Finite Group Databasebeta

← #11058615

Subgroups — #11058615

Order 768.

2468 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5726C211yesmaximal, characteristic, complemented
2C2×#5580C211yesmaximal, characteristic, complemented
3C3×#2568C211yesmaximal, characteristic, complemented
4#83269C211yesmaximal, characteristic, complemented
5#82500C211yesmaximal, characteristic, complemented
6#78239C214yesmaximal, complemented
7#78238C214yesmaximal, complemented
8#76642C212yesmaximal, complemented
9#76624C212yesmaximal, complemented
10#76621C212yesmaximal, complemented
11#76621C212yesmaximal, complemented
12#76618C212yesmaximal, complemented
13#76482C212yesmaximal, complemented
14#74239C212yesmaximal, complemented
15#74163C212yesmaximal, complemented
16C4⋊C4×D12C211yesmaximal, characteristic, complemented
17C4×#895C211yesmaximal, characteristic, complemented
18#38908—31nomaximal, Sylow
19C22×#239C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×C4×Q8C2211yescharacteristic
22C2×#947C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C2×#946C2212yes—
25C2×#946C2212yes—
26C2×#946C2212yes—
27#5726—28no—
28#5580—28no—
29C2×#898C2212yes—
30C2×#895C2211yescharacteristic
31C2×#895C2211yescharacteristic
32C2×#895C2212yes—
33C2×#894C2212yes—
34C2×#894C2214yes—
35C2×D3×C4⋊C4C2212yes—
36C2×D3×C4⋊C4C2212yes—
37C2×#890C2211yescharacteristic
38C2×C4×D12C2211yescharacteristic
39C2×C4×D12C2212yes—
40C2×C4×D12C2212yes—
41C2×C4×D12C2212yes—
42C2×C4×D12C2211yescharacteristic
43C2×#872C2212yes—
44C2×C42×D3C2211yescharacteristic
45C3×#400C2214yes—
46C3×#391C2212yes—
47C3×#391C2212yes—
48C3×#391C2212yes—
49C3×#382C2212yes—
50C3×C4×C4⋊C4C2211yescharacteristic
51#5229C2212yes—
52#4994C2214yes—
53#4988C2211yescharacteristic
54#4987C2211yescharacteristic
55#4987C2212yes—
56#4987C2212yes—
57#4987C2212yes—
58#4987C2212yes—
59#4984C2211yescharacteristic
60#4972C2212yes—
61#4972C2212yes—
62#4939C2212yes—
63C4×(C2×D3)⋊C4C2212yes—
64#4935C2211yescharacteristic
65#4928C2212yes—
66#4928C2212yes—
67#4676C2214yes—
68#4675C2214yes—
69#4674C2214yes—
70#4672C2214yes—
71#4671C2214yes—
72#4670C2212yes—
73#4668C2214yes—
74#4668C2214yes—
75#4667C2214yes—
76#4667C2214yes—
77#4667C2214yes—
78#4665C2212yes—
79#4665C2214yes—
80#4665C2214yes—
81#4665C2214yes—
82#4665C2214yes—
83#4658C2214yes—
84#4657C2214yes—
85#4657C2214yes—
86C2×#547—31no—
87C2×#529—31no—
88#2857—31no—
89#2695—34no—
90#2693—34no—
91#2625—32no—
92#2568D311yescharacteristic, complemented
93#2538—31no—
94#2535—32no—
95#2442—32no—
96#2427—32no—
97#2417—32no—
98#2417—32no—
99#2407—32no—
100D4×C4⋊C4—31no—
101#2311—32no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C22×C3×Q8C2311yescharacteristic
105C2×#239—28no—
106C2×#239—28no—
107C2×#239—44no—
108C22×D12C2312yes—
109C22×D12C2312yes—
110C22×D12C2314yes—
111C22×D12C2311yescharacteristic
112C22×D12C2311yescharacteristic
113C22×C4×D3C2312yes—
114C22×C4×D3C2311yescharacteristic
115C22×C4×D3C2311yescharacteristic
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2314yes—
118C22×C4×D3C2312yes—
119C22×C4×D3C2314yes—
120C3×C4⋊Q8—24no—
