Finite Group Databasebeta

← C2×#10595431 #11902457

Subgroups — C2×#10595431 #11902457

Order 1152.

4245 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3832C211yesmaximal, characteristic, complemented
2C22×D3×D12C211yesmaximal, characteristic, complemented
3C2×C3×#947C211yesmaximal, characteristic, complemented
4C2×C3×#946C211yesmaximal, characteristic, complemented
5#10595431C2116yesmaximal, direct product factor
6C2×#63923C212yesmaximal, complemented
7C2×#63921C212yesmaximal, complemented
8C2×#63916C211yesmaximal, characteristic, complemented
9C2×#63910C212yesmaximal, complemented
10C2×C4×#626C211yesmaximal, characteristic, complemented
11C2×#63894C211yesmaximal, characteristic, complemented
12C2×#63853C212yesmaximal, complemented
13C2×#5676—31nomaximal
14C2×#5630—31nomaximal
15C23×D32C2212yes—
16C22×C32×Q8C2211yescharacteristic, complemented
17C2×#3832—28no—
18C2×#3832C2218yescomplemented
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2212yescomplemented
21C22×C4×C3⋊D3C2212yescomplemented
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×#626C2212yes—
26C22×#626C2211yescharacteristic
27C22×#626C2212yescomplemented
28C22×#624C2212yescomplemented
29C2×D3×D12—28no—
30C2×D3×D12C2218yescomplemented
31C3×#947C2218yescomplemented
32C3×#946C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×(C2×D3)⋊C4C2212yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yescomplemented
36C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C3×Dic3⋊C4C2212yescomplemented
38C2×C3×C4×Dic3C2211yescharacteristic, complemented
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×#3722C2212yescomplemented
41C2×#3722C2211yescharacteristic, complemented
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2212yescomplemented
44#63923C22116yescomplemented
45#63921C22116yescomplemented
46#63916C2218yescomplemented
47#63910C22116yescomplemented
48C4×#626C2218yescomplemented
49#63894C2218yescomplemented
50#63853C22116yescomplemented
51C22×#239—31no—
52C22×#239—31no—
53C22×#239—61no—
54C22×D3×D4—31no—
55C23×D12—31no—
56C2×C3×#124—31no—
57C2×C3×C22⋊Q8—31no—
58C2×#947D311yescharacteristic, complemented
59C2×#946D311yescharacteristic, complemented
60C2×#938—31no—
61C2×C4×#67—31no—
62#5676—316no—
63#5630—316no—
64C2×#895—31no—
65C2×#895—32no—
66C2×#894—32no—
67C2×#893—31no—
68C2×#884—32no—
69C2×#883—32no—
70C2×#882—32no—
71C2×#882—32no—
72C2×D3×C22⋊C4—32no—
73C2×D3×C22⋊C4—32no—
74C2×C4×D12—31no—
75C2×C4×D12—31no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3⋊D3C2312yes—
78C23×C3×D3C2312yes—
79C23×C3×D3C2311yescharacteristic
80C22×D32—28no—
81C22×D32—28no—
82C22×D32—44no—
83C22×D32C2318yes—
84C2×C32×Q8—24no—
