Finite Group Databasebeta

← #11034678

Subgroups — #11034678

Order 768.

2246 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#67C211yesmaximal, characteristic
2C2×#5639C211yesmaximal, characteristic
3C3×#2434C211yesmaximal, characteristic, complemented
4#84062C211yesmaximal, characteristic, complemented
5#83269C211yesmaximal, characteristic, complemented
6#83238C211yesmaximal, characteristic, complemented
7#83232C211yesmaximal, characteristic, complemented
8#83227C211yesmaximal, characteristic, complemented
9#82786C211yesmaximal, characteristic, complemented
10#77251C214yesmaximal, complemented
11#77217C214yesmaximal, complemented
12D3×#391C211yesmaximal, characteristic, complemented
13#76559C211yesmaximal, characteristic, complemented
14#76541C211yesmaximal, characteristic, complemented
15#76520C211yesmaximal, characteristic, complemented
16#74604C214yesmaximal
17#74513C214yesmaximal, complemented
18#73562C211yesmaximal, characteristic
19#73514C211yesmaximal, characteristic, complemented
20#38081—31nomaximal, Sylow
21C23×C3×Q8C2211yescharacteristic
22C22×D3×Q8C2211yescharacteristic
23C2×C3×C4⋊Q8C2211yescharacteristic
24C2×C3×C4⋊Q8C2211yescharacteristic
25C2×C3×C22⋊Q8C2211yescharacteristic
26Q8×#67—28no—
27C2×#946C2211yescharacteristic
28C2×#946C2211yescharacteristic
29C2×#946C2212yes—
30C2×Q8×Dic3C2211yescharacteristic
31C2×Q8×Dic3C2211yescharacteristic
32C2×#944C2211yescharacteristic
33C2×#944C2212yes—
34C2×#944C2211yescharacteristic
35C2×C4×#67C2212yes—
36C2×C4×#67C2211yescharacteristic
37C2×#926C2211yescharacteristic
38C2×#926C2211yescharacteristic
39C2×#924C2212yes—
40C2×#924C2211yescharacteristic
41#5639—28no—
42C2×#892C2212yes—
43C2×D3×C4⋊C4C2211yescharacteristic
44C2×#890C2211yescharacteristic
45C2×#889C2212yes—
46C2×#883C2212yes—
47C2×#879C2212yes—
48C2×C42×D3C2211yescharacteristic
49C3×#395C2214yes—
50C3×#391C2211yescharacteristic
51C3×#391C2211yescharacteristic
52C3×#385C2214yes—
53C3×C4×C22⋊C4C2211yescharacteristic
54#5229C2211yescharacteristic
55#5229C2211yescharacteristic
56#5229C2211yescharacteristic
57#5229C2211yescharacteristic
58#5229C2211yescharacteristic
59#5229C2214yes—
60#5211C2214yes—
61#4989C2214yes—
62#4987C2214yes—
63#4982C2214yes—
64#4982C2214yes—
65#4980C2214yes—
66#4980C2214yes—
67#4979C2214yes—
68#4977C2211yescharacteristic
69#4976C2214yes—
70#4973C2211yescharacteristic
71#4972C2214yes—
72#4956C2212yes—
73#4953C2214yes—
74#4952C2214yes—
75#4945C2212yes—
76C4×(C2×D3)⋊C4C2211yescharacteristic
77#4936C2211yescharacteristic
78#4935C2211yescharacteristic
79#4932C2211yescharacteristic
80C4×Dic3⋊C4C2211yescharacteristic
81#4929C2211yescharacteristic
82#4929C2211yescharacteristic
83#4668C2212yes—
