Finite Group Databasebeta

← #11633939

Subgroups — #11633939

Order 768.

2534 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5728C211yesmaximal, characteristic, complemented
2C2×#5555C211yesmaximal, characteristic, complemented
3C3×#2542C211yesmaximal, characteristic, complemented
4#83240C211yesmaximal, characteristic, complemented
5#82815C212yesmaximal, complemented
6#82779C212yesmaximal, complemented
7#82755C212yesmaximal, complemented
8#82747C212yesmaximal, complemented
9C4×#938C211yesmaximal, characteristic, complemented
10#78064C214yesmaximal, complemented
11#78026C214yesmaximal, complemented
12#76435C212yesmaximal, complemented
13#76301C212yesmaximal, complemented
14#74369C212yesmaximal, complemented
15#74363C212yesmaximal, complemented
16C4×#895C211yesmaximal, characteristic, complemented
17#73651C211yesmaximal, characteristic, complemented
18#59040—31nomaximal, Sylow
19C22×#237C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×C22⋊Q8C2212yes—
22C2×C3×C22⋊Q8C2212yes—
23C2×C3×C4×D4C2211yescharacteristic
24C2×#947C2212yes—
25C2×#946C2212yes—
26C2×Q8×Dic3C2212yes—
27C2×#938C2211yescharacteristic
28C2×#930C2212yes—
29C2×C4×#67C2212yes—
30C22×C4⋊Dic3C2212yes—
31#5728—28no—
32#5555—28no—
33C2×#897C2212yes—
34C2×#897C2212yes—
35C2×#895C2211yescharacteristic
36C2×#892C2212yes—
37C2×#890C2212yes—
38C2×#887C2212yes—
39C2×#886C2214yes—
40C2×C4×D12C2211yescharacteristic
41C2×C4×D12C2212yes—
42C2×C42×D3C2211yescharacteristic
43C2×#869C2211yescharacteristic
44C2×C4×Dic6C2212yes—
45C3×#399C2214yes—
46C3×#390C2212yes—
47C3×#384C2212yes—
48C3×C4×C4⋊C4C2211yescharacteristic
49#5229C2212yes—
50#5221C2211yescharacteristic
51C4×#217C2212yes—
52#4994C2214yes—
53#4994C2214yes—
54#4993C2214yes—
55#4992C2214yes—
56#4990C2214yes—
57#4988C2211yescharacteristic
58#4988C2214yes—
59#4987C2212yes—
60#4987C2211yescharacteristic
61#4987C2212yes—
62#4987C2211yescharacteristic
63#4984C2211yescharacteristic
64#4984C2214yes—
65#4982C2214yes—
66#4980C2214yes—
67Dic3×C4⋊C4C2212yes—
68#4972C2212yes—
69#4972C2211yescharacteristic
70#4961C2214yes—
71#4960C2214yes—
72#4958C2214yes—
73#4957C2214yes—
74#4957C2214yes—
75#4956C2212yes—
76#4950C2214yes—
77#4944C2212yes—
78#4942C2214yes—
79Dic3×C22⋊C4C2214yes—
80C4×(C2×D3)⋊C4C2212yes—
81C4×C4⋊Dic3C2211yescharacteristic
82#4929C2212yes—
83#4670C2212yes—
84#4665C2212yes—
85#4654C2214yes—
86C2×#547—31no—
87C2×#533—31no—
88#2694—34no—
89#2547—31no—
90#2542D311yescharacteristic, complemented
91#2540—32no—
92#2538—32no—
93#2471—34no—
94#2426—32no—
95#2423—32no—
96#2417—32no—
97#2407—32no—
98#2365—31no—
99#2360—32no—
100#2341—32no—
101C4×#121—31no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4C2312yes—
106C22×#67C2314yes—
107C22×#67C2312yes—
108C23×Dic3C2314yes—
109C2×#237—28no—
110C2×#237—28no—
111C2×#237—44no—
112C22×D12C2311yescharacteristic
113C22×D12C2312yes—
114C22×C4×D3C2311yescharacteristic
115C22×C4×D3C2312yes—
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×Dic6C2312yes—
119C3×C4⋊Q8—24no—
120C3×C22⋊Q8—28no—
121C3×C22⋊Q8—44no—
