Finite Group Databasebeta

← #11069677

Subgroups — #11069677

Order 768.

2306 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5733C212yesmaximal, complemented
2C3×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
3#82500C212yesmaximal, complemented
4#82476C212yesmaximal, complemented
5#76571C214yesmaximal, complemented
6#76219C212yesmaximal, complemented
7#76218C212yesmaximal, complemented
8#76113C214yesmaximal, complemented
9#74370C212yesmaximal, complemented
10#73800C211yesmaximal, characteristic, complemented
11#73799C211yesmaximal, characteristic
12#73780C212yesmaximal, complemented
13#73692C212yesmaximal, complemented
14#73653C211yesmaximal, characteristic, complemented
15#73650C211yesmaximal, characteristic, complemented
16#73313C211yesmaximal, characteristic, complemented
17#73299C211yesmaximal, characteristic, complemented
18#39387—31nomaximal, Sylow
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×C4×Q8C2212yes—
21C2×#947C2214yes—
22C2×#946C2214yes—
23#5733—216no—
24C2×#898C2214yes—
25C2×#897C2212yes—
26C2×#897C2212yes—
27C2×#895C2212yes—
28C2×#895C2212yes—
29C2×#894C2214yes—
30C2×#893C2212yes—
31C2×#887C2212yes—
32C2×#875C2212yes—
33C2×#875C2212yes—
34C2×#874C2211yescharacteristic
35C2×#874C2212yes—
36C2×C4×D12C2211yescharacteristic
37C2×C4×D12C2212yes—
38C2×#872C2212yes—
39C2×#869C2211yescharacteristic
40C3×#391C2212yes—
41C3×#389C2212yes—
42C3×#389C2211yescharacteristic
43C3×#389C2211yescharacteristic
44C3×#384C2211yescharacteristic
45C3×C4×C4⋊C4C2212yes—
46C3×C4×C4⋊C4C2211yescharacteristic
47C3×C4×C4⋊C4C2211yescharacteristic
48C3×C43C2211yescharacteristic
49#4994C2214yes—
50#4994C2214yes—
51#4994C2214yes—
52#4991C2214yes—
53#4991C2214yes—
54#4991C2214yes—
55#4988C2214yes—
56#4988C2212yes—
57#4987C2214yes—
58#4973C2212yes—
59#4940C2212yes—
60#4940C2212yes—
61#4939C2212yes—
62#4939C2211yescharacteristic
63#4939C2212yes—
64#4939C2212yes—
65#4939C2212yes—
66#4939C2211yescharacteristic
67#4939C2212yes—
68#4939C2212yes—
69#4939C2212yes—
70C4×(C2×D3)⋊C4C2212yes—
71#4935C2212yes—
72C4×C4⋊Dic3C2212yes—
73C4×C4⋊Dic3C2211yescharacteristic
74#4928C2212yes—
75#4928C2211yescharacteristic
76#4928C2211yescharacteristic
77#4677C2214yes—
78#4674C2214yes—
79#4672C2214yes—
80#4671C2214yes—
81#4670C2214yes—
82#4665C2214yes—
83#4665C2214yes—
84#4653C2214yes—
85C2×#542—32no—
86#2858—31no—
87#2730—34no—
88#2705—34no—
89#2620—32no—
90#2548—32no—
91#2542—31no—
92#2541—31no—
93#2538—32no—
94#2512—32no—
95#2445—32no—
96#2427—32no—
97#2426—32no—
98#2366—31no—
99#2365—31no—
100C4×C4⋊Q8D311yescharacteristic, complemented
101#2293—31no—
102C22×C3×Q8C2312yes—
103C22×D12C2311yescharacteristic
104C22×D12C2312yes—
105C22×D12C2312yes—
106C22×D12C2312yes—
107C22×D12C2314yes—
108C22×D12C2314yes—
109C22×C4×D3C2312yes—
110C22×C4×D3C2314yes—
111C22×Dic6C2312yes—
112C3×C4⋊Q8D418yescomplemented
113C3×C4×Q8—44no—
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2312yes—
