116yes—
268C2×#67—316no—
269C2×#67—316no—
270C2×#67—616no—
271C2×#67—128no—
272C22×Dic3—34no—
273C22×Dic3—316no—
274C22×Dic3—34no—
275C22×Dic3—34no—
276C22×Dic3—34no—
277C22×Dic3—34no—
278C22×Dic3—34no—
279C22×Dic3—34no—
280C22×Dic3—616no—
281C2×C4×D3—316no—
282C2×C4×D3—128no—
283C2×Dic6—316no—
284C2×Dic6—316no—
285C2×Dic6—316no—
286C2×Dic6—616no—
287C2×Dic6—128no—
288C2×Dic6—128no—
289C3×C4⋊C4C22×D3116yes—
290C3×C4⋊C4C22×D3116yes—
291C3×C22⋊C4C22×D3116yes—
292C3×C22⋊C4C22×D3116yes—
293C3×C22⋊C4C22×D3116yes—
294#217—316no—
295#217—316no—
296#217—316no—
297#217—316no—
298#217—316no—
299(C2×D3)⋊C4—316no—
300(C2×D3)⋊C4—316no—
301(C2×D3)⋊C4—316no—
302(C2×D3)⋊C4—316no—
303C4⋊Dic3—316no—
304C4⋊Dic3—316no—
305Dic3⋊C4—316no—
306Dic3⋊C4—316no—
307Dic3⋊C4—316no—
308Dic3⋊C4—316no—
309Dic3⋊C4—316no—
310Dic3⋊C4—316no—
311C4×Dic3—316no—
312C4×Dic3—316no—
313C4×Dic3—316no—
314C4×Dic3—316no—
315C22×C32—22no—
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—22no—
319C22×C32—22no—
320C22×C32—22no—
321C22×C32—44no—
322C22×C32—44no—
323C22×C32C2×#4112yes—
324C22×C32H(5,𝔽2)12yes—
325C22×C322−1+412yes—
326C22×C32C2511yescharacteristic
327C2×C3⋊D3—22no—
328C2×C3⋊D3—22no—
329C2×C3⋊D3—22no—
330C2×C3⋊D3—44no—
331C32×C4—22no—
332C32×C4—22no—
333C32×C4—22no—
334C32×C4—22no—
335C32×C4—22no—
336C3⋊Dic3—22no—
337C3⋊Dic3—22no—
338C3⋊Dic3—22no—
339C3⋊Dic3—22no—
340C3⋊Dic3—22no—
341C3⋊Dic3—22no—
342C3⋊Dic3C2×#4114yes—
343C22×Q8—91no—
344C22×Q8—91no—
345C22×Q8—91no—
346C22×D4—91no—
347C22×D4—91no—
348C22×D4C2×C3⋊D311yescharacteristic
349C23×C4—91no—
350C23×C4—91no—
351C23×C4C2×C3⋊D311yescharacteristic
352C4⋊Q8—98no—
353#126—98no—
354#126—98no—
355#124—98no—
356#124—98no—
357#124—98no—
358#123—98no—
359#123C2×C3⋊D318yescomplemented
360C22⋊Q8—98no—
361C22⋊Q8—98no—
362C22⋊Q8—98no—
363#121—98no—
364C4×Q8—98no—
365C4×D4—98no—
366#117—98no—
367C2×C4⋊C4—91no—
368C2×C4⋊C4—91no—
369C2×C4⋊C4—91no—
370C2×C4⋊C4—91no—
371C2×C4⋊C4—91no—
372C2×C4⋊C4—91no—
373C2×C4⋊C4—91no—
374C2×C4⋊C4—91no—
375C2×C4⋊C4C2×C3⋊D311yescharacteristic
376C2×C4⋊C4C2×C3⋊D311yescharacteristic
377C2×C22⋊C4—91no—
378C2×C22⋊C4—91no—
379C2×C22⋊C4—91no—
380C2×C22⋊C4—91no—
381C2×C22⋊C4—91no—
382C2×C22⋊C4—91no—
383C2×C22⋊C4—91no—
384C2×C22⋊C4—91no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4C2×C3⋊D311yescharacteristic
387C2×C22⋊C4C2×C3⋊D311yescharacteristic
388C2×C22⋊C4C2×C3⋊D311yescharacteristic
389C2×C42—91no—
390C2×C42—91no—
391C2×C42—91no—
392C2×C42—91no—
393C23×C3—28no—
394C23×C3—28no—
395C23×C3—28no—
396C23×C3—28no—
397C23×C3—28no—
398C23×C3—28no—
399C23×C3C23×D318yes—
400C23×C3C23×D318yes—
401C23×C3C23×D314yes—
402C22×D3—38no—
403C22×D3—68no—
