Finite Group Databasebeta

← #11884009

Subgroups — #11884009

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
1C2×#63794C211yesmaximal, characteristic, complemented
2C2×D3×#204C211yesmaximal, characteristic, complemented
3D122C211yesmaximal, characteristic, complemented
4#10593899C211yesmaximal, characteristic, complemented
5#10592411C211yesmaximal, characteristic, complemented
6C3×#4710C211yesmaximal, characteristic, complemented
7C3×#4706C211yesmaximal, characteristic, complemented
8#10590967C211yesmaximal, characteristic, complemented
9#10590951C211yesmaximal, characteristic, complemented
10#10590947C211yesmaximal, characteristic, complemented
11#10590946C211yesmaximal, characteristic, complemented
12#10590838C211yesmaximal, characteristic, complemented
13#10590832C211yesmaximal, characteristic, complemented
14#10590367C211yesmaximal, characteristic, complemented
15#10590366C211yesmaximal, characteristic, complemented
16#79794—31nomaximal
17#79494—31nomaximal
18C2×D3×D12—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×#3745C2211yescharacteristic, complemented
24C2×#3745C2211yescharacteristic, complemented
25C2×#3744C2211yescharacteristic, complemented
26C2×#3744C2211yescharacteristic, complemented
27#64084C2211yescharacteristic, complemented
28#64083C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
31C2×C3×D3×C8C2211yescharacteristic, complemented
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34C3×C4×Dic6C2211yescharacteristic, complemented
35#63923—21no—
36#63923—21no—
37#63909—21no—
38#63909C2211yescharacteristic
39#63909C2211yescharacteristic
40#63909C2211yescharacteristic, complemented
41#63895—21no—
42#63886—21no—
43#63880—21no—
44#63857C2211yescharacteristic, complemented
45#63852—21no—
46C2×#3717C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50#63794—24no—
51D3×#204—24no—
52C32×#97C2211yescharacteristic, complemented
53C3×#821C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×#818C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×D3×SD16—31no—
65C2×#908—31no—
66C22×#204—31no—
67#5576—31no—
68#5552—31no—
69D4×D12—31no—
70D4×D12—31no—
71C3×#440—31no—
72C3×#435—31no—
73#5134—31no—
74#5115—31no—
75#5027—31no—
76#5016—31no—
77#4886—31no—
78#4883—31no—
79#4848—31no—
80#4844—31no—
81#4810—31no—
82#4806—31no—
83#4776—31no—
84#4773—31no—
85#4738—31no—
86#4734—31no—
87#4732—31no—
88#4731—31no—
89#4712—31no—
90#4712—31no—
91#4712—61no—
92#4710D311yescharacteristic, complemented
93#4706D311yescharacteristic, complemented
94C22×D32—21no—
95C22×D32—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×#634C2311yescharacteristic
102C2×C3×D12D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—22no—
119D3×D12—41no—
120D3×D12—41no—
121D3×D12—44no—
122#3799—22no—
123#3799—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128C32×C42C2311yescharacteristic
129#3752—21no—
130#3752—21no—
131#3745—22no—
132#3745—41no—
133#3744—22no—
134#3744—41no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3D411yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×C4×Dic3—21no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C3×#204D414yescomplemented
146C3×ΓL(1,𝔽25)—22no—
147C3×D3×C8—22no—
148Dic3⋊Dic3—21no—
149#3722—21no—
150#3722—21no—
151#3722—21no—
152(C2×D3)⋊Dic3—21no—
153#3717—22no—
154#3717—22no—
155#3716—22no—
156#3714—22no—
157#3265—91noSylow
158C2×#239—31no—
159C2×D3×Q8—31no—
160C2×D3×D4—31no—
161C2×D3×D4—31no—
162C2×D3×D4—61no—
163C2×#235—31no—
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—61no—
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×M16—31no—
170C22×C3×C8—31no—
171C3×C4×Q8—31no—
172C3×C4×D4—31no—
173C3×C4×D4—31no—
174C2×#215—31no—
175C2×#215—31no—
176#939—61no—
177C2×#214—31no—
178C2×#213—31no—
179#930—31no—
180#930—31no—
181#930—31no—
182#930—61no—
183#924—31no—
184#914—64no—
185D3×SD16—64no—
186#908—64no—
187C2×D24—31no—
188C2×D24—31no—
189C2×D24—31no—
190C2×D24—31no—
191C2×D24—31no—