85C2×C32×Q8C2314yescomplemented
86C22×C32×C4C2312yes—
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89#3832—232no—
90C2×C4⋊(C3⋊D3)—28no—
91C2×C4⋊(C3⋊D3)D418yescomplemented
92C2×C4⋊(C3⋊D3)C2314yes—
93C2×C4⋊(C3⋊D3)C2318yescomplemented
94C2×C4×C3⋊D3—28no—
95C2×C4×C3⋊D3—24no—
96C2×C4×C3⋊D3C2318yescomplemented
97C2×C4×C3⋊D3C2314yescomplemented
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2312yes—
102C2×C3×D12—24no—
103C2×C3×D12C2314yes—
104C2×C3×C4×D3—24no—
105C2×C3×C4×D3C2314yes—
106C2×#626—28no—
107C2×#626—24no—
108C2×#626—44no—
109C2×#626C2318yes—
110C2×#626C2314yes—
111C2×#626C2318yescomplemented
112C2×#624—44no—
113C2×#624C2318yescomplemented
114D3×D12—232no—
115C3×(C2×D3)⋊C4C2318yes—
116C3×(C2×D3)⋊C4C2318yescomplemented
117C3×(C2×D3)⋊C4C2318yescomplemented
118C3×C4⋊Dic3C2314yescomplemented
119C3×Dic3⋊C4C2318yescomplemented
120C3×C4×Dic3C2314yescomplemented
121Dic3⋊Dic3C2314yescomplemented
122#3722C2318yescomplemented
123#3722C2314yescomplemented
124(C2×D3)⋊Dic3C2314yes—
125(C2×D3)⋊Dic3C2318yescomplemented
126C2×#546—91noSylow
127C24×D3—32no—
128C24×D3—32no—
129C22×C3×Q8—21no—
130C22×C3×Q8C2×D311yescharacteristic, complemented
131C22×C3×Q8C2×D311yescharacteristic, complemented
132C22×C3×D4—31no—
133C23×C3×C4—31no—
134C22×#67—32no—
135C22×#67—31no—
136C22×#67—32no—
137C2×#239—38no—
138C2×#239—38no—
139C2×#239—68no—
140C2×#239—68no—
141C2×#239—68no—
142C2×#239—616no—
143C2×D3×D4—38no—
144C2×D3×D4—68no—
145C22×D12—31no—
146C22×D12—31no—
147C22×D12—32no—
148C22×D12—31no—
149C22×D12—32no—
150C22×D12—32no—
151C22×D12—32no—
152C22×D12—38no—
153C22×D12—61no—
154C22×D12—62no—
155C22×D12—68no—
156C22×D12C2×D311yescharacteristic
157C22×C4×D3—31no—
158C22×C4×D3—32no—
159C22×C4×D3—32no—
160C22×C4×D3—31no—
161C22×C4×D3—32no—
162C22×C4×D3—32no—
163C22×C4×D3—62no—
164C22×C4×D3—61no—
165C22×C4×D3C2×D311yescharacteristic
166C3×#124—38no—
167C3×C22⋊Q8—38no—
168C2×C3×C4⋊C4—32no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C22⋊C4—32no—
171C2×C3×C22⋊C4—32no—
172C2×C3×C22⋊C4—32no—
173C2×C3×C42—31no—
174C2×#217—31no—
175C2×#217—32no—
176#947C2×D318yescomplemented
177#946C2×D318yescomplemented
178#938—38no—
179C4×#67—38no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—32no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4C2×D312yes—
187C2×(C2×D3)⋊C4C2×D312yescomplemented
188C2×(C2×D3)⋊C4C2×D312yescomplemented
189C2×C4⋊Dic3—31no—
190C2×C4⋊Dic3C2×D311yescharacteristic, complemented
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4C2×D312yescomplemented
193C2×C4×Dic3C2×D311yescharacteristic, complemented
194#895—38no—
195#895—316no—
196#894—316no—
197#893—38no—
198#884—316no—
199#883—316no—
200#882—316no—
