Finite Group Databasebeta

← C2×#10595401 #11902627

Subgroups — C2×#10595401 #11902627

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×D3×Q8C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×#64155C211yesmaximal, characteristic, complemented
4C2×C3×#947C211yesmaximal, characteristic, complemented
5#10595401C2116yesmaximal, direct product factor
6C2×#63908C211yesmaximal, characteristic, complemented
7C2×#63907C212yesmaximal, complemented
8C2×#63906C212yesmaximal, complemented
9C2×C4×#626C211yesmaximal, characteristic, complemented
10C2×#63887C212yesmaximal, complemented
11C2×#63879C212yesmaximal, complemented
12C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
13C2×#5817—31nomaximal
14C2×#5677—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C3×D3×Q8—28no—
18C2×C3×D3×Q8C2218yescomplemented
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2212yes—
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2212yes—
23C22×C3×Dic6C2211yescharacteristic
24C22×#626C2212yes—
25C22×#626C2211yescharacteristic
26C22×#625C2212yes—
27C22×D3×Dic3C2212yes—
28C2×#3796—28no—
29C2×#3796C2218yescomplemented
30#64155C2218yescomplemented
31C2×#3752C2212yes—
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×#3750C2212yes—
34C3×#947C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×(C2×D3)⋊C4C2212yes—
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2212yes—
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2212yes—
43C2×Dic32C2212yes—
44#63908C2218yescomplemented
45#63907C22116yescomplemented
46#63906C22116yescomplemented
47C4×#626C2218yescomplemented
48#63887C22116yescomplemented
49#63879C22116yescomplemented
50Dic3×Dic6C2218yescomplemented
51C23×C3×Q8—31no—
52C22×#239—31no—
53C22×D3×Q8D311yescharacteristic, complemented
54C22×#237—31no—
55C2×C3×#124—31no—
56#5817—316no—
57C2×#947—32no—
58C2×#947D311yescharacteristic, complemented
59C2×#946—31no—
60C2×#946—31no—
61C2×#946—32no—
62C2×#946—61no—
63C2×Q8×Dic3—31no—
64C2×#938—31no—
65C2×#930—31no—
66C2×#930—32no—
67C2×C4×#67—32no—
68C2×C4×#67—31no—
69#5677—316no—
70C2×#885—32no—
71C2×#884—32no—
72C2×#67⋊C4—32no—
73C2×#878—32no—
74C2×C4×D12—31no—
75C2×C4×Dic6—31no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C2×C32×Q8—24no—
80C2×C32×Q8C2314yes—
81C22×C32×C4C2312yes—
82C22×C32×C4C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2312yes—
85C2×C4×C3⋊D3—24no—
86C2×C4×C3⋊D3C2314yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
91C3×D3×Q8—232no—
92C2×C3×D12—24no—
93C2×C3×D12C2314yes—
94C2×C3×C4×D3—24no—
95C2×C3×C4×D3—28no—
96C2×C3×C4×D3C2318yes—
97C2×C3×C4×D3C2314yes—
98C2×C3×Dic6—28no—
99C2×C3×Dic6D418yescomplemented
100C2×C3×Dic6C2318yes—
101C2×C3×Dic6C2314yes—
102C2×#626—24no—
103C2×#626—28no—
104C2×#626C2318yes—
105C2×#626C2314yes—
106C2×#625—28no—
107C2×#625C2318yes—
108C2×D3×Dic3—28no—
109C2×D3×Dic3C2318yes—
110#3796—232no—
111#3752C2318yes—
112C4⋊(C3⋊Dic3)C2314yes—
113#3750C2318yes—
114C3×(C2×D3)⋊C4C2318yes—
115C3×(C2×D3)⋊C4C2318yes—
116C3×C4×Dic3C2314yes—
117Dic3⋊Dic3C2318yes—
