Finite Group Databasebeta

← C2×#10593905 #11902616

Subgroups — C2×#10593905 #11902616

Order 1152.

3389 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×C4×#634C211yesmaximal, characteristic, complemented
4C2×C3×#875C211yesmaximal, characteristic, complemented
5C2×C3×C4×D12C211yesmaximal, characteristic, complemented
6C2×#63915C212yesmaximal, complemented
7C2×#63908C211yesmaximal, characteristic, complemented
8C2×#63902C212yesmaximal, complemented
9C2×#63899C212yesmaximal, complemented
10C2×#63885C212yesmaximal, complemented
11C2×#63856C211yesmaximal, characteristic, complemented
12#10593905C2116yesmaximal, direct product factor
13C2×#5677—31nomaximal
14C2×#5552—31nomaximal
15C22×#634C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2212yes—
22C22×#625C2212yes—
23C22×#625C2212yes—
24C22×D3×Dic3C2212yes—
25C22×D3×Dic3C2212yes—
26C2×#3795—28no—
27C2×#3795C2218yescomplemented
28C2×D3×Dic6—28no—
29C2×D3×Dic6C2218yescomplemented
30C2×C32×C42C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C2×#3750C2212yes—
33C2×C4×C3⋊Dic3C2212yes—
34C4×#634C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C3×#875C2218yescomplemented
41C3×C4×D12C2218yescomplemented
42C2×#3724C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45#63915C22116yescomplemented
46#63908C2218yescomplemented
47#63902C22116yescomplemented
48#63899C22116yescomplemented
49#63885C22116yescomplemented
50#63856C2218yescomplemented
51C22×D3×Q8—31no—
52C22×#237—31no—
53C22×#235—31no—
54C23×Dic6—31no—
55C2×C3×#124—31no—
56C2×C3×C4×D4—31no—
57C2×#946—31no—
58C2×#939—32no—
59C2×#938—31no—
60C2×#930—31no—
61C2×#924—31no—
62#5677—316no—
63#5552—316no—
64C2×#896—32no—
65C2×#885—32no—
66C2×#885—32no—
67C2×#884—32no—
68C2×#67⋊C4—32no—
69C2×#67⋊C4—32no—
70C2×#878—32no—
71C2×#875D311yescharacteristic, complemented
72C2×C4×D12D311yescharacteristic, complemented
73C2×C4×Dic6—31no—
74C2×C4×Dic6—31no—
75C2×C4×Dic6—61no—
76C23×C3×D3C2312yes—
77C23×C3×D3C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C3⋊Dic3C2312yes—
83C22×C3⋊Dic3C2312yes—
84C2×#634D418yescomplemented
85C2×#634C2314yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C2×C3×D12—24no—
90C2×C3×D12—24no—
91C2×C3×D12C2314yes—
92C2×C3×D12C2314yes—
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3—24no—
95C2×C3×C4×D3C2314yes—
96C2×C3×C4×D3C2314yes—
97C2×C3×Dic6—24no—
98C2×C3×Dic6C2314yes—
99C2×#627—28no—
100C2×#627C2318yes—
101C2×#625—28no—
102C2×#625—28no—
103C2×#625C2318yes—
104C2×#625C2318yes—
105C2×D3×Dic3—28no—
106C2×D3×Dic3—28no—
107C2×D3×Dic3C2318yes—
