Finite Group Databasebeta

← #10972876

Subgroups — #10972876

Order 768.

2378 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
1C22×Q8×Dic3C211yesmaximal, characteristic, complemented
2C2×#5538C211yesmaximal, characteristic
3C3×#2409C211yesmaximal, characteristic, complemented
4#84068C211yesmaximal, characteristic, complemented
5#82778C212yesmaximal, complemented
6#82744C212yesmaximal, complemented
7#82373C211yesmaximal, characteristic, complemented
8#77205C212yesmaximal, complemented
9#77192C212yesmaximal, complemented
10#76813C212yesmaximal, complemented
11#76804C212yesmaximal, complemented
12#76611C212yesmaximal, complemented
13#76548C212yesmaximal, complemented
14#74872C212yesmaximal
15#74691C212yesmaximal, complemented
16#74589C212yesmaximal, complemented
17#74407C212yesmaximal, complemented
18#74027C211yesmaximal, characteristic, complemented
19#73864C211yesmaximal, characteristic, complemented
20#35247—31nomaximal, Sylow
21C23×C3×Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2212yes—
23C2×C3×C4×D4C2211yescharacteristic
24C2×#946C2212yes—
25C2×Q8×Dic3—28no—
26C2×Q8×Dic3C2212yes—
27C2×Q8×Dic3C2212yes—
28C2×Q8×Dic3C2212yes—
29C2×Q8×Dic3C2212yes—
30C2×#939C2211yescharacteristic
31C2×#935C2211yescharacteristic
32C2×#935C2212yes—
33C2×C4×#67C2211yescharacteristic
34C2×C4×#67C2211yescharacteristic
35C2×#926C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C22×C4⋊Dic3C2212yes—
38C22×C4×Dic3C2212yes—
39C22×C4×Dic3C2211yescharacteristic
40#5538—28no—
41C2×#898C2211yescharacteristic
42C2×#889C2211yescharacteristic
43C2×#886C2211yescharacteristic
44C2×#886C2212yes—
45C2×#885C2211yescharacteristic
46C2×#879C2211yescharacteristic
47C2×#878C2211yescharacteristic
48C2×#877C2212yes—
49C2×#872C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51C3×#395C2212yes—
52C3×#393C2212yes—
53C3×#391C2212yes—
54C3×#386C2212yes—
55C3×#385C2212yes—
56C3×#380C2211yescharacteristic
57#5231C2212yes—
58#5230C2212yes—
59#5229C2212yes—
60#5213C2212yes—
61#5212C2212yes—
62#5212C2211yescharacteristic
63#5210C2212yes—
64#4994C2214yes—
65#4987C2212yes—
66#4984C2212yes—
67#4984C2214yes—
68#4981C2212yes—
69#4980C2214yes—
70#4976C2214yes—
71#4975C2212yes—
72Dic3×C4⋊C4C2212yes—
73#4957C2214yes—
74#4953C2212yes—
75#4951C2214yes—
76#4951C2214yes—
77#4948C2214yes—
78#4943C2212yes—
79#4943C2212yes—
80#4942C2212yes—
81#4928C2212yes—
82#4674C2212yes—
83#4670C2214yes—
84#4669C2214yes—
85#4661C2214yes—
86#4661C2212yes—
87#4657C2214yes—
88#4652C2214yes—
89#4650C2212yes—
90#4649C2212yes—
91#4647C2214yes—
92#4647C2214yes—
93#4646C2214yes—
94C2×#529—31no—
95C22×C4×Q8—31no—
96#2855—32no—
97#2854—32no—
98#2637—32no—
99#2637—32no—
100#2592—32no—
101#2584—32no—
102#2582—32no—
103#2538—32no—
104#2486—31no—
105#2486—31no—
106#2413—32no—
107#2413—32no—