117C2×C3×C4⋊C4C2312yes—
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C42C2312yes—
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C2×C3×C42C2312yes—
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2311yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C2×C3×C42C2311yescharacteristic
132#947—216no—
133#946—216no—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2312yes—
138C2×(C2×D3)⋊C4C2314yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2312yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2314yes—
156C2×C4⋊Dic3C2314yes—
157C2×Dic3⋊C4C2314yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2312yes—
160C2×C4×Dic3C2314yes—
161C2×C4×Dic3C2312yes—
162#898—216no—
163#897—28no—
164#897—44no—
165#895—28no—
166#895—44no—
167#894—216no—
168#893—28no—
169#887—28no—
170#875—28no—
171#875—44no—
172#874—24no—
173#874—44no—
174C4×D12—24no—
175C4×D12—44no—
176#872—28no—
177#869—24no—
178C3×#95C2312yes—
179C3×#95C2312yes—
180C3×#95C2312yes—
181C3×#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187#542—616no—
188C2×C4⋊Q8—31no—
189C2×C4⋊Q8C2×D311yescharacteristic
190C2×#127—31no—
191C2×#127—32no—
192C2×#126—34no—
193C2×#124—34no—
194C2×#124—32no—
195C2×#124—32no—
196C2×#123—34no—
197C2×C22⋊Q8—34no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×#121—32no—
201C2×#121—32no—
202C2×C4×Q8—32no—
203C2×C4×Q8C2×D312yes—
204C2×C4×D4—32no—
205C2×C4×D4—31no—
206C2×C4×D4—32no—
207C2×#117—32no—
208#399—34no—
209#397—34no—
210#396—34no—
211#396—34no—
212#396—34no—
213#394—34no—
214#394—34no—
215#394—34no—
216#394—34no—
217#392—34no—
218#391—32no—
219#391C2×D312yes—
220#390—32no—
221#390—34no—
222#390—32no—
223#390—32no—
224#390—32no—
225#390—32no—
226#390—32no—
227#390—31no—
228#390—32no—
229#390—32no—
230#390—31no—
231#389—32no—
232#389—31no—
233#389—31no—
234#389C2×D311yescharacteristic
235#389C2×D311yescharacteristic
236#389C2×D312yes—
237#388—32no—
238#388—32no—
239#388—34no—
240#387—34no—
241#386—34no—
242#386—34no—
243#384—32no—
244#384C2×D311yescharacteristic
245#380—34no—
246C4×C4⋊C4—31no—
247C4×C4⋊C4—32no—
248C4×C4⋊C4C2×D311yescharacteristic
249C4×C4⋊C4C2×D311yescharacteristic
250C4×C4⋊C4C2×D312yes—
251C4×C22⋊C4—32no—
252C43C2×D311yescharacteristic
253C23×D3C2412yes—
254C23×D3C2414yes—
255C2×C3×Q8—42no—
256C2×C3×Q8—42no—
257C2×C3×Q8C2×D418yes—
258C22×C3×C4C2412yes—
259C22×C3×C4C2411yescharacteristic
260C22×C3×C4C2411yescharacteristic
261C22×C3×C4C2412yes—
262C22×C3×C4C2412yes—
263C22×C3×C4C2412yes—
264C22×C3×C4C2411yescharacteristic
265C22×C3×C4C2411yescharacteristic
266C22×C3×C4C2411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C22×Dic3C2412yes—
270C22×Dic3C2412yes—
271C22×Dic3C2414yes—
272C22×Dic3C2412yes—
273C2×D12—24no—
274C2×D12—22no—
275C2×D12—24no—
276C2×D12—24no—
277C2×D12—24no—
278C2×D12—22no—
279C2×D12—24no—
280C2×D12—22no—
281C2×D12—24no—
282C2×D12—28no—
283C2×D12—24no—