84#4664C2214yes—
85D3×#95C2214yes—
86#4661C2214yes—
87#4660C2214yes—
88#4658C2214yes—
89#4658C2214yes—
90#4655C2212yes—
91#4654C2214yes—
92#4653C2214yes—
93#4646C2214yes—
94C2×#552—31no—
95C2×D4×Q8—31no—
96#2857—31no—
97#2713—34no—
98#2689—34no—
99#2642—31no—
100#2621—31no—
101#2565—31no—
102#2546—31no—
103#2503—31no—
104#2499—31no—
105#2438—34no—
106#2434—31no—
107#2434D311yescharacteristic, complemented
108#2419—34no—
109#2327—31no—
110#2310—31no—
111C2×#391—31no—
112#2290—31no—
113C22×C3×Q8—24no—
114C22×C3×Q8—24no—
115C22×C3×Q8—42no—
116C22×C3×Q8C2311yescharacteristic
117C22×C3×Q8C2311yescharacteristic
118C22×C3×Q8C2312yes—
119C22×C3×Q8C2311yescharacteristic
120C23×C3×C4C2312yes—
121C23×C3×C4C2311yescharacteristic
122C22×#67C2311yescharacteristic
123C2×D3×Q8—24no—
124C2×D3×Q8—24no—
125C2×D3×Q8—42no—
126C22×C4×D3C2312yes—
127C22×C4×D3C2312yes—
128C22×C4×D3C2312yes—
129C22×C4×D3C2311yescharacteristic
130C22×Dic6C2311yescharacteristic
131C22×Dic6C2312yes—
132C3×C4⋊Q8—24no—
133C3×C4⋊Q8—42no—
134C3×C22⋊Q8—24no—
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2314yes—
137C2×C3×C4⋊C4C2312yes—
138C2×C3×C4⋊C4C2314yes—
139C2×C3×C22⋊C4C2312yes—
140C2×C3×C22⋊C4C2312yes—
141C2×C3×C42C2311yescharacteristic
142C2×C3×C42C2311yescharacteristic
143C2×#217C2312yes—
144C2×#217C2312yes—
145C2×#217C2312yes—
146C2×#217C2311yescharacteristic
147#946—24no—
148#946—24no—
149#946—28no—
150Q8×Dic3—24no—
151Q8×Dic3—24no—
152#944—28no—
153#944—24no—
154#944—42no—
155C4×#67—28no—
156C4×#67D418yes—
157C2×(C2×D3)⋊C4C2312yes—
158C2×(C2×D3)⋊C4C2312yes—
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2311yescharacteristic
161#926—24no—
162#926—42no—
163C2×C4⋊Dic3C2314yes—
164C2×C4⋊Dic3C2312yes—
165C2×C4⋊Dic3C2312yes—
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4⋊Dic3C2311yescharacteristic
168C2×C4⋊Dic3C2311yescharacteristic
169C2×C4⋊Dic3C2312yes—
170C2×C4⋊Dic3C2312yes—
171#924—24no—
172#924—28no—
173C2×Dic3⋊C4C2312yes—
174C2×Dic3⋊C4C2312yes—
175C2×Dic3⋊C4C2312yes—
176C2×Dic3⋊C4C2312yes—
177C2×Dic3⋊C4C2312yes—
178C2×Dic3⋊C4C2312yes—
179C2×Dic3⋊C4C2312yes—
180C2×Dic3⋊C4C2312yes—
181C2×Dic3⋊C4C2314yes—
182C2×Dic3⋊C4C2311yescharacteristic
183C2×C4×Dic3C2312yes—
184C2×C4×Dic3C2312yes—
185C2×C4×Dic3C2311yescharacteristic
186C2×C4×Dic3C2311yescharacteristic
187C2×C4×Dic3C2312yes—
188C2×C4×Dic3C2312yes—
189C2×C4×Dic3C2311yescharacteristic
190#892—28no—
191D3×C4⋊C4—24no—
192#890—24no—
193#889—28no—
194#883—28no—
195#879—28no—
196C42×D3—42no—
197C3×#95C2314yes—
198C3×#95C2312yes—
199C3×#95C2314yes—
200C3⋊#95C2314yes—
201C3⋊#95C2314yes—
202C3⋊#95C2314yes—
203C3⋊#95C2314yes—
204C3⋊#95C2314yes—
205C3⋊#95C2312yes—
206C3⋊#95C2314yes—
207C3⋊#95C2314yes—
208C3⋊#95C2312yes—