108C2×D3×Dic3C2318yes—
109#3795—232no—
110D3×Dic6—232no—
111C32×C42C2314yes—
112C4⋊(C3⋊Dic3)C2314yes—
113#3750C2318yes—
114C4×C3⋊Dic3C2318yes—
115C3×(C2×D3)⋊C4C2318yes—
116C3×(C2×D3)⋊C4C2314yes—
117C3×(C2×D3)⋊C4C2318yes—
118C3×(C2×D3)⋊C4C2314yes—
119C3×C4⋊Dic3C2314yes—
120#3724C2318yes—
121(C2×D3)⋊Dic3C2318yes—
122(C2×D3)⋊Dic3C2318yes—
123C2×#548—91noSylow
124C22×C3×Q8—31no—
125C22×C3×D4—31no—
126C22×C3×D4—31no—
127C23×C3×C4—31no—
128C23×C3×C4—31no—
129C22×#67—32no—
130C22×#67—32no—
131C22×#67—32no—
132C22×#67—32no—
133C23×Dic3—32no—
134C23×Dic3—32no—
135C2×D3×Q8—38no—
136C2×D3×Q8—68no—
137C2×#237—38no—
138C2×#237—68no—
139C2×#235—38no—
140C2×#235—68no—
141C22×D12C2×D311yescharacteristic
142C22×D12C2×D311yescharacteristic
143C22×C4×D3—32no—
144C22×C4×D3—32no—
145C22×C4×D3C2×D311yescharacteristic
146C22×C4×D3C2×D311yescharacteristic
147C22×Dic6—31no—
148C22×Dic6—31no—
149C22×Dic6—32no—
150C22×Dic6—32no—
151C22×Dic6—38no—
152C22×Dic6—61no—
153C22×Dic6—68no—
154C22×Dic6C2×D311yescharacteristic
155C3×#124—38no—
156C3×C4×D4—38no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C22⋊C4—32no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—32no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C42—21no—
163C2×C3×C42C2×D311yescharacteristic
164C2×C3×C42C2×D311yescharacteristic
165C2×#217—32no—
166C2×#217—32no—
167#946—38no—
168#939—316no—
169#938—38no—
170#930—38no—
171C2×(C2×D3)⋊C4—32no—
172C2×(C2×D3)⋊C4—32no—
173C2×(C2×D3)⋊C4C2×D311yescharacteristic
174C2×(C2×D3)⋊C4C2×D311yescharacteristic
175C2×(C2×D3)⋊C4C2×D312yes—
176C2×(C2×D3)⋊C4C2×D312yes—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—61no—
180C2×C4⋊Dic3C2×D311yescharacteristic
181#924—38no—
182C2×Dic3⋊C4—32no—
183C2×Dic3⋊C4—32no—
184C2×Dic3⋊C4—32no—
185C2×Dic3⋊C4—32no—
186C2×Dic3⋊C4—62no—
187C2×C4×Dic3—32no—
188C2×C4×Dic3—32no—
189C2×C4×Dic3—62no—
190#896—316no—
191#885—316no—
192#885—316no—
193#884—316no—
194#67⋊C4—316no—
195#67⋊C4—316no—
196#878—316no—
197#875C2×D318yescomplemented
198C4×D12C2×D318yescomplemented
199C4×Dic6—38no—
200C4×Dic6—38no—
201C4×Dic6—68no—
202C23×C32C2411yescharacteristic
203C22×C3×D3—22no—
204C22×C3×D3—22no—
205C22×C3×D3—24no—
206C22×C3×D3—22no—
207C22×C3×D3—24no—
208C22×C3×D3—22no—
209C22×C3×D3—24no—
210C22×C3×D3—22no—
211C22×C3×D3#4114yescomplemented
212C22×C3×D3C2412yes—
213C22×C3×D3C2414yes—
214C22×C3×D3C2412yes—
215C2×C32×C4—22no—
216C2×C32×C4—22no—
217C2×C32×C4C2×D414yes—
218C2×C32×C4C2412yes—
219C2×C32×C4C2412yes—
220C2×C32×C4C2412yes—
221C2×C3⋊Dic3—24no—
222C2×C3⋊Dic3C2×D418yes—
223C2×C3⋊Dic3C2414yes—