121C3×C4×Q8—24no—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2312yes—
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C42C2312yes—
129C2×C3×C42C2312yes—
130C2×C3×C42C2311yescharacteristic
131#947—24no—
132#946—28no—
133#946—24no—
134#946—44no—
135#946—44no—
136C2×(C2×D3)⋊C4C2312yes—
137C2×(C2×D3)⋊C4C2312yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2312yes—
144C2×(C2×D3)⋊C4C2312yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2312yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2312yes—
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2311yescharacteristic
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2312yes—
160C2×Dic3⋊C4C2312yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2314yes—
164C2×C4×Dic3C2311yescharacteristic
165C2×C4×Dic3C2311yescharacteristic
166C2×C4×Dic3C2311yescharacteristic
167#898—28no—
168#895—28no—
169#895—24no—
170#895—24no—
171#894—216no—
172#894—28no—
173D3×C4⋊C4—28no—
174D3×C4⋊C4—44no—
175#890—24no—
176C4×D12—28no—
177C4×D12—24no—
178C4×D12—44no—
179C4×D12—44no—
180C4×D12D418yescomplemented
181#872—28no—
182C42×D3—24no—
183C3×#95C2314yes—
184C3×#95C2314yes—
185C3×#95C2314yes—
186C3×#95C2314yes—
187C3×#95C2312yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2312yes—
193C3⋊#95C2314yes—
194C22×#41—32no—
195#547—68no—
196C2×C4⋊Q8C2×D311yescharacteristic
197#529—68no—
198C2×#126—32no—
199C2×#125—31no—
200C2×#124—31no—
201C2×#123—32no—
202C2×#123—34no—
203C2×C22⋊Q8—32no—
204C2×C22⋊Q8—31no—
205C2×C22⋊Q8—32no—
206C2×C22⋊Q8—32no—
207C2×#121—31no—
208C2×#121—31no—
209C2×#121—32no—
210C2×C4×Q8C2×D311yescharacteristic
211C2×C4×D4—31no—
212C2×C4×D4—32no—
213C2×C4×D4—31no—
214C2×C4×D4—32no—
215C2×C4×D4—32no—
216C2×#117—32no—
217C22×C4⋊C4—32no—
218C22×C4⋊C4—32no—
219C22×C42—31no—
220#400—34no—
221#400C2×D314yes—
222#398—34no—
223#398—34no—
224#397—34no—
225#397—34no—
226#396—34no—
227#396—34no—
228#394—34no—
229#392—34no—
230#391—32no—
231#391C2×D312yes—
232#391C2×D312yes—
233#391C2×D312yes—
234#390—31no—
235#390—32no—
236#389—32no—
237#389—32no—
238#389—31no—
239#389—32no—
240#389—32no—
241#388—32no—
242#386—34no—
243#386—34no—
244#386—34no—
245#386—34no—
246#386—32no—
247#385—34no—
248#385—34no—
249#384—31no—
250#382C2×D312yes—
251#380—32no—
252#380—32no—
253#380—32no—
254#380—31no—
255#380—32no—
256#380—34no—
257#380—34no—
258#380—34no—
259C4×C4⋊C4C2×D311yescharacteristic
260C4×C22⋊C4—32no—
261C23×D3C2412yes—
262C23×D3C2412yes—
263C23×D3C2411yescharacteristic
264C2×C3×Q8—22no—
265C2×C3×Q8—24no—
266C2×C3×Q8—24no—
267C2×C3×Q8—22no—
268C2×C3×Q8—24no—
269C2×C3×Q8—22no—
270C22×C3×C4C2412yes—
271C22×C3×C4C2414yes—
272C22×C3×C4C2412yes—
273C22×C3×C4C2412yes—
274C22×C3×C4C2412yes—
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C22×C3×C4C2411yescharacteristic
278C22×Dic3C2411yescharacteristic
279C22×Dic3C2411yescharacteristic
280C22×Dic3C2412yes—
281C22×Dic3C2414yes—
282C22×Dic3C2411yescharacteristic
283C22×Dic3C2412yes—
284#239—432no—
285C2×D12—22no—
286C2×D12—22no—
287C2×D12—22no—
288C2×D12—22no—
289C2×D12—24no—
290C2×D12—28no—
291C2×D12—24no—
292C2×D12—28no—
293C2×D12—24no—
294C2×D12—24no—
295C2×D12—42no—