209C3⋊#95C2312yes—
210C3⋊#95C2314yes—
211C3⋊#95C2314yes—
212C3⋊#95C2312yes—
213C3⋊#95C2314yes—
214C23×Q8—31no—
215C23×Q8C2×D311yescharacteristic
216#552—68no—
217D4×Q8—68no—
218C2×C4⋊Q8—31no—
219C2×C4⋊Q8—32no—
220C2×C4⋊Q8—31no—
221C2×C4⋊Q8C2×D311yescharacteristic
222C2×C4⋊Q8C2×D311yescharacteristic
223C2×#126—32no—
224C2×#125—31no—
225C2×#125—32no—
226C2×#123—32no—
227C2×C22⋊Q8—31no—
228C2×C22⋊Q8—31no—
229C2×C22⋊Q8—32no—
230C2×C22⋊Q8—31no—
231C2×C22⋊Q8—32no—
232C2×C22⋊Q8C2×D311yescharacteristic
233C2×C4×Q8—31no—
234C2×C4×Q8—31no—
235C2×C4×D4—31no—
236C2×C4×D4—32no—
237C2×#117—31no—
238C2×#117—31no—
239C2×#117—32no—
240C22×C4⋊C4—31no—
241C22×C42—31no—
242#400—34no—
243#400—34no—
244#400—34no—
245#398—34no—
246#398—34no—
247#398—34no—
248#397—34no—
249#397—34no—
250#395—34no—
251#395C2×D314yes—
252#391—31no—
253#391—31no—
254#391—31no—
255#391—34no—
256#391—31no—
257#391—31no—
258#391—31no—
259#391—31no—
260#391—31no—
261#391—34no—
262#391C2×D311yescharacteristic
263#391C2×D311yescharacteristic
264#389—34no—
265#389—34no—
266#388—32no—
267#387—34no—
268#387—34no—
269#387—34no—
270#387—34no—
271#387—32no—
272#386—32no—
273#385—34no—
274#385—32no—
275#385C2×D314yes—
276#384—31no—
277#382—31no—
278#382—31no—
279#381—34no—
280#381—34no—
281#380—34no—
282C4×C4⋊C4—31no—
283C4×C22⋊C4—31no—
284C4×C22⋊C4C2×D311yescharacteristic
285#376—31no—
286C2×#95—34no—
287C24×C3C2411yescharacteristic
288C23×D3C2411yescharacteristic
289C2×C3×Q8—22no—
290C2×C3×Q8—24no—
291C2×C3×Q8—22no—
292C2×C3×Q8—22no—
293C2×C3×Q8—22no—
294C2×C3×Q8—24no—
295C2×C3×Q8—22no—
296C2×C3×Q8—22no—
297C2×C3×Q8—22no—
298C2×C3×Q8—22no—
299C2×C3×Q8—42no—
300C2×C3×Q8—416no—
301C2×C3×Q8#4114yes—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—24no—
305C22×C3×C4—24no—
306C22×C3×C4—42no—
307C22×C3×C4C2×D414yes—
308C22×C3×C4C2412yes—
309C22×C3×C4C2412yes—
310C22×C3×C4C2412yes—
311C22×C3×C4C2412yes—
312C22×C3×C4C2411yescharacteristic
313C22×C3×C4C2412yes—
314C22×C3×C4C2412yes—
315C22×C3×C4C2411yescharacteristic
316C2×#67—24no—
317C2×#67C2×D414yes—
318C22×Dic3C2412yes—
319C22×Dic3C2412yes—
320C22×Dic3C2412yes—
321C22×Dic3C2412yes—
322C22×Dic3C2412yes—
323C22×Dic3C2412yes—
324C22×Dic3C2411yescharacteristic
325C22×Dic3C2411yescharacteristic
326C22×Dic3C2411yescharacteristic
327D3×Q8—416no—
328C2×C4×D3—22no—
329C2×C4×D3—22no—
330C2×C4×D3—24no—
331C2×C4×D3—24no—
332C2×C4×D3—24no—
333C2×C4×D3—28no—
334C2×C4×D3—24no—
335C2×C4×D3—24no—
336C2×C4×D3—42no—
337C2×C4×D3—42no—
338C2×C4×D3C2×D414yes—
339C2×Dic6—22no—
340C2×Dic6—24no—
341C2×Dic6—22no—
342C2×Dic6—22no—
343C2×Dic6—24no—
344C2×Dic6—42no—
345C3×C4⋊C4—24no—
346C3×C4⋊C4—22no—
347C3×C4⋊C4—28no—
348C3×C4⋊C4—44no—
349C3×C22⋊C4—24no—
