Finite Group Databasebeta

← C2×#10594902 #11902620

Subgroups — C2×#10594902 #11902620

Order 1152.

3453 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×C3×Dic6C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×#64139C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×#63978C212yesmaximal, complemented
6C2×#63952C212yesmaximal, complemented
7C2×#63907C212yesmaximal, complemented
8#10594902C2116yesmaximal, direct product factor
9C2×#63888C212yesmaximal, complemented
10C2×#63864C211yesmaximal, characteristic, complemented
11C2×#63856C211yesmaximal, characteristic, complemented
12C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
13C2×#5817—31nomaximal
14C2×#5552—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2212yes—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2212yes—
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6—28no—
22C22×C3×Dic6C2211yescharacteristic
23C22×C3×Dic6C2212yes—
24C22×C3×Dic6C2211yescharacteristic
25C22×C3×Dic6C2218yescomplemented
26C22×#626C2212yes—
27C22×#624C2212yes—
28C2×#3799—28no—
29C2×#3799C2218yescomplemented
30#64139C2218yescomplemented
31C2×#3752C2212yes—
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C3×C4×#67C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38#63978C22116yescomplemented
39C2×#3724C2212yes—
40C2×Dic3⋊Dic3C2212yes—
41C2×#3722C2212yes—
42C2×#3722C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×Dic32C2212yes—
45#63952C22116yescomplemented
46#63907C22116yescomplemented
47#63888C22116yescomplemented
48#63864C2218yescomplemented
49#63856C2218yescomplemented
50Dic3×Dic6C2218yescomplemented
51C23×C3×Q8—31no—
52C22×#239—31no—
53C22×#235—31no—
54C23×Dic6D311yescharacteristic, complemented
55C2×C3×C4×D4—31no—
56#5817—316no—
57C2×#947—32no—
58C2×#947—31no—
59C2×#946—31no—
60C2×#946—32no—
61C2×Q8×Dic3—31no—
62C2×#939—32no—
63C2×#930—31no—
64C2×#930—31no—
65C2×#930—32no—
66C2×#930—61no—
67C2×C4×#67—32no—
68C2×C4×#67D311yescharacteristic, complemented
69C2×#924—31no—
70#5552—316no—
71C2×#896—32no—
72C2×#885—32no—
73C2×#67⋊C4—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
83C2×#638—28no—
84C2×#638C2318yes—
85C22×C3⋊Dic3C2312yes—
86C2×C4⋊(C3⋊D3)—24no—
87C2×C4⋊(C3⋊D3)C2314yes—
88C2×C3×#67—24no—
89C2×C3×#67C2314yes—
90C22×C3×Dic3—28no—
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2318yes—
96C22×C3×Dic3C2312yes—
97C2×C3×C4×D3—24no—
98C2×C3×C4×D3C2314yes—
99C2×C3×Dic6—24no—
100C2×C3×Dic6—28no—
101C2×C3×Dic6—232no—
102C2×C3×Dic6D418yescomplemented
103C2×C3×Dic6C2314yes—
104C2×C3×Dic6C2318yes—
105C2×C3×Dic6C2314yes—
106C2×#626—28no—
107C2×#626C2318yes—
108C2×#624—28no—
109C2×#624C2318yes—
110#3799—232no—
111#3752C2318yes—
112C4⋊(C3⋊Dic3)C2314yes—
113C3×#217C2314yes—
114C3×(C2×D3)⋊C4C2314yes—
115C3×Dic3⋊C4C2314yes—
116C3×C4×Dic3C2314yes—
117#3724C2318yes—
118Dic3⋊Dic3C2318yes—
119#3722C2318yes—
120#3722C2318yes—
121(C2×D3)⋊Dic3C2318yes—
122Dic32C2318yes—
123C2×#548—91noSylow
124C22×C3×Q8—31no—
125C22×C3×Q8—32no—
126C22×C3×Q8—31no—
127C22×C3×Q8—38no—
128C22×C3×Q8—68no—
129C22×C3×D4—31no—
130C23×C3×C4—21no—
131C23×C3×C4—32no—
132C23×C3×C4—31no—
133C23×C3×C4C2×D311yescharacteristic
134C23×C3×C4C2×D311yescharacteristic