224C2×C3⋊Dic3C2414yes—
225#634C2×D4116yescomplemented
226C2×C3×Dic3—22no—
227C2×C3×Dic3—24no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3C2412yes—
230C2×C3×Dic3C2414yes—
231C2×C3×Dic3C2412yes—
232C3×D12—28no—
233C3×D12—28no—
234C3×C4×D3—28no—
235C3×C4×D3—28no—
236C3×Dic6—28no—
237#627—216no—
238#625—216no—
239#625—216no—
240D3×Dic3—216no—
241D3×Dic3—216no—
242C22×#41—91no—
243C23×Q8—91no—
244#548—916no—
245C2×#124—31no—
246C2×#124—92no—
247C2×C22⋊Q8—92no—
248C2×C22⋊Q8—91no—
249C2×#121—92no—
250C2×#121—91no—
251C2×C4×Q8—91no—
252C2×C4×D4—31no—
253C2×C4×D4—92no—
254C24×C3—31no—
255C24×C3—31no—
256C24×C3—32no—
257C23×D3C22×D311yescharacteristic
258C23×D3C22×D312yes—
259C23×D3C22×D311yescharacteristic
260C2×C3×Q8—34no—
261C2×C3×Q8—64no—
262C2×C3×D4—34no—
263C2×C3×D4—34no—
264C2×C3×D4—64no—
265C2×C3×D4—64no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—31no—
270C22×C3×C4—32no—
271C22×C3×C4—31no—
272C22×C3×C4—34no—
273C22×C3×C4—34no—
274C22×C3×C4—64no—
275C22×C3×C4—64no—
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C2×#67—38no—
283C2×#67—38no—
284C2×#67—38no—
285C2×#67—38no—
286C2×#67—68no—
287C2×#67—68no—
288C2×#67—68no—
289C2×#67—68no—
290C22×Dic3—32no—
291C22×Dic3—32no—
292C22×Dic3—32no—
293C22×Dic3—32no—
294C22×Dic3—38no—
295C22×Dic3—38no—
296C22×Dic3—62no—
297C22×Dic3—62no—
298C22×Dic3—68no—
299C22×Dic3—68no—
300C22×Dic3C22×D311yescharacteristic
301C22×Dic3C22×D312yes—
302C22×Dic3C22×D311yescharacteristic
303D3×Q8—632no—
304#237—632no—
305#235—632no—
306C2×D12—24no—
307C2×D12—24no—
308C2×D12C22×D314yes—
309C2×D12C22×D314yes—
310C2×C4×D3—24no—
311C2×C4×D3—24no—
312C2×C4×D3—38no—
313C2×C4×D3—38no—
314C2×C4×D3—68no—
315C2×C4×D3—68no—
316C2×C4×D3C22×D314yes—
317C2×C4×D3C22×D314yes—
318C2×Dic6—24no—
319C2×Dic6—38no—
320C2×Dic6—38no—
321C2×Dic6—34no—
322C2×Dic6—34no—
323C2×Dic6—38no—
324C2×Dic6—38no—
325C2×Dic6—64no—
326C2×Dic6—68no—
327C2×Dic6—632no—
328C2×Dic6—68no—
329C2×Dic6—68no—
330C2×Dic6C22×D314yes—
331C3×C4⋊C4—34no—
332C3×C22⋊C4—38no—
333C3×C22⋊C4—34no—
334C3×C22⋊C4—38no—
335C3×C22⋊C4—34no—
336C3×C42—24no—
337C3×C42C22×D314yes—
338C3×C42C22×D314yes—
339#217—38no—
340#217—38no—
341(C2×D3)⋊C4—38no—
342(C2×D3)⋊C4—38no—
343(C2×D3)⋊C4C22×D314yes—
344(C2×D3)⋊C4C22×D314yes—
345(C2×D3)⋊C4C22×D318yes—
346(C2×D3)⋊C4C22×D318yes—
347C4⋊Dic3—34no—
348C4⋊Dic3—34no—
349C4⋊Dic3—64no—
350C4⋊Dic3C22×D314yes—
351Dic3⋊C4—38no—
352Dic3⋊C4—38no—
353Dic3⋊C4—38no—
354Dic3⋊C4—38no—
355Dic3⋊C4—68no—
356C4×Dic3—38no—
357C4×Dic3—38no—
358C4×Dic3—68no—
359C22×C32C22×D412yes—
360C22×C32C2×#4112yes—
