Finite Group Databasebeta

← #11884021

Subgroups — #11884021

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5609C211yesmaximal, characteristic, complemented
2C2×D3×#214C211yesmaximal, characteristic, complemented
3#10594899C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592741C211yesmaximal, characteristic, complemented
6C3×#5037C211yesmaximal, characteristic, complemented
7#10591469C211yesmaximal, characteristic, complemented
8#10591447C211yesmaximal, characteristic, complemented
9#10591438C211yesmaximal, characteristic, complemented
10#10591172C211yesmaximal, characteristic, complemented
11#10591151C211yesmaximal, characteristic, complemented
12#10590603C211yesmaximal, characteristic, complemented
13#10590530C211yesmaximal, characteristic, complemented
14#10590499C211yesmaximal, characteristic, complemented
15#10590478C211yesmaximal, characteristic, complemented
16#83491—31nomaximal
17#80121—31nomaximal
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic, complemented
23C32×#121C2211yescharacteristic
24C2×#3754C2211yescharacteristic, complemented
25#64133C2211yescharacteristic, complemented
26C2×#3748C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic
28C3×#937—21no—
29C2×C3×#214C2211yescharacteristic, complemented
30C2×C3×#213C2211yescharacteristic, complemented
31C3×C4×#67C2211yescharacteristic
32C3×#895C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×#884—21no—
35C3×#882—21no—
36#63970—21no—
37#63959—21no—
38D3×#214—24no—
39#63908C2211yescharacteristic, complemented
40#63879—21no—
41#63860C2211yescharacteristic, complemented
42#63851—21no—
43Dic3×Dic6C2211yescharacteristic, complemented
44C2×#3716C2211yescharacteristic
45C2×#3716C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic, complemented
48#63823—24no—
49C2×#3713C2211yescharacteristic
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×D42—31no—
64#5831—31no—
65C2×#949—31no—
66C22×#214—31no—
67C2×#932—31no—
68C2×D3×SD16—31no—
69#5609D311yescharacteristic, complemented
70#5552—31no—
71C3×#449—31no—
72#5218—31no—
73#5217—31no—
74#5163—31no—
75#5156—31no—
76#5154—31no—
77#5075—31no—
78#5074—31no—
79#5042—31no—
80#5042—31no—
81#5042—61no—
82#5040—31no—
83#5038—31no—
84#5037D311yescharacteristic, complemented
85#5018—31no—
86#5016—31no—
87#5011—31no—
88#4817—31no—
89#4806—31no—
90#4787—31no—
91#4775—31no—
92#4731—31no—
93#4728—31no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C3×D3×D4—22no—
106C3×D3×D4—41no—
107C3×D3×D4—44no—
108C3×#235—22no—
109C3×#235—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×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—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128#3757—21no—
129#3754—22no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750—21no—
132#3748—22no—
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#217D411yescharacteristic
136C3×#214—22no—
137C3×#213—41no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×Dic3⋊C4D411yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145Dic3⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149Dic32—21no—
150#3716—22no—
151#3716—41no—
152#3715—22no—
153#3715D414yescomplemented
154#3713—22no—
155#3713—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C22×C3×D4—61no—
162C2×D3×Q8—31no—
163C2×D3×D4—21no—
164C2×D3×D4C2×D311yescharacteristic
165C2×#235C2×D311yescharacteristic, complemented
166C22×D12C2×D311yescharacteristic
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C3×#127—31no—
171C3×#121—21no—
172C3×#121—31no—
173C3×#121—61no—
174C3×#121C2×D311yescharacteristic
175C3×#121C2×D311yescharacteristic
176C3×#120—61no—
177C3×#120—61no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180#949—64no—
181Q8×Dic3—31no—
182C2×#215—31no—
183C2×#215—31no—
184#940C2×D311yescharacteristic
185#939—61no—
186#938—31no—
187#938—61no—
188#937—21no—
189#936—31no—
190#936—61no—
191C2×#214—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—61no—
198C2×#214—64no—
199C2×#214C2×D311yescharacteristic, complemented
200#932—64no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213C2×D311yescharacteristic, complemented
206#930—31no—
207C4×#67—61no—
208C4×#67C2×D311yescharacteristic
209#924—31no—
210#924—31no—
211#924—61no—
212#924—61no—
213C2×#208—31no—
214C2×#208—31no—
215C2×#208—61no—
216C22×C3⋊C8—31no—
217D3×SD16—64no—