122C3×C4×D4—24no—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2314yes—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2314yes—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4C2314yes—
131C2×C3×C22⋊C4C2312yes—
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C42C2312yes—
134C2×C3×C42C2311yescharacteristic
135C2×#217C2312yes—
136C2×#217C2312yes—
137C2×#217C2312yes—
138#947—44no—
139#946—28no—
140Q8×Dic3—28no—
141#938—24no—
142#930—28no—
143C4×#67—44no—
144C2×(C2×D3)⋊C4C2312yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2312yes—
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×C4⋊Dic3—28no—
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2314yes—
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2314yes—
160C2×C4⋊Dic3C2312yes—
161C2×C4⋊Dic3C2312yes—
162C2×C4⋊Dic3C2312yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2314yes—
165C2×Dic3⋊C4C2312yes—
166C2×C4×Dic3C2311yescharacteristic
167C2×C4×Dic3C2312yes—
168C2×C4×Dic3C2311yescharacteristic
169C2×C4×Dic3C2314yes—
170C2×C4×Dic3C2311yescharacteristic
171C2×C4×Dic3C2314yes—
172#897—28no—
173#897—28no—
174#895—24no—
175#892—28no—
176#890—28no—
177#887—28no—
178#886—216no—
179C4×D12—24no—
180C4×D12—44no—
181C42×D3—24no—
182#869D418yescomplemented
183C4×Dic6—44no—
184C3×#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2312yes—
190C3⋊#95C2314yes—
191C3⋊#95C2312yes—
192C3⋊#95C2314yes—
193C3⋊#95C2312yes—
194C22×#41—32no—
195#547—68no—
196#533—68no—
197C2×C4⋊Q8—31no—
198C2×C4⋊Q8C2×D311yescharacteristic
199C2×#125—32no—
200C2×#124—32no—
201C2×#123—34no—
202C2×C22⋊Q8—32no—
203C2×C22⋊Q8—32no—
204C2×C22⋊Q8—32no—
205C2×C22⋊Q8C2×D312yes—
206C2×C22⋊Q8C2×D312yes—
207C2×#121—31no—
208C2×#121—32no—
209C2×#121—31no—
210C2×C4×Q8—32no—
211C2×C4×Q8—32no—
212C2×C4×Q8—32no—
213C2×C4×D4—32no—
214C2×C4×D4—31no—
215C2×C4×D4—32no—
216C2×C4×D4C2×D311yescharacteristic
217C2×#117—32no—
218C22×C4⋊C4—32no—
219C22×C42—31no—
220#399—34no—
221#399C2×D314yes—
222#398—34no—
223#397—34no—
224#396—34no—
225#396—34no—
226#394—34no—
227#392—34no—
228#391—32no—
229#391—32no—
230#390—31no—
231#390—31no—
232#390—34no—
233#390—34no—
234#390—34no—
235#390C2×D312yes—
236#389—31no—
237#389—34no—
238#389—32no—
239#389—31no—
240#388—34no—
241#388—32no—
242#388—32no—
243#387—34no—
244#387—34no—
245#386—32no—
246#386—34no—
247#386—32no—
248#385—34no—
249#384C2×D312yes—
250#380—32no—
251#380—32no—
252#380—31no—
253#380—31no—
254#380—34no—
255C4×C4⋊C4—32no—
256C4×C4⋊C4—31no—
257C4×C4⋊C4C2×D311yescharacteristic
258C4×C22⋊C4—32no—
259C4×C22⋊C4—34no—
260C4×C22⋊C4—32no—
261C24×C3C2412yes—
262C23×D3C2412yes—
263C23×D3C2411yescharacteristic
264C2×C3×Q8—24no—
265C2×C3×Q8—24no—
266C2×C3×Q8—24no—
267C2×C3×D4—22no—
268C2×C3×D4—22no—
269C2×C3×D4#4114yes—
270C22×C3×C4—24no—
271C22×C3×C4—24no—
272C22×C3×C4—24no—
273C22×C3×C4C2412yes—
274C22×C3×C4C2414yes—
275C22×C3×C4C2412yes—
276C22×C3×C4C2411yescharacteristic
277C22×C3×C4C2412yes—
278C22×C3×C4C2411yescharacteristic
279C22×C3×C4C2411yescharacteristic
280C2×#67—24no—
281C2×#67—28no—
282C2×#67—24no—
