Finite Group Databasebeta

← #11884408

Subgroups — #11884408

Order 1152.

1096 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5834C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×#63947C211yesmaximal, characteristic, complemented
4#10594886C211yesmaximal, characteristic, complemented
5#10592938C211yesmaximal, characteristic, complemented
6#10591604C211yesmaximal, characteristic, complemented
7#10591586C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10591519C211yesmaximal, characteristic, complemented
10#10591498C211yesmaximal, characteristic, complemented
11#10591469C211yesmaximal, characteristic, complemented
12#10591428C211yesmaximal, characteristic, complemented
13#10591176C211yesmaximal, characteristic, complemented
14#10591160C211yesmaximal, characteristic, complemented
15#10591147C211yesmaximal, characteristic, complemented
16#83955—31nomaximal
17#83577—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic, complemented
24#64133C2211yescharacteristic
25C3×#949—24no—
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C3×#940—21no—
30C3×#940C2211yescharacteristic, complemented
31C3×#938—21no—
32C3×#938C2211yescharacteristic, complemented
33C2×C3×#213C2211yescharacteristic
34C2×C3×#213C2211yescharacteristic
35C3×#930—21no—
36C3×#930C2211yescharacteristic
37C3×C4×#67—21no—
38C3×C4×#67C2211yescharacteristic
39C2×C3×#208C2211yescharacteristic
40#63976—21no—
41D3×#217—21no—
42#63947—24no—
43#63908C2211yescharacteristic
44Dic3×D12C2211yescharacteristic
45#63885—21no—
46#63884—21no—
47#63860C2211yescharacteristic
48C2×#3716C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63657C2211yescharacteristic
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C3×#550—31no—
65#5834D311yescharacteristic, complemented
66C2×#950—31no—
67C2×#949D311yescharacteristic, complemented
68#5806—31no—
69C2×#916—31no—
70#5550—31no—
71#5239—31no—
72#5239—31no—
73#5239—61no—
74#5238—31no—
75#5217—31no—
76#5172—31no—
77#5166—31no—
78#5164—31no—
79#5158—31no—
80#5157—31no—
81#5154—31no—
82#5150—31no—
83#5134—31no—
84#5127—31no—
85#5074—31no—
86#5072—31no—
87#5042—31no—
88#5038—31no—
89#5037—31no—
90#5036—31no—
91#5028—31no—
92#5026—31no—
93#5011—31no—
94C23×C3×D3—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67D411yescharacteristic
108C3×#239—22no—
109C3×#239—41no—
110C2×C3×D12—22no—
111C2×C3×D12—21no—
112C2×C3×D12—21no—
113C2×C3×D12—41no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3C2311yescharacteristic
119C2×#625—21no—
120C2×#625—21no—
121C2×D3×Dic3—21no—
122C2×D3×Dic3—21no—
123#3795—22no—
124#3795—41no—
125#3757—21no—
126#3756—22no—
127#3754—41no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217—21no—
133C3×#217D411yescharacteristic
134C3×#215—22no—
135C3×#215D414yescomplemented
136C3×#213—22no—
137C3×#213—22no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4D411yescharacteristic
143C3×C4×Dic3—21no—
144C3×C4×Dic3C2311yescharacteristic
145C3×#208—22no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3716—22no—
153#3713—22no—
154#3713—41no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41C2×D311yescharacteristic
160C2×C3×#41C2×D311yescharacteristic
161C22×C3×D4—31no—
162C2×#239C2×D311yescharacteristic, complemented
163C2×#237—31no—
164C2×#235—31no—
165C22×D12C2×D311yescharacteristic
166C3×AGL(1,ℤ/8)—64no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C2×C3×D8—31no—
171C2×C3×M16—31no—
172C3×#127—31no—
173C3×#127—61no—
174C3×#121—31no—
175C3×#121—31no—
176C3×#121—61no—
177C3×#121—61no—
178C3×C4×Q8—31no—
179C3×C4×D4—31no—
180C3×C4×D4—61no—
181#953—61no—
182C2×#217—61no—
183#950—64no—
184#949—24no—
185Q8×Dic3C2×D311yescharacteristic, complemented
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—61no—
189C2×#215C2×D311yescharacteristic
190C2×#215C2×D311yescharacteristic
191#940—21no—
192#940C2×D311yescharacteristic, complemented
193#939—61no—
194#938—21no—
