Finite Group Databasebeta

← C2×#10594369 #11900779

Subgroups — C2×#10594369 #11900779

Order 1152.

3669 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×#3796C212yesmaximal, complemented
2C2×#64102C211yesmaximal, characteristic, complemented
3C2×C3×#895C211yesmaximal, characteristic, complemented
4C2×C3×#888C211yesmaximal, characteristic, complemented
5C2×#63911C211yesmaximal, characteristic, complemented
6C2×#63909C211yesmaximal, characteristic, complemented
7C2×#63907C212yesmaximal, complemented
8C2×#63898C211yesmaximal, characteristic, complemented
9C2×#63886C212yesmaximal, complemented
10C2×#63881C212yesmaximal, complemented
11C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
12#10594369C2116yesmaximal, direct product factor
13C2×#5725—31nomaximal
14C2×#5596—31nomaximal
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2212yes—
17C22×C3×D12C2212yes—
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2212yes—
21C22×#626C2212yes—
22C22×#626C2212yes—
23C22×#626C2212yes—
24C22×D3×Dic3C2212yes—
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C2×#3796—216no—
28C2×#3796C22116yescomplemented
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×#3752C2212yes—
31C2×C4×C3⋊Dic3C2211yescharacteristic
32#64102C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×C4×Dic3C2211yescharacteristic
37C3×#895C2218yescomplemented
38C3×#888C2218yescomplemented
39C2×#3722C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63911C2218yescomplemented
44#63909C2218yescomplemented
45#63907C22116yescomplemented
46#63898C2218yescomplemented
47#63886C22116yescomplemented
48#63881C22116yescomplemented
49C4×D3×Dic3C2218yescomplemented
50C22×#239—32no—
51C22×#237—32no—
52C2×C3×C4⋊Q8—31no—
53C2×C3×#121—31no—
54C2×#947—32no—
55C2×#940—31no—
56C2×#939—32no—
57C2×D4×Dic3—31no—
58C2×#930—31no—
59C22×C4×Dic3—31no—
60#5725—316no—
61#5596—316no—
62C2×#895—32no—
63C2×#895—31no—
64C2×#895D311yescharacteristic, complemented
65C2×#893—31no—
66C2×#893—31no—
67C2×#893—31no—
68C2×#893—32no—
69C2×#893—61no—
70C2×#888D311yescharacteristic, complemented
71C2×#885—32no—
72C2×#67⋊C4—32no—
73C2×#874—31no—
74C2×C42×D3—31no—
75C23×C3⋊D3C2312yes—
76C23×C3×D3C2312yes—
77C23×C3×D3C2311yescharacteristic
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C2×C4⋊(C3⋊D3)—24no—
83C2×C4⋊(C3⋊D3)C2314yes—
84C2×C4×C3⋊D3—28no—
85C2×C4×C3⋊D3C2318yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C2×C3×D12—28no—
91C2×C3×D12—24no—
92C2×C3×D12C2318yes—
93C2×C3×D12C2314yes—
94C2×C3×C4×D3—24no—
95C2×C3×C4×D3C2314yes—
96C2×C3×Dic6—28no—
97C2×C3×Dic6C2318yes—
98C2×#626—28no—
99C2×#626—28no—
100C2×#626—28no—
101C2×#626C2318yes—
102C2×#626C2318yes—