350C3×C22⋊C4—24no—
351C3×C42—22no—
352C3×C42—22no—
353#217—24no—
354#217—24no—
355#217—42no—
356#217C2×D414yes—
357(C2×D3)⋊C4—24no—
358(C2×D3)⋊C4—24no—
359(C2×D3)⋊C4—24no—
360(C2×D3)⋊C4C2×D414yes—
361C4⋊Dic3—22no—
362C4⋊Dic3—22no—
363C4⋊Dic3—22no—
364C4⋊Dic3—28no—
365C4⋊Dic3—24no—
366C4⋊Dic3—24no—
367C4⋊Dic3—24no—
368C4⋊Dic3—42no—
369Dic3⋊C4—24no—
370Dic3⋊C4—24no—
371Dic3⋊C4—24no—
372Dic3⋊C4—24no—
373Dic3⋊C4—24no—
374Dic3⋊C4—24no—
375Dic3⋊C4—24no—
376Dic3⋊C4—24no—
377Dic3⋊C4—44no—
378Dic3⋊C4C2×D414yes—
379C4×Dic3—24no—
380C4×Dic3—22no—
381C4×Dic3—22no—
382C4×Dic3—24no—
383C4×Dic3—24no—
384C4×Dic3—42no—
385C4×Dic3C2×D414yes—
386C22×Q8—24no—
387C22×Q8—24no—
388C22×Q8—31no—
389C22×Q8—32no—
390C22×Q8—42no—
391C22×Q8—64no—
392C22×Q8—64no—
393C22×Q8—122no—
394C22×Q8C22×D311yescharacteristic
395C22×Q8C22×D311yescharacteristic
396C22×Q8C22×D312yes—
397C22×Q8C22×D311yescharacteristic
398C22×D4—31no—
399C23×C4—31no—
400C23×C4—32no—
401C23×C4—32no—
402C23×C4—32no—
403C23×C4C22×D312yes—
404C23×C4C22×D311yescharacteristic
405C4⋊Q8—24no—
406C4⋊Q8—42no—
407C4⋊Q8—64no—
408C4⋊Q8—68no—
409C4⋊Q8—122no—
410#126—68no—
411#125—64no—
412#125—68no—
413#123—68no—
414C22⋊Q8—24no—
415C22⋊Q8—68no—
416C22⋊Q8—68no—
417C22⋊Q8—64no—
418C22⋊Q8—64no—
419C22⋊Q8—64no—
420C4×Q8—64no—
421C4×Q8—64no—
422C4×D4—38no—
423C4×D4—68no—
424#117—68no—
425#117—64no—
426#117—122no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—32no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—32no—
432C2×C4⋊C4—32no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—32no—
435C2×C4⋊C4—32no—
436C2×C4⋊C4—32no—
437C2×C4⋊C4—32no—
438C2×C4⋊C4—32no—
439C2×C4⋊C4—32no—
440C2×C4⋊C4—32no—
441C2×C4⋊C4—32no—
442C2×C4⋊C4—34no—
443C2×C4⋊C4—32no—
444C2×C4⋊C4—34no—
445C2×C4⋊C4—64no—
446C2×C4⋊C4C22×D311yescharacteristic
447C2×C4⋊C4C22×D312yes—
448C2×C4⋊C4C22×D314yes—
449C2×C4⋊C4C22×D314yes—
450C2×C22⋊C4—31no—
451C2×C22⋊C4—31no—
452C2×C22⋊C4—32no—
453C2×C22⋊C4—32no—
454C2×C22⋊C4—32no—
455C2×C22⋊C4—32no—
456C2×C22⋊C4—32no—
457C2×C22⋊C4—32no—
458C2×C22⋊C4C22×D312yes—
459C2×C22⋊C4C22×D312yes—
460C2×C42—31no—
461C2×C42—32no—
462C2×C42—32no—
463C2×C42—31no—
464C2×C42—31no—
465C2×C42—32no—
466C2×C42—32no—
467C2×C42—122no—
468C2×C42C22×D311yescharacteristic
469C2×C42C22×D311yescharacteristic
470#95—34no—
471#95—34no—
472#95—34no—
473#95—32no—
474#95—32no—
475#95—32no—
476#95—32no—
477#95—34no—
478#95—34no—
479#95—34no—
480#95—34no—
481#95—34no—
482#95—34no—
483#95—34no—
484#95C22×D314yes—
485#95C22×D312yes—
486#95C22×D314yes—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3C22×D412yes—
492C23×C3C2511yescharacteristic
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—22no—
496C22×D3C22×D412yes—
497C22×D32−1+414yes—
