Finite Group Databasebeta

← C2×#10594518 #11900778

Subgroups — C2×#10594518 #11900778

Order 1152.

3669 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C212yesmaximal, complemented
2C2×#64104C211yesmaximal, characteristic, complemented
3C2×C3×#893C211yesmaximal, characteristic, complemented
4C2×C3×#888C211yesmaximal, characteristic, complemented
5C2×#63916C211yesmaximal, characteristic, complemented
6C2×#63911C211yesmaximal, characteristic, complemented
7C2×#63910C212yesmaximal, complemented
8C2×#63907C212yesmaximal, complemented
9C2×#63904C212yesmaximal, complemented
10C2×#63894C211yesmaximal, characteristic, complemented
11C2×C4×#624C211yesmaximal, characteristic, complemented
12#10594518C2116yesmaximal, direct product factor
13C2×#5725—31nomaximal
14C2×#5548—31nomaximal
15C22×C4⋊(C3⋊D3)C2212yes—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2212yes—
20C22×C3×Dic6C2212yes—
21C22×#626C2212yes—
22C22×#626C2212yes—
23C22×#626C2212yes—
24C22×#624C2212yes—
25C22×#624C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C2×#3799—216no—
28C2×#3799C22116yescomplemented
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×#3752C2212yes—
31#64104C2218yescomplemented
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C3×#893C2218yescomplemented
38C3×#888C2218yescomplemented
39C2×#3722C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63916C2218yescomplemented
44#63911C2218yescomplemented
45#63910C22116yescomplemented
46#63907C22116yescomplemented
47#63904C22116yescomplemented
48#63894C2218yescomplemented
49C4×#624C2218yescomplemented
50C22×#239—32no—
51C22×#235—32no—
52C2×C3×C4⋊Q8—31no—
53C2×C3×C4×D4—31no—
54C2×#947—32no—
55C2×#940—31no—
56C2×#938—31no—
57C2×C4×#67—32no—
58#5725—316no—
59#5548—316no—
60C2×#895—31no—
61C2×#895—31no—
62C2×#895—31no—
63C2×#895—32no—
64C2×#895—61no—
65C2×#893—32no—
66C2×#893—31no—
67C2×#893D311yescharacteristic, complemented
68C2×#888D311yescharacteristic, complemented
69C2×#885—32no—
70C2×#884—32no—
71C2×#874—31no—
72C2×C4×D12—31no—
73C2×C42×D3—31no—
74C2×C42×D3—31no—
75C23×C3⋊D3C2312yes—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2312yes—
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C2×C4⋊(C3⋊D3)—28no—
82C2×C4⋊(C3⋊D3)—24no—
83C2×C4⋊(C3⋊D3)C2318yes—
84C2×C4⋊(C3⋊D3)C2314yes—
85C2×C4×C3⋊D3—24no—
86C2×C4×C3⋊D3C2314yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2311yescharacteristic
92C2×C3×D12—24no—
93C2×C3×D12C2314yes—
94C2×C3×C4×D3—28no—
95C2×C3×C4×D3C2318yes—
96C2×C3×Dic6—28no—
97C2×C3×Dic6C2318yes—
98C2×#626—28no—
99C2×#626—28no—
100C2×#626—28no—
101C2×#626C2318yes—
102C2×#626C2318yes—
