Finite Group Databasebeta

← C2×#10594918 #11902621

Subgroups — C2×#10594918 #11902621

Order 1152.

3665 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
1C23×#634C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×#63980C212yesmaximal, complemented
6C2×#67⋊Dic3C212yesmaximal, complemented
7C2×#63913C212yesmaximal, complemented
8#10594918C2116yesmaximal, direct product factor
9C2×#63896C212yesmaximal, complemented
10C2×#63860C211yesmaximal, characteristic, complemented
11C2×#63857C211yesmaximal, characteristic, complemented
12C2×#63844C211yesmaximal, characteristic, complemented
13C2×#5598—31nomaximal
14C2×#5552—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C23×C3⋊Dic3C2212yes—
17C22×#634—28no—
18C22×#634C2211yescharacteristic
19C22×#634C2212yes—
20C22×#634C2211yescharacteristic
21C22×#634C2218yescomplemented
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2212yes—
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×#625C2212yes—
27C22×D3×Dic3C2212yes—
28C2×#3795—28no—
29C2×#3795C2218yescomplemented
30C2×C3×#217C2211yescharacteristic
31C3×#930C2218yescomplemented
32C3×C4×#67C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2212yes—
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38#63980C22116yescomplemented
39#67⋊Dic3C22116yescomplemented
40C2×#3724C2212yes—
41C2×Dic3⋊Dic3C2212yes—
42C2×(C2×D3)⋊Dic3C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45C2×Dic32C2212yes—
46#63913C22116yescomplemented
47#63896C22116yescomplemented
48#63860C2218yescomplemented
49#63857C2218yescomplemented
50#63844C2218yescomplemented
51C22×#237—31no—
52C22×#235—31no—
53C23×Dic6—31no—
54C23×Dic6—31no—
55C23×Dic6—61no—
56C2×C3×#121—31no—
57C2×C3×C4×D4—31no—
58C2×#939—32no—
59C2×#939—32no—
60C2×#936—31no—
61C2×D4×Dic3—32no—
62C2×#930D311yescharacteristic, complemented
63C2×C4×#67D311yescharacteristic, complemented
64C2×#924—31no—
65#5598—316no—
66#5552—316no—
67C2×#897—31no—
68C2×#896—32no—
69C2×#887—31no—
70C2×#885—32no—
71C2×#885—32no—
72C2×#67⋊C4—32no—
73C2×#878—32no—
74C2×#875—31no—
75C2×C4×Dic6—31no—
76C24×C32C2311yescharacteristic
77C23×C3×D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C22×C32×C4—24no—
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2314yes—
82C22×C32×C4C2311yescharacteristic
83C22×C3⋊Dic3—28no—
84C22×C3⋊Dic3C2312yes—
85C22×C3⋊Dic3C2318yes—
86C22×C3⋊Dic3C2312yes—
87C2×#634—24no—
88C2×#634—28no—
89C2×#634—232no—
90C2×#634D418yescomplemented
91C2×#634C2314yes—
92C2×#634C2318yes—
93C2×#634C2314yes—
94C2×C3×#67—24no—
95C2×C3×#67—28no—
96C2×C3×#67C2314yes—
97C2×C3×#67C2318yes—
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×#625—28no—
107C2×#625C2318yes—
108C2×D3×Dic3—28no—
109C2×D3×Dic3C2318yes—
110#3795—232no—
111C3×#217C2314yes—
112C3×(C2×D3)⋊C4C2314yes—
113C3×(C2×D3)⋊C4C2318yes—
114C3×C4⋊Dic3C2314yes—
115C3×Dic3⋊C4C2314yes—
116C3×C4×Dic3C2314yes—
117#3724C2318yes—
118Dic3⋊Dic3C2318yes—
119(C2×D3)⋊Dic3C2318yes—
120(C2×D3)⋊Dic3C2318yes—
121(C2×D3)⋊Dic3C2318yes—
122Dic32C2318yes—
123C2×#548—91noSylow
124C22×C3×D4—32no—
125C22×C3×D4—31no—
126C22×C3×D4—31no—
127C23×C3×C4—21no—
128C23×C3×C4—31no—
129C23×C3×C4C2×D311yescharacteristic
130C23×C3×C4C2×D311yescharacteristic
