Finite Group Databasebeta

← #11634123

Subgroups — #11634123

Order 768.

2602 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#556C211yesmaximal, characteristic, complemented
2C2×#5725C211yesmaximal, characteristic, complemented
3#83229C211yesmaximal, characteristic, complemented
4#83117C214yesmaximal, complemented
5#83106C214yesmaximal, complemented
6#82974C212yesmaximal, complemented
7#82958C212yesmaximal, complemented
8#82779C212yesmaximal, complemented
9#82756C212yesmaximal, complemented
10C4×#946C211yesmaximal, characteristic, complemented
11#82476C211yesmaximal, characteristic, complemented
12#82469C212yesmaximal, complemented
13#82457C212yesmaximal, complemented
14C4×#938C211yesmaximal, characteristic, complemented
15#82378C211yesmaximal, characteristic, complemented
16#82276C212yesmaximal, complemented
17#82244C212yesmaximal, complemented
18#59049—31nomaximal, Sylow
19C22×#239C2212yes—
20C3×#556—28no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#126C2214yes—
23C2×C3×#124C2212yes—
24C2×C3×C22⋊Q8C2212yes—
25C2×C3×C4×Q8C2212yes—
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×#117C2212yes—
29C2×#947C2212yes—
30C2×#947C2212yes—
31C2×#946C2211yescharacteristic
32C2×Q8×Dic3C2212yes—
33C2×#940C2212yes—
34C2×#938C2211yescharacteristic
35C2×#930C2212yes—
36C2×#930C2212yes—
37C2×C4×#67C2212yes—
38#5725—28no—
39C2×#895C2212yes—
40C2×#895C2212yes—
41C2×#893C2212yes—
42C2×#893C2212yes—
43C2×#874C2211yescharacteristic
44C2×C42×D3C2211yescharacteristic
45#5229C2212yes—
46#5229C2211yescharacteristic
47#5221C2211yescharacteristic
48C4×#217C2212yes—
49#4993C2214yes—
50#4992C2214yes—
51#4991C2214yes—
52#4989C2212yes—
53#4988C2212yes—
54#4988C2214yes—
55#4988C2212yes—
56#4987C2211yescharacteristic
57#4987C2214yes—
58#4987C2211yescharacteristic
59#4984C2212yes—
60#4980C2214yes—
61#4978C2212yes—
62Dic3×C4⋊C4C2212yes—
63#4972C2211yescharacteristic
64#4972C2211yescharacteristic
65#4961C2214yes—
66#4961C2214yes—
67#4960C2214yes—
68#4960C2214yes—
69#4960C2214yes—
70#4957C2214yes—
71#4957C2214yes—
72#4956C2214yes—
73#4956C2214yes—
74#4956C2212yes—
75#4944C2212yes—
76#4940C2214yes—
77#4940C2214yes—
78#4939C2212yes—
79#4939C2212yes—
80#4939C2214yes—
81C4×(C2×D3)⋊C4C2212yes—
82C4×(C2×D3)⋊C4C2214yes—
83C4×C4⋊Dic3C2211yescharacteristic
84C4×C4⋊Dic3C2211yescharacteristic
85C4×Dic3⋊C4C2212yes—
86C2×#556D311yescharacteristic, complemented
87C2×#532—31no—
88#2714—34no—
89#2548—32no—
90#2548—31no—
91#2541—31no—
92#2540—32no—
93#2467—34no—
94#2448—32no—
95#2431—32no—
96#2427—32no—
97#2414—32no—
98#2365—31no—
99#2363—32no—
100#2341—32no—
101C4×C22⋊Q8—31no—
102C4×#121—31no—
103C22×C3×Q8C2311yescharacteristic
104C22×C3×Q8C2312yes—
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4C2312yes—
107C22×#67C2314yes—
108C22×#67C2312yes—
109C22×#67C2314yes—
110C2×#239—28no—
111C2×#239—28no—
112C2×#239—44no—
113C22×D12C2312yes—
114C22×D12C2312yes—
115C22×D12C2314yes—
116C22×D12C2312yes—
117C22×C4×D3C2311yescharacteristic
118C22×C4×D3C2314yes—
119C22×C4×D3C2311yescharacteristic
120C22×C4×D3C2311yescharacteristic
121C3×C4⋊Q8D418yescomplemented