361C22×C322−1+412yes—
362C22×C32C2511yescharacteristic
363C2×C3×D3—28no—
364C2×C3×D3—22no—
365C2×C3×D3—22no—
366C2×C3×D3—24no—
367C2×C3×D3—22no—
368C2×C3×D3—24no—
369C2×C3×D3—22no—
370C2×C3×D3—22no—
371C2×C3×D3—24no—
372C2×C3×D3—48no—
373C2×C3×D3—44no—
374C2×C3×D3C2×#4114yescomplemented
375C32×C4—22no—
376C32×C4—22no—
377C32×C4C22×D414yes—
378C3⋊Dic3—24no—
379C3⋊Dic3C22×D418yes—
380C3×Dic3—22no—
381C3×Dic3—24no—
382C3×Dic3—22no—
383C2×#41—98no—
384C2×#41—188no—
385C22×Q8—31no—
386C22×Q8—92no—
387C22×Q8—98no—
388C22×Q8—91no—
389C22×Q8—188no—
390C22×D4—31no—
391C22×D4—31no—
392C22×D4—92no—
393C22×D4—92no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—92no—
397C23×C4—92no—
398#124—38no—
399#124—916no—
400C22⋊Q8—916no—
401C22⋊Q8—98no—
402#121—916no—
403#121—98no—
404C4×Q8—98no—
405C4×D4—38no—
406C4×D4—916no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—92no—
409C2×C4⋊C4—92no—
410C2×C4⋊C4—91no—
411C2×C22⋊C4—31no—
412C2×C22⋊C4—31no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—92no—
416C2×C22⋊C4—92no—
417C2×C42—92no—
418C2×C42D3211yescharacteristic
419C23×C3—21no—
420C23×C3—34no—
421C23×C3—32no—
422C23×C3—32no—
423C23×C3—34no—
424C23×C3—62no—
425C23×C3—62no—
426C23×C3—64no—
427C23×C3—64no—
428C23×C3—62no—
429C23×C3—62no—
430C23×C3—62no—
431C23×C3—64no—
432C23×C3C23×D311yescharacteristic
433C23×C3C23×D311yescharacteristic
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—24no—
439C22×D3—24no—
440C22×D3—24no—
441C22×D3—22no—
442C22×D3#23514yescomplemented
443C22×D3C23×D312yes—
444C22×D3C23×D314yes—
445C22×D3C23×D312yes—
446C3×Q8—68no—
447C3×D4—68no—
448C3×D4—68no—
449C2×C3×C4—24no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—24no—
458C2×C3×C4—32no—
459C2×C3×C4—34no—
460C2×C3×C4—32no—
461C2×C3×C4—42no—
462C2×C3×C4—62no—
463C2×C3×C4—64no—
464C2×C3×C4—62no—
465C2×C3×C4—68no—
466C2×C3×C4—68no—
467C2×C3×C4D3×D414yes—
468C2×C3×C4D3×D414yes—
469C2×C3×C4C23×D312yes—
470C2×C3×C4C23×D312yes—
471C2×C3×C4C23×D312yes—
472C2×C3×C4C23×D312yes—
473C2×C3×C4C23×D312yes—
474C2×C3×C4C23×D312yes—
475#67—616no—
476#67—616no—
477#67—616no—
478#67—616no—
479C2×Dic3—24no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—38no—
483C2×Dic3—38no—
484C2×Dic3—34no—
485C2×Dic3—34no—
486C2×Dic3—34no—
487C2×Dic3—34no—
488C2×Dic3—68no—
489C2×Dic3—64no—
490C2×Dic3—64no—
491C2×Dic3—616no—
492C2×Dic3—616no—
493C2×Dic3—64no—
494C2×Dic3—64no—
495C2×Dic3—124no—
496C2×Dic3C23×D312yes—
497C2×Dic3C23×D314yes—
498C2×Dic3C23×D312yes—
499D12—28no—
500D12—28no—
501C4×D3—28no—
502C4×D3—28no—
503C4×D3—616no—
