Finite Group Databasebeta

← #11889095

Subgroups — #11889095

Order 1152.

962 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×D12C211yesmaximal, characteristic
2C3×#5541C211yesmaximal, characteristic, complemented
3#10592710C211yesmaximal, characteristic, complemented
4#10591180C211yesmaximal, characteristic, complemented
5#10591179C211yesmaximal, characteristic, complemented
6#10591169C211yesmaximal, characteristic, complemented
7#10591169C211yesmaximal, characteristic, complemented
8#10591090C211yesmaximal, characteristic, complemented
9#10591089C211yesmaximal, characteristic, complemented
10#10591085C211yesmaximal, characteristic, complemented
11C2×#63562C211yesmaximal, characteristic, complemented
12#10590364C211yesmaximal, characteristic, complemented
13#10590358C211yesmaximal, characteristic, complemented
14#10590279C211yesmaximal, characteristic, complemented
15#10590270C211yesmaximal, characteristic, complemented
16#83599—31nomaximal
17#83484—31nomaximal
18C2×C3×D3×D4—21no—
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C2×#3748C2211yescharacteristic, complemented
23C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24C3×#935—21no—
25C3×#930C2211yescharacteristic
26C3×#930C2211yescharacteristic
27C3×#926C2211yescharacteristic, complemented
28C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
29C3×#924C2211yescharacteristic, complemented
30C3×#924C2211yescharacteristic, complemented
31C3×#895—21no—
32C3×#889—21no—
33C3×#882—21no—
34C3×#882—21no—
35C3×#879—21no—
36C3×#877—21no—
37C3×#874C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic
39C3×#870C2211yescharacteristic, complemented
40C3×C4×Dic6C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic, complemented
44#63657C2211yescharacteristic, complemented
45#63657C2211yescharacteristic, complemented
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
47#63630C2211yescharacteristic, complemented
48#63576C2211yescharacteristic, complemented
49#63576C2211yescharacteristic, complemented
50#63574C2211yescharacteristic, complemented
51#63565C2211yescharacteristic, complemented
52#63562C2211yescharacteristic
53#63562C2211yescharacteristic
54#63562C2211yescharacteristic
55#63562C2211yescharacteristic, complemented
56#63562C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61C3×#552—31no—
62C3×D42—31no—
63D4×D12D311yescharacteristic
64#5541D311yescharacteristic, complemented
65#5218—31no—
66#5218—31no—
67#5215—31no—
68C2×#832—31no—
69#5075—31no—
70#5071—31no—
71#5067—31no—
72#5066—31no—
73#5049—31no—
74#5048—31no—
75#5046—31no—
76#5046—31no—
77#5042—31no—
78#5041—31no—
79#5035—31no—
80#5033—31no—
81#5027—31no—
82#5026—31no—
83#5018—31no—
84#5011—31no—
85#5011—31no—
86#5011—61no—
87#5009—31no—
88#5003—31no—
89#5001—31no—
90#4967—31no—
91C2×#809—31no—
92C23×C3×D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4D411yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C3×D3×D4—44no—
101C2×C3×D12—22no—
102C2×C3×D12—22no—
103C2×C3×D12—21no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—41no—
108C2×C3×D12—41no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×Dic6C2311yescharacteristic
114C32×C4⋊C4D411yescharacteristic
115C32×C22⋊C4D411yescharacteristic
116C32×C22⋊C4D411yescharacteristic
117C32×C42C2311yescharacteristic
118#3748—41no—
119C2×C3⋊(C3⋊C8)—41no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×#217—21no—
125C3×#217—21no—
126C3×#217—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3—21no—
141C3×C4×Dic3—21no—
142#3715—22no—
143#3715—41no—
144#3715—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C22×C3×D4—61no—
149C2×D3×D4—21no—
150C22×D12C2×D311yescharacteristic
151C22×D12C2×D311yescharacteristic
152C3×#127—31no—
153C3×#126—61no—