103C2×#626C2318yes—
104C2×#624—28no—
105C2×#624—24no—
106C2×#624D418yescomplemented
107C2×#624C2318yes—
108C2×#624C2314yes—
109C2×#624C2314yes—
110#3799—264no—
111C32×C4⋊C4C2314yes—
112#3752C2318yes—
113C3×(C2×D3)⋊C4C2318yes—
114C3×C4⋊Dic3C2314yes—
115C3×Dic3⋊C4C2318yes—
116C3×C4×Dic3C2314yes—
117C3×C4×Dic3C2314yes—
118#3722C2318yes—
119(C2×D3)⋊Dic3C2318yes—
120Dic32C2314yes—
121Dic32C2314yes—
122C2×#532—91noSylow
123C22×C3×Q8—32no—
124C22×C3×D4—31no—
125C23×C3×C4—32no—
126C22×#67—32no—
127C22×#67—32no—
128C22×#67—32no—
129C2×#239—316no—
130C2×#239—616no—
131C2×#235—316no—
132C2×#235—616no—
133C22×D12—32no—
134C22×D12—32no—
135C22×D12—32no—
136C22×D12—32no—
137C22×D12—32no—
138C22×D12—31no—
139C22×D12—31no—
140C22×D12—61no—
141C22×D12—62no—
142C22×D12C2×D311yescharacteristic
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—32no—
148C22×C4×D3—32no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—61no—
152C22×C4×D3C2×D312yes—
153C22×Dic6C2×D312yes—
154C3×C4⋊Q8—38no—
155C3×C4×D4—38no—
156C2×C3×C4⋊C4—21no—
157C2×C3×C4⋊C4—32no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4C2×D311yescharacteristic
160C2×C3×C4⋊C4C2×D311yescharacteristic
161C2×C3×C22⋊C4—32no—
162C2×C3×C42—31no—
163C2×C3×C42—31no—
164C2×#217—32no—
165#947—316no—
166#940—38no—
167#938—38no—
168C4×#67—316no—
169C2×(C2×D3)⋊C4—32no—
170C2×(C2×D3)⋊C4—32no—
171C2×(C2×D3)⋊C4—32no—
172C2×(C2×D3)⋊C4—32no—
173C2×(C2×D3)⋊C4—32no—
174C2×(C2×D3)⋊C4—62no—
175C2×(C2×D3)⋊C4C2×D312yes—
176C2×C4⋊Dic3C2×D311yescharacteristic
177C2×Dic3⋊C4C2×D312yes—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3C2×D311yescharacteristic
183C2×C4×Dic3C2×D311yescharacteristic
184#895—38no—
185#895—38no—
186#895—38no—
187#895—316no—
188#895—68no—
189#893—316no—
190#893—38no—
191#893C2×D318yescomplemented
192#888C2×D318yescomplemented
193#885—316no—
194#884—316no—
195#874—38no—
196C4×D12—38no—
197C42×D3—38no—
198C42×D3—38no—
199C23×C32C2411yescharacteristic
200C22×C3⋊D3—22no—
201C22×C3⋊D3—22no—
202C22×C3⋊D3—24no—
203C22×C3⋊D3—24no—
204C22×C3⋊D3—24no—
205C22×C3⋊D3C2×D414yes—
206C22×C3⋊D3C2414yes—
207C22×C3⋊D3C2412yes—
208C22×C3×D3—24no—
209C22×C3×D3—24no—
210C22×C3×D3—24no—
211C22×C3×D3C2414yes—
212C2×C32×C4—24no—
213C2×C32×C4#4114yescomplemented
214C2×C32×C4C2414yes—
215C2×C32×C4C2412yes—
216C2×C3⋊Dic3—22no—
217C2×C3⋊Dic3C2412yes—
218C4⋊(C3⋊D3)—216no—
219C4⋊(C3⋊D3)—28no—
220C4×C3⋊D3—28no—
221C2×C3×Dic3—24no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3C2×D414yes—
224C2×C3×Dic3C2×D414yes—
225C2×C3×Dic3#4114yescomplemented
226C2×C3×Dic3C2412yes—
227C2×C3×Dic3C2414yes—
228C2×C3×Dic3C2412yes—
