Finite Group Databasebeta

← C2×#10594899 #11902614

Subgroups — C2×#10594899 #11902614

Order 1152.

3401 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64133C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×#63970C212yesmaximal, complemented
6C2×#63959C212yesmaximal, complemented
7C2×#63908C211yesmaximal, characteristic, complemented
8#10594899C2116yesmaximal, direct product factor
9C2×#63879C212yesmaximal, complemented
10C2×#63860C211yesmaximal, characteristic, complemented
11C2×#63851C212yesmaximal, complemented
12C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
13C2×#5831—31nomaximal
14C2×#5552—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×C3×#67C2212yes—
19C2×C3×#235—28no—
20C2×C3×#235C2218yescomplemented
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2212yes—
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#627C2212yes—
26C22×#625C2212yes—
27C22×D3×Dic3C2212yes—
28C2×D3×Dic6—28no—
29C2×D3×Dic6C2218yescomplemented
30C2×#3757C2212yes—
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32#64133C2218yescomplemented
33C2×#3750C2212yes—
34C2×C3×#217C2211yescharacteristic
35C3×C4×#67C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39#63970C22116yescomplemented
40C2×Dic3⋊Dic3C2212yes—
41C2×(C2×D3)⋊Dic3C2212yes—
42C2×(C2×D3)⋊Dic3C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44#63959C22116yescomplemented
45C2×Dic32C2212yes—
46#63908C2218yescomplemented
47#63879C22116yescomplemented
48#63860C2218yescomplemented
49#63851C22116yescomplemented
50Dic3×Dic6C2218yescomplemented
51C22×C3×#41—31no—
52C22×D3×Q8—31no—
53C22×#235D311yescharacteristic, complemented
54C23×Dic6—31no—
55C2×C3×C4×D4—31no—
56#5831—316no—
57C2×Q8×Dic3—31no—
58C2×#939—32no—
59C2×#938—32no—
60C2×#938—31no—
61C2×#936—32no—
62C2×#936—31no—
63C2×#930—31no—
64C2×C4×#67—32no—
65C2×C4×#67D311yescharacteristic, complemented
66C2×#924—31no—
67C2×#924—31no—
68C2×#924—32no—
69C2×#924—61no—
70#5552—316no—
71C2×#896—32no—
72C2×#885—32no—
73C2×#67⋊C4—32no—
74C2×#875—31no—
75C2×C4×Dic6—31no—
76C24×C32C2311yescharacteristic
77C23×C3×D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C22×C32×C4—24no—
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2314yes—
82C22×C32×C4C2311yescharacteristic
83C22×C3⋊Dic3C2312yes—
84C22×C3⋊Dic3C2312yes—
85C2×#634—24no—
86C2×#634C2314yes—
87C2×C3×#67—24no—
88C2×C3×#67—28no—
89C2×C3×#67C2314yes—
90C2×C3×#67C2318yes—
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2312yes—
95C3×#235—232no—
96C2×C3×D12—24no—
97C2×C3×D12C2314yes—
98C2×C3×C4×D3—24no—
99C2×C3×C4×D3—28no—
100C2×C3×C4×D3C2314yes—
101C2×C3×C4×D3C2318yes—
102C2×C3×Dic6D418yescomplemented
103C2×C3×Dic6C2314yes—
104C2×#627—28no—
105C2×#627C2318yes—
106C2×#625—28no—
107C2×#625C2318yes—
108C2×D3×Dic3—28no—
109C2×D3×Dic3C2318yes—
110D3×Dic6—232no—
111#3757C2318yes—
112C4⋊(C3⋊Dic3)C2314yes—
113#3750C2318yes—
114C3×#217C2314yes—
115C3×(C2×D3)⋊C4C2314yes—
116C3×Dic3⋊C4C2314yes—
117C3×C4×Dic3C2314yes—
118Dic3⋊Dic3C2318yes—
119(C2×D3)⋊Dic3C2318yes—
120(C2×D3)⋊Dic3C2318yes—
121(C2×D3)⋊Dic3C2318yes—
122Dic32C2318yes—
123C2×#548—91noSylow
124C2×C3×#41—38no—
