Finite Group Databasebeta

← #11884415

Subgroups — #11884415

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5834C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C2×#63939C211yesmaximal, characteristic, complemented
4#10595067C211yesmaximal, characteristic, complemented
5#10592937C211yesmaximal, characteristic, complemented
6#10591607C211yesmaximal, characteristic, complemented
7#10591597C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10591515C211yesmaximal, characteristic, complemented
10#10591502C211yesmaximal, characteristic, complemented
11#10591472C211yesmaximal, characteristic, complemented
12#10591428C211yesmaximal, characteristic, complemented
13#10591164C211yesmaximal, characteristic, complemented
14#10591161C211yesmaximal, characteristic, complemented
15#10591155C211yesmaximal, characteristic, complemented
16#83922—31nomaximal
17#83577—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×#3753C2211yescharacteristic
24#64139C2211yescharacteristic
25C3×#950—24no—
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C3×#940—21no—
30C3×#940C2211yescharacteristic, complemented
31C3×#938—21no—
32C3×#938C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic
35C3×#930—21no—
36C3×#930C2211yescharacteristic, complemented
37C3×C4×#67—21no—
38C3×C4×#67C2211yescharacteristic
39C22×C3×C3⋊C8C2211yescharacteristic, complemented
40#63983—21no—
41#63971—21no—
42#63939—24no—
43D3×(C2×D3)⋊C4—21no—
44Dic3×D12C2211yescharacteristic
45#63864C2211yescharacteristic
46#63856C2211yescharacteristic
47#63850—21no—
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63657C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64C3×#550—31no—
65#5834D311yescharacteristic, complemented
66#5829—31no—
67C2×#950D311yescharacteristic, complemented
68C2×#949—31no—
69C2×#914—31no—
70#5550—31no—
71#5239—31no—
72#5238—31no—
73#5238—31no—
74#5238—31no—
75#5238—61no—
76#5187—31no—
77#5185—31no—
78#5176—31no—
79#5174—31no—
80#5164—31no—
81#5156—31no—
82#5150—31no—
83#5115—31no—
84#5111—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—
94C22×D32—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×#638—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67D411yescharacteristic
110C3×#239—22no—
111C3×#239—41no—
112C3×#235—22no—
113C3×#235—41no—
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×#626—21no—
122C2×D3×Dic3—21no—
123D3×D12—22no—
124D3×D12—41no—
125#3755—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×#217D411yescharacteristic
133C3×#216—22no—
134C3×#215D414yescomplemented
135C3×#214—22no—
136C3×#213—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4D411yescharacteristic
142C3×C4×Dic3—21no—
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—
155#3711—22no—
156#3268—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C2×C3×#41C2×D311yescharacteristic, complemented
161C2×C3×#41C2×D311yescharacteristic, complemented
162C2×#239C2×D311yescharacteristic
163C2×D3×D4—31no—
164C2×#235C2×D311yescharacteristic
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×#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#950—24no—
182#949—64no—
183#947—31no—
184#946—31no—
185Q8×Dic3C2×D311yescharacteristic, complemented
186C2×#216C2×D311yescharacteristic, complemented
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—61no—
191C2×#215C2×D311yescharacteristic
192#940—21no—
193#940C2×D311yescharacteristic, complemented
194#939—61no—
195#938—21no—
196#938C2×D311yescharacteristic
197#937—61no—
198#937—61no—
199D4×Dic3—31no—
200C2×#214—31no—
201C2×#214C2×D311yescharacteristic, complemented