195#938—31no—
196#938C2×D311yescharacteristic, complemented
197#937—61no—
198#936—31no—
199#935—61no—
200D4×Dic3—31no—
201C2×#214—31no—
202C2×#214—31no—
203C2×#214—31no—
204C2×#214—61no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—31no—
209C2×#213C2×D311yescharacteristic
210C2×#213C2×D311yescharacteristic
211#930—21no—
212#930—31no—
213#930C2×D311yescharacteristic
214C4×#67—21no—
215C4×#67C2×D311yescharacteristic
216#924—31no—
217#924—31no—
218#924—61no—
219C2×#208C2×D311yescharacteristic
220C22×C3⋊C8—31no—
221#916—64no—
222C2×#204—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—61no—
232#832—31no—
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(C2×D3)⋊C8—31no—
244#818—31no—
245#816—31no—
246#815—31no—
247Dic3⋊C8—31no—
248#810—31no—
249#809—31no—
250#809—31no—
251#807—31no—
252C4⋊(C3⋊C8)—31no—
253#803—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
263C32×Q8—21no—
264C32×Q8C2×D412yes—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—42no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—42no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276#634—21no—
277#634—21no—
278C3×#67—41no—
279C3×#67—42no—
280C3×#67—81no—
281C3×#67—81no—
282C3×#67—81no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—42no—
293C3×D12—42no—
294C3×D12C2×D412yes—
295C3×C4×D3—21no—
296C3×C4×D3—21no—
297C3×C4×D3—42no—
298#625—42no—
299#625—81no—
300D3×Dic3—42no—
301D3×Dic3—81no—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—31no—
307C2×#135—91no—
308#550—31no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—91no—
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—22no—
324C3×#41—22no—
325C3×#41—42no—
326C3×#41—41no—
327C3×#41—41no—
328C3×#41—42no—
329C3×#41—62no—
330C3×#41—121no—
331C2×C3×Q8—21no—
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—41no—
342C2×C3×D4—62no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—121no—
350C2×C3×D4C22×D311yescharacteristic
351C2×C3×D4C22×D311yescharacteristic
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—31no—
356C22×C3×C4—41no—
357C22×C3×C4—61no—
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C2×#67—21no—
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—21no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—61no—
367C2×#67—61no—
368C2×#67#6711yescharacteristic
369C22×Dic3—61no—
370C22×Dic3—61no—
371#239—22no—
372#239—41no—
373#237—62no—
374#237—121no—
375#235—62no—
376#235—121no—
377C2×D12—22no—
378C2×D12—21no—
379C2×D12—21no—
380C2×D12—41no—
381C2×D12C22×D311yescharacteristic
382C2×D12C22×D311yescharacteristic
383C2×D12C22×D311yescharacteristic
384C2×C4×D3—21no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6—31no—
389C2×Dic6—31no—
390C2×Dic6—61no—
391C3×SD16—34no—
392C3×SD16—62no—
393C3×D8—62no—
394C3×D8—62no—
395C3×M16—62no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—31no—
400C3×C4⋊C4—61no—
401C3×C22⋊C4—31no—
402C3×C22⋊C4—31no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C42—31no—
406C3×C42—61no—
407#217—21no—
408#217—61no—
409#217—61no—
410#217—61no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217—121no—
415#217#6711yescharacteristic
416#216—62no—
417#216—62no—
418#216—122no—
419#215—22no—
420#215#6714yescomplemented
421#214—62no—
422#214—121no—
423#214—121no—
424#214—122no—
425#213—22no—
426#213—22no—
427#213—62no—
428#213—62no—
429#213—121no—
430#213—121no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4#6711yescharacteristic
437C4⋊Dic3—21no—
438C4⋊Dic3—31no—
439C4⋊Dic3—31no—
440C4⋊Dic3—61no—
441C4⋊Dic3C22×D311yescharacteristic
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4—121no—
445Dic3⋊C4#6711yescharacteristic
446C4×Dic3—21no—
447C4×Dic3C22×D311yescharacteristic
448#208—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
458#204—62no—
459D3×C8—62no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3×D3—22no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—84no—