498C3×Q8—28no—
499C3×Q8—48no—
500C3×Q8—44no—
501C3×Q8—44no—
502C2×C3×C4—22no—
503C2×C3×C4—21no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—28no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—24no—
520C2×C3×C4—48no—
521C2×C3×C4C22×D412yes—
522C2×C3×C4C22×D412yes—
523C2×C3×C4C2×#4114yes—
524C2×C3×C4C2×#4112yes—
525C2×C3×C4H(5,𝔽2)12yes—
526C2×C3×C42−1+414yes—
527#67—28no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—24no—
542C2×Dic3—24no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—24no—
546C2×Dic3—22no—
547C2×Dic3C22×D412yes—
548C2×Dic3C22×D412yes—
549C2×Dic3C22×D412yes—
550C4×D3—28no—
551C4×D3—48no—
552C4×D3—48no—
553C4×D3—48no—
554Dic6—48no—
555Dic6—44no—
556C24—31no—
557C24C23×D311yescharacteristic
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—24no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—24no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—42no—
569C2×Q8—416no—
570C2×Q8—64no—
571C2×Q8—62no—
572C2×Q8—64no—
573C2×Q8—62no—
574C2×Q8—62no—
575C2×Q8—122no—
576C2×Q8—1216no—
577C2×Q8#23714yes—
578C2×D4—34no—
579C2×D4—64no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—34no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—32no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—42no—
595C22×C4—64no—
596C22×C4—64no—
597C22×C4—64no—
598C22×C4—68no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4—64no—
602C22×C4—64no—
603C22×C4—122no—
604C22×C4—122no—
605C22×C4D3×D414yes—
606C22×C4C23×D312yes—
607C22×C4C23×D312yes—
608C22×C4C23×D312yes—
609C22×C4C23×D312yes—
610C22×C4C23×D311yescharacteristic
611C22×C4C23×D312yes—
612C22×C4C23×D312yes—
613C22×C4C23×D311yescharacteristic
614C4⋊C4—22no—
615C4⋊C4—24no—
616C4⋊C4—28no—
617C4⋊C4—34no—
618C4⋊C4—44no—
619C4⋊C4—64no—
620C4⋊C4—64no—
621C4⋊C4—64no—
622C4⋊C4—64no—
623C4⋊C4—64no—
624C4⋊C4—64no—
625C4⋊C4—64no—
626C4⋊C4—64no—
627C4⋊C4—64no—
628C4⋊C4—62no—
629C4⋊C4—62no—
630C4⋊C4—62no—
631C4⋊C4—64no—
632C4⋊C4—64no—
633C4⋊C4—68no—
634C4⋊C4—122no—
635C4⋊C4—124no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—34no—
639C22⋊C4—34no—
640C22⋊C4—64no—
641C22⋊C4—64no—
642C22⋊C4—64no—
643C22⋊C4—64no—
644C22⋊C4—64no—
645C22⋊C4—122no—
646C42—22no—
647C42—22no—
648C42—34no—
649C42—64no—
650C42—64no—
651C42—64no—
652C42—62no—
653C42—62no—
654C42—122no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3C23×D411yescharacteristic
661C22×C3C22×#4111yescharacteristic
662C22×C3C2×H(5,𝔽2)11yescharacteristic
663C22×C3C2×2−1+412yes—
664C22×C3C2×2−1+412yes—
665C2×D3—22no—
666C2×D3—22no—
667C2×D3—24no—
668C2×D3—24no—
669C2×D3#53614yes—
670C3×C4—24no—
671C3×C4—22no—
672C3×C4—24no—
673C3×C4—42no—
674C3×C4—42no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4#54614yes—