296C2×D12—42no—
297C2×D12—44no—
298C2×D12C2×D414yes—
299C2×D12#4114yes—
300C2×C4×D3—24no—
301C2×C4×D3—24no—
302C2×C4×D3—28no—
303C2×C4×D3—22no—
304C2×C4×D3—22no—
305C2×C4×D3—22no—
306C2×C4×D3—22no—
307C2×C4×D3—24no—
308C2×C4×D3—22no—
309C2×C4×D3—22no—
310C2×C4×D3—24no—
311C2×C4×D3—22no—
312C2×C4×D3—24no—
313C2×C4×D3—22no—
314C2×C4×D3—28no—
315C2×C4×D3—41no—
316C2×C4×D3—44no—
317C2×C4×D3—44no—
318C2×C4×D3—44no—
319C2×C4×D3—44no—
320C2×C4×D3C2×D418yes—
321C3×C4⋊C4—22no—
322C3×C4⋊C4—24no—
323C3×C4⋊C4—24no—
324C3×C4⋊C4—24no—
325C3×C4⋊C4—22no—
326C3×C4⋊C4—22no—
327C3×C42—24no—
328C3×C42—24no—
329C3×C42C2×D414yes—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—44no—
341(C2×D3)⋊C4—42no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4C2×D418yes—
345C4⋊Dic3—22no—
346C4⋊Dic3—24no—
347C4⋊Dic3—24no—
348C4⋊Dic3—24no—
349C4⋊Dic3—42no—
350C4⋊Dic3—42no—
351C4⋊Dic3C2×D414yes—
352Dic3⋊C4—24no—
353Dic3⋊C4—24no—
354Dic3⋊C4—28no—
355Dic3⋊C4—44no—
356Dic3⋊C4—44no—
357Dic3⋊C4—44no—
358C4×Dic3—22no—
359C4×Dic3—22no—
360C4×Dic3—22no—
361C2×#41—68no—
362C2×#41—68no—
363C2×#41—124no—
364C22×Q8C22×D311yescharacteristic
365C22×Q8C22×D312yes—
366C22×D4—31no—
367C22×D4—31no—
368C22×D4—32no—
369C22×D4—32no—
370C22×D4—34no—
371C23×C4—32no—
372C23×C4—32no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—34no—
376C23×C4—31no—
377C23×C4—34no—
378C4⋊Q8—24no—
379#126—68no—
380#125—64no—
381#124—64no—
382#123—68no—
383#123—616no—
384C22⋊Q8—64no—
385C22⋊Q8—68no—
386C22⋊Q8—124no—
387C22⋊Q8—124no—
388#121—64no—
389#121—68no—
390#121—64no—
391C4×Q8—24no—
392C4×D4—38no—
393C4×D4—68no—
394C4×D4—64no—
395C4×D4—124no—
396C4×D4—124no—
397#117—68no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—32no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—32no—
411C2×C4⋊C4—68no—
412C2×C4⋊C4—124no—
413C2×C4⋊C4C22×D311yescharacteristic
414C2×C4⋊C4C22×D312yes—
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C4⋊C4C22×D312yes—
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C4⋊C4C22×D312yes—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—32no—
427C2×C22⋊C4—32no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—32no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4—32no—
433C2×C22⋊C4—34no—
434C2×C42—31no—
435C2×C42—31no—
436C2×C42—31no—
437C2×C42—64no—
438C2×C42C22×D312yes—
439C2×C42C22×D312yes—
440C2×C42C22×D311yescharacteristic
441#95—32no—
442#95—32no—
443#95—34no—
444#95—34no—
445#95—34no—
446#95—34no—
447#95C22×D312yes—
448#95C22×D314yes—
449#95C22×D314yes—
450#95C22×D314yes—
451#95C22×D314yes—
452C23×C3C2511yescharacteristic
453C22×D3—21no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—22no—
459C22×D3—21no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—21no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—21no—
471C22×D3C22×D414yes—
472C22×D3C2×#4114yes—
473C22×D32−1+412yes—
474C3×Q8—44no—
475C3×Q8—48no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—24no—
481C2×C3×C4—22no—
482C2×C3×C4—24no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—24no—
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×C4C22×D412yes—