131C22×#67—32no—
132C22×#67—32no—
133C22×#67C2×D312yes—
134C22×#67C2×D311yescharacteristic
135C23×Dic3—32no—
136C23×Dic3—32no—
137C23×Dic3—32no—
138C23×Dic3—62no—
139C2×#237—38no—
140C2×#237—68no—
141C2×#235—38no—
142C2×#235—68no—
143C22×D12C2×D311yescharacteristic
144C22×C4×D3—32no—
145C22×C4×D3C2×D311yescharacteristic
146C22×Dic6—31no—
147C22×Dic6—31no—
148C22×Dic6—31no—
149C22×Dic6—32no—
150C22×Dic6—32no—
151C22×Dic6—31no—
152C22×Dic6—38no—
153C22×Dic6—38no—
154C22×Dic6—61no—
155C22×Dic6—61no—
156C22×Dic6—62no—
157C22×Dic6—68no—
158C22×Dic6—68no—
159C22×Dic6—68no—
160C22×Dic6—616no—
161C3×#121—38no—
162C3×C4×D4—38no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—32no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C42—31no—
169C2×#217—32no—
170C2×#217—32no—
171C2×#217—32no—
172C2×#217C2×D311yescharacteristic
173#939—316no—
174#939—316no—
175#936—38no—
176D4×Dic3—316no—
177#930C2×D318yescomplemented
178C4×#67C2×D318yescomplemented
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4C2×D311yescharacteristic
183C2×(C2×D3)⋊C4C2×D312yes—
184C2×C4⋊Dic3—32no—
185C2×C4⋊Dic3C2×D311yescharacteristic
186#924—38no—
187C2×Dic3⋊C4—32no—
188C2×Dic3⋊C4—32no—
189C2×Dic3⋊C4—32no—
190C2×Dic3⋊C4C2×D311yescharacteristic
191C2×C4×Dic3—32no—
192C2×C4×Dic3—32no—
193C2×C4×Dic3C2×D311yescharacteristic
194#897—38no—
195#896—316no—
196#887—38no—
197#885—316no—
198#885—316no—
199#67⋊C4—316no—
200#878—316no—
201#875—38no—
202C4×Dic6—38no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32#4114yescomplemented
206C23×C32C2412yes—
207C23×C32C2411yescharacteristic
208C22×C3×D3—24no—
209C22×C3×D3—22no—
210C22×C3×D3—22no—
211C22×C3×D3—24no—
212C22×C3×D3—24no—
213C22×C3×D3—22no—
214C22×C3×D3C2414yes—
215C22×C3×D3C2412yes—
216C2×C32×C4—22no—
217C2×C32×C4—28no—
218C2×C32×C4C2×D414yes—
219C2×C32×C4C2412yes—
220C2×C32×C4C2412yes—
221C2×C3⋊Dic3—24no—
222C2×C3⋊Dic3—216no—
223C2×C3⋊Dic3C2×D418yes—
224C2×C3⋊Dic3C2414yes—
225C2×C3⋊Dic3C2414yes—
226#634—28no—
227#634—216no—
228#634C2×D4116yescomplemented
229C3×#67—28no—
230C3×#67—216no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3C2412yes—
236C2×C3×Dic3C2414yes—
237C2×C3×Dic3C2412yes—
238C2×C3×Dic3C2412yes—
239C3×D12—28no—
240C3×C4×D3—28no—
241#625—216no—
242D3×Dic3—216no—
243C22×#41—91no—
244C23×Q8—91no—
245#548—916no—
246C2×#124—91no—
247C2×#124—92no—
248C2×C22⋊Q8—92no—
249C2×C22⋊Q8—91no—
250C2×#121—31no—
251C2×#121—92no—
252C2×C4×Q8—91no—
253C2×C4×D4—31no—
254C2×C4×D4—92no—
255C24×C3—21no—
256C24×C3—32no—
257C24×C3—31no—
258C24×C3C22×D311yescharacteristic
259C24×C3C22×D311yescharacteristic
260C23×D3C22×D312yes—
261C23×D3C22×D311yescharacteristic
262C2×C3×D4—38no—
263C2×C3×D4—34no—
264C2×C3×D4—34no—
265C2×C3×D4—68no—
266C2×C3×D4—64no—
267C2×C3×D4—64no—
268C22×C3×C4—28no—
269C22×C3×C4—24no—
270C22×C3×C4—24no—
271C22×C3×C4—24no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—31no—
275C22×C3×C4—32no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—34no—
279C22×C3×C4—64no—
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D314yes—
283C22×C3×C4C22×D314yes—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C2×#67—24no—
287C2×#67—28no—
288C2×#67—38no—
