Finite Group Databasebeta

← C2×#10595254 #11902439

Subgroups — C2×#10595254 #11902439

Order 1152.

4481 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C3×#237C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#63981C212yesmaximal, complemented
5C2×#63978C212yesmaximal, complemented
6C2×#63966C212yesmaximal, complemented
7C22×#3722C212yesmaximal, complemented
8#10595254C2116yesmaximal, direct product factor
9C2×#63909C211yesmaximal, characteristic, complemented
10C2×C4×#626C211yesmaximal, characteristic, complemented
11C2×#63871C211yesmaximal, characteristic, complemented
12C2×#63864C211yesmaximal, characteristic, complemented
13C2×#5829—31nomaximal
14C2×#5554—31nomaximal
15C24×C3⋊D3C2212yes—
16C22×C32×D4C2211yescharacteristic
17C22×#638C2212yes—
18C2×D4×C3⋊D3—28no—
19C2×D4×C3⋊D3C2218yescomplemented
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×#67C2212yescomplemented
23C23×C3×Dic3C2212yescomplemented
24C23×C3×Dic3C2212yescomplemented
25C2×C3×#237—28no—
26C2×C3×#237C2218yescomplemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×Dic6C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic
30C22×#626C2212yescomplemented
31C2×C3×#217C2212yescomplemented
32C3×D4×Dic3C2218yescomplemented
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C2×C3×C4×Dic3C2211yescharacteristic, complemented
35#63981C22116yescomplemented
36#63978C22116yescomplemented
37#63966C22116yescomplemented
38C2×Dic3⋊Dic3C2212yescomplemented
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×#3722C2212yes—
41C2×#3722C2211yescharacteristic
42C2×#3722C22116yescomplemented
43C2×#3722C2212yescomplemented
44C2×#3722C2212yescomplemented
45C2×#3722C2212yescomplemented
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47#63909C2218yescomplemented
48C4×#626C2218yescomplemented
49#63871C2218yescomplemented
50#63864C2218yescomplemented
51C22×C3×#41—31no—
52C22×#237D311yescharacteristic, complemented
53C22×D3×D4—31no—
54C22×D3×D4—31no—
55C22×D3×D4—61no—
56C2×C3×C4×D4—31no—
57#5829—316no—
58C2×#947—31no—
59C2×#946—31no—
60C2×#939—32no—
61C2×#937—32no—
62C2×D4×Dic3D311yescharacteristic, complemented
63C2×#930—32no—
64C2×#930—31no—
65C2×#929—32no—
66C2×C4×#67—31no—
67C22×(C2×D3)⋊C4—32no—
68C22×(C2×D3)⋊C4—32no—
69#5554—316no—
70C2×#897—31no—
71C2×#895—31no—
72C2×#886—32no—
73C2×#882—32no—
74C2×#875—31no—
75C2×C4×D12—31no—
76C24×C32C2312yes—
77C23×C3⋊D3—28no—
78C23×C3⋊D3—28no—
79C23×C3⋊D3—44no—
80C23×C3⋊D3C2312yes—
81C23×C3⋊D3C2318yes—
82C23×C3⋊D3C2311yescharacteristic
83C23×C3×D3C2311yescharacteristic
84C2×C32×D4D418yescomplemented
85C2×C32×D4C2314yes—
86C22×C32×C4C2311yescharacteristic
87C2×#638—28no—
88C2×#638C2318yes—
89C22×C3⋊Dic3C2311yescharacteristic
90D4×C3⋊D3—232no—
91C2×C4⋊(C3⋊D3)—24no—