494C2×C3×C4C22×D412yes—
495C2×C3×C4C22×D412yes—
496C2×C3×C4C2×#4112yes—
497C2×C3×C4H(5,𝔽2)12yes—
498C2×C3×C4H(5,𝔽2)12yes—
499C2×C3×C42−1+412yes—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—22no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—24no—
509C2×Dic3—22no—
510C2×Dic3—24no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—22no—
514C2×Dic3—21no—
515C2×Dic3—24no—
516C2×Dic3—21no—
517C2×Dic3C22×D414yes—
518D12—28no—
519D12—28no—
520D12—48no—
521D12—48no—
522D12—416no—
523C4×D3—216no—
524C4×D3—416no—
525C4×D3—44no—
526C4×D3—44no—
527C4×D3—48no—
528C4×D3—44no—
529C4×D3—88no—
530C24—32no—
531C24—32no—
532C24—31no—
533#41—1232no—
534C2×Q8—22no—
535C2×Q8—24no—
536C2×Q8—22no—
537C2×Q8—24no—
538C2×Q8—22no—
539C2×Q8—24no—
540C2×D4—34no—
541C2×D4—34no—
542C2×D4—64no—
543C2×D4—68no—
544C2×D4—64no—
545C2×D4—68no—
546C2×D4—64no—
547C2×D4—64no—
548C2×D4—62no—
549C2×D4—62no—
550C2×D4—62no—
551C2×D4—62no—
552C2×D4—122no—
553C2×D4—124no—
554C2×D4—122no—
555C22×C4—32no—
556C22×C4—38no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—32no—
560C22×C4—34no—
561C22×C4—31no—
562C22×C4—68no—
563C22×C4—68no—
564C22×C4—62no—
565C22×C4—64no—
566C22×C4—64no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—64no—
571C22×C4—64no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—64no—
576C22×C4—62no—
577C22×C4—124no—
578C22×C4—121no—
579C22×C4—124no—
580C22×C4—124no—
581C22×C4—124no—
582C22×C4C23×D312yes—
583C22×C4C23×D312yes—
584C22×C4C23×D314yes—
585C22×C4C23×D312yes—
586C22×C4C23×D312yes—
587C22×C4C23×D311yescharacteristic
588C22×C4C23×D311yescharacteristic
589C22×C4C23×D311yescharacteristic
590C4⋊C4—24no—
591C4⋊C4—22no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—34no—
597C4⋊C4—68no—
598C4⋊C4—64no—
599C4⋊C4—64no—
600C4⋊C4—64no—
601C4⋊C4—62no—
602C4⋊C4—64no—
603C4⋊C4—64no—
604C4⋊C4—124no—
605C4⋊C4—122no—
606C4⋊C4—124no—
607C4⋊C4—124no—
608C4⋊C4—122no—
609C22⋊C4—38no—
610C22⋊C4—64no—
611C22⋊C4—64no—
612C22⋊C4—64no—
613C22⋊C4—64no—
614C22⋊C4—68no—
615C22⋊C4—64no—
616C22⋊C4—64no—
617C22⋊C4—124no—
618C22⋊C4—122no—
619C22⋊C4—122no—
620C22⋊C4—124no—
621C22⋊C4—124no—
622C22⋊C4—124no—
623C22⋊C4—122no—
624C42—24no—
625C42—24no—
626C42—62no—
627C42—62no—
628C42—62no—
629C42D3×D414yes—
630C22×C3C23×D411yescharacteristic
631C22×C3C22×#4111yescharacteristic
632C22×C3C2×H(5,𝔽2)11yescharacteristic
633C22×C3C2×H(5,𝔽2)11yescharacteristic
634C22×C3C2×2−1+411yescharacteristic
635C22×C3C2×2−1+411yescharacteristic
636C22×C3#58511yescharacteristic
637C2×D3—24no—
638C2×D3—24no—
639C2×D3—24no—
640C2×D3—22no—
641C2×D3—24no—
642C2×D3—24no—
643C2×D3—22no—
644C2×D3—24no—
645C2×D3—22no—
646C2×D3—41no—
647C2×D3—42no—
648C2×D3—41no—
649C2×D3—42no—
650C2×D3—41no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—41no—
655C2×D3—42no—
656C2×D3—42no—
657C2×D3—42no—
658C3×C4—22no—
659C3×C4—42no—
660C3×C4—44no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4—42no—
664C3×C4#53714yes—
665C3×C4#54614yes—
666Dic3—24no—
667Dic3—41no—
668Dic3—42no—
669Dic3—41no—
670Dic3—41no—
671Dic3—44no—
672C23—34no—
673C23—34no—
674C23—32no—
675C23—61no—
676C23—62no—
677C23—62no—