125C2×C3×#41—68no—
126C22×C3×Q8—31no—
127C22×C3×D4—32no—
128C22×C3×D4—31no—
129C22×C3×D4—31no—
130C23×C3×C4—21no—
131C23×C3×C4—31no—
132C23×C3×C4—32no—
133C23×C3×C4C2×D311yescharacteristic
134C23×C3×C4C2×D311yescharacteristic
135C22×#67—32no—
136C22×#67—32no—
137C22×#67C2×D312yes—
138C22×#67C2×D311yescharacteristic
139C23×Dic3—32no—
140C2×D3×Q8—38no—
141C2×D3×Q8—68no—
142C2×#235—28no—
143C2×#235C2×D318yescomplemented
144C22×D12C2×D311yescharacteristic
145C22×C4×D3—32no—
146C22×C4×D3C2×D312yes—
147C22×C4×D3C2×D311yescharacteristic
148C22×Dic6—31no—
149C22×Dic6—31no—
150C22×Dic6—32no—
151C22×Dic6—32no—
152C22×Dic6—38no—
153C22×Dic6—61no—
154C22×Dic6—68no—
155C22×Dic6C2×D311yescharacteristic
156C3×C4×D4—38no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C42—31no—
161C2×#217—32no—
162C2×#217—32no—
163C2×#217—32no—
164C2×#217—32no—
165C2×#217—32no—
166C2×#217—62no—
167C2×#217C2×D311yescharacteristic
168Q8×Dic3—38no—
169#939—316no—
170#938—316no—
171#938—38no—
172#936—316no—
173#936—38no—
174#930—38no—
175C4×#67—316no—
176C4×#67C2×D318yescomplemented
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—32no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4C2×D311yescharacteristic
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—32no—
184C2×C4⋊Dic3—61no—
185#924—38no—
186#924—38no—
187#924—316no—
188#924—68no—
189C2×Dic3⋊C4—32no—
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4—32no—
192C2×Dic3⋊C4—62no—
193C2×Dic3⋊C4C2×D311yescharacteristic
194C2×C4×Dic3—32no—
195C2×C4×Dic3—32no—
196C2×C4×Dic3C2×D311yescharacteristic
197#896—316no—
198#885—316no—
199#67⋊C4—316no—
200#875—38no—
201C4×Dic6—38no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32C2412yes—
206C23×C32C2411yescharacteristic
207C22×C3×D3—22no—
208C22×C3×D3—22no—
209C22×C3×D3—24no—
210C22×C3×D3—24no—
211C22×C3×D3—24no—
212C22×C3×D3#4114yescomplemented
213C22×C3×D3C2414yes—
214C22×C3×D3C2412yes—
215C2×C32×C4—22no—
216C2×C32×C4—28no—
217C2×C32×C4C2×D414yes—
218C2×C32×C4C2412yes—
219C2×C32×C4C2412yes—
220C2×C3⋊Dic3—24no—
221C2×C3⋊Dic3—24no—
222C2×C3⋊Dic3C2414yes—
223C2×C3⋊Dic3C2414yes—
224#634—28no—
225C3×#67—28no—
226C3×#67—216no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3C2×D418yes—
231C2×C3×Dic3C2412yes—
232C2×C3×Dic3C2412yes—
233C2×C3×Dic3C2412yes—
234C2×C3×Dic3C2414yes—
235C3×D12—28no—
236C3×C4×D3—28no—
237C3×C4×D3—216no—
238C3×Dic6C2×D4116yescomplemented
239#627—216no—
240#625—216no—
241D3×Dic3—216no—
242C22×#41—31no—
243C23×Q8—91no—
244#548—916no—
245C2×#124—91no—
246C2×#124—92no—
247C2×C22⋊Q8—92no—
248C2×C22⋊Q8—91no—
249C2×#121—91no—
250C2×#121—92no—
251C2×C4×Q8—91no—
252C2×C4×D4—31no—
253C2×C4×D4—92no—
254C24×C3—21no—
255C24×C3—31no—
256C24×C3—32no—
257C24×C3C22×D311yescharacteristic
258C24×C3C22×D311yescharacteristic
259C23×D3C22×D312yes—
260C23×D3C22×D311yescharacteristic
261C3×#41—632no—
262C2×C3×Q8—38no—
263C2×C3×Q8—34no—
264C2×C3×D4—38no—
265C2×C3×D4—34no—
266C2×C3×D4—34no—
267C2×C3×D4—68no—
268C2×C3×D4—64no—
269C2×C3×D4—64no—
270C22×C3×C4—24no—
271C22×C3×C4—24no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—24no—