103C2×#626C2318yes—
104C2×D3×Dic3—28no—
105C2×D3×Dic3—24no—
106C2×D3×Dic3D418yescomplemented
107C2×D3×Dic3C2318yes—
108C2×D3×Dic3C2314yes—
109C2×D3×Dic3C2314yes—
110#3796—264no—
111C32×C4⋊C4C2314yes—
112#3752C2318yes—
113C4×C3⋊Dic3C2314yes—
114C3×(C2×D3)⋊C4C2318yes—
115C3×C4⋊Dic3C2314yes—
116C3×Dic3⋊C4C2318yes—
117C3×C4×Dic3C2314yes—
118#3722C2318yes—
119(C2×D3)⋊Dic3C2318yes—
120Dic32C2314yes—
121Dic32C2314yes—
122C2×#532—91noSylow
123C22×C3×Q8—32no—
124C22×C3×D4—32no—
125C22×C3×D4—31no—
126C23×C3×C4—31no—
127C22×#67—32no—
128C22×#67—32no—
129C22×#67—32no—
130C23×Dic3—31no—
131C23×Dic3—32no—
132C23×Dic3—31no—
133C2×#239—316no—
134C2×#239—616no—
135C2×#237—316no—
136C2×#237—616no—
137C22×D12—32no—
138C22×D12—32no—
139C22×D12—32no—
140C22×D12—31no—
141C22×D12—31no—
142C22×D12—61no—
143C22×D12C2×D312yes—
144C22×D12C2×D311yescharacteristic
145C22×C4×D3—31no—
146C22×C4×D3—32no—
147C22×C4×D3—31no—
148C22×C4×D3—32no—
149C22×C4×D3—32no—
150C22×C4×D3—62no—
151C22×C4×D3C2×D311yescharacteristic
152C22×Dic6C2×D312yes—
153C3×C4⋊Q8—38no—
154C3×#121—38no—
155C2×C3×C4⋊C4—21no—
156C2×C3×C4⋊C4—32no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4C2×D311yescharacteristic
159C2×C3×C4⋊C4C2×D311yescharacteristic
160C2×C3×C22⋊C4—32no—
161C2×C3×C42—31no—
162C2×#217—32no—
163#947—316no—
164#940—38no—
165#939—316no—
166D4×Dic3—38no—
167#930—38no—
168C2×(C2×D3)⋊C4—32no—
169C2×(C2×D3)⋊C4—32no—
170C2×(C2×D3)⋊C4—32no—
171C2×(C2×D3)⋊C4—32no—
172C2×(C2×D3)⋊C4—32no—
173C2×(C2×D3)⋊C4—62no—
174C2×(C2×D3)⋊C4C2×D312yes—
175C2×C4⋊Dic3C2×D311yescharacteristic
176C2×Dic3⋊C4C2×D312yes—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—38no—
184C2×C4×Dic3—61no—
185C2×C4×Dic3C2×D311yescharacteristic
186#895—316no—
187#895—38no—
188#895C2×D318yescomplemented
189#893—38no—
190#893—38no—
191#893—38no—
192#893—316no—
193#893—68no—
194#888C2×D318yescomplemented
195#885—316no—
196#67⋊C4—316no—
197#874—38no—
198C42×D3—38no—
199C23×C32C2411yescharacteristic
200C22×C3⋊D3—24no—
201C22×C3⋊D3—24no—
202C22×C3⋊D3—24no—
203C22×C3⋊D3C2414yes—
204C22×C3×D3—22no—
205C22×C3×D3—22no—
206C22×C3×D3—24no—
207C22×C3×D3—24no—
208C22×C3×D3—24no—
209C22×C3×D3C2×D414yes—
210C22×C3×D3C2414yes—
211C22×C3×D3C2412yes—
212C2×C32×C4—24no—
213C2×C32×C4#4114yescomplemented
214C2×C32×C4C2414yes—
215C2×C32×C4C2412yes—
216C2×C3⋊Dic3—22no—
217C2×C3⋊Dic3C2×D414yes—
218C2×C3⋊Dic3C2412yes—
219C2×C3⋊Dic3C2412yes—
220C4⋊(C3⋊D3)—28no—
221C4×C3⋊D3—216no—
222C2×C3×Dic3—24no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3C2×D414yes—
225C2×C3×Dic3#4114yescomplemented
226C2×C3×Dic3C2412yes—
227C2×C3×Dic3C2414yes—
228C2×C3×Dic3C2412yes—
229C2×C3×Dic3C2412yes—
230C3×D12—216no—