192C2×D24—61no—
193C2×D24—61no—
194C2×#204—31no—
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—61no—
202C2×#204—61no—
203C2×#204—64no—
204C2×#204C2×D311yescharacteristic
205C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
206C2×D3×C8C2×D311yescharacteristic, complemented
207#897—31no—
208#897—61no—
209#896—61no—
210#895—31no—
211#895—31no—
212#895—31no—
213#895—61no—
214#895—61no—
215#885—61no—
216#882—61no—
217#882—61no—
218#882—61no—
219#882—61no—
220#67⋊C4—61no—
221#875—31no—
222#875—31no—
223#875—61no—
224#875—61no—
225#874—31no—
226#874—31no—
227#874—61no—
228C4×D12—61no—
229C4×D12C2×D311yescharacteristic
230C4×D12C2×D311yescharacteristic
231C4×Dic6C2×D311yescharacteristic, complemented
232C3×#107—31no—
233C3×C4⋊C8—31no—
234C3×#103—31no—
235C3×#102—31no—
236C3×C22⋊C8—31no—
237C3×C22⋊C8—31no—
238C3×#97—21no—
239C3×#97C2×D311yescharacteristic, complemented
240C3×#97C2×D311yescharacteristic, complemented
241#821—31no—
242#821—31no—
243#821—31no—
244#821C2×D311yescharacteristic
245(C2×D3)⋊C8C2×D311yescharacteristic, complemented
246(C2×D3)⋊C8C2×D311yescharacteristic, complemented
247#818C2×D311yescharacteristic, complemented
248#816—31no—
249#816C2×D311yescharacteristic, complemented
250#810—31no—
251#809—31no—
252#809—31no—
253#809—31no—
254C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—42no—
278C4⋊(C3⋊D3)—81no—
279#634—21no—
280#634—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—22no—
287C3×D12—21no—
288C3×D12C2×D412yes—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6C2×D412yescomplemented
296#627—42no—
297#626—42no—
298#626—42no—
299#626—42no—
300#626—42no—
301#626—42no—
302#626—42no—
303#624—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C32×C8C2×D412yescomplemented
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
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—31no—
323#435—31no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C22×Dic3—61no—
341#239—62no—
342#239—121no—
343D3×Q8—62no—
344D3×Q8—121no—
345D3×D4—62no—
346D3×D4—62no—
347D3×D4—121no—
348D3×D4—121no—
349D3×D4—124no—
350#235—62no—
351#235—121no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—31no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—62no—
362C2×D12—62no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—121no—
374C2×D12—121no—
375C2×D12—121no—
376C2×D12—121no—
377C2×D12—124no—
378C2×D12D1211yescharacteristic
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—34no—
395C3×M16—62no—
396C2×C3×C8—21no—
397C2×C3×C8—21no—
398C2×C3×C8—31no—
399C2×C3×C8—31no—
400C2×C3×C8—62no—
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C2×C3×C8C22×D311yescharacteristic
405C3×C4⋊C4—31no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—61no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—31no—
411C3×C22⋊C4—61no—
412C3×C42—21no—
413C3×C42—61no—
414C3×C42C22×D311yescharacteristic
415C3×C42C22×D311yescharacteristic
416#217—61no—
417#215—62no—
418#215—62no—
419#214—62no—
420#213—62no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—121no—
434(C2×D3)⋊C4—121no—
435(C2×D3)⋊C4D1211yescharacteristic
436(C2×D3)⋊C4D1211yescharacteristic
437C4⋊Dic3—61no—
438C4⋊Dic3D1211yescharacteristic
439C4⋊Dic3C22×D311yescharacteristic
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—21no—
442Dic3⋊C4—61no—
443C4×Dic3—21no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446D24—62no—
447D24—62no—
448D24—62no—
449D24—122no—
450D24—121no—
451D24—121no—
452D24—122no—
453#204—62no—
454#204—62no—
455#204—62no—
456#204—62no—
457#204—62no—
458#204—122no—
459#204—121no—
460#204—121no—
461#204—122no—
462#204D1214yescomplemented
463ΓL(1,𝔽25)—22no—
464D3×C8—22no—
465C22×C32C22×D411yescharacteristic
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
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×D3AGL(1,ℤ/8)12yescomplemented
484D32—84no—
485D32—84no—
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—91no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—91no—
