Finite Group Databasebeta

← #10811368

Subgroups — #10811368

Order 768.

1132 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5565C211yesmaximal, characteristic
2C3×D4×M16C211yesmaximal, characteristic, complemented
3D4×#208C211yesmaximal, characteristic, complemented
4#72002C211yesmaximal, characteristic, complemented
5#72002C211yesmaximal, characteristic, complemented
6#71987C211yesmaximal, characteristic, complemented
7C2×#4554C211yesmaximal, characteristic, complemented
8#70527C211yesmaximal, characteristic, complemented
9#70525C211yesmaximal, characteristic, complemented
10#69985C211yesmaximal, characteristic, complemented
11#69985C211yesmaximal, characteristic, complemented
12#69974C211yesmaximal, characteristic, complemented
13#69973C211yesmaximal, characteristic, complemented
14#69880C211yesmaximal, characteristic, complemented
15C4×#823C211yesmaximal, characteristic, complemented
16#22482—31nomaximal, Sylow
17C22×C3×M16C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#939C412yes—
21C2×#930C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#926C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×#208C2211yescharacteristic
26C22×#208C2211yescharacteristic
27#5565—21no—
28#5565—21no—
29#5565—21no—
30#5565—21no—
31#5565—21no—
32#5565—21no—
33#5565—21no—
34#5565—21no—
35C2×#898C412yes—
36C2×#883C412yes—
37C2×#67⋊C4C412yes—
38C2×C4×D12C2211yescharacteristic
39C2×#870C2211yescharacteristic
40C3×#436—21no—
41C3×#435—21no—
42C3×#435—21no—
43C3×C8×D4—21no—
44C3×#423C2211yescharacteristic
45C3×#407C2211yescharacteristic
46C3×#407C2211yescharacteristic
47C3×C4×M16C2211yescharacteristic
48#5207C2211yescharacteristic
49#5207C2211yescharacteristic
50C2×#823C2211yescharacteristic
51C2×#823C2211yescharacteristic
52C2×#823C2211yescharacteristic
53C2×#823C2211yescharacteristic
54#5012—21no—
55#5011—21no—
56#5011—21no—
57D4×C3⋊C8—21no—
58#4924C2211yescharacteristic
59C4×#208C2211yescharacteristic
60#4554C2211yescharacteristic
61#4554C2211yescharacteristic
62#4554C2211yescharacteristic
63#4554C2211yescharacteristic
64#4554C2211yescharacteristic
65#4554C2211yescharacteristic
66#4554C2211yescharacteristic
67#4554C2211yescharacteristic
68#4554C2211yescharacteristic
69#4554C2211yescharacteristic
70#4554C2211yescharacteristic
71#4554C2211yescharacteristic
72C2×#553—31no—
73D4×M16—31no—
74D4×M16D311yescharacteristic, complemented
75#1998—31no—
76#1998—31no—
77#1900—31no—
78#1900—31no—
79#1900—31no—
80#1900—31no—
81#1822—31no—
82#1821—31no—
83#1800—31no—
84C4×#100—31no—
85#1742—31no—
86C2×#343—31no—
87C22×C3×D4C2×C411yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C22×#67C2×C412yes—
91C22×#67C2×C412yes—
92C23×Dic3C2×C412yes—
93C22×D12C2311yescharacteristic
94C22×C4×D3C2×C412yes—
95C2×C3×M16—21no—
96C2×C3×M16—21no—
97C2×C3×M16—22no—
98C2×C3×M16—22no—
99C2×C3×M16—41no—
100C2×C3×M16—41no—
101C2×C3×M16C2311yescharacteristic
102C2×C3×M16C2311yescharacteristic
103C2×C3×M16C2311yescharacteristic