231C3×D12—28no—
232C3×C4×D3—28no—
233C3×Dic6—216no—
234#626—216no—
235#626—216no—
236#626—216no—
237D3×Dic3—216no—
238D3×Dic3—28no—
239D3×Dic3C2×D4116yescomplemented
240C22×#41—92no—
241#532—916no—
242C2×C4⋊Q8—31no—
243C2×#127—91no—
244C2×#124—92no—
245C2×#121—31no—
246C2×#121—91no—
247C2×#121—92no—
248C2×C4×D4—92no—
249C2×C4×D4—91no—
250C2×C4×D4—91no—
251C22×C42—91no—
252C24×C3—31no—
253C24×C3—32no—
254C23×D3—32no—
255C23×D3—32no—
256C23×D3—62no—
257C23×D3C22×D312yes—
258C23×D3C22×D311yescharacteristic
259C2×C3×Q8—38no—
260C2×C3×Q8—68no—
261C2×C3×D4—34no—
262C2×C3×D4—38no—
263C2×C3×D4—68no—
264C2×C3×D4—64no—
265C22×C3×C4—21no—
266C22×C3×C4—22no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—32no—
271C22×C3×C4—34no—
272C22×C3×C4—64no—
273C22×C3×C4C22×D312yes—
274C22×C3×C4C22×D312yes—
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C22×D311yescharacteristic
277C2×#67—38no—
278C2×#67—38no—
279C2×#67—38no—
280C2×#67—68no—
281C2×#67—68no—
282C2×#67—68no—
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—38no—
286C22×Dic3—34no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—38no—
290C22×Dic3—34no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3—68no—
294C22×Dic3—64no—
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D312yes—
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D311yescharacteristic
299#239—664no—
300#237—664no—
301C2×D12—28no—
302C2×D12—24no—
303C2×D12—38no—
304C2×D12—38no—
305C2×D12—38no—
306C2×D12—34no—
307C2×D12—34no—
308C2×D12—64no—
309C2×D12—68no—
310C2×D12—68no—
311C2×D12—68no—
312C2×D12—68no—
313C2×D12—64no—
314C2×D12—64no—
315C2×D12C22×D314yes—
316C2×D12C22×D318yes—
317C2×C4×D3—24no—
318C2×C4×D3—38no—
319C2×C4×D3—34no—
320C2×C4×D3—34no—
321C2×C4×D3—38no—
322C2×C4×D3—38no—
323C2×C4×D3—38no—
324C2×C4×D3—68no—
325C2×C4×D3—68no—
326C2×C4×D3—68no—
327C2×C4×D3—68no—
328C2×C4×D3—64no—
329C2×C4×D3—128no—
330C2×C4×D3C22×D314yes—
331C2×Dic6—28no—
332C2×Dic6C22×D318yes—
333C3×C4⋊C4—24no—
334C3×C4⋊C4—38no—
335C3×C4⋊C4—34no—
336C3×C4⋊C4C22×D314yes—
337C3×C4⋊C4C22×D314yes—
338C3×C22⋊C4—38no—
339C3×C42—34no—
340#217—38no—
341(C2×D3)⋊C4—38no—
342(C2×D3)⋊C4—38no—
343(C2×D3)⋊C4—38no—
344(C2×D3)⋊C4—38no—
345(C2×D3)⋊C4—38no—
346(C2×D3)⋊C4—68no—
347(C2×D3)⋊C4C22×D318yes—
348C4⋊Dic3C22×D314yes—
349Dic3⋊C4C22×D318yes—
350C4×Dic3—34no—
351C4×Dic3—34no—
352C4×Dic3—34no—
353C4×Dic3—34no—
354C4×Dic3—34no—
355C4×Dic3—34no—
356C4×Dic3—64no—
357C4×Dic3C22×D314yes—
358C22×C32C22×D412yes—
359C22×C32C2×#4112yes—
360C22×C32C2×#4112yes—
361C22×C32C2511yescharacteristic
362C2×C3⋊D3—24no—
363C2×C3⋊D3—24no—
364C2×C3⋊D3—24no—
365C2×C3⋊D3—48no—
366C2×C3×D3—28no—
367C2×C3×D3—22no—
