Finite Group Databasebeta

← #11883958

Subgroups — #11883958

Order 1152.

1154 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5552C211yesmaximal, characteristic, complemented
2C3×D4×D12C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592710C211yesmaximal, characteristic, complemented
6#10591180C211yesmaximal, characteristic, complemented
7#10591171C211yesmaximal, characteristic, complemented
8#10591169C211yesmaximal, characteristic, complemented
9#10591166C211yesmaximal, characteristic, complemented
10#10591161C211yesmaximal, characteristic, complemented
11#10591160C211yesmaximal, characteristic, complemented
12#10590364C211yesmaximal, characteristic, complemented
13#10590358C211yesmaximal, characteristic, complemented
14#10590354C211yesmaximal, characteristic, complemented
15#10590348C211yesmaximal, characteristic, complemented
16#83542—31nomaximal
17#83491—31nomaximal
18C2×C3×D3×D4—21no—
19C2×C3×#235C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic, complemented
23C32×C4×D4C2211yescharacteristic
24C2×#3748C2211yescharacteristic, complemented
25C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×#939—21no—
27C3×#930C2211yescharacteristic
28C3×#930C2211yescharacteristic
29C3×#930C2211yescharacteristic, complemented
30C3×#924C2211yescharacteristic, complemented
31C3×#896—21no—
32C3×#895—21no—
33C3×#885—21no—
34C3×#882—21no—
35C3×#882—21no—
36C3×#67⋊C4—21no—
37C3×#875C2211yescharacteristic, complemented
38C3×#874C2211yescharacteristic
39C3×C4×D12C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic, complemented
41C2×#3715—24no—
42C2×#3715C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×#3715C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48#63823—24no—
49C2×#3713C2211yescharacteristic
50C2×#3713C2211yescharacteristic, complemented
51C2×#3713C2211yescharacteristic, complemented
52#63657C2211yescharacteristic, complemented
53#63657C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C3×#548—31no—
64C3×D42—31no—
65C2×#949—31no—
66C22×#215—31no—
67C22×#214—31no—
68C2×#932—31no—
69#5552D311yescharacteristic, complemented
70D4×D12D311yescharacteristic, complemented
71#5238—31no—
72#5227—31no—
73#5218—31no—
74#5217—31no—
75#5075—31no—
76#5074—31no—
77#5058—31no—
78#5057—31no—
79#5049—31no—
80#5046—31no—
81#5042—31no—
82#5040—31no—
83#5038—31no—
84#5038—31no—
85#5037—31no—
86#5036—31no—
87#5027—31no—
88#5026—31no—
89#5018—31no—
90#5016—31no—
91#5011—31no—
92#5011—31no—
93#5011—61no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4D411yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C3×D3×D4—44no—
105C3×#235—22no—
106C3×#235—41no—
107C2×C3×D12—22no—
108C2×C3×D12—22no—
109C2×C3×D12—21no—
110C2×C3×D12—21no—
111C2×C3×D12—21no—
112C2×C3×D12—21no—
113C2×C3×D12—41no—
114C2×C3×D12—41no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×Dic6—22no—
122C2×C3×Dic6—21no—
123C2×C3×Dic6—41no—
124C2×C3×Dic6C2311yescharacteristic
125C2×C3×Dic6C2311yescharacteristic
126C32×C4⋊C4D411yescharacteristic
127C32×C22⋊C4D411yescharacteristic
128C32×C22⋊C4D411yescharacteristic
129C32×C42C2311yescharacteristic
130#3748—22no—
131C2×C3⋊(C3⋊C8)—22no—
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136C3×#217—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4—21no—
143C3×C4⋊Dic3C2311yescharacteristic
144C3×C4⋊Dic3C2311yescharacteristic
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4—21no—
