Finite Group Databasebeta

← #11885824

Subgroups — #11885824

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 929 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5829C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4#10595067C211yesmaximal, characteristic, complemented
5#10592937C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591635C211yesmaximal, characteristic, complemented
8#10591609C211yesmaximal, characteristic, complemented
9#10591567C211yesmaximal, characteristic, complemented
10#10591471C211yesmaximal, characteristic, complemented
11#10591458C211yesmaximal, characteristic, complemented
12Dic3×#213C211yesmaximal, characteristic, complemented
13#10591164C211yesmaximal, characteristic, complemented
14#10591161C211yesmaximal, characteristic, complemented
15C3⋊C8×#67C211yesmaximal, characteristic, complemented
16#83918—31nomaximal
17#83505—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C2×D3×D12C2211yescharacteristic
22C2×#3755C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic
24#64139C2211yescharacteristic, complemented
25C3×#950—24no—
26C3×#947C2211yescharacteristic, complemented
27C3×#946C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#939—21no—
31C3×#937—21no—
32C3×D4×Dic3C2211yescharacteristic, complemented
33C2×C3×#214C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic
35C3×#930C2211yescharacteristic, complemented
36C3×#929—21no—
37C3×C4×#67C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4—21no—
39C22×C3×C3⋊C8C2211yescharacteristic, complemented
40#63983—21no—
41#63971—21no—
42D3×#213—24no—
43D3×(C2×D3)⋊C4—21no—
44Dic3×D12C2211yescharacteristic, complemented
45#63864C2211yescharacteristic, complemented
46#63856C2211yescharacteristic
47#63850—21no—
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63657C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64C3×#546—31no—
65#5829—31no—
66#5829D311yescharacteristic, complemented
67C2×#950D311yescharacteristic, complemented
68C22×#213—31no—
69C2×D3×D8—31no—
70#5550—31no—
71#5238—31no—
72#5238—31no—
73#5238—31no—
74#5238—61no—
75#5218—31no—
76#5191—31no—
77#5188—31no—
78#5169—31no—
79#5169—31no—
80#5165—31no—
81#5165—31no—
82Dic3×D8—31no—
83#5115—31no—
84C8×#67—31no—
85#5059—31no—
86#5057—31no—
87#5051—31no—
88#5046—31no—
89#5038—31no—
90#5037—31no—
91#5016—31no—
92C4×#213—31no—
93D4×C3⋊C8—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C32×#41—22no—
97C32×#41—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4—21no—
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4—21no—
102C22×C32×C4C2311yescharacteristic
103C2×#638—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67D411yescharacteristic
109C22×C3×Dic3—21no—
110C3×D3×D4—22no—
111C3×D3×D4—41no—
112C3×#235—22no—
113C3×#235—41no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×#626—21no—
120C2×D3×Dic3—21no—
121D3×D12—22no—
122D3×D12—41no—
123#3755—41no—
124#3753—22no—
125#3752—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×#216—22no—
132C3×#215—22no—
133C3×#214—22no—
134C3×#213D414yescomplemented
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4D411yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C2×C3×C3⋊C8—22no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147#3724—21no—
148#3722—21no—
149#3722—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3715—41no—
153#3714—22no—
154#3713—22no—
155D3×C3⋊C8—22no—
156#3280—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41C2×D311yescharacteristic, complemented