368C2×C3×D3—22no—
369C2×C3×D3—24no—
370C2×C3×D3—24no—
371C2×C3×D3—24no—
372C2×C3×D3—48no—
373C2×C3×D3C22×D414yes—
374C32×C4—24no—
375C32×C4C2×#4114yescomplemented
376C3⋊Dic3—22no—
377C3⋊Dic3C22×D414yes—
378C3×Dic3—24no—
379C3×Dic3—22no—
380C3×Dic3C22×D414yes—
381C3×Dic3C2×#4114yescomplemented
382C2×#41—916no—
383C2×#41—1816no—
384C22×Q8—32no—
385C22×D4—31no—
386C22×D4—32no—
387C22×D4—92no—
388C22×D4—92no—
389C22×D4—92no—
390C22×D4—91no—
391C23×C4—31no—
392C23×C4—91no—
393C23×C4—92no—
394C23×C4—91no—
395C23×C4—92no—
396C4⋊Q8—38no—
397#127—98no—
398#124—916no—
399#121—38no—
400#121—98no—
401#121—916no—
402C4×D4—916no—
403C4×D4—98no—
404C4×D4—98no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4D3211yescharacteristic
408C2×C22⋊C4—32no—
409C2×C22⋊C4—92no—
410C2×C22⋊C4—92no—
411C2×C22⋊C4—92no—
412C2×C42—31no—
413C2×C42—98no—
414C2×C42—91no—
415C2×C42—91no—
416C2×C42—91no—
417C23×C3—21no—
418C23×C3—34no—
419C23×C3—32no—
420C23×C3—34no—
421C23×C3—62no—
422C23×C3—62no—
423C23×C3—64no—
424C23×C3—64no—
425C23×C3—64no—
426C23×C3C23×D311yescharacteristic
427C23×C3C23×D311yescharacteristic
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—24no—
431C22×D3—24no—
432C22×D3—24no—
433C22×D3—34no—
434C22×D3—34no—
435C22×D3—64no—
436C22×D3—68no—
437C22×D3—64no—
438C22×D3—64no—
439C22×D3—64no—
440C22×D3—64no—
441C22×D3—64no—
442C22×D3—64no—
443C22×D3—124no—
444C22×D3—124no—
445C22×D3D3×D414yes—
446C22×D3C23×D314yes—
447C22×D3C23×D312yes—
448C3×Q8—616no—
449C3×D4—616no—
450C3×D4—68no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—22no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—34no—
457C2×C3×C4—34no—
458C2×C3×C4—32no—
459C2×C3×C4—32no—
460C2×C3×C4—32no—
461C2×C3×C4—34no—
462C2×C3×C4—44no—
463C2×C3×C4—64no—
464C2×C3×C4—62no—
465C2×C3×C4—68no—
466C2×C3×C4#23714yescomplemented
467C2×C3×C4#23914yescomplemented
468C2×C3×C4C23×D314yes—
469C2×C3×C4C23×D314yes—
470C2×C3×C4C23×D312yes—
471C2×C3×C4C23×D312yes—
472#67—616no—
473#67—616no—
474#67—616no—
475C2×Dic3—24no—
476C2×Dic3—22no—
477C2×Dic3—34no—
478C2×Dic3—34no—
479C2×Dic3—32no—
480C2×Dic3—32no—
481C2×Dic3—316no—
482C2×Dic3—32no—
483C2×Dic3—32no—
484C2×Dic3—64no—
485C2×Dic3—62no—
486C2×Dic3—62no—
487C2×Dic3—616no—
488C2×Dic3—62no—
489C2×Dic3—62no—
490C2×Dic3—68no—
491C2×Dic3—122no—
492C2×Dic3D3×D414yes—
493C2×Dic3#23914yescomplemented
494C2×Dic3C23×D312yes—
495C2×Dic3C23×D314yes—
496C2×Dic3C23×D312yes—
497C2×Dic3C23×D312yes—
498D12—216no—
499D12—28no—
500D12—616no—
501D12—616no—
502D12—616no—
503D12—616no—
504D12—68no—
505D12—68no—
506C4×D3—28no—
507C4×D3—316no—
508C4×D3—616no—
509C4×D3—616no—
510C4×D3—616no—
511C4×D3—68no—
512C4×D3—1216no—
513Dic6—216no—