135C22×#67—32no—
136C22×#67—32no—
137C22×#67—32no—
138C22×#67—62no—
139C22×#67C2×D311yescharacteristic
140C23×Dic3C2×D312yes—
141C2×#239—38no—
142C2×#239—68no—
143C2×#235—38no—
144C2×#235—68no—
145C22×D12—32no—
146C22×D12—31no—
147C22×D12—31no—
148C22×D12—61no—
149C22×C4×D3—32no—
150C22×C4×D3—32no—
151C22×C4×D3C2×D311yescharacteristic
152C22×Dic6—28no—
153C22×Dic6C2×D311yescharacteristic
154C22×Dic6C2×D312yes—
155C22×Dic6C2×D311yescharacteristic
156C22×Dic6C2×D318yescomplemented
157C3×C4×D4—38no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C42—31no—
162C2×#217—32no—
163C2×#217C2×D311yescharacteristic
164#947—316no—
165#947—38no—
166#946—38no—
167#946—316no—
168Q8×Dic3—38no—
169#939—316no—
170#930—38no—
171#930—38no—
172#930—316no—
173#930—68no—
174C4×#67—316no—
175C4×#67C2×D318yescomplemented
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—32no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—62no—
184C2×(C2×D3)⋊C4C2×D311yescharacteristic
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3—32no—
188C2×C4⋊Dic3—61no—
189#924—38no—
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4—32no—
192C2×Dic3⋊C4—32no—
193C2×Dic3⋊C4C2×D311yescharacteristic
194C2×C4×Dic3—32no—
195C2×C4×Dic3—32no—
196C2×C4×Dic3C2×D311yescharacteristic
197#896—316no—
198#885—316no—
199#67⋊C4—316no—
200#875—38no—
201C4×Dic6—38no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32#4114yescomplemented
205C23×C32C2412yes—
206C23×C32C2411yescharacteristic
207C22×C3⋊D3—24no—
208C22×C3⋊D3—24no—
209C22×C3⋊D3—24no—
210C22×C3⋊D3C2414yes—
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3C2412yes—
215C2×C32×C4—22no—
216C2×C32×C4—28no—
217C2×C32×C4C2×D414yes—
218C2×C32×C4C2412yes—
219C2×C32×C4C2412yes—
220#638—216no—
221C2×C3⋊Dic3—24no—
222C2×C3⋊Dic3C2414yes—
223C4⋊(C3⋊D3)—28no—
224C3×#67—28no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—24no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—216no—
230C2×C3×Dic3C2×D418yes—
231C2×C3×Dic3C2412yes—
232C2×C3×Dic3C2414yes—
233C2×C3×Dic3C2412yes—
234C2×C3×Dic3C2412yes—
235C2×C3×Dic3C2414yes—
236C3×C4×D3—28no—
237C3×Dic6—28no—
238C3×Dic6—216no—
239C3×Dic6C2×D4116yescomplemented
240#626—216no—
241#624—216no—
242C22×#41—91no—
243C23×Q8—31no—
244#548—916no—
245C2×#124—91no—
246C2×#124—92no—
247C2×C22⋊Q8—92no—
248C2×C22⋊Q8—91no—
249C2×#121—92no—
250C2×#121—91no—
251C2×C4×Q8—91no—
252C2×C4×D4—31no—
253C2×C4×D4—92no—
254C24×C3—21no—
255C24×C3—31no—
256C24×C3C22×D311yescharacteristic
257C24×C3C22×D311yescharacteristic
258C23×D3—32no—
259C23×D3—32no—
260C23×D3—62no—
261C23×D3C22×D311yescharacteristic
262C2×C3×Q8—38no—
263C2×C3×Q8—34no—
264C2×C3×Q8—38no—
265C2×C3×Q8—34no—
266C2×C3×Q8—68no—
267C2×C3×Q8—632no—
268C2×C3×Q8—64no—
269C2×C3×D4—34no—
270C2×C3×D4—64no—
271C22×C3×C4—24no—
272C22×C3×C4—24no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—24no—
276C22×C3×C4—32no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—32no—
281C22×C3×C4—38no—
282C22×C3×C4—34no—
283C22×C3×C4—44no—
284C22×C3×C4—68no—
285C22×C3×C4—64no—
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D314yes—
289C22×C3×C4C22×D314yes—
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C2×#67—24no—