104C2×C3×M16C2311yescharacteristic
105C22×C3×C8—21no—
106C22×C3×C8—21no—
107C3×C4×D4D411yescharacteristic
108C3×C4×D4D411yescharacteristic
109C3×C4×D4D411yescharacteristic
110C3×C4×D4D411yescharacteristic
111C3×C4×D4D411yescharacteristic
112C3×C4×D4D411yescharacteristic
113C3×C4×D4D411yescharacteristic
114C3×C4×D4D411yescharacteristic
115C2×C3×C4⋊C4C2×C411yescharacteristic
116C2×C3×C22⋊C4C2×C411yescharacteristic
117C2×C3×C22⋊C4C2×C411yescharacteristic
118C2×C3×C42C2311yescharacteristic
119C2×#217C2×C412yes—
120#939—22no—
121#939—22no—
122#939—22no—
123#939—22no—
124#930—21no—
125#930—21no—
126#930—21no—
127#930—21no—
128#930—21no—
129#930—21no—
130#930—21no—
131#930—21no—
132C2×(C2×D3)⋊C4C2×C412yes—
133C2×(C2×D3)⋊C4C2×C412yes—
134C2×(C2×D3)⋊C4C2×C412yes—
135#926—21no—
136#926—21no—
137#926—21no—
138#926—21no—
139C2×C4⋊Dic3—21no—
140C2×C4⋊Dic3—21no—
141C2×C4⋊Dic3—21no—
142C2×C4⋊Dic3—21no—
143C2×C4⋊Dic3C2×C412yes—
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147C2×Dic3⋊C4C2×C412yes—
148C2×Dic3⋊C4C2×C412yes—
149C2×C4×Dic3C2×C412yes—
150C2×#208—21no—
151C2×#208—21no—
152C2×#208—22no—
153C2×#208—22no—
154C2×#208—41no—
155C2×#208—41no—
156C2×#208C2311yescharacteristic
157C2×#208C2311yescharacteristic
158C2×#208C2311yescharacteristic
159C2×#208C2311yescharacteristic
160C22×C3⋊C8—21no—
161C22×C3⋊C8—21no—
162#898—22no—
163#898—22no—
164#898—22no—
165#898—22no—
166#883—22no—
167#883—22no—
168#883—22no—
169#883—22no—
170#67⋊C4—22no—
171#67⋊C4—22no—
172#67⋊C4—22no—
173#67⋊C4—22no—
174C4×D12—21no—
175C4×D12—21no—
176C4×D12—21no—
177C4×D12—21no—
178#870—21no—
179#870—21no—
180#870—21no—
181#870—21no—
182C3×C4⋊C8—21no—
183C3×C4⋊C8—21no—
184C3×C22⋊C8—21no—
185C3×C22⋊C8—21no—
186C3×C22⋊C8—21no—
187C3×C22⋊C8—21no—
188C3×#97—21no—
189C3×C4×C8—21no—
190#830—21no—
191#830—21no—
192#830—21no—
193#830—21no—
194#823—22no—
195#823—22no—
196#823—41no—
197#823—41no—
198C4⋊(C3⋊C8)—21no—
199C4⋊(C3⋊C8)—21no—
200#803—21no—
201C4×C3⋊C8—21no—
202C22×M16—31no—
203C22×M16—31no—
204C22×M16C2×D311yescharacteristic
205C22×M16C2×D311yescharacteristic
206#553—61no—
207#553—61no—
208#553—61no—
209#553—61no—
210#553—61no—
211#553—61no—
212#553—61no—
213#553—61no—
214C2×#126—32no—
215C2×#125—31no—
216C2×#123—32no—
217C2×#121—32no—
218C2×#121—31no—
219C2×#121—31no—
220C2×C4×D4—32no—
221C2×C4×D4—31no—
222C2×C4×D4C2×D311yescharacteristic
223C2×#117—31no—
224C22×C4⋊C4—31no—
225#436—21no—
226#436—61no—
227#435—21no—
228#435—21no—
229#435—61no—
230#435—61no—
231C8×D4—21no—
232C8×D4—61no—
233#423—31no—
234#423C2×D311yescharacteristic
235C2×#100—31no—
236C2×#100—31no—
237C2×#100—31no—
238C2×#100—31no—
239#407—31no—
240#407—31no—
241#407C2×D311yescharacteristic
242#407C2×D311yescharacteristic
243C4×M16—31no—
244C4×M16C2×D311yescharacteristic
245#343—31no—
246#343—31no—
247#343—31no—
248#343—31no—
249#343—31no—
250#343—31no—
251#343—31no—
252#343—31no—
253#343—31no—
254#343—31no—
255#343—31no—
256#343—31no—
257C24×C3C22×C411yescharacteristic