201#882—316no—
202D3×C22⋊C4—316no—
203D3×C22⋊C4—316no—
204C4×D12—38no—
205C4×D12—38no—
206C23×C32C2411yescharacteristic
207C22×C3⋊D3—22no—
208C22×C3⋊D3—24no—
209C22×C3⋊D3—24no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3—22no—
212C22×C3⋊D3C2×D418yes—
213C22×C3⋊D3C2412yes—
214C22×C3⋊D3C2414yes—
215C22×C3×D3—22no—
216C22×C3×D3—22no—
217C22×C3×D3—24no—
218C22×C3×D3—24no—
219C22×C3×D3—24no—
220C22×C3×D3#4114yescomplemented
221C22×C3×D3C2414yes—
222C22×C3×D3C2412yes—
223C2×D32—216no—
224C2×D32—216no—
225C2×D32—48no—
226C2×D32—432no—
227C32×Q8—28no—
228C2×C32×C4—24no—
229C2×C32×C4C2×D414yes—
230C2×C32×C4C2414yes—
231C2×C32×C4C2412yes—
232C2×C3⋊Dic3—22no—
233C2×C3⋊Dic3C2412yes—
234C4⋊(C3⋊D3)—216no—
235C4⋊(C3⋊D3)C2×D4116yescomplemented
236C4×C3⋊D3—216no—
237C4×C3⋊D3—28no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—24no—
242C2×C3×Dic3C2412yes—
243C2×C3×Dic3C2414yes—
244C2×C3×Dic3C2412yes—
245C2×C3×Dic3C2412yes—
246C3×D12—28no—
247C3×C4×D3—28no—
248#626—216no—
249#626—28no—
250#626—48no—
251#624—48no—
252C22×#41—91no—
253C23×D4—91no—
254#546—916no—
255C2×#124—31no—
256C2×#123—92no—
257C2×C22⋊Q8—31no—
258C2×#121—92no—
259C2×#121—91no—
260C2×#120—92no—
261C2×C4×D4—91no—
262C2×C4×D4—91no—
263C22×C22⋊C4—92no—
264C24×C3—31no—
265C24×C3—32no—
266C23×D3—32no—
267C23×D3—32no—
268C23×D3—31no—
269C23×D3—31no—
270C23×D3—38no—
271C23×D3—38no—
272C23×D3—62no—
273C23×D3—61no—
274C23×D3—68no—
275C23×D3—68no—
276C23×D3—68no—
277C23×D3—68no—
278C23×D3—124no—
279C23×D3—124no—
280C23×D3C22×D312yes—
281C23×D3C22×D311yescharacteristic
282C2×C3×Q8—28no—
283C2×C3×Q8—24no—
284C2×C3×Q8—24no—
285C2×C3×Q8—24no—
286C2×C3×Q8C22×D314yescomplemented
287C2×C3×Q8C22×D314yescomplemented
288C2×C3×D4—34no—
289C2×C3×D4—64no—
290C22×C3×C4—22no—
291C22×C3×C4—21no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—32no—
296C22×C3×C4—34no—
297C22×C3×C4—64no—
298C22×C3×C4C22×D312yes—
299C22×C3×C4C22×D312yes—
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C2×#67—34no—
303C2×#67—38no—
304C2×#67—38no—
305C2×#67—68no—
306C2×#67—64no—
307C2×#67—124no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—61no—
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D312yes—
315#239—632no—
316#239—632no—
317#239—664no—
318D3×D4—632no—
319C2×D12—24no—
320C2×D12—38no—
321C2×D12—38no—
322C2×D12—34no—
323C2×D12—34no—
324C2×D12—34no—
325C2×D12—38no—
326C2×D12—38no—
327C2×D12—38no—
328C2×D12—38no—
329C2×D12—68no—
330C2×D12—64no—
331C2×D12—68no—
332C2×D12—632no—
333C2×D12—68no—
334C2×D12—68no—
335C2×D12—616no—
336C2×D12—68no—
337C2×D12—64no—
338C2×D12—124no—
339C2×D12C22×D314yes—
340C2×C4×D3—24no—
341C2×C4×D3—34no—
342C2×C4×D3—38no—
343C2×C4×D3—38no—