108#2409—31no—
109#2409D311yescharacteristic, complemented
110#2323—32no—
111#2323—32no—
112#2285—31no—
113C22×C3×Q8—28no—
114C22×C3×Q8—24no—
115C22×C3×Q8C2312yes—
116C22×C3×Q8C2312yes—
117C22×C3×D4C2311yescharacteristic
118C23×C3×C4C2312yes—
119C23×C3×C4C2311yescharacteristic
120C23×C3×C4C2311yescharacteristic
121C22×#67C2311yescharacteristic
122C22×#67C2311yescharacteristic
123C23×Dic3C2312yes—
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C22×C4×D3C2311yescharacteristic
127C22×Dic6C2311yescharacteristic
128C3×C22⋊Q8—28no—
129C3×C4×D4—24no—
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C4⋊C4C2314yes—
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C22⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4C2314yes—
136C2×C3×C22⋊C4C2311yescharacteristic
137C2×C3×C42C2311yescharacteristic
138C2×#217C2312yes—
139C2×#217C2311yescharacteristic
140C2×#217C2311yescharacteristic
141C2×#217C2311yescharacteristic
142C2×#217C2311yescharacteristic
143C2×#217C2314yes—
144#946—28no—
145Q8×Dic3—28no—
146Q8×Dic3—28no—
147Q8×Dic3—28no—
148Q8×Dic3—28no—
149#939—24no—
150#935—24no—
151#935—44no—
152C4×#67—24no—
153C4×#67—24no—
154C2×(C2×D3)⋊C4C2311yescharacteristic
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2311yescharacteristic
157C2×(C2×D3)⋊C4C2311yescharacteristic
158C2×(C2×D3)⋊C4C2311yescharacteristic
159C2×(C2×D3)⋊C4C2314yes—
160#926—24no—
161C2×C4⋊Dic3—24no—
162C2×C4⋊Dic3—28no—
163C2×C4⋊Dic3C2314yes—
164C2×C4⋊Dic3C2314yes—
165C2×C4⋊Dic3C2311yescharacteristic
166C2×C4⋊Dic3C2312yes—
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2311yescharacteristic
170C2×C4⋊Dic3C2311yescharacteristic
171C2×C4⋊Dic3C2314yes—
172C2×Dic3⋊C4C2314yes—
173C2×Dic3⋊C4C2311yescharacteristic
174C2×Dic3⋊C4C2311yescharacteristic
175C2×Dic3⋊C4C2314yes—
176C2×Dic3⋊C4C2311yescharacteristic
177C2×Dic3⋊C4C2311yescharacteristic
178C2×Dic3⋊C4C2311yescharacteristic
179C2×Dic3⋊C4C2311yescharacteristic
180C2×Dic3⋊C4C2314yes—
181C2×Dic3⋊C4C2314yes—
182C2×C4×Dic3—28no—
183C2×C4×Dic3D418yes—
184C2×C4×Dic3C2314yes—
185C2×C4×Dic3C2314yes—
186C2×C4×Dic3C2311yescharacteristic
187C2×C4×Dic3C2314yes—
188C2×C4×Dic3C2311yescharacteristic
189C2×C4×Dic3C2311yescharacteristic
190C2×C4×Dic3C2311yescharacteristic
191C2×C4×Dic3C2311yescharacteristic
192#898—24no—
193#889—24no—
194#886—24no—
195#886—44no—
196#885—24no—
197#879—24no—
198#878—24no—
199#877—44no—
200#872—24no—
201C4×Dic6—24no—
202C3×#95C2314yes—
203C3×#95C2314yes—
204C3×#95C2312yes—
205C3⋊#95C2314yes—
206C3⋊#95C2314yes—
207C3⋊#95C2314yes—
208C3⋊#95C2314yes—
209C3⋊#95C2314yes—
210C3⋊#95C2312yes—
211C3⋊#95C2314yes—
212C3⋊#95C2314yes—
213C23×Q8C2×D311yescharacteristic
214#529—68no—
215C2×#126—31no—
216C2×#126—31no—
217C2×#125—31no—
218C2×#124—31no—
219C2×#123—31no—
220C2×#123—32no—
221C2×#123—31no—
