Finite Group Databasebeta

← #11034681

Subgroups — #11034681

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×C3×D4×Q8C211yesmaximal, characteristic
2C2×#5541C211yesmaximal, characteristic
3#84065C211yesmaximal, characteristic, complemented
4#84065C211yesmaximal, characteristic, complemented
5#84062C211yesmaximal, characteristic, complemented
6C2×#5229C211yesmaximal, characteristic, complemented
7#83247C214yesmaximal, complemented
8#83245C211yesmaximal, characteristic, complemented
9#83239C211yesmaximal, characteristic, complemented
10#82811C211yesmaximal, characteristic, complemented
11#82795C214yesmaximal, complemented
12#82786C211yesmaximal, characteristic, complemented
13#82776C211yesmaximal, characteristic, complemented
14#82774C211yesmaximal, characteristic, complemented
15#82762C214yesmaximal, complemented
16#82477C211yesmaximal, characteristic, complemented
17#82456C211yesmaximal, characteristic, complemented
18#82354C214yesmaximal
19#82318C211yesmaximal, characteristic
20#38081—31nomaximal, Sylow
21C23×C3×Q8C2211yescharacteristic
22C23×C3×Q8C2211yescharacteristic
23C3×D4×Q8—28no—
24C2×C3×C4⋊Q8C2211yescharacteristic
25C2×C3×C4⋊Q8C2212yes—
26C2×C3×C22⋊Q8C2212yes—
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×C22⋊Q8C2212yes—
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4C2212yes—
32C2×C3×C4×D4C2211yescharacteristic
33C2×#944C2211yescharacteristic
34C2×#944C2211yescharacteristic
35C2×#944C2211yescharacteristic
36C2×#935C2212yes—
37C2×#926C2211yescharacteristic
38C2×#926C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic
40C2×#924C2211yescharacteristic
41C2×#924C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43#5541—28no—
44C2×#889C2212yes—
45C2×#879C2212yes—
46C2×#877C2212yes—
47C2×#870C2211yescharacteristic
48C2×C4×Dic6C2211yescharacteristic
49#5230C2214yes—
50#5230C2214yes—
51#5229C2211yescharacteristic
52#5229C2211yescharacteristic
53#5229C2211yescharacteristic
54#5229C2211yescharacteristic
55#5229C2211yescharacteristic
56#5229C2211yescharacteristic
57#5229C2211yescharacteristic
58#5229C2211yescharacteristic
59#5229C2211yescharacteristic
60#5229C2214yes—
61#5229C2214yes—
62#5220C2212yes—
63#5211C2214yes—
64#5210C2214yes—
65#5210C2214yes—
66C4×#217C2211yescharacteristic
67C4×#217C2211yescharacteristic
68C2×C3⋊#95C2214yes—
69#4986C2214yes—
70#4985C2214yes—
71#4985C2214yes—
72#4983C2214yes—
73#4982C2214yes—
74#4982C2214yes—
75#4980C2212yes—
76#4978C2214yes—
77#4978C2214yes—
78#4977C2211yescharacteristic
79#4977C2211yescharacteristic
80#4976C2214yes—
81#4975C2211yescharacteristic
82#4973C2211yescharacteristic
83#4972C2214yes—
84#4952C2214yes—
85#4952C2214yes—
86#4951C2212yes—
87#4950C2212yes—
88#4943C2214yes—
89#4942C2214yes—
90C4×C4⋊Dic3C2211yescharacteristic
91#4933C2214yes—
92#4933C2214yes—
93#4932C2211yescharacteristic
94C2×#552—31no—
95C2×D4×Q8D311yescharacteristic
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#2434—31no—
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—24no—
116C22×C3×Q8—24no—
117C22×C3×Q8—42no—
118C22×C3×Q8—42no—
119C22×C3×Q8C2311yescharacteristic