147C3×C4×Dic3—21no—
148#3715—22no—
149#3715—22no—
150#3715—22no—
151#3715—22no—
152#3715—41no—
153#3715D414yescomplemented
154#3713—22no—
155#3713—22no—
156#3713—41no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C22×C3×D4—61no—
163C2×D3×D4—21no—
164C2×#235C2×D311yescharacteristic, complemented
165C22×D12C2×D311yescharacteristic
166C22×D12C2×D311yescharacteristic
167C22×Dic6C2×D311yescharacteristic, complemented
168C3×#127—31no—
169C3×#124—31no—
170C3×#124—61no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—61no—
173C3×#121—31no—
174C3×#121—31no—
175C3×#121—31no—
176C3×#121—61no—
177C3×#121—61no—
178C3×#120—61no—
179C3×#120—61no—
180C3×C4×Q8—31no—
181C3×C4×D4—21no—
182C3×C4×D4—31no—
183C3×C4×D4—61no—
184C3×C4×D4C2×D311yescharacteristic
185C3×C4×D4C2×D311yescharacteristic
186#949—64no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—64no—
194#939—21no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—64no—
202#932—64no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—31no—
209#930C2×D311yescharacteristic
210#930C2×D311yescharacteristic
211#930C2×D311yescharacteristic, complemented
212#924C2×D311yescharacteristic, complemented
213C2×#208—31no—
214C2×#208—31no—
215C2×#208—61no—
216C22×C3⋊C8—31no—
217C22×C3⋊C8—31no—
218C22×C3⋊C8—61no—
219#896—21no—
220#895—21no—
221#885—21no—
222#882—21no—
223#882—21no—
224#67⋊C4—21no—
225#875C2×D311yescharacteristic, complemented
226#874C2×D311yescharacteristic
227C4×D12C2×D311yescharacteristic
228C4×Dic6C2×D311yescharacteristic, complemented
229#835—31no—
230#835—31no—
231#832—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#830—31no—
236#830—31no—
237#830—31no—
238#830—31no—
239#830—61no—
240#830—61no—
241#810—31no—
242#810—31no—
243#809—31no—
244#809—31no—
245#809—31no—
246#809—31no—
247#807—31no—
248#807—31no—
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—61no—
252#803—31no—
253#803—31no—
254#803—61no—
255C23×C32C2×D411yescharacteristic
256C23×C32C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—42no—
264C22×C3×D3—42no—
265C22×C3×D3—81no—
266C22×C3×D3—81no—
267C32×D4—22no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2411yescharacteristic
277C3×#67—42no—
278C3×#67—42no—
279C3×#67—42no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—42no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—42no—
294C3×D12—42no—
295C3×D12—42no—
296C3×D12—81no—
297C3×D12C2×D412yes—
298C3×C4×D3—42no—
299C3×C4×D3—42no—
300C3×Dic6—21no—
301C3×Dic6—21no—
302C3×Dic6—21no—
303C3×Dic6—42no—
304C3×Dic6C2×D412yescomplemented
305C3⋊(C3⋊C8)—21no—
306C3⋊(C3⋊C8)—21no—
307C3⋊(C3⋊C8)—21no—
308C3⋊(C3⋊C8)C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—31no—
312D42—31no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C24×C3—61no—
326C23×D3—21no—
327C23×D3—21no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—31no—
331C2×C3×Q8—31no—
332C2×C3×Q8—62no—
333C2×C3×Q8—61no—
334C2×C3×Q8—121no—
335C2×C3×D4—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—62no—
341C2×C3×D4—62no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4—121no—
351C2×C3×D4—121no—
352C2×C3×D4—124no—
353C2×C3×D4#6711yescharacteristic
354C2×C3×D4#6711yescharacteristic
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—61no—
358C22×C3×C4—61no—
359C22×C3×C4—61no—
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C2×#67—21no—
365C2×#67—21no—
366C2×#67—21no—