293C2×#67—38no—
294C2×#67—38no—
295C2×#67—38no—
296C2×#67—68no—
297C2×#67—68no—
298C2×#67—68no—
299C2×#67—68no—
300C2×#67—128no—
301C2×#67C22×D314yes—
302C22×Dic3—28no—
303C22×Dic3—32no—
304C22×Dic3—32no—
305C22×Dic3—62no—
306C22×Dic3C22×D318yes—
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D312yes—
311C22×Dic3C22×D312yes—
312#239—632no—
313#235—632no—
314C2×D12—38no—
315C2×D12—34no—
316C2×D12—34no—
317C2×D12—64no—
318C2×D12—68no—
319C2×D12—64no—
320C2×D12—64no—
321C2×D12—124no—
322C2×C4×D3—24no—
323C2×C4×D3—38no—
324C2×C4×D3—38no—
325C2×C4×D3—68no—
326C2×C4×D3—68no—
327C2×C4×D3C22×D314yes—
328C2×Dic6—24no—
329C2×Dic6—28no—
330C2×Dic6—232no—
331C2×Dic6#6718yescomplemented
332C2×Dic6C22×D314yes—
333C2×Dic6C22×D318yes—
334C2×Dic6C22×D314yes—
335C3×C4⋊C4—34no—
336C3×C22⋊C4—34no—
337C3×C22⋊C4—34no—
338C3×C42—34no—
339#217—38no—
340#217C22×D314yes—
341(C2×D3)⋊C4—38no—
342(C2×D3)⋊C4—38no—
343(C2×D3)⋊C4—38no—
344(C2×D3)⋊C4—38no—
345(C2×D3)⋊C4—38no—
346(C2×D3)⋊C4—38no—
347(C2×D3)⋊C4—38no—
348(C2×D3)⋊C4—68no—
349(C2×D3)⋊C4C22×D314yes—
350C4⋊Dic3—34no—
351C4⋊Dic3—34no—
352C4⋊Dic3—38no—
353C4⋊Dic3—64no—
354Dic3⋊C4—38no—
355Dic3⋊C4—38no—
356Dic3⋊C4—38no—
357Dic3⋊C4C22×D314yes—
358C4×Dic3—38no—
359C4×Dic3—38no—
360C4×Dic3C22×D314yes—
361C22×C32—28no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32C22×D412yes—
365C22×C32C2×#4112yes—
366C22×C32C2×#4114yescomplemented
367C22×C322−1+412yes—
368C22×C32C2511yescharacteristic
369C2×C3⋊D3—24no—
370C2×C3⋊D3—24no—
371C2×C3⋊D3—24no—
372C2×C3⋊D3—48no—
373C2×C3×D3—22no—
374C2×C3×D3—22no—
375C2×C3×D3—22no—
376C2×C3×D3—44no—
377C32×C4—22no—
378C32×C4C22×D414yes—
379C3⋊Dic3—24no—
380C3×Dic3—22no—
381C3×Dic3—24no—
382C3×Dic3—22no—
383C3×Dic3—22no—
384C3×Dic3C22×D418yes—
385C2×#41—98no—
386C2×#41—188no—
387C22×Q8—31no—
388C22×Q8—32no—
389C22×Q8—31no—
390C22×Q8—38no—
391C22×Q8—68no—
392C22×D4—31no—
393C22×D4—92no—
394C22×D4—92no—
395C22×D4—91no—
396C23×C4—32no—
397C23×C4—31no—
398C23×C4—92no—
399C23×C4D3211yescharacteristic
400#124—98no—
401#124—916no—
402C22⋊Q8—916no—
403C22⋊Q8—98no—
404#121—916no—
405#121—98no—
406C4×Q8—98no—
407C4×D4—38no—
408C4×D4—916no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—92no—
411C2×C4⋊C4—92no—
412C2×C4⋊C4—91no—
413C2×C22⋊C4—31no—
414C2×C22⋊C4—31no—
415C2×C22⋊C4—92no—
416C2×C22⋊C4—92no—
417C2×C22⋊C4—92no—
418C2×C22⋊C4—92no—
419C2×C42—31no—
420C2×C42—92no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—21no—
427C23×C3—24no—
428C23×C3—32no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—62no—
432C23×C3—62no—
433C23×C3—62no—
434C23×C3#23514yescomplemented
435C23×C3#23914yescomplemented
436C23×C3C23×D312yes—
437C23×C3C23×D312yes—
438C23×C3C23×D311yescharacteristic
439C23×C3C23×D311yescharacteristic
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—22no—
443C22×D3—34no—
444C22×D3—34no—
445C22×D3—64no—
446C22×D3—64no—
447C22×D3—64no—
448C22×D3—64no—
449C22×D3—64no—
450C22×D3—64no—
451C22×D3—64no—
452C22×D3—124no—
453C22×D3—124no—
454C22×D3—124no—
455C22×D3C23×D312yes—
456C3×Q8—316no—
457C3×Q8—616no—
458C3×Q8—68no—
459C3×D4—68no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—28no—
463C2×C3×C4—28no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—24no—