122C3×#126—216no—
123C3×#124—28no—
124C3×C22⋊Q8—28no—
125C3×C4×Q8—28no—
126C3×C4×Q8—24no—
127C3×C4×D4—24no—
128C3×#117—28no—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2312yes—
132C2×C3×C4⋊C4C2314yes—
133C2×C3×C4⋊C4C2312yes—
134C2×C3×C4⋊C4C2312yes—
135C2×C3×C22⋊C4C2312yes—
136C2×C3×C22⋊C4C2314yes—
137C2×C3×C22⋊C4C2314yes—
138C2×C3×C42C2312yes—
139C2×C3×C42C2314yes—
140C2×C3×C42C2311yescharacteristic
141C2×#217C2312yes—
142C2×#217C2312yes—
143C2×#217C2312yes—
144#947—28no—
145#947—44no—
146#946—24no—
147Q8×Dic3—44no—
148#940—44no—
149#938—24no—
150#930—28no—
151#930—44no—
152C4×#67—44no—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2312yes—
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2311yescharacteristic
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4⋊Dic3C2314yes—
168C2×C4⋊Dic3C2311yescharacteristic
169C2×Dic3⋊C4C2312yes—
170C2×Dic3⋊C4C2312yes—
171C2×Dic3⋊C4C2312yes—
172C2×C4×Dic3C2311yescharacteristic
173C2×C4×Dic3C2312yes—
174C2×C4×Dic3C2312yes—
175C2×C4×Dic3C2311yescharacteristic
176C2×C4×Dic3C2311yescharacteristic
177C2×C4×Dic3C2314yes—
178#895—28no—
179#895—28no—
180#893—28no—
181#893—28no—
182#874—24no—
183C42×D3—24no—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2312yes—
189C3⋊#95C2312yes—
190C3⋊#95C2312yes—
191C3⋊#95C2312yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C22×#41—32no—
195#556—28no—
196#532—68no—
197C2×C4⋊Q8C2×D311yescharacteristic
198C2×#127—32no—
199C2×#127—31no—
200C2×#126C2×D314yes—
201C2×#124—32no—
202C2×#124—32no—
203C2×#124C2×D312yes—
204C2×C22⋊Q8—31no—
205C2×C22⋊Q8C2×D312yes—
206C2×#121—31no—
207C2×#121—32no—
208C2×#121—32no—
209C2×#121—32no—
210C2×#121—32no—
211C2×C4×Q8—32no—
212C2×C4×Q8C2×D312yes—
213C2×C4×Q8C2×D311yescharacteristic
214C2×C4×D4—32no—
215C2×C4×D4—32no—
216C2×C4×D4—32no—
217C2×C4×D4C2×D311yescharacteristic
218C2×#117C2×D312yes—
219C22×C42—31no—
220#399—34no—
221#397—34no—
222#394—34no—
223#394—34no—
224#394—34no—
225#392—34no—
226#392—34no—
227#392—34no—
228#391—32no—
229#391—31no—
230#390—31no—
231#390—32no—
232#390—34no—
233#390—32no—
234#390—34no—
235#390—34no—
236#390—34no—
237#390—32no—
238#390—32no—
239#389—31no—
240#389—32no—
241#389—31no—
242#388—32no—
243#388—34no—
244#388—34no—
245#387—34no—
246#387—32no—
247#386—34no—
248#386—34no—
249#386—32no—
250#385—32no—
251#380—31no—
252#380—34no—
253#380—31no—
254C4×C4⋊C4—32no—
255C4×C4⋊C4—31no—
256C4×C4⋊C4—31no—
257C4×C4⋊C4—32no—
258C4×C22⋊C4—32no—
259C4×C22⋊C4—34no—
260C4×C22⋊C4—32no—
261C24×C3C2412yes—
262C23×D3C2414yes—
263C23×D3C2411yescharacteristic
264C2×C3×Q8—22no—
265C2×C3×Q8—24no—
266C2×C3×Q8—22no—
267C2×C3×Q8—24no—
268C2×C3×Q8—22no—
269C2×C3×Q8C2×D418yes—
270C2×C3×D4—22no—
271C2×C3×D4—22no—
272C2×C3×D4—22no—
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4—24no—
276C22×C3×C4C2412yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2414yes—
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C2×#67—24no—
284C2×#67—28no—
285C2×#67—42no—
286C2×#67—42no—
287C2×#67—44no—
288C2×#67—44no—
289C2×#67—44no—
290C2×#67—44no—
291C2×#67—44no—
292C22×Dic3C2412yes—