229C2×C3×Dic3C2412yes—
230C2×C3×Dic3C2412yes—
231C3×D12—28no—
232C3×C4×D3—216no—
233C3×Dic6—216no—
234#626—216no—
235#626—216no—
236#626—216no—
237#624—216no—
238#624—28no—
239#624C2×D4116yescomplemented
240C22×#41—92no—
241#532—916no—
242C2×C4⋊Q8—31no—
243C2×#127—91no—
244C2×#124—92no—
245C2×#121—92no—
246C2×#121—91no—
247C2×#121—91no—
248C2×C4×D4—31no—
249C2×C4×D4—91no—
250C2×C4×D4—92no—
251C22×C42—91no—
252C24×C3—32no—
253C23×D3—31no—
254C23×D3—31no—
255C23×D3—32no—
256C23×D3—32no—
257C23×D3—61no—
258C23×D3—62no—
259C23×D3C22×D312yes—
260C2×C3×Q8—38no—
261C2×C3×Q8—68no—
262C2×C3×D4—34no—
263C2×C3×D4—64no—
264C22×C3×C4—21no—
265C22×C3×C4—22no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—32no—
271C22×C3×C4—38no—
272C22×C3×C4—68no—
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—61no—
286C22×Dic3C22×D311yescharacteristic
287C22×Dic3C22×D312yes—
288C22×Dic3C22×D311yescharacteristic
289C22×Dic3C22×D311yescharacteristic
290C22×Dic3C22×D311yescharacteristic
291#239—664no—
292#235—664no—
293C2×D12—24no—
294C2×D12—38no—
295C2×D12—38no—
296C2×D12—38no—
297C2×D12—34no—
298C2×D12—34no—
299C2×D12—38no—
300C2×D12—38no—
301C2×D12—64no—
302C2×D12—68no—
303C2×D12—68no—
304C2×D12—68no—
305C2×D12—68no—
306C2×D12—68no—
307C2×D12—68no—
308C2×D12—64no—
309C2×D12—64no—
310C2×D12—124no—
311C2×D12—128no—
312C2×D12C22×D314yes—
313C2×C4×D3—28no—
314C2×C4×D3—38no—
315C2×C4×D3—38no—
316C2×C4×D3—34no—
317C2×C4×D3—34no—
318C2×C4×D3—34no—
319C2×C4×D3—34no—
320C2×C4×D3—34no—
321C2×C4×D3—34no—
322C2×C4×D3—38no—
323C2×C4×D3—38no—
324C2×C4×D3—64no—
325C2×C4×D3—64no—
326C2×C4×D3—68no—
327C2×C4×D3—64no—
328C2×C4×D3—64no—
329C2×C4×D3—68no—
330C2×C4×D3—64no—
331C2×C4×D3—124no—
332C2×C4×D3C22×D318yes—
333C2×Dic6—28no—
334C2×Dic6C22×D318yes—
335C3×C4⋊C4—24no—
336C3×C4⋊C4—38no—
337C3×C4⋊C4—34no—
338C3×C4⋊C4C22×D314yes—
339C3×C4⋊C4C22×D314yes—
340C3×C22⋊C4—38no—
341C3×C42—34no—
342C3×C42—34no—
343#217—38no—
344(C2×D3)⋊C4—38no—
345(C2×D3)⋊C4—38no—
346(C2×D3)⋊C4—38no—
347(C2×D3)⋊C4—38no—
348(C2×D3)⋊C4—38no—
349(C2×D3)⋊C4—68no—
350(C2×D3)⋊C4C22×D318yes—
351C4⋊Dic3C22×D314yes—
352Dic3⋊C4C22×D318yes—
353C4×Dic3—34no—
354C4×Dic3—34no—
355C4×Dic3—34no—
356C4×Dic3—34no—
357C4×Dic3C22×D314yes—
358C4×Dic3C22×D314yes—
359C22×C32C22×D412yes—
360C22×C32C2×#4112yes—
361C22×C32C2×#4112yes—
362C22×C32C2511yescharacteristic
363C2×C3⋊D3—28no—
364C2×C3⋊D3—22no—
365C2×C3⋊D3—22no—
366C2×C3⋊D3—24no—
367C2×C3⋊D3—24no—
368C2×C3⋊D3—24no—
369C2×C3⋊D3—48no—
370C2×C3⋊D3C22×D414yes—
371C2×C3×D3—24no—
372C2×C3×D3—24no—
373C2×C3×D3—24no—
374C2×C3×D3—48no—
375C32×C4—24no—
376C32×C4C2×#4114yescomplemented
377C3⋊Dic3—22no—
