Finite Group Databasebeta

← #11884012

Subgroups — #11884012

Order 1152.

1164 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5717C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10593899C211yesmaximal, characteristic, complemented
5#10592773C211yesmaximal, characteristic, complemented
6C3×#5075C211yesmaximal, characteristic, complemented
7#10591521C211yesmaximal, characteristic, complemented
8#10591517C211yesmaximal, characteristic, complemented
9#10591462C211yesmaximal, characteristic, complemented
10#10591459C211yesmaximal, characteristic, complemented
11#10591449C211yesmaximal, characteristic, complemented
12#10591448C211yesmaximal, characteristic, complemented
13#10590366C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83491—31nomaximal
17#80404—31nomaximal
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C32×#127C2211yescharacteristic
24C2×#3754C2211yescharacteristic, complemented
25C2×#3754C2211yescharacteristic, complemented
26C2×#3753C2211yescharacteristic, complemented
27C2×#3753C2211yescharacteristic, complemented
28#64084C2211yescharacteristic, complemented
29C3×#938—21no—
30C3×#938C2211yescharacteristic
31C3×#938C2211yescharacteristic
32C3×#937—21no—
33C3×#937—21no—
34C2×C3×#214C2211yescharacteristic, complemented
35C2×C3×#214C2211yescharacteristic, complemented
36C3×C4×D12C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic, complemented
39#63934—24no—
40D3×#214—24no—
41#63909C2211yescharacteristic, complemented
42#63895—21no—
43#63886—21no—
44#63880—21no—
45#63857C2211yescharacteristic, complemented
46#63852—21no—
47C2×#3716C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63630C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×D42—31no—
64C22×#214—31no—
65C2×#932—31no—
66C2×#914—31no—
67C2×D3×SD16—31no—
68#5717D311yescharacteristic, complemented
69#5576—31no—
70#5552—31no—
71C3×#460—31no—
72#5218—31no—
73#5217—31no—
74#5172—31no—
75#5170—31no—
76#5075D311yescharacteristic, complemented
77#5074—31no—
78#5074—31no—
79#5074—61no—
80#5042—31no—
81#5040—31no—
82#5038—31no—
83#5037—31no—
84#5026—31no—
85#5018—31no—
86#5016—31no—
87#5011—31no—
88#4844—31no—
89#4836—31no—
90#4780—31no—
91#4776—31no—
92#4775—31no—
93#4773—31no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4—21no—
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×#634C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C3×D3×D4—22no—
107C3×D3×D4—22no—
108C3×D3×D4—41no—
109C3×D3×D4—41no—
110C3×D3×D4—44no—
111C2×C3×D12D411yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#627—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#624—21no—
121C2×D3×Dic3—21no—
122#3799—22no—
123#3799—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C32×C42C2311yescharacteristic
127#3754—22no—
128#3754—41no—
129#3753—22no—
130#3753—41no—
131#3752—21no—
132#3752—21no—
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#217—21no—
136C3×#217—21no—
137C3×#214—22no—
138C3×#214—22no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3D411yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×C4⋊Dic3C2311yescharacteristic
145C3×Dic3⋊C4—21no—
146C3×C4×Dic3—21no—
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149Dic3⋊Dic3—21no—
150#3722—21no—
151(C2×D3)⋊Dic3—21no—
152#3716—22no—
153#3715D414yescomplemented
154#3714—22no—
155#3711—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C22×C3×D4—61no—
161C2×#239—31no—
162C2×D3×Q8—31no—
163C2×D3×D4—21no—
164C2×D3×D4C2×D311yescharacteristic