283C2×#67—28no—
284C2×#67—42no—
285C2×#67—44no—
286C22×Dic3—28no—
287C22×Dic3—28no—
288C22×Dic3—44no—
289C22×Dic3C2412yes—
290C22×Dic3C2412yes—
291C22×Dic3C2412yes—
292C22×Dic3C2411yescharacteristic
293C22×Dic3C2411yescharacteristic
294C22×Dic3C2414yes—
295C22×Dic3C2411yescharacteristic
296#237—432no—
297C2×D12—24no—
298C2×D12—22no—
299C2×D12—24no—
300C2×D12—22no—
301C2×D12—22no—
302C2×D12—42no—
303C2×C4×D3—22no—
304C2×C4×D3—22no—
305C2×C4×D3—22no—
306C2×C4×D3—22no—
307C2×C4×D3—22no—
308C2×C4×D3—24no—
309C2×C4×D3—22no—
310C2×C4×D3—22no—
311C2×C4×D3—24no—
312C2×C4×D3—22no—
313C2×C4×D3—24no—
314C2×C4×D3—22no—
315C2×Dic6—24no—
316C2×Dic6—24no—
317C2×Dic6C2×D418yes—
318C3×C4⋊C4—24no—
319C3×C4⋊C4—24no—
320C3×C4⋊C4—22no—
321C3×C4⋊C4—28no—
322C3×C4⋊C4—22no—
323C3×C4⋊C4—44no—
324C3×C4⋊C4#4114yescomplemented
325C3×C22⋊C4—24no—
326C3×C22⋊C4—28no—
327C3×C22⋊C4—44no—
328C3×C42—24no—
329C3×C42C2×D414yes—
330#217—24no—
331#217—24no—
332#217—42no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—28no—
336(C2×D3)⋊C4—28no—
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—42no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4—44no—
343C4⋊Dic3—22no—
344C4⋊Dic3—22no—
345C4⋊Dic3—22no—
346C4⋊Dic3—28no—
347C4⋊Dic3—28no—
348C4⋊Dic3—42no—
349C4⋊Dic3C2×D418yes—
350C4⋊Dic3C2×D418yes—
351Dic3⋊C4—28no—
352Dic3⋊C4—44no—
353Dic3⋊C4—42no—
354C4×Dic3—22no—
355C4×Dic3—22no—
356C4×Dic3—22no—
357C4×Dic3—24no—
358C4×Dic3—28no—
359C4×Dic3—44no—
360C2×#41—68no—
361C2×#41—68no—
362C2×#41—124no—
363C22×Q8—32no—
364C22×Q8C22×D312yes—
365C22×D4—32no—
366C22×D4—34no—
367C22×D4—31no—
368C22×D4—32no—
369C22×D4C22×D311yescharacteristic
370C23×C4—34no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—32no—
375C23×C4C22×D312yes—
376C4⋊Q8—24no—
377C4⋊Q8—38no—
378#125—68no—
379#124—124no—
380#123—616no—
381C22⋊Q8—28no—
382C22⋊Q8—44no—
383C22⋊Q8—68no—
384C22⋊Q8—68no—
385C22⋊Q8—68no—
386#121—68no—
387#121—64no—
388#121—64no—
389C4×Q8—68no—
390C4×Q8—68no—
391C4×Q8—124no—
392C4×D4—24no—
393C4×D4—64no—
394C4×D4—124no—
395C4×D4—124no—
396#117—68no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—34no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—68no—
409C2×C4⋊C4C22×D312yes—
410C2×C4⋊C4C22×D311yescharacteristic
411C2×C4⋊C4C22×D312yes—
412C2×C4⋊C4C22×D311yescharacteristic
413C2×C4⋊C4C22×D314yes—
414C2×C4⋊C4C22×D314yes—
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—32no—
426C2×C22⋊C4—32no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4C22×D312yes—
430C2×C22⋊C4C22×D314yes—
431C2×C22⋊C4C22×D314yes—
432C2×C42—34no—
433C2×C42—32no—
434C2×C42—31no—
435C2×C42—31no—
436C2×C42—31no—
437C2×C42—34no—
438C2×C42—64no—
439C2×C42C22×D312yes—
440C2×C42C22×D311yescharacteristic
441#95—32no—
442#95—32no—
443#95—34no—
444#95—32no—
445#95—32no—
446#95—34no—
447#95—32no—
448#95—34no—
449#95—34no—
450#95C22×D312yes—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3C2×#4114yes—
458C23×C3C2511yescharacteristic
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D32−1+412yes—
473C3×Q8—48no—
474C3×D4—28no—