367C2×#67—21no—
368C22×Dic3—21no—
369D3×D4—44no—
370#235—22no—
371#235—41no—
372C2×D12—22no—
373C2×D12—22no—
374C2×D12—21no—
375C2×D12—21no—
376C2×D12—21no—
377C2×D12—21no—
378C2×D12—41no—
379C2×D12—41no—
380C2×D12C22×D311yescharacteristic
381C2×D12C22×D311yescharacteristic
382C2×D12C22×D311yescharacteristic
383C2×D12C22×D311yescharacteristic
384C2×C4×D3—21no—
385C2×C4×D3—21no—
386C2×Dic6—22no—
387C2×Dic6—21no—
388C2×Dic6—41no—
389C2×Dic6C22×D311yescharacteristic
390C2×Dic6C22×D311yescharacteristic
391C3×C4⋊C4—21no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—61no—
395C3×C4⋊C4—61no—
396C3×C4⋊C4#6711yescharacteristic
397C3×C4⋊C4#6711yescharacteristic
398C3×C22⋊C4—21no—
399C3×C22⋊C4—21no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4#6711yescharacteristic
408C3×C22⋊C4#6711yescharacteristic
409C3×C22⋊C4#6711yescharacteristic
410C3×C22⋊C4#6711yescharacteristic
411C3×C42—21no—
412C3×C42—61no—
413C3×C42C22×D311yescharacteristic
414C3×C42C22×D311yescharacteristic
415#217—21no—
416#215—34no—
417#215—62no—
418#215—62no—
419#215—62no—
420#215—62no—
421#215—121no—
422#214—34no—
423#214—62no—
424#214—62no—
425#214—62no—
426#214—62no—
427#214—121no—
428#213—62no—
429#213—62no—
430#213—62no—
431#213—62no—
432#213—121no—
433#213—121no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—21no—
440C4⋊Dic3C22×D311yescharacteristic
441C4⋊Dic3C22×D311yescharacteristic
442Dic3⋊C4—21no—
443Dic3⋊C4—21no—
444C4×Dic3—21no—
445#208—62no—
446#208—62no—
447#208—122no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—31no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8—61no—
458C2×C3⋊C8—61no—
459C2×C3⋊C8—61no—
460C2×C3⋊C8—62no—
461C2×C3⋊C8—62no—
462C2×C3⋊C8—122no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32AGL(1,ℤ/8)12yescomplemented
469C22×C32C22×D411yescharacteristic
470C2×C3×D3—22no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—84no—
483C2×C3×D3—84no—
484C32×C4—21no—
485C32×C4—21no—
486C32×C4—21no—
487C32×C4—21no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
490C3×Dic3—22no—
491C3×Dic3—41no—
492C3×Dic3—41no—
493C3×Dic3—41no—
494C2×#41—31no—
495C22×Q8—31no—
496C22×D4—31no—
497C22×D4—31no—
498C22×D4—61no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—91no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—91no—
512#127—31no—
513#124—31no—
514#124—61no—
515C22⋊Q8—31no—
516C22⋊Q8—61no—
517#121—31no—
518#121—31no—
519#121—31no—
520#121—61no—
521#121—61no—
522#120—61no—
523#120—61no—
524C4×Q8—31no—
525C4×D4—31no—
526C4×D4—61no—
527C4×D4D3211yescharacteristic
528#107—91no—
529C4⋊C8—91no—
530#103—91no—
531#103—91no—
532#102—91no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—91no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—122no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—241no—
550C23×C3—241no—
551C23×C3C2×#6711yescharacteristic
552C23×C3C2×#6711yescharacteristic
553C23×C3C2×#6711yescharacteristic
554C23×C3C2×#6711yescharacteristic
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—42no—
560C22×D3—42no—
561C22×D3—42no—
562C22×D3—42no—
563C22×D3—81no—
564C22×D3—81no—
565C3×Q8—32no—
566C3×Q8—61no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×Q8—122no—
570C3×D4—22no—
571C3×D4—22no—
572C3×D4—32no—
573C3×D4—42no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—122no—
582C3×D4—122no—
583C3×D4—122no—
584C3×D4—122no—
585C3×D4—122no—
586C3×D4—122no—
587C3×D4—122no—