258C24×C3C22×C411yescharacteristic
259C23×D3C22×C412yes—
260C2×C3×D4—42no—
261C2×C3×D4C22⋊C411yescharacteristic
262C2×C3×D4C22⋊C411yescharacteristic
263C2×C3×D4C22⋊C411yescharacteristic
264C2×C3×D4C22⋊C411yescharacteristic
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4C22×C411yescharacteristic
274C22×C3×C4C22×C411yescharacteristic
275C22×C3×C4C22×C411yescharacteristic
276C22×C3×C4C22×C411yescharacteristic
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2×D411yescharacteristic
285C22×C3×C4C2411yescharacteristic
286C2×#67—22no—
287C2×#67—22no—
288C2×#67—22no—
289C2×#67—22no—
290C2×#67—44no—
291C2×#67—82no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—82no—
295C22×Dic3C22×C412yes—
296C22×Dic3C22×C412yes—
297C22×Dic3C22×C412yes—
298C2×D12—21no—
299C2×D12—21no—
300C2×D12—21no—
301C2×D12—21no—
302C2×D12—21no—
303C2×D12—21no—
304C2×C4×D3—22no—
305C2×C4×D3—22no—
306C2×C4×D3—82no—
307C3×M16—21no—
308C3×M16—21no—
309C3×M16—21no—
310C3×M16—21no—
311C3×M16—21no—
312C3×M16—21no—
313C3×M16—21no—
314C3×M16—42no—
315C3×M16—42no—
316C3×M16#4112yes—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—42no—
322C2×C3×C8—42no—
323C3×C4⋊C4C22⋊C411yescharacteristic
324C3×C4⋊C4C22⋊C411yescharacteristic
325C3×C4⋊C4C22⋊C411yescharacteristic
326C3×C4⋊C4C22⋊C411yescharacteristic
327C3×C22⋊C4C22⋊C411yescharacteristic
328C3×C22⋊C4C22⋊C411yescharacteristic
329C3×C22⋊C4C22⋊C411yescharacteristic
330C3×C22⋊C4C22⋊C411yescharacteristic
331C3×C22⋊C4C22⋊C411yescharacteristic
332C3×C22⋊C4C22⋊C411yescharacteristic
333C3×C22⋊C4C22⋊C411yescharacteristic
334C3×C22⋊C4C22⋊C411yescharacteristic
335C3×C42C2×D411yescharacteristic
336C3×C42C2×D411yescharacteristic
337C3×C42C2×D411yescharacteristic
338C3×C42C2×D411yescharacteristic
339#217—22no—
340#217—22no—
341(C2×D3)⋊C4—22no—
342(C2×D3)⋊C4—22no—
343(C2×D3)⋊C4—22no—
344(C2×D3)⋊C4—22no—
345(C2×D3)⋊C4—22no—
346(C2×D3)⋊C4—22no—
347C4⋊Dic3—22no—
348C4⋊Dic3—22no—
349C4⋊Dic3—21no—
350C4⋊Dic3—21no—
351C4⋊Dic3—21no—
352C4⋊Dic3—21no—
353C4⋊Dic3—21no—
354C4⋊Dic3—21no—
355Dic3⋊C4—22no—
356Dic3⋊C4—22no—
357Dic3⋊C4—22no—
358Dic3⋊C4—22no—
359C4×Dic3—22no—
360C4×Dic3—22no—
361#208—21no—
362#208—21no—
363#208—21no—
364#208—21no—
365#208—21no—
366#208—21no—
367#208—21no—
368#208—42no—
369#208—42no—
370#208#4112yes—
371C2×C3⋊C8—21no—
372C2×C3⋊C8—21no—
373C2×C3⋊C8—21no—
374C2×C3⋊C8—21no—
375C2×C3⋊C8—42no—
376C2×C3⋊C8—42no—
377C22×D4—32no—
378C22×D4—32no—
379C22×D4—31no—
380C22×D4C4×D311yescharacteristic
381C23×C4—32no—
382C23×C4—32no—
383C23×C4C22×D311yescharacteristic
384C23×C4C22×D311yescharacteristic
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—22no—
388C2×M16—22no—
389C2×M16—31no—
390C2×M16—31no—
391C2×M16—31no—
392C2×M16—31no—
393C2×M16—41no—
394C2×M16—41no—
395C2×M16—61no—
396C2×M16—61no—
397C2×M16—62no—
398C2×M16—62no—
399C2×M16—121no—
400C2×M16—121no—
401C2×M16C22×D311yescharacteristic
402C2×M16C22×D311yescharacteristic
403C2×M16C22×D311yescharacteristic
404C2×M16C22×D311yescharacteristic