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—61no—
208C2×#213C2×D311yescharacteristic
209#930—21no—
210#930—31no—
211#930—31no—
212#930—61no—
213#930C2×D311yescharacteristic, complemented
214#929—61no—
215C4×#67—21no—
216C4×#67C2×D311yescharacteristic
217C2×(C2×D3)⋊C4—61no—
218#924—31no—
219C2×#208—31no—
220C22×C3⋊C8C2×D311yescharacteristic, complemented
221#914—64no—
222C2×D24—31no—
223C2×ΓL(1,𝔽25)—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—
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×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
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
274#638—81no—
275C2×C3⋊Dic3—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C3×#67—41no—
279C3×#67—42no—
280C3×#67—42no—
281C3×#67—81no—
282C3×#67—81no—
283C3×#67—81no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—42no—
293C3×D12C2×D412yes—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—42no—
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×AGL(1,ℤ/8)—91no—
307C2×#135—31no—
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—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—22no—
324C3×#41—22no—
325C3×#41—42no—
326C3×#41—41no—
327C3×#41—41no—
328C3×#41—42no—
329C3×#41—62no—
330C3×#41—62no—
331C3×#41—121no—
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—61no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
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×C4—61no—
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—21no—
364C2×#67—21no—
365C2×#67—21no—
366C2×#67—61no—
367C2×#67—61no—
368C2×#67—61no—
369C2×#67—121no—
370C2×#67#6711yescharacteristic
371C22×Dic3—61no—
372#239—22no—
373#239—41no—
374D3×D4—62no—
375D3×D4—121no—
376#235—22no—
377#235—41no—
378C2×D12—21no—
379C2×D12—31no—
380C2×D12—31no—
381C2×D12—61no—
382C2×D12—62no—
383C2×D12—61no—
384C2×D12—121no—
385C2×D12C22×D311yescharacteristic
386C2×D12C22×D311yescharacteristic
387C2×C4×D3—21no—
388C2×C4×D3—21no—
389C2×C4×D3—61no—
390C2×C4×D3C22×D311yescharacteristic
391C2×Dic6C22×D311yescharacteristic
392C3×Q16—62no—
393C3×SD16—34no—
394C3×SD16—62no—
395C3×D8—62no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8—62no—
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×C42—31no—
407C3×C42—61no—
408#217—21no—
409#217—61no—
410#217—61no—
411#217#6711yescharacteristic
412#216—22no—
413#215—62no—
414#215—62no—
415#215—122no—
416#215—121no—
417#215#6714yescomplemented
418#214—22no—
419#214—121no—
420#213—22no—
421#213—62no—
422#213—62no—
423#213—62no—
424#213—121no—
425#213—121no—
426#213—122no—
427(C2×D3)⋊C4—21no—
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—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—121no—
437(C2×D3)⋊C4#6711yescharacteristic
438C4⋊Dic3—21no—
439C4⋊Dic3—31no—
440C4⋊Dic3—31no—
441C4⋊Dic3—61no—
442C4⋊Dic3C22×D311yescharacteristic
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445Dic3⋊C4#6711yescharacteristic
446C4×Dic3—21no—
447C4×Dic3C22×D311yescharacteristic
448#208—62no—
449C2×C3⋊C8—22no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8C22×D311yescharacteristic
457C2×C3⋊C8C22×D311yescharacteristic
458D24—62no—
459ΓL(1,𝔽25)—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—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—22no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479D32—84no—
480C32×C4—21no—
481C32×C4—22no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—31no—
492C2×#41D3211yescharacteristic, complemented
493C22×D4—91no—
494AGL(1,ℤ/8)—184no—
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×M16—91no—
