Finite Group Databasebeta

← #11058653

Subgroups — #11058653

Order 768.

2276 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Q8C211yesmaximal, characteristic, complemented
2C2×#5557C211yesmaximal, characteristic
3#84068C212yesmaximal, complemented
4#84062C212yesmaximal, complemented
5#83269C211yesmaximal, characteristic, complemented
6#83258C212yesmaximal, complemented
7#83244C211yesmaximal, characteristic, complemented
8#83241C212yesmaximal, complemented
9#82814C212yesmaximal, complemented
10#82795C214yesmaximal, complemented
11#82794C214yesmaximal, complemented
12#82787C212yesmaximal, complemented
13C4×#946C211yesmaximal, characteristic, complemented
14#82482C211yesmaximal, characteristic, complemented
15#82405C212yesmaximal
16#82359C212yesmaximal, complemented
17#82337C211yesmaximal, characteristic, complemented
18#38911—31nomaximal, Sylow
19C23×C3×Q8C2212yes—
20C3×D4×Q8—28no—
21C2×C3×C4⋊Q8C2212yes—
22C2×C3×C4⋊Q8C2211yescharacteristic
23C2×C3×C22⋊Q8C2212yes—
24C2×C3×C22⋊Q8C2214yes—
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4C2212yes—
27C2×C3×C4×D4C2211yescharacteristic
28C2×#946C2211yescharacteristic
29C2×#946C2212yes—
30C2×#938C2211yescharacteristic
31C2×#936C2211yescharacteristic
32C2×C4×#67C2212yes—
33C2×#926C2212yes—
34C2×#926C2212yes—
35#5557—28no—
36C2×#897C2211yescharacteristic
37C2×#890C2211yescharacteristic
38C2×#883C2212yes—
39C2×#879C2212yes—
40C2×C42×D3C2211yescharacteristic
41C2×C4×Dic6C2211yescharacteristic
42#5231C2214yes—
43#5230C2214yes—
44#5229C2214yes—
45#5229C2212yes—
46#5229C2212yes—
47#5229C2212yes—
48#5229C2211yescharacteristic
49#5229C2214yes—
50#5229C2212yes—
51#5221C2212yes—
52#5213C2214yes—
53#5212C2212yes—
54#5211C2214yes—
55#5211C2214yes—
56#5210C2214yes—
57#4990C2214yes—
58#4989C2212yes—
59#4987C2211yescharacteristic
60#4987C2212yes—
61#4987C2212yes—
62#4986C2214yes—
63#4985C2214yes—
64#4982C2214yes—
65#4981C2214yes—
66#4978C2212yes—
67#4977C2212yes—
68#4976C2214yes—
69Dic3×C4⋊C4C2212yes—
70#4973C2212yes—
71#4972C2212yes—
72#4972C2212yes—
73#4972C2211yescharacteristic
74#4972C2212yes—
75#4959C2214yes—
76#4952C2214yes—
77#4952C2214yes—
78#4952C2214yes—
79#4951C2214yes—
80C4×(C2×D3)⋊C4C2212yes—
81#4935C2211yescharacteristic
82C4×C4⋊Dic3C2211yescharacteristic
83C4×Dic3⋊C4C2212yes—
84#4929C2212yes—
85#4928C2212yes—
86C2×D4×Q8D311yescharacteristic, complemented
87C2×#529—31no—
88#2857—31no—
89#2689—34no—
90#2687—34no—
91#2625—32no—
92#2582—31no—
93#2568—31no—
94#2550—32no—
95#2492—32no—
96#2447—32no—
97#2420—32no—
98#2415—32no—
99#2409—32no—
100#2354—31no—
101#2310—32no—
102C4×C22⋊Q8—31no—
103C22×C3×Q8—28no—
104C22×C3×Q8—28no—
105C22×C3×Q8—44no—
106C22×C3×Q8C2312yes—
107C22×C3×Q8C2314yes—
108C22×C3×Q8C2311yescharacteristic
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4C2314yes—
111C23×C3×C4C2312yes—
112C22×#67C2312yes—
113C22×C4×D3C2311yescharacteristic