344C2×C4×D3—34no—
345C2×C4×D3—38no—
346C2×C4×D3—38no—
347C2×C4×D3—68no—
348C2×C4×D3—64no—
349C2×C4×D3—68no—
350C2×C4×D3—68no—
351C2×C4×D3—616no—
352C2×C4×D3—68no—
353C2×C4×D3—64no—
354C2×C4×D3—64no—
355C2×C4×D3—124no—
356C2×C4×D3—124no—
357C2×C4×D3C22×D314yes—
358C3×C4⋊C4—34no—
359C3×C4⋊C4—38no—
360C3×C22⋊C4—38no—
361C3×C22⋊C4—38no—
362C3×C22⋊C4—38no—
363C3×C42—34no—
364#217—34no—
365#217—38no—
366(C2×D3)⋊C4—34no—
367(C2×D3)⋊C4—38no—
368(C2×D3)⋊C4—38no—
369(C2×D3)⋊C4—34no—
370(C2×D3)⋊C4—38no—
371(C2×D3)⋊C4—34no—
372(C2×D3)⋊C4C22×D318yes—
373(C2×D3)⋊C4C22×D318yescomplemented
374(C2×D3)⋊C4C22×D318yescomplemented
375C4⋊Dic3—34no—
376C4⋊Dic3C22×D314yescomplemented
377Dic3⋊C4—34no—
378Dic3⋊C4C22×D318yescomplemented
379C4×Dic3C22×D314yescomplemented
380C22×C32C22×D412yes—
381C22×C32C2×#4112yes—
382C22×C32H(5,𝔽2)12yes—
383C22×C32C2511yescharacteristic
384C2×C3⋊D3—22no—
385C2×C3⋊D3—216no—
386C2×C3⋊D3—24no—
387C2×C3⋊D3—24no—
388C2×C3⋊D3—22no—
389C2×C3⋊D3—22no—
390C2×C3⋊D3—44no—
391C2×C3⋊D3C22×D418yes—
392C2×C3×D3—28no—
393C2×C3×D3—22no—
394C2×C3×D3—22no—
395C2×C3×D3—24no—
396C2×C3×D3—24no—
397C2×C3×D3—24no—
398C2×C3×D3—48no—
399C2×C3×D3C2×#4114yescomplemented
400D32—432no—
401C32×C4—24no—
402C32×C4C22×D414yes—
403C3⋊Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—22no—
407C3×Dic3—24no—
408C25—92no—
409C2×#41—98no—
410C2×#41—188no—
411C22×Q8D3211yescharacteristic, complemented
412C22×D4—31no—
413C22×D4—98no—
414C22×D4—91no—
415C22×D4—92no—
416C22×D4—92no—
417C22×D4—91no—
418C22×D4—92no—
419C22×D4—188no—
420C23×C4—31no—
421C23×C4—92no—
422C23×C4—92no—
423C23×C4—91no—
424#124—38no—
425#123—916no—
426C22⋊Q8—38no—
427#121—916no—
428#121—98no—
429#120—916no—
430C4×D4—98no—
431C4×D4—98no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—32no—
434C2×C4⋊C4—91no—
435C2×C22⋊C4—32no—
436C2×C22⋊C4—32no—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—916no—
439C2×C22⋊C4—92no—
440C2×C22⋊C4—91no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—92no—
443C2×C42—31no—
444C23×C3—21no—
445C23×C3—34no—
446C23×C3—32no—
447C23×C3—34no—
448C23×C3—62no—
449C23×C3—62no—
450C23×C3—64no—
451C23×C3—64no—
452C23×C3—64no—
453C23×C3C23×D311yescharacteristic
454C23×C3C23×D311yescharacteristic
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—24no—
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—38no—
461C22×D3—38no—
462C22×D3—34no—
463C22×D3—34no—
464C22×D3—32no—
465C22×D3—32no—
466C22×D3—68no—
467C22×D3—64no—
468C22×D3—62no—
469C22×D3—616no—
470C22×D3—616no—
471C22×D3—616no—
472C22×D3—64no—
473C22×D3—64no—
474C22×D3—64no—
475C22×D3—64no—
476C22×D3—64no—
477C22×D3—62no—
478C22×D3—62no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—62no—