404C22×D3—68no—
405C22×D3—68no—
406C3×D4—416no—
407C2×C3×C4—28no—
408C2×C3×C4—28no—
409C2×C3×C4—28no—
410C2×C3×C4—28no—
411C2×C3×C4—28no—
412C2×C3×C4—416no—
413C2×C3×C4C23×D318yes—
414C2×C3×C4C23×D318yes—
415C2×C3×C4C23×D318yes—
416C2×C3×C4C23×D318yes—
417C2×C3×C4C23×D318yes—
418#67—632no—
419#67—1216no—
420C2×Dic3—316no—
421C2×Dic3—38no—
422C2×Dic3—38no—
423C2×Dic3—38no—
424C2×Dic3—38no—
425C2×Dic3—38no—
426C2×Dic3—38no—
427C2×Dic3—38no—
428C2×Dic3—632no—
429C2×Dic3—68no—
430C2×Dic3—68no—
431C2×Dic3—68no—
432C2×Dic3—68no—
433C2×Dic3—68no—
434C2×Dic3—68no—
435C4×D3—1216no—
436Dic6—632no—
437Dic6—1216no—
438Dic6—1216no—
439C2×C32—42no—
440C2×C32—42no—
441C2×C32#54214yescomplemented
442C2×C32C22×#4111yescharacteristic
443C2×C32C2×H(5,𝔽2)11yescharacteristic
444C2×C32C2×2−1+411yescharacteristic
445C3⋊D3—42no—
446C24—91no—
447C24C22×C3⋊D311yescharacteristic
448C24C22×C3⋊D311yescharacteristic
449C2×Q8—94no—
450C2×Q8—94no—
451C2×Q8—94no—
452C2×Q8—184no—
453C2×Q8—362no—
454C2×Q8—362no—
455C2×D4—42no—
456C2×D4—94no—
457C2×D4—94no—
458C2×D4—184no—
459C2×D4—362no—
460C2×D4C22×C3⋊D314yes—
461C22×C4—42no—
462C22×C4—91no—
463C22×C4—94no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—91no—
467C22×C4—91no—
468C22×C4—91no—
469C22×C4—91no—
470C22×C4—94no—
471C22×C4—184no—
472C22×C4—362no—
473C22×C4C22×C3⋊D311yescharacteristic
474C22×C4C22×C3⋊D311yescharacteristic
475C22×C4C22×C3⋊D311yescharacteristic
476C22×C4C22×C3⋊D311yescharacteristic
477C22×C4C22×C3⋊D311yescharacteristic
478C22×C4C22×C3⋊D314yes—
479C4⋊C4—94no—
480C4⋊C4—94no—
481C4⋊C4—94no—
482C4⋊C4—94no—
483C4⋊C4—94no—
484C4⋊C4—94no—
485C4⋊C4—94no—
486C4⋊C4—94no—
487C4⋊C4C22×C3⋊D314yes—
488C4⋊C4C22×C3⋊D314yes—
489C22⋊C4—94no—
490C22⋊C4—94no—
491C22⋊C4—94no—
492C22⋊C4—94no—
493C22⋊C4—94no—
494C22⋊C4—94no—
495C22⋊C4—94no—
496C22⋊C4—94no—
497C22⋊C4—94no—
498C22⋊C4C22×C3⋊D314yes—
499C22⋊C4C22×C3⋊D314yes—
500C22⋊C4C22×C3⋊D314yes—
501C42—94no—
502C42—94no—
503C42—94no—
504C42—94no—
505C22×C3—28no—
506C22×C3—28no—
507C22×C3—28no—
508C22×C3—28no—
509C22×C3—28no—
510C22×C3—28no—
511C22×C3—416no—
512C22×C3—416no—
513C22×C3#100418yes—
514C22×C3D3×#4118yes—
515C22×C3#101018yes—
516C22×C3C24×D314yes—
517C2×D3—68no—
518C2×D3—68no—
519C2×D3—68no—
520C2×D3—1216no—
521C3×C4—28no—
522C3×C4—28no—
523C3×C4—28no—
524C3×C4—28no—
525C3×C4—28no—
526Dic3—316no—
527Dic3—68no—
528Dic3—68no—
529Dic3—68no—
530Dic3—68no—
531Dic3—68no—
532Dic3—68no—
533C32C2×#54211yescharacteristic, complemented, Sylow
534C23—22no—
535C23—22no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—92no—
541C23—182no—
542C23—182no—
543C23—182no—
544C23C23×C3⋊D312yes—