293C22×Dic3C2412yes—
294C22×Dic3C2411yescharacteristic
295C22×Dic3C2412yes—
296C22×Dic3C2411yescharacteristic
297C22×Dic3C2411yescharacteristic
298C22×Dic3C2412yes—
299#239—432no—
300C2×D12—28no—
301C2×D12—24no—
302C2×D12—24no—
303C2×D12—24no—
304C2×D12—28no—
305C2×D12—24no—
306C2×D12—24no—
307C2×D12—24no—
308C2×D12—24no—
309C2×D12—42no—
310C2×D12—42no—
311C2×D12—44no—
312C2×C4×D3—22no—
313C2×C4×D3—22no—
314C2×C4×D3—22no—
315C2×C4×D3—22no—
316C2×C4×D3—28no—
317C2×C4×D3—22no—
318C2×C4×D3—22no—
319C2×C4×D3—28no—
320C2×C4×D3—41no—
321C2×C4×D3—41no—
322C2×C4×D3—44no—
323C2×C4×D3#4114yes—
324C3×C4⋊C4—22no—
325C3×C4⋊C4—22no—
326C3×C4⋊C4—28no—
327C3×C4⋊C4—24no—
328C3×C4⋊C4C2×D418yes—
329C3×C4⋊C4C2×D418yes—
330C3×C22⋊C4—28no—
331C3×C22⋊C4—24no—
332C3×C22⋊C4—28no—
333C3×C42—28no—
334C3×C42—24no—
335C3×C42C2×D414yes—
336#217—24no—
337#217—42no—
338#217—42no—
339(C2×D3)⋊C4—28no—
340(C2×D3)⋊C4—28no—
341(C2×D3)⋊C4—28no—
342(C2×D3)⋊C4—24no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—44no—
345(C2×D3)⋊C4—42no—
346(C2×D3)⋊C4—42no—
347(C2×D3)⋊C4—44no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—44no—
350C4⋊Dic3—22no—
351C4⋊Dic3—22no—
352C4⋊Dic3—22no—
353C4⋊Dic3—44no—
354C4⋊Dic3#4114yescomplemented
355Dic3⋊C4—24no—
356Dic3⋊C4—42no—
357Dic3⋊C4—42no—
358C4×Dic3—22no—
359C4×Dic3—22no—
360C4×Dic3—22no—
361C4×Dic3—24no—
362C4×Dic3—24no—
363C4×Dic3—44no—
364C2×#41—68no—
365C2×#41—68no—
366C2×#41—124no—
367C22×Q8C22×D311yescharacteristic
368C22×Q8C22×D312yes—
369C22×D4—32no—
370C22×D4—34no—
371C22×D4—34no—
372C22×D4—32no—
373C22×D4—32no—
374C22×D4—34no—
375C22×D4—32no—
376C22×D4C22×D311yescharacteristic
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—34no—
380C23×C4—31no—
381C23×C4C22×D312yes—
382C4⋊Q8#6718yescomplemented
383#127—64no—
384#127—124no—
385#126—216no—
386#124—28no—
387#124—68no—
388#124—124no—
389C22⋊Q8—28no—
390C22⋊Q8—64no—
391#121—68no—
392#121—64no—
393#121—68no—
394#121—68no—
395#121—124no—
396C4×Q8—28no—
397C4×Q8—24no—
398C4×Q8—124no—
399C4×D4—24no—
400C4×D4—68no—
401C4×D4—68no—
402C4×D4—124no—
403#117—28no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—32no—
409C2×C4⋊C4—32no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—32no—
412C2×C4⋊C4C22×D311yescharacteristic
413C2×C4⋊C4C22×D311yescharacteristic
414C2×C4⋊C4C22×D314yes—
415C2×C4⋊C4C22×D312yes—
416C2×C4⋊C4C22×D312yes—
417C2×C4⋊C4C22×D312yes—
418C2×C22⋊C4—32no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—32no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—32no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4C22×D314yes—
433C2×C22⋊C4C22×D312yes—
434C2×C22⋊C4C22×D314yes—
435C2×C42—31no—
436C2×C42—31no—
437C2×C42—32no—
438C2×C42—32no—
439C2×C42—31no—
440C2×C42—34no—
441C2×C42—64no—
442C2×C42C22×D314yes—
443C2×C42C22×D312yes—
444C2×C42C22×D311yescharacteristic
445#95—32no—
446#95—32no—
447#95—32no—
448#95—32no—
449#95—32no—
450#95—32no—
451#95—32no—
452#95—32no—
453#95—34no—
454#95—34no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3C2511yescharacteristic
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—24no—
470C22×D3—24no—
