Finite Group Databasebeta

← C2×#10594922 #11900451

Subgroups — C2×#10594922 #11900451

Order 1152.

4441 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C2×C3×#924C211yesmaximal, characteristic, complemented
5C2×#63981C212yesmaximal, complemented
6C2×#67⋊Dic3C212yesmaximal, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8#10594922C2116yesmaximal, direct product factor
9C2×#63881C212yesmaximal, complemented
10C2×#63871C211yesmaximal, characteristic, complemented
11C2×#63853C212yesmaximal, complemented
12C2×#63849C211yesmaximal, characteristic, complemented
13C2×#5627—31nomaximal
14C2×#5606—31nomaximal
15C24×C3⋊D3C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C23×C3⋊Dic3C2211yescharacteristic
18C22×C4×C3⋊D3—28no—
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C4×C3⋊D3C2218yescomplemented
24C22×C3×#67C2212yes—
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×Dic6C2211yescharacteristic, complemented
27C22×#626C2212yes—
28C22×#626C2212yes—
29C22×D3×Dic3C2212yescomplemented
30C2×#3796—28no—
31C2×#3796C2218yescomplemented
32C2×C3×#217C2212yes—
33C3×#930C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2212yescomplemented
35C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
36C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
37C3×#924C2218yescomplemented
38C2×C3×Dic3⋊C4C2212yescomplemented
39#63981C22116yescomplemented
40#67⋊Dic3C22116yescomplemented
41C2×Dic3⋊Dic3C2212yescomplemented
42C2×#3722C2212yes—
43C2×#3722C2212yes—
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45C2×Dic32C2212yescomplemented
46#63916C2218yescomplemented
47#63881C22116yescomplemented
48#63871C2218yescomplemented
49#63853C22116yescomplemented
50#63849C2218yescomplemented
51C22×#239—31no—
52C22×#237—31no—
53C23×C4×D3—31no—
54C23×C4×D3—31no—
55C23×C4×D3—61no—
56C2×C3×C22⋊Q8—31no—
57C2×C3×#121—31no—
58C2×#946—31no—
59C2×#938—31no—
60C2×#937—32no—
61C2×D4×Dic3—32no—
62C2×#930D311yescharacteristic, complemented
63C2×#924D311yescharacteristic, complemented
64#5627—316no—
65#5606—316no—
66C2×#897—31no—
67C2×#895—31no—
68C2×#894—32no—
69C2×#893—32no—
70C2×#892—31no—
71C2×#892—31no—
72C2×#883—32no—
73C2×#882—32no—
74C2×#67⋊C4—32no—
75C2×#67⋊C4—32no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3—24no—
78C23×C3⋊D3—24no—
79C23×C3⋊D3—24no—
80C23×C3⋊D3C2314yes—
81C23×C3⋊D3C2311yescharacteristic
82C23×C3⋊D3C2311yescharacteristic
83C23×C3×D3C2312yes—
84C22×C32×C4—24no—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2314yes—
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3—24no—
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2314yes—
91C22×C3⋊Dic3C2311yescharacteristic
92C2×C4×C3⋊D3—24no—
93C2×C4×C3⋊D3—24no—
94C2×C4×C3⋊D3—24no—