275C22×C3×C4—32no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—38no—
280C22×C3×C4—34no—
281C22×C3×C4—44no—
282C22×C3×C4—68no—
283C22×C3×C4—64no—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D314yes—
287C22×C3×C4C22×D314yes—
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C2×#67—24no—
291C2×#67—28no—
292C2×#67—38no—
293C2×#67—38no—
294C2×#67—68no—
295C2×#67—68no—
296C2×#67C22×D318yes—
297C2×#67C22×D314yes—
298C22×Dic3—32no—
299C22×Dic3—32no—
300C22×Dic3—32no—
301C22×Dic3—32no—
302C22×Dic3—38no—
303C22×Dic3—62no—
304C22×Dic3—62no—
305C22×Dic3—68no—
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D312yes—
310D3×Q8—632no—
311#235—232no—
312C2×D12—24no—
313C2×D12C22×D314yes—
314C2×C4×D3—24no—
315C2×C4×D3—28no—
316C2×C4×D3—38no—
317C2×C4×D3—68no—
318C2×C4×D3C22×D318yes—
319C2×C4×D3C22×D314yes—
320C2×Dic6—34no—
321C2×Dic6—34no—
322C2×Dic6—38no—
323C2×Dic6—38no—
324C2×Dic6—64no—
325C2×Dic6—68no—
326C2×Dic6—64no—
327C2×Dic6—64no—
328C2×Dic6—68no—
329C2×Dic6—632no—
330C2×Dic6—124no—
331C2×Dic6#6718yescomplemented
332C2×Dic6C22×D314yes—
333C3×C4⋊C4—34no—
334C3×C22⋊C4—34no—
335C3×C22⋊C4—34no—
336C3×C42—34no—
337#217—38no—
338#217—38no—
339#217—38no—
340#217—38no—
341#217—38no—
342#217—68no—
343#217C22×D314yes—
344(C2×D3)⋊C4—38no—
345(C2×D3)⋊C4—38no—
346(C2×D3)⋊C4—38no—
347(C2×D3)⋊C4C22×D314yes—
348C4⋊Dic3—34no—
349C4⋊Dic3—34no—
350C4⋊Dic3—38no—
351C4⋊Dic3—64no—
352Dic3⋊C4—38no—
353Dic3⋊C4—38no—
354Dic3⋊C4—38no—
355Dic3⋊C4—68no—
356Dic3⋊C4C22×D314yes—
357C4×Dic3—38no—
358C4×Dic3—38no—
359C4×Dic3C22×D314yes—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32—22no—
363C22×C32—44no—
364C22×C32C22×D412yes—
365C22×C32C2×#4112yes—
366C22×C322−1+412yes—
367C22×C32C2511yescharacteristic
368C2×C3×D3—28no—
369C2×C3×D3—22no—
370C2×C3×D3—22no—
371C2×C3×D3—24no—
372C2×C3×D3—24no—
373C2×C3×D3—24no—
374C2×C3×D3—48no—
375C2×C3×D3C2×#4114yescomplemented
376C32×C4—22no—
377C32×C4C22×D414yes—
378C3⋊Dic3—24no—
379C3⋊Dic3—24no—
380C3×Dic3—22no—
381C3×Dic3—22no—
382C3×Dic3—22no—
383C3×Dic3C22×D418yes—
384C2×#41—38no—
385C2×#41—68no—
386C22×Q8—31no—
387C22×Q8—92no—
388C22×Q8—98no—
389C22×Q8—91no—
390C22×Q8—188no—
391C22×D4—31no—
392C22×D4—32no—
393C22×D4—31no—
394C22×D4—92no—
395C23×C4—31no—
396C23×C4—32no—
397C23×C4—92no—
398C23×C4D3211yescharacteristic
399#124—98no—
400#124—916no—
401C22⋊Q8—916no—
402C22⋊Q8—98no—
403#121—98no—
404#121—916no—
405C4×Q8—98no—
406C4×D4—38no—
407C4×D4—916no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—92no—
410C2×C4⋊C4—92no—
411C2×C4⋊C4—91no—
412C2×C22⋊C4—31no—
413C2×C22⋊C4—31no—
414C2×C22⋊C4—92no—
415C2×C22⋊C4—92no—
416C2×C22⋊C4—92no—
417C2×C22⋊C4—92no—
418C2×C42—31no—
419C2×C42—92no—
420C23×C3—24no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—21no—
429C23×C3—34no—
430C23×C3—32no—
431C23×C3—34no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—62no—
435C23×C3—62no—
436C23×C3—64no—
437C23×C3—64no—
438C23×C3—64no—
439C23×C3C23×D312yes—
440C23×C3C23×D312yes—
441C23×C3C23×D311yescharacteristic
442C23×C3C23×D311yescharacteristic
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—24no—
446C22×D3—24no—
447C22×D3—24no—
448C22×D3#23514yescomplemented