114C22×C4×D3C2311yescharacteristic
115C22×C4×D3C2311yescharacteristic
116C22×Dic6C2311yescharacteristic
117C3×C4⋊Q8—28no—
118C3×C4⋊Q8—24no—
119C3×C22⋊Q8—28no—
120C3×C22⋊Q8—216no—
121C3×C4×Q8—24no—
122C3×C4×D4—28no—
123C3×C4×D4D418yes—
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2314yes—
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4C2314yes—
131C2×C3×C22⋊C4C2312yes—
132C2×C3×C42C2312yes—
133C2×C3×C42C2311yescharacteristic
134C2×#217C2312yes—
135C2×#217C2312yes—
136C2×#217C2312yes—
137C2×#217C2314yes—
138C2×#217C2314yes—
139#946—24no—
140#946—44no—
141#938—24no—
142#936—24no—
143C4×#67—28no—
144C2×(C2×D3)⋊C4C2312yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2314yes—
148#926—28no—
149#926—44no—
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2312yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2312yes—
160C2×Dic3⋊C4C2312yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2314yes—
164C2×C4×Dic3C2311yescharacteristic
165C2×C4×Dic3C2312yes—
166C2×C4×Dic3C2312yes—
167C2×C4×Dic3C2311yescharacteristic
168C2×C4×Dic3C2311yescharacteristic
169C2×C4×Dic3C2314yes—
170#897—24no—
171#890—24no—
172#883—28no—
173#879—28no—
174C42×D3—24no—
175C4×Dic6—24no—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2312yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C23×Q8C2×D312yes—
192D4×Q8—28no—
193C2×C4⋊Q8C2×D311yescharacteristic
194C2×C4⋊Q8C2×D312yes—
195#529—68no—
196C2×#126—32no—
197C2×#125—31no—
198C2×#124—31no—
199C2×#123—32no—
200C2×C22⋊Q8—31no—
201C2×C22⋊Q8—32no—
202C2×C22⋊Q8—31no—
203C2×C22⋊Q8C2×D312yes—
204C2×C22⋊Q8C2×D314yes—
205C2×#121—31no—
206C2×C4×Q8—31no—
207C2×C4×Q8C2×D311yescharacteristic
208C2×C4×D4—32no—
209C2×C4×D4C2×D312yes—
210C2×C4×D4C2×D311yescharacteristic
211C2×#117—32no—
212C2×#117—32no—
213C22×C42—31no—
214#400—34no—
215#400—34no—
216#398—34no—
217#398—34no—
218#397—34no—
219#397—34no—
220#397—34no—
221#395—34no—
222#394—34no—
223#393—34no—
224#391—31no—
225#391—32no—
226#391—32no—
227#391—32no—
228#391—34no—
229#391—34no—
230#391—32no—
231#391—32no—
232#391—32no—
233#390—32no—
234#389—32no—
235#389—32no—
236#389—32no—
237#389—31no—
238#389—34no—
239#389—32no—
240#388—34no—
241#388—34no—
242#387—32no—
243#386—34no—
244#385—34no—
245#385—32no—
246#384—31no—
247#382—32no—
248#381—34no—
249#381—34no—
250#380—32no—
251#380—32no—
252#380—32no—
253#380—31no—
254C4×C4⋊C4—32no—
255C4×C4⋊C4—31no—
256C4×C4⋊C4—32no—
257C4×C22⋊C4—32no—
258C24×C3C2412yes—
259C23×D3C2411yescharacteristic
260C2×C3×Q8—22no—
261C2×C3×Q8—28no—
262C2×C3×Q8—24no—
263C2×C3×Q8—28no—
264C2×C3×Q8—24no—
265C2×C3×Q8—22no—
266C2×C3×Q8—24no—
267C2×C3×Q8—44no—
268C2×C3×Q8—432no—
269C2×C3×Q8#4114yes—
270C2×C3×D4—22no—
271C2×C3×D4—22no—
272C2×C3×D4C2×D414yes—
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4—28no—
276C22×C3×C4—28no—
277C22×C3×C4—44no—
278C22×C3×C4C2×D418yes—
