Finite Group Databasebeta

← #11884432

Subgroups — #11884432

Order 1152.

1119 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3C2×#63935C211yesmaximal, characteristic, complemented
4#10595007C211yesmaximal, characteristic, complemented
5#10592916C211yesmaximal, characteristic, complemented
6#10591521C211yesmaximal, characteristic, complemented
7#10591498C211yesmaximal, characteristic, complemented
8#10591483C211yesmaximal, characteristic, complemented
9#10591481C211yesmaximal, characteristic, complemented
10#10591450C211yesmaximal, characteristic, complemented
11#10591442C211yesmaximal, characteristic, complemented
12#10591440C211yesmaximal, characteristic, complemented
13#10591178C211yesmaximal, characteristic, complemented
14#10591170C211yesmaximal, characteristic, complemented
15#10591147C211yesmaximal, characteristic, complemented
16#83955—31nomaximal
17#83507—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23C2×#3753C2211yescharacteristic
24#64139C2211yescharacteristic
25C3×#953—21no—
26C2×C3×#217—21no—
27C3×#939—21no—
28C3×#938C2211yescharacteristic
29C3×#936C2211yescharacteristic
30C3×#935—21no—
31C3×D4×Dic3C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic
34C3×#932—24no—
35C2×C3×#213C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C3×C4×#67C2211yescharacteristic
38C3×#924C2211yescharacteristic
39C2×C3×#208C2211yescharacteristic
40#63979—21no—
41#63958—21no—
42#63935—24no—
43#63911C2211yescharacteristic, complemented
44#63908C2211yescharacteristic, complemented
45#63906—21no—
46#63904—21no—
47Dic3×Dic6C2211yescharacteristic, complemented
48C2×#3718C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic
53#63659C2211yescharacteristic
54#63657C2211yescharacteristic
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C3×#546—31no—
65#5834—31no—
66C2×#950—31no—
67#5806D311yescharacteristic, complemented
68C2×#932D311yescharacteristic, complemented
69C2×#916—31no—
70#5553—31no—
71#5239—31no—
72#5238—31no—
73#5217—31no—
74#5217—31no—
75#5217—61no—
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#5058—31no—
86#5054—31no—
87#5049—31no—
88#5047—31no—
89#5038—31no—
90#5037—31no—
91#5018—31no—
92#5015—31no—
93#5011—31no—
94C24×C32—21no—
95C2×C32×D4—22no—
96C2×C32×D4—21no—
97C2×C32×D4—41no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67D411yescharacteristic
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C3×#237—22no—
110C3×#237—41no—
111C3×#235—22no—
112C3×#235—41no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×#626—21no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#625—21no—
122C2×#624—21no—
123#3799—22no—
124#3799—41no—
125#3753—22no—
126#3753—41no—
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#217—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×#217—21no—
135C3×#217—21no—
136C3×#217D411yescharacteristic
137C3×#214—22no—
138C3×#214D414yescomplemented
139C3×#213—22no—
140C3×#213—22no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3C2311yescharacteristic
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4D411yescharacteristic
145C3×C4×Dic3C2311yescharacteristic
146C3×#208—22no—
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149Dic3⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3718—22no—
153#3717—22no—
154#3715—41no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C22×C3×D4—21no—
160C22×C3×D4C2×D311yescharacteristic
161C22×C3×D4C2×D311yescharacteristic
162C2×#239—31no—
163C2×#237C2×D311yescharacteristic
164C2×#235—31no—
165C2×#235C2×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×#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#953—21no—
182C2×#217—21no—
183#950—64no—
184Q8×Dic3—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#215—31no—
188C2×#215—31no—
189#940—31no—
190#940—61no—
191#940—61no—
192#939—21no—
193#938—31no—
194#938—61no—
195#938C2×D311yescharacteristic
196#936C2×D311yescharacteristic