504C4×D3—616no—
505Dic6—28no—
506Dic6—316no—
507Dic6—316no—
508Dic6—616no—
509Dic6—616no—
510Dic6—616no—
511C2×C32#54814yescomplemented
512C2×C32C23×D411yescharacteristic
513C2×C32C22×#4111yescharacteristic
514C2×C32C2×2−1+411yescharacteristic
515C3×D3—24no—
516C3×D3—44no—
517C3×D3—42no—
518C24—31no—
519C24—32no—
520C24—31no—
521#41—1832no—
522C2×Q8—34no—
523C2×Q8—64no—
524C2×Q8—98no—
525C2×Q8—94no—
526C2×Q8—98no—
527C2×Q8—188no—
528C2×Q8—1832no—
529C2×D4—34no—
530C2×D4—34no—
531C2×D4—64no—
532C2×D4—64no—
533C2×D4—98no—
534C2×D4—98no—
535C2×D4—188no—
536C2×D4—188no—
537C22×C4—32no—
538C22×C4—31no—
539C22×C4—31no—
540C22×C4—34no—
541C22×C4—34no—
542C22×C4—64no—
543C22×C4—64no—
544C22×C4—98no—
545C22×C4—98no—
546C22×C4—92no—
547C22×C4—92no—
548C22×C4—188no—
549C22×C4—188no—
550C22×C4C2×D3211yescharacteristic
551C22×C4C2×D3211yescharacteristic
552C22×C4C2×D3211yescharacteristic
553C4⋊C4—34no—
554C4⋊C4—98no—
555C4⋊C4—98no—
556C4⋊C4—94no—
557C22⋊C4—34no—
558C22⋊C4—34no—
559C22⋊C4—38no—
560C22⋊C4—38no—
561C22⋊C4—98no—
562C22⋊C4—98no—
563C42—98no—
564C42C2×D3214yes—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—21no—
569C22×C3—34no—
570C22×C3—68no—
571C22×C3—62no—
572C22×C3—62no—
573C22×C3—64no—
574C22×C3—64no—
575C22×C3—62no—
576C22×C3—62no—
577C22×C3—62no—
578C22×C3—64no—
579C22×C3—124no—
580C22×C3—128no—
581C22×C3C2×#23512yes—
582C22×C3C2×D3×D412yes—
583C22×C3C2×D3×D412yes—
584C22×C3D3×#4112yes—
585C22×C3#101012yes—
586C22×C3#101012yes—
587C22×C3C24×D311yescharacteristic
588C22×C3C24×D311yescharacteristic
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—28no—
592C2×D3—22no—
593C2×D3—22no—
594C2×D3—24no—
595C2×D3—24no—
596C2×D3—24no—
597C2×D3—22no—
598C2×D3—48no—
599C2×D3—44no—
600C2×D3C2×#23514yescomplemented
601C3×C4—24no—
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—24no—
607C3×C4—42no—
608C3×C4—62no—
609C3×C4—64no—
610C3×C4—62no—
611C3×C4C2×D3×D414yes—
612C3×C4C2×D3×D414yes—
613Dic3—24no—
614Dic3—22no—
615Dic3—22no—
616Dic3—38no—
617Dic3—38no—
618Dic3—68no—
619Dic3—64no—
620Dic3—64no—
621Dic3—124no—
622C32C2×#54811yescharacteristic, complemented, Sylow
623C23—34no—
624C23—32no—
625C23—34no—
626C23—32no—
627C23—62no—
628C23—62no—
629C23—64no—
630C23—62no—
631C23—62no—
632C23—64no—
633C23—62no—
634C23—64no—
635C23C22×D3211yescharacteristic
636Q8—68no—
637Q8—916no—
638Q8—1816no—
639D4—68no—
640D4—68no—
641D4—1816no—
642D4—1816no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—34no—
646C2×C4—32no—
647C2×C4—32no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—64no—