506C22×C8—31no—
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×C3D3×D411yescharacteristic
543C23×C3C2×#6711yescharacteristic
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—121no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—241no—
554C22×D3—241no—
555C22×D3C2×#6711yescharacteristic
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—22no—
559C3×Q8—41no—
560C3×Q8—61no—
561C3×Q8—61no—
562C3×Q8D3×D412yes—
563C3×Q8C2×#6712yes—
564C3×D4—22no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—21no—
569C3×D4—32no—
570C3×D4—41no—
571C3×D4—42no—
572C3×D4—42no—
573C3×D4—44no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—122no—
578C3×D4—121no—
579C3×D4—122no—
580C3×D4—122no—
581C3×D4—241no—
582C3×D4—241no—
583C3×D4—241no—
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—21no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—42no—
599C2×C3×C4—42no—
600C2×C3×C4—44no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—122no—
606C2×C3×C4—122no—
607C2×C3×C4D3×D411yescharacteristic
608C2×C3×C4C2×#6711yescharacteristic
609C2×C3×C4C23×D311yescharacteristic
610C2×C3×C4C23×D311yescharacteristic
611#67—41no—
612#67—42no—
613#67—42no—
614#67—81no—
615#67—81no—
616#67—81no—
617#67—122no—
618#67—241no—
619#67—241no—
620#67—242no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—121no—
626C2×Dic3—241no—
627C2×Dic3C2×#6711yescharacteristic
628C2×Dic3C2×#6711yescharacteristic
629C2×Dic3C2×#6711yescharacteristic
630D12—21no—
631D12—21no—
632D12—21no—
633D12—42no—
634D12—61no—
635D12—61no—
636D12—61no—
637D12—61no—
638D12—121no—
639D12—121no—
640D12—122no—
641D12C2×#6712yes—
642C4×D3—21no—
643C4×D3—21no—
644C4×D3—42no—
645C4×D3—42no—
646C4×D3—241no—
647Dic6—21no—
648Dic6—21no—
649C3×C8—32no—
650C3×C8—61no—
651C3⋊C8—21no—
652C3⋊C8—61no—
653C3⋊C8—61no—
654C3⋊C8—61no—
655C3⋊C8—61no—
656C3⋊C8—121no—
657C3⋊C8—121no—
658C3⋊C8C2×#6712yes—
659C2×C32—41no—
660C2×C32—81no—
661C2×C32D4211yescharacteristic
662C2×C32#57511yescharacteristic
663C2×C32#57611yescharacteristic
664C3⋊D3—81no—
665C3×D3—41no—
666C3×D3—42no—
667C3×D3—81no—
668C24—181no—
669#41—22no—
670#41—41no—
671#41—62no—
672#41—62no—
673#41—121no—
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—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—91no—
688C2×D4—181no—
689C2×D4—182no—
690C2×D4—181no—
691C2×D4—361no—
692C2×D4C2×D3211yescharacteristic
693C22×C4—21no—
694C22×C4—31no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—181no—
698C22×C4C2×D3211yescharacteristic
699Q16—62no—
700SD16—34no—
701SD16—62no—
702SD16—182no—
703SD16—361no—
704D8—62no—
705D8—182no—
706D8—182no—
707D8—361no—
708M16—182no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—62no—
712C2×C8—91no—
713C2×C8—91no—
714C4⋊C4—31no—
715C4⋊C4—31no—
716C4⋊C4—61no—
717C4⋊C4—91no—
718C4⋊C4—181no—
719C22⋊C4—31no—
720C22⋊C4—31no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C42—31no—
729C42—61no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—42no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—61no—
748C22×C3—61no—
749C22×C3—62no—
750C22×C3—61no—
751C22×C3—81no—
752C22×C3—81no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C22×#6711yescharacteristic
760C2×D3—21no—
761C2×D3—22no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—244no—
779C2×D3—244no—
780C3×C4—21no—
781C3×C4—22no—
782C3×C4—21no—
783C3×C4—22no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—41no—
787C3×C4—42no—
788C3×C4—61no—
789C3×C4—61no—
790C3×C4—61no—
791C3×C4—121no—
792C3×C4—121no—
793C3×C4C2×D3×D411yescharacteristic
794C3×C4#100411yescharacteristic