154C3×#125—31no—
155C3×#125—61no—
156C3×#123—61no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×#121—31no—
160C3×#121—31no—
161C3×#121—61no—
162C3×#120—61no—
163C3×#120—61no—
164C3×C4×Q8—31no—
165C3×C4×D4—21no—
166C3×C4×D4—31no—
167C3×C4×D4C2×D311yescharacteristic
168C3×C4×D4C2×D311yescharacteristic
169C3×#117—31no—
170C3×#117—61no—
171C2×C3×C4⋊C4—31no—
172C2×#215—31no—
173C2×#215—31no—
174C2×#215—31no—
175#935—21no—
176C2×#214—31no—
177C2×#214—31no—
178C2×#214—31no—
179#930C2×D311yescharacteristic
180#930C2×D311yescharacteristic
181#926C2×D311yescharacteristic, complemented
182C2×C4⋊Dic3C2×D311yescharacteristic, complemented
183#924C2×D311yescharacteristic, complemented
184#924C2×D311yescharacteristic, complemented
185C2×#208—31no—
186C2×#208—31no—
187C2×#208—61no—
188C22×C3⋊C8—31no—
189C22×C3⋊C8—31no—
190C22×C3⋊C8—61no—
191#895—21no—
192#889—21no—
193#882—21no—
194#882—21no—
195#879—21no—
196#877—21no—
197#874C2×D311yescharacteristic
198C4×D12C2×D311yescharacteristic
199#870C2×D311yescharacteristic, complemented
200C4×Dic6C2×D311yescharacteristic, complemented
201#835—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#830—31no—
212#830—31no—
213#830—31no—
214#830—31no—
215#830—61no—
216#830—61no—
217#810—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#808—31no—
228#808—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233C4⋊(C3⋊C8)—31no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—61no—
236#803—31no—
237#803—31no—
238#803—61no—
239C23×C32C2×D411yescharacteristic
240C23×C32C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—42no—
245C22×C3×D3—42no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C22×C3×D3—81no—
250C32×D4—22no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260C3×#67—42no—
261C3×#67—42no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—42no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—42no—
274C3×D12—42no—
275C3×D12—42no—
276C3×D12—81no—
277C3×D12#4112yes—
278C3×C4×D3—42no—
279C3×Dic6—21no—
280C3×Dic6—21no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3⋊(C3⋊C8)—21no—
284C3⋊(C3⋊C8)—21no—
285#552—31no—
286D42—31no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C24×C3—61no—
301C24×C3—61no—
302C23×D3—21no—
303C23×D3—21no—
304C2×C3×Q8—31no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—62no—
310C2×C3×D4—62no—
311C2×C3×D4—61no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4—121no—
318C2×C3×D4—121no—
319C2×C3×D4—124no—
320C2×C3×D4#6711yescharacteristic
321C2×C3×D4#6711yescharacteristic
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C2×#67—21no—
331C2×#67—21no—
332C22×Dic3—21no—
333D3×D4—44no—
334C2×D12—22no—
335C2×D12—22no—
336C2×D12—21no—
337C2×D12—21no—
338C2×D12—21no—
339C2×D12—21no—
340C2×D12—41no—
341C2×D12—41no—
342C2×D12C22×D311yescharacteristic
343C2×D12C22×D311yescharacteristic
344C2×D12C22×D311yescharacteristic
345C2×C4×D3—21no—
346C2×Dic6C22×D311yescharacteristic
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4#6711yescharacteristic
359C3×C4⋊C4#6711yescharacteristic
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4#6711yescharacteristic
369C3×C22⋊C4#6711yescharacteristic
370C3×C22⋊C4#6711yescharacteristic
371C3×C22⋊C4#6711yescharacteristic
372C3×C42—21no—
373C3×C42—61no—
374C3×C42—61no—
375C3×C42C22×D311yescharacteristic
376C3×C42C22×D311yescharacteristic
377#217—21no—
378#217—21no—
379#217—21no—
380#215—62no—
381#215—121no—
382#215—121no—
383#214—62no—
384#214—121no—
385#214—121no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399C4×Dic3—21no—
400C4×Dic3—21no—
401#208—121no—
402#208—121no—
403#208—122no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8—61no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8—121no—
