Finite Group Databasebeta

← #11884477

Subgroups — #11884477

Order 1152.

1092 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5676C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3C2×#63934C211yesmaximal, characteristic, complemented
4#10593902C211yesmaximal, characteristic, complemented
5#10592757C211yesmaximal, characteristic, complemented
6C3×#5054C211yesmaximal, characteristic, complemented
7#10591657C211yesmaximal, characteristic, complemented
8#10591589C211yesmaximal, characteristic, complemented
9#10591588C211yesmaximal, characteristic, complemented
10#10591521C211yesmaximal, characteristic, complemented
11#10591449C211yesmaximal, characteristic, complemented
12#10591448C211yesmaximal, characteristic, complemented
13#10590358C211yesmaximal, characteristic, complemented
14#10590349C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83507—31nomaximal
17#80628—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C32×#124C2211yescharacteristic
23C2×#3755C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27#64083C2211yescharacteristic, complemented
28C3×#946C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic, complemented
30C3×#938C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C3×#884—21no—
33C3×#883—21no—
34C3×#882—21no—
35C3×D3×C22⋊C4—21no—
36C3×C4×D12C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic, complemented
39#63949—24no—
40#63934—24no—
41#63911—21no—
42#63910—21no—
43#63910—21no—
44#63909C2211yescharacteristic
45#63909C2211yescharacteristic, complemented
46#63894—21no—
47C2×#3715C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63630C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic
55C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#950—31no—
65C2×#932—31no—
66C2×#919—31no—
67C2×#914—31no—
68#5676D311yescharacteristic, complemented
69#5577—31no—
70#5553—31no—
71C3×#464—31no—
72#5238—31no—
73#5217—31no—
74#5187—31no—
75#5172—31no—
76#5058—31no—
77#5058—31no—
78#5058—61no—
79#5054D311yescharacteristic, complemented
80#5049—31no—
81#5047—31no—
82#5038—31no—
83#5037—31no—
84#5026—31no—
85#5018—31no—
86#5015—31no—
87#5011—31no—
88#4843—31no—
89#4836—31no—
90#4812—31no—
91#4810—31no—
92#4775—31no—
93#4773—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×#239—22no—
104C3×#239—41no—
105C3×D3×D4—22no—
106C3×D3×D4—41no—
107C2×C3×D12—21no—
108C2×C3×D12D411yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#624—21no—
120C2×#624—21no—
121#3799—22no—
122#3799—22no—
123#3799—41no—
124#3799—41no—
125C32×C22⋊C4—21no—
126C32×C22⋊C4—21no—
127C32×C42C2311yescharacteristic
128#3755—22no—
129#3755—41no—
130#3753—22no—
131#3753—41no—
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C3×#217—21no—
135C3×#216—22no—
136C3×#214—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×C4⋊Dic3D411yescharacteristic
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×C4×Dic3—21no—
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149#3722—21no—
150#3722—21no—
151#3715D414yescomplemented
152#3714—22no—
153#3714—22no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×#239C2×D311yescharacteristic
162C2×D3×D4C2×D311yescharacteristic
163C2×#235—31no—
164C2×#235—31no—
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C3×#124—21no—
168C3×#124C2×D311yescharacteristic
169C3×#124C2×D311yescharacteristic
170C3×#123—61no—
171C3×C22⋊Q8—31no—
172C3×#121—31no—
173C3×#121—61no—
174C3×#120—61no—
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C2×C3×C22⋊C4—61no—
179#950—64no—
180#946C2×D311yescharacteristic
181C2×#216C2×D311yescharacteristic, complemented
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—61no—
188C2×#215—61no—
189#940—61no—
190#938C2×D311yescharacteristic
191C2×#214—31no—
192C2×#214C2×D311yescharacteristic
193#932—64no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—61no—
201C2×#213—61no—
202#930—31no—
203#930—31no—
204C2×#208—31no—