118Dic3⋊Dic3C2314yes—
119#3722C2314yes—
120(C2×D3)⋊Dic3C2314yes—
121(C2×D3)⋊Dic3C2318yes—
122Dic32C2318yes—
123C2×#548—91noSylow
124C22×C3×Q8—21no—
125C22×C3×Q8—38no—
126C22×C3×Q8—31no—
127C22×C3×Q8—32no—
128C22×C3×Q8—68no—
129C22×C3×Q8C2×D311yescharacteristic
130C22×C3×Q8C2×D311yescharacteristic
131C22×C3×D4—31no—
132C23×C3×C4—32no—
133C23×C3×C4—31no—
134C22×#67—32no—
135C22×#67—32no—
136C22×#67—32no—
137C22×#67—31no—
138C23×Dic3—32no—
139C2×#239—38no—
140C2×#239—68no—
141C2×D3×Q8—28no—
142C2×D3×Q8C2×D318yescomplemented
143C2×#237—38no—
144C2×#237—68no—
145C22×D12—32no—
146C22×D12—31no—
147C22×D12C2×D311yescharacteristic
148C22×C4×D3—32no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—61no—
152C22×C4×D3C2×D311yescharacteristic
153C22×C4×D3C2×D312yes—
154C22×Dic6C2×D312yes—
155C22×Dic6C2×D311yescharacteristic
156C3×#124—38no—
157C2×C3×C22⋊C4—32no—
158C2×C3×C22⋊C4—32no—
159C2×C3×C42—31no—
160C2×#217—32no—
161C2×#217—31no—
162#947—316no—
163#947C2×D318yescomplemented
164#946—38no—
165#946—38no—
166#946—316no—
167#946—68no—
168Q8×Dic3—38no—
169#938—38no—
170#930—38no—
171#930—316no—
172C4×#67—316no—
173C4×#67—38no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—62no—
181C2×(C2×D3)⋊C4C2×D312yes—
182C2×(C2×D3)⋊C4C2×D312yes—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—32no—
187C2×C4⋊Dic3—61no—
188C2×Dic3⋊C4—32no—
189C2×Dic3⋊C4—32no—
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—62no—
193C2×C4×Dic3—32no—
194C2×C4×Dic3—32no—
195C2×C4×Dic3C2×D311yescharacteristic
196#885—316no—
197#884—316no—
198#67⋊C4—316no—
199#878—316no—
200C4×D12—38no—
201C4×Dic6—38no—
202C23×C32C2411yescharacteristic
203C22×C3⋊D3—22no—
204C22×C3⋊D3—22no—
205C22×C3⋊D3—22no—
206C22×C3⋊D3C2412yes—
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—
215C32×Q8—28no—
216C2×C32×C4—24no—
217C2×C32×C4C2×D414yes—
218C2×C32×C4C2414yes—
219C2×C32×C4C2412yes—
220C2×C3⋊Dic3—22no—
221C2×C3⋊Dic3—24no—
222C2×C3⋊Dic3C2414yes—
223C2×C3⋊Dic3C2412yes—
224C4×C3⋊D3—28no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3C2×D418yes—
229C2×C3×Dic3C2412yes—
230C2×C3×Dic3C2412yes—
231C2×C3×Dic3C2412yes—
232C2×C3×Dic3C2414yes—
233C3×D12—28no—
234C3×C4×D3—28no—
235C3×C4×D3—216no—
236C3×Dic6—216no—
237C3×Dic6C2×D4116yescomplemented
238#626—28no—
239#626—216no—
240#625—216no—
241D3×Dic3—216no—
242C22×#41—91no—
243C23×Q8—31no—
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—91no—
253C2×C4×D4—92no—
254C24×C3—31no—
255C24×C3—32no—
256C23×D3—31no—
257C23×D3—31no—
258C23×D3—61no—
259C23×D3C22×D312yes—
260C23×D3C22×D311yescharacteristic
261C2×C3×Q8—24no—
262C2×C3×Q8—24no—
263C2×C3×Q8—24no—
264C2×C3×Q8—38no—
265C2×C3×Q8—34no—
266C2×C3×Q8—38no—
267C2×C3×Q8—44no—
268C2×C3×Q8—68no—
269C2×C3×Q8—632no—
270C2×C3×Q8C22×D314yes—
271C2×C3×Q8C22×D314yes—
272C2×C3×D4—34no—
273C2×C3×D4—64no—
274C22×C3×C4—21no—
275C22×C3×C4—22no—
276C22×C3×C4—32no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—38no—
281C22×C3×C4—34no—
282C22×C3×C4—68no—
283C22×C3×C4—64no—
284C22×C3×C4C22×D312yes—
285C22×C3×C4C22×D312yes—