588C3×D4—241no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—122no—
611C2×C3×C4—122no—
612C2×C3×C4—122no—
613C2×C3×C4C2×#6711yescharacteristic
614C2×C3×C4C2×#6711yescharacteristic
615C2×C3×C4C2×#6711yescharacteristic
616C2×C3×C4C2×#6711yescharacteristic
617C2×C3×C4C2×#6711yescharacteristic
618C2×C3×C4C2×#6711yescharacteristic
619C2×C3×C4C2×#6711yescharacteristic
620C2×C3×C4C2×#6711yescharacteristic
621C2×C3×C4C23×D311yescharacteristic
622C2×C3×C4C23×D311yescharacteristic
623#67—42no—
624#67—42no—
625#67—42no—
626#67—42no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—42no—
632D12—21no—
633D12—21no—
634D12—21no—
635D12—21no—
636D12—21no—
637D12—21no—
638D12—21no—
639D12—42no—
640D12—42no—
641D12—42no—
642D12—81no—
643D12D3×D412yes—
644C4×D3—42no—
645C4×D3—42no—
646Dic6—21no—
647Dic6—21no—
648Dic6—21no—
649Dic6—42no—
650Dic6D3×D412yescomplemented
651C3⋊C8—32no—
652C3⋊C8—32no—
653C3⋊C8—62no—
654C3⋊C8—61no—
655C3⋊C8—61no—
656C3⋊C8—61no—
657C3⋊C8—61no—
658C3⋊C8—61no—
659C3⋊C8—61no—
660C3⋊C8—121no—
661C3⋊C8—121no—
662C3⋊C8—121no—
663C2×C32—22no—
664C2×C32—41no—
665C2×C32D4211yescharacteristic
666C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
667C2×C32#57711yescharacteristic
668C3×D3—42no—
669C3×D3—81no—
670C3×D3—81no—
671C3×D3—81no—
672C24—61no—
673C24—61no—
674#41—62no—
675#41—121no—
676C2×Q8—31no—
677C2×Q8—31no—
678C2×Q8—62no—
679C2×Q8—61no—
680C2×Q8—121no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—31no—
685C2×D4—62no—
686C2×D4—62no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—121no—
696C2×D4—121no—
697C2×D4—124no—
698C2×D4#62511yescharacteristic
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4C2×D3211yescharacteristic
703C22×C4C2×D3211yescharacteristic
704SD16—94no—
705SD16—182no—
706SD16—182no—
707SD16—182no—
708SD16—182no—
709SD16—361no—
710D8—182no—
711D8—182no—
712D8—361no—
713M16—182no—
714C2×C8—91no—
715C2×C8—91no—
716C2×C8—91no—
717C2×C8—91no—
718C2×C8—182no—
719C4⋊C4—31no—
720C4⋊C4—31no—
721C4⋊C4—61no—
722C4⋊C4—61no—
723C4⋊C4#62511yescharacteristic
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—61no—
730C22⋊C4—61no—
731C22⋊C4#62511yescharacteristic
732C22⋊C4#62511yescharacteristic
733C42—61no—
734C42C2×D3211yescharacteristic
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—22no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—62no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—244no—
765C22×C3—244no—
766C22×C3#93212yescomplemented
767C22×C3#94912yescomplemented
768C22×C3C22×#6711yescharacteristic
769C22×C3C22×#6711yescharacteristic
770C2×D3—22no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—84no—
783C2×D3—84no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—41no—
795C3×C4—41no—
796C3×C4—41no—
797C3×C4—41no—
798C3×C4—62no—
799C3×C4—121no—
800C3×C4—121no—
801C3×C4—121no—
802C3×C4C2×D3×D411yescharacteristic
803C3×C4C2×D3×D411yescharacteristic
804C3×C4#100411yescharacteristic
805C3×C4#100411yescharacteristic
806Dic3—22no—
807Dic3—41no—
808Dic3—41no—
809Dic3—41no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—61no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—122no—
816C23—122no—
817C23—122no—
818C23—122no—
819C23—241no—
820C23—241no—
821C23C2×#62511yescharacteristic
822C23C2×#62511yescharacteristic
823Q8—32no—
824Q8—61no—
825Q8—61no—
826Q8—61no—
827Q8—122no—
828D4—22no—
829D4—32no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—61no—