218C2×#204—31no—
219C2×#204—31no—
220C2×D3×C8—31no—
221#896—61no—
222#895C2×D311yescharacteristic
223#893C2×D311yescharacteristic
224#885—61no—
225#884—21no—
226#882—21no—
227#67⋊C4—61no—
228#875—31no—
229C4×Dic6—31no—
230C3×#103—31no—
231C3×#102—31no—
232C3×C22⋊C8—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#830—31no—
239#830C2×D311yescharacteristic, complemented
240#821—31no—
241#821—31no—
242(C2×D3)⋊C8—31no—
243#815—31no—
244Dic3⋊C8—31no—
245#810—31no—
246#810—31no—
247#810—61no—
248#810C2×D311yescharacteristic, complemented
249#809C2×D311yescharacteristic, complemented
250#807—31no—
251#807—31no—
252#807—61no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—42no—
264C22×C3×D3—81no—
265C22×C3×D3—81no—
266C22×C3×D3C2×D411yescharacteristic
267C32×D4—21no—
268C32×D4—21no—
269C32×D4—42no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277#634—21no—
278#634—21no—
279C3×#67—22no—
280C3×#67—42no—
281C3×#67—42no—
282C3×#67—42no—
283C3×#67—81no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—42no—
294C3×D12—42no—
295C3×D12C2×D412yes—
296C3×C4×D3—21no—
297C3×C4×D3—21no—
298C3×C4×D3—42no—
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)C2×D412yescomplemented
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—91no—
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—31no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C24×C3—61no—
326C23×D3—21no—
327C23×D3—21no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—31no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—41no—
339C2×C3×D4—62no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—62no—
345C2×C3×D4—61no—
346C2×C3×D4—61no—
347C2×C3×D4—121no—
348C2×C3×D4—121no—
349C2×C3×D4—124no—
350C2×C3×D4C22×D311yescharacteristic
351C2×C3×D4C22×D311yescharacteristic
352C22×C3×C4—21no—
353C22×C3×C4—31no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C2×#67—21no—
359C2×#67—21no—
360C2×#67—21no—
361C2×#67—21no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67#6711yescharacteristic
365C22×Dic3—61no—
366D3×Q8—62no—
367D3×Q8—121no—
368D3×D4—22no—
369D3×D4—41no—
370D3×D4—44no—
371#235—22no—
372#235—41no—
373C2×D12—22no—
374C2×D12—21no—
375C2×D12—21no—
376C2×D12—41no—
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—21no—
382C2×C4×D3—61no—
383C2×C4×D3C22×D311yescharacteristic
384C2×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6—62no—
388C2×Dic6—61no—
389C2×Dic6—61no—
390C2×Dic6—121no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—62no—
393C3×D8—121no—
394C2×C3×C8—31no—
395C2×C3×C8—31no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—31no—
398C3×C4⋊C4C22×D311yescharacteristic
399C3×C4⋊C4C22×D311yescharacteristic
400C3×C22⋊C4—21no—
401C3×C22⋊C4—21no—
402C3×C22⋊C4—31no—
403C3×C22⋊C4—31no—
404C3×C22⋊C4—41no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C42—31no—
408#217—61no—
409#217—61no—
410#217—61no—
411#217—61no—
412#217—61no—
413#217—121no—
414#217#6711yescharacteristic
415#215—34no—
416#215—62no—
417#214—22no—
418#214—34no—
419#214—62no—
420#214—62no—
421#214—62no—
422#214—62no—
423#214—122no—
424#214—121no—
425#213—41no—
426#213—62no—
427#213—62no—
428#213—62no—
429#213—62no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4#6711yescharacteristic
436C4⋊Dic3—31no—
437C4⋊Dic3—31no—
438C4⋊Dic3—61no—
439C4⋊Dic3—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4—121no—
444Dic3⋊C4#6711yescharacteristic
445C4×Dic3—61no—
446C4×Dic3—61no—
447C4×Dic3C22×D311yescharacteristic
448#208—62no—
449#208—62no—
450#208—122no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8—62no—
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460#204—62no—
461#204—121no—
462D3×C8—62no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
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—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—84no—
482C2×C3×D3—84no—
483C2×C3×D3AGL(1,ℤ/8)12yescomplemented
484C32×C4—21no—
485C32×C4—41no—
486C32×C4C22×D411yescharacteristic
487C32×C4H(5,𝔽2)11yescharacteristic
488C3⋊Dic3—41no—
489C3⋊Dic3—41no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C2×#41—31no—
495C22×Q8—91no—
496C22×D4—31no—
497C22×D4—31no—
498C22×D4—61no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—31no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—91no—
512#127—31no—