417C2×C3⋊C8—121no—
418C2×C3⋊C8—122no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32AGL(1,ℤ/8)12yes—
425C22×C32C22×D411yescharacteristic
426C2×C3×D3—22no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—84no—
436C2×C3×D3—84no—
437C32×C4—21no—
438C32×C4—21no—
439C32×C4—21no—
440C32×C4—21no—
441C32×C4C2×#4111yescharacteristic
442C32×C4H(5,𝔽2)11yescharacteristic
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—31no—
449C22×D4—31no—
450C22×D4—61no—
451C2×SD16—91no—
452C2×SD16—91no—
453C2×SD16—91no—
454C2×M16—91no—
455C22×C8—91no—
456#127—31no—
457#126—61no—
458#125—31no—
459#125—61no—
460#123—61no—
461C22⋊Q8—31no—
462C22⋊Q8—31no—
463#121—31no—
464#121—31no—
465#121—61no—
466#120—61no—
467#120—61no—
468C4×Q8—31no—
469C4×D4—31no—
470C4×D4D3211yescharacteristic
471#117—31no—
472#117—61no—
473C2×C4⋊C4—31no—
474#107—91no—
475#107—91no—
476#106—91no—
477C4⋊C8—91no—
478#103—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—91no—
489C22⋊C8—91no—
490#97—91no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3—122no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—122no—
500C23×C3—241no—
501C23×C3—241no—
502C23×C3C2×#6711yescharacteristic
503C23×C3C2×#6711yescharacteristic
504C23×C3C2×#6711yescharacteristic
505C23×C3C2×#6711yescharacteristic
506C22×D3—21no—
507C22×D3—21no—
508C22×D3—21no—
509C22×D3—42no—
510C22×D3—42no—
511C22×D3—42no—
512C22×D3—42no—
513C22×D3—81no—
514C22×D3—81no—
515C3×Q8—61no—
516C3×Q8—61no—
517C3×D4—22no—
518C3×D4—22no—
519C3×D4—32no—
520C3×D4—42no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—61no—
525C3×D4—61no—
526C3×D4—122no—
527C3×D4—122no—
528C3×D4—122no—
529C3×D4—122no—
530C3×D4—122no—
531C3×D4—241no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—122no—
555C2×C3×C4—122no—
556C2×C3×C4C2×#6711yescharacteristic
557C2×C3×C4C2×#6711yescharacteristic
558C2×C3×C4C2×#6711yescharacteristic
559C2×C3×C4C2×#6711yescharacteristic
560C2×C3×C4C2×#6711yescharacteristic
561C2×C3×C4C2×#6711yescharacteristic
562C2×C3×C4C2×#6711yescharacteristic
563C2×C3×C4C2×#6711yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566#67—42no—
567#67—42no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—42no—
574D12—21no—
575D12—21no—
576D12—21no—
577D12—21no—
578D12—21no—
579D12—42no—
580D12—42no—
581D12—42no—
582D12—81no—
583D12#23712yes—
584C4×D3—42no—
585Dic6—21no—
586Dic6—21no—
587C3⋊C8—62no—
588C3⋊C8—61no—
589C3⋊C8—61no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—61no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C3⋊C8—121no—
597C3⋊C8—121no—
598C3⋊C8—121no—
599C2×C32—22no—
600C2×C32—41no—
601C2×C32#54611yescharacteristic
602C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
603C2×C32#57711yescharacteristic
604C3×D3—42no—
605C3×D3—81no—
606C3×D3—81no—
607C24—61no—
608C24—61no—
609C2×Q8—31no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—62no—
614C2×D4—62no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—121no—
622C2×D4—121no—
623C2×D4—124no—
624C2×D4#62511yescharacteristic
625C22×C4—61no—
626C22×C4—61no—
627C22×C4C2×D3211yescharacteristic
628C22×C4C2×D3211yescharacteristic
629SD16—182no—
630SD16—361no—
631SD16—361no—
632M16—361no—
633C2×C8—91no—
634C2×C8—91no—
635C2×C8—91no—
636C2×C8—91no—
637C2×C8—361no—
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4#62511yescharacteristic
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—61no—
653C22⋊C4—61no—
654C22⋊C4—61no—
655C22⋊C4#62511yescharacteristic
656C22⋊C4#62511yescharacteristic
657C42—61no—
658C42—61no—
659C42C2×D3211yescharacteristic
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—22no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—62no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—244no—