95C2×C4×C3⋊D3—232no—
96C2×C4×C3⋊D3D418yescomplemented
97C2×C4×C3⋊D3C2314yes—
98C2×C4×C3⋊D3C2314yes—
99C2×C4×C3⋊D3C2314yes—
100C2×C4×C3⋊D3C2314yes—
101C2×C3×#67—28no—
102C2×C3×#67C2318yes—
103C22×C3×Dic3C2312yes—
104C22×C3×Dic3C2312yes—
105C22×C3×Dic3C2312yes—
106C2×C3×D12—24no—
107C2×C3×D12C2314yescomplemented
108C2×C3×Dic6—24no—
109C2×C3×Dic6C2314yescomplemented
110C2×#626—28no—
111C2×#626—28no—
112C2×#626C2318yes—
113C2×#626C2318yes—
114C2×D3×Dic3—28no—
115C2×D3×Dic3C2318yescomplemented
116#3796—232no—
117C3×#217C2318yes—
118C3×(C2×D3)⋊C4C2318yescomplemented
119C3×C4⋊Dic3C2314yescomplemented
120C3×C4⋊Dic3C2314yescomplemented
121C3×Dic3⋊C4C2318yescomplemented
122Dic3⋊Dic3C2318yescomplemented
123#3722C2318yes—
124#3722C2318yes—
125(C2×D3)⋊Dic3C2318yescomplemented
126Dic32C2318yescomplemented
127C2×#525—91noSylow
128C24×D3—31no—
129C24×D3—31no—
130C24×D3—61no—
131C22×C3×Q8—31no—
132C22×C3×D4—32no—
133C22×C3×D4—31no—
134C23×C3×C4—21no—
135C23×C3×C4C2×D311yescharacteristic
136C23×C3×C4C2×D311yescharacteristic
137C22×#67—32no—
138C22×#67—32no—
139C22×#67C2×D312yes—
140C23×Dic3—31no—
141C23×Dic3—31no—
142C23×Dic3—32no—
143C23×Dic3—61no—
144C2×#239—38no—
145C2×#239—68no—
146C2×#237—38no—
147C2×#237—68no—
148C22×D12—32no—
149C22×D12—32no—
150C22×D12C2×D311yescharacteristic, complemented
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—32no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—38no—
161C22×C4×D3—38no—
162C22×C4×D3—61no—
163C22×C4×D3—61no—
164C22×C4×D3—61no—
165C22×C4×D3—61no—
166C22×C4×D3—68no—
167C22×C4×D3—68no—
168C22×C4×D3—68no—
169C22×C4×D3—616no—
170C22×Dic6C2×D311yescharacteristic, complemented
171C3×C22⋊Q8—38no—
172C3×#121—38no—
173C2×C3×C4⋊C4—32no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C22⋊C4—32no—
177C2×C3×C22⋊C4—32no—
178C2×#217—32no—
179C2×#217C2×D312yes—
180#946—38no—
181#938—38no—
182#937—316no—
183D4×Dic3—316no—
184#930C2×D318yescomplemented
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—32no—
190C2×(C2×D3)⋊C4C2×D312yescomplemented
191C2×C4⋊Dic3—32no—
192C2×C4⋊Dic3C2×D311yescharacteristic, complemented
193C2×C4⋊Dic3C2×D311yescharacteristic, complemented
194#924C2×D318yescomplemented
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4C2×D312yescomplemented
197C2×C4×Dic3—32no—
198C2×C4×Dic3—32no—
199#897—38no—
200#895—38no—
201#894—316no—
202#893—316no—
203#892—38no—
204#892—38no—
205#883—316no—
206#882—316no—
207#67⋊C4—316no—
208#67⋊C4—316no—
209C23×C32—22no—
210C23×C32—22no—
211C23×C32#4114yescomplemented
212C23×C32C2412yes—
213C23×C32C2411yescharacteristic
214C22×C3⋊D3—232no—
215C22×C3⋊D3—22no—
216C22×C3⋊D3—22no—
217C22×C3⋊D3—22no—
218C22×C3⋊D3—22no—
219C22×C3⋊D3—28no—
220C22×C3⋊D3—28no—