120C22×C3×Q8C2311yescharacteristic
121C22×C3×Q8C2312yes—
122C22×C3×Q8C2312yes—
123C22×C3×Q8C2311yescharacteristic
124C22×C3×D4C2311yescharacteristic
125C23×C3×C4C2312yes—
126C23×C3×C4C2312yes—
127C23×C3×C4C2311yescharacteristic
128C23×C3×C4C2311yescharacteristic
129C23×Dic3C2312yes—
130C23×Dic3C2312yes—
131C22×Dic6C2311yescharacteristic
132C3×C4⋊Q8—28no—
133C3×C4⋊Q8—24no—
134C3×C22⋊Q8—24no—
135C3×C22⋊Q8—24no—
136C3×C22⋊Q8—28no—
137C3×C22⋊Q8—28no—
138C3×C4×Q8—24no—
139C3×C4×D4—28no—
140C3×C4×D4D418yes—
141C2×C3×C4⋊C4C2312yes—
142C2×C3×C4⋊C4C2311yescharacteristic
143C2×C3×C4⋊C4C2312yes—
144C2×C3×C4⋊C4C2312yes—
145C2×C3×C4⋊C4C2312yes—
146C2×C3×C4⋊C4C2312yes—
147C2×C3×C4⋊C4C2311yescharacteristic
148C2×C3×C22⋊C4C2312yes—
149C2×C3×C22⋊C4C2312yes—
150C2×C3×C22⋊C4C2311yescharacteristic
151C2×C3×C22⋊C4C2311yescharacteristic
152C2×C3×C42C2312yes—
153C2×C3×C42C2311yescharacteristic
154C2×#217C2312yes—
155C2×#217C2312yes—
156C2×#217C2312yes—
157C2×#217C2312yes—
158C2×#217C2312yes—
159C2×#217C2312yes—
160#944—24no—
161#944—42no—
162#944—42no—
163#935—28no—
164#926—24no—
165#926—42no—
166C2×C4⋊Dic3—24no—
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2311yescharacteristic
169C2×C4⋊Dic3C2311yescharacteristic
170C2×C4⋊Dic3C2311yescharacteristic
171C2×C4⋊Dic3C2312yes—
172C2×C4⋊Dic3C2312yes—
173#924—24no—
174#924—24no—
175C2×Dic3⋊C4C2312yes—
176C2×Dic3⋊C4C2312yes—
177C2×Dic3⋊C4C2314yes—
178C2×Dic3⋊C4C2314yes—
179C2×Dic3⋊C4C2312yes—
180C2×Dic3⋊C4C2312yes—
181C2×Dic3⋊C4C2312yes—
182C2×Dic3⋊C4C2314yes—
183C2×Dic3⋊C4C2314yes—
184C2×C4×Dic3—42no—
185C2×C4×Dic3C2311yescharacteristic
186C2×C4×Dic3C2311yescharacteristic
187C2×C4×Dic3C2311yescharacteristic
188C2×C4×Dic3C2311yescharacteristic
189C2×C4×Dic3C2312yes—
190C2×C4×Dic3C2312yes—
191C2×C4×Dic3C2312yes—
192#889—28no—
193#879—28no—
194#877—28no—
195#870—24no—
196C4×Dic6—24no—
197C3⋊#95C2312yes—
198C3⋊#95C2312yes—
199C3⋊#95C2312yes—
200C3⋊#95C2314yes—
201C3⋊#95C2314yes—
202C3⋊#95C2314yes—
203C3⋊#95C2314yes—
204C3⋊#95C2314yes—
205C3⋊#95C2314yes—
206C3⋊#95C2314yes—
207C3⋊#95C2314yes—
208C3⋊#95C2314yes—
209C3⋊#95C2312yes—
210C3⋊#95C2312yes—
211C3⋊#95C2314yes—
212C3⋊#95C2314yes—
213C3⋊#95C2314yes—
214C23×Q8C2×D311yescharacteristic
215C23×Q8C2×D311yescharacteristic
216#552—68no—
217D4×Q8—28no—
218C2×C4⋊Q8—31no—
219C2×C4⋊Q8—31no—
220C2×C4⋊Q8—31no—
221C2×C4⋊Q8C2×D311yescharacteristic
222C2×C4⋊Q8C2×D312yes—
223C2×#126—32no—
224C2×#125—32no—
225C2×#125—31no—
226C2×#123—32no—
227C2×C22⋊Q8—31no—
228C2×C22⋊Q8—31no—
229C2×C22⋊Q8C2×D311yescharacteristic
230C2×C22⋊Q8C2×D311yescharacteristic
231C2×C22⋊Q8C2×D312yes—
232C2×C22⋊Q8C2×D312yes—
233C2×C4×Q8—31no—
234C2×C4×Q8C2×D311yescharacteristic
235C2×C4×D4C2×D312yes—
236C2×C4×D4C2×D311yescharacteristic
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#395—34no—
252#391—31no—
253#391—31no—
254#391—31no—
255#391—31no—
256#391—34no—
257#391—31no—
258#391—31no—
259#391—31no—
260#391—31no—
261#391—34no—
262#391—31no—
263#391—31no—
264#389—34no—
265#389—34no—
266#388—32no—
267#387—34no—
268#387—34no—
269#387—32no—
270#387—34no—
271#387—34no—
272#386—32no—
273#385—34no—