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C2×#67—38no—
289C2×#67—38no—
290C2×#67—38no—
291C2×#67—34no—
292C2×#67—64no—
293C2×#67—68no—
294C2×#67—68no—
295C2×#67—68no—
296C22×Dic3—32no—
297C22×Dic3—32no—
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—38no—
301C22×Dic3—61no—
302C22×Dic3—62no—
303C22×Dic3—68no—
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D312yes—
308#239—632no—
309D3×Q8—232no—
310#237—632no—
311C2×D12—24no—
312C2×D12—34no—
313C2×D12—38no—
314C2×D12—68no—
315C2×D12—64no—
316C2×D12C22×D314yes—
317C2×C4×D3—24no—
318C2×C4×D3—28no—
319C2×C4×D3—38no—
320C2×C4×D3—34no—
321C2×C4×D3—34no—
322C2×C4×D3—64no—
323C2×C4×D3—68no—
324C2×C4×D3—64no—
325C2×C4×D3—64no—
326C2×C4×D3—124no—
327C2×C4×D3C22×D314yes—
328C2×C4×D3C22×D318yes—
329C2×Dic6—28no—
330C2×Dic6#6718yescomplemented
331C2×Dic6C22×D318yes—
332C2×Dic6C22×D314yes—
333C3×C22⋊C4—38no—
334C3×C22⋊C4—38no—
335C3×C42—34no—
336#217—38no—
337#217—34no—
338(C2×D3)⋊C4—34no—
339(C2×D3)⋊C4—38no—
340(C2×D3)⋊C4—38no—
341(C2×D3)⋊C4—38no—
342(C2×D3)⋊C4—34no—
343(C2×D3)⋊C4—34no—
344(C2×D3)⋊C4—68no—
345(C2×D3)⋊C4C22×D318yes—
346(C2×D3)⋊C4C22×D318yes—
347C4⋊Dic3—34no—
348C4⋊Dic3—34no—
349C4⋊Dic3—34no—
350C4⋊Dic3—38no—
351C4⋊Dic3—64no—
352Dic3⋊C4—38no—
353Dic3⋊C4—38no—
354Dic3⋊C4—38no—
355Dic3⋊C4—34no—
356Dic3⋊C4—68no—
357C4×Dic3—38no—
358C4×Dic3—38no—
359C4×Dic3C22×D314yes—
360C22×C32C22×D412yes—
361C22×C32C2×#4112yes—
362C22×C322−1+412yes—
363C22×C32C2511yescharacteristic
364C2×C3⋊D3—22no—
365C2×C3⋊D3—22no—
366C2×C3⋊D3—22no—
367C2×C3⋊D3—44no—
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—24no—
377C32×C4C22×D414yes—
378C3⋊Dic3—22no—
379C3⋊Dic3—24no—
380C3×Dic3—22no—
381C3×Dic3—22no—
382C3×Dic3—22no—
383C3×Dic3C22×D418yes—
384C2×#41—98no—
385C2×#41—188no—
386C22×Q8—38no—
387C22×Q8—31no—
388C22×Q8—32no—
389C22×Q8—68no—
390C22×Q8D3211yescharacteristic
391C22×D4—31no—
392C22×D4—91no—
393C22×D4—92no—
394C22×D4—92no—
395C23×C4—32no—
396C23×C4—31no—
397C23×C4—92no—
398C23×C4—91no—
399#124—38no—
400#124—916no—
401C22⋊Q8—916no—
402C22⋊Q8—98no—
403#121—916no—
404#121—98no—
405C4×Q8—98no—
406C4×D4—98no—
407C4×D4—916no—
408C2×C4⋊C4—91no—
409C2×C4⋊C4—92no—
410C2×C4⋊C4—92no—
411C2×C4⋊C4—91no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4—91no—
415C2×C22⋊C4—91no—
416C2×C22⋊C4—92no—
417C2×C22⋊C4—92no—
418C2×C42—31no—
419C2×C42—92no—
420C23×C3—21no—
421C23×C3—34no—
422C23×C3—32no—
423C23×C3—34no—
424C23×C3—62no—
425C23×C3—62no—
426C23×C3—64no—
427C23×C3—64no—
428C23×C3—64no—
429C23×C3C23×D311yescharacteristic
430C23×C3C23×D311yescharacteristic
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—24no—
434C22×D3—24no—
435C22×D3—24no—
436C22×D3—32no—
437C22×D3—32no—
438C22×D3—62no—
439C22×D3—64no—
440C22×D3—62no—
441C22×D3—62no—
442C22×D3—62no—
443C22×D3—62no—
444C22×D3—62no—
445C22×D3—62no—
446C22×D3—122no—
447C22×D3—122no—
448C22×D3#23914yescomplemented
449C22×D3C23×D314yes—
450C22×D3C23×D312yes—
451C3×Q8—28no—
452C3×Q8—28no—
453C3×Q8—316no—
454C3×Q8—48no—
455C3×Q8—616no—
456C3×D4—68no—