221C22×C3⋊D3—28no—
222C22×C3⋊D3C2×D414yes—
223C22×C3⋊D3#4114yescomplemented
224C22×C3⋊D3C2412yes—
225C22×C3⋊D3C2412yes—
226C22×C3×D3—24no—
227C22×C3×D3—24no—
228C22×C3×D3—24no—
229C22×C3×D3C2414yes—
230C2×C32×C4—22no—
231C2×C32×C4—28no—
232C2×C32×C4C2×D414yes—
233C2×C32×C4C2412yes—
234C2×C32×C4C2412yes—
235C2×C3⋊Dic3—22no—
236C2×C3⋊Dic3—28no—
237C2×C3⋊Dic3C2×D414yes—
238C2×C3⋊Dic3C2412yes—
239C2×C3⋊Dic3C2412yes—
240C4×C3⋊D3—28no—
241C4×C3⋊D3—28no—
242C4×C3⋊D3—28no—
243C4×C3⋊D3C2×D4116yescomplemented
244C3×#67—216no—
245C2×C3×Dic3—24no—
246C2×C3×Dic3—24no—
247C2×C3×Dic3—24no—
248C2×C3×Dic3C2414yes—
249C2×C3×Dic3C2414yes—
250C2×C3×Dic3C2414yes—
251C3×D12—28no—
252C3×Dic6—28no—
253#626—216no—
254#626—216no—
255D3×Dic3—216no—
256C22×#41—91no—
257C24×C4—91no—
258#525—916no—
259C2×#123—92no—
260C2×C22⋊Q8—31no—
261C2×C22⋊Q8—91no—
262C2×#121—31no—
263C2×#121—91no—
264C2×#120—92no—
265C2×C4×D4—92no—
266C2×C4×D4—92no—
267C2×#117—91no—
268C24×C3—21no—
269C24×C3—32no—
270C24×C3C22×D311yescharacteristic
271C24×C3C22×D311yescharacteristic
272C23×D3—31no—
273C23×D3—31no—
274C23×D3—31no—
275C23×D3—31no—
276C23×D3—34no—
277C23×D3—34no—
278C23×D3—61no—
279C23×D3—61no—
280C23×D3—64no—
281C23×D3—64no—
282C23×D3—64no—
283C23×D3—64no—
284C23×D3—64no—
285C23×D3—68no—
286C23×D3—68no—
287C23×D3—68no—
288C23×D3—64no—
289C23×D3—64no—
290C23×D3C22×D312yes—
291C2×C3×Q8—34no—
292C2×C3×Q8—64no—
293C2×C3×D4—38no—
294C2×C3×D4—34no—
295C2×C3×D4—68no—
296C2×C3×D4—64no—
297C22×C3×C4—28no—
298C22×C3×C4—24no—
299C22×C3×C4—24no—
300C22×C3×C4—24no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—32no—
304C22×C3×C4—32no—
305C22×C3×C4—32no—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D314yes—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D314yes—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—28no—
313C2×#67—38no—
314C2×#67—38no—
315C2×#67—68no—
316C2×#67—68no—
317C2×#67C22×D318yes—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—34no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—34no—
324C22×Dic3—38no—
325C22×Dic3—61no—
326C22×Dic3—64no—
327C22×Dic3—61no—
328C22×Dic3—68no—
329C22×Dic3—64no—
330C22×Dic3—64no—
331C22×Dic3—68no—
332C22×Dic3C22×D312yes—
333C22×Dic3C22×D312yes—
334C22×Dic3C22×D312yes—
335#239—632no—
336#237—632no—
337C2×D12—24no—
338C2×D12—38no—
339C2×D12—38no—
340C2×D12—68no—
341C2×D12—68no—
342C2×D12C22×D314yescomplemented
343C2×C4×D3—38no—
344C2×C4×D3—38no—
345C2×C4×D3—34no—
346C2×C4×D3—34no—
347C2×C4×D3—38no—
348C2×C4×D3—34no—
349C2×C4×D3—34no—
350C2×C4×D3—34no—
351C2×C4×D3—34no—
352C2×C4×D3—34no—
353C2×C4×D3—34no—
354C2×C4×D3—68no—
355C2×C4×D3—64no—
356C2×C4×D3—64no—
357C2×C4×D3—64no—
358C2×C4×D3—64no—
359C2×C4×D3—632no—
360C2×C4×D3—632no—