405C22×C8—21no—
406C22×C8—21no—
407C22×C8—61no—
408C22×C8—61no—
409#126—62no—
410#126—62no—
411#126—62no—
412#126—62no—
413#125—61no—
414#125—61no—
415#125—61no—
416#125—61no—
417#123—62no—
418#123—62no—
419#123—62no—
420#123—62no—
421#121—62no—
422#121—62no—
423#121—62no—
424#121—62no—
425#121—61no—
426#121—61no—
427#121—61no—
428#121—61no—
429#121—61no—
430#121—61no—
431#121—61no—
432#121—61no—
433C4×D4—62no—
434C4×D4—62no—
435C4×D4—62no—
436C4×D4—62no—
437C4×D4—61no—
438C4×D4—61no—
439C4×D4—61no—
440C4×D4—61no—
441C4×D4D1211yescharacteristic
442C4×D4D1211yescharacteristic
443C4×D4D1211yescharacteristic
444C4×D4D1211yescharacteristic
445C4×D4#6711yescharacteristic
446C4×D4#6711yescharacteristic
447C4×D4#6711yescharacteristic
448C4×D4#6711yescharacteristic
449#117—61no—
450#117—61no—
451#117—61no—
452#117—61no—
453C2×C4⋊C4—32no—
454C2×C4⋊C4—32no—
455C2×C4⋊C4—32no—
456C2×C4⋊C4—31no—
457C2×C4⋊C4—31no—
458C2×C4⋊C4—31no—
459C2×C4⋊C4—61no—
460C2×C4⋊C4—61no—
461C2×C4⋊C4—61no—
462C2×C4⋊C4—61no—
463C2×C4⋊C4C4×D311yescharacteristic
464C2×C22⋊C4—32no—
465C2×C22⋊C4—32no—
466C2×C22⋊C4—32no—
467C2×C22⋊C4—32no—
468C2×C22⋊C4C4×D311yescharacteristic
469C2×C22⋊C4C4×D311yescharacteristic
470C2×C42—32no—
471C2×C42C22×D311yescharacteristic
472C4⋊C8—21no—
473C4⋊C8—21no—
474C4⋊C8—61no—
475C4⋊C8—61no—
476#100—62no—
477#100—62no—
478#100—121no—
479#100—121no—
480C22⋊C8—21no—
481C22⋊C8—21no—
482C22⋊C8—21no—
483C22⋊C8—21no—
484C22⋊C8—61no—
485C22⋊C8—61no—
486C22⋊C8—61no—
487C22⋊C8—61no—
488#97—21no—
489#97—61no—
490C4×C8—21no—
491C4×C8—61no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—22no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3C2×C22⋊C411yescharacteristic
501C23×C3C2×C22⋊C411yescharacteristic
502C23×C3C2×C22⋊C411yescharacteristic
503C23×C3C2×C22⋊C411yescharacteristic
504C23×C3C23×C411yescharacteristic
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—42no—
509C22×D3—42no—
510C3×D4—22no—
511C3×D4—22no—
512C3×D4—41no—
513C3×D4—41no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4C2×C22⋊C411yescharacteristic
537C2×C3×C4C2×C22⋊C411yescharacteristic
538C2×C3×C4C2×C22⋊C411yescharacteristic
539C2×C3×C4C2×C22⋊C411yescharacteristic
540C2×C3×C4C2×C22⋊C411yescharacteristic
541C2×C3×C4C2×C22⋊C411yescharacteristic
542C2×C3×C4C2×C22⋊C411yescharacteristic
543C2×C3×C4C2×C22⋊C411yescharacteristic
544C2×C3×C4C22×D411yescharacteristic
545C2×C3×C4C22×D411yescharacteristic
546C2×C3×C4C2×#4111yescharacteristic
547C2×C3×C4C2×#4111yescharacteristic
548C2×C3×C4H(5,𝔽2)11yescharacteristic
549C2×C3×C42−1+411yescharacteristic
550#67—44no—
551#67—44no—
552#67—82no—
553#67—82no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—42no—
558C2×Dic3—42no—
559C2×Dic3—42no—
560C2×Dic3—82no—
561C2×Dic3—82no—
562D12—41no—
563D12—41no—
564D12—41no—
565D12—41no—
566C4×D3—82no—
567C4×D3—82no—
568C3×C8—22no—
569C3×C8—41no—
570C3×C8—41no—
571C3×C8—41no—
572C3⋊C8—22no—
573C3⋊C8—41no—
574C3⋊C8—41no—
575C3⋊C8—41no—
576C24—32no—
577C24C2×C4×D311yescharacteristic