165C2×D3×D4C2×D311yescharacteristic
166C2×#235—31no—
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C3×#127—21no—
171C3×#127C2×D311yescharacteristic
172C3×#127C2×D311yescharacteristic
173C3×#121—31no—
174C3×#121—31no—
175C3×#121—61no—
176C3×#120—61no—
177C3×#120—61no—
178C3×C4×Q8—31no—
179C3×C4×D4—31no—
180C3×C4×D4—31no—
181C2×#215—31no—
182#939—61no—
183#938—21no—
184#938C2×D311yescharacteristic
185#938C2×D311yescharacteristic
186#937—21no—
187#937—21no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—61no—
195C2×#214—61no—
196C2×#214—64no—
197C2×#214C2×D311yescharacteristic, complemented
198C2×#214C2×D311yescharacteristic, complemented
199#932—64no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—61no—
206C2×#213—61no—
207#930—31no—
208#924—31no—
209C2×#208—31no—
210C22×C3⋊C8—31no—
211#914—64no—
212D3×SD16—64no—
213C2×D24—31no—
214C2×#204—31no—
215C2×ΓL(1,𝔽25)—31no—
216C2×D3×C8—31no—
217#897—31no—
218#897—61no—
219#896—61no—
220#895—31no—
221#895—61no—
222#885—61no—
223#67⋊C4—61no—
224#875—31no—
225#875—31no—
226#875—61no—
227#875—61no—
228C4×D12—61no—
229C4×D12C2×D311yescharacteristic
230C4×D12C2×D311yescharacteristic
231C4×Dic6C2×D311yescharacteristic, complemented
232C3×C4⋊C8—31no—
233C3×#102—31no—
234C3×#102—31no—
235#835—31no—
236#832—31no—
237#832C2×D311yescharacteristic, complemented
238#832C2×D311yescharacteristic, complemented
239#830—31no—
240#830—31no—
241#821—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244#816—31no—
245#810—31no—
246#810—31no—
247#809—31no—
248#809—31no—
249#807—31no—
250#807—31no—
251C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
252#803—31no—
253#803—31no—
254#803—61no—
255C23×C32—21no—
256C23×C32—21no—
257C22×C3⋊D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—81no—
264C22×C3×D3—81no—
265C22×C3×D3C2×D411yescharacteristic
266C22×C3×D3C2×D411yescharacteristic
267C32×D4—21no—
268C32×D4—21no—
269C32×D4—21no—
270C32×D4—21no—
271C32×D4—42no—
272C32×D4—81no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276C2×C3⋊Dic3—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—21no—
279#634—21no—
280#634—21no—
281C3×#67—42no—
282C3×#67—42no—
283C3×#67—42no—
284C3×#67—42no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C3×D12—22no—
291C3×D12—21no—
292C3×D12C2×D412yes—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—21no—
297C3×C4×D3—42no—
298C3×Dic6—21no—
299C3×Dic6C2×D412yescomplemented
300#627—42no—
301#626—42no—
302#626—42no—
303#624—42no—
304D3×Dic3—42no—
305C3⋊(C3⋊C8)—21no—
306C3⋊(C3⋊C8)C2×D412yescomplemented
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—31no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—31no—
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—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—41no—
338C2×C3×D4—41no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—62no—
342C2×C3×D4—62no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—121no—
346C2×C3×D4—121no—
347C2×C3×D4—124no—
348C2×C3×D4C22×D311yescharacteristic
349C2×C3×D4C22×D311yescharacteristic
350C2×C3×D4C22×D311yescharacteristic
351C2×C3×D4C22×D311yescharacteristic
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—61no—
355C2×#67—21no—
356C2×#67—21no—
357C2×#67—21no—
358C2×#67—21no—
359C2×#67—61no—
360C2×#67—61no—
361C22×Dic3—61no—
362#239—62no—
363#239—121no—
364D3×Q8—62no—
365D3×Q8—121no—
366D3×D4—22no—
367D3×D4—22no—
368D3×D4—41no—
369D3×D4—41no—
370D3×D4—44no—
371#235—62no—
372#235—121no—
373C2×D12—31no—