361C2×C4×D3—64no—
362C2×C4×D3—64no—
363C2×C4×D3—68no—
364C2×C4×D3—64no—
365C2×C4×D3—64no—
366C2×C4×D3—664no—
367C2×C4×D3—68no—
368C2×C4×D3—68no—
369C2×C4×D3—68no—
370C2×C4×D3—64no—
371C2×C4×D3—64no—
372C2×Dic6—24no—
373C2×Dic6C22×D314yescomplemented
374C3×C4⋊C4—34no—
375C3×C4⋊C4—34no—
376C3×C4⋊C4—38no—
377C3×C22⋊C4—38no—
378C3×C22⋊C4—38no—
379#217—38no—
380#217C22×D318yes—
381(C2×D3)⋊C4—38no—
382(C2×D3)⋊C4—38no—
383(C2×D3)⋊C4—38no—
384(C2×D3)⋊C4—38no—
385(C2×D3)⋊C4—38no—
386(C2×D3)⋊C4C22×D318yescomplemented
387C4⋊Dic3—38no—
388C4⋊Dic3C22×D314yescomplemented
389C4⋊Dic3C22×D314yescomplemented
390Dic3⋊C4—38no—
391Dic3⋊C4C22×D318yescomplemented
392C4×Dic3—38no—
393C4×Dic3—38no—
394C22×C32—28no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32C22×D412yes—
398C22×C32C2×#4112yes—
399C22×C32C2×#4112yes—
400C22×C32C2×#4114yescomplemented
401C22×C32C2511yescharacteristic
402C2×C3⋊D3—232no—
403C2×C3⋊D3—28no—
404C2×C3⋊D3—28no—
405C2×C3⋊D3—22no—
406C2×C3⋊D3—22no—
407C2×C3⋊D3—22no—
408C2×C3⋊D3—22no—
409C2×C3⋊D3C22×D414yes—
410C2×C3⋊D3C2×#4114yescomplemented
411C2×C3×D3—24no—
412C2×C3×D3—24no—
413C2×C3×D3—24no—
414C2×C3×D3—48no—
415C32×C4—22no—
416C32×C4C22×D414yes—
417C3⋊Dic3—22no—
418C3⋊Dic3C22×D414yes—
419C3×Dic3—24no—
420C3×Dic3—24no—
421C3×Dic3—24no—
422C25—91no—
423C2×#41—98no—
424C2×#41—188no—
425C22×Q8—31no—
426C22×D4—32no—
427C22×D4—31no—
428C22×D4—92no—
429C22×D4—92no—
430C23×C4—92no—
431C23×C4—91no—
432C23×C4—91no—
433C23×C4—91no—
434C23×C4—91no—
435C23×C4—91no—
436C23×C4—98no—
437C23×C4—188no—
438C23×C4D3211yescharacteristic
439#123—916no—
440C22⋊Q8—38no—
441C22⋊Q8—98no—
442#121—38no—
443#121—98no—
444#120—916no—
445C4×D4—916no—
446C4×D4—916no—
447#117—98no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—32no—
451C2×C4⋊C4—92no—
452C2×C22⋊C4—32no—
453C2×C22⋊C4—32no—
454C2×C22⋊C4—92no—
455C2×C22⋊C4—92no—
456C2×C22⋊C4—92no—
457C2×C42—92no—
458C23×C3—24no—
459C23×C3—24no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—21no—
466C23×C3—24no—
467C23×C3—34no—
468C23×C3—64no—
469C23×C3—64no—
470C23×C3—64no—
471C23×C3#23714yescomplemented
472C23×C3#23914yescomplemented
473C23×C3C23×D312yes—
474C23×C3C23×D312yes—
475C23×C3C23×D311yescharacteristic
476C23×C3C23×D311yescharacteristic
477C22×D3—24no—
478C22×D3—24no—
479C22×D3—24no—
480C22×D3—34no—
481C22×D3—34no—
482C22×D3—34no—
483C22×D3—34no—
484C22×D3—32no—
485C22×D3—32no—
486C22×D3—32no—
487C22×D3—32no—
488C22×D3—64no—
489C22×D3—64no—
490C22×D3—62no—
491C22×D3—62no—
492C22×D3—68no—
493C22×D3—68no—
494C22×D3—68no—
495C22×D3—68no—
496C22×D3—616no—
497C22×D3—64no—
498C22×D3—616no—
499C22×D3—664no—
500C22×D3—632no—
501C22×D3—632no—
502C22×D3—64no—
503C22×D3—64no—
504C22×D3—616no—
505C22×D3—64no—