92C2×C4⋊(C3⋊D3)C2314yes—
93C2×C4×C3⋊D3—24no—
94C2×C4×C3⋊D3C2314yes—
95C2×C3×#67—28no—
96C2×C3×#67C2318yescomplemented
97C22×C3×Dic3—28no—
98C22×C3×Dic3—44no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2312yes—
102C22×C3×Dic3C2312yes—
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2318yescomplemented
105C22×C3×Dic3C2318yescomplemented
106C3×#237—232no—
107C2×C3×C4×D3—24no—
108C2×C3×C4×D3C2314yescomplemented
109C2×C3×Dic6—24no—
110C2×C3×Dic6C2314yescomplemented
111C2×#626—24no—
112C2×#626—44no—
113C2×#626C2314yes—
114C2×#626C2318yescomplemented
115C3×#217C2318yescomplemented
116C3×C4⋊Dic3C2314yescomplemented
117C3×C4×Dic3C2314yescomplemented
118Dic3⋊Dic3C2318yescomplemented
119Dic3⋊Dic3C2314yescomplemented
120#3722C2318yes—
121#3722C2314yes—
122#3722C2318yescomplemented
123#3722C2318yescomplemented
124#3722C2318yescomplemented
125(C2×D3)⋊Dic3C2314yescomplemented
126C2×#546—91noSylow
127C24×D3—32no—
128C24×D3—32no—
129C24×D3—62no—
130C2×C3×#41—38no—
131C2×C3×#41—68no—
132C22×C3×Q8—31no—
133C22×C3×D4—21no—
134C22×C3×D4—32no—
135C22×C3×D4C2×D311yescharacteristic
136C22×C3×D4C2×D311yescharacteristic
137C23×C3×C4—32no—
138C23×C3×C4—32no—
139C23×C3×C4—31no—
140C22×#67—32no—
141C22×#67—32no—
142C22×#67—31no—
143C22×#67—32no—
144C22×#67—62no—
145C22×#67C2×D312yescomplemented
146C23×Dic3C2×D312yescomplemented
147C23×Dic3C2×D312yescomplemented
148C2×#237—28no—
149C2×#237C2×D318yescomplemented
150C2×D3×D4—38no—
151C2×D3×D4—38no—
152C2×D3×D4—68no—
153C2×D3×D4—616no—
154C2×D3×D4—68no—
155C2×D3×D4—68no—
156C22×D12—31no—
157C22×D12—31no—
158C22×D12—31no—
159C22×D12—32no—
160C22×D12—61no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—61no—
164C22×C4×D3C2×D311yescharacteristic, complemented
165C22×Dic6C2×D311yescharacteristic, complemented
166C3×C4×D4—38no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—32no—
169C2×C3×C42—31no—
170C2×#217—31no—
171C2×#217C2×D312yescomplemented
172#947—38no—
173#946—38no—
174#939—316no—
175#937—316no—
176D4×Dic3C2×D318yescomplemented
177#930—316no—
178#930—38no—
179#929—316no—
180C4×#67—38no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—32no—
184C2×(C2×D3)⋊C4—32no—
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—32no—
190C2×(C2×D3)⋊C4—32no—
191C2×(C2×D3)⋊C4—32no—
192C2×(C2×D3)⋊C4—316no—
193C2×(C2×D3)⋊C4—316no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—32no—
196C2×C4⋊Dic3C2×D311yescharacteristic, complemented
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—32no—
199C2×C4×Dic3C2×D311yescharacteristic, complemented
200#897—38no—
201#895—38no—
202#886—316no—
203#882—316no—
204#875—38no—
205C4×D12—38no—
206C23×C32—24no—
207C23×C32—24no—
208C23×C32C2×D418yes—
209C23×C32C2414yes—
210C23×C32C2411yescharacteristic