449C22×D3C23×D314yes—
450C22×D3C23×D312yes—
451C3×Q8—316no—
452C3×D4—616no—
453C3×D4—68no—
454C3×D4—68no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—28no—
458C2×C3×C4—28no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—24no—
462C2×C3×C4—38no—
463C2×C3×C4—34no—
464C2×C3×C4—32no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—48no—
468C2×C3×C4—42no—
469C2×C3×C4—616no—
470C2×C3×C4—62no—
471C2×C3×C4—62no—
472C2×C3×C4—62no—
473C2×C3×C4—68no—
474C2×C3×C4D3×D414yes—
475C2×C3×C4C2×#6714yes—
476C2×C3×C4C23×D312yes—
477C2×C3×C4C23×D312yes—
478C2×C3×C4C23×D312yes—
479C2×C3×C4C23×D312yes—
480#67—28no—
481#67—216no—
482#67—616no—
483#67—616no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—34no—
488C2×Dic3—34no—
489C2×Dic3—34no—
490C2×Dic3—34no—
491C2×Dic3—64no—
492C2×Dic3—64no—
493C2×Dic3—64no—
494C2×Dic3—64no—
495C2×Dic3—64no—
496C2×Dic3—64no—
497C2×Dic3—616no—
498C2×Dic3—124no—
499C2×Dic3—124no—
500C2×Dic3C2×#6718yes—
501C2×Dic3C23×D312yes—
502C2×Dic3C23×D312yes—
503C2×Dic3C23×D312yes—
504C2×Dic3C23×D314yes—
505D12—28no—
506C4×D3—28no—
507C4×D3—216no—
508C4×D3—616no—
509Dic6—616no—
510Dic6—68no—
511Dic6—68no—
512Dic6—616no—
513Dic6—128no—
514Dic6C2×#67116yescomplemented
515C2×C32—42no—
516C2×C32#54814yescomplemented
517C2×C32C23×D411yescharacteristic
518C2×C32C22×#4111yescharacteristic
519C2×C32C2×2−1+411yescharacteristic
520C3×D3—24no—
521C3×D3—44no—
522C24—31no—
523C24—32no—
524C24C2×D3211yescharacteristic
525#41—632no—
526C2×Q8—34no—
527C2×Q8—38no—
528C2×Q8—98no—
529C2×Q8—94no—
530C2×Q8—188no—
531C2×Q8—1832no—
532C2×Q8—184no—
533C2×D4—34no—
534C2×D4—38no—
535C2×D4—34no—
536C2×D4—68no—
537C2×D4—64no—
538C2×D4—64no—
539C2×D4—98no—
540C2×D4—188no—
541C22×C4—24no—
542C22×C4—32no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—34no—
547C22×C4—38no—
548C22×C4—68no—
549C22×C4—64no—
550C22×C4—98no—
551C22×C4—92no—
552C22×C4—92no—
553C22×C4—188no—
554C22×C4C2×D3214yes—
555C22×C4C2×D3211yescharacteristic
556C22×C4C2×D3211yescharacteristic
557C4⋊C4—34no—
558C4⋊C4—98no—
559C4⋊C4—98no—
560C4⋊C4—94no—
561C22⋊C4—34no—
562C22⋊C4—34no—
563C22⋊C4—98no—
564C22⋊C4—98no—
565C22⋊C4—98no—
566C22⋊C4—98no—
567C42—34no—
568C42—98no—
569C22×C3—24no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—21no—
580C22×C3—34no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—48no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—62no—
587C22×C3—62no—
588C22×C3—68no—
589C22×C3—64no—
590C22×C3—64no—
591C22×C3—64no—
592C22×C3—128no—
593C22×C3C2×#23512yes—
594C22×C3C2×D3×D412yes—
595C22×C3D3×#4112yes—
596C22×C3#101012yes—
597C22×C3#101012yes—
598C22×C3C22×#6712yes—
599C22×C3C24×D311yescharacteristic
600C22×C3C24×D311yescharacteristic
601C2×D3—22no—
602C2×D3—22no—
603C2×D3—28no—
604C2×D3—24no—
605C2×D3—24no—
606C2×D3—24no—
607C2×D3—48no—
608C2×D3C2×#23514yescomplemented
609C3×C4—22no—
610C3×C4—22no—
611C3×C4—24no—
612C3×C4—38no—
613C3×C4—42no—
614C3×C4—62no—
615C3×C4—62no—
616C3×C4—62no—
617C3×C4C2×D3×D414yes—
618C3×C4C22×#6714yes—
619Dic3—22no—
620Dic3—22no—
621Dic3—22no—
622Dic3—64no—
623Dic3—64no—
624Dic3—64no—
625Dic3—64no—
626Dic3—124no—
627Dic3—124no—