197#935—21no—
198D4×Dic3C2×D311yescharacteristic
199C2×#214—31no—
200C2×#214C2×D311yescharacteristic
201C2×#214C2×D311yescharacteristic
202#932—24no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—61no—
208C2×#213—61no—
209C2×#213C2×D311yescharacteristic
210C2×#213C2×D311yescharacteristic
211#930—31no—
212#930—31no—
213#930—31no—
214#930—61no—
215#930—61no—
216C4×#67—61no—
217C4×#67C2×D311yescharacteristic
218#924C2×D311yescharacteristic
219C2×#208C2×D311yescharacteristic
220C22×C3⋊C8—31no—
221#916—64no—
222C2×#204—31no—
223C2×D3×C8—31no—
224#893—61no—
225#884—61no—
226#884—61no—
227#874—31no—
228C4×Dic6—31no—
229#835—31no—
230#835—31no—
231#832—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—61no—
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×C32—21no—
256C23×C32—42no—
257C23×C32—42no—
258C23×C32—81no—
259C23×C32C2×D411yescharacteristic
260C22×C3⋊D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3C2×D411yescharacteristic
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—21no—
266C32×D4—42no—
267C32×D4C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272#638—81no—
273C2×C3⋊Dic3—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C3×#67—41no—
277C3×#67—42no—
278C3×#67—42no—
279C3×#67—81no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—42no—
284C2×C3×Dic3—81no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6C2×D412yes—
297#626—42no—
298#626—42no—
299#626—81no—
300#625—81no—
301#624—42no—
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—91no—
309#546—31no—
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—21no—
322C24×C3—21no—
323C24×C3—41no—
324C3×#41—62no—
325C3×#41—62no—
326C3×#41—121no—
327C3×#41—121no—
328C2×C3×Q8—31no—
329C2×C3×Q8—31no—
330C2×C3×D4—22no—
331C2×C3×D4—22no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—41no—
339C2×C3×D4—42no—
340C2×C3×D4—41no—
341C2×C3×D4—41no—
342C2×C3×D4—42no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4C22×D311yescharacteristic
347C2×C3×D4C22×D311yescharacteristic
348C2×C3×D4C22×D311yescharacteristic
349C2×C3×D4C22×D311yescharacteristic
350C22×C3×C4—21no—
351C22×C3×C4—31no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C22×C3×C4—61no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C2×#67—21no—
358C2×#67—21no—
359C2×#67—21no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—61no—
367C2×#67—121no—
368C2×#67#6711yescharacteristic
369C22×Dic3—21no—
370C22×Dic3—21no—
371#239—62no—
372#239—121no—
373#237—22no—
374#237—41no—
375#235—22no—
376#235—41no—
377#235—62no—
378#235—121no—
379C2×D12—31no—
380C2×D12—31no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—61no—
384C2×D12—61no—
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3C22×D311yescharacteristic
390C2×Dic6C22×D311yescharacteristic
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—34no—
393C3×SD16—62no—
394C3×D8—62no—
395C3×D8—62no—
396C3×M16—62no—
397C2×C3×C8—31no—
398C2×C3×C8—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×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C42—31no—
410#217—21no—
411#217—21no—
412#217—21no—
413#217—21no—
414#217—21no—
415#217—61no—
416#217#6711yescharacteristic
417#216—62no—
418#216—62no—
419#215—62no—
420#215—121no—
421#214—22no—
422#214—121no—
423#214#6714yescomplemented
424#213—22no—
425#213—22no—
426#213—62no—
427#213—62no—
428#213—122no—
429#213—121no—
430#213—121no—
431#213—122no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—121no—
436(C2×D3)⋊C4#6711yescharacteristic
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—61no—
440C4⋊Dic3—61no—
441C4⋊Dic3C22×D311yescharacteristic
442Dic3⋊C4—21no—
443Dic3⋊C4—61no—
444Dic3⋊C4#6711yescharacteristic
445C4×Dic3—61no—
446C4×Dic3—61no—
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—22no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—84no—
470C22×C32C22×D411yescharacteristic