211C22×C3⋊D3—22no—
212C22×C3⋊D3—22no—
213C22×C3⋊D3—24no—
214C22×C3⋊D3—216no—
215C22×C3⋊D3—24no—
216C22×C3⋊D3—24no—
217C22×C3⋊D3—216no—
218C22×C3⋊D3—48no—
219C22×C3⋊D3—432no—
220C22×C3⋊D3#4114yescomplemented
221C22×C3⋊D3C2414yes—
222C22×C3⋊D3C2412yes—
223C22×C3×D3—22no—
224C22×C3×D3—22no—
225C22×C3×D3—22no—
226C22×C3×D3C2412yes—
227C32×D4C2×D4116yescomplemented
228C2×C32×C4C2×D414yes—
229C2×C32×C4C2412yes—
230#638—216no—
231C2×C3⋊Dic3—22no—
232C2×C3⋊Dic3C2412yes—
233C4⋊(C3⋊D3)—28no—
234C4×C3⋊D3—28no—
235C3×#67—216no—
236C2×C3×Dic3—24no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—216no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—24no—
241C2×C3×Dic3—22no—
242C2×C3×Dic3—48no—
243C2×C3×Dic3C2412yes—
244C2×C3×Dic3C2414yes—
245C2×C3×Dic3C2412yes—
246C2×C3×Dic3C2414yes—
247C2×C3×Dic3C2412yes—
248C3×C4×D3—28no—
249C3×Dic6—28no—
250#626—28no—
251#626—48no—
252C22×#41—31no—
253C23×D4—91no—
254#546—916no—
255C2×#124—91no—
256C2×#123—92no—
257C2×C22⋊Q8—91no—
258C2×#121—91no—
259C2×#121—92no—
260C2×#120—92no—
261C2×C4×D4—31no—
262C2×C4×D4—91no—
263C22×C22⋊C4—92no—
264C24×C3—22no—
265C24×C3—31no—
266C24×C3C22×D312yes—
267C24×C3C22×D312yes—
268C23×D3—31no—
269C23×D3—31no—
270C23×D3—32no—
271C23×D3—32no—
272C23×D3—38no—
273C23×D3—38no—
274C23×D3—61no—
275C23×D3—62no—
276C23×D3—68no—
277C23×D3—68no—
278C23×D3—68no—
279C23×D3—616no—
280C23×D3—68no—
281C23×D3—68no—
282C23×D3—128no—
283C23×D3—124no—
284C23×D3—124no—
285C23×D3—128no—
286C23×D3C22×D311yescharacteristic
287C3×#41—632no—
288C2×C3×Q8—34no—
289C2×C3×Q8—64no—
290C2×C3×D4—28no—
291C2×C3×D4—24no—
292C2×C3×D4—38no—
293C2×C3×D4—68no—
294C2×C3×D4D1218yescomplemented
295C2×C3×D4#6718yescomplemented
296C2×C3×D4C22×D314yes—
297C2×C3×D4C22×D314yes—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—32no—
301C22×C3×C4—31no—
302C22×C3×C4—32no—
303C22×C3×C4—31no—
304C22×C3×C4—38no—
305C22×C3×C4—38no—
306C22×C3×C4—34no—
307C22×C3×C4—68no—
308C22×C3×C4—64no—
309C22×C3×C4—124no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—28no—
313C2×#67—38no—
314C2×#67—38no—
315C2×#67—34no—
316C2×#67—38no—
317C2×#67—68no—
318C2×#67—64no—
319C2×#67—616no—
320C2×#67—68no—
321C2×#67—68no—
322C2×#67—124no—
323C2×#67C22×D318yescomplemented
324C22×Dic3—28no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—44no—
328C22×Dic3—61no—
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D312yes—
332C22×Dic3C22×D312yes—
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D318yescomplemented
335C22×Dic3C22×D318yescomplemented
336#237—232no—
337D3×D4—664no—
338D3×D4—632no—
339D3×D4—632no—
340C2×D12—34no—
341C2×D12—34no—
342C2×D12—34no—
343C2×D12—38no—
344C2×D12—64no—
345C2×D12—68no—
346C2×D12—64no—
347C2×D12—64no—
348C2×D12—64no—
349C2×D12—124no—
350C2×C4×D3—24no—