837D4—122no—
838D4—122no—
839D4—122no—
840D4—122no—
841D4—122no—
842D4—122no—
843D4—122no—
844D4—241no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—122no—
854C2×C4—122no—
855C2×C4—122no—
856C2×C4C2×#62511yescharacteristic
857C2×C4C2×#62511yescharacteristic
858C2×C4C2×#62511yescharacteristic
859C2×C4C2×#62511yescharacteristic
860C2×C4C22×D3211yescharacteristic
861C8—92no—
862C8—181no—
863C8—181no—
864C8—181no—
865C2×C3—22no—
866C2×C3—22no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—42no—
871C2×C3—41no—
872C2×C3—41no—
873C2×C3—81no—
874C2×C3—122no—
875C2×C3—241no—
876C2×C3—241no—
877C2×C3—241no—
878C2×C3C2×#93211yescharacteristic
879C2×C3D4×#6711yescharacteristic
880C2×C3D4×#6711yescharacteristic
881C2×C3C2×#94911yescharacteristic
882C2×C3#583611yescharacteristic
883C2×C3#583711yescharacteristic
884D3—42no—
885D3—81no—
886D3—81no—
887D3—81no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—62no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—244no—
906C22—244no—
907C22#6382312yescomplemented
908C22C22×#62511yescharacteristic
909C4—21no—
910C4—21no—
911C4—21no—
912C4—21no—
913C4—62no—
914C4—121no—
915C4—121no—
916C4—121no—
917C4D32×D411yescharacteristic
918C4#6431311yescharacteristic
919C3—21no—
920C3#8349111yescharacteristic, complemented
921C3#8354211yescharacteristic, complemented
922C2—22no—
923C2—41no—
924C2—122no—
925C2—241no—
926C2—241no—
927C2—241no—
928C2C2×#6382311yescharacteristic
929C2D4×#62511yescharacteristic
930C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3265
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
1. C3×#5552C2semidirect
2. C3×D4×D12C2semidirect
3. C22×#3715C2semidirect
4. C2×#63823C2semidirect
5. #10592710C2semidirect
6. #10591180C2semidirect
7. #10591171C2semidirect
8. #10591169C2semidirect
9. #10591166C2semidirect
10. #10591161C2semidirect
11. #10591160C2semidirect
12. #10590364C2semidirect
13. #10590358C2semidirect
14. #10590354C2semidirect
15. #10590348C2semidirect
19. C2×C3×#235C22semidirect
22. C22×C3×Dic6C22semidirect
24. C2×#3748C22semidirect
25. C22×C3⋊(C3⋊C8)C22semidirect
29. C3×#930C22semidirect
30. C3×#924C22semidirect
37. C3×#875C22semidirect
40. C3×C4×Dic6C22semidirect
44. C2×#3715C22semidirect
45. C2×#3715C22semidirect
46. C2×#3715C22semidirect
47. C2×#3715C22semidirect
50. C2×#3713C22semidirect
51. C2×#3713C22semidirect
52. #63657C22semidirect
53. #63657C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. #63630C22semidirect
56. #63576C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
60. #63562C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
69. #5552D3semidirect
70. D4×D12D3semidirect
153. #3715D4semidirect
164. C2×#235C2×D3semidirect
167. C22×Dic6C2×D3semidirect
211. #930C2×D3semidirect
212. #924C2×D3semidirect
225. #875C2×D3semidirect
228. C4×Dic6C2×D3semidirect
304. C3×Dic6C2×D4semidirect
308. C3⋊(C3⋊C8)C2×D4semidirect
468. C22×C32AGL(1,ℤ/8)semidirect
650. Dic6D3×D4semidirect
766. C22×C3#932semidirect
767. C22×C3#949semidirect
810. C32#3265semidirect
907. C22#63823semidirect
920. C3#83491semidirect
921. C3#83542semidirect

Maximal subgroups

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

subgroupindex
C3×#55522
C3×D4×D122
C22×#37152
C2×#638232
#105927102
#105911802
#105911712
#105911692
#105911662
#105911612
#105911602
#105903642
#105903582
#105903542
#105903482
#835423
#834913