274#385—34no—
275#385—32no—
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⋊C4—31no—
285#376—31no—
286C2×#95—34no—
287C24×C3C2411yescharacteristic
288C24×C3C2411yescharacteristic
289C2×C3×Q8—22no—
290C2×C3×Q8—24no—
291C2×C3×Q8—24no—
292C2×C3×Q8—22no—
293C2×C3×Q8—22no—
294C2×C3×Q8—24no—
295C2×C3×Q8—24no—
296C2×C3×Q8—22no—
297C2×C3×Q8—22no—
298C2×C3×Q8—22no—
299C2×C3×Q8—22no—
300C2×C3×Q8—22no—
301C2×C3×Q8—42no—
302C2×C3×Q8—42no—
303C2×C3×Q8—416no—
304C2×C3×Q8—416no—
305C2×C3×Q8#4114yes—
306C2×C3×D4—24no—
307C2×C3×D4C2×D414yes—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—24no—
313C22×C3×C4—24no—
314C22×C3×C4—24no—
315C22×C3×C4—24no—
316C22×C3×C4—42no—
317C22×C3×C4—42no—
318C22×C3×C4C2×D414yes—
319C22×C3×C4C2×D414yes—
320C22×C3×C4C2412yes—
321C22×C3×C4C2412yes—
322C22×C3×C4C2412yes—
323C22×C3×C4C2411yescharacteristic
324C22×C3×C4C2411yescharacteristic
325C22×C3×C4C2411yescharacteristic
326C22×C3×C4C2411yescharacteristic
327C22×C3×C4C2412yes—
328C22×C3×C4C2411yescharacteristic
329C22×Dic3—24no—
330C22×Dic3—24no—
331C22×Dic3—28no—
332C22×Dic3—24no—
333C22×Dic3—42no—
334C22×Dic3C2412yes—
335C22×Dic3C2412yes—
336C22×Dic3C2412yes—
337C22×Dic3C2412yes—
338C22×Dic3C2412yes—
339C22×Dic3C2412yes—
340C22×Dic3C2412yes—
341C22×Dic3C2412yes—
342C2×Dic6—22no—
343C2×Dic6—22no—
344C2×Dic6—22no—
345C3×C4⋊C4—24no—
346C3×C4⋊C4—24no—
347C3×C4⋊C4—22no—
348C3×C4⋊C4—24no—
349C3×C4⋊C4—24no—
350C3×C4⋊C4—24no—
351C3×C4⋊C4C2×D414yes—
352C3×C22⋊C4—24no—
353C3×C22⋊C4—24no—
354C3×C22⋊C4C2×D414yes—
355C3×C22⋊C4C2×D414yes—
356C3×C42—24no—
357C3×C42C2×D414yes—
358#217—24no—
359#217—24no—
360#217—24no—
361#217—24no—
362#217—24no—
363#217—42no—
364C4⋊Dic3—22no—
365C4⋊Dic3—22no—
366C4⋊Dic3—22no—
367C4⋊Dic3—24no—
368C4⋊Dic3—24no—
369C4⋊Dic3—42no—
370Dic3⋊C4—24no—
371Dic3⋊C4—24no—
372Dic3⋊C4—24no—
373Dic3⋊C4—24no—
374Dic3⋊C4—24no—
375Dic3⋊C4—28no—
376Dic3⋊C4—28no—
377Dic3⋊C4—44no—
378Dic3⋊C4—44no—
379C4×Dic3—24no—
380C4×Dic3—24no—
381C4×Dic3—22no—
382C4×Dic3—22no—
383C4×Dic3—22no—
384C4×Dic3—22no—
385C4×Dic3—42no—
386C22×Q8—24no—
387C22×Q8—24no—
388C22×Q8—24no—
389C22×Q8—24no—
390C22×Q8—31no—
391C22×Q8—42no—
392C22×Q8—42no—
393C22×Q8C22×D311yescharacteristic
394C22×Q8C22×D311yescharacteristic
395C22×Q8C22×D312yes—
396C22×Q8C22×D312yes—
397C22×Q8C22×D311yescharacteristic
398C22×D4C22×D311yescharacteristic
399C23×C4—32no—
400C23×C4—32no—
401C23×C4C22×D312yes—
402C23×C4C22×D312yes—
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D311yescharacteristic
405C4⋊Q8—28no—
406C4⋊Q8—24no—
407C4⋊Q8—64no—
408C4⋊Q8—122no—
409C4⋊Q8—122no—
410#126—68no—
411#125—68no—
412#125—64no—
413#123—68no—
414C22⋊Q8—24no—
415C22⋊Q8—24no—
416C22⋊Q8—28no—
417C22⋊Q8—28no—
418C22⋊Q8—64no—
419C22⋊Q8—64no—
420C4×Q8—24no—
421C4×Q8—64no—
422C4×D4—28no—
423C4×D4#6718yes—
424#117—64no—
425#117—68no—
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—32no—
434C2×C4⋊C4—32no—
435C2×C4⋊C4—32no—
436C2×C4⋊C4—34no—
437C2×C4⋊C4—32no—
438C2×C4⋊C4—34no—
439C2×C4⋊C4—32no—
440C2×C4⋊C4—34no—
441C2×C4⋊C4—34no—
442C2×C4⋊C4—64no—
443C2×C4⋊C4C22×D312yes—
444C2×C4⋊C4C22×D311yescharacteristic