351C2×C4×D3—34no—
352C2×C4×D3—34no—
353C2×C4×D3—64no—
354C2×C4×D3—68no—
355C2×C4×D3—64no—
356C2×C4×D3—64no—
357C2×C4×D3C22×D314yescomplemented
358C2×Dic6—24no—
359C2×Dic6C22×D314yescomplemented
360C3×C4⋊C4—34no—
361C3×C22⋊C4—38no—
362C3×C42—34no—
363#217—34no—
364#217C22×D318yescomplemented
365(C2×D3)⋊C4—34no—
366(C2×D3)⋊C4—34no—
367(C2×D3)⋊C4—38no—
368(C2×D3)⋊C4—38no—
369(C2×D3)⋊C4—38no—
370(C2×D3)⋊C4—38no—
371(C2×D3)⋊C4—34no—
372(C2×D3)⋊C4—38no—
373(C2×D3)⋊C4—38no—
374(C2×D3)⋊C4—38no—
375(C2×D3)⋊C4—38no—
376C4⋊Dic3—34no—
377C4⋊Dic3—38no—
378C4⋊Dic3C22×D314yescomplemented
379Dic3⋊C4—34no—
380Dic3⋊C4—38no—
381C4×Dic3C22×D314yescomplemented
382C22×C32—216no—
383C22×C32—24no—
384C22×C32—24no—
385C22×C32C22×D418yes—
386C22×C32C22×D412yes—
387C22×C32C2×#4112yes—
388C22×C32H(5,𝔽2)12yes—
389C22×C32C2511yescharacteristic
390C2×C3⋊D3—28no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
393C2×C3⋊D3—24no—
394C2×C3⋊D3—24no—
395C2×C3⋊D3—24no—
396C2×C3⋊D3—432no—
397C2×C3⋊D3—48no—
398C2×C3⋊D3C2×#4114yescomplemented
399C2×C3×D3—22no—
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—44no—
403C32×C4C22×D414yes—
404C3⋊Dic3—22no—
405C3×Dic3—24no—
406C3×Dic3—22no—
407C3×Dic3—22no—
408C3×Dic3—24no—
409C3×Dic3—22no—
410C25—92no—
411C2×#41—38no—
412C2×#41—68no—
413C22×Q8—31no—
414C22×D4—32no—
415C22×D4—91no—
416C22×D4—92no—
417C22×D4—92no—
418C22×D4—98no—
419C22×D4—91no—
420C22×D4—188no—
421C22×D4D3211yescharacteristic
422C23×C4—32no—
423C23×C4—32no—
424C23×C4—31no—
425C23×C4—91no—
426#124—98no—
427#123—916no—
428C22⋊Q8—98no—
429#121—98no—
430#121—916no—
431#120—916no—
432C4×D4—38no—
433C4×D4—98no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—92no—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—91no—
439C2×C22⋊C4—92no—
440C2×C22⋊C4—92no—
441C2×C22⋊C4—92no—
442C2×C22⋊C4—916no—
443C2×C22⋊C4—92no—
444C2×C22⋊C4—91no—
445C2×C42—31no—
446C23×C3—24no—
447C23×C3—24no—
448C23×C3—24no—
449C23×C3—24no—
450C23×C3—24no—
451C23×C3—21no—
452C23×C3—28no—
453C23×C3—32no—
454C23×C3—44no—
455C23×C3—44no—
456C23×C3—62no—
457C23×C3—62no—
458C23×C3—62no—
459C23×C3C2×D1218yes—
460C23×C3C2×#6718yes—
461C23×C3C23×D314yes—
462C23×C3C23×D314yes—
463C23×C3C23×D311yescharacteristic
464C23×C3C23×D311yescharacteristic
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—34no—
469C22×D3—34no—
470C22×D3—32no—
471C22×D3—32no—
472C22×D3—34no—
473C22×D3—34no—
474C22×D3—64no—
475C22×D3—62no—
476C22×D3—64no—
477C22×D3—616no—
478C22×D3—616no—
479C22×D3—64no—
480C22×D3—64no—
481C22×D3—62no—
482C22×D3—62no—
483C22×D3—62no—
484C22×D3—62no—
485C22×D3—68no—
486C22×D3—632no—
487C22×D3—64no—
488C22×D3—616no—
489C22×D3—64no—
490C22×D3—64no—
491C22×D3—64no—
492C22×D3—64no—
493C22×D3—64no—
494C22×D3—616no—
495C22×D3—1216no—