480C32×C4—22no—
481C32×C4—21no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—41no—
485C3⋊Dic3—41no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—91no—
492C2×#41D3211yescharacteristic
493C22×D4—31no—
494AGL(1,ℤ/8)—64no—
495#135—184no—
496C2×Q16—91no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—31no—
502C2×D8—31no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—31no—
506C22×C8—91no—
507#127—31no—
508#127—61no—
509#124—91no—
510#123—181no—
511C22⋊Q8—91no—
512#121—31no—
513#121—31no—
514#121—61no—
515#121—61no—
516#121—91no—
517#121—181no—
518#120—181no—
519C4×Q8—31no—
520C4×D4—31no—
521C4×D4—61no—
522C4×D4—91no—
523C2×C22⋊C4—181no—
524#107—91no—
525C4⋊C8—91no—
526#103—91no—
527#103—91no—
528#102—91no—
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—21no—
538C23×C3—31no—
539C23×C3—41no—
540C23×C3—61no—
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—21no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—81no—
554C22×D3C2×#6711yescharacteristic
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—22no—
558C3×Q8—41no—
559C3×Q8D3×D412yes—
560C3×Q8C2×#6712yes—
561C3×D4—22no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—32no—
567C3×D4—41no—
568C3×D4—42no—
569C3×D4—42no—
570C3×D4—44no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—122no—
577C3×D4—122no—
578C3×D4—121no—
579C3×D4—122no—
580C3×D4—241no—
581C3×D4—241no—
582C3×D4—241no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—31no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—42no—
598C2×C3×C4—42no—
599C2×C3×C4—44no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—122no—
604C2×C3×C4D3×D411yescharacteristic
605C2×C3×C4C2×#6711yescharacteristic
606C2×C3×C4C23×D311yescharacteristic
607C2×C3×C4C23×D311yescharacteristic
608#67—41no—
609#67—42no—
610#67—81no—
611#67—81no—
612#67—81no—
613#67—122no—
614#67—122no—
615#67—241no—
616#67—241no—
617C2×Dic3—21no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—121no—
623C2×Dic3—121no—
624C2×Dic3—122no—
625C2×Dic3—241no—
626C2×Dic3C2×#6711yescharacteristic
627C2×Dic3C2×#6711yescharacteristic
628C2×Dic3C2×#6711yescharacteristic
629D12—21no—
630D12—21no—
631D12—21no—
632D12—21no—
633D12—21no—
634D12—42no—
635D12—42no—
636D12C2×#6712yes—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—42no—
640C4×D3—122no—
641C4×D3—241no—
642Dic6—61no—
643Dic6—61no—
644Dic6—61no—
645Dic6—61no—
646Dic6—121no—
647Dic6—121no—
648C3×C8—32no—
649C3×C8—61no—
650C3⋊C8—21no—
651C3⋊C8—61no—
652C3⋊C8—61no—
653C3⋊C8—61no—
654C3⋊C8—61no—
655C3⋊C8—121no—
656C3⋊C8—121no—
657C3⋊C8C2×#6712yes—
658C2×C32—41no—
659C2×C32—81no—
660C2×C32D4211yescharacteristic
661C2×C32#57511yescharacteristic
662C2×C32#57611yescharacteristic
663C3×D3—41no—
664C3×D3—42no—
665C3×D3—81no—
666C3×D3—81no—
667C24—61no—
668#41—22no—
669#41—41no—
670#41—62no—
671#41—121no—
672#41—182no—
673#41—361no—
674C2×Q8—91no—
675C2×Q8C2×D3211yescharacteristic
676C2×D4—21no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—62no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—61no—
688C2×D4—121no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4C2×D3211yescharacteristic
692C22×C4—21no—
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—181no—
696C22×C4—181no—
697C22×C4C2×D3211yescharacteristic
698Q16—182no—
699SD16—34no—
700SD16—62no—
701SD16—182no—
702SD16—361no—
703D8—62no—
704D8—62no—
705D8—182no—
706D8—361no—
707M16—62no—
708C2×C8—31no—
709C2×C8—31no—
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—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C42—31no—
728C42—61no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—42no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—62no—
749C22×C3—61no—
750C22×C3—81no—
751C22×C3—81no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—244no—
761C22×C3C2×D3×D411yescharacteristic
762C22×C3C22×#6711yescharacteristic