506C22×D3—62no—
507C22×D3—62no—
508C22×D3—62no—
509C22×D3—62no—
510C22×D3—68no—
511C22×D3—62no—
512C22×D3—62no—
513C22×D3—68no—
514C22×D3—62no—
515C22×D3—62no—
516C22×D3C23×D314yes—
517C3×Q8—68no—
518C3×D4—616no—
519C3×D4—68no—
520C2×C3×C4—24no—
521C2×C3×C4—216no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—28no—
525C2×C3×C4—28no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—24no—
529C2×C3×C4—34no—
530C2×C3×C4—34no—
531C2×C3×C4—34no—
532C2×C3×C4—64no—
533C2×C3×C4—64no—
534C2×C3×C4—64no—
535C2×C3×C4D3×D414yes—
536C2×C3×C4D3×D414yes—
537C2×C3×C4C23×D312yes—
538C2×C3×C4C23×D312yes—
539C2×C3×C4C23×D312yes—
540C2×C3×C4C23×D312yes—
541#67—216no—
542#67—616no—
543#67—616no—
544C2×Dic3—24no—
545C2×Dic3—24no—
546C2×Dic3—24no—
547C2×Dic3—34no—
548C2×Dic3—34no—
549C2×Dic3—32no—
550C2×Dic3—32no—
551C2×Dic3—32no—
552C2×Dic3—32no—
553C2×Dic3—64no—
554C2×Dic3—62no—
555C2×Dic3—62no—
556C2×Dic3—616no—
557C2×Dic3—68no—
558C2×Dic3—68no—
559C2×Dic3—616no—
560C2×Dic3—64no—
561C2×Dic3—62no—
562C2×Dic3—62no—
563C2×Dic3C23×D314yes—
564C2×Dic3C23×D314yes—
565C2×Dic3C23×D314yes—
566D12—28no—
567D12—616no—
568D12—616no—
569C4×D3—316no—
570C4×D3—316no—
571C4×D3—616no—
572C4×D3—68no—
573C4×D3—68no—
574C4×D3—616no—
575C4×D3—68no—
576C4×D3—68no—
577C4×D3—616no—
578C4×D3—616no—
579C4×D3—616no—
580C4×D3—68no—
581C4×D3—68no—
582Dic6—28no—
583C2×C32—24no—
584C2×C32#52514yescomplemented
585C2×C32C23×D411yescharacteristic
586C2×C32C22×#4111yescharacteristic
587C2×C32C22×#4111yescharacteristic
588C3⋊D3—24no—
589C3⋊D3—24no—
590C3×D3—44no—
591C24—32no—
592C24—91no—
593C24—91no—
594C24—94no—
595C24—184no—
596C24—184no—
597C24—184no—
598C24C2×D3211yescharacteristic
599#41—1832no—
600C2×Q8—34no—
601C2×Q8—64no—
602C2×D4—38no—
603C2×D4—34no—
604C2×D4—68no—
605C2×D4—64no—
606C2×D4—98no—
607C2×D4—98no—
608C2×D4—188no—
609C2×D4—188no—
610C22×C4—24no—
611C22×C4—32no—
612C22×C4—32no—
613C22×C4—32no—
614C22×C4—98no—
615C22×C4—91no—
616C22×C4—94no—
617C22×C4—98no—
618C22×C4—94no—
619C22×C4—91no—
620C22×C4—94no—
621C22×C4—94no—
622C22×C4—94no—
623C22×C4—184no—
624C22×C4—1832no—
625C22×C4—184no—
626C22×C4—188no—
627C22×C4—184no—
628C22×C4—184no—
629C22×C4C2×D3214yes—
630C22×C4C2×D3211yescharacteristic
631C22×C4C2×D3211yescharacteristic
632C4⋊C4—34no—
633C4⋊C4—34no—
634C4⋊C4—38no—
635C4⋊C4—98no—
636C22⋊C4—38no—
637C22⋊C4—38no—
638C22⋊C4—98no—
639C22⋊C4—98no—
640C22⋊C4—98no—
641C42—98no—
642C22×C3—24no—
643C22×C3—24no—
644C22×C3—216no—
645C22×C3—22no—
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—28no—
650C22×C3—28no—
651C22×C3—22no—
652C22×C3—24no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—21no—
656C22×C3—64no—
657C22×C3—64no—
658C22×C3—64no—
659C22×C3—128no—