467C2×C3×C4—38no—
468C2×C3×C4—34no—
469C2×C3×C4—32no—
470C2×C3×C4—32no—
471C2×C3×C4—32no—
472C2×C3×C4—34no—
473C2×C3×C4—48no—
474C2×C3×C4—42no—
475C2×C3×C4—616no—
476C2×C3×C4—64no—
477C2×C3×C4—62no—
478C2×C3×C4—62no—
479C2×C3×C4—62no—
480C2×C3×C4—68no—
481C2×C3×C4D3×D414yes—
482C2×C3×C4C2×#6714yes—
483C2×C3×C4C23×D312yes—
484C2×C3×C4C23×D312yes—
485C2×C3×C4C23×D312yes—
486C2×C3×C4C23×D312yes—
487#67—28no—
488#67—616no—
489#67—616no—
490#67—616no—
491#67—1216no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—24no—
496C2×Dic3—216no—
497C2×Dic3—34no—
498C2×Dic3—34no—
499C2×Dic3—64no—
500C2×Dic3—64no—
501C2×Dic3—64no—
502C2×Dic3—124no—
503C2×Dic3C2×#6718yes—
504C2×Dic3C23×D312yes—
505C2×Dic3C23×D312yes—
506C2×Dic3C23×D312yes—
507C2×Dic3C23×D314yes—
508C2×Dic3C23×D314yes—
509D12—616no—
510D12—68no—
511D12—68no—
512D12—128no—
513C4×D3—28no—
514C4×D3—616no—
515C4×D3—616no—
516Dic6—28no—
517Dic6—216no—
518Dic6C2×#67116yescomplemented
519C2×C32—24no—
520C2×C32#54814yescomplemented
521C2×C32C23×D411yescharacteristic
522C2×C32C22×#4111yescharacteristic
523C2×C32C2×2−1+411yescharacteristic
524C3⋊D3—44no—
525C3×D3—42no—
526C24—31no—
527C24—92no—
528C24C2×D3211yescharacteristic
529#41—1832no—
530C2×Q8—34no—
531C2×Q8—38no—
532C2×Q8—34no—
533C2×Q8—38no—
534C2×Q8—68no—
535C2×Q8—632no—
536C2×Q8—64no—
537C2×D4—34no—
538C2×D4—64no—
539C2×D4—98no—
540C2×D4—98no—
541C2×D4—94no—
542C2×D4—188no—
543C2×D4—188no—
544C2×D4—184no—
545C22×C4—24no—
546C22×C4—32no—
547C22×C4—38no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—32no—
552C22×C4—34no—
553C22×C4—68no—
554C22×C4—64no—
555C22×C4—98no—
556C22×C4—92no—
557C22×C4—188no—
558C22×C4C2×D3214yes—
559C22×C4C2×D3211yescharacteristic
560C22×C4C2×D3211yescharacteristic
561C4⋊C4—34no—
562C4⋊C4—98no—
563C4⋊C4—98no—
564C4⋊C4—94no—
565C22⋊C4—34no—
566C22⋊C4—34no—
567C22⋊C4—98no—
568C22⋊C4—98no—
569C22⋊C4—98no—
570C22⋊C4—98no—
571C42—34no—
572C42—98no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—28no—
578C22×C3—28no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—24no—
582C22×C3—22no—
583C22×C3—21no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—48no—
587C22×C3—62no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3—124no—
591C22×C3C2×#23512yes—
592C22×C3C2×#23514yescomplemented
593C22×C3C2×D3×D412yes—
594C22×C3C2×#23912yes—
595C22×C3C2×#23914yescomplemented
596C22×C3#100712yes—
597C22×C3#101012yes—
598C22×C3C22×#6712yes—
599C22×C3C24×D311yescharacteristic
600C22×C3C24×D311yescharacteristic
601C2×D3—22no—
602C2×D3—22no—
603C2×D3—22no—
604C2×D3—44no—
605C2×D3—64no—
606C2×D3—64no—
607C2×D3—64no—
608C2×D3—64no—
609C2×D3—64no—
610C2×D3—64no—
611C2×D3—124no—
612C2×D3—124no—
613C2×D3—124no—
614C2×D3—128no—
615C2×D3—128no—
616C2×D3—248no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—24no—
620C3×C4—38no—
621C3×C4—42no—
622C3×C4—64no—
623C3×C4—62no—
624C3×C4—62no—
625C3×C4—62no—
626C3×C4C2×D3×D414yes—
627C3×C4C22×#6714yes—
628Dic3—22no—
629Dic3—22no—
630Dic3—22no—
631Dic3—24no—
632Dic3—64no—
633Dic3—64no—
634Dic3—124no—
635Dic3C22×#6718yes—
636C32C2×#54811yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—32no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23—94no—
