Finite Group Databasebeta

← #11883967

Subgroups — #11883967

Order 1152.

1186 conjugacy classes of subgroups.

The subgroup lattice has 943 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×#67C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10594899C211yesmaximal, characteristic, complemented
5#10592917C211yesmaximal, characteristic, complemented
6#10591517C211yesmaximal, characteristic, complemented
7#10591498C211yesmaximal, characteristic, complemented
8#10591469C211yesmaximal, characteristic, complemented
9#10591468C211yesmaximal, characteristic, complemented
10#10591447C211yesmaximal, characteristic, complemented
11#10591440C211yesmaximal, characteristic, complemented
12#10591438C211yesmaximal, characteristic, complemented
13#10591176C211yesmaximal, characteristic, complemented
14#10591161C211yesmaximal, characteristic, complemented
15#10591147C211yesmaximal, characteristic, complemented
16#83953—31nomaximal
17#83491—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic
24C2×#3754C2211yescharacteristic, complemented
25#64133C2211yescharacteristic, complemented
26C3×#953—21no—
27C3×#940C2211yescharacteristic
28C3×#939—21no—
29C3×#938C2211yescharacteristic
30C3×#937—21no—
31C3×D4×Dic3C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic, complemented
34C3×#932—24no—
35C2×C3×#213C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic, complemented
37C3×#930C2211yescharacteristic
38C3×C4×#67C2211yescharacteristic
39C2×C3×#208C2211yescharacteristic, complemented
40#63970—21no—
41#63959—21no—
42D3×#214—24no—
43#63908C2211yescharacteristic, complemented
44#63879—21no—
45#63860C2211yescharacteristic, complemented
46#63851—21no—
47Dic3×Dic6C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic
53#63659C2211yescharacteristic, complemented
54#63657C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C3×D42—31no—
65#5831—31no—
66D4×#67D311yescharacteristic, complemented
67C22×#214—31no—
68C2×#932D311yescharacteristic, complemented
69C2×D3×SD16—31no—
70#5552—31no—
71#5238—31no—
72#5218—31no—
73#5218—31no—
74#5218—61no—
75#5217—31no—
76#5170—31no—
77#5164—31no—
78#5163—31no—
79#5157—31no—
80#5156—31no—
81#5154—31no—
82#5153—31no—
83#5134—31no—
84#5127—31no—
85#5075—31no—
86#5074—31no—
87#5042—31no—
88#5040—31no—
89#5038—31no—
90#5037—31no—
91#5018—31no—
92#5016—31no—
93#5011—31no—
94C24×C32—21no—
95C23×C3×D3—21no—
96C2×C32×D4—22no—
97C2×C32×D4—21no—
98C2×C32×D4—41no—
99C2×C32×D4C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—44no—
110C2×C3×#67D411yescharacteristic
111C22×C3×Dic3—21no—
112C3×D3×D4—22no—
113C3×D3×D4—41no—
114C3×#235—22no—
115C3×#235—41no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×#627—21no—
122C2×#625—21no—
123C2×D3×Dic3—21no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126#3757—21no—
127#3754—22no—
128#3754—41no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3750—21no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#217—21no—
134C3×#217—21no—
135C3×#217D411yescharacteristic
136C3×#214—22no—
137C3×#214D414yescomplemented
138C3×#213—22no—
139C3×#213—22no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3C2311yescharacteristic
143C3×Dic3⋊C4D411yescharacteristic
144C3×C4×Dic3C2311yescharacteristic
145C3×#208—22no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148Dic3⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152Dic32—21no—
153#3716—22no—
154#3715—22no—
155#3713—41no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×D4—21no—
160C22×C3×D4—31no—
161C22×C3×D4—61no—
162C22×C3×D4C2×D311yescharacteristic