284C2×D12—44no—
285C2×D12—44no—
286C2×D12—44no—
287C2×D12—42no—
288C2×D12—42no—
289C2×D12—44no—
290C2×D12—44no—
291C2×C4×D3—24no—
292C2×C4×D3—24no—
293C2×C4×D3—24no—
294C2×C4×D3—28no—
295C2×C4×D3—44no—
296C2×C4×D3—44no—
297C2×Dic6—24no—
298C2×Dic6—24no—
299C2×Dic6—24no—
300C3×C4⋊C4—22no—
301C3×C4⋊C4—22no—
302C3×C4⋊C4—42no—
303C3×C4⋊C4—42no—
304C3×C4⋊C4—42no—
305C3×C4⋊C4—42no—
306C3×C4⋊C4C2×D414yes—
307C3×C4⋊C4C2×D414yes—
308C3×C4⋊C4C2×D418yes—
309C3×C42—24no—
310C3×C42—24no—
311C3×C42—22no—
312C3×C42—22no—
313C3×C42—22no—
314C3×C42—41no—
315C3×C42—41no—
316C3×C42C2×D414yes—
317C3×C42#4114yes—
318(C2×D3)⋊C4—24no—
319(C2×D3)⋊C4—24no—
320(C2×D3)⋊C4—28no—
321(C2×D3)⋊C4—28no—
322(C2×D3)⋊C4—28no—
323(C2×D3)⋊C4—28no—
324(C2×D3)⋊C4—28no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—44no—
327(C2×D3)⋊C4—44no—
328(C2×D3)⋊C4—44no—
329(C2×D3)⋊C4—44no—
330(C2×D3)⋊C4—44no—
331(C2×D3)⋊C4—42no—
332(C2×D3)⋊C4—44no—
333(C2×D3)⋊C4—42no—
334C4⋊Dic3—28no—
335C4⋊Dic3—24no—
336C4⋊Dic3—24no—
337C4⋊Dic3—22no—
338C4⋊Dic3—22no—
339C4⋊Dic3—22no—
340C4⋊Dic3—44no—
341Dic3⋊C4—24no—
342Dic3⋊C4—24no—
343Dic3⋊C4—28no—
344C4×Dic3—24no—
345C4×Dic3—28no—
346C22×Q8—32no—
347C22×Q8C22×D312yes—
348C22×D4—32no—
349C22×D4—32no—
350C22×D4—31no—
351C22×D4—34no—
352C22×D4—32no—
353C22×D4—34no—
354C23×C4—32no—
355C23×C4—34no—
356C4⋊Q8—64no—
357C4⋊Q8D1218yescomplemented
358#127—64no—
359#127—124no—
360#126—616no—
361#124—616no—
362#124—68no—
363#124—124no—
364#123—616no—
365C22⋊Q8—616no—
366C22⋊Q8—68no—
367C22⋊Q8—124no—
368#121—68no—
369#121—124no—
370C4×Q8—44no—
371C4×Q8—68no—
372C4×D4—68no—
373C4×D4—64no—
374C4×D4—124no—
375#117—68no—
376C2×C4⋊C4—32no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—34no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4C22×D311yescharacteristic
387C2×C4⋊C4C22×D311yescharacteristic
388C2×C4⋊C4C22×D312yes—
389C2×C4⋊C4C22×D312yes—
390C2×C4⋊C4C22×D312yes—
391C2×C4⋊C4C22×D312yes—
392C2×C4⋊C4C22×D311yescharacteristic
393C2×C4⋊C4C22×D311yescharacteristic
394C2×C4⋊C4C22×D312yes—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—32no—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—34no—
411C2×C42—32no—
412C2×C42—34no—
413C2×C42C22×D312yes—
414C2×C42C22×D311yescharacteristic
415C2×C42C22×D312yes—
416C2×C42C22×D311yescharacteristic
417C2×C42C22×D311yescharacteristic
418C2×C42C22×D311yescharacteristic
419C2×C42C22×D311yescharacteristic
420C2×C42C22×D311yescharacteristic
421C2×C42C22×D311yescharacteristic
422#95—32no—
423#95—32no—
424#95—32no—
425#95—34no—
426#95—34no—
427#95C22×D312yes—
428#95C22×D312yes—
429#95C22×D312yes—
430#95C22×D312yes—
431C23×C3C2511yescharacteristic
432C22×D3—22no—
433C22×D3—24no—
434C22×D3—22no—
435C22×D3—24no—
436C22×D3—24no—
437C22×D3—22no—
438C22×D3—24no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—24no—
442C22×D3—22no—
443C22×D3—24no—
444C22×D3—22no—
445C22×D3—24no—
446C3×Q8—48no—