660C22×C3C2×D3×D412yes—
661C22×C3C2×D3×D412yes—
662C22×C3C2×#23712yes—
663C22×C3C2×#23714yescomplemented
664C22×C3C2×#23912yes—
665C22×C3C2×#23914yescomplemented
666C22×C3D3×#4112yes—
667C22×C3D3×#4112yes—
668C22×C3C24×D311yescharacteristic
669C22×C3C24×D311yescharacteristic
670C2×D3—24no—
671C2×D3—24no—
672C2×D3—24no—
673C2×D3—34no—
674C2×D3—34no—
675C2×D3—34no—
676C2×D3—34no—
677C2×D3—48no—
678C2×D3—64no—
679C2×D3—64no—
680C2×D3—64no—
681C2×D3—664no—
682C2×D3—632no—
683C2×D3—632no—
684C2×D3—64no—
685C2×D3—64no—
686C2×D3—64no—
687C2×D3—616no—
688C2×D3—616no—
689C2×D3—62no—
690C2×D3—62no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—62no—
694C2×D3—62no—
695C2×D3—62no—
696C2×D3—62no—
697C2×D3—68no—
698C2×D3—68no—
699C2×D3—68no—
700C2×D3—68no—
701C3×C4—24no—
702C3×C4—22no—
703C3×C4—22no—
704C3×C4—24no—
705C3×C4—64no—
706C3×C4—64no—
707C3×C4—64no—
708C3×C4C2×D3×D414yes—
709C3×C4C2×D3×D414yes—
710Dic3—24no—
711Dic3—24no—
712Dic3—24no—
713Dic3—34no—
714Dic3—34no—
715Dic3—64no—
716Dic3—64no—
717Dic3—62no—
718Dic3—62no—
719C32C2×#52511yescharacteristic, complemented, Sylow
720C23—22no—
721C23—22no—
722C23—34no—
723C23—64no—
724C23—64no—
725C23—64no—
726C23—94no—
727C23—94no—
728C23—92no—
729C23—92no—
730C23—188no—
731C23—188no—
732C23—1832no—
733C23—182no—
734C23—182no—
735C23—188no—
736C23—182no—
737C23—182no—
738C23#379614yescomplemented
739C23C22×D3212yes—
740C23C22×D3211yescharacteristic
741Q8—68no—
742D4—616no—
743D4—68no—
744D4—1816no—
745D4—1816no—
746C2×C4—22no—
747C2×C4—28no—
748C2×C4—34no—
749C2×C4—34no—
750C2×C4—34no—
751C2×C4—64no—
752C2×C4—64no—
753C2×C4—64no—
754C2×C4—94no—
755C2×C4—92no—
756C2×C4—916no—
757C2×C4—92no—
758C2×C4—188no—
759C2×C4—188no—
760C2×C4—1816no—
761C2×C4—188no—
762C2×C4—182no—
763C2×C4—188no—
764C2×C4#381114yes—
765C2×C4C22×D3212yes—
766C2×C4C22×D3212yes—
767C2×C3—28no—
768C2×C3—24no—
769C2×C3—24no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—24no—
774C2×C3—124no—
775C2×C3#560614yescomplemented
776C2×C3#562714yescomplemented
777C2×C3C22×D3×D411yescharacteristic
778C2×C3C22×D3×D411yescharacteristic
779C2×C3C22×#23711yescharacteristic
780C2×C3C22×#23911yescharacteristic
781C2×C3C2×D3×#4111yescharacteristic
782C2×C3C2×D3×#4111yescharacteristic
783D3—44no—
784D3—68no—
785D3—68no—
786D3—64no—
787D3—64no—
788D3—64no—
789D3—64no—
790C22—22no—
791C22—22no—
792C22—28no—
793C22—64no—
794C22—64no—
795C22—64no—
796C22—94no—
797C22—94no—
798C22—128no—
799C22—1832no—
800C22—182no—
801C22—182no—
802C22—182no—
803C22—182no—
804C22—188no—
805C22—188no—
806C22C2×#379612yes—
807C22C2×#379614yescomplemented
808C22#6430612yes—
809C22C2×#381112yes—
810C22C23×D3211yescharacteristic
811C4—22no—
812C4—64no—
813C4—64no—
814C4—64no—