374C2×D12—31no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12#6711yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3C22×D311yescharacteristic
385C2×C4×D3C22×D311yescharacteristic
386C2×Dic6—31no—
387C2×Dic6—31no—
388C2×Dic6—61no—
389C2×Dic6—62no—
390C2×Dic6—61no—
391C2×Dic6—61no—
392C2×Dic6—121no—
393C2×Dic6C22×D311yescharacteristic
394C3×SD16—62no—
395C3×SD16—62no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—31no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4—61no—
402C3×C22⋊C4—31no—
403C3×C22⋊C4—31no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C42—21no—
408C3×C42—61no—
409C3×C42C22×D311yescharacteristic
410C3×C42C22×D311yescharacteristic
411#217—21no—
412#217—21no—
413#217—61no—
414#215—34no—
415#214—22no—
416#214—22no—
417#214—34no—
418#214—62no—
419#214—62no—
420#214—62no—
421#214—122no—
422#214—121no—
423#214—121no—
424#214—122no—
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—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—121no—
441(C2×D3)⋊C4—121no—
442(C2×D3)⋊C4#6711yescharacteristic
443(C2×D3)⋊C4#6711yescharacteristic
444C4⋊Dic3—61no—
445C4⋊Dic3#6711yescharacteristic
446C4⋊Dic3C22×D311yescharacteristic
447C4⋊Dic3C22×D311yescharacteristic
448Dic3⋊C4—21no—
449Dic3⋊C4—61no—
450C4×Dic3—21no—
451#208—62no—
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—62no—
459C2×C3⋊C8C22×D311yescharacteristic
460C2×C3⋊C8C22×D311yescharacteristic
461D24—62no—
462#204—62no—
463ΓL(1,𝔽25)—62no—
464D3×C8—62no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32C22×D411yescharacteristic
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—22no—
479C2×C3×D3—21no—
480C2×C3×D3—21no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—84no—
484C2×C3×D3—84no—
485C2×C3×D3AGL(1,ℤ/8)12yescomplemented
486C32×C4—21no—
487C32×C4—21no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
490C3⋊Dic3—41no—
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—91no—
497C22×Q8—91no—
498C22×D4—31no—
499C22×D4—31no—
500C22×D4—61no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—91no—
510C2×D8—91no—
511C2×D8—91no—
512C2×M16—91no—
513C22×C8—91no—
514#127D3211yescharacteristic
515#124—91no—
516#124—181no—
517C22⋊Q8—91no—
518C22⋊Q8—181no—
519#121—31no—
520#121—31no—
521#121—61no—
522#121—91no—
523#121—181no—
524#120—61no—
525#120—61no—
526C4×Q8—31no—
527C4×D4—31no—
528C4×D4—31no—
529C4×D4—181no—
530#107—91no—
531C4⋊C8—31no—
532#103—91no—
533#103—91no—
534#102—31no—
535#102—31no—
536#102—91no—
537#102—91no—
538C22⋊C8—91no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—31no—
546C23×C3—31no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—61no—
550C23×C3—122no—
551C23×C3—122no—
552C23×C3—122no—
553C23×C3—122no—
554C23×C3—241no—
555C23×C3—241no—
556C22×D3—21no—
557C22×D3—42no—
558C22×D3—42no—
559C22×D3—42no—
560C22×D3—42no—
561C22×D3—61no—
562C22×D3—61no—
563C22×D3—81no—
564C22×D3—81no—
565C22×D3—121no—
566C22×D3C2×#6711yescharacteristic
567C22×D3C2×#6711yescharacteristic
568C3×Q8—32no—
569C3×Q8—61no—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—32no—
579C3×D4—41no—
580C3×D4—41no—
581C3×D4—41no—
582C3×D4—41no—
583C3×D4—42no—
584C3×D4—42no—
585C3×D4—62no—
586C3×D4—61no—
587C3×D4—82no—
588C3×D4—81no—
589C3×D4—81no—
590C3×D4—82no—
591C3×D4—122no—
592C3×D4—122no—
593C3×D4—122no—
594C3×D4—122no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—122no—
608C2×C3×C4D3×D411yescharacteristic
609C2×C3×C4D3×D411yescharacteristic
610C2×C3×C4C2×#6711yescharacteristic