496C22×D3—124no—
497C22×D3—124no—
498C22×D3—128no—
499C22×D3—128no—
500C22×D3—1232no—
501C22×D3—1232no—
502C22×D3—1216no—
503C22×D3—1264no—
504C22×D3C23×D312yes—
505C3×Q8—68no—
506C3×D4—216no—
507C3×D4—616no—
508C3×D4C2×D12116yescomplemented
509C3×D4C2×#67116yescomplemented
510C2×C3×C4—22no—
511C2×C3×C4—24no—
512C2×C3×C4—32no—
513C2×C3×C4—34no—
514C2×C3×C4—32no—
515C2×C3×C4—34no—
516C2×C3×C4—32no—
517C2×C3×C4—62no—
518C2×C3×C4—64no—
519C2×C3×C4—616no—
520C2×C3×C4—62no—
521C2×C3×C4—64no—
522C2×C3×C4—62no—
523C2×C3×C4—68no—
524C2×C3×C4—128no—
525C2×C3×C4C2×D1214yes—
526C2×C3×C4C2×#6714yes—
527C2×C3×C4C23×D312yes—
528C2×C3×C4C23×D312yes—
529#67—216no—
530#67—68no—
531#67—632no—
532#67—616no—
533#67—616no—
534#67—128no—
535C2×Dic3—22no—
536C2×Dic3—24no—
537C2×Dic3—22no—
538C2×Dic3—24no—
539C2×Dic3—22no—
540C2×Dic3—216no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—48no—
544C2×Dic3—62no—
545C2×Dic3—64no—
546C2×Dic3—62no—
547C2×Dic3—62no—
548C2×Dic3C23×D312yes—
549C2×Dic3C23×D312yes—
550C2×Dic3C23×D314yes—
551C2×Dic3C23×D314yes—
552C2×Dic3C23×D312yes—
553D12—616no—
554D12—68no—
555D12—68no—
556D12—68no—
557D12—128no—
558C4×D3—28no—
559C4×D3—616no—
560C4×D3—68no—
561C4×D3—68no—
562Dic6—28no—
563C2×C32—28no—
564C2×C32#54614yescomplemented
565C2×C32C23×D411yescharacteristic
566C2×C32C22×#4111yescharacteristic
567C2×C32C2×H(5,𝔽2)11yescharacteristic
568C3⋊D3—24no—
569C3⋊D3—44no—
570C3×D3—42no—
571C24—31no—
572C24—91no—
573C24—92no—
574C24—98no—
575C24—188no—
576C24—188no—
577C24—364no—
578C24C2×D3212yes—
579#41—632no—
580C2×Q8—34no—
581C2×Q8—64no—
582C2×D4—38no—
583C2×D4—68no—
584C2×D4—94no—
585C2×D4—98no—
586C2×D4—98no—
587C2×D4—94no—
588C2×D4—184no—
589C2×D4—188no—
590C2×D4—1832no—
591C2×D4—184no—
592C2×D4—364no—
593C2×D4#62618yescomplemented
594C2×D4C2×D3214yes—
595C22×C4—38no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—32no—
599C22×C4—31no—
600C22×C4—32no—
601C22×C4—38no—
602C22×C4—34no—
603C22×C4—68no—
604C22×C4—64no—
605C22×C4—91no—
606C22×C4—94no—
607C22×C4—124no—
608C22×C4—184no—
609C22×C4C2×D3211yescharacteristic
610C4⋊C4—34no—
611C4⋊C4—94no—
612C4⋊C4—98no—
613C22⋊C4—38no—
614C22⋊C4—94no—
615C22⋊C4—98no—
616C22⋊C4—98no—
617C22⋊C4—98no—
618C22⋊C4—98no—
619C22⋊C4—94no—
620C42—34no—
621C22×C3—24no—
622C22×C3—24no—
623C22×C3—24no—
624C22×C3—24no—
625C22×C3—216no—
626C22×C3—216no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—28no—
631C22×C3—21no—
632C22×C3—44no—
633C22×C3—44no—
634C22×C3—416no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3—124no—
639C22×C3C22×D1218yes—
640C22×C3C22×D1212yes—
641C22×C3#100412yes—
642C22×C3D3×#4112yes—
643C22×C3D3×#4112yes—
644C22×C3#100912yes—
645C22×C3C22×#6718yes—
646C22×C3C22×#6712yes—
647C22×C3C24×D311yescharacteristic