578C24C2×C4×D311yescharacteristic
579C2×D4—42no—
580C2×D4—62no—
581C2×D4—62no—
582C2×D4—62no—
583C2×D4—62no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—124no—
591C2×D4—242no—
592C2×D4(C2×D3)⋊C411yescharacteristic
593C2×D4(C2×D3)⋊C411yescharacteristic
594C2×D4(C2×D3)⋊C411yescharacteristic
595C2×D4(C2×D3)⋊C411yescharacteristic
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—32no—
605C22×C4—32no—
606C22×C4—32no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—242no—
612C22×C4—242no—
613C22×C4C2×C4×D311yescharacteristic
614C22×C4C2×C4×D311yescharacteristic
615C22×C4C2×C4×D311yescharacteristic
616C22×C4C2×C4×D311yescharacteristic
617C22×C4C2×D1211yescharacteristic
618C22×C4C2×D1211yescharacteristic
619C22×C4C2×D1211yescharacteristic
620C22×C4C2×D1211yescharacteristic
621C22×C4C2×#6711yescharacteristic
622C22×C4C2×#6711yescharacteristic
623C22×C4C2×#6711yescharacteristic
624C22×C4C2×#6711yescharacteristic
625C22×C4C23×D311yescharacteristic
626M16—21no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—21no—
633M16—32no—
634M16—42no—
635M16—42no—
636M16—61no—
637M16—61no—
638M16—61no—
639M16—61no—
640M16—61no—
641M16—61no—
642M16—61no—
643M16—122no—
644M16—122no—
645M16#23712yes—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—42no—
651C2×C8—42no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8—61no—
655C2×C8—61no—
656C2×C8—122no—
657C2×C8—122no—
658C4⋊C4—62no—
659C4⋊C4—62no—
660C4⋊C4—62no—
661C4⋊C4—62no—
662C4⋊C4—62no—
663C4⋊C4—62no—
664C4⋊C4—61no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4—61no—
670C4⋊C4(C2×D3)⋊C411yescharacteristic
671C4⋊C4(C2×D3)⋊C411yescharacteristic
672C4⋊C4(C2×D3)⋊C411yescharacteristic
673C4⋊C4(C2×D3)⋊C411yescharacteristic
674C22⋊C4—62no—
675C22⋊C4—62no—
676C22⋊C4—62no—
677C22⋊C4—62no—
678C22⋊C4—62no—
679C22⋊C4—62no—
680C22⋊C4—62no—
681C22⋊C4—62no—
682C22⋊C4(C2×D3)⋊C411yescharacteristic
683C22⋊C4(C2×D3)⋊C411yescharacteristic
684C22⋊C4(C2×D3)⋊C411yescharacteristic
685C22⋊C4(C2×D3)⋊C411yescharacteristic
686C22⋊C4(C2×D3)⋊C411yescharacteristic
687C22⋊C4(C2×D3)⋊C411yescharacteristic
688C22⋊C4(C2×D3)⋊C411yescharacteristic
689C22⋊C4(C2×D3)⋊C411yescharacteristic
690C42—62no—
691C42—62no—
692C42C2×D1211yescharacteristic
693C42C2×D1211yescharacteristic
694C42C2×#6711yescharacteristic
695C42C2×#6711yescharacteristic
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—81no—
712C22×C3—81no—
713C22×C3#41312yes—
714C22×C3C22×C22⋊C411yescharacteristic
715C22×C3C4×#4111yescharacteristic
716C22×C3#52011yescharacteristic
717C2×D3—42no—
718C2×D3—42no—
719C2×D3—42no—
720C2×D3—82no—
721C2×D3—82no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—21no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4#54611yescharacteristic
731C3×C4#54611yescharacteristic
732C3×C4#54711yescharacteristic
733C3×C4#54711yescharacteristic
734Dic3—42no—
735Dic3—42no—
736Dic3—42no—
737C23—22no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—62no—
746C23—62no—