644C23—184no—
645C23—184no—
646C23—184no—
647C23#379914yescomplemented
648C23C22×D3212yes—
649C23C22×D3211yescharacteristic
650Q8—316no—
651Q8—616no—
652Q8—68no—
653D4—68no—
654D4—1816no—
655D4—1816no—
656D4—188no—
657C2×C4—22no—
658C2×C4—28no—
659C2×C4—38no—
660C2×C4—34no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—34no—
665C2×C4—616no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—64no—
670C2×C4—68no—
671C2×C4—94no—
672C2×C4—1816no—
673C2×C4—184no—
674C2×C4D3×#6714yes—
675C2×C4C22×D3212yes—
676C2×C4C22×D3212yes—
677C2×C3—24no—
678C2×C3—24no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—24no—
682C2×C3—21no—
683C2×C3—44no—
684C2×C3—122no—
685C2×C3#555214yescomplemented
686C2×C3#581714yescomplemented
687C2×C3C22×#23511yescharacteristic
688C2×C3C22×D3×D411yescharacteristic
689C2×C3C22×#23911yescharacteristic
690C2×C3C2×#100711yescharacteristic
691C2×C3C2×#101011yescharacteristic
692C2×C3C23×#6711yescharacteristic
693D3—42no—
694D3—124no—
695D3—124no—
696D3—244no—
697C22—22no—
698C22—28no—
699C22—22no—
700C22—62no—
701C22—62no—
702C22—62no—
703C22—124no—
704C22—184no—
705C22—184no—
706C22—184no—
707C22—368no—
708C22#6429712yes—
709C22C2×#379912yes—
710C22C2×#379914yescomplemented
711C22C2×D3×#6712yes—
712C22C23×D3211yescharacteristic
713C4—22no—
714C4—38no—
715C4—62no—
716C4—62no—
717C4—62no—
718C4—64no—
719C4—184no—
720C4C2×D3×#6714yes—
721C3—21no—
722C3C2×#555211yescharacteristic, complemented
723C3C2×#581711yescharacteristic, complemented
724C2—24no—
725C2—122no—
726C2—364no—
727C2#1059490214yesdirect product factor
728C2C2×#6429711yescharacteristic
729C2C22×#379911yescharacteristic
730C2C22×D3×#6711yescharacteristic
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×C3×Dic6C2semidirect
2. C22×#3799C2semidirect
3. C2×#64139C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×#63978C2semidirect
6. C2×#63952C2semidirect
7. C2×#63907C2semidirect
8. #10594902C2direct (N × H)
9. C2×#63888C2semidirect
10. C2×#63864C2semidirect
11. C2×#63856C2semidirect
12. C2×Dic3×Dic6C2semidirect
25. C22×C3×Dic6C22semidirect
29. C2×#3799C22semidirect
30. #64139C22semidirect
34. C3×C4×#67C22semidirect
38. #63978C22semidirect
45. #63952C22semidirect
46. #63907C22semidirect
47. #63888C22semidirect
48. #63864C22semidirect
49. #63856C22semidirect
50. Dic3×Dic6C22semidirect
54. C23×Dic6D3semidirect
68. C2×C4×#67D3semidirect
102. C2×C3×Dic6D4semidirect
156. C22×Dic6C2×D3semidirect
175. C4×#67C2×D3semidirect
204. C23×C32#41semidirect
239. C3×Dic6C2×D4semidirect
331. C2×Dic6#67semidirect
366. C22×C32C2×#41semidirect
434. C23×C3#235semidirect
435. C23×C3#239semidirect
518. Dic6C2×#67semidirect
520. C2×C32#548semidirect
592. C22×C3C2×#235semidirect
595. C22×C3C2×#239semidirect
636. C32C2×#548semidirect
647. C23#3799semidirect
685. C2×C3#5552semidirect
686. C2×C3#5817semidirect
710. C22C2×#3799semidirect
722. C3C2×#5552semidirect
723. C3C2×#5817semidirect
727. C2#10594902direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Dic62
C22×#37992
C2×#641392
C2×C3×C4×#672
C2×#639782
C2×#639522
C2×#639072
#105949022
C2×#638882
C2×#638642
C2×#638562
C2×Dic3×Dic62
C2×#58173
C2×#55523