678Dic3—22no—
679Dic3—22no—
680Dic3—22no—
681Dic3—42no—
682Dic3—42no—
683Dic3—42no—
684Dic3—42no—
685Dic3—42no—
686Dic3—42no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—22no—
691C23—32no—
692C23—34no—
693C23—61no—
694C23—61no—
695C23—62no—
696C23C2×D3×D412yes—
697C23C24×D311yescharacteristic
698Q8—28no—
699Q8—48no—
700Q8—44no—
701Q8—44no—
702Q8—128no—
703Q8—124no—
704D4—68no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—28no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—32no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—48no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—68no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—64no—
741C2×C4—64no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—64no—
746C2×C4—62no—
747C2×C4—128no—
748C2×C4—128no—
749C2×C4—128no—
750C2×C4C2×D3×D412yes—
751C2×C4C2×D3×D412yes—
752C2×C4C2×#23714yes—
753C2×C4C2×#23712yes—
754C2×C4#100412yes—
755C2×C4#100714yes—
756C2×C3—42no—
757C2×C3C2×#53611yescharacteristic
758C2×C3C2×#54611yescharacteristic
759C2×C3#349911yescharacteristic
760C2×C3#352312yes—
761C2×C3#353812yes—
762D3—24no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—34no—
767C22—42no—
768C22—42no—
769C22—62no—
770C22—62no—
771C22—64no—
772C22—64no—
773C22C22×D3×D411yescharacteristic
774C22C22×#23711yescharacteristic
775C22C2×#100411yescharacteristic
776C22C2×#100712yes—
777C22D3×2−1+412yes—
778C4—22no—
779C4—24no—
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—62no—
786C4—62no—
787C4—62no—
788C4—122no—
789C4—122no—
790C4—122no—
791C4—122no—
792C4—122no—
793C4—122no—
794C4#559114yes—
795C3#3808111yescharacteristic, complemented, Sylow
796C2—42no—
797C2—64no—
798C2C2×#559111yescharacteristic
799C2#8621411yescharacteristic
800C2D3×#53611yescharacteristic
801C2#8675312yes—
802C2#8676212yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2434C2
prime radicalC22×#67C23
hypercenter#2434D3
hypocenterC3#38081
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2434

Complements

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

NH ≅ G/Ntype
3. C3×#2434C2semidirect
4. #84062C2semidirect
5. #83269C2semidirect
6. #83238C2semidirect
7. #83232C2semidirect
8. #83227C2semidirect
9. #82786C2semidirect
10. #77251C2semidirect
11. #77217C2semidirect
12. D3×#391C2semidirect
13. #76559C2semidirect
14. #76541C2semidirect
15. #76520C2semidirect
17. #74513C2semidirect
19. #73514C2semidirect
107. #2434D3semidirect
795. C3#38081semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#672
C2×#56392
C3×#24342
#840622
#832692
#832382
#832322
#832272
#827862
#772512
#772172
D3×#3912
#765592
#765412
#765202
#746042
#745132
#735622
#735142
#380813