457C2×C3×C4—24no—
458C2×C3×C4—24no—
459C2×C3×C4—22no—
460C2×C3×C4—24no—
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—44no—
468C2×C3×C4—616no—
469C2×C3×C4—62no—
470C2×C3×C4—62no—
471C2×C3×C4—62no—
472C2×C3×C4—68no—
473C2×C3×C4D3×D414yes—
474C2×C3×C4C2×#6714yes—
475C2×C3×C4C23×D314yes—
476C2×C3×C4C23×D314yes—
477C2×C3×C4C23×D312yes—
478C2×C3×C4C23×D312yes—
479#67—68no—
480#67—616no—
481#67—616no—
482#67—616no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—34no—
487C2×Dic3—34no—
488C2×Dic3—32no—
489C2×Dic3—32no—
490C2×Dic3—62no—
491C2×Dic3—64no—
492C2×Dic3—62no—
493C2×Dic3—64no—
494C2×Dic3—64no—
495C2×Dic3—62no—
496C2×Dic3—616no—
497C2×Dic3—122no—
498C2×Dic3—124no—
499C2×Dic3C2×#6718yes—
500C2×Dic3C23×D312yes—
501C2×Dic3C23×D312yes—
502C2×Dic3C23×D312yes—
503C2×Dic3C23×D314yes—
504D12—28no—
505D12—616no—
506D12—68no—
507C4×D3—28no—
508C4×D3—216no—
509C4×D3—616no—
510C4×D3—68no—
511C4×D3—68no—
512C4×D3—128no—
513Dic6—216no—
514Dic6C2×#67116yescomplemented
515C2×C32#54814yescomplemented
516C2×C32C23×D411yescharacteristic
517C2×C32C22×#4111yescharacteristic
518C2×C32C2×2−1+411yescharacteristic
519C3⋊D3—42no—
520C3×D3—24no—
521C3×D3—44no—
522C24—31no—
523C24—32no—
524C24—91no—
525#41—1832no—
526C2×Q8—24no—
527C2×Q8—34no—
528C2×Q8—38no—
529C2×Q8—38no—
530C2×Q8—68no—
531C2×Q8—632no—
532C2×Q8C2×D3214yes—
533C2×D4—34no—
534C2×D4—64no—
535C2×D4—94no—
536C2×D4—98no—
537C2×D4—98no—
538C2×D4—188no—
539C2×D4—184no—
540C2×D4—188no—
541C22×C4—32no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—38no—
546C22×C4—34no—
547C22×C4—68no—
548C22×C4—64no—
549C22×C4—98no—
550C22×C4—92no—
551C22×C4—91no—
552C22×C4—94no—
553C22×C4—188no—
554C22×C4—184no—
555C22×C4C2×D3212yes—
556C22×C4C2×D3211yescharacteristic
557C4⋊C4—94no—
558C4⋊C4—98no—
559C4⋊C4—98no—
560C4⋊C4—94no—
561C22⋊C4—38no—
562C22⋊C4—38no—
563C22⋊C4—94no—
564C22⋊C4—94no—
565C22⋊C4—98no—
566C22⋊C4—98no—
567C42—34no—
568C42—98no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—21no—
573C22×C3—34no—
574C22×C3—68no—
575C22×C3—62no—
576C22×C3—62no—
577C22×C3—64no—
578C22×C3—64no—
579C22×C3—64no—
580C22×C3—128no—
581C22×C3C2×D3×D412yes—
582C22×C3C2×#23912yes—
583C22×C3#100712yes—
584C22×C3D3×#4112yes—
585C22×C3#101012yes—
586C22×C3C22×#6712yes—
587C22×C3C24×D311yescharacteristic
588C22×C3C24×D311yescharacteristic
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—28no—
592C2×D3—24no—
593C2×D3—24no—
594C2×D3—24no—
595C2×D3—48no—
596C2×D3—64no—
597C2×D3—62no—
598C2×D3—62no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—62no—
602C2×D3—62no—
603C2×D3—122no—
604C2×D3—122no—
605C2×D3—128no—
606C2×D3—124no—
607C2×D3—124no—
608C2×D3C2×#23914yescomplemented
609C3×C4—24no—
610C3×C4—24no—
611C3×C4—24no—
612C3×C4—38no—
613C3×C4—44no—
614C3×C4—62no—
615C3×C4—62no—
616C3×C4—62no—
617C3×C4C2×D3×D414yes—
618C3×C4C22×#6714yes—
619Dic3—22no—
620Dic3—22no—
621Dic3—22no—
622Dic3—62no—
623Dic3—64no—
624Dic3—64no—
625Dic3—62no—
626Dic3—122no—
627Dic3—124no—
628Dic3C22×#6718yes—
629C32C2×#54811yescharacteristic, complemented, Sylow