279C22×C3×C4C2414yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2412yes—
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2412yes—
284C22×C3×C4C2411yescharacteristic
285C22×C3×C4C2411yescharacteristic
286C2×#67—24no—
287C2×#67—24no—
288C2×#67—42no—
289C22×Dic3C2412yes—
290C22×Dic3C2411yescharacteristic
291C22×Dic3C2412yes—
292C22×Dic3C2412yes—
293C22×Dic3C2411yescharacteristic
294C22×Dic3C2412yes—
295C22×Dic3C2414yes—
296C22×Dic3C2411yescharacteristic
297C2×C4×D3—22no—
298C2×C4×D3—22no—
299C2×C4×D3—22no—
300C2×C4×D3—22no—
301C2×C4×D3—22no—
302C2×C4×D3—22no—
303C2×C4×D3—22no—
304C2×C4×D3—22no—
305C2×C4×D3—41no—
306C2×Dic6—22no—
307C2×Dic6—22no—
308C2×Dic6—22no—
309C3×C4⋊C4—24no—
310C3×C4⋊C4—24no—
311C3×C4⋊C4—22no—
312C3×C4⋊C4—28no—
313C3×C4⋊C4—24no—
314C3×C4⋊C4C2×D414yes—
315C3×C22⋊C4—28no—
316C3×C22⋊C4C2×D418yes—
317C3×C42—24no—
318C3×C42C2×D414yes—
319#217—24no—
320#217—24no—
321#217—24no—
322#217—44no—
323#217—44no—
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—44no—
328C4⋊Dic3—22no—
329C4⋊Dic3—24no—
330C4⋊Dic3—24no—
331C4⋊Dic3—22no—
332C4⋊Dic3—22no—
333C4⋊Dic3—24no—
334C4⋊Dic3—24no—
335C4⋊Dic3—42no—
336Dic3⋊C4—24no—
337Dic3⋊C4—24no—
338Dic3⋊C4—24no—
339Dic3⋊C4—42no—
340Dic3⋊C4—44no—
341Dic3⋊C4—44no—
342C4×Dic3—24no—
343C4×Dic3—22no—
344C4×Dic3—22no—
345C4×Dic3—22no—
346C4×Dic3—24no—
347C4×Dic3—44no—
348C22×Q8—28no—
349C22×Q8—28no—
350C22×Q8—31no—
351C22×Q8—44no—
352C22×Q8C22×D312yes—
353C22×Q8C22×D314yes—
354C22×Q8C22×D311yescharacteristic
355C22×D4—32no—
356C22×D4C22×D311yescharacteristic
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4C22×D314yes—
361C23×C4C22×D312yes—
362C4⋊Q8—28no—
363C4⋊Q8—24no—
364#126—68no—
365#125—64no—
366#124—64no—
367#123—68no—
368C22⋊Q8—28no—
369C22⋊Q8—216no—
370C22⋊Q8—64no—
371C22⋊Q8—64no—
372C22⋊Q8—124no—
373#121—64no—
374C4×Q8—24no—
375C4×Q8—64no—
376C4×D4—28no—
377C4×D4—68no—
378C4×D4#6718yes—
379#117—68no—
380#117—124no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—32no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4C22×D312yes—
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D312yes—
398C2×C4⋊C4C22×D312yes—
399C2×C4⋊C4C22×D314yes—
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C22⋊C4—32no—
402C2×C22⋊C4—32no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4C22×D314yes—
411C2×C22⋊C4C22×D312yes—
412C2×C42—31no—
413C2×C42—32no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—32no—
417C2×C42—34no—
418C2×C42—64no—
419C2×C42C22×D312yes—
420C2×C42C22×D311yescharacteristic
421#95—32no—
422#95—32no—
423#95—32no—
424#95—34no—
425#95—32no—
426#95—32no—
427#95—34no—
428#95—34no—
429#95—34no—
430#95—34no—
431#95—34no—
432#95—34no—
433#95—34no—
434#95—34no—
435#95—34no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3C22×D414yes—
443C23×C3C2511yescharacteristic
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D32−1+412yes—
451C3×Q8—28no—
452C3×Q8—416no—