475C2×C3×C4—22no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—24no—
480C2×C3×C4—22no—
481C2×C3×C4—24no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—24no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—48no—
489C2×C3×C4C22×D412yes—
490C2×C3×C4C22×D412yes—
491C2×C3×C4C22×D412yes—
492C2×C3×C4C2×#4114yes—
493C2×C3×C4C2×#4112yes—
494C2×C3×C4C2×#4112yes—
495C2×C3×C4H(5,𝔽2)12yes—
496C2×C3×C4H(5,𝔽2)12yes—
497#67—416no—
498#67—48no—
499C2×Dic3—21no—
500C2×Dic3—24no—
501C2×Dic3—24no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—416no—
519C2×Dic3C22×D418yes—
520C2×Dic32−1+412yes—
521D12—48no—
522D12—44no—
523C4×D3—28no—
524C4×D3—44no—
525C4×D3—48no—
526C4×D3—44no—
527Dic6—216no—
528C24—31no—
529C24—32no—
530C24C23×D312yes—
531#41—1232no—
532C2×Q8—24no—
533C2×Q8—24no—
534C2×Q8—24no—
535C2×Q8—38no—
536C2×Q8—64no—
537C2×Q8—64no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—64no—
541C2×D4—68no—
542C2×D4—64no—
543C2×D4—64no—
544C2×D4—68no—
545C2×D4—62no—
546C2×D4—64no—
547C2×D4—62no—
548C2×D4—62no—
549C2×D4—122no—
550C2×D4—122no—
551C2×D4—124no—
552C2×D4#23914yes—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—31no—
557C22×C4—34no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—68no—
566C22×C4—62no—
567C22×C4—68no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—64no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—64no—
575C22×C4—62no—
576C22×C4—64no—
577C22×C4—124no—
578C22×C4C23×D312yes—
579C22×C4C23×D314yes—
580C22×C4C23×D312yes—
581C22×C4C23×D311yescharacteristic
582C22×C4C23×D312yes—
583C22×C4C23×D311yescharacteristic
584C22×C4C23×D311yescharacteristic
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—24no—
588C4⋊C4—28no—
589C4⋊C4—22no—
590C4⋊C4—38no—
591C4⋊C4—38no—
592C4⋊C4—44no—
593C4⋊C4—68no—
594C4⋊C4—68no—
595C4⋊C4—68no—
596C4⋊C4—62no—
597C4⋊C4—62no—
598C4⋊C4—62no—
599C4⋊C4—122no—
600C4⋊C4—122no—
601C4⋊C4—124no—
602C4⋊C4#23714yescomplemented
603C22⋊C4—24no—
604C22⋊C4—28no—
605C22⋊C4—44no—
606C22⋊C4—68no—
607C22⋊C4—68no—
608C22⋊C4—64no—
609C22⋊C4—64no—
610C22⋊C4—64no—
611C22⋊C4—64no—
612C22⋊C4—64no—
613C22⋊C4—122no—
614C22⋊C4—122no—
615C22⋊C4—122no—
616C22⋊C4—124no—
617C22⋊C4—124no—
618C22⋊C4—122no—
619C42—24no—
620C42—68no—
621C42—62no—
622C42—62no—
623C42—62no—
624C42—64no—
625C42—124no—
626C42D3×D414yes—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3C23×D411yescharacteristic
635C22×C3C22×#4111yescharacteristic
636C22×C3C22×#4111yescharacteristic
637C22×C3C2×H(5,𝔽2)11yescharacteristic
638C22×C3C2×H(5,𝔽2)11yescharacteristic
639C22×C3C2×2−1+411yescharacteristic
640C22×C3C2×2−1+411yescharacteristic
641C2×D3—22no—
642C2×D3—22no—
643C2×D3—22no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—42no—
649C2×D3—42no—
650C2×D3—42no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—42no—
655C3×C4—22no—
656C3×C4—24no—
657C3×C4—42no—
658C3×C4—44no—
659C3×C4—42no—
660C3×C4#54614yes—
661C3×C4#55014yes—
662Dic3—28no—
663Dic3—22no—
664Dic3—41no—
665Dic3—42no—
666Dic3—41no—
667Dic3—42no—