445C2×C4⋊C4C22×D312yes—
446C2×C4⋊C4C22×D312yes—
447C2×C4⋊C4C22×D312yes—
448C2×C4⋊C4C22×D312yes—
449C2×C4⋊C4C22×D311yescharacteristic
450C2×C22⋊C4—32no—
451C2×C22⋊C4—32no—
452C2×C22⋊C4—32no—
453C2×C22⋊C4—32no—
454C2×C22⋊C4—32no—
455C2×C22⋊C4—32no—
456C2×C22⋊C4C22×D312yes—
457C2×C22⋊C4C22×D312yes—
458C2×C22⋊C4C22×D311yescharacteristic
459C2×C22⋊C4C22×D311yescharacteristic
460C2×C42—32no—
461C2×C42—32no—
462C2×C42—31no—
463C2×C42—31no—
464C2×C42—31no—
465C2×C42—31no—
466C2×C42—32no—
467C2×C42—122no—
468C2×C42C22×D312yes—
469C2×C42C22×D311yescharacteristic
470#95—34no—
471#95—34no—
472#95—34no—
473#95—34no—
474#95—32no—
475#95—32no—
476#95—32no—
477#95—32no—
478#95—32no—
479#95—34no—
480#95—34no—
481#95—34no—
482#95—34no—
483#95—34no—
484#95—34no—
485#95—34no—
486#95—34no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—22no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3C22×D412yes—
495C23×C3C22×D412yes—
496C23×C32−1+414yes—
497C23×C3C2511yescharacteristic
498C3×Q8—28no—
499C3×Q8—48no—
500C3×Q8—48no—
501C3×Q8—44no—
502C3×Q8—44no—
503C3×D4—28no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—28no—
513C2×C3×C4—28no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—24no—
522C2×C3×C4—48no—
523C2×C3×C4—48no—
524C2×C3×C4C22×D412yes—
525C2×C3×C4C22×D412yes—
526C2×C3×C4C22×D412yes—
527C2×C3×C4C22×D412yes—
528C2×C3×C4C22×D412yes—
529C2×C3×C4C2×#4114yes—
530C2×C3×C4C2×#4112yes—
531C2×C3×C4H(5,𝔽2)12yes—
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—22no—
542C2×Dic3—22no—
543C2×Dic3—24no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—24no—
549C2×Dic3—24no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—48no—
553C2×Dic3—48no—
554C2×Dic32−1+414yes—
555Dic6—44no—
556C24C23×D311yescharacteristic
557C24C23×D311yescharacteristic
558C2×Q8—24no—
559C2×Q8—24no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—24no—
567C2×Q8—24no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—416no—
573C2×Q8—416no—
574C2×Q8—62no—
575C2×Q8—62no—
576C2×Q8—62no—
577C2×Q8#23714yes—
578C2×D4—24no—
579C2×D4C2×#6714yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—32no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—32no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—64no—
599C22×C4—64no—
600C22×C4—68no—
601C22×C4—64no—
602C22×C4—122no—
603C22×C4C2×#6714yes—
604C22×C4C2×#6714yes—
605C22×C4C23×D312yes—
606C22×C4C23×D312yes—
607C22×C4C23×D312yes—
608C22×C4C23×D312yes—
609C22×C4C23×D311yescharacteristic
610C22×C4C23×D311yescharacteristic
611C22×C4C23×D311yescharacteristic
612C22×C4C23×D311yescharacteristic
613C22×C4C23×D311yescharacteristic
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—22no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—68no—
621C4⋊C4—64no—
622C4⋊C4—68no—
623C4⋊C4—62no—
624C4⋊C4—62no—
625C4⋊C4—64no—
626C4⋊C4—64no—
627C4⋊C4—62no—
628C4⋊C4—64no—
629C4⋊C4—64no—
630C4⋊C4—64no—
631C4⋊C4—64no—
632C4⋊C4—122no—
633C4⋊C4—124no—
634C4⋊C4—124no—
635C4⋊C4C2×#6714yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—64no—
639C22⋊C4—64no—
640C22⋊C4—64no—
641C22⋊C4—64no—
642C22⋊C4—64no—
643C22⋊C4—122no—