763C2×D3—21no—
764C2×D3—22no—
765C2×D3—21no—
766C2×D3—21no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—84no—
776C3×C4—22no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—22no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—41no—
783C3×C4—42no—
784C3×C4—61no—
785C3×C4—61no—
786C3×C4—61no—
787C3×C4—121no—
788C3×C4C2×D3×D411yescharacteristic
789C3×C4#100411yescharacteristic
790C3×C4#100411yescharacteristic
791C3×C4C22×#6711yescharacteristic
792Dic3—21no—
793Dic3—21no—
794Dic3—21no—
795Dic3—41no—
796Dic3—121no—
797Dic3—121no—
798Dic3—121no—
799Dic3—121no—
800Dic3—241no—
801Dic3—241no—
802C32#326811yescharacteristic, complemented, Sylow
803C23—21no—
804C23—31no—
805C23—61no—
806C23—61no—
807C23—61no—
808C23—122no—
809C23—122no—
810C23—241no—
811C23D3×#6711yescharacteristic
812Q8—21no—
813Q8—181no—
814Q8—181no—
815Q8D3×#6712yes—
816D4—21no—
817D4—21no—
818D4—32no—
819D4—42no—
820D4—61no—
821D4—61no—
822D4—61no—
823D4—61no—
824D4—61no—
825D4—122no—
826D4—122no—
827D4—121no—
828D4—122no—
829D4—241no—
830D4—241no—
831D4—241no—
832D4—362no—
833D4—721no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—31no—
838C2×C4—31no—
839C2×C4—31no—
840C2×C4—42no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—122no—
845C2×C4—181no—
846C2×C4—181no—
847C2×C4—362no—
848C2×C4—721no—
849C2×C4D3×#6711yescharacteristic
850C2×C4C22×D3211yescharacteristic
851C8—32no—
852C8—61no—
853C8—181no—
854C8—181no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—41no—
859C2×C3—41no—
860C2×C3—81no—
861C2×C3—82no—
862C2×C3—81no—
863C2×C3—81no—
864C2×C3—122no—
865C2×C3—121no—
866C2×C3—241no—
867C2×C3—241no—
868C2×C3#577311yescharacteristic
869C2×C3#577411yescharacteristic
870C2×C3D4×#6711yescharacteristic
871C2×C3D4×#6711yescharacteristic
872C2×C3#582211yescharacteristic
873C2×C3#583511yescharacteristic
874D3—41no—
875D3—42no—
876D3—81no—
877D3—81no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—61no—
885C22—61no—
886C22—61no—
887C22—62no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—244no—
897C22C2×D3×#6711yescharacteristic
898C4—21no—
899C4—22no—
900C4—61no—
901C4—61no—
902C4—61no—
903C4—121no—
904C4—361no—
905C4—361no—
906C4C2×D3×#6711yescharacteristic
907C4#6433011yescharacteristic
908C3—21no—
909C3#8357711yescharacteristic, complemented
910C3#8395511yescharacteristic, complemented
911C2—41no—
912C2—81no—
913C2—121no—
914C2—122no—
915C2—241no—
916C2—241no—
917C2#1059545411yescharacteristic
918C2#1059546911yescharacteristic
919C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3268
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×#5834C2semidirect
2. C2×C3×#949C2semidirect
3. C2×#63947C2semidirect
4. #10594886C2semidirect
5. #10592938C2semidirect
6. #10591604C2semidirect
7. #10591586C2semidirect
8. #10591566C2semidirect
9. #10591519C2semidirect
10. #10591498C2semidirect
11. #10591469C2semidirect
12. #10591428C2semidirect
13. #10591176C2semidirect
14. #10591160C2semidirect
15. #10591147C2semidirect
19. C2×C3×#239C22semidirect
22. C2×#3756C22semidirect
23. C2×#3754C22semidirect
26. C3×Q8×Dic3C22semidirect
30. C3×#940C22semidirect
32. C3×#938C22semidirect
48. C2×#3716C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63662C22semidirect
53. #63659C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63563C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
65. #5834D3semidirect
67. C2×#949D3semidirect
135. C3×#215D4semidirect
162. C2×#239C2×D3semidirect
185. Q8×Dic3C2×D3semidirect
192. #940C2×D3semidirect
196. #938C2×D3semidirect
420. #215#67semidirect
802. C32#3268semidirect
909. C3#83577semidirect
910. C3#83955semidirect

Maximal subgroups

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

subgroupindex
C3×#58342
C2×C3×#9492
C2×#639472
#105948862
#105929382
#105916042
#105915862
#105915662
#105915192
#105914982
#105914692
#105914282
#105911762
#105911602
#105911472
#839553
#835773