289C2×#67—38no—
290C2×#67—68no—
291C2×#67—68no—
292C2×#67C22×D318yes—
293C2×#67C22×D314yes—
294C22×Dic3—32no—
295C22×Dic3—32no—
296C22×Dic3—38no—
297C22×Dic3—32no—
298C22×Dic3—32no—
299C22×Dic3—38no—
300C22×Dic3—38no—
301C22×Dic3—62no—
302C22×Dic3—68no—
303C22×Dic3—62no—
304C22×Dic3—68no—
305C22×Dic3—68no—
306C22×Dic3—68no—
307C22×Dic3—616no—
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D312yes—
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312#237—632no—
313#235—632no—
314C2×D12—24no—
315C2×D12C22×D314yes—
316C2×C4×D3—24no—
317C2×C4×D3—38no—
318C2×C4×D3—68no—
319C2×C4×D3C22×D314yes—
320C2×Dic6—38no—
321C2×Dic6—38no—
322C2×Dic6—34no—
323C2×Dic6—34no—
324C2×Dic6—34no—
325C2×Dic6—38no—
326C2×Dic6—38no—
327C2×Dic6—34no—
328C2×Dic6—68no—
329C2×Dic6—64no—
330C2×Dic6—64no—
331C2×Dic6—68no—
332C2×Dic6—632no—
333C2×Dic6—632no—
334C2×Dic6—68no—
335C2×Dic6—68no—
336C2×Dic6—616no—
337C2×Dic6—664no—
338C2×Dic6—68no—
339C2×Dic6—64no—
340C2×Dic6—64no—
341C3×C4⋊C4—34no—
342C3×C4⋊C4—34no—
343C3×C22⋊C4—34no—
344C3×C22⋊C4—38no—
345C3×C22⋊C4—34no—
346C3×C42—34no—
347#217—38no—
348#217—38no—
349#217—38no—
350#217C22×D314yes—
351(C2×D3)⋊C4—38no—
352(C2×D3)⋊C4—38no—
353(C2×D3)⋊C4—38no—
354(C2×D3)⋊C4C22×D314yes—
355(C2×D3)⋊C4C22×D318yes—
356C4⋊Dic3—38no—
357C4⋊Dic3C22×D314yes—
358Dic3⋊C4—38no—
359Dic3⋊C4—38no—
360Dic3⋊C4—38no—
361Dic3⋊C4C22×D314yes—
362C4×Dic3—38no—
363C4×Dic3—38no—
364C4×Dic3C22×D314yes—
365C22×C32—28no—
366C22×C32—22no—
367C22×C32—22no—
368C22×C32C22×D412yes—
369C22×C32C2×#4112yes—
370C22×C32C2×#4114yescomplemented
371C22×C322−1+412yes—
372C22×C32C2511yescharacteristic
373C2×C3×D3—24no—
374C2×C3×D3—22no—
375C2×C3×D3—22no—
376C2×C3×D3—24no—
377C2×C3×D3—24no—
378C2×C3×D3—22no—
379C2×C3×D3—44no—
380C2×C3×D3—48no—
381C32×C4—22no—
382C32×C4C22×D414yes—
383C3⋊Dic3—24no—
384C3⋊Dic3C22×D418yes—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—24no—
388C3×Dic3—22no—
389C2×#41—98no—
390C2×#41—188no—
391C22×Q8—91no—
392C22×Q8—92no—
393C22×Q8—91no—
394C22×Q8—98no—
395C22×Q8—188no—
396C22×D4—31no—
397C22×D4—32no—
398C22×D4—31no—
399C22×D4—92no—
400C23×C4—31no—
401C23×C4—92no—
402C23×C4—92no—
403C23×C4D3211yescharacteristic
404#124—98no—
405#124—916no—
406C22⋊Q8—916no—
407C22⋊Q8—98no—
408#121—38no—
409#121—916no—
410C4×Q8—98no—
411C4×D4—38no—
412C4×D4—916no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—92no—
416C2×C4⋊C4—92no—
417C2×C22⋊C4—31no—
418C2×C22⋊C4—31no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—92no—
421C2×C22⋊C4—92no—
422C2×C22⋊C4—92no—
423C2×C42—31no—
424C2×C42—92no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—21no—
433C23×C3—24no—
434C23×C3—34no—
435C23×C3—32no—
436C23×C3—64no—
437C23×C3—64no—
438C23×C3—62no—
439C23×C3—62no—
440C23×C3—64no—
441C23×C3—62no—
442C23×C3#23514yescomplemented
443C23×C3#23714yescomplemented
444C23×C3C23×D312yes—
445C23×C3C23×D312yes—
446C23×C3C23×D311yescharacteristic
447C23×C3C23×D311yescharacteristic
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—24no—
451C22×D3—24no—
452C22×D3—22no—
453C22×D3—24no—
454C22×D3C23×D314yes—
455C22×D3C23×D312yes—
456C3×D4—616no—
457C3×D4—68no—
458C3×D4—68no—
459C2×C3×C4—24no—