378C3×Dic3—24no—
379C3×Dic3—22no—
380C3×Dic3C22×D414yes—
381C3×Dic3C22×D414yes—
382C3×Dic3C2×#4114yescomplemented
383C2×#41—916no—
384C2×#41—1816no—
385C22×Q8—32no—
386C22×D4—31no—
387C22×D4—92no—
388C22×D4—92no—
389C22×D4—92no—
390C22×D4—91no—
391C22×D4—92no—
392C23×C4—32no—
393C23×C4—91no—
394C23×C4—92no—
395C23×C4—91no—
396C23×C4—91no—
397C4⋊Q8—38no—
398#127—98no—
399#124—916no—
400#121—916no—
401#121—98no—
402#121—98no—
403C4×D4—38no—
404C4×D4—98no—
405C4×D4—916no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4D3211yescharacteristic
409C2×C22⋊C4—32no—
410C2×C22⋊C4—92no—
411C2×C22⋊C4—92no—
412C2×C22⋊C4—92no—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—98no—
416C2×C42—91no—
417C2×C42—91no—
418C23×C3—21no—
419C23×C3—34no—
420C23×C3—64no—
421C23×C3—64no—
422C23×C3—64no—
423C23×C3C23×D311yescharacteristic
424C23×C3C23×D311yescharacteristic
425C22×D3—24no—
426C22×D3—24no—
427C22×D3—24no—
428C22×D3—34no—
429C22×D3—34no—
430C22×D3—32no—
431C22×D3—32no—
432C22×D3—34no—
433C22×D3—34no—
434C22×D3—64no—
435C22×D3—62no—
436C22×D3—64no—
437C22×D3—62no—
438C22×D3—62no—
439C22×D3—62no—
440C22×D3—62no—
441C22×D3—64no—
442C22×D3—64no—
443C22×D3—64no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—64no—
447C22×D3—122no—
448C22×D3—122no—
449C22×D3—124no—
450C22×D3—124no—
451C22×D3—124no—
452C22×D3C23×D314yes—
453C3×Q8—616no—
454C3×D4—68no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—22no—
458C2×C3×C4—24no—
459C2×C3×C4—24no—
460C2×C3×C4—34no—
461C2×C3×C4—34no—
462C2×C3×C4—34no—
463C2×C3×C4—32no—
464C2×C3×C4—32no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—34no—
468C2×C3×C4—44no—
469C2×C3×C4—616no—
470C2×C3×C4—64no—
471C2×C3×C4—62no—
472C2×C3×C4#23514yescomplemented
473C2×C3×C4#23914yescomplemented
474C2×C3×C4C23×D314yes—
475C2×C3×C4C23×D314yes—
476C2×C3×C4C23×D312yes—
477C2×C3×C4C23×D312yes—
478#67—616no—
479#67—616no—
480#67—616no—
481C2×Dic3—24no—
482C2×Dic3—22no—
483C2×Dic3—32no—
484C2×Dic3—32no—
485C2×Dic3—62no—
486C2×Dic3—62no—
487C2×Dic3—62no—
488C2×Dic3—122no—
489C2×Dic3D3×D414yes—
490C2×Dic3D3×D414yes—
491C2×Dic3#23914yescomplemented
492C2×Dic3C23×D312yes—
493C2×Dic3C23×D314yes—
494C2×Dic3C23×D312yes—
495C2×Dic3C23×D312yes—
496C2×Dic3C23×D312yes—
497D12—28no—
498D12—616no—
499D12—616no—
500D12—616no—
501D12—616no—
502D12—616no—
503D12—68no—
504D12—68no—
505D12—128no—
506D12—1216no—
507C4×D3—216no—
508C4×D3—316no—
509C4×D3—316no—
510C4×D3—68no—
511C4×D3—616no—
512C4×D3—68no—
513C4×D3—68no—
514C4×D3—616no—
515C4×D3—68no—
516C4×D3—128no—
517Dic6—216no—
518C2×C32#53214yescomplemented
519C2×C32C23×D411yescharacteristic