222C2×#123—32no—
223C2×C22⋊Q8—32no—
224C2×C22⋊Q8—31no—
225C2×C22⋊Q8C2×D312yes—
226C2×#121—31no—
227C2×C4×Q8—32no—
228C2×C4×Q8—32no—
229C2×C4×Q8—32no—
230C2×C4×Q8—32no—
231C2×C4×Q8—31no—
232C2×C4×Q8—68no—
233C2×C4×D4—31no—
234C2×C4×D4—31no—
235C2×C4×D4C2×D311yescharacteristic
236C2×#117—31no—
237C2×#117—32no—
238C2×#117—31no—
239C22×C4⋊C4—32no—
240C22×C4⋊C4—31no—
241C22×C42—31no—
242C22×C42—32no—
243#398—32no—
244#398—34no—
245#398—34no—
246#398—32no—
247#397—32no—
248#397—32no—
249#396—34no—
250#396—34no—
251#395—32no—
252#395C2×D312yes—
253#393—32no—
254#393C2×D312yes—
255#391—32no—
256#391—34no—
257#391C2×D312yes—
258#390—34no—
259#389—32no—
260#389—34no—
261#389—34no—
262#389—32no—
263#389—34no—
264#389—34no—
265#388—34no—
266#388—34no—
267#388—34no—
268#388—34no—
269#387—34no—
270#387—34no—
271#386—32no—
272#386C2×D312yes—
273#385—32no—
274#385C2×D312yes—
275#384—32no—
276#382—32no—
277#381—32no—
278#381—32no—
279#380—32no—
280#380—31no—
281#380—32no—
282#380—32no—
283#380C2×D311yescharacteristic
284C4×C4⋊C4—32no—
285C4×C4⋊C4—32no—
286C24×C3C2411yescharacteristic
287C24×C3C2411yescharacteristic
288C23×D3C2411yescharacteristic
289C2×C3×Q8—232no—
290C2×C3×Q8—24no—
291C2×C3×Q8—24no—
292C2×C3×Q8—28no—
293C2×C3×Q8—24no—
294C2×C3×Q8#4118yes—
295C2×C3×D4—22no—
296C2×C3×D4—22no—
297C2×C3×D4—22no—
298C22×C3×C4—24no—
299C22×C3×C4—28no—
300C22×C3×C4—24no—
301C22×C3×C4—22no—
302C22×C3×C4—24no—
303C22×C3×C4C2×D414yes—
304C22×C3×C4C2411yescharacteristic
305C22×C3×C4C2411yescharacteristic
306C22×C3×C4C2414yes—
307C22×C3×C4C2411yescharacteristic
308C22×C3×C4C2411yescharacteristic
309C22×C3×C4C2414yes—
310C22×C3×C4C2411yescharacteristic
311C2×#67—22no—
312C2×#67—22no—
313C2×#67—22no—
314C2×#67—22no—
315C2×#67—24no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—24no—
319C22×Dic3—24no—
320C22×Dic3—24no—
321C22×Dic3—24no—
322C22×Dic3C2×D414yes—
323C22×Dic3C2×D414yes—
324C22×Dic3C2411yescharacteristic
325C22×Dic3C2414yes—
326C22×Dic3C2414yes—
327C22×Dic3C2411yescharacteristic
328C22×Dic3C2411yescharacteristic
329C22×Dic3C2411yescharacteristic
330C22×Dic3C2411yescharacteristic
331C22×Dic3C2411yescharacteristic
332C22×Dic3C2411yescharacteristic
333C2×C4×D3—22no—
334C2×C4×D3—24no—
335C2×Dic6—22no—
336C2×Dic6—24no—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—24no—
339C3×C4⋊C4—28no—
340C3×C22⋊C4—22no—
341C3×C22⋊C4—24no—
342C3×C22⋊C4—22no—
343C3×C22⋊C4—28no—
344C3×C42—22no—
345#217—22no—
346#217—24no—
347#217—22no—
348#217—22no—
349#217—22no—
350#217—44no—
351(C2×D3)⋊C4—22no—
352(C2×D3)⋊C4—28no—
353(C2×D3)⋊C4—22no—
354(C2×D3)⋊C4—22no—
355(C2×D3)⋊C4—22no—
356(C2×D3)⋊C4—44no—
357C4⋊Dic3—24no—
358C4⋊Dic3—24no—
359C4⋊Dic3—24no—
360C4⋊Dic3—22no—
361C4⋊Dic3—22no—
362C4⋊Dic3—22no—
363C4⋊Dic3—28no—
364C4⋊Dic3—28no—
365C4⋊Dic3—44no—