460C2×C3×C4—216no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—28no—
464C2×C3×C4—28no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—24no—
468C2×C3×C4—32no—
469C2×C3×C4—34no—
470C2×C3×C4—32no—
471C2×C3×C4—32no—
472C2×C3×C4—64no—
473C2×C3×C4—62no—
474C2×C3×C4—62no—
475C2×C3×C4—62no—
476C2×C3×C4—68no—
477C2×C3×C4D3×D414yes—
478C2×C3×C4D3×D414yes—
479C2×C3×C4C23×D312yes—
480C2×C3×C4C23×D312yes—
481C2×C3×C4C23×D312yes—
482C2×C3×C4C23×D312yes—
483#67—28no—
484#67—216no—
485#67—616no—
486#67—616no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—24no—
490C2×Dic3—22no—
491C2×Dic3—38no—
492C2×Dic3—38no—
493C2×Dic3—34no—
494C2×Dic3—34no—
495C2×Dic3—34no—
496C2×Dic3—34no—
497C2×Dic3—68no—
498C2×Dic3—64no—
499C2×Dic3—64no—
500C2×Dic3—616no—
501C2×Dic3—616no—
502C2×Dic3—616no—
503C2×Dic3—632no—
504C2×Dic3—68no—
505C2×Dic3—64no—
506C2×Dic3—64no—
507C2×Dic3C23×D312yes—
508C2×Dic3C23×D314yes—
509C2×Dic3C23×D312yes—
510C2×Dic3C23×D312yes—
511D12—28no—
512C4×D3—28no—
513C4×D3—616no—
514Dic6—316no—
515Dic6—316no—
516Dic6—616no—
517Dic6—616no—
518Dic6—616no—
519Dic6—632no—
520Dic6—616no—
521Dic6—68no—
522Dic6—68no—
523C2×C32—24no—
524C2×C32#54814yescomplemented
525C2×C32C23×D411yescharacteristic
526C2×C32C22×#4111yescharacteristic
527C2×C32C2×2−1+411yescharacteristic
528C3×D3—44no—
529C3×D3—42no—
530C24—31no—
531C24—32no—
532C24C2×D3211yescharacteristic
533#41—1832no—
534C2×Q8—94no—
535C2×Q8—98no—
536C2×Q8—94no—
537C2×Q8—98no—
538C2×Q8—188no—
539C2×Q8—1832no—
540C2×Q8—184no—
541C2×D4—34no—
542C2×D4—38no—
543C2×D4—34no—
544C2×D4—64no—
545C2×D4—68no—
546C2×D4—64no—
547C2×D4—98no—
548C2×D4—188no—
549C22×C4—24no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—32no—
553C22×C4—31no—
554C22×C4—34no—
555C22×C4—64no—
556C22×C4—98no—
557C22×C4—92no—
558C22×C4—98no—
559C22×C4—92no—
560C22×C4—188no—
561C22×C4—188no—
562C22×C4C2×D3214yes—
563C22×C4C2×D3211yescharacteristic
564C22×C4C2×D3211yescharacteristic
565C4⋊C4—34no—
566C4⋊C4—34no—
567C4⋊C4—98no—
568C4⋊C4—98no—
569C22⋊C4—34no—
570C22⋊C4—34no—
571C22⋊C4—38no—
572C22⋊C4—98no—
573C22⋊C4—98no—
574C22⋊C4—98no—
575C42—34no—
576C42—98no—
577C22×C3—24no—
578C22×C3—24no—
579C22×C3—216no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—28no—
585C22×C3—28no—
586C22×C3—22no—
587C22×C3—24no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—21no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—62no—
594C22×C3—62no—
595C22×C3—62no—
596C22×C3—64no—
597C22×C3—128no—
598C22×C3—124no—
599C22×C3C2×#23512yes—
600C22×C3C2×#23514yescomplemented
601C22×C3C2×D3×D412yes—
602C22×C3C2×D3×D412yes—
603C22×C3C2×#23712yes—
604C22×C3C2×#23714yescomplemented
605C22×C3#101012yes—
606C22×C3#101012yes—
607C22×C3C24×D311yescharacteristic
608C22×C3C24×D311yescharacteristic
609C2×D3—22no—
610C2×D3—22no—
611C2×D3—24no—
612C2×D3—24no—
613C2×D3—24no—
614C2×D3—22no—
615C2×D3—44no—
616C2×D3—48no—
617C3×C4—24no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—24no—
621C3×C4—64no—
622C3×C4—62no—
623C3×C4—62no—
624C3×C4—62no—
625C3×C4C2×D3×D414yes—
626C3×C4C2×D3×D414yes—
627Dic3—22no—
628Dic3—22no—
629Dic3—24no—
630Dic3—22no—
631Dic3—38no—
632Dic3—38no—
633Dic3—68no—
634Dic3—68no—
635Dic3—64no—
636Dic3—64no—