630C23—34no—
631C23—32no—
632C23—34no—
633C23—62no—
634C23—62no—
635C23—64no—
636C23—64no—
637C23—64no—
638C23—92no—
639C23—182no—
640C23—182no—
641C23—182no—
642C23C22×D3211yescharacteristic
643Q8—28no—
644Q8—316no—
645Q8—616no—
646D4—68no—
647D4—1816no—
648D4—188no—
649D4—1816no—
650C2×C4—24no—
651C2×C4—38no—
652C2×C4—34no—
653C2×C4—32no—
654C2×C4—32no—
655C2×C4—32no—
656C2×C4—616no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—68no—
661C2×C4—94no—
662C2×C4—92no—
663C2×C4—1816no—
664C2×C4—184no—
665C2×C4—182no—
666C2×C4—188no—
667C2×C4D3×#6714yes—
668C2×C4C22×D3214yes—
669C2×C4C22×D3212yes—
670C2×C3—21no—
671C2×C3—24no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—64no—
675C2×C3—124no—
676C2×C3#567714yescomplemented
677C2×C3#581714yescomplemented
678C2×C3C22×D3×D411yescharacteristic
679C2×C3C22×#23911yescharacteristic
680C2×C3C2×#100711yescharacteristic
681C2×C3C2×D3×#4111yescharacteristic
682C2×C3C2×#101011yescharacteristic
683C2×C3C23×#6711yescharacteristic
684D3—24no—
685D3—44no—
686D3—124no—
687D3—122no—
688D3—122no—
689C22—34no—
690C22—62no—
691C22—68no—
692C22—62no—
693C22—64no—
694C22—64no—
695C22—64no—
696C22—128no—
697C22—182no—
698C22—182no—
699C22—182no—
700C22—364no—
701C22#6431512yes—
702C22D3×#23912yes—
703C22C2×D3×#6712yes—
704C22C23×D3211yescharacteristic
705C4—24no—
706C4—38no—
707C4—62no—
708C4—62no—
709C4—62no—
710C4—184no—
711C4—182no—
712C4C2×D3×#6714yes—
713C3—21no—
714C3C2×#567711yescharacteristic, complemented
715C3C2×#581711yescharacteristic, complemented
716C2—64no—
717C2—124no—
718C2—362no—
719C2#1059540114yesdirect product factor
720C2C2×#6431511yescharacteristic
721C2C2×D3×#23911yescharacteristic
722C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×Q8C2semidirect
2. C22×#3796C2semidirect
3. C2×#64155C2semidirect
4. C2×C3×#947C2semidirect
5. #10595401C2direct (N × H)
6. C2×#63908C2semidirect
7. C2×#63907C2semidirect
8. C2×#63906C2semidirect
9. C2×C4×#626C2semidirect
10. C2×#63887C2semidirect
11. C2×#63879C2semidirect
12. C2×Dic3×Dic6C2semidirect
18. C2×C3×D3×Q8C22semidirect
29. C2×#3796C22semidirect
30. #64155C22semidirect
34. C3×#947C22semidirect
44. #63908C22semidirect
45. #63907C22semidirect
46. #63906C22semidirect
47. C4×#626C22semidirect
48. #63887C22semidirect
49. #63879C22semidirect
50. Dic3×Dic6C22semidirect
53. C22×D3×Q8D3semidirect
58. C2×#947D3semidirect
99. C2×C3×Dic6D4semidirect
142. C2×D3×Q8C2×D3semidirect
163. #947C2×D3semidirect
212. C22×C3×D3#41semidirect
237. C3×Dic6C2×D4semidirect
330. C2×Dic6#67semidirect
375. C2×C3×D3C2×#41semidirect
448. C22×D3#239semidirect
514. Dic6C2×#67semidirect
515. C2×C32#548semidirect
608. C2×D3C2×#239semidirect
629. C32C2×#548semidirect
676. C2×C3#5677semidirect
677. C2×C3#5817semidirect
714. C3C2×#5677semidirect
715. C3C2×#5817semidirect
719. C2#10595401direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C22×#37962
C2×#641552
C2×C3×#9472
#105954012
C2×#639082
C2×#639072
C2×#639062
C2×C4×#6262
C2×#638872
C2×#638792
C2×Dic3×Dic62
C2×#58173
C2×#56773