651C2×C4—68no—
652C2×C4—68no—
653C2×C4—98no—
654C2×C4—94no—
655C2×C4—94no—
656C2×C4—1816no—
657C2×C4—1816no—
658C2×C4—184no—
659C2×C4#380214yes—
660C2×C4C22×D3212yes—
661C2×C4C22×D3212yes—
662C2×C4C22×D3212yes—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—24no—
667C2×C3—64no—
668C2×C3—122no—
669C2×C3—124no—
670C2×C3#555214yescomplemented
671C2×C3#567714yescomplemented
672C2×C3C22×#23511yescharacteristic
673C2×C3C22×D3×D411yescharacteristic
674C2×C3C22×D3×D411yescharacteristic
675C2×C3C2×D3×#4111yescharacteristic
676C2×C3C2×#101011yescharacteristic
677C2×C3C2×#101011yescharacteristic
678D3—24no—
679D3—44no—
680D3—42no—
681C22—34no—
682C22—62no—
683C22—62no—
684C22—68no—
685C22—64no—
686C22—62no—
687C22—62no—
688C22—64no—
689C22—62no—
690C22—64no—
691C22—124no—
692C22—128no—
693C22#6429812yes—
694C22C2×#380212yes—
695C22D3×#23512yes—
696C22C23×D3211yescharacteristic
697C4—22no—
698C4—22no—
699C4—62no—
700C4—62no—
701C4—64no—
702C4—98no—
703C4—184no—
704C4C2×#380214yes—
705C3—21no—
706C3C2×#555211yescharacteristic, complemented
707C3C2×#567711yescharacteristic, complemented
708C2—64no—
709C2—122no—
710C2—124no—
711C2#1059390514yesdirect product factor
712C2C2×#6429811yescharacteristic
713C2C22×#380211yescharacteristic
714C2C2×D3×#23511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3795C2semidirect
2. C22×D3×Dic6C2semidirect
3. C2×C4×#634C2semidirect
4. C2×C3×#875C2semidirect
5. C2×C3×C4×D12C2semidirect
6. C2×#63915C2semidirect
7. C2×#63908C2semidirect
8. C2×#63902C2semidirect
9. C2×#63899C2semidirect
10. C2×#63885C2semidirect
11. C2×#63856C2semidirect
12. #10593905C2direct (N × H)
27. C2×#3795C22semidirect
29. C2×D3×Dic6C22semidirect
34. C4×#634C22semidirect
40. C3×#875C22semidirect
41. C3×C4×D12C22semidirect
45. #63915C22semidirect
46. #63908C22semidirect
47. #63902C22semidirect
48. #63899C22semidirect
49. #63885C22semidirect
50. #63856C22semidirect
71. C2×#875D3semidirect
72. C2×C4×D12D3semidirect
84. C2×#634D4semidirect
197. #875C2×D3semidirect
198. C4×D12C2×D3semidirect
211. C22×C3×D3#41semidirect
225. #634C2×D4semidirect
374. C2×C3×D3C2×#41semidirect
442. C22×D3#235semidirect
511. C2×C32#548semidirect
600. C2×D3C2×#235semidirect
622. C32C2×#548semidirect
670. C2×C3#5552semidirect
671. C2×C3#5677semidirect
706. C3C2×#5552semidirect
707. C3C2×#5677semidirect
711. C2#10593905direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37952
C22×D3×Dic62
C2×C4×#6342
C2×C3×#8752
C2×C3×C4×D122
C2×#639152
C2×#639082
C2×#639022
C2×#638992
C2×#638852
C2×#638562
#105939052
C2×#56773
C2×#55523