637C32C2×#54811yescharacteristic, complemented, Sylow
638C23—22no—
639C23—22no—
640C23—32no—
641C23—34no—
642C23—62no—
643C23—64no—
644C23—62no—
645C23—64no—
646C23—62no—
647C23—64no—
648C23#379514yescomplemented
649C23C22×D3212yes—
650C23C22×D3211yescharacteristic
651Q8—916no—
652Q8—1816no—
653Q8—188no—
654D4—68no—
655D4—616no—
656D4—68no—
657D4—1816no—
658C2×C4—22no—
659C2×C4—28no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—34no—
663C2×C4—32no—
664C2×C4—62no—
665C2×C4—64no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—68no—
669C2×C4—98no—
670C2×C4—94no—
671C2×C4—94no—
672C2×C4—1816no—
673C2×C4—1816no—
674C2×C4—184no—
675C2×C4#381114yes—
676C2×C4C22×D3212yes—
677C2×C4C22×D3212yes—
678C2×C3—28no—
679C2×C3—24no—
680C2×C3—24no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—24no—
685C2×C3—122no—
686C2×C3—124no—
687C2×C3#555214yescomplemented
688C2×C3#559814yescomplemented
689C2×C3C22×#23511yescharacteristic
690C2×C3C22×D3×D411yescharacteristic
691C2×C3C22×D3×D411yescharacteristic
692C2×C3C22×#23711yescharacteristic
693C2×C3C2×#101011yescharacteristic
694C2×C3C2×#101011yescharacteristic
695D3—44no—
696D3—42no—
697C22—22no—
698C22—22no—
699C22—28no—
700C22—62no—
701C22—64no—
702C22—62no—
703C22—64no—
704C22—62no—
705C22—64no—
706C22—124no—
707C22—128no—
708C22C2×#379512yes—
709C22C2×#379514yescomplemented
710C22#6429812yes—
711C22C2×#381112yes—
712C22C23×D3211yescharacteristic
713C4—22no—
714C4—62no—
715C4—64no—
716C4—62no—
717C4—62no—
718C4—98no—
719C4—184no—
720C4C2×#381114yes—
721C3—21no—
722C3C2×#555211yescharacteristic, complemented
723C3C2×#559811yescharacteristic, complemented
724C2—24no—
725C2—122no—
726C2—124no—
727C2#1059491814yesdirect product factor
728C2C22×#379511yescharacteristic
729C2C2×#6429811yescharacteristic
730C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×#634C2semidirect
2. C22×#3795C2semidirect
3. C2×C3×#930C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×#63980C2semidirect
6. C2×#67⋊Dic3C2semidirect
7. C2×#63913C2semidirect
8. #10594918C2direct (N × H)
9. C2×#63896C2semidirect
10. C2×#63860C2semidirect
11. C2×#63857C2semidirect
12. C2×#63844C2semidirect
21. C22×#634C22semidirect
29. C2×#3795C22semidirect
31. C3×#930C22semidirect
32. C3×C4×#67C22semidirect
38. #63980C22semidirect
39. #67⋊Dic3C22semidirect
46. #63913C22semidirect
47. #63896C22semidirect
48. #63860C22semidirect
49. #63857C22semidirect
50. #63844C22semidirect
62. C2×#930D3semidirect
63. C2×C4×#67D3semidirect
90. C2×#634D4semidirect
177. #930C2×D3semidirect
178. C4×#67C2×D3semidirect
205. C23×C32#41semidirect
228. #634C2×D4semidirect
370. C22×C32C2×#41semidirect
442. C23×C3#235semidirect
443. C23×C3#237semidirect
524. C2×C32#548semidirect
600. C22×C3C2×#235semidirect
604. C22×C3C2×#237semidirect
637. C32C2×#548semidirect
648. C23#3795semidirect
687. C2×C3#5552semidirect
688. C2×C3#5598semidirect
709. C22C2×#3795semidirect
722. C3C2×#5552semidirect
723. C3C2×#5598semidirect
727. C2#10594918direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6342
C22×#37952
C2×C3×#9302
C2×C3×C4×#672
C2×#639802
C2×#67⋊Dic32
C2×#639132
#105949182
C2×#638962
C2×#638602
C2×#638572
C2×#638442
C2×#55983
C2×#55523