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—31no—
513C22×C8—31no—
514#127—91no—
515#124—91no—
516#124—181no—
517C22⋊Q8—91no—
518C22⋊Q8—181no—
519#121—91no—
520#121—91no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—31no—
527C4×D4—31no—
528C4×D4—31no—
529C4×D4—181no—
530#107—31no—
531C4⋊C8—31no—
532#103—31no—
533#103—91no—
534#102—31no—
535#102—91no—
536#102—91no—
537#102—91no—
538C22⋊C8—31no—
539C22⋊C8—31no—
540#97D3211yescharacteristic, complemented
541C23×C3—31no—
542C23×C3—31no—
543C23×C3—61no—
544C22×D3—21no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—121no—
552C22×D3—121no—
553C22×D3—121no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3—241no—
565C22×D3—241no—
566C22×D3C2×D1211yescharacteristic
567C22×D3C2×D1211yescharacteristic
568C3×Q8—32no—
569C3×Q8—61no—
570C3×D4—32no—
571C3×D4—62no—
572C3×D4—61no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—122no—
586C2×C3×C4C2×D1211yescharacteristic
587C2×C3×C4C2×D1211yescharacteristic
588C2×C3×C4D3×D411yescharacteristic
589C2×C3×C4D3×D411yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—121no—
604C2×Dic3—122no—
605C2×Dic3C2×D1211yescharacteristic
606C2×Dic3C2×D1211yescharacteristic
607D12—22no—
608D12—21no—
609D12—61no—
610D12—61no—
611D12—61no—
612D12—61no—
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—121no—
626D12—121no—
627D12—122no—
628D12—122no—
629D12—122no—
630D12—122no—
631D12—122no—
632D12—122no—
633D12—122no—
634D12—122no—
635D12—242no—
636D12—241no—
637D12—241no—
638D12—242no—
639D12C2×D1212yes—
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—
657Dic6C2×D1212yescomplemented
658C3×C8—22no—
659C3×C8—21no—
660C3×C8—21no—
661C3×C8—22no—
662C3×C8—61no—
663C3×C8—61no—
664C3×C8C2×D1212yescomplemented
665C3×C8D3×D412yescomplemented
666C3⋊C8—21no—
667C3⋊C8—21no—
668C2×C32D4211yescharacteristic
669C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
670C2×C32#57711yescharacteristic
671C3⋊D3—81no—
672C3⋊D3—81no—
673C3⋊D3—81no—
674C3×D3—22no—
675C3×D3—41no—
676C3×D3—42no—
677C24—181no—
678C24—181no—
679#41—182no—
680#41—361no—
681C2×Q8—31no—
682C2×Q8—91no—
683C2×Q8—181no—
684C2×Q8—182no—
685C2×Q8—361no—
686C2×D4—31no—
687C2×D4—31no—
688C2×D4—91no—
689C2×D4—91no—
690C2×D4—91no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—182no—
694C2×D4—182no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—361no—
702C2×D4—361no—
703C2×D4—364no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—61no—
707C22×C4—181no—
708C22×C4—181no—
709SD16—34no—
710SD16—182no—
711SD16—182no—
712SD16—182no—
713SD16—182no—
714SD16—361no—
715D8—182no—
716D8—182no—
717D8—361no—
718M16—62no—
719C2×C8—31no—
720C2×C8—31no—
721C2×C8—62no—
722C2×C8C2×D3211yescharacteristic
723C2×C8C2×D3211yescharacteristic
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—181no—
733C22⋊C4—181no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C42—61no—
739C42C2×D3211yescharacteristic
740C22×C3—21no—
741C22×C3—32no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—62no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3C22×D1211yescharacteristic
751C22×C3C2×D3×D411yescharacteristic
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—22no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—121no—
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—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—241no—
781C2×D3—241no—
782C2×D3—241no—
783C2×D3—241no—
784C2×D3—241no—
785C2×D3—241no—
786C2×D3—241no—
787C2×D3—244no—
788C2×D3—244no—
789C2×D3—244no—
790C2×D3—244no—
791C2×D3#90812yescomplemented
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—61no—
801C3×C4—62no—
802C3×C4—61no—
803C3×C4—121no—
804C3×C4—121no—
805C3×C4C22×D1211yescharacteristic
806C3×C4C2×D3×D411yescharacteristic
807C3×C4#100911yescharacteristic
808C3×C4#100911yescharacteristic
809Dic3—22no—
810Dic3—21no—
811Dic3—21no—
812Dic3—41no—
813Dic3—41no—
814Dic3—121no—
815Dic3—121no—
816Dic3—241no—