447C2×C3×C4—21no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4C22×D414yes—
470C2×C3×C4C22×D412yes—
471C2×C3×C4C22×D412yes—
472C2×C3×C4C22×D414yes—
473C2×C3×C4C22×D412yes—
474C2×C3×C4C2×#4112yes—
475C2×C3×C4C2×#4112yes—
476C2×C3×C4C2×#4112yes—
477C2×C3×C4H(5,𝔽2)12yes—
478C2×C3×C4H(5,𝔽2)12yes—
479C2×C3×C42−1+412yes—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—24no—
483C2×Dic3—22no—
484C2×Dic3—24no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—24no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492D12—44no—
493D12—48no—
494D12—48no—
495D12—88no—
496D12—84no—
497D12—88no—
498C4×D3—48no—
499C4×D3—88no—
500Dic6—48no—
501C24—34no—
502C24—32no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—64no—
506C2×Q8—64no—
507C2×Q8—64no—
508C2×Q8C2×D1218yes—
509C2×D4—64no—
510C2×D4—68no—
511C2×D4—64no—
512C2×D4—62no—
513C2×D4—62no—
514C2×D4—64no—
515C2×D4—64no—
516C2×D4—64no—
517C2×D4—64no—
518C2×D4—62no—
519C2×D4—64no—
520C2×D4—124no—
521C2×D4—124no—
522C2×D4—124no—
523C2×D4—122no—
524C2×D4—122no—
525C2×D4—124no—
526C2×D4—124no—
527C22×C4—32no—
528C22×C4—32no—
529C22×C4—34no—
530C22×C4—32no—
531C22×C4—64no—
532C22×C4—64no—
533C22×C4—64no—
534C22×C4—68no—
535C22×C4—124no—
536C22×C4—124no—
537C22×C4C23×D312yes—
538C22×C4C23×D311yescharacteristic
539C22×C4C23×D311yescharacteristic
540C22×C4C23×D312yes—
541C22×C4C23×D312yes—
542C22×C4C23×D312yes—
543C22×C4C23×D311yescharacteristic
544C22×C4C23×D311yescharacteristic
545C22×C4C23×D311yescharacteristic
546C22×C4C23×D311yescharacteristic
547C22×C4C23×D311yescharacteristic
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—64no—
555C4⋊C4—64no—
556C4⋊C4—68no—
557C4⋊C4—68no—
558C4⋊C4—62no—
559C4⋊C4—62no—
560C4⋊C4—64no—
561C4⋊C4—64no—
562C4⋊C4—62no—
563C4⋊C4—124no—
564C4⋊C4C2×D1214yes—
565C4⋊C4C2×D1214yes—
566C4⋊C4C2×D1218yes—
567C22⋊C4—64no—
568C22⋊C4—64no—
569C22⋊C4—68no—
570C22⋊C4—68no—
571C22⋊C4—68no—
572C22⋊C4—68no—
573C22⋊C4—68no—
574C22⋊C4—64no—
575C22⋊C4—124no—
576C22⋊C4—124no—
577C22⋊C4—124no—
578C22⋊C4—124no—
579C22⋊C4—124no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—124no—
583C42—24no—
584C42—22no—
585C42—24no—
586C42—22no—
587C42—22no—
588C42—41no—
589C42—41no—
590C42—64no—
591C42—68no—
592C42C2×D1214yes—
593C42#23914yes—
594C22×C3C23×D411yescharacteristic
595C22×C3C22×#4111yescharacteristic
596C22×C3C2×H(5,𝔽2)11yescharacteristic
597C22×C3C2×H(5,𝔽2)11yescharacteristic
598C22×C3C2×2−1+411yescharacteristic
599C22×C3#58511yescharacteristic
600C22×C3#58511yescharacteristic
601C2×D3—42no—
602C2×D3—44no—
603C2×D3—42no—
604C2×D3—44no—
605C2×D3—44no—
606C2×D3—42no—
607C2×D3—42no—
608C2×D3—44no—
609C2×D3—44no—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—44no—
613C2×D3—44no—
614C2×D3—42no—
615C3×C4—24no—
616C3×C4—24no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4#54214yescomplemented
625C3×C4#55014yes—
626Dic3—44no—
627Dic3—42no—
628Dic3—42no—
629Dic3—42no—