366Dic3⋊C4—22no—
367Dic3⋊C4—28no—
368Dic3⋊C4—22no—
369Dic3⋊C4—22no—
370Dic3⋊C4—22no—
371Dic3⋊C4—22no—
372Dic3⋊C4—22no—
373Dic3⋊C4—28no—
374Dic3⋊C4—44no—
375Dic3⋊C4—44no—
376C4×Dic3—22no—
377C4×Dic3—28no—
378C4×Dic3—28no—
379C4×Dic3—44no—
380C4×Dic3C2×D414yes—
381C4×Dic3C2×D414yes—
382C4×Dic3C2×D414yes—
383C4×Dic3C2×D414yes—
384C22×Q8—28no—
385C22×Q8—24no—
386C22×Q8—31no—
387C22×Q8C22×D312yes—
388C22×Q8C22×D312yes—
389C22×D4—31no—
390C22×D4—31no—
391C22×D4C22×D311yescharacteristic
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—32no—
395C23×C4—31no—
396C23×C4C22×D312yes—
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399#126—64no—
400#126—64no—
401#125—64no—
402#124—64no—
403#123—64no—
404#123—64no—
405#123—124no—
406#123—124no—
407C22⋊Q8—28no—
408C22⋊Q8—64no—
409C22⋊Q8—68no—
410#121—64no—
411C4×Q8—64no—
412C4×Q8—68no—
413C4×Q8—68no—
414C4×Q8—68no—
415C4×Q8—68no—
416C4×D4—24no—
417C4×D4—64no—
418C4×D4—64no—
419#117—64no—
420#117—64no—
421#117—124no—
422C2×C4⋊C4—32no—
423C2×C4⋊C4—34no—
424C2×C4⋊C4—34no—
425C2×C4⋊C4—32no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—32no—
436C2×C4⋊C4—34no—
437C2×C4⋊C4—34no—
438C2×C4⋊C4—34no—
439C2×C4⋊C4—34no—
440C2×C4⋊C4—34no—
441C2×C4⋊C4—68no—
442C2×C4⋊C4—64no—
443C2×C4⋊C4C22×D311yescharacteristic
444C2×C4⋊C4C22×D312yes—
445C2×C4⋊C4C22×D314yes—
446C2×C22⋊C4—31no—
447C2×C22⋊C4—31no—
448C2×C22⋊C4—32no—
449C2×C22⋊C4—31no—
450C2×C22⋊C4—31no—
451C2×C22⋊C4—31no—
452C2×C22⋊C4—31no—
453C2×C22⋊C4—31no—
454C2×C22⋊C4—31no—
455C2×C22⋊C4—34no—
456C2×C22⋊C4—34no—
457C2×C22⋊C4—34no—
458C2×C22⋊C4C22×D312yes—
459C2×C22⋊C4C22×D311yescharacteristic
460C2×C22⋊C4C22×D311yescharacteristic
461C2×C22⋊C4C22×D314yes—
462C2×C42—38no—
463C2×C42—31no—
464C2×C42—31no—
465C2×C42—31no—
466C2×C42—31no—
467C2×C42—31no—
468C2×C42—34no—
469C2×C42—34no—
470C2×C42—34no—
471C2×C42—68no—
472C2×C42C22×D311yescharacteristic
473#95—34no—
474#95—32no—
475#95—34no—
476#95—34no—
477#95—34no—
478#95—34no—
479#95—34no—
480#95—34no—
481#95C22×D312yes—
482#95C22×D314yes—
483#95C22×D314yes—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—21no—
487C23×C3—22no—
488C23×C3—21no—
489C23×C3—22no—
490C23×C3—21no—
491C23×C3C22×D412yes—
492C23×C3H(5,𝔽2)12yes—
493C23×C32−1+412yes—
494C23×C3C2511yescharacteristic
495C22×D3—21no—
496C22×D3—22no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—22no—
500C3×Q8—216no—
501C3×Q8—216no—
502C3×D4—44no—
503C2×C3×C4—216no—
504C2×C3×C4—24no—
505C2×C3×C4—22no—
506C2×C3×C4—24no—
507C2×C3×C4—28no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—24no—
512C2×C3×C4—22no—
513C2×C3×C4—24no—
514C2×C3×C4—21no—
515C2×C3×C4—24no—
516C2×C3×C4—22no—
517C2×C3×C4—21no—
518C2×C3×C4—44no—
519C2×C3×C4C22×D412yes—
520C2×C3×C4C22×D412yes—
521C2×C3×C4C2×#4118yes—
522C2×C3×C4C2×#4114yes—
523#67—44no—