817C32#326511yescharacteristic, complemented, Sylow
818C23—31no—
819C23—31no—
820C23—61no—
821C23—181no—
822C23—181no—
823C23—181no—
824C23—362no—
825C23—362no—
826C23—362no—
827C23—362no—
828C23—721no—
829C23—721no—
830Q8—32no—
831Q8—61no—
832Q8—181no—
833Q8—181no—
834Q8—362no—
835D4—32no—
836D4—62no—
837D4—61no—
838D4—181no—
839D4—181no—
840D4—181no—
841D4—181no—
842D4—181no—
843D4—181no—
844D4—362no—
845D4—362no—
846D4—362no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—362no—
851D4—721no—
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×D1211yescharacteristic
866C2×C4D3×D1211yescharacteristic
867C2×C4C22×D3211yescharacteristic
868C8—21no—
869C8—61no—
870C8—61no—
871C8D3×D1212yescomplemented
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—62no—
876C2×C3—122no—
877C2×C3—121no—
878C2×C3D4×D1211yescharacteristic
879C2×C3D4×D1211yescharacteristic
880C2×C3C2×#90811yescharacteristic
881C2×C3#575111yescharacteristic
882C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
883C2×C3#577811yescharacteristic
884D3—22no—
885D3—41no—
886D3—42no—
887D3—241no—
888D3—241no—
889D3—241no—
890D3—241no—
891D3—241no—
892D3—241no—
893D3—481no—
894D3—481no—
895D3—481no—
896C22—32no—
897C22—61no—
898C22—61no—
899C22—61no—
900C22—61no—
901C22—61no—
902C22—62no—
903C22—121no—
904C22—121no—
905C22—361no—
906C22—361no—
907C22—361no—
908C22—361no—
909C22—361no—
910C22—361no—
911C22—361no—
912C22—361no—
913C22—361no—
914C22—724no—
915C22—724no—
916C22C2×D3×D1211yescharacteristic
917C4—21no—
918C4—21no—
919C4—61no—
920C4—61no—
921C4—62no—
922C4—121no—
923C4—121no—
924C4—361no—
925C4C2×D3×D1211yescharacteristic
926C4#6430811yescharacteristic
927C3—21no—
928C3#7949411yescharacteristic, complemented
929C3#7979411yescharacteristic, complemented
930C2—62no—
931C2—121no—
932C2—122no—
933C2—721no—
934C2—721no—
935C2—721no—
936C2D12211yescharacteristic
937C2D3×#90811yescharacteristic
938C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
hypercenter#97D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×#63794C2semidirect
2. C2×D3×#204C2semidirect
3. D122C2semidirect
4. #10593899C2semidirect
5. #10592411C2semidirect
6. C3×#4710C2semidirect
7. C3×#4706C2semidirect
8. #10590967C2semidirect
9. #10590951C2semidirect
10. #10590947C2semidirect
11. #10590946C2semidirect
12. #10590838C2semidirect
13. #10590832C2semidirect
14. #10590367C2semidirect
15. #10590366C2semidirect
21. C2×#3799C22semidirect
22. C2×D3×Dic6C22semidirect
23. C2×#3745C22semidirect
24. C2×#3745C22semidirect
25. C2×#3744C22semidirect
26. C2×#3744C22semidirect
27. #64084C22semidirect
30. C2×C3×ΓL(1,𝔽25)C22semidirect
31. C2×C3×D3×C8C22semidirect
34. C3×C4×Dic6C22semidirect
40. #63909C22semidirect
44. #63857C22semidirect
46. C2×#3717C22semidirect
47. C2×#3717C22semidirect
52. C32×#97C22semidirect
54. C3×(C2×D3)⋊C8C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×#818C22semidirect
57. C3×#816C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63564C22semidirect
92. #4710D3semidirect
93. #4706D3semidirect
145. C3×#204D4semidirect
205. C2×ΓL(1,𝔽25)C2×D3semidirect
206. C2×D3×C8C2×D3semidirect
231. C4×Dic6C2×D3semidirect
239. C3×#97C2×D3semidirect
240. C3×#97C2×D3semidirect
245. (C2×D3)⋊C8C2×D3semidirect
246. (C2×D3)⋊C8C2×D3semidirect
247. #818C2×D3semidirect
249. #816C2×D3semidirect
254. C4⋊(C3⋊C8)C2×D3semidirect
295. C3×Dic6C2×D4semidirect
306. C32×C8C2×D4semidirect
462. #204D12semidirect
483. C2×C3×D3AGL(1,ℤ/8)semidirect
540. #97D32semidirect
657. Dic6C2×D12semidirect
664. C3×C8C2×D12semidirect
665. C3×C8D3×D4semidirect
791. C2×D3#908semidirect
817. C32#3265semidirect
871. C8D3×D12semidirect
928. C3#79494semidirect
929. C3#79794semidirect

Maximal subgroups

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

subgroupindex
C2×#637942
C2×D3×#2042
D1222
#105938992
#105924112
C3×#47102
C3×#47062
#105909672
#105909512
#105909472
#105909462
#105908382
#105908322
#105903672
#105903662
#797943
#794943