747C23—62no—
748C23—122no—
749C23—122no—
750C23C2×(C2×D3)⋊C411yescharacteristic
751C23C2×(C2×D3)⋊C411yescharacteristic
752C23C2×(C2×D3)⋊C411yescharacteristic
753C23C2×(C2×D3)⋊C411yescharacteristic
754C23C22×C4×D311yescharacteristic
755D4—22no—
756D4—22no—
757D4—41no—
758D4—41no—
759D4—124no—
760D4—124no—
761D4—121no—
762D4—121no—
763D4—121no—
764D4—121no—
765D4—242no—
766D4—242no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—122no—
793C2×C4—122no—
794C2×C4—122no—
795C2×C4—242no—
796C2×C4—242no—
797C2×C4—242no—
798C2×C4—242no—
799C2×C4C2×(C2×D3)⋊C411yescharacteristic
800C2×C4C2×(C2×D3)⋊C411yescharacteristic
801C2×C4C2×(C2×D3)⋊C411yescharacteristic
802C2×C4C2×(C2×D3)⋊C411yescharacteristic
803C2×C4C2×(C2×D3)⋊C411yescharacteristic
804C2×C4C2×(C2×D3)⋊C411yescharacteristic
805C2×C4C2×(C2×D3)⋊C411yescharacteristic
806C2×C4C2×(C2×D3)⋊C411yescharacteristic
807C2×C4C22×D1211yescharacteristic
808C2×C4C2×#23711yescharacteristic
809C2×C4#100411yescharacteristic
810C2×C4D3×#4111yescharacteristic
811C2×C4#101011yescharacteristic
812C2×C4C22×#6711yescharacteristic
813C8—22no—
814C8—41no—
815C8—41no—
816C8—41no—
817C8—62no—
818C8—121no—
819C8—121no—
820C8—121no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—22no—
824C2×C3—41no—
825C2×C3—41no—
826C2×C3—41no—
827C2×C3#233911yescharacteristic
828C2×C3C2×#41311yescharacteristic
829C2×C3#288811yescharacteristic
830D3—82no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—42no—
845C22—42no—
846C22—81no—
847C22—81no—
848C22—122no—
849C22—122no—
850C22—122no—
851C22—242no—
852C22—242no—
853C22#513212yes—
854C22C4×#23711yescharacteristic
855C22#554611yescharacteristic
856C22C22×(C2×D3)⋊C411yescharacteristic
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—122no—
866C4—122no—
867C4—122no—
868C4#555411yescharacteristic
869C4#555511yescharacteristic
870C4#580611yescharacteristic
871C4#582411yescharacteristic
872C3#2248211yescharacteristic, complemented, Sylow
873C2—21no—
874C2—21no—
875C2—22no—
876C2—41no—
877C2—41no—
878C2—41no—
879C2—242no—
880C2#8233011yescharacteristic
881C2C2×#513211yescharacteristic
882C2#8381311yescharacteristic
subgroupG/H
centerC22C22×(C2×D3)⋊C4
commutatorC23×C3C23×C4
FrattiniC22×C4C23×D3
FittingC3×D4×M16C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5565C2
cosocleC22×C3×C4C24
hypercenterD4×M16D3
hypocenterC3#22482
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. C3×D4×M16C2semidirect
3. D4×#208C2semidirect
4. #72002C2semidirect
5. #72002C2semidirect
6. #71987C2semidirect
7. C2×#4554C2semidirect
8. #70527C2semidirect
9. #70525C2semidirect
10. #69985C2semidirect
11. #69985C2semidirect
12. #69974C2semidirect
13. #69973C2semidirect
14. #69880C2semidirect
15. C4×#823C2semidirect
74. D4×M16D3semidirect
872. C3#22482semidirect

Maximal subgroups

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

subgroupindex
C2×#55652
C3×D4×M162
D4×#2082
#720022
#719872
C2×#45542
#705272
#705252
#699852
#699742
#699732
#698802
C4×#8232
#224823