514C2×C32#53214yescomplemented
515C2×C32C23×D411yescharacteristic
516C2×C32C22×#4111yescharacteristic
517C2×C32C22×#4111yescharacteristic
518C3⋊D3—44no—
519C3×D3—24no—
520C3×D3—44no—
521C24—31no—
522C24—32no—
523C24—92no—
524#41—1864no—
525C2×Q8—38no—
526C2×Q8—68no—
527C2×D4—34no—
528C2×D4—38no—
529C2×D4—68no—
530C2×D4—64no—
531C2×D4—98no—
532C2×D4—98no—
533C2×D4—98no—
534C2×D4—94no—
535C2×D4—188no—
536C2×D4—188no—
537C2×D4—188no—
538C2×D4—184no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—32no—
543C22×C4—34no—
544C22×C4—64no—
545C22×C4—94no—
546C22×C4—98no—
547C22×C4—94no—
548C22×C4—98no—
549C22×C4—91no—
550C22×C4—91no—
551C22×C4—98no—
552C22×C4—188no—
553C22×C4—184no—
554C22×C4—188no—
555C22×C4C2×D3212yes—
556C22×C4C2×D3211yescharacteristic
557C4⋊C4—38no—
558C4⋊C4—34no—
559C4⋊C4C2×D3214yes—
560C22⋊C4—38no—
561C22⋊C4—98no—
562C22⋊C4—98no—
563C22⋊C4—98no—
564C42—34no—
565C42—94no—
566C42—94no—
567C42—94no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—21no—
572C22×C3—34no—
573C22×C3—62no—
574C22×C3—62no—
575C22×C3—68no—
576C22×C3—64no—
577C22×C3—64no—
578C22×C3—64no—
579C22×C3—128no—
580C22×C3C2×D3×D412yes—
581C22×C3C2×D3×D412yes—
582C22×C3C2×#23712yes—
583C22×C3C2×#23912yes—
584C22×C3C2×#23912yes—
585C22×C3D3×#4112yes—
586C22×C3C24×D311yescharacteristic
587C22×C3C24×D311yescharacteristic
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—28no—
591C2×D3—24no—
592C2×D3—24no—
593C2×D3—24no—
594C2×D3—48no—
595C2×D3—68no—
596C2×D3—64no—
597C2×D3—64no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—64no—
601C2×D3—64no—
602C2×D3—124no—
603C2×D3—124no—
604C2×D3—1216no—
605C2×D3—128no—
606C2×D3—128no—
607C2×D3C2×D3×D414yes—
608C3×C4—24no—
609C3×C4—24no—
610C3×C4—24no—
611C3×C4—34no—
612C3×C4—34no—
613C3×C4—44no—
614C3×C4—64no—
615C3×C4—62no—
616C3×C4C2×#23714yescomplemented
617C3×C4C2×#23914yescomplemented
618Dic3—24no—
619Dic3—22no—
620Dic3—34no—
621Dic3—34no—
622Dic3—64no—
623Dic3—62no—
624Dic3—62no—
625Dic3—122no—
626Dic3C2×D3×D414yes—
627Dic3C2×#23914yescomplemented
628C32C2×#53211yescharacteristic, complemented, Sylow
629C23—34no—
630C23—32no—
631C23—34no—
632C23—62no—
633C23—62no—
634C23—64no—
635C23—64no—
636C23—64no—
637C23—94no—
638C23—184no—
639C23—184no—
640C23—184no—
641C23C22×D3211yescharacteristic
642Q8—616no—
643D4—616no—
644D4—68no—
645D4—1816no—
646D4—1816no—
647D4—1816no—
648D4—188no—
649C2×C4—24no—
650C2×C4—34no—
651C2×C4—34no—
652C2×C4—32no—
653C2×C4—32no—
654C2×C4—32no—
655C2×C4—34no—
656C2×C4—62no—
657C2×C4—64no—
658C2×C4—68no—
659C2×C4—916no—
660C2×C4—94no—
661C2×C4—92no—
662C2×C4—92no—
663C2×C4—1816no—
664C2×C4—188no—
665C2×C4—1816no—
666C2×C4—182no—