160C2×C3×#41C2×D311yescharacteristic, complemented
161C22×C3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4C2×D311yescharacteristic
164C2×#235C2×D311yescharacteristic, complemented
165C22×D12—31no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C22×C3×C8—31no—
172C3×#124—31no—
173C3×#123—61no—
174C3×C22⋊Q8—31no—
175C3×#121—31no—
176C3×#121—61no—
177C3×#120—61no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C2×C3×C22⋊C4—61no—
181#950—24no—
182#947—31no—
183#947C2×D311yescharacteristic, complemented
184#946—31no—
185#946C2×D311yescharacteristic
186C2×#216C2×D311yescharacteristic, complemented
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—61no—
191C2×#215C2×D311yescharacteristic, complemented
192#939—21no—
193#939—61no—
194#937—21no—
195#937—61no—
196#937—61no—
197D4×Dic3—31no—
198D4×Dic3C2×D311yescharacteristic, complemented
199C2×#214—31no—
200C2×#214C2×D311yescharacteristic, complemented
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—61no—
207C2×#213—64no—
208C2×#213C2×D311yescharacteristic
209#930—31no—
210#930—31no—
211#930—61no—
212#930C2×D311yescharacteristic, complemented
213#929—21no—
214#929—61no—
215C4×#67C2×D311yescharacteristic
216C2×(C2×D3)⋊C4—21no—
217C2×(C2×D3)⋊C4—61no—
218#924—31no—
219C22×C3⋊C8—31no—
220C22×C3⋊C8C2×D311yescharacteristic, complemented
221D3×D8—64no—
222C2×D24—31no—
223C2×D3×C8—31no—
224#894—61no—
225#884—61no—
226D3×C22⋊C4—61no—
227#875—31no—
228C4×D12—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—61no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#830—31no—
239#830—31no—
240#830—31no—
241#830—61no—
242#821—31no—
243#821—31no—
244(C2×D3)⋊C8—31no—
245#818—31no—
246Dic3⋊C8—31no—
247C8×Dic3—31no—
248#810—31no—
249#809—31no—
250#809—31no—
251#807—31no—
252C4⋊(C3⋊C8)—31no—
253C4×C3⋊C8—31no—
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C32×Q8—21no—
267C32×Q8—21no—
268C32×D4—21no—
269C32×D4—42no—
270C32×D4C2×D412yes—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—42no—
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2411yescharacteristic
277#638—81no—
278C2×C3⋊Dic3—21no—
279C4⋊(C3⋊D3)—21no—
280C4⋊(C3⋊D3)—21no—
281C3×#67—22no—
282C3×#67—42no—
283C3×#67—42no—
284C3×#67—81no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—81no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—21no—
294C3×D12C2×D412yes—
295C3×C4×D3—21no—
296C3×C4×D3—21no—
297C3×C4×D3—42no—
298C3×Dic6—21no—
299C3×Dic6—21no—
300#626—42no—
301D3×Dic3—81no—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#135—31no—
307C22×D8—91no—
308#546—31no—
309#546—91no—
310#495—91no—
311#467—91no—
312#466—91no—
313#463—91no—
314#463—91no—
315#450—91no—
316#450—91no—
317#449—91no—
318#449—91no—
319C4×D8—91no—
320C8×D4—91no—
321C24×C3—61no—
322C23×D3—21no—
323C23×D3—61no—
324C23×D3—61no—
325C3×#41—22no—
326C3×#41—22no—
327C3×#41—42no—
328C3×#41—41no—
329C3×#41—41no—
330C3×#41—42no—
331C3×#41—62no—
332C3×#41—121no—
333C2×C3×Q8—21no—
334C2×C3×Q8—31no—
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—31no—
341C2×C3×D4—31no—
342C2×C3×D4—31no—
343C2×C3×D4—41no—
344C2×C3×D4—61no—
345C2×C3×D4—62no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—121no—
349C2×C3×D4C22×D311yescharacteristic
350C2×C3×D4C22×D311yescharacteristic
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—31no—
355C22×C3×C4—41no—
356C22×C3×C4—61no—
357C22×C3×C4—61no—
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C2×#67—21no—
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—121no—
367C2×#67#6711yescharacteristic