482C22×D3—62no—
483C22×D3—616no—
484C22×D3—124no—
485C22×D3—124no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—128no—
489C22×D3—128no—
490C22×D3—1232no—
491C22×D3—1232no—
492C22×D3#23914yescomplemented
493C22×D3C23×D314yes—
494C22×D3C23×D312yes—
495C3×Q8—216no—
496C3×Q8—28no—
497C3×Q8—28no—
498C3×D4—68no—
499C2×C3×C4—28no—
500C2×C3×C4—24no—
501C2×C3×C4—24no—
502C2×C3×C4—24no—
503C2×C3×C4—22no—
504C2×C3×C4—24no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—34no—
509C2×C3×C4—62no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—64no—
513C2×C3×C4—68no—
514C2×C3×C4D3×D414yes—
515C2×C3×C4D3×D414yes—
516C2×C3×C4C23×D314yes—
517C2×C3×C4C23×D314yes—
518C2×C3×C4C23×D312yes—
519C2×C3×C4C23×D312yes—
520#67—616no—
521#67—68no—
522#67—128no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—24no—
527C2×Dic3—32no—
528C2×Dic3—32no—
529C2×Dic3—62no—
530C2×Dic3—64no—
531C2×Dic3—62no—
532C2×Dic3—62no—
533C2×Dic3C23×D312yes—
534C2×Dic3C23×D312yes—
535C2×Dic3C23×D312yes—
536C2×Dic3C23×D314yes—
537D12—28no—
538D12—316no—
539D12—316no—
540D12—616no—
541D12—616no—
542D12—616no—
543D12—632no—
544D12—616no—
545D12—68no—
546D12—128no—
547C4×D3—28no—
548C4×D3—616no—
549C4×D3—616no—
550C4×D3—632no—
551C4×D3—616no—
552C4×D3—68no—
553C4×D3—68no—
554C4×D3—128no—
555C4×D3—128no—
556C2×C32#54614yescomplemented
557C2×C32C23×D411yescharacteristic
558C2×C32C22×#4111yescharacteristic
559C2×C32C2×H(5,𝔽2)11yescharacteristic
560C3⋊D3—28no—
561C3⋊D3—42no—
562C3×D3—24no—
563C3×D3—44no—
564C24—31no—
565C24—32no—
566C24—98no—
567C24—92no—
568C24—91no—
569C24—188no—
570C24—188no—
571C24—364no—
572#41—1832no—
573C2×Q8—24no—
574C2×Q8C2×D3214yescomplemented
575C2×D4—34no—
576C2×D4—64no—
577C2×D4—94no—
578C2×D4—98no—
579C2×D4—98no—
580C2×D4—94no—
581C2×D4—98no—
582C2×D4—98no—
583C2×D4—188no—
584C2×D4—1832no—
585C2×D4—184no—
586C2×D4—188no—
587C2×D4—364no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—32no—
591C22×C4—31no—
592C22×C4—34no—
593C22×C4—64no—
594C22×C4—98no—
595C22×C4—91no—
596C22×C4—98no—
597C22×C4—94no—
598C22×C4—188no—
599C22×C4—184no—
600C22×C4—364no—
601C22×C4C2×D3212yes—
602C22×C4C2×D3211yescharacteristic
603C4⋊C4—34no—
604C4⋊C4—38no—
605C4⋊C4—94no—
606C22⋊C4—38no—
607C22⋊C4—38no—
608C22⋊C4—38no—
609C22⋊C4—98no—
610C22⋊C4—94no—
611C22⋊C4—94no—
612C22⋊C4—98no—
613C42—34no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—21no—
618C22×C3—34no—
619C22×C3—68no—
620C22×C3—62no—
621C22×C3—62no—
622C22×C3—64no—
623C22×C3—64no—
624C22×C3—64no—
625C22×C3—128no—
626C22×C3C2×D3×D412yes—
627C22×C3C2×D3×D412yes—
628C22×C3C2×#23912yes—
629C22×C3D3×#4112yes—
630C22×C3#100912yes—
631C22×C3#100912yes—