520C2×C32C22×#4111yescharacteristic
521C2×C32C22×#4111yescharacteristic
522C3⋊D3—24no—
523C3⋊D3—44no—
524C3×D3—44no—
525C24—32no—
526C24—91no—
527C24—92no—
528#41—1864no—
529C2×Q8—38no—
530C2×Q8—68no—
531C2×D4—34no—
532C2×D4—64no—
533C2×D4—98no—
534C2×D4—98no—
535C2×D4—98no—
536C2×D4—94no—
537C2×D4—98no—
538C2×D4—188no—
539C2×D4—188no—
540C2×D4—188no—
541C2×D4—188no—
542C2×D4—184no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—32no—
548C22×C4—38no—
549C22×C4—68no—
550C22×C4—94no—
551C22×C4—98no—
552C22×C4—94no—
553C22×C4—98no—
554C22×C4—91no—
555C22×C4—94no—
556C22×C4—188no—
557C22×C4—184no—
558C22×C4—184no—
559C22×C4C2×D3212yes—
560C22×C4C2×D3211yescharacteristic
561C4⋊C4—38no—
562C4⋊C4—34no—
563C4⋊C4C2×D3214yes—
564C22⋊C4—38no—
565C22⋊C4—98no—
566C22⋊C4—98no—
567C22⋊C4—98no—
568C42—34no—
569C42—34no—
570C42—94no—
571C42—94no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—21no—
576C22×C3—64no—
577C22×C3—64no—
578C22×C3—64no—
579C22×C3—128no—
580C22×C3C2×#23512yes—
581C22×C3C2×D3×D412yes—
582C22×C3C2×D3×D412yes—
583C22×C3C2×#23912yes—
584C22×C3C2×#23912yes—
585C22×C3D3×#4112yes—
586C22×C3C24×D311yescharacteristic
587C22×C3C24×D311yescharacteristic
588C2×D3—24no—
589C2×D3—24no—
590C2×D3—24no—
591C2×D3—34no—
592C2×D3—34no—
593C2×D3—48no—
594C2×D3—64no—
595C2×D3—62no—
596C2×D3—62no—
597C2×D3—62no—
598C2×D3—62no—
599C2×D3—68no—
600C2×D3—68no—
601C2×D3—64no—
602C2×D3—64no—
603C2×D3—64no—
604C2×D3—64no—
605C2×D3—64no—
606C2×D3—64no—
607C2×D3—122no—
608C2×D3—122no—
609C2×D3—128no—
610C2×D3—124no—
611C2×D3—124no—
612C2×D3—124no—
613C2×D3—128no—
614C2×D3—128no—
615C2×D3—248no—
616C3×C4—24no—
617C3×C4—24no—
618C3×C4—24no—
619C3×C4—34no—
620C3×C4—34no—
621C3×C4—34no—
622C3×C4—44no—
623C3×C4—64no—
624C3×C4—62no—
625C3×C4C2×#23514yescomplemented
626C3×C4C2×#23914yescomplemented
627Dic3—24no—
628Dic3—22no—
629Dic3—62no—
630Dic3—62no—
631Dic3—122no—
632Dic3C2×D3×D414yes—
633Dic3C2×D3×D414yes—
634Dic3C2×#23914yescomplemented
635C32C2×#53211yescharacteristic, complemented, Sylow
636C23—34no—
637C23—64no—
638C23—64no—
639C23—64no—
640C23—94no—
641C23—92no—
642C23—94no—
643C23—182no—
644C23—182no—
645C23—184no—
646C23—184no—
647C23—184no—
648C23C22×D3211yescharacteristic
649Q8—616no—
650D4—68no—
651D4—1816no—
652D4—1816no—
653D4—1816no—
654D4—1816no—
655D4—188no—
656C2×C4—24no—
657C2×C4—34no—
658C2×C4—34no—
659C2×C4—34no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—34no—
665C2×C4—616no—
666C2×C4—64no—
667C2×C4—62no—
668C2×C4—916no—
669C2×C4—92no—
670C2×C4—1816no—
671C2×C4—188no—
672C2×C4—182no—
673C2×C4—188no—
674C2×C4#379914yescomplemented