205C22×C3⋊C8—31no—
206#919—64no—
207#914—64no—
208C2×D24—31no—
209C2×D24—31no—
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212#895—31no—
213#895—31no—
214#895—61no—
215#895—61no—
216#893—61no—
217#884—21no—
218#884—61no—
219#884—61no—
220#883—21no—
221#882—21no—
222D3×C22⋊C4—21no—
223#874—31no—
224#874—31no—
225#874—61no—
226#874—61no—
227C4×D12—61no—
228C4×D12C2×D311yescharacteristic
229C4×D12C2×D311yescharacteristic
230C4×Dic6C2×D311yescharacteristic, complemented
231C3×C4⋊C8—31no—
232C3×#103—31no—
233C3×#102—31no—
234#835—31no—
235#835C2×D311yescharacteristic, complemented
236#832—31no—
237#832C2×D311yescharacteristic
238#830—31no—
239#830—31no—
240#821—31no—
241#821—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244#810—31no—
245#809—31no—
246#809—31no—
247#809—31no—
248#807—31no—
249#807—31no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251#803—31no—
252#803—31no—
253#803—61no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C22×C3×D3C2×D411yescharacteristic
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—42no—
276C4⋊(C3⋊D3)—81no—
277C3×#67—42no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—41no—
286C3×D12—42no—
287C3×D12C2×D412yes—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×C4×D3—81no—
294C3×Dic6—21no—
295C3×Dic6C2×D412yes—
296#626—42no—
297#626—42no—
298#626—81no—
299#626—81no—
300#624—42no—
301#624—42no—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—31no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—31no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—62no—
324C3×#41—121no—
325C2×C3×Q8—21no—
326C2×C3×Q8—31no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—62no—
335C2×C3×D4—61no—
336C2×C3×D4—121no—
337C2×C3×D4C22×D311yescharacteristic
338C2×C3×D4C22×D311yescharacteristic
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—61no—
342C22×C3×C4—61no—
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349#239—22no—
350#239—41no—
351#239—62no—
352#239—62no—
353#239—121no—
354#239—121no—
355D3×D4—22no—
356D3×D4—41no—
357#235—62no—
358#235—62no—
359#235—121no—
360#235—121no—
361C2×D12—21no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—121no—
377C2×D12—121no—
378C2×D12#6711yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—21no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3C22×D311yescharacteristic
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6C22×D311yescharacteristic
389C3×Q16—62no—
390C3×SD16—62no—
391C2×C3×C8—31no—
392C2×C3×C8—31no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—31no—
395C3×C4⋊C4—31no—
396C3×C4⋊C4—61no—
397C3×C4⋊C4—61no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—21no—
400C3×C22⋊C4—21no—
401C3×C22⋊C4—21no—
402C3×C22⋊C4—31no—
403C3×C22⋊C4—31no—
404C3×C22⋊C4—41no—
405C3×C22⋊C4—41no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C42—21no—
410C3×C42—61no—
411C3×C42C22×D311yescharacteristic
412C3×C42C22×D311yescharacteristic
413#217—21no—
414#216—22no—
415#215—34no—
416#215—62no—
417#215—62no—
418#215—122no—
419#215—121no—
420#215—121no—
421#215—122no—
422#214—22no—
423#214—34no—
424#213—62no—
425#213—62no—
426#213—62no—
427#213—62no—
428#213—122no—
429#213—121no—
430#213—121no—
431#213—122no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4#6711yescharacteristic
439(C2×D3)⋊C4#6711yescharacteristic
440C4⋊Dic3#6711yescharacteristic
441C4⋊Dic3C22×D311yescharacteristic
442C4⋊Dic3C22×D311yescharacteristic
443Dic3⋊C4—21no—
444Dic3⋊C4—21no—
445C4×Dic3—21no—
446#208—62no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8—62no—
454C2×C3⋊C8C22×D311yescharacteristic
455C2×C3⋊C8C22×D311yescharacteristic
456D24—62no—
457D24—62no—
458ΓL(1,𝔽25)—62no—
459D3×C8—62no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—84no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4—41no—
483C32×C4C22×D411yescharacteristic
484C32×C4H(5,𝔽2)11yescharacteristic