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C32×C4—21no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3⋊Dic3—41no—
484C3×Dic3—21no—
485C3×Dic3—22no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—31no—
492C2×#41—91no—
493C22×D4D3211yescharacteristic
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—91no—
508#127—181no—
509#124—31no—
510#123—61no—
511C22⋊Q8—31no—
512#121—31no—
513#121—61no—
514#121—91no—
515#121—91no—
516#121—181no—
517#121—181no—
518#120—61no—
519C4×Q8—91no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—181no—
523C2×C22⋊C4—61no—
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—21no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—42no—
544C23×C3—42no—
545C23×C3—42no—
546C23×C3—42no—
547C23×C3—44no—
548C23×C3—61no—
549C23×C3—82no—
550C23×C3—81no—
551C23×C3—81no—
552C23×C3—82no—
553C23×C3D3×D411yescharacteristic
554C23×C3C2×#6711yescharacteristic
555C22×D3—21no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—121no—
559C22×D3C2×#6711yescharacteristic
560C3×Q8—32no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×Q8—61no—
564C3×D4—22no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—22no—
572C3×D4—41no—
573C3×D4—41no—
574C3×D4—42no—
575C3×D4—42no—
576C3×D4—44no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—121no—
580C3×D4—122no—
581C3×D4—122no—
582C3×D4—241no—
583C3×D4D3×D412yes—
584C3×D4C2×#6712yes—
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—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—122no—
602C2×C3×C4—122no—
603C2×C3×C4—241no—
604C2×C3×C4D3×D411yescharacteristic
605C2×C3×C4C2×#6711yescharacteristic
606C2×C3×C4C23×D311yescharacteristic
607C2×C3×C4C23×D311yescharacteristic
608#67—41no—
609#67—42no—
610#67—42no—
611#67—81no—
612#67—122no—
613#67—122no—
614#67—241no—
615#67—241no—
616#67—241no—
617#67—241no—
618#67—241no—
619#67—242no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—42no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—81no—
627C2×Dic3—121no—
628C2×Dic3C2×#6711yescharacteristic
629C2×Dic3C2×#6711yescharacteristic
630C2×Dic3C2×#6711yescharacteristic
631D12—21no—
632D12—21no—
633D12—61no—
634D12—61no—
635D12—61no—
636D12—61no—
637D12—121no—
638D12—121no—
639D12—122no—
640D12—122no—
641D12—241no—
642C4×D3—21no—
643C4×D3—21no—
644C4×D3—42no—
645C4×D3—122no—
646C4×D3—122no—
647Dic6—21no—
648Dic6—21no—
649Dic6—21no—
650Dic6C2×#6712yes—
651C3×C8—32no—
652C3×C8—61no—
653C3⋊C8—21no—
654C3⋊C8—61no—
655C3⋊C8—61no—
656C3⋊C8—61no—
657C3⋊C8—61no—
658C3⋊C8—121no—
659C3⋊C8—121no—
660C3⋊C8C2×#6712yes—
661C2×C32—41no—
662C2×C32—42no—
663C2×C32—81no—
664C2×C32D4211yescharacteristic
665C2×C32#57511yescharacteristic
666C2×C32#57611yescharacteristic
667C3⋊D3—81no—
668C3×D3—41no—
669C3×D3—81no—
670C24—21no—
671#41—62no—
672#41—62no—
673#41—121no—
674#41—121no—
675#41—182no—
676#41—361no—
677C2×Q8—31no—
678C2×Q8—31no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—41no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—91no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4C2×D3211yescharacteristic
694C2×D4C2×D3211yescharacteristic
695C22×C4—31no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—181no—
700C22×C4C2×D3211yescharacteristic
701Q16—182no—
702SD16—34no—
703SD16—62no—
704SD16—182no—
705SD16—361no—
706D8—62no—
707D8—62no—
708D8—182no—
709D8—361no—
710M16—62no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—91no—
714C2×C8—91no—
715C2×C8—182no—
716C4⋊C4—31no—
717C4⋊C4—31no—
718C4⋊C4—61no—
719C4⋊C4—91no—
720C4⋊C4—181no—
721C22⋊C4—31no—
722C22⋊C4—31no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C42—31no—
731C42—181no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—22no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—22no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—42no—
745C22×C3—42no—
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—41no—
755C22×C3—41no—
756C22×C3—61no—
757C22×C3—61no—