453C3×Q8—48no—
454C3×D4—28no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—216no—
462C2×C3×C4—22no—
463C2×C3×C4—24no—
464C2×C3×C4—24no—
465C2×C3×C4—24no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—416no—
469C2×C3×C4C22×D412yes—
470C2×C3×C4C22×D414yes—
471C2×C3×C4C22×D412yes—
472C2×C3×C4C22×D412yes—
473C2×C3×C4C2×#4114yes—
474C2×C3×C4C2×#4112yes—
475C2×C3×C4H(5,𝔽2)12yes—
476C2×C3×C42−1+412yes—
477C2×C3×C42−1+412yes—
478#67—48no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—21no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—24no—
488C2×Dic3—21no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—24no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—22no—
499C2×Dic3—21no—
500C2×Dic3—22no—
501C2×Dic3—24no—
502C2×Dic3—22no—
503C4×D3—44no—
504C4×D3—44no—
505C4×D3—44no—
506Dic6—44no—
507C24—31no—
508C24C23×D312yes—
509C2×Q8—28no—
510C2×Q8—24no—
511C2×Q8—22no—
512C2×Q8—24no—
513C2×Q8—22no—
514C2×Q8—28no—
515C2×Q8—24no—
516C2×Q8—44no—
517C2×Q8—432no—
518C2×Q8—62no—
519C2×Q8—62no—
520C2×Q8—62no—
521C2×Q8#23714yes—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—64no—
525C2×D4—64no—
526C2×D4—122no—
527C2×D4C2×#6714yes—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—32no—
533C22×C4—31no—
534C22×C4—32no—
535C22×C4—32no—
536C22×C4—31no—
537C22×C4—34no—
538C22×C4—32no—
539C22×C4—31no—
540C22×C4—44no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—121no—
550C22×C4C2×#6718yes—
551C22×C4C23×D314yes—
552C22×C4C23×D312yes—
553C22×C4C23×D312yes—
554C22×C4C23×D312yes—
555C22×C4C23×D311yescharacteristic
556C22×C4C23×D311yescharacteristic
557C22×C4C23×D311yescharacteristic
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—28no—
562C4⋊C4—24no—
563C4⋊C4—64no—
564C4⋊C4—62no—
565C4⋊C4—62no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—64no—
569C4⋊C4—64no—
570C4⋊C4—64no—
571C4⋊C4—62no—
572C4⋊C4—64no—
573C4⋊C4—124no—
574C4⋊C4—122no—
575C4⋊C4—124no—
576C4⋊C4—122no—
577C4⋊C4C2×#6714yes—
578C22⋊C4—28no—
579C22⋊C4—64no—
580C22⋊C4—64no—
581C22⋊C4—64no—
582C22⋊C4—64no—
583C22⋊C4—64no—
584C22⋊C4—64no—
585C22⋊C4—124no—
586C22⋊C4—124no—
587C22⋊C4—124no—
588C22⋊C4C2×#6718yes—
589C42—24no—
590C42—64no—
591C42—62no—
592C42—62no—
593C42—62no—
594C42—64no—
595C42—124no—
596C42C2×#6714yes—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—42no—
604C22×C3C23×D411yescharacteristic
605C22×C3C22×#4111yescharacteristic
606C22×C3C2×H(5,𝔽2)11yescharacteristic
607C22×C3C2×2−1+411yescharacteristic
608C22×C3C2×2−1+411yescharacteristic
609C22×C3C2×2−1+411yescharacteristic
610C22×C3#58511yescharacteristic
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—22no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C3×C4—24no—
619C3×C4—24no—
620C3×C4—22no—
621C3×C4—44no—
622C3×C4—42no—
623C3×C4#53614yes—
624C3×C4#54614yes—
625Dic3—42no—
626Dic3—41no—
627Dic3—41no—
628Dic3—41no—
629Dic3—42no—