611C2×C3×C4C2×#6711yescharacteristic
612C2×C3×C4C23×D311yescharacteristic
613C2×C3×C4C23×D311yescharacteristic
614#67—42no—
615#67—42no—
616#67—42no—
617#67—42no—
618#67—122no—
619#67—122no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—121no—
626C2×Dic3—122no—
627C2×Dic3C2×#6711yescharacteristic
628C2×Dic3C2×#6711yescharacteristic
629D12—22no—
630D12—21no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—121no—
636D12—121no—
637D12—122no—
638D12—122no—
639D12D3×D412yes—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—21no—
643C4×D3—21no—
644C4×D3—42no—
645C4×D3—122no—
646C4×D3—122no—
647C4×D3—122no—
648Dic6—21no—
649Dic6—61no—
650Dic6—61no—
651Dic6—61no—
652Dic6—61no—
653Dic6—121no—
654Dic6—121no—
655Dic6—122no—
656Dic6—122no—
657Dic6D3×D412yescomplemented
658C3×C8—61no—
659C3×C8—61no—
660C3⋊C8—21no—
661C3⋊C8—21no—
662C3⋊C8—32no—
663C3⋊C8—32no—
664C3⋊C8—62no—
665C3⋊C8—62no—
666C3⋊C8—61no—
667C3⋊C8—61no—
668C2×C32—81no—
669C2×C32—81no—
670C2×C32D4211yescharacteristic
671C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
672C2×C32#57711yescharacteristic
673C3⋊D3—81no—
674C3×D3—22no—
675C3×D3—41no—
676C3×D3—42no—
677C24—61no—
678C24—61no—
679#41—182no—
680#41—361no—
681C2×Q8—31no—
682C2×Q8—91no—
683C2×Q8—181no—
684C2×Q8—182no—
685C2×Q8—361no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4—62no—
693C2×D4—62no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—91no—
697C2×D4—121no—
698C2×D4—121no—
699C2×D4—124no—
700C2×D4—181no—
701C2×D4—181no—
702C2×D4C2×D3211yescharacteristic
703C2×D4C2×D3211yescharacteristic
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—61no—
707C22×C4—181no—
708C22×C4—181no—
709SD16—62no—
710SD16—62no—
711SD16—94no—
712SD16—182no—
713SD16—182no—
714SD16—361no—
715D8—182no—
716D8—182no—
717D8—361no—
718M16—182no—
719C2×C8—31no—
720C2×C8—31no—
721C2×C8—91no—
722C2×C8—91no—
723C2×C8—182no—
724C4⋊C4—31no—
725C4⋊C4—31no—
726C4⋊C4—31no—
727C4⋊C4—61no—
728C4⋊C4—181no—
729C22⋊C4—31no—
730C22⋊C4—31no—
731C22⋊C4—61no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C42—61no—
739C42C2×D3211yescharacteristic
740C22×C3—21no—
741C22×C3—32no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—61no—
755C22×C3—61no—
756C22×C3—61no—
757C22×C3—61no—
758C22×C3—61no—
759C22×C3—62no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3—81no—
763C22×C3—81no—
764C22×C3—81no—
765C22×C3—81no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—244no—
769C22×C3—244no—
770C22×C3C2×D3×D411yescharacteristic
771C22×C3C22×#6711yescharacteristic
772C2×D3—21no—
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—21no—
776C2×D3—22no—
777C2×D3—21no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—84no—
781C2×D3—84no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—241no—
789C2×D3—241no—
790C2×D3—241no—
791C2×D3#93212yescomplemented
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—41no—
799C3×C4—41no—
800C3×C4—62no—
801C3×C4—61no—
802C3×C4—61no—
803C3×C4—121no—
804C3×C4—121no—
805C3×C4C2×D3×D411yescharacteristic
806C3×C4C2×D3×D411yescharacteristic
807C3×C4#100411yescharacteristic
808C3×C4#100911yescharacteristic
809Dic3—21no—
810Dic3—21no—
811Dic3—22no—
812Dic3—41no—
813Dic3—41no—
814Dic3—121no—
815Dic3—121no—
816Dic3—241no—
817C32#326511yescharacteristic, complemented, Sylow
818C23—21no—
819C23—21no—
820C23—31no—
821C23—31no—
822C23—61no—
823C23—122no—
824C23—122no—
825C23—122no—
826C23—122no—
827C23—181no—
828C23—241no—
829C23—241no—
830Q8—32no—
831Q8—61no—
832Q8—181no—