630C23—64no—
631C23—62no—
632C23—64no—
633C23—62no—
634C23—62no—
635C23—64no—
636C23—64no—
637C23—62no—
638C23—64no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—64no—
643C23—64no—
644C23C24×D311yescharacteristic
645Q8—48no—
646Q8—128no—
647D4—128no—
648D4—124no—
649D4—128no—
650D4—248no—
651D4—244no—
652D4—248no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—62no—
676C2×C4—64no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—64no—
682C2×C4—62no—
683C2×C4—64no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—128no—
688C2×C4—248no—
689C2×C4C22×D1214yes—
690C2×C4C22×D1212yes—
691C2×C4C22×D1212yes—
692C2×C4C22×D1214yes—
693C2×C4C22×D1212yes—
694C2×C4#100412yes—
695C2×C4C2×#23912yes—
696C2×C4C2×#23912yes—
697C2×C4C2×#23912yes—
698C2×C4#100712yes—
699C2×C4#100912yes—
700C2×C3C2×#54211yescharacteristic
701C2×C3C2×#55011yescharacteristic
702C2×C3#349611yescharacteristic
703C2×C3#349711yescharacteristic
704C2×C3#351011yescharacteristic
705C2×C3#354611yescharacteristic
706C2×C3#355411yescharacteristic
707D3—82no—
708D3—84no—
709C22—124no—
710C22—122no—
711C22—124no—
712C22—122no—
713C22—122no—
714C22—124no—
715C22—124no—
716C22—122no—
717C22—124no—
718C22—122no—
719C22—122no—
720C22—124no—
721C22—124no—
722C22—122no—
723C22C23×D1211yescharacteristic
724C22C2×#100411yescharacteristic
725C22C22×#23911yescharacteristic
726C22C2×#100711yescharacteristic
727C22C2×#100911yescharacteristic
728C22#596411yescharacteristic
729C22#596411yescharacteristic
730C4—24no—
731C4—24no—
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—42no—
737C4—42no—
738C4—41no—
739C4—122no—
740C4—122no—
741C4—124no—
742C4—122no—
743C4#557714yes—
744C4#573314yescomplemented
745C3#3938711yescharacteristic, complemented, Sylow
746C2—244no—
747C2—242no—
748C2#8578611yescharacteristic
749C2C2×#557711yescharacteristic
750C2#8581811yescharacteristic
751C2C2×#573311yescharacteristic
752C2#8624911yescharacteristic
753C2#8626311yescharacteristic
754C2#8628911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×C4⋊Q8C2
prime radical#73799C2
hypercenterC4×C4⋊Q8D3
hypocenterC3#39387
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#5733C2semidirect
2. C3×C4×C4⋊Q8C2semidirect
3. #82500C2semidirect
4. #82476C2semidirect
5. #76571C2semidirect
6. #76219C2semidirect
7. #76218C2semidirect
8. #76113C2semidirect
9. #74370C2semidirect
10. #73800C2semidirect
12. #73780C2semidirect
13. #73692C2semidirect
14. #73653C2semidirect
15. #73650C2semidirect
16. #73313C2semidirect
17. #73299C2semidirect
100. C4×C4⋊Q8D3semidirect
112. C3×C4⋊Q8D4semidirect
357. C4⋊Q8D12semidirect
624. C3×C4#542semidirect
744. C4#5733semidirect
745. C3#39387semidirect

Maximal subgroups

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

subgroupindex
C2×#57332
C3×C4×C4⋊Q82
#825002
#824762
#765712
#762192
#762182
#761132
#743702
#738002
#737992
#737802
#736922
#736532
#736502
#733132
#732992
#393873