648C22×C3C24×D311yescharacteristic
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—34no—
653C2×D3—34no—
654C2×D3—44no—
655C2×D3—64no—
656C2×D3—64no—
657C2×D3—64no—
658C2×D3—616no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—68no—
664C2×D3—68no—
665C2×D3—68no—
666C2×D3—64no—
667C2×D3—64no—
668C2×D3—64no—
669C2×D3—64no—
670C2×D3—64no—
671C2×D3—64no—
672C2×D3—124no—
673C2×D3—124no—
674C2×D3—1232no—
675C2×D3—1232no—
676C2×D3—1264no—
677C2×D3—1216no—
678C2×D3—128no—
679C2×D3—128no—
680C3×C4—24no—
681C3×C4—62no—
682C3×C4—64no—
683C3×C4—62no—
684C3×C4—64no—
685C3×C4—62no—
686C3×C4C22×D1214yes—
687C3×C4C22×#6714yes—
688Dic3—22no—
689Dic3—24no—
690Dic3—22no—
691Dic3—24no—
692Dic3—22no—
693Dic3—64no—
694Dic3—62no—
695Dic3—62no—
696C32C2×#54611yescharacteristic, complemented, Sylow
697C23—24no—
698C23—24no—
699C23—32no—
700C23—62no—
701C23—62no—
702C23—62no—
703C23—94no—
704C23—92no—
705C23—94no—
706C23—1816no—
707C23—182no—
708C23—182no—
709C23—184no—
710C23—184no—
711C23—1816no—
712C23—184no—
713C23—368no—
714C23—3632no—
715C23C2×#62618yes—
716C23C22×D3214yes—
717C23C22×D3211yescharacteristic
718Q8—68no—
719D4—616no—
720D4—188no—
721D4—1816no—
722D4—188no—
723D4—368no—
724D4C2×#626116yescomplemented
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—34no—
728C2×C4—32no—
729C2×C4—34no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—64no—
733C2×C4—62no—
734C2×C4—64no—
735C2×C4—616no—
736C2×C4—68no—
737C2×C4—92no—
738C2×C4—128no—
739C2×C4—182no—
740C2×C4—188no—
741C2×C4C2×#62614yes—
742C2×C4C22×D3212yes—
743C2×C3—28no—
744C2×C3—28no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—24no—
749C2×C3—48no—
750C2×C3—122no—
751C2×C3#555414yescomplemented
752C2×C3#582914yescomplemented
753C2×C3C23×D1211yescharacteristic
754C2×C3C2×#100411yescharacteristic
755C2×C3C2×D3×#4111yescharacteristic
756C2×C3C2×D3×#4111yescharacteristic
757C2×C3C2×#100911yescharacteristic
758C2×C3C23×#6711yescharacteristic
759D3—42no—
760D3—68no—
761D3—64no—
762D3—64no—
763D3—128no—
764D3—124no—
765D3—124no—
766C22—24no—
767C22—24no—
768C22—216no—
769C22—62no—
770C22—62no—
771C22—62no—
772C22—94no—
773C22—124no—
774C22—182no—
775C22—182no—
776C22—188no—
777C22—184no—
778C22—184no—
779C22—184no—
780C22—3632no—
781C22—368no—
782C22#6431212yes—
783C22#6431412yes—
784C22C22×#62618yes—
785C22C22×#62612yes—
786C22C23×D3211yescharacteristic
787C4—62no—
788C4—62no—
789C4—64no—
790C4—62no—
791C4—64no—
792C4—182no—
793C4C22×#62614yes—
794C3—21no—
795C3C2×#555411yescharacteristic, complemented
796C3C2×#582911yescharacteristic, complemented
797C2—28no—
798C2—122no—
799C2—184no—
800C2—364no—
801C2#1059525414yesdirect product factor
802C2C2×#6431211yescharacteristic
803C2C2×#6431411yescharacteristic