687C22×C3—244no—
688C22×C3#93212yes—
689C22×C3#94912yes—
690C22×C3C22×#6711yescharacteristic
691C22×C3C22×#6711yescharacteristic
692C2×D3—22no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—84no—
702C2×D3—84no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4—121no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4C2×#23711yescharacteristic
723C3×C4#100411yescharacteristic
724C3×C4D3×#4111yescharacteristic
725C3×C4#100911yescharacteristic
726Dic3—41no—
727Dic3—41no—
728Dic3—41no—
729Dic3—41no—
730Dic3—41no—
731C32#331011yescharacteristic, complemented, Sylow
732C23—61no—
733C23—61no—
734C23—61no—
735C23—122no—
736C23—122no—
737C23—122no—
738C23—122no—
739C23—241no—
740C23—241no—
741C23C2×#62511yescharacteristic
742C23C2×#62511yescharacteristic
743Q8—61no—
744Q8—61no—
745D4—22no—
746D4—32no—
747D4—61no—
748D4—61no—
749D4—61no—
750D4—61no—
751D4—61no—
752D4—122no—
753D4—122no—
754D4—122no—
755D4—122no—
756D4—122no—
757D4—241no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4C2×#62511yescharacteristic
770C2×C4C2×#62511yescharacteristic
771C2×C4C2×#62511yescharacteristic
772C2×C4C2×#62511yescharacteristic
773C2×C4C22×D3211yescharacteristic
774C8—181no—
775C8—181no—
776C8—181no—
777C8—181no—
778C2×C3—22no—
779C2×C3—22no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—42no—
784C2×C3—41no—
785C2×C3—41no—
786C2×C3—81no—
787C2×C3—122no—
788C2×C3—241no—
789C2×C3—241no—
790C2×C3C2×#93211yescharacteristic
791C2×C3#580611yescharacteristic
792C2×C3C2×#94911yescharacteristic
793C2×C3#582911yescharacteristic
794C2×C3#583611yescharacteristic
795C2×C3#583711yescharacteristic
796D3—42no—
797D3—81no—
798D3—81no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—62no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—244no—
814C22—244no—
815C22#6382312yes—
816C22C22×#62511yescharacteristic
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—121no—
825C4—121no—
826C4D3×#23711yescharacteristic
827C4#6431411yescharacteristic
828C3—21no—
829C3#8348411yescharacteristic, complemented
830C3#8359911yescharacteristic, complemented
831C2—22no—
832C2—41no—
833C2—122no—
834C2—241no—
835C2—241no—
836C2C2×#6382311yescharacteristic
837C2#1059524411yescharacteristic
838C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×D4×D12C2
hypercenterC4×D4D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5541C2semidirect
3. #10592710C2semidirect
4. #10591180C2semidirect
5. #10591179C2semidirect
6. #10591169C2semidirect
7. #10591169C2semidirect
8. #10591090C2semidirect
9. #10591089C2semidirect
10. #10591085C2semidirect
11. C2×#63562C2semidirect
12. #10590364C2semidirect
13. #10590358C2semidirect
14. #10590279C2semidirect
15. #10590270C2semidirect
22. C2×#3748C22semidirect
23. C22×C3⋊(C3⋊C8)C22semidirect
27. C3×#926C22semidirect
28. C2×C3×C4⋊Dic3C22semidirect
29. C3×#924C22semidirect
30. C3×#924C22semidirect
39. C3×#870C22semidirect
40. C3×C4×Dic6C22semidirect
42. C2×#3715C22semidirect
43. C2×#3715C22semidirect
44. #63657C22semidirect
45. #63657C22semidirect
46. C4⋊(C3⋊(C3⋊C8))C22semidirect
47. #63630C22semidirect
48. #63576C22semidirect
49. #63576C22semidirect
50. #63574C22semidirect
51. #63565C22semidirect
55. #63562C22semidirect
56. #63562C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
64. #5541D3semidirect
181. #926C2×D3semidirect
182. C2×C4⋊Dic3C2×D3semidirect
183. #924C2×D3semidirect
184. #924C2×D3semidirect
199. #870C2×D3semidirect
200. C4×Dic6C2×D3semidirect
731. C32#3310semidirect
829. C3#83484semidirect
830. C3#83599semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D122
C3×#55412
#105927102
#105911802
#105911792
#105911692
#105910902
#105910892
#105910852
C2×#635622
#105903642
#105903582
#105902792
#105902702
#835993
#834843