815C4—94no—
816C4—182no—
817C4C2×#381114yes—
818C3—21no—
819C3C2×#560611yescharacteristic, complemented
820C3C2×#562711yescharacteristic, complemented
821C2—24no—
822C2—124no—
823C2—184no—
824C2—184no—
825C2#1059492214yesdirect product factor
826C2C22×#379611yescharacteristic
827C2C2×#6430611yescharacteristic
828C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C4×C3⋊D3C2semidirect
2. C22×#3796C2semidirect
3. C2×C3×#930C2semidirect
4. C2×C3×#924C2semidirect
5. C2×#63981C2semidirect
6. C2×#67⋊Dic3C2semidirect
7. C2×#63916C2semidirect
8. #10594922C2direct (N × H)
9. C2×#63881C2semidirect
10. C2×#63871C2semidirect
11. C2×#63853C2semidirect
12. C2×#63849C2semidirect
23. C22×C4×C3⋊D3C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×Dic6C22semidirect
29. C22×D3×Dic3C22semidirect
31. C2×#3796C22semidirect
33. C3×#930C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×C4⋊Dic3C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C3×#924C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. #63981C22semidirect
40. #67⋊Dic3C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×Dic32C22semidirect
46. #63916C22semidirect
47. #63881C22semidirect
48. #63871C22semidirect
49. #63853C22semidirect
50. #63849C22semidirect
62. C2×#930D3semidirect
63. C2×#924D3semidirect
96. C2×C4×C3⋊D3D4semidirect
107. C2×C3×D12C23semidirect
109. C2×C3×Dic6C23semidirect
115. C2×D3×Dic3C23semidirect
118. C3×(C2×D3)⋊C4C23semidirect
119. C3×C4⋊Dic3C23semidirect
120. C3×C4⋊Dic3C23semidirect
121. C3×Dic3⋊C4C23semidirect
122. Dic3⋊Dic3C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
126. Dic32C23semidirect
150. C22×D12C2×D3semidirect
170. C22×Dic6C2×D3semidirect
184. #930C2×D3semidirect
190. C2×(C2×D3)⋊C4C2×D3semidirect
192. C2×C4⋊Dic3C2×D3semidirect
193. C2×C4⋊Dic3C2×D3semidirect
194. #924C2×D3semidirect
196. C2×Dic3⋊C4C2×D3semidirect
211. C23×C32#41semidirect
223. C22×C3⋊D3#41semidirect
243. C4×C3⋊D3C2×D4semidirect
342. C2×D12C22×D3semidirect
373. C2×Dic6C22×D3semidirect
386. (C2×D3)⋊C4C22×D3semidirect
388. C4⋊Dic3C22×D3semidirect
389. C4⋊Dic3C22×D3semidirect
391. Dic3⋊C4C22×D3semidirect
400. C22×C32C2×#41semidirect
410. C2×C3⋊D3C2×#41semidirect
471. C23×C3#237semidirect
472. C23×C3#239semidirect
584. C2×C32#525semidirect
663. C22×C3C2×#237semidirect
665. C22×C3C2×#239semidirect
719. C32C2×#525semidirect
738. C23#3796semidirect
775. C2×C3#5606semidirect
776. C2×C3#5627semidirect
807. C22C2×#3796semidirect
819. C3C2×#5606semidirect
820. C3C2×#5627semidirect
825. C2#10594922direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C22×#37962
C2×C3×#9302
C2×C3×#9242
C2×#639812
C2×#67⋊Dic32
C2×#639162
#105949222
C2×#638812
C2×#638712
C2×#638532
C2×#638492
C2×#56273
C2×#56063