632C22×C3C24×D311yescharacteristic
633C22×C3C24×D311yescharacteristic
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—28no—
637C2×D3—24no—
638C2×D3—24no—
639C2×D3—24no—
640C2×D3—38no—
641C2×D3—38no—
642C2×D3—48no—
643C2×D3—68no—
644C2×D3—616no—
645C2×D3—64no—
646C2×D3—64no—
647C2×D3—64no—
648C2×D3—64no—
649C2×D3—616no—
650C2×D3—64no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—124no—
658C2×D3—124no—
659C2×D3—1216no—
660C2×D3—122no—
661C2×D3—122no—
662C2×D3—1232no—
663C2×D3—1232no—
664C2×D3—128no—
665C2×D3—124no—
666C2×D3—124no—
667C2×D3C2×#23914yescomplemented
668C3×C4—28no—
669C3×C4—24no—
670C3×C4—24no—
671C3×C4—24no—
672C3×C4—62no—
673C3×C4—62no—
674C3×C4—62no—
675C3×C4—64no—
676C3×C4C2×D3×D414yes—
677C3×C4C2×D3×D414yes—
678Dic3—22no—
679Dic3—22no—
680Dic3—22no—
681Dic3—24no—
682Dic3—64no—
683Dic3—62no—
684Dic3—62no—
685C32C2×#54611yescharacteristic, complemented, Sylow
686C23—34no—
687C23—32no—
688C23—34no—
689C23—62no—
690C23—62no—
691C23—64no—
692C23—64no—
693C23—64no—
694C23—98no—
695C23—94no—
696C23—92no—
697C23—1816no—
698C23—1816no—
699C23—184no—
700C23—184no—
701C23—182no—
702C23—182no—
703C23—182no—
704C23—368no—
705C23—3632no—
706C23C22×D3211yescharacteristic
707Q8—28no—
708D4—68no—
709D4—916no—
710D4—1816no—
711D4—188no—
712D4—1816no—
713D4—368no—
714C2×C4—24no—
715C2×C4—32no—
716C2×C4—32no—
717C2×C4—34no—
718C2×C4—32no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—64no—
722C2×C4—62no—
723C2×C4—68no—
724C2×C4—92no—
725C2×C4—1816no—
726C2×C4—182no—
727C2×C4—188no—
728C2×C4—368no—
729C2×C4#381114yes—
730C2×C4C22×D3214yes—
731C2×C4C22×D3212yes—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—24no—
736C2×C3—64no—
737C2×C3—124no—
738C2×C3#563014yescomplemented
739C2×C3#567614yescomplemented
740C2×C3C22×D3×D411yescharacteristic
741C2×C3C22×D3×D411yescharacteristic
742C2×C3C22×#23911yescharacteristic
743C2×C3C2×D3×#4111yescharacteristic
744C2×C3C2×#100911yescharacteristic
745C2×C3C2×#100911yescharacteristic
746D3—24no—
747D3—44no—
748D3—68no—
749D3—68no—
750D3—128no—
751D3—124no—
752D3—122no—
753D3—122no—
754C22—34no—
755C22—62no—
756C22—62no—
757C22—68no—
758C22—64no—
759C22—64no—
760C22—64no—
761C22—98no—
762C22—128no—
763C22—184no—
764C22—184no—
765C22—1816no—
766C22—182no—
767C22—182no—
768C22—182no—
769C22—3632no—
770C22—364no—
771C22D3×#23912yes—
772C22#6432012yes—
773C22C2×#381112yes—
774C22C23×D3211yescharacteristic
775C4—24no—
776C4—62no—
777C4—62no—
778C4—64no—
779C4—62no—
780C4—182no—
781C4C2×#381114yes—
782C3—21no—
783C3C2×#563011yescharacteristic, complemented
784C3C2×#567611yescharacteristic, complemented
785C2—64no—
786C2—124no—
787C2—188no—
788C2—362no—