368C22×Dic3—21no—
369C22×Dic3—61no—
370D3×D4—22no—
371D3×D4—41no—
372D3×D4—62no—
373D3×D4—121no—
374#235—22no—
375#235—41no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—61no—
379C2×D12—62no—
380C2×D12—61no—
381C2×D12—121no—
382C2×D12C22×D311yescharacteristic
383C2×D12C22×D311yescharacteristic
384C2×C4×D3—21no—
385C2×C4×D3—61no—
386C2×C4×D3C22×D311yescharacteristic
387C2×Dic6C22×D311yescharacteristic
388C3×Q16—62no—
389C3×SD16—62no—
390C3×SD16—62no—
391C3×D8—34no—
392C2×C3×C8—31no—
393C2×C3×C8—31no—
394C2×C3×C8—62no—
395C3×C4⋊C4—31no—
396C3×C4⋊C4—31no—
397C3×C4⋊C4—61no—
398C3×C22⋊C4—31no—
399C3×C22⋊C4—31no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C42—31no—
406#217—21no—
407#217—61no—
408#217—61no—
409#217#6711yescharacteristic
410#216—22no—
411#215—22no—
412#215—121no—
413#215—121no—
414#215—121no—
415#215—122no—
416#214—22no—
417#214—121no—
418#213—62no—
419#213—62no—
420#213—62no—
421#213—62no—
422#213—62no—
423#213—122no—
424#213#6714yescomplemented
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—121no—
438(C2×D3)⋊C4#6711yescharacteristic
439C4⋊Dic3—31no—
440C4⋊Dic3—31no—
441C4⋊Dic3—61no—
442C4⋊Dic3C22×D311yescharacteristic
443Dic3⋊C4—21no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4#6711yescharacteristic
447C4×Dic3C22×D311yescharacteristic
448C2×C3⋊C8—22no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8—62no—
456C2×C3⋊C8C22×D311yescharacteristic
457C2×C3⋊C8C22×D311yescharacteristic
458D24—62no—
459D3×C8—62no—
460C22×C32—21no—
461C22×C32—22no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
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—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—84no—
479C2×C3×D3#13512yescomplemented
480D32—84no—
481C32×C4—21no—
482C32×C4—41no—
483C32×C4C22×D411yescharacteristic
484C32×C4H(5,𝔽2)11yescharacteristic
485C3⋊Dic3—41no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—31no—
492C2×#41D3211yescharacteristic, complemented
493C22×D4—31no—
494C22×D4—91no—
495#135—64no—
496C2×Q16—31no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—31no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×D8—184no—
506C22×C8—31no—
507C22×C8—91no—
508#124—31no—
509#124—91no—
510#123—61no—
511#123—181no—
512C22⋊Q8—31no—
513C22⋊Q8—91no—
514#121—31no—
515#121—61no—
516#121—91no—
517#121—181no—
518#120—61no—
519#120—181no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—91no—
523C2×C22⋊C4—61no—
524C2×C22⋊C4—181no—
525#107—91no—
526C4⋊C8—91no—
527#103—91no—
528#103—91no—
529#102—91no—
530#102—91no—
531#102—91no—
532#102—91no—
533C22⋊C8—91no—
534C22⋊C8—91no—
535C4×C8—91no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—31no—
540C23×C3—41no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—122no—
544C23×C3—122no—
545C23×C3—241no—
546C23×C3D3×D411yescharacteristic
547C23×C3C2×#6711yescharacteristic
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—81no—
555C22×D3—121no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3C2×#6711yescharacteristic
563C3×Q8—22no—
564C3×Q8—21no—
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—41no—
569C3×Q8—61no—
570C3×Q8—61no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—22no—
574C3×D4—32no—
575C3×D4—41no—
576C3×D4—42no—
577C3×D4—42no—
578C3×D4—44no—
579C3×D4—62no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—122no—
584C3×D4—122no—
585C3×D4—241no—
586C3×D4D3×D412yes—
587C3×D4C2×#6712yes—
588C2×C3×C4—21no—
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—31no—
597C2×C3×C4—31no—