471C22×D3—24no—
472C22×D3—24no—
473C22×D3—24no—
474C22×D3—24no—
475C22×D3—24no—
476C22×D3C2×#4112yes—
477C3×Q8—216no—
478C3×Q8—44no—
479C3×D4—44no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—48no—
494C2×C3×C4C22×D412yes—
495C2×C3×C4C22×D418yes—
496C2×C3×C4C22×D412yes—
497C2×C3×C4C22×D412yes—
498C2×C3×C4C2×#4112yes—
499C2×C3×C4C2×#4112yes—
500C2×C3×C4H(5,𝔽2)12yes—
501C2×C3×C4H(5,𝔽2)12yes—
502#67—48no—
503#67—88no—
504#67—88no—
505C2×Dic3—21no—
506C2×Dic3—22no—
507C2×Dic3—21no—
508C2×Dic3—22no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—21no—
518C2×Dic3—22no—
519C2×Dic3—21no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—21no—
524C2×Dic3C2×#4114yes—
525C2×Dic3C2×#4112yes—
526D12—416no—
527D12—48no—
528D12—48no—
529D12—48no—
530C4×D3—28no—
531C4×D3—416no—
532C4×D3—44no—
533C4×D3—44no—
534C24—31no—
535C24—34no—
536C24C23×D312yes—
537#41—1232no—
538C2×Q8—24no—
539C2×Q8—22no—
540C2×Q8—24no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8C2×#6718yes—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—68no—
548C2×D4—68no—
549C2×D4—64no—
550C2×D4—64no—
551C2×D4—64no—
552C2×D4—64no—
553C2×D4—64no—
554C2×D4—64no—
555C2×D4—64no—
556C2×D4—68no—
557C2×D4—64no—
558C2×D4—124no—
559C2×D4—122no—
560C2×D4—122no—
561C2×D4—122no—
562C2×D4—122no—
563C2×D4—124no—
564C2×D4—124no—
565C2×D4—124no—
566C2×D4—124no—
567C2×D4—124no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—31no—
572C22×C4—32no—
573C22×C4—34no—
574C22×C4—32no—
575C22×C4—32no—
576C22×C4—31no—
577C22×C4—32no—
578C22×C4—31no—
579C22×C4—68no—
580C22×C4—62no—
581C22×C4—62no—
582C22×C4—62no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—68no—
587C22×C4—124no—
588C22×C4—121no—
589C22×C4—121no—
590C22×C4C23×D312yes—
591C22×C4C23×D312yes—
592C22×C4C23×D312yes—
593C22×C4C23×D311yescharacteristic
594C22×C4C23×D314yes—
595C22×C4C23×D311yescharacteristic
596C22×C4C23×D311yescharacteristic
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—28no—
600C4⋊C4—24no—
601C4⋊C4—34no—
602C4⋊C4—64no—
603C4⋊C4—62no—
604C4⋊C4—62no—
605C4⋊C4—62no—
606C4⋊C4—122no—
607C4⋊C4—124no—
608C4⋊C4—122no—
609C4⋊C4C2×#6718yes—
610C4⋊C4C2×#6718yes—
611C22⋊C4—28no—
612C22⋊C4—24no—
613C22⋊C4—28no—
614C22⋊C4—68no—
615C22⋊C4—64no—
616C22⋊C4—64no—
617C22⋊C4—68no—
618C22⋊C4—68no—
619C22⋊C4—122no—
620C22⋊C4—124no—
621C22⋊C4—124no—
622C22⋊C4—124no—
623C22⋊C4—124no—
624C22⋊C4—122no—
625C22⋊C4—124no—
626C22⋊C4—122no—
627C22⋊C4—122no—
628C42—28no—
629C42—24no—
630C42—64no—
631C42—64no—
632C42—62no—
633C42—62no—
634C42—62no—
635C42—124no—
636C42C2×#6714yes—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3C23×D411yescharacteristic
645C22×C3C22×#4111yescharacteristic
646C22×C3C22×#4111yescharacteristic
647C22×C3C2×H(5,𝔽2)11yescharacteristic
648C22×C3C2×H(5,𝔽2)11yescharacteristic
649C22×C3#58511yescharacteristic
650C22×C3#58511yescharacteristic
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—44no—
659C2×D3—44no—
660C2×D3—44no—
661C2×D3—44no—
662C2×D3—44no—
663C2×D3—44no—
664C2×D3—44no—
665C3×C4—28no—
666C3×C4—22no—
667C3×C4—42no—
668C3×C4—42no—
669C3×C4—42no—
670C3×C4#54614yes—