668Dic3—42no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—32no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23—62no—
683C23—62no—
684C23—62no—
685C23—62no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23C2×#23914yes—
690C23C24×D311yescharacteristic
691Q8—48no—
692Q8—616no—
693D4—28no—
694D4—128no—
695D4—1216no—
696D4—128no—
697D4—124no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—38no—
712C2×C4—32no—
713C2×C4—48no—
714C2×C4—68no—
715C2×C4—61no—
716C2×C4—64no—
717C2×C4—64no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—62no—
722C2×C4—61no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—61no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—1216no—
735C2×C4—124no—
736C2×C4—128no—
737C2×C4—124no—
738C2×C4C2×D3×D412yes—
739C2×C4C2×D3×D412yes—
740C2×C4C2×D3×D412yes—
741C2×C4C2×#23714yes—
742C2×C4C2×#23712yes—
743C2×C4#100412yes—
744C2×C4C2×#23912yes—
745C2×C4#100912yes—
746C2×C3—44no—
747C2×C3C2×#54611yescharacteristic
748C2×C3C2×#55011yescharacteristic
749C2×C3#348211yescharacteristic
750C2×C3#348611yescharacteristic
751C2×C3#352011yescharacteristic
752C2×C3#352011yescharacteristic
753C2×C3#354811yescharacteristic
754D3—42no—
755D3—82no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—62no—
764C22—62no—
765C22—62no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—122no—
771C22—122no—
772C22—122no—
773C22—122no—
774C22—122no—
775C22—122no—
776C22—122no—
777C22C22×D3×D411yescharacteristic
778C22C22×#23711yescharacteristic
779C22C2×#100411yescharacteristic
780C22C22×#23911yescharacteristic
781C22C2×#100911yescharacteristic
782C22D3×2−1+411yescharacteristic
783C22D3×2−1+411yescharacteristic
784C4—22no—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—44no—
789C4—62no—
790C4—68no—
791C4—122no—
792C4—121no—
793C4—122no—
794C4—121no—
795C4—122no—
796C4#563014yes—
797C4#571814yes—
798C3#5904011yescharacteristic, complemented, Sylow
799C2—44no—
800C2—122no—
801C2—242no—
802C2C2×#563011yescharacteristic
803C2C2×#571811yescharacteristic
804C2#8635511yescharacteristic
805C2#8668511yescharacteristic
806C2#8669311yescharacteristic
807C2#8674411yescharacteristic
808C2#8675111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2542C2
hypercenter#2542D3
hypocenterC3#59040
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. C2×#5728C2semidirect
2. C2×#5555C2semidirect
3. C3×#2542C2semidirect
4. #83240C2semidirect
5. #82815C2semidirect
6. #82779C2semidirect
7. #82755C2semidirect
8. #82747C2semidirect
9. C4×#938C2semidirect
10. #78064C2semidirect
11. #78026C2semidirect
12. #76435C2semidirect
13. #76301C2semidirect
14. #74369C2semidirect
15. #74363C2semidirect
16. C4×#895C2semidirect
17. #73651C2semidirect
90. #2542D3semidirect
182. #869D4semidirect
324. C3×C4⋊C4#41semidirect
602. C4⋊C4#237semidirect
798. C3#59040semidirect

Maximal subgroups

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

subgroupindex
C2×#57282
C2×#55552
C3×#25422
#832402
#828152
#827792
#827552
#827472
C4×#9382
#780642
#780262
#764352
#763012
#743692
#743632
C4×#8952
#736512
#590403