644C22⋊C4C2×#6714yes—
645C22⋊C4C2×#6714yes—
646C42—24no—
647C42—62no—
648C42—62no—
649C42—62no—
650C42—62no—
651C42—64no—
652C42—64no—
653C42—122no—
654C42C2×#6714yes—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—24no—
658C22×C3—24no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3#53614yes—
665C22×C3C23×D411yescharacteristic
666C22×C3C22×#4111yescharacteristic
667C22×C3C2×H(5,𝔽2)11yescharacteristic
668C22×C3C2×2−1+412yes—
669C22×C3C2×2−1+412yes—
670C3×C4—22no—
671C3×C4—22no—
672C3×C4—22no—
673C3×C4—24no—
674C3×C4—22no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4—42no—
678C3×C4#54614yes—
679Dic3—24no—
680Dic3—42no—
681Dic3—42no—
682Dic3—42no—
683Dic3—42no—
684Dic3—42no—
685Dic3—42no—
686Dic3—42no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—21no—
691C23—21no—
692C23—22no—
693C23—22no—
694C23#100714yes—
695C23C22×#6712yes—
696C23C22×#6712yes—
697C23C24×D311yescharacteristic
698Q8—28no—
699Q8—48no—
700Q8—48no—
701Q8—44no—
702Q8—44no—
703Q8—124no—
704D4—28no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—34no—
724C2×C4—48no—
725C2×C4—48no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—64no—
736C2×C4—64no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—64no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—128no—
747C2×C4—128no—
748C2×C4C2×#23714yes—
749C2×C4C2×#23712yes—
750C2×C4#100412yes—
751C2×C4C22×#6712yes—
752C2×C4C22×#6712yes—
753C2×C4C22×#6712yes—
754C2×C4C22×#6712yes—
755C2×C4C22×#6712yes—
756C2×C3—24no—
757C2×C3—42no—
758C2×C3C2×#53611yescharacteristic
759C2×C3C2×#54611yescharacteristic
760C2×C3#349911yescharacteristic
761C2×C3#352312yes—
762C2×C3#353812yes—
763C22—22no—
764C22—24no—
765C22—24no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—42no—
771C22—42no—
772C22#581614yes—
773C22C22×#23711yescharacteristic
774C22C2×#100411yescharacteristic
775C22C2×#100712yes—
776C22D3×2−1+412yes—
777C22C23×#6711yescharacteristic
778C4—22no—
779C4—22no—
780C4—24no—
781C4—22no—
782C4—22no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—64no—
787C4—122no—
788C4—122no—
789C4—122no—
790C4—122no—
791C4—122no—
792C4—122no—
793C4—122no—
794C4#580614yes—
795C3#3808111yescharacteristic, complemented, Sylow
796C2—24no—
797C2—42no—
798C2#8675212yes—
799C2#8676212yes—
800C2C2×#580611yescharacteristic
801C2C2×#581611yescharacteristic
802C2#8729211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×D4×Q8C2
prime radicalC22×C3×D4C23
hypercenterC2×D4×Q8D3
hypocenterC3#38081
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
3. #84065C2semidirect
4. #84065C2semidirect
5. #84062C2semidirect
6. C2×#5229C2semidirect
7. #83247C2semidirect
8. #83245C2semidirect
9. #83239C2semidirect
10. #82811C2semidirect
11. #82795C2semidirect
12. #82786C2semidirect
13. #82776C2semidirect
14. #82774C2semidirect
15. #82762C2semidirect
16. #82477C2semidirect
17. #82456C2semidirect
795. C3#38081semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Q82
C2×#55412
#840652
#840622
C2×#52292
#832472
#832452
#832392
#828112
#827952
#827862
#827762
#827742
#827622
#824772
#824562
#823542
#823182
#380813