833Q8—181no—
834Q8—362no—
835D4—21no—
836D4—21no—
837D4—21no—
838D4—21no—
839D4—32no—
840D4—42no—
841D4—62no—
842D4—61no—
843D4—81no—
844D4—122no—
845D4—122no—
846D4—122no—
847D4—122no—
848D4—181no—
849D4—181no—
850D4—362no—
851D4—362no—
852C2×C4—31no—
853C2×C4—31no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—122no—
862C2×C4—181no—
863C2×C4—362no—
864C2×C4—362no—
865C2×C4D3×#6711yescharacteristic
866C2×C4D3×#6711yescharacteristic
867C2×C4C22×D3211yescharacteristic
868C8—61no—
869C8—61no—
870C8—92no—
871C8—181no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—62no—
876C2×C3—81no—
877C2×C3—81no—
878C2×C3—81no—
879C2×C3—81no—
880C2×C3—121no—
881C2×C3—122no—
882C2×C3—161no—
883C2×C3—161no—
884C2×C3#560911yescharacteristic
885C2×C3#576211yescharacteristic
886C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
887C2×C3C2×#93211yescharacteristic
888C2×C3D4×#6711yescharacteristic
889C2×C3#583611yescharacteristic
890D3—22no—
891D3—41no—
892D3—42no—
893D3—241no—
894D3—241no—
895D3—481no—
896C22—32no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—61no—
904C22—61no—
905C22—61no—
906C22—61no—
907C22—61no—
908C22—62no—
909C22—121no—
910C22—121no—
911C22—244no—
912C22—244no—
913C22—361no—
914C22—361no—
915C22—361no—
916C22C2×D3×#6711yescharacteristic
917C4—21no—
918C4—21no—
919C4—61no—
920C4—61no—
921C4—62no—
922C4—121no—
923C4—121no—
924C4—361no—
925C4D32×D411yescharacteristic
926C4#6431411yescharacteristic
927C3—21no—
928C3#8040411yescharacteristic, complemented
929C3#8349111yescharacteristic, complemented
930C2—62no—
931C2—81no—
932C2—81no—
933C2—121no—
934C2—122no—
935C2—721no—
936C2D3×#93211yescharacteristic
937C2#1059510511yescharacteristic
938C2#1059528811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5717C2semidirect
2. C2×#63934C2semidirect
3. C2×D3×#214C2semidirect
4. #10593899C2semidirect
5. #10592773C2semidirect
6. C3×#5075C2semidirect
7. #10591521C2semidirect
8. #10591517C2semidirect
9. #10591462C2semidirect
10. #10591459C2semidirect
11. #10591449C2semidirect
12. #10591448C2semidirect
13. #10590366C2semidirect
14. #10590358C2semidirect
15. #10590330C2semidirect
21. C2×#3799C22semidirect
22. C2×D3×Dic6C22semidirect
24. C2×#3754C22semidirect
25. C2×#3754C22semidirect
26. C2×#3753C22semidirect
27. C2×#3753C22semidirect
28. #64084C22semidirect
34. C2×C3×#214C22semidirect
35. C2×C3×#214C22semidirect
38. C3×C4×Dic6C22semidirect
41. #63909C22semidirect
45. #63857C22semidirect
50. C2×#3711C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63630C22semidirect
53. C3×#832C22semidirect
54. C3×#832C22semidirect
55. C3×C4⋊(C3⋊C8)C22semidirect
56. #63576C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
59. #63564C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
68. #5717D3semidirect
76. #5075D3semidirect
153. #3715D4semidirect
197. C2×#214C2×D3semidirect
198. C2×#214C2×D3semidirect
231. C4×Dic6C2×D3semidirect
237. #832C2×D3semidirect
238. #832C2×D3semidirect
251. C4⋊(C3⋊C8)C2×D3semidirect
299. C3×Dic6C2×D4semidirect
306. C3⋊(C3⋊C8)C2×D4semidirect
485. C2×C3×D3AGL(1,ℤ/8)semidirect
657. Dic6D3×D4semidirect
791. C2×D3#932semidirect
817. C32#3265semidirect
928. C3#80404semidirect
929. C3#83491semidirect

Maximal subgroups

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

subgroupindex
C3×#57172
C2×#639342
C2×D3×#2142
#105938992
#105927732
C3×#50752
#105915212
#105915172
#105914622
#105914592
#105914492
#105914482
#105903662
#105903582
#105903302
#834913
#804043