630Dic3—42no—
631Dic3—42no—
632Dic3—44no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—32no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23C22×#6714yes—
647C23C24×D311yescharacteristic
648Q8—28no—
649Q8—416no—
650Q8—48no—
651Q8—124no—
652D4—28no—
653D4—128no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—216no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—416no—
668C2×C4—62no—
669C2×C4—61no—
670C2×C4—62no—
671C2×C4—64no—
672C2×C4—61no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—64no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—61no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—64no—
685C2×C4—61no—
686C2×C4—62no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—124no—
693C2×C4—124no—
694C2×C4—124no—
695C2×C4C2×#23714yes—
696C2×C4C2×#23712yes—
697C2×C4#100412yes—
698C2×C4#100712yes—
699C2×C4#100712yes—
700C2×C4C22×#6712yes—
701C2×C4C22×#6714yes—
702C2×C4C22×#6712yes—
703C2×C4C22×#6712yes—
704C2×C3—44no—
705C2×C3C2×#53611yescharacteristic
706C2×C3C2×#54611yescharacteristic
707C2×C3#348911yescharacteristic
708C2×C3#351811yescharacteristic
709C2×C3#352311yescharacteristic
710C2×C3#355211yescharacteristic
711C2×C3#355411yescharacteristic
712D3—42no—
713C22—24no—
714C22—24no—
715C22—24no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—62no—
721C22—62no—
722C22—62no—
723C22—121no—
724C22—121no—
725C22—121no—
726C22—121no—
727C22C22×#23711yescharacteristic
728C22C2×#100411yescharacteristic
729C22C2×#100711yescharacteristic
730C22C2×#100711yescharacteristic
731C22D3×2−1+411yescharacteristic
732C22#596811yescharacteristic
733C22C23×#6711yescharacteristic
734C4—24no—
735C4—24no—
736C4—22no—
737C4—44no—
738C4—42no—
739C4—121no—
740C4—121no—
741C4—122no—
742C4—122no—
743C4—122no—
744C4—124no—
745C4—121no—
746C4—122no—
747C4#580614yes—
748C4#581614yes—
749C3#3891111yescharacteristic, complemented, Sylow
750C2—44no—
751C2—122no—
752C2#8675011yescharacteristic
753C2#8675311yescharacteristic
754C2#8676411yescharacteristic
755C2#8676511yescharacteristic
756C2C2×#580611yescharacteristic
757C2C2×#581611yescharacteristic
758C2#8729511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×D4×Q8C2
prime radicalC2×#938C22
hypercenterC2×D4×Q8D3
hypocenterC3#38911
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×Q8C2semidirect
3. #84068C2semidirect
4. #84062C2semidirect
5. #83269C2semidirect
6. #83258C2semidirect
7. #83244C2semidirect
8. #83241C2semidirect
9. #82814C2semidirect
10. #82795C2semidirect
11. #82794C2semidirect
12. #82787C2semidirect
13. C4×#946C2semidirect
14. #82482C2semidirect
16. #82359C2semidirect
17. #82337C2semidirect
86. C2×D4×Q8D3semidirect
749. C3#38911semidirect

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×#55572
#840682
#840622
#832692
#832582
#832442
#832412
#828142
#827952
#827942
#827872
C4×#9462
#824822
#824052
#823592
#823372
#389113