163C22×C3×D4C2×D311yescharacteristic
164C22×#67—21no—
165C2×D3×Q8—31no—
166C2×D3×D4C2×D311yescharacteristic
167C2×#235C2×D311yescharacteristic, complemented
168C22×Dic6—31no—
169C3×AGL(1,ℤ/8)—64no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×M16—31no—
175C3×#127—31no—
176C3×#121—31no—
177C3×#121—31no—
178C3×#121—61no—
179C3×#120—61no—
180C3×#120—61no—
181C3×C4×D4—31no—
182C3×C4×D4—31no—
183#953—21no—
184Q8×Dic3—31no—
185C2×#215—31no—
186#940C2×D311yescharacteristic
187#939—21no—
188#939—61no—
189#938—31no—
190#938—61no—
191#938C2×D311yescharacteristic
192#937—21no—
193#936—31no—
194#936—61no—
195D4×Dic3C2×D311yescharacteristic
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—61no—
203C2×#214—61no—
204C2×#214—64no—
205C2×#214C2×D311yescharacteristic
206C2×#214C2×D311yescharacteristic, complemented
207#932—24no—
208C2×#213—31no—
209C2×#213—31no—
210C2×#213C2×D311yescharacteristic
211C2×#213C2×D311yescharacteristic, complemented
212#930—31no—
213#930C2×D311yescharacteristic
214C4×#67—61no—
215C4×#67C2×D311yescharacteristic
216#924—31no—
217#924—31no—
218#924—61no—
219#924—61no—
220C2×#208C2×D311yescharacteristic, complemented
221C22×C3⋊C8—31no—
222D3×SD16—64no—
223C2×#204—31no—
224C2×D3×C8—31no—
225#896—61no—
226#885—61no—
227#67⋊C4—61no—
228#875—31no—
229C4×Dic6—31no—
230#835—31no—
231#832—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#832—61no—
239#830—31no—
240#830—31no—
241#830—31no—
242#830—61no—
243#821—31no—
244(C2×D3)⋊C8—31no—
245#818—31no—
246#816—31no—
247#815—31no—
248Dic3⋊C8—31no—
249#810—31no—
250#810—31no—
251#809—31no—
252#807—31no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—42no—
258C23×C32—42no—
259C23×C32—81no—
260C23×C32C2×D411yescharacteristic
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—42no—
264C22×C3×D3—42no—
265C22×C3×D3—81no—
266C22×C3×D3C2×D411yescharacteristic
267C32×D4—21no—
268C32×D4—21no—
269C32×D4—21no—
270C32×D4—42no—
271C32×D4C2×D412yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278#634—21no—
279#634—21no—
280C3×#67—22no—
281C3×#67—42no—
282C3×#67—42no—
283C3×#67—42no—
284C3×#67—42no—
285C3×#67—42no—
286C3×#67—81no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—42no—
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C2×C3×Dic3C2×D411yescharacteristic
293C3×D12—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×C4×D3—21no—
298C3×C4×D3—21no—
299C3×C4×D3—42no—
300C3×Dic6—21no—
301C3×Dic6C2×D412yescomplemented
302#627—42no—
303#625—42no—
304D3×Dic3—42no—
305C3⋊(C3⋊C8)—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—31no—
310C22×SD16—91no—
311#548—91no—
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—21no—
325C24×C3—21no—
326C24×C3—41no—
327C24×C3—61no—
328C23×D3—21no—
329C3×#41—62no—
330C3×#41—121no—
331C2×C3×Q8—31no—
332C2×C3×D4—22no—
333C2×C3×D4—22no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—41no—
342C2×C3×D4—42no—
343C2×C3×D4—41no—
344C2×C3×D4—41no—
345C2×C3×D4—42no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—62no—
350C2×C3×D4—61no—
351C2×C3×D4—61no—
352C2×C3×D4—61no—
353C2×C3×D4—121no—
354C2×C3×D4—124no—
355C2×C3×D4C22×D311yescharacteristic
356C2×C3×D4C22×D311yescharacteristic
357C2×C3×D4C22×D311yescharacteristic
358C2×C3×D4C22×D311yescharacteristic
359C22×C3×C4—21no—
360C22×C3×C4—31no—
361C22×C3×C4—61no—
362C22×C3×C4—61no—
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C2×#67—21no—
366C2×#67—21no—
367C2×#67—21no—
368C2×#67—21no—
369C2×#67—21no—
370C2×#67—21no—
371C2×#67—44no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67#6711yescharacteristic