675C2×C4C22×D3214yes—
676C2×C4C22×D3212yes—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—24no—
681C2×C3—124no—
682C2×C3#554814yescomplemented
683C2×C3#572514yescomplemented
684C2×C3C22×#23511yescharacteristic
685C2×C3C22×D3×D411yescharacteristic
686C2×C3C22×D3×D411yescharacteristic
687C2×C3C22×#23911yescharacteristic
688C2×C3C22×#23911yescharacteristic
689C2×C3C2×D3×#4111yescharacteristic
690D3—44no—
691D3—64no—
692D3—64no—
693D3—124no—
694D3—124no—
695D3—124no—
696D3—244no—
697C22—64no—
698C22—64no—
699C22—64no—
700C22—94no—
701C22—128no—
702C22—182no—
703C22—182no—
704C22—188no—
705C22—184no—
706C22—184no—
707C22—184no—
708C22—368no—
709C22C2×#379912yes—
710C22D32×D412yes—
711C22D3×#23912yes—
712C22C23×D3211yescharacteristic
713C4—24no—
714C4—34no—
715C4—34no—
716C4—34no—
717C4—64no—
718C4—62no—
719C4—182no—
720C4C2×#379914yescomplemented
721C3—21no—
722C3C2×#554811yescharacteristic, complemented
723C3C2×#572511yescharacteristic, complemented
724C2—124no—
725C2—184no—
726C2—364no—
727C2#1059451814yesdirect product factor
728C2C22×#379911yescharacteristic
729C2C2×D32×D411yescharacteristic
730C2C2×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×#3799C2semidirect
2. C2×#64104C2semidirect
3. C2×C3×#893C2semidirect
4. C2×C3×#888C2semidirect
5. C2×#63916C2semidirect
6. C2×#63911C2semidirect
7. C2×#63910C2semidirect
8. C2×#63907C2semidirect
9. C2×#63904C2semidirect
10. C2×#63894C2semidirect
11. C2×C4×#624C2semidirect
12. #10594518C2direct (N × H)
28. C2×#3799C22semidirect
31. #64104C22semidirect
37. C3×#893C22semidirect
38. C3×#888C22semidirect
43. #63916C22semidirect
44. #63911C22semidirect
45. #63910C22semidirect
46. #63907C22semidirect
47. #63904C22semidirect
48. #63894C22semidirect
49. C4×#624C22semidirect
67. C2×#893D3semidirect
68. C2×#888D3semidirect
106. C2×#624D4semidirect
191. #893C2×D3semidirect
192. #888C2×D3semidirect
213. C2×C32×C4#41semidirect
225. C2×C3×Dic3#41semidirect
239. #624C2×D4semidirect
376. C32×C4C2×#41semidirect
382. C3×Dic3C2×#41semidirect
472. C2×C3×C4#235semidirect
473. C2×C3×C4#239semidirect
491. C2×Dic3#239semidirect
518. C2×C32#532semidirect
625. C3×C4C2×#235semidirect
626. C3×C4C2×#239semidirect
634. Dic3C2×#239semidirect
635. C32C2×#532semidirect
674. C2×C4#3799semidirect
682. C2×C3#5548semidirect
683. C2×C3#5725semidirect
720. C4C2×#3799semidirect
722. C3C2×#5548semidirect
723. C3C2×#5725semidirect
727. C2#10594518direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C2×#641042
C2×C3×#8932
C2×C3×#8882
C2×#639162
C2×#639112
C2×#639102
C2×#639072
C2×#639042
C2×#638942
C2×C4×#6242
#105945182
C2×#57253
C2×#55483