545C23C23×C3⋊D312yes—
546C23C23×C3⋊D311yescharacteristic
547Q8—188no—
548Q8—364no—
549Q8—364no—
550D4—44no—
551D4—188no—
552D4—364no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—44no—
559C2×C4—94no—
560C2×C4—92no—
561C2×C4—92no—
562C2×C4—92no—
563C2×C4—92no—
564C2×C4—92no—
565C2×C4—92no—
566C2×C4—92no—
567C2×C4—188no—
568C2×C4—182no—
569C2×C4—182no—
570C2×C4—182no—
571C2×C4—182no—
572C2×C4—182no—
573C2×C4—182no—
574C2×C4—364no—
575C2×C4C23×C3⋊D312yes—
576C2×C4C23×C3⋊D312yes—
577C2×C4C23×C3⋊D312yes—
578C2×C4C23×C3⋊D312yes—
579C2×C4C23×C3⋊D312yes—
580C2×C3—48no—
581C2×C3—48no—
582C2×C3#5662116yescomplemented
583C2×C3C2×#100414yes—
584C2×C3C2×D3×#4114yes—
585C2×C3C2×#101014yes—
586D3—128no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—44no—
594C22—44no—
595C22—182no—
596C22—182no—
597C22—182no—
598C22—364no—
599C22#6436112yes—
600C22#41×C3⋊D312yes—
601C22#6436712yes—
602C22C24×C3⋊D311yescharacteristic
603C4—22no—
604C4—22no—
605C4—22no—
606C4—22no—
607C4—22no—
608C4—94no—
609C4—182no—
610C4—182no—
611C4—182no—
612C4—182no—
613C4—182no—
614C4—182no—
615C3C2×#566214yescomplemented
616C2—42no—
617C2—42no—
618C2—362no—
619C2#1059613314yesdirect product factor
620C2C2×#6436111yescharacteristic
621C2C2×#41×C3⋊D311yescharacteristic
622C2C2×#6436711yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×#123C2
socleC23×C32C24
prime radicalC2×#64148C2
hypercenterC2×#123C3⋊D3
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C32×#123C2semidirect
3. C2×#64145C2semidirect
4. C2×C4×#638C2semidirect
5. C2×#64133C2semidirect
6. #10596133C2direct (N × H)
7. C2×#64107C2semidirect
8. C2×#64105C2semidirect
9. C2×#64097C2semidirect
10. C2×#64096C2semidirect
11. C2×#64094C2semidirect
12. C2×#64094C2semidirect
13. C2×#64092C2semidirect
14. C2×#64088C2semidirect
15. C2×#64087C2semidirect
16. C2×#64086C2semidirect
27. C32×#123C22semidirect
39. #64145C22semidirect
40. C4×#638C22semidirect
47. #64133C22semidirect
58. #64107C22semidirect
59. #64105C22semidirect
60. #64097C22semidirect
61. #64096C22semidirect
62. #64094C22semidirect
63. #64094C22semidirect
64. #64092C22semidirect
65. #64088C22semidirect
66. #64087C22semidirect
67. #64086C22semidirect
68. C2×C3×#123D3semidirect
153. C3×#123C2×D3semidirect
248. C2×#123C3⋊D3semidirect
359. #123C2×C3⋊D3semidirect
441. C2×C32#542semidirect
533. C32C2×#542semidirect
582. C2×C3#5662semidirect
615. C3C2×#5662semidirect
619. C2#10596133direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1232
C2×#641482
C2×#641452
C2×C4×#6382
C2×#641332
#105961332
C2×#641072
C2×#641052
C2×#640972
C2×#640962
C2×#640942
C2×#640922
C2×#640882
C2×#640872
C2×#640862
C2×#56623