375C22×Dic3—21no—
376C22×Dic3—61no—
377D3×Q8—62no—
378D3×Q8—121no—
379D3×D4—22no—
380D3×D4—41no—
381#235—22no—
382#235—41no—
383C2×D12C22×D311yescharacteristic
384C2×D12C22×D311yescharacteristic
385C2×C4×D3—21no—
386C2×C4×D3—61no—
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6—31no—
389C2×Dic6—31no—
390C2×Dic6—61no—
391C2×Dic6—62no—
392C2×Dic6—61no—
393C2×Dic6—61no—
394C2×Dic6—121no—
395C2×Dic6C22×D311yescharacteristic
396C3×SD16—34no—
397C3×SD16—62no—
398C3×D8—62no—
399C3×D8—62no—
400C3×M16—62no—
401C2×C3×C8—31no—
402C2×C3×C8—31no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—31no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C42—31no—
411#217—21no—
412#217—21no—
413#217—61no—
414#217—61no—
415#217—61no—
416#217—61no—
417#217—61no—
418#217—121no—
419#217#6711yescharacteristic
420#215—62no—
421#214—22no—
422#214—62no—
423#214—62no—
424#214—62no—
425#214—62no—
426#214—122no—
427#214—121no—
428#214—121no—
429#214—122no—
430#214#6714yescomplemented
431#213—22no—
432#213—22no—
433#213—121no—
434#213—121no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4#6711yescharacteristic
440C4⋊Dic3—31no—
441C4⋊Dic3—31no—
442C4⋊Dic3—61no—
443C4⋊Dic3—61no—
444C4⋊Dic3C22×D311yescharacteristic
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447Dic3⋊C4—61no—
448Dic3⋊C4—121no—
449Dic3⋊C4#6711yescharacteristic
450C4×Dic3—61no—
451C4×Dic3—61no—
452C4×Dic3C22×D311yescharacteristic
453#208—22no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—31no—
456C2×C3⋊C8—31no—
457C2×C3⋊C8—31no—
458C2×C3⋊C8—61no—
459C2×C3⋊C8—61no—
460C2×C3⋊C8—62no—
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D311yescharacteristic
463#204—62no—
464D3×C8—62no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—22no—
468C22×C32—21no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—84no—
475C22×C32C22×D411yescharacteristic
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—84no—
485C2×C3×D3AGL(1,ℤ/8)12yescomplemented
486C32×C4—21no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—41no—
490C3⋊Dic3—41no—
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C2×#41—31no—
497C22×Q8—91no—
498C22×D4—31no—
499C22×D4—61no—
500C22×D4D3211yescharacteristic
501AGL(1,ℤ/8)—64no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—31no—
510C2×D8—31no—
511C2×D8—91no—
512C2×M16—31no—
513C22×C8—91no—
514#127—31no—
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—91no—
527C4×D4—31no—
528C4×D4—31no—
529C4×D4—181no—
530#107—91no—
531C4⋊C8—91no—
532#103—91no—
533#103—91no—
534#102—91no—
535#102—91no—
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—21no—
546C23×C3—31no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—42no—
550C23×C3—42no—
551C23×C3—42no—
552C23×C3—42no—
553C23×C3—44no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—82no—
557C23×C3—81no—
558C23×C3—81no—
559C23×C3—82no—
560C23×C3—122no—
561C23×C3—122no—
562C23×C3—241no—
563C23×C3D3×D411yescharacteristic
564C23×C3C2×#6711yescharacteristic
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—42no—
568C22×D3—42no—
569C22×D3—81no—
570C22×D3C2×#6711yescharacteristic
571C3×Q8—32no—
572C3×Q8—61no—
573C3×D4—22no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—22no—
581C3×D4—41no—
582C3×D4—41no—
583C3×D4—42no—
584C3×D4—42no—
585C3×D4—44no—
586C3×D4—62no—
587C3×D4—61no—
588C3×D4—61no—
589C3×D4—61no—
590C3×D4—61no—
591C3×D4—122no—
592C3×D4—122no—
593C3×D4—122no—
594C3×D4—122no—
595C3×D4—122no—
596C3×D4—241no—
597C3×D4D3×D412yes—
598C3×D4C2×#6712yes—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—31no—