758C22×C3—61no—
759C22×C3—81no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3—81no—
763C22×C3—84no—
764C22×C3—84no—
765C22×C3—88no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3C2×D3×D411yescharacteristic
770C22×C3C22×#6711yescharacteristic
771C2×D3—21no—
772C2×D3—21no—
773C2×D3—21no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—241no—
784C2×D3—241no—
785C2×D3—241no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—41no—
791C3×C4—61no—
792C3×C4—61no—
793C3×C4—61no—
794C3×C4—62no—
795C3×C4—121no—
796C3×C4—121no—
797C3×C4C2×D3×D411yescharacteristic
798C3×C4#100411yescharacteristic
799C3×C4#100411yescharacteristic
800C3×C4C22×#6711yescharacteristic
801Dic3—22no—
802Dic3—21no—
803Dic3—21no—
804Dic3—21no—
805Dic3—41no—
806Dic3—41no—
807Dic3—121no—
808Dic3—121no—
809Dic3—241no—
810C32#326811yescharacteristic, complemented, Sylow
811C23—21no—
812C23—21no—
813C23—31no—
814C23—42no—
815C23—42no—
816C23—61no—
817C23—81no—
818C23—181no—
819C23D3×#6711yescharacteristic
820Q8—32no—
821Q8—61no—
822Q8—61no—
823Q8—61no—
824D4—21no—
825D4—21no—
826D4—21no—
827D4—42no—
828D4—61no—
829D4—61no—
830D4—121no—
831D4—122no—
832D4—122no—
833D4—181no—
834D4—181no—
835D4—241no—
836D4—362no—
837D4—362no—
838D4—721no—
839D4—721no—
840D4—721no—
841D4D3×#6712yes—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—31no—
845C2×C4—31no—
846C2×C4—31no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—122no—
853C2×C4—122no—
854C2×C4—181no—
855C2×C4—241no—
856C2×C4—362no—
857C2×C4D3×#6711yescharacteristic
858C2×C4C22×D3211yescharacteristic
859C8—32no—
860C8—61no—
861C8—181no—
862C8—181no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—42no—
867C2×C3—41no—
868C2×C3—42no—
869C2×C3—41no—
870C2×C3—42no—
871C2×C3—82no—
872C2×C3—82no—
873C2×C3—81no—
874C2×C3—81no—
875C2×C3—121no—
876C2×C3—241no—
877C2×C3#577311yescharacteristic
878C2×C3#577411yescharacteristic
879C2×C3D4×#6711yescharacteristic
880C2×C3D4×#6711yescharacteristic
881C2×C3#582211yescharacteristic
882C2×C3#583511yescharacteristic
883D3—41no—
884D3—81no—
885D3—241no—
886D3—241no—
887D3—481no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—61no—
898C22—61no—
899C22—61no—
900C22—84no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—361no—
905C22—361no—
906C22—361no—
907C22C2×D3×#6711yescharacteristic
908C4—21no—
909C4—61no—
910C4—61no—
911C4—61no—
912C4—62no—
913C4—121no—
914C4—121no—
915C4—361no—
916C4C2×D3×#6711yescharacteristic
917C4#6433011yescharacteristic
918C3—21no—
919C3#8350711yescharacteristic, complemented
920C3#8395511yescharacteristic, complemented
921C2—41no—
922C2—42no—
923C2—81no—
924C2—121no—
925C2—241no—
926C2—721no—
927C2#1059509511yescharacteristic
928C2#1059509711yescharacteristic
929C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3268
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×#5806C2semidirect
2. C2×C3×#932C2semidirect
3. C2×#63935C2semidirect
4. #10595007C2semidirect
5. #10592916C2semidirect
6. #10591521C2semidirect
7. #10591498C2semidirect
8. #10591483C2semidirect
9. #10591481C2semidirect
10. #10591450C2semidirect
11. #10591442C2semidirect
12. #10591440C2semidirect
13. #10591178C2semidirect
14. #10591170C2semidirect
15. #10591147C2semidirect
21. C2×#3799C22semidirect
43. #63911C22semidirect
44. #63908C22semidirect
47. Dic3×Dic6C22semidirect
48. C2×#3718C22semidirect
49. C2×#3717C22semidirect
50. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
58. #63565C22semidirect
59. #63564C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
67. #5806D3semidirect
68. C2×#932D3semidirect
138. C3×#214D4semidirect
423. #214#67semidirect
810. C32#3268semidirect
919. C3#83507semidirect
920. C3#83955semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
C2×C3×#9322
C2×#639352
#105950072
#105929162
#105915212
#105914982
#105914832
#105914812
#105914502
#105914422
#105914402
#105911782
#105911702
#105911472
#839553
#835073