628Dic3C22×#6718yes—
629C32C2×#54811yescharacteristic, complemented, Sylow
630C23—22no—
631C23—22no—
632C23—22no—
633C23—34no—
634C23—32no—
635C23—34no—
636C23—62no—
637C23—62no—
638C23—64no—
639C23—64no—
640C23—64no—
641C23C22×D3212yes—
642C23C22×D3211yescharacteristic
643Q8—316no—
644Q8—1816no—
645Q8—188no—
646D4—616no—
647D4—68no—
648D4—68no—
649D4—1816no—
650C2×C4—22no—
651C2×C4—28no—
652C2×C4—38no—
653C2×C4—34no—
654C2×C4—32no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—616no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—68no—
662C2×C4—94no—
663C2×C4—94no—
664C2×C4—1816no—
665C2×C4—184no—
666C2×C4—184no—
667C2×C4D3×#6714yes—
668C2×C4C22×D3212yes—
669C2×C4C22×D3212yes—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—24no—
673C2×C3—21no—
674C2×C3—44no—
675C2×C3—42no—
676C2×C3—42no—
677C2×C3—64no—
678C2×C3—124no—
679C2×C3#555214yescomplemented
680C2×C3#583114yescomplemented
681C2×C3C22×#23511yescharacteristic
682C2×C3C22×D3×D411yescharacteristic
683C2×C3C2×D3×#4111yescharacteristic
684C2×C3C2×#101011yescharacteristic
685C2×C3C2×#101011yescharacteristic
686C2×C3C23×#6711yescharacteristic
687D3—24no—
688D3—44no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—34no—
693C22—44no—
694C22—62no—
695C22—68no—
696C22—62no—
697C22—64no—
698C22—64no—
699C22—64no—
700C22—128no—
701C22#6429812yes—
702C22D3×#23512yes—
703C22C2×D3×#6712yes—
704C22C23×D3211yescharacteristic
705C4—22no—
706C4—38no—
707C4—62no—
708C4—62no—
709C4—62no—
710C4—184no—
711C4—184no—
712C4C2×D3×#6714yes—
713C3—21no—
714C3C2×#555211yescharacteristic, complemented
715C3C2×#583111yescharacteristic, complemented
716C2—42no—
717C2—64no—
718C2—124no—
719C2#1059489914yesdirect product factor
720C2C2×#6429811yescharacteristic
721C2C2×D3×#23511yescharacteristic
722C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C22×D3×Dic6C2semidirect
3. C2×#64133C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×#63970C2semidirect
6. C2×#63959C2semidirect
7. C2×#63908C2semidirect
8. #10594899C2direct (N × H)
9. C2×#63879C2semidirect
10. C2×#63860C2semidirect
11. C2×#63851C2semidirect
12. C2×Dic3×Dic6C2semidirect
20. C2×C3×#235C22semidirect
29. C2×D3×Dic6C22semidirect
32. #64133C22semidirect
35. C3×C4×#67C22semidirect
39. #63970C22semidirect
44. #63959C22semidirect
46. #63908C22semidirect
47. #63879C22semidirect
48. #63860C22semidirect
49. #63851C22semidirect
50. Dic3×Dic6C22semidirect
53. C22×#235D3semidirect
65. C2×C4×#67D3semidirect
102. C2×C3×Dic6D4semidirect
143. C2×#235C2×D3semidirect
176. C4×#67C2×D3semidirect
212. C22×C3×D3#41semidirect
238. C3×Dic6C2×D4semidirect
331. C2×Dic6#67semidirect
375. C2×C3×D3C2×#41semidirect
448. C22×D3#235semidirect
514. Dic6C2×#67semidirect
516. C2×C32#548semidirect
608. C2×D3C2×#235semidirect
629. C32C2×#548semidirect
679. C2×C3#5552semidirect
680. C2×C3#5831semidirect
714. C3C2×#5552semidirect
715. C3C2×#5831semidirect
719. C2#10594899direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×D3×Dic62
C2×#641332
C2×C3×C4×#672
C2×#639702
C2×#639592
C2×#639082
#105948992
C2×#638792
C2×#638602
C2×#638512
C2×Dic3×Dic62
C2×#58313
C2×#55523