795C3×C4#100411yescharacteristic
796C3×C4C22×#6711yescharacteristic
797Dic3—21no—
798Dic3—21no—
799Dic3—21no—
800Dic3—41no—
801Dic3—41no—
802Dic3—121no—
803Dic3—121no—
804Dic3—241no—
805C32#326811yescharacteristic, complemented, Sylow
806C23—21no—
807C23—31no—
808C23—61no—
809C23—61no—
810C23—181no—
811C23—362no—
812C23—362no—
813C23—721no—
814C23D3×#6711yescharacteristic
815Q8—21no—
816Q8—61no—
817Q8—61no—
818Q8D3×#6712yes—
819D4—21no—
820D4—21no—
821D4—32no—
822D4—42no—
823D4—61no—
824D4—61no—
825D4—61no—
826D4—122no—
827D4—121no—
828D4—122no—
829D4—122no—
830D4—181no—
831D4—181no—
832D4—241no—
833D4—241no—
834D4—241no—
835D4—362no—
836D4—721no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—31no—
841C2×C4—31no—
842C2×C4—31no—
843C2×C4—42no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—122no—
849C2×C4—122no—
850C2×C4—181no—
851C2×C4—721no—
852C2×C4D3×#6711yescharacteristic
853C2×C4C22×D3211yescharacteristic
854C8—32no—
855C8—61no—
856C8—181no—
857C8—181no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—41no—
862C2×C3—41no—
863C2×C3—81no—
864C2×C3—82no—
865C2×C3—81no—
866C2×C3—81no—
867C2×C3—122no—
868C2×C3—121no—
869C2×C3—241no—
870C2×C3#576811yescharacteristic
871C2×C3#576911yescharacteristic
872C2×C3D4×#6711yescharacteristic
873C2×C3D4×#6711yescharacteristic
874C2×C3#582211yescharacteristic
875C2×C3#583511yescharacteristic
876D3—41no—
877D3—42no—
878D3—81no—
879D3—241no—
880D3—241no—
881D3—481no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—61no—
889C22—61no—
890C22—61no—
891C22—62no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—361no—
898C22—361no—
899C22—361no—
900C22—724no—
901C22C2×D3×#6711yescharacteristic
902C4—21no—
903C4—22no—
904C4—61no—
905C4—61no—
906C4—61no—
907C4—121no—
908C4—121no—
909C4—361no—
910C4C2×D3×#6711yescharacteristic
911C4#6433011yescharacteristic
912C3—21no—
913C3#8357711yescharacteristic, complemented
914C3#8392211yescharacteristic, complemented
915C2—41no—
916C2—81no—
917C2—121no—
918C2—122no—
919C2—241no—
920C2—721no—
921C2#1059545311yescharacteristic
922C2#1059545611yescharacteristic
923C2#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×#950C2semidirect
3. C2×#63939C2semidirect
4. #10595067C2semidirect
5. #10592937C2semidirect
6. #10591607C2semidirect
7. #10591597C2semidirect
8. #10591566C2semidirect
9. #10591515C2semidirect
10. #10591502C2semidirect
11. #10591472C2semidirect
12. #10591428C2semidirect
13. #10591164C2semidirect
14. #10591161C2semidirect
15. #10591155C2semidirect
18. C2×C32×#41C22semidirect
26. C3×Q8×Dic3C22semidirect
27. C2×C3×#216C22semidirect
30. C3×#940C22semidirect
33. C2×C3×#214C22semidirect
36. C3×#930C22semidirect
39. C22×C3×C3⋊C8C22semidirect
48. C2×#3715C22semidirect
52. #63662C22semidirect
53. #63659C22semidirect
54. #63657C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
59. #63563C22semidirect
62. #63554C22semidirect
65. #5834D3semidirect
67. C2×#950D3semidirect
134. C3×#215D4semidirect
160. C2×C3×#41C2×D3semidirect
161. C2×C3×#41C2×D3semidirect
185. Q8×Dic3C2×D3semidirect
186. C2×#216C2×D3semidirect
193. #940C2×D3semidirect
201. C2×#214C2×D3semidirect
213. #930C2×D3semidirect
220. C22×C3⋊C8C2×D3semidirect
417. #215#67semidirect
492. C2×#41D32semidirect
805. C32#3268semidirect
913. C3#83577semidirect
914. C3#83922semidirect

Maximal subgroups

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

subgroupindex
C3×#58342
C2×C3×#9502
C2×#639392
#105950672
#105929372
#105916072
#105915972
#105915662
#105915152
#105915022
#105914722
#105914282
#105911642
#105911612
#105911552
#839223
#835773