606C2×C3×C4—31no—
607C2×C3×C4—31no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—122no—
615C2×C3×C4—122no—
616C2×C3×C4D3×D411yescharacteristic
617C2×C3×C4C2×#6711yescharacteristic
618C2×C3×C4C23×D311yescharacteristic
619C2×C3×C4C23×D311yescharacteristic
620#67—22no—
621#67—42no—
622#67—42no—
623#67—42no—
624#67—42no—
625#67—42no—
626#67—81no—
627#67—122no—
628#67—122no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—42no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—121no—
637C2×Dic3—121no—
638C2×Dic3—122no—
639C2×Dic3C2×#6711yescharacteristic
640C2×Dic3C2×#6711yescharacteristic
641C2×Dic3C2×#6711yescharacteristic
642D12—21no—
643D12—21no—
644D12—21no—
645D12—21no—
646C4×D3—21no—
647C4×D3—21no—
648C4×D3—42no—
649C4×D3—122no—
650Dic6—21no—
651Dic6—61no—
652Dic6—61no—
653Dic6—61no—
654Dic6—61no—
655Dic6—121no—
656Dic6—121no—
657Dic6—122no—
658Dic6—122no—
659Dic6C2×#6712yescomplemented
660C3×C8—32no—
661C3×C8—61no—
662C3⋊C8—21no—
663C3⋊C8—61no—
664C3⋊C8—61no—
665C3⋊C8—61no—
666C3⋊C8—61no—
667C3⋊C8—121no—
668C3⋊C8—121no—
669C3⋊C8C2×#6712yescomplemented
670C2×C32—41no—
671C2×C32—42no—
672C2×C32—81no—
673C2×C32D4211yescharacteristic
674C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
675C2×C32#57711yescharacteristic
676C3×D3—22no—
677C3×D3—81no—
678C3×D3—81no—
679C24—21no—
680C24—61no—
681#41—62no—
682#41—121no—
683C2×Q8—31no—
684C2×Q8—91no—
685C2×Q8—181no—
686C2×Q8—182no—
687C2×Q8—361no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—31no—
691C2×D4—31no—
692C2×D4—31no—
693C2×D4—41no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—61no—
697C2×D4—62no—
698C2×D4—61no—
699C2×D4—61no—
700C2×D4—61no—
701C2×D4—121no—
702C2×D4—124no—
703C2×D4—181no—
704C2×D4C2×D3211yescharacteristic
705C2×D4C2×D3211yescharacteristic
706C22×C4—31no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—181no—
710C22×C4C2×D3211yescharacteristic
711SD16—34no—
712SD16—62no—
713SD16—182no—
714SD16—182no—
715SD16—182no—
716SD16—361no—
717D8—62no—
718D8—62no—
719D8—361no—
720M16—62no—
721C2×C8—31no—
722C2×C8—31no—
723C2×C8—91no—
724C2×C8—91no—
725C2×C8—182no—
726C4⋊C4—31no—
727C4⋊C4—31no—
728C4⋊C4—91no—
729C4⋊C4—181no—
730C4⋊C4—181no—
731C22⋊C4—31no—
732C22⋊C4—31no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—61no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C42—31no—
741C42—181no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—22no—
748C22×C3—21no—
749C22×C3—22no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—32no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—61no—
768C22×C3—61no—
769C22×C3—81no—
770C22×C3—81no—
771C22×C3—81no—
772C22×C3—81no—
773C22×C3—84no—
774C22×C3—84no—
775C22×C3—88no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—121no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3—121no—
782C22×C3—244no—
783C22×C3C2×D3×D411yescharacteristic
784C22×C3C22×#6711yescharacteristic
785C2×D3—21no—
786C2×D3—21no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3—84no—
794C2×D3#93212yescomplemented
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—41no—
800C3×C4—61no—
801C3×C4—61no—
802C3×C4—61no—
803C3×C4—62no—
804C3×C4—121no—
805C3×C4C2×D3×D411yescharacteristic
806C3×C4#100411yescharacteristic
807C3×C4#100411yescharacteristic
808C3×C4C22×#6711yescharacteristic
809Dic3—21no—
810Dic3—22no—
811Dic3—21no—
812Dic3—21no—
813Dic3—41no—
814Dic3—121no—
815Dic3—121no—
816Dic3—121no—
817Dic3—121no—
818Dic3—241no—
819Dic3—241no—
820C32#326511yescharacteristic, complemented, Sylow
821C23—21no—
822C23—21no—