485C3×Dic3—22no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—91no—
492C2×#41—91no—
493C22×D4—31no—
494AGL(1,ℤ/8)—184no—
495#135—184no—
496C2×Q16—31no—
497C2×SD16—31no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—91no—
506C22×C8—91no—
507#127—91no—
508#127—181no—
509#124D3211yescharacteristic
510#123—61no—
511C22⋊Q8—31no—
512#121—31no—
513#121—61no—
514#121—91no—
515#121—91no—
516#121—181no—
517#121—181no—
518#120—61no—
519C4×Q8—31no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—181no—
523C2×C22⋊C4—61no—
524#107—91no—
525C4⋊C8—31no—
526#103—31no—
527#103—91no—
528#102—31no—
529#102—91no—
530#102—91no—
531#102—91no—
532C22⋊C8—91no—
533C22⋊C8—91no—
534#97—91no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—31no—
538C23×C3—31no—
539C23×C3—41no—
540C23×C3—61no—
541C23×C3—122no—
542C23×C3—122no—
543C23×C3—241no—
544C22×D3—21no—
545C22×D3—42no—
546C22×D3—42no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—81no—
552C22×D3—121no—
553C22×D3—121no—
554C22×D3C2×#6711yescharacteristic
555C22×D3C2×#6711yescharacteristic
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—32no—
561C3×Q8—41no—
562C3×Q8—41no—
563C3×Q8—61no—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—32no—
569C3×D4—41no—
570C3×D4—41no—
571C3×D4—61no—
572C3×D4—121no—
573C3×D4—122no—
574C3×D4—122no—
575C3×D4—241no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—41no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—122no—
592C2×C3×C4—241no—
593C2×C3×C4D3×D411yescharacteristic
594C2×C3×C4D3×D411yescharacteristic
595C2×C3×C4C2×#6711yescharacteristic
596C2×C3×C4C2×#6711yescharacteristic
597C2×C3×C4C23×D311yescharacteristic
598C2×C3×C4C23×D311yescharacteristic
599#67—42no—
600#67—81no—
601#67—122no—
602#67—122no—
603#67—241no—
604#67—241no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3C2×#6711yescharacteristic
609C2×Dic3C2×#6711yescharacteristic
610D12—21no—
611D12—41no—
612D12—42no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—61no—
621D12—121no—
622D12—121no—
623D12—121no—
624D12—121no—
625D12—122no—
626D12—122no—
627D12—122no—
628D12—122no—
629D12—242no—
630D12—241no—
631D12—241no—
632D12—242no—
633D12—241no—
634D12—241no—
635D12D3×D412yes—
636C4×D3—21no—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—42no—
641C4×D3—81no—
642C4×D3—122no—
643C4×D3—122no—
644C4×D3—122no—
645C4×D3—122no—
646Dic6—21no—
647Dic6D3×D412yes—
648C3×C8—61no—
649C3×C8—61no—
650C3⋊C8—21no—
651C3⋊C8—21no—
652C3⋊C8—32no—
653C3⋊C8—32no—
654C3⋊C8—62no—
655C3⋊C8—62no—
656C3⋊C8—61no—
657C3⋊C8—61no—
658C2×C32—81no—
659C2×C32D4211yescharacteristic
660C2×C32#57511yescharacteristic
661C2×C32#57611yescharacteristic
662C3⋊D3—81no—
663C3⋊D3—81no—
664C3×D3—41no—
665C3×D3—41no—
666C3×D3—42no—
667C24—61no—
668#41—62no—
669#41—121no—
670#41—182no—
671#41—182no—
672#41—361no—
673#41—361no—
674C2×Q8—31no—
675C2×Q8C2×D3211yescharacteristic
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—62no—
681C2×D4—61no—
682C2×D4—91no—
683C2×D4—91no—
684C2×D4—121no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4C2×D3211yescharacteristic
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—181no—
697C22×C4—181no—
698Q16—62no—
699SD16—62no—
700SD16—94no—
701SD16—182no—
702SD16—361no—
703D8—182no—
704D8—182no—
705D8—182no—
706D8—361no—
707M16—182no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—91no—
711C2×C8—91no—
712C2×C8—182no—
713C4⋊C4—31no—
714C4⋊C4—31no—
715C4⋊C4—31no—
716C4⋊C4—61no—
717C4⋊C4—61no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—31no—
721C22⋊C4—31no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C42—61no—
728C42C2×D3211yescharacteristic
729C22×C3—21no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—62no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—244no—
749C22×C3C2×D3×D411yescharacteristic
750C22×C3C22×#6711yescharacteristic
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—22no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—84no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—241no—