678C23—61no—
679C23—62no—
680C23—62no—
681C23—61no—
682C23—61no—
683C23—62no—
684C23—61no—
685C23—62no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23—62no—
690C23—62no—
691C23—62no—
692C23—61no—
693C23C24×D311yescharacteristic
694Q8—48no—
695Q8—44no—
696D4—68no—
697D4—68no—
698D4—1216no—
699D4—128no—
700D4—128no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—34no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—616no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—62no—
726C2×C4—61no—
727C2×C4—62no—
728C2×C4—61no—
729C2×C4—64no—
730C2×C4—61no—
731C2×C4—64no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—64no—
737C2×C4—124no—
738C2×C4—1216no—
739C2×C4—124no—
740C2×C4—124no—
741C2×C4—128no—
742C2×C4—248no—
743C2×C4C2×D3×D412yes—
744C2×C4C2×D3×D412yes—
745C2×C4C2×D3×D412yes—
746C2×C4#100712yes—
747C2×C4D3×#4112yes—
748C2×C4#100912yes—
749C2×C4#100912yes—
750C2×C3C2×#53711yescharacteristic
751C2×C3C2×#54611yescharacteristic
752C2×C3#348911yescharacteristic
753C2×C3#351511yescharacteristic
754C2×C3#352011yescharacteristic
755C2×C3#354611yescharacteristic
756C2×C3#355211yescharacteristic
757D3—44no—
758D3—44no—
759D3—42no—
760C22—64no—
761C22—64no—
762C22—62no—
763C22—64no—
764C22—62no—
765C22—64no—
766C22—64no—
767C22—64no—
768C22—62no—
769C22—121no—
770C22—122no—
771C22—122no—
772C22—121no—
773C22—122no—
774C22—122no—
775C22—121no—
776C22—122no—
777C22—121no—
778C22—122no—
779C22—122no—
780C22—122no—
781C22C22×D3×D411yescharacteristic
782C22C2×#100711yescharacteristic
783C22C2×D3×#4111yescharacteristic
784C22C2×#100911yescharacteristic
785C22C2×#100911yescharacteristic
786C22D3×2−1+411yescharacteristic
787C22#596811yescharacteristic
788C4—22no—
789C4—44no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—64no—
795C4—121no—
796C4—121no—
797C4—121no—
798C4—122no—
799C4—124no—
800C4#562914yes—
801C4#567614yes—
802C3#3890811yescharacteristic, complemented, Sylow
803C2—124no—
804C2—124no—
805C2—122no—
806C2C2×#562911yescharacteristic
807C2C2×#567611yescharacteristic
808C2#8635611yescharacteristic
809C2#8699011yescharacteristic
810C2#8700911yescharacteristic
811C2#8702111yescharacteristic
812C2#8703411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2568C2
hypercenter#2568D3
hypocenterC3#38908
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2568

Complements

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

NH ≅ G/Ntype
1. C2×#5726C2semidirect
2. C2×#5580C2semidirect
3. C3×#2568C2semidirect
4. #83269C2semidirect
5. #82500C2semidirect
6. #78239C2semidirect
7. #78238C2semidirect
8. #76642C2semidirect
9. #76624C2semidirect
10. #76621C2semidirect
11. #76621C2semidirect
12. #76618C2semidirect
13. #76482C2semidirect
14. #74239C2semidirect
15. #74163C2semidirect
16. C4⋊C4×D12C2semidirect
17. C4×#895C2semidirect
92. #2568D3semidirect
180. C4×D12D4semidirect
802. C3#38908semidirect

Maximal subgroups

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

subgroupindex
C2×#57262
C2×#55802
C3×#25682
#832692
#825002
#782392
#782382
#766422
#766242
#766212
#766182
#764822
#742392
#741632
C4⋊C4×D122
C4×#8952
#389083