524#67—44no—
525C2×Dic3—28no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—22no—
531C2×Dic3—28no—
532C2×Dic3—24no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—22no—
537C2×Dic3—24no—
538C2×Dic3—24no—
539C2×Dic3—24no—
540C2×Dic3—21no—
541C2×Dic3—24no—
542C2×Dic3—22no—
543C2×Dic3—24no—
544C2×Dic3—21no—
545C2×Dic3—48no—
546C2×Dic3C22×D412yes—
547C2×Dic3C22×D412yes—
548C2×Dic3C22×D412yes—
549C2×Dic3C22×D412yes—
550C2×Dic32−1+414yes—
551C4×D3—44no—
552Dic6—44no—
553C24—31no—
554C24C23×D311yescharacteristic
555C24C23×D311yescharacteristic
556C2×Q8—232no—
557C2×Q8—24no—
558C2×Q8—24no—
559C2×Q8—28no—
560C2×Q8—24no—
561C2×Q8—62no—
562C2×Q8—64no—
563C2×Q8#23718yes—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—62no—
568C2×D4—64no—
569C2×D4—62no—
570C2×D4—62no—
571C2×D4—62no—
572C22×C4—24no—
573C22×C4—28no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—31no—
578C22×C4—34no—
579C22×C4—34no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—34no—
585C22×C4—34no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—64no—
589C22×C4—62no—
590C22×C4—62no—
591C22×C4—64no—
592C22×C4—64no—
593C22×C4—64no—
594C22×C4—62no—
595C22×C4—64no—
596C22×C4D3×D414yes—
597C22×C4C23×D311yescharacteristic
598C22×C4C23×D311yescharacteristic
599C22×C4C23×D314yes—
600C22×C4C23×D311yescharacteristic
601C22×C4C23×D311yescharacteristic
602C22×C4C23×D314yes—
603C22×C4C23×D311yescharacteristic
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—28no—
607C4⋊C4—68no—
608C4⋊C4—68no—
609C4⋊C4—62no—
610C4⋊C4—62no—
611C4⋊C4—62no—
612C4⋊C4—62no—
613C4⋊C4—62no—
614C4⋊C4—62no—
615C4⋊C4—62no—
616C4⋊C4—62no—
617C4⋊C4—68no—
618C4⋊C4—64no—
619C4⋊C4—64no—
620C4⋊C4—62no—
621C4⋊C4—68no—
622C4⋊C4—64no—
623C4⋊C4—124no—
624C4⋊C4—124no—
625C4⋊C4—124no—
626C22⋊C4—22no—
627C22⋊C4—24no—
628C22⋊C4—22no—
629C22⋊C4—28no—
630C22⋊C4—62no—
631C22⋊C4—62no—
632C22⋊C4—62no—
633C22⋊C4—62no—
634C22⋊C4—62no—
635C22⋊C4—62no—
636C22⋊C4—62no—
637C22⋊C4—64no—
638C22⋊C4—62no—
639C22⋊C4—68no—
640C22⋊C4—124no—
641C22⋊C4—124no—
642C42—22no—
643C42—34no—
644C42—34no—
645C42—34no—
646C42—34no—
647C42—68no—
648C42—68no—
649C42—62no—
650C42—124no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—24no—
654C22×C3—24no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3#53714yes—
661C22×C3C23×D411yescharacteristic
662C22×C3C22×#4112yes—
663C22×C3C2×H(5,𝔽2)11yescharacteristic
664C22×C3C2×2−1+411yescharacteristic
665C22×C3C2×2−1+412yes—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—42no—
670C2×D3—42no—
671C3×C4—22no—
672C3×C4—28no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—44no—
677C3×C4#52514yes—
678Dic3—22no—
679Dic3—22no—
680Dic3—22no—
681Dic3—41no—
682Dic3—41no—
683Dic3—44no—
684Dic3—41no—
685Dic3—44no—
686Dic3#53614yes—
687C23—22no—
688C23—22no—
689C23—21no—