789C2#1059543114yesdirect product factor
790C2C2×D3×#23911yescharacteristic
791C2C2×#6432011yescharacteristic
792C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3832C2semidirect
2. C22×D3×D12C2semidirect
3. C2×C3×#947C2semidirect
4. C2×C3×#946C2semidirect
5. #10595431C2direct (N × H)
6. C2×#63923C2semidirect
7. C2×#63921C2semidirect
8. C2×#63916C2semidirect
9. C2×#63910C2semidirect
10. C2×C4×#626C2semidirect
11. C2×#63894C2semidirect
12. C2×#63853C2semidirect
16. C22×C32×Q8C22semidirect
18. C2×#3832C22semidirect
20. C22×C4⋊(C3⋊D3)C22semidirect
21. C22×C4×C3⋊D3C22semidirect
22. C22×C4×C3⋊D3C22semidirect
27. C22×#626C22semidirect
28. C22×#624C22semidirect
30. C2×D3×D12C22semidirect
31. C3×#947C22semidirect
32. C3×#946C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×C4×Dic3C22semidirect
39. C2×Dic3⋊Dic3C22semidirect
40. C2×#3722C22semidirect
41. C2×#3722C22semidirect
43. C2×(C2×D3)⋊Dic3C22semidirect
44. #63923C22semidirect
45. #63921C22semidirect
46. #63916C22semidirect
47. #63910C22semidirect
48. C4×#626C22semidirect
49. #63894C22semidirect
50. #63853C22semidirect
58. C2×#947D3semidirect
59. C2×#946D3semidirect
85. C2×C32×Q8C23semidirect
91. C2×C4⋊(C3⋊D3)D4semidirect
93. C2×C4⋊(C3⋊D3)C23semidirect
96. C2×C4×C3⋊D3C23semidirect
97. C2×C4×C3⋊D3C23semidirect
111. C2×#626C23semidirect
113. C2×#624C23semidirect
116. C3×(C2×D3)⋊C4C23semidirect
117. C3×(C2×D3)⋊C4C23semidirect
118. C3×C4⋊Dic3C23semidirect
119. C3×Dic3⋊C4C23semidirect
120. C3×C4×Dic3C23semidirect
121. Dic3⋊Dic3C23semidirect
122. #3722C23semidirect
123. #3722C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
130. C22×C3×Q8C2×D3semidirect
131. C22×C3×Q8C2×D3semidirect
176. #947C2×D3semidirect
177. #946C2×D3semidirect
187. C2×(C2×D3)⋊C4C2×D3semidirect
188. C2×(C2×D3)⋊C4C2×D3semidirect
190. C2×C4⋊Dic3C2×D3semidirect
192. C2×Dic3⋊C4C2×D3semidirect
193. C2×C4×Dic3C2×D3semidirect
220. C22×C3×D3#41semidirect
235. C4⋊(C3⋊D3)C2×D4semidirect
286. C2×C3×Q8C22×D3semidirect
287. C2×C3×Q8C22×D3semidirect
373. (C2×D3)⋊C4C22×D3semidirect
374. (C2×D3)⋊C4C22×D3semidirect
376. C4⋊Dic3C22×D3semidirect
378. Dic3⋊C4C22×D3semidirect
379. C4×Dic3C22×D3semidirect
399. C2×C3×D3C2×#41semidirect
411. C22×Q8D32semidirect
492. C22×D3#239semidirect
556. C2×C32#546semidirect
574. C2×Q8C2×D32semidirect
667. C2×D3C2×#239semidirect
685. C32C2×#546semidirect
738. C2×C3#5630semidirect
739. C2×C3#5676semidirect
783. C3C2×#5630semidirect
784. C3C2×#5676semidirect
789. C2#10595431direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38322
C22×D3×D122
C2×C3×#9472
C2×C3×#9462
#105954312
C2×#639232
C2×#639212
C2×#639162
C2×#639102
C2×C4×#6262
C2×#638942
C2×#638532
C2×#56763
C2×#56303