774C2×D3—241no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—241no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—62no—
790C3×C4—61no—
791C3×C4—61no—
792C3×C4—81no—
793C3×C4—121no—
794C3×C4—121no—
795C3×C4C2×D3×D411yescharacteristic
796C3×C4C2×D3×D411yescharacteristic
797C3×C4#100411yescharacteristic
798C3×C4#100911yescharacteristic
799Dic3—21no—
800Dic3—21no—
801Dic3—22no—
802Dic3—41no—
803Dic3—41no—
804C32#326811yescharacteristic, complemented, Sylow
805C23—21no—
806C23—31no—
807C23—31no—
808C23—61no—
809C23—122no—
810C23—122no—
811C23—181no—
812C23—181no—
813C23—241no—
814Q8—21no—
815Q8—21no—
816Q8—32no—
817Q8—61no—
818D4—21no—
819D4—21no—
820D4—32no—
821D4—61no—
822D4—121no—
823D4—122no—
824D4—122no—
825D4—181no—
826D4—181no—
827D4—181no—
828D4—181no—
829D4—241no—
830D4—362no—
831D4—362no—
832D4—362no—
833D4—721no—
834D4—721no—
835D4—721no—
836C2×C4—21no—
837C2×C4—31no—
838C2×C4—31no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—122no—
847C2×C4—241no—
848C2×C4—362no—
849C2×C4—362no—
850C2×C4D3×#6711yescharacteristic
851C2×C4D3×#6711yescharacteristic
852C2×C4C22×D3211yescharacteristic
853C8—61no—
854C8—61no—
855C8—92no—
856C8—181no—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—81no—
861C2×C3—81no—
862C2×C3—121no—
863C2×C3—121no—
864C2×C3—122no—
865C2×C3—161no—
866C2×C3#560911yescharacteristic
867C2×C3#576911yescharacteristic
868C2×C3#577711yescharacteristic
869C2×C3D4×#6711yescharacteristic
870C2×C3#582211yescharacteristic
871C2×C3#583511yescharacteristic
872D3—41no—
873D3—41no—
874D3—42no—
875D3—241no—
876D3—241no—
877D3—241no—
878D3—241no—
879D3—481no—
880D3—481no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—61no—
885C22—61no—
886C22—61no—
887C22—61no—
888C22—61no—
889C22—61no—
890C22—62no—
891C22—121no—
892C22—121no—
893C22—244no—
894C22—361no—
895C22—361no—
896C22—361no—
897C22—361no—
898C22—361no—
899C22—361no—
900C22C2×D3×#6711yescharacteristic
901C4—21no—
902C4—21no—
903C4—41no—
904C4—61no—
905C4—61no—
906C4—62no—
907C4—121no—
908C4—121no—
909C4D32×D411yescharacteristic
910C4#6431411yescharacteristic
911C3—21no—
912C3#8062811yescharacteristic, complemented
913C3#8350711yescharacteristic, complemented
914C2—81no—
915C2—121no—
916C2—121no—
917C2—122no—
918C2—721no—
919C2—721no—
920C2#1059528811yescharacteristic
921C2#1059545611yescharacteristic
922C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
hypercenter#124D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5676C2semidirect
2. C2×#63949C2semidirect
3. C2×#63934C2semidirect
4. #10593902C2semidirect
5. #10592757C2semidirect
6. C3×#5054C2semidirect
7. #10591657C2semidirect
8. #10591589C2semidirect
9. #10591588C2semidirect
10. #10591521C2semidirect
11. #10591449C2semidirect
12. #10591448C2semidirect
13. #10590358C2semidirect
14. #10590349C2semidirect
15. #10590330C2semidirect
21. C2×#3799C22semidirect
23. C2×#3755C22semidirect
24. C2×#3755C22semidirect
27. #64083C22semidirect
29. C2×C3×#216C22semidirect
38. C3×C4×Dic6C22semidirect
45. #63909C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63630C22semidirect
53. C3×#835C22semidirect
55. C3×C4⋊(C3⋊C8)C22semidirect
56. #63576C22semidirect
57. #63565C22semidirect
58. #63564C22semidirect
59. #63564C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
68. #5676D3semidirect
79. #5054D3semidirect
151. #3715D4semidirect
181. C2×#216C2×D3semidirect
230. C4×Dic6C2×D3semidirect
235. #835C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
804. C32#3268semidirect
912. C3#80628semidirect
913. C3#83507semidirect

Maximal subgroups

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

subgroupindex
C3×#56762
C2×#639492
C2×#639342
#105939022
#105927572
C3×#50542
#105916572
#105915892
#105915882
#105915212
#105914492
#105914482
#105903582
#105903492
#105903302
#835073
#806283