667C2×C4#379614yescomplemented
668C2×C4C22×D3214yes—
669C2×C4C22×D3212yes—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—24no—
673C2×C3—21no—
674C2×C3—64no—
675C2×C3—124no—
676C2×C3#559614yescomplemented
677C2×C3#572514yescomplemented
678C2×C3C22×D3×D411yescharacteristic
679C2×C3C22×D3×D411yescharacteristic
680C2×C3C22×#23711yescharacteristic
681C2×C3C22×#23911yescharacteristic
682C2×C3C22×#23911yescharacteristic
683C2×C3C2×D3×#4111yescharacteristic
684D3—24no—
685D3—44no—
686D3—128no—
687D3—124no—
688D3—124no—
689C22—34no—
690C22—62no—
691C22—68no—
692C22—62no—
693C22—64no—
694C22—64no—
695C22—64no—
696C22—128no—
697C22—184no—
698C22—184no—
699C22—184no—
700C22—368no—
701C22C2×#379612yes—
702C22D32×D412yes—
703C22D3×#23912yes—
704C22C23×D3211yescharacteristic
705C4—24no—
706C4—34no—
707C4—34no—
708C4—62no—
709C4—64no—
710C4—94no—
711C4—182no—
712C4C2×#379614yescomplemented
713C3—21no—
714C3C2×#559611yescharacteristic, complemented
715C3C2×#572511yescharacteristic, complemented
716C2—64no—
717C2—124no—
718C2—364no—
719C2#1059436914yesdirect product factor
720C2C22×#379611yescharacteristic
721C2C2×D32×D411yescharacteristic
722C2C2×D3×#23911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3796C2semidirect
2. C2×#64102C2semidirect
3. C2×C3×#895C2semidirect
4. C2×C3×#888C2semidirect
5. C2×#63911C2semidirect
6. C2×#63909C2semidirect
7. C2×#63907C2semidirect
8. C2×#63898C2semidirect
9. C2×#63886C2semidirect
10. C2×#63881C2semidirect
11. C2×C4×D3×Dic3C2semidirect
12. #10594369C2direct (N × H)
28. C2×#3796C22semidirect
32. #64102C22semidirect
37. C3×#895C22semidirect
38. C3×#888C22semidirect
43. #63911C22semidirect
44. #63909C22semidirect
45. #63907C22semidirect
46. #63898C22semidirect
47. #63886C22semidirect
48. #63881C22semidirect
49. C4×D3×Dic3C22semidirect
64. C2×#895D3semidirect
70. C2×#888D3semidirect
106. C2×D3×Dic3D4semidirect
188. #895C2×D3semidirect
194. #888C2×D3semidirect
213. C2×C32×C4#41semidirect
225. C2×C3×Dic3#41semidirect
239. D3×Dic3C2×D4semidirect
375. C32×C4C2×#41semidirect
381. C3×Dic3C2×#41semidirect
466. C2×C3×C4#237semidirect
467. C2×C3×C4#239semidirect
493. C2×Dic3#239semidirect
514. C2×C32#532semidirect
616. C3×C4C2×#237semidirect
617. C3×C4C2×#239semidirect
627. Dic3C2×#239semidirect
628. C32C2×#532semidirect
667. C2×C4#3796semidirect
676. C2×C3#5596semidirect
677. C2×C3#5725semidirect
712. C4C2×#3796semidirect
714. C3C2×#5596semidirect
715. C3C2×#5725semidirect
719. C2#10594369direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C2×#641022
C2×C3×#8952
C2×C3×#8882
C2×#639112
C2×#639092
C2×#639072
C2×#638982
C2×#638862
C2×#638812
C2×C4×D3×Dic32
#105943692
C2×#57253
C2×#55963