671C3×C4#55014yes—
672Dic3—22no—
673Dic3—24no—
674Dic3—41no—
675Dic3—41no—
676Dic3—42no—
677Dic3—42no—
678Dic3—42no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—32no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—61no—
692C23—61no—
693C23—64no—
694C23—64no—
695C23—64no—
696C23—64no—
697C23—64no—
698C23—64no—
699C23—64no—
700C23C24×D311yescharacteristic
701Q8—216no—
702Q8—44no—
703D4—44no—
704D4—1216no—
705D4—128no—
706D4—128no—
707D4—128no—
708D4—128no—
709D4—248no—
710D4—248no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—34no—
725C2×C4—32no—
726C2×C4—48no—
727C2×C4—62no—
728C2×C4—61no—
729C2×C4—62no—
730C2×C4—61no—
731C2×C4—68no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—61no—
740C2×C4—62no—
741C2×C4—61no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—1216no—
748C2×C4—124no—
749C2×C4—124no—
750C2×C4D3×#4112yes—
751C2×C4D3×#4112yes—
752C2×C4#100912yes—
753C2×C4#100912yes—
754C2×C4C22×#6718yes—
755C2×C4C22×#6712yes—
756C2×C4C22×#6712yes—
757C2×C4C22×#6712yes—
758C2×C3—82no—
759C2×C3C2×#54611yescharacteristic
760C2×C3C2×#55011yescharacteristic
761C2×C3#348011yescharacteristic
762C2×C3#348711yescharacteristic
763C2×C3#350611yescharacteristic
764C2×C3#351411yescharacteristic
765C2×C3#354611yescharacteristic
766D3—42no—
767D3—84no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—62no—
776C22—62no—
777C22—62no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—124no—
783C22—124no—
784C22—124no—
785C22—124no—
786C22—124no—
787C22—124no—
788C22—124no—
789C22C2×D3×#4111yescharacteristic
790C22C2×D3×#4111yescharacteristic
791C22C2×#100911yescharacteristic
792C22C2×#100911yescharacteristic
793C22#596811yescharacteristic
794C22#596811yescharacteristic
795C22C23×#6711yescharacteristic
796C4—28no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—64no—
802C4—62no—
803C4—122no—
804C4—122no—
805C4—122no—
806C4—121no—
807C4—121no—
808C4#582914yes—
809C4#583414yes—
810C3#5904911yescharacteristic, complemented, Sylow
811C2—82no—
812C2—122no—
813C2—244no—
814C2#8698011yescharacteristic
815C2#8698611yescharacteristic
816C2#8700511yescharacteristic
817C2#8700911yescharacteristic
818C2C2×#582911yescharacteristic
819C2C2×#583411yescharacteristic
820C2#8729011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#556C2
hypercenterC2×#556D3
hypocenterC3#59049
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×C3×#556C2semidirect
2. C2×#5725C2semidirect
3. #83229C2semidirect
4. #83117C2semidirect
5. #83106C2semidirect
6. #82974C2semidirect
7. #82958C2semidirect
8. #82779C2semidirect
9. #82756C2semidirect
10. C4×#946C2semidirect
11. #82476C2semidirect
12. #82469C2semidirect
13. #82457C2semidirect
14. C4×#938C2semidirect
15. #82378C2semidirect
16. #82276C2semidirect
17. #82244C2semidirect
86. C2×#556D3semidirect
121. C3×C4⋊Q8D4semidirect
354. C4⋊Dic3#41semidirect
382. C4⋊Q8#67semidirect
810. C3#59049semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5562
C2×#57252
#832292
#831172
#831062
#829742
#829582
#827792
#827562
C4×#9462
#824762
#824692
#824572
C4×#9382
#823782
#822762
#822442
#590493