598C2×C3×C4—31no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—42no—
603C2×C3×C4—42no—
604C2×C3×C4—44no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—122no—
610C2×C3×C4—241no—
611C2×C3×C4D3×D411yescharacteristic
612C2×C3×C4C2×#6711yescharacteristic
613C2×C3×C4C23×D311yescharacteristic
614C2×C3×C4C23×D311yescharacteristic
615#67—22no—
616#67—42no—
617#67—42no—
618#67—81no—
619#67—122no—
620#67—241no—
621#67—241no—
622#67—242no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—81no—
628C2×Dic3—121no—
629C2×Dic3—241no—
630C2×Dic3C2×#6711yescharacteristic
631C2×Dic3C2×#6711yescharacteristic
632C2×Dic3C2×#6711yescharacteristic
633D12—21no—
634D12—21no—
635D12—21no—
636D12—61no—
637D12—61no—
638D12—61no—
639D12—61no—
640D12—121no—
641D12—121no—
642D12—122no—
643D12C2×#6712yes—
644C4×D3—21no—
645C4×D3—21no—
646C4×D3—42no—
647C4×D3—241no—
648Dic6—21no—
649Dic6—21no—
650C3×C8—32no—
651C3×C8—61no—
652C3⋊C8—21no—
653C3⋊C8—61no—
654C3⋊C8—61no—
655C3⋊C8—61no—
656C3⋊C8—61no—
657C3⋊C8—121no—
658C3⋊C8—121no—
659C3⋊C8C2×#6712yes—
660C2×C32—42no—
661C2×C32—41no—
662C2×C32D4211yescharacteristic
663C2×C32C2×#13511yescharacteristic
664C2×C32#57611yescharacteristic
665C3⋊D3—81no—
666C3×D3—22no—
667C3×D3—42no—
668C3×D3—81no—
669C24—61no—
670C24—181no—
671#41—22no—
672#41—41no—
673#41—62no—
674#41—121no—
675C2×Q8—31no—
676C2×Q8C2×D3211yescharacteristic
677C2×D4—21no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—61no—
682C2×D4—62no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—91no—
686C2×D4—121no—
687C2×D4—181no—
688C2×D4—182no—
689C2×D4—181no—
690C2×D4—361no—
691C2×D4C2×D3211yescharacteristic
692C22×C4—21no—
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—181no—
697C22×C4C2×D3211yescharacteristic
698Q16—62no—
699SD16—62no—
700SD16—62no—
701SD16—361no—
702SD16—361no—
703D8—34no—
704D8—182no—
705D8—182no—
706D8—182no—
707C2×C8—31no—
708C2×C8—31no—
709C2×C8—62no—
710C2×C8—91no—
711C2×C8—91no—
712C2×C8—182no—
713C4⋊C4—31no—
714C4⋊C4—31no—
715C4⋊C4—61no—
716C4⋊C4—91no—
717C4⋊C4—181no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C42—31no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—22no—
735C22×C3—21no—
736C22×C3—22no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—32no—
741C22×C3—41no—
742C22×C3—42no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—62no—
752C22×C3—81no—
753C22×C3—81no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—244no—
760C22×C3C2×D3×D411yescharacteristic
761C22×C3C22×#6711yescharacteristic
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—22no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—84no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—241no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—244no—
781C2×D3—244no—
782C2×D3#95012yescomplemented
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—41no—
788C3×C4—42no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—61no—
792C3×C4—61no—
793C3×C4—61no—
794C3×C4—121no—
795C3×C4—121no—
796C3×C4C2×D3×D411yescharacteristic
797C3×C4#100411yescharacteristic
798C3×C4#100411yescharacteristic
799C3×C4C22×#6711yescharacteristic
800Dic3—21no—
801Dic3—21no—
802Dic3—21no—
803Dic3—41no—
804Dic3—41no—
805Dic3—121no—
806Dic3—121no—
807Dic3—241no—
808C32#328011yescharacteristic, complemented, Sylow
809C23—21no—
810C23—31no—
811C23—61no—
812C23—61no—
813C23—122no—
814C23—122no—
815C23—181no—
816C23—241no—
817C23—362no—
818C23—362no—
819C23—721no—
820C23D3×#6711yescharacteristic
821Q8—21no—
822Q8—21no—
823Q8—61no—
824Q8—61no—