804C2C23×#62611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D4×C3⋊D3C2semidirect
2. C22×C3×#237C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×#63981C2semidirect
5. C2×#63978C2semidirect
6. C2×#63966C2semidirect
7. C22×#3722C2semidirect
8. #10595254C2direct (N × H)
9. C2×#63909C2semidirect
10. C2×C4×#626C2semidirect
11. C2×#63871C2semidirect
12. C2×#63864C2semidirect
19. C2×D4×C3⋊D3C22semidirect
22. C22×C3×#67C22semidirect
23. C23×C3×Dic3C22semidirect
24. C23×C3×Dic3C22semidirect
26. C2×C3×#237C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×C3×Dic6C22semidirect
30. C22×#626C22semidirect
31. C2×C3×#217C22semidirect
32. C3×D4×Dic3C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. #63981C22semidirect
36. #63978C22semidirect
37. #63966C22semidirect
38. C2×Dic3⋊Dic3C22semidirect
39. C2×Dic3⋊Dic3C22semidirect
42. C2×#3722C22semidirect
43. C2×#3722C22semidirect
44. C2×#3722C22semidirect
45. C2×#3722C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. #63909C22semidirect
48. C4×#626C22semidirect
49. #63871C22semidirect
50. #63864C22semidirect
52. C22×#237D3semidirect
62. C2×D4×Dic3D3semidirect
84. C2×C32×D4D4semidirect
96. C2×C3×#67C23semidirect
104. C22×C3×Dic3C23semidirect
105. C22×C3×Dic3C23semidirect
108. C2×C3×C4×D3C23semidirect
110. C2×C3×Dic6C23semidirect
114. C2×#626C23semidirect
115. C3×#217C23semidirect
116. C3×C4⋊Dic3C23semidirect
117. C3×C4×Dic3C23semidirect
118. Dic3⋊Dic3C23semidirect
119. Dic3⋊Dic3C23semidirect
122. #3722C23semidirect
123. #3722C23semidirect
124. #3722C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
145. C22×#67C2×D3semidirect
146. C23×Dic3C2×D3semidirect
147. C23×Dic3C2×D3semidirect
149. C2×#237C2×D3semidirect
164. C22×C4×D3C2×D3semidirect
165. C22×Dic6C2×D3semidirect
171. C2×#217C2×D3semidirect
176. D4×Dic3C2×D3semidirect
196. C2×C4⋊Dic3C2×D3semidirect
199. C2×C4×Dic3C2×D3semidirect
220. C22×C3⋊D3#41semidirect
227. C32×D4C2×D4semidirect
294. C2×C3×D4D12semidirect
295. C2×C3×D4#67semidirect
323. C2×#67C22×D3semidirect
334. C22×Dic3C22×D3semidirect
335. C22×Dic3C22×D3semidirect
357. C2×C4×D3C22×D3semidirect
359. C2×Dic6C22×D3semidirect
364. #217C22×D3semidirect
378. C4⋊Dic3C22×D3semidirect
381. C4×Dic3C22×D3semidirect
398. C2×C3⋊D3C2×#41semidirect
508. C3×D4C2×D12semidirect
509. C3×D4C2×#67semidirect
564. C2×C32#546semidirect
593. C2×D4#626semidirect
696. C32C2×#546semidirect
724. D4C2×#626semidirect
751. C2×C3#5554semidirect
752. C2×C3#5829semidirect
795. C3C2×#5554semidirect
796. C3C2×#5829semidirect
801. C2#10595254direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C22×C3×#2372
C2×C3×D4×Dic32
C2×#639812
C2×#639782
C2×#639662
C22×#37222
#105952542
C2×#639092
C2×C4×#6262
C2×#638712
C2×#638642
C2×#58293
C2×#55543