690C23—22no—
691C23—21no—
692C23—21no—
693C23—22no—
694C23—61no—
695C23—62no—
696C23—61no—
697C23—61no—
698C23—62no—
699C23C2×D3×D412yes—
700C23#100712yes—
701C23#100912yes—
702C23C24×D311yescharacteristic
703Q8—216no—
704Q8—216no—
705Q8—124no—
706D4—44no—
707D4—124no—
708D4—124no—
709C2×C4—216no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—28no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—24no—
721C2×C4—21no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—32no—
725C2×C4—34no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—44no—
730C2×C4—68no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—62no—
736C2×C4—68no—
737C2×C4—64no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—64no—
742C2×C4—62no—
743C2×C4—64no—
744C2×C4—61no—
745C2×C4—64no—
746C2×C4—64no—
747C2×C4—61no—
748C2×C4—64no—
749C2×C4—62no—
750C2×C4—128no—
751C2×C4—124no—
752C2×C4C2×D3×D412yes—
753C2×C4C2×D3×D412yes—
754C2×C4C2×#23718yes—
755C2×C4C2×#23714yes—
756C2×C3—24no—
757C2×C3—81no—
758C2×C3C2×#52511yescharacteristic
759C2×C3C2×#53611yescharacteristic
760C2×C3C2×#53711yescharacteristic
761C2×C3#352212yes—
762C2×C3#352312yes—
763D3—81no—
764C22—22no—
765C22—22no—
766C22—24no—
767C22—24no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—121no—
774C22—121no—
775C22—122no—
776C22—121no—
777C22—122no—
778C22#562914yes—
779C22C22×D3×D411yescharacteristic
780C22C22×#23712yes—
781C22C2×#100711yescharacteristic
782C22C2×#100911yescharacteristic
783C22D3×2−1+412yes—
784C4—22no—
785C4—28no—
786C4—34no—
787C4—41no—
788C4—41no—
789C4—44no—
790C4—41no—
791C4—62no—
792C4—62no—
793C4—62no—
794C4—121no—
795C4—121no—
796C4—124no—
797C4—124no—
798C4—121no—
799C4#558614yes—
800C3#3524711yescharacteristic, complemented, Sylow
801C2—24no—
802C2—81no—
803C2—241no—
804C2C2×#558611yescharacteristic
805C2C2×#562911yescharacteristic
806C2D3×#53611yescharacteristic
807C2#8672212yes—
808C2#8675212yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2409C2
prime radicalC2×#939C22
hypercenter#2409D3
hypocenterC3#35247
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2409

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic3C2semidirect
3. C3×#2409C2semidirect
4. #84068C2semidirect
5. #82778C2semidirect
6. #82744C2semidirect
7. #82373C2semidirect
8. #77205C2semidirect
9. #77192C2semidirect
10. #76813C2semidirect
11. #76804C2semidirect
12. #76611C2semidirect
13. #76548C2semidirect
15. #74691C2semidirect
16. #74589C2semidirect
17. #74407C2semidirect
18. #74027C2semidirect
19. #73864C2semidirect
109. #2409D3semidirect
800. C3#35247semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic32
C2×#55382
C3×#24092
#840682
#827782
#827442
#823732
#772052
#771922
#768132
#768042
#766112
#765482
#748722
#746912
#745892
#744072
#740272
#738642
#352473