825D4—21no—
826D4—32no—
827D4—42no—
828D4—62no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—122no—
833D4—122no—
834D4—181no—
835D4—181no—
836D4—241no—
837D4—362no—
838D4—721no—
839D4D3×#6712yes—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—31no—
844C2×C4—31no—
845C2×C4—31no—
846C2×C4—42no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—122no—
852C2×C4—181no—
853C2×C4—241no—
854C2×C4—721no—
855C2×C4D3×#6711yescharacteristic
856C2×C4C22×D3211yescharacteristic
857C8—32no—
858C8—61no—
859C8—181no—
860C8—181no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—42no—
865C2×C3—41no—
866C2×C3—41no—
867C2×C3—42no—
868C2×C3—62no—
869C2×C3—81no—
870C2×C3—82no—
871C2×C3—122no—
872C2×C3—241no—
873C2×C3D3×#13511yescharacteristic
874C2×C3#576911yescharacteristic
875C2×C3D4×#6711yescharacteristic
876C2×C3D4×#6711yescharacteristic
877C2×C3C2×#95011yescharacteristic
878C2×C3#583511yescharacteristic
879D3—22no—
880D3—42no—
881D3—81no—
882D3—241no—
883D3—241no—
884D3—481no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—32no—
890C22—41no—
891C22—41no—
892C22—61no—
893C22—61no—
894C22—62no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—244no—
901C22—361no—
902C22—361no—
903C22—361no—
904C22—724no—
905C22C2×D3×#6711yescharacteristic
906C4—21no—
907C4—41no—
908C4—61no—
909C4—61no—
910C4—61no—
911C4—121no—
912C4—121no—
913C4—361no—
914C4C2×D3×#6711yescharacteristic
915C4#6433011yescharacteristic
916C3—21no—
917C3#8350511yescharacteristic, complemented
918C3#8391811yescharacteristic, complemented
919C2—41no—
920C2—42no—
921C2—62no—
922C2—122no—
923C2—241no—
924C2—721no—
925C2D3×#95011yescharacteristic
926C2#1059545611yescharacteristic
927C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5829C2semidirect
2. C2×C3×#950C2semidirect
3. C2×D3×#213C2semidirect
4. #10595067C2semidirect
5. #10592937C2semidirect
6. #10591651C2semidirect
7. #10591635C2semidirect
8. #10591609C2semidirect
9. #10591567C2semidirect
10. #10591471C2semidirect
11. #10591458C2semidirect
12. Dic3×#213C2semidirect
13. #10591164C2semidirect
14. #10591161C2semidirect
15. C3⋊C8×#67C2semidirect
18. C2×C32×#41C22semidirect
20. C2×C3×#235C22semidirect
22. C2×#3755C22semidirect
24. #64139C22semidirect
26. C3×#947C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#215C22semidirect
32. C3×D4×Dic3C22semidirect
33. C2×C3×#214C22semidirect
35. C3×#930C22semidirect
39. C22×C3×C3⋊C8C22semidirect
44. Dic3×D12C22semidirect
45. #63864C22semidirect
48. C2×#3715C22semidirect
52. #63662C22semidirect
53. #63659C22semidirect
54. #63657C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
58. #63564C22semidirect
59. #63563C22semidirect
60. #63562C22semidirect
62. Dic3×C3⋊C8C22semidirect
66. #5829D3semidirect
67. C2×#950D3semidirect
134. C3×#213D4semidirect
159. C2×C3×#41C2×D3semidirect
160. C2×C3×#41C2×D3semidirect
164. C2×#235C2×D3semidirect
183. #947C2×D3semidirect
186. C2×#216C2×D3semidirect
191. C2×#215C2×D3semidirect
198. D4×Dic3C2×D3semidirect
200. C2×#214C2×D3semidirect
212. #930C2×D3semidirect
220. C22×C3⋊C8C2×D3semidirect
424. #213#67semidirect
479. C2×C3×D3#135semidirect
492. C2×#41D32semidirect
782. C2×D3#950semidirect
808. C32#3280semidirect
917. C3#83505semidirect
918. C3#83918semidirect

Maximal subgroups

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

subgroupindex
C3×#58292
C2×C3×#9502
C2×D3×#2132
#105950672
#105929372
#105916512
#105916352
#105916092
#105915672
#105914712
#105914582
Dic3×#2132
#105911642
#105911612
C3⋊C8×#672
#839183
#835053