823C23—31no—
824C23—42no—
825C23—42no—
826C23—61no—
827C23—61no—
828C23—81no—
829C23—122no—
830C23—122no—
831C23—241no—
832C23D3×#6711yescharacteristic
833Q8—32no—
834Q8—61no—
835Q8—181no—
836Q8—181no—
837Q8—362no—
838D4—21no—
839D4—21no—
840D4—21no—
841D4—42no—
842D4—62no—
843D4—61no—
844D4—61no—
845D4—61no—
846D4—61no—
847D4—122no—
848D4—122no—
849D4—122no—
850D4—122no—
851D4—122no—
852D4—241no—
853D4—362no—
854D4D3×#6712yes—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—31no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—122no—
865C2×C4—122no—
866C2×C4—181no—
867C2×C4—181no—
868C2×C4—362no—
869C2×C4D3×#6711yescharacteristic
870C2×C4C22×D3211yescharacteristic
871C8—32no—
872C8—61no—
873C8—181no—
874C8—181no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—42no—
879C2×C3—42no—
880C2×C3—41no—
881C2×C3—41no—
882C2×C3—42no—
883C2×C3—62no—
884C2×C3—82no—
885C2×C3—82no—
886C2×C3—81no—
887C2×C3—81no—
888C2×C3—241no—
889C2×C3—241no—
890C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
891C2×C3#577511yescharacteristic
892C2×C3C2×#93211yescharacteristic
893C2×C3D4×#6711yescharacteristic
894C2×C3D4×#6711yescharacteristic
895C2×C3#583611yescharacteristic
896D3—22no—
897D3—81no—
898D3—81no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—22no—
903C22—32no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—61no—
910C22—61no—
911C22—84no—
912C22—121no—
913C22—121no—
914C22—121no—
915C22—121no—
916C22—121no—
917C22—121no—
918C22—244no—
919C22C2×D3×#6711yescharacteristic
920C4—21no—
921C4—61no—
922C4—61no—
923C4—61no—
924C4—62no—
925C4—121no—
926C4—361no—
927C4—361no—
928C4C2×D3×#6711yescharacteristic
929C4#6433011yescharacteristic
930C3—21no—
931C3#8349111yescharacteristic, complemented
932C3#8395311yescharacteristic, complemented
933C2—41no—
934C2—42no—
935C2—62no—
936C2—81no—
937C2—241no—
938C2—241no—
939C2D3×#93211yescharacteristic
940C2#1059510611yescharacteristic
941C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C3×D4×#67C2semidirect
2. C2×C3×#932C2semidirect
3. C2×D3×#214C2semidirect
4. #10594899C2semidirect
5. #10592917C2semidirect
6. #10591517C2semidirect
7. #10591498C2semidirect
8. #10591469C2semidirect
9. #10591468C2semidirect
10. #10591447C2semidirect
11. #10591440C2semidirect
12. #10591438C2semidirect
13. #10591176C2semidirect
14. #10591161C2semidirect
15. #10591147C2semidirect
21. C2×C3×#235C22semidirect
22. C2×D3×Dic6C22semidirect
24. C2×#3754C22semidirect
25. #64133C22semidirect
33. C2×C3×#214C22semidirect
36. C2×C3×#213C22semidirect
39. C2×C3×#208C22semidirect
43. #63908C22semidirect
45. #63860C22semidirect
47. Dic3×Dic6C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. #63659C22semidirect
54. #63657C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
59. #63563C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
66. D4×#67D3semidirect
68. C2×#932D3semidirect
137. C3×#214D4semidirect
167. C2×#235C2×D3semidirect
206. C2×#214C2×D3semidirect
211. C2×#213C2×D3semidirect
220. C2×#208C2×D3semidirect
301. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
430. #214#67semidirect
485. C2×C3×D3AGL(1,ℤ/8)semidirect
659. Dic6C2×#67semidirect
669. C3⋊C8C2×#67semidirect
794. C2×D3#932semidirect
820. C32#3265semidirect
931. C3#83491semidirect
932. C3#83953semidirect

Maximal subgroups

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

subgroupindex
C3×D4×#672
C2×C3×#9322
C2×D3×#2142
#105948992
#105929172
#105915172
#105914982
#105914692
#105914682
#105914472
#105914402
#105914382
#105911762
#105911612
#105911472
#839533
#834913