513#124—91no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—31no—
518#121—61no—
519#121—91no—
520#121—181no—
521#121D3211yescharacteristic
522#120—61no—
523#120—61no—
524C4×Q8—91no—
525C4×D4—31no—
526C4×D4—31no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8—91no—
530#103—31no—
531#103—91no—
532#102—31no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—31no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—31no—
543C23×C3—41no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—122no—
550C23×C3—122no—
551C23×C3—241no—
552C23×C3—241no—
553C23×C3D3×D411yescharacteristic
554C23×C3C2×#6711yescharacteristic
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—42no—
559C22×D3—42no—
560C22×D3—42no—
561C22×D3—42no—
562C22×D3—81no—
563C22×D3—81no—
564C22×D3C2×#6711yescharacteristic
565C3×Q8—32no—
566C3×Q8—61no—
567C3×D4—21no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—32no—
572C3×D4—41no—
573C3×D4—41no—
574C3×D4—42no—
575C3×D4—42no—
576C3×D4—62no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—82no—
583C3×D4—122no—
584C3×D4—122no—
585C3×D4—122no—
586C3×D4—122no—
587C3×D4—122no—
588C3×D4—241no—
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—21no—
597C2×C3×C4—31no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—122no—
607C2×C3×C4—122no—
608C2×C3×C4D3×D411yescharacteristic
609C2×C3×C4C2×#6711yescharacteristic
610C2×C3×C4C23×D311yescharacteristic
611C2×C3×C4C23×D311yescharacteristic
612#67—22no—
613#67—42no—
614#67—42no—
615#67—42no—
616#67—81no—
617#67—122no—
618#67—122no—
619C2×Dic3—21no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—121no—
625C2×Dic3—121no—
626C2×Dic3—122no—
627C2×Dic3C2×#6711yescharacteristic
628C2×Dic3C2×#6711yescharacteristic
629C2×Dic3C2×#6711yescharacteristic
630D12—21no—
631D12—21no—
632D12—21no—
633D12—21no—
634D12—21no—
635D12—42no—
636D12—42no—
637D12D3×D412yes—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—42no—
641C4×D3—42no—
642C4×D3—122no—
643Dic6—21no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—61no—
648Dic6—121no—
649Dic6—121no—
650Dic6—122no—
651Dic6—122no—
652Dic6D3×D412yescomplemented
653C3×C8—61no—
654C3×C8—61no—
655C3⋊C8—21no—
656C3⋊C8—21no—
657C3⋊C8—32no—
658C3⋊C8—32no—
659C3⋊C8—62no—
660C3⋊C8—61no—
661C3⋊C8—61no—
662C3⋊C8—121no—
663C2×C32—41no—
664C2×C32—81no—
665C2×C32D4211yescharacteristic
666C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
667C2×C32#57711yescharacteristic
668C3×D3—22no—
669C3×D3—42no—
670C3×D3—81no—
671C3×D3—81no—
672C24—61no—
673C24—61no—
674#41—62no—
675#41—121no—
676C2×Q8—31no—
677C2×Q8—91no—
678C2×Q8—181no—
679C2×Q8—182no—
680C2×Q8—361no—
681C2×D4—21no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—31no—
685C2×D4—31no—
686C2×D4—62no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—61no—
691C2×D4—62no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—121no—
695C2×D4—121no—
696C2×D4—124no—
697C2×D4—181no—
698C2×D4C2×D3211yescharacteristic
699C22×C4—31no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—181no—
703C22×C4C2×D3211yescharacteristic
704SD16—62no—
705SD16—94no—
706SD16—182no—
707SD16—182no—
708SD16—182no—
709SD16—361no—
710D8—121no—
711D8—182no—
712D8—182no—
713M16—182no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—91no—
717C2×C8—91no—
718C2×C8—182no—
719C4⋊C4—31no—
720C4⋊C4—91no—
721C4⋊C4—181no—
722C4⋊C4—181no—
723C4⋊C4C2×D3211yescharacteristic
724C22⋊C4—21no—
725C22⋊C4—31no—
726C22⋊C4—31no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—31no—
734C42—181no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—32no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—61no—
753C22×C3—61no—
754C22×C3—62no—
755C22×C3—81no—
756C22×C3—81no—
757C22×C3—81no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—244no—
767C22×C3—244no—
768C22×C3C2×D3×D411yescharacteristic
769C22×C3C22×#6711yescharacteristic
770C2×D3—21no—
771C2×D3—21no—
772C2×D3—22no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—84no—
782C2×D3—84no—
783C2×D3#93212yescomplemented
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—61no—
792C3×C4—61no—
793C3×C4—62no—
794C3×C4—61no—
795C3×C4—81no—
796C3×C4C2×D3×D411yescharacteristic
797C3×C4C2×D3×D411yescharacteristic
798C3×C4#100411yescharacteristic
799C3×C4#100411yescharacteristic
800Dic3—21no—
801Dic3—21no—
802Dic3—21no—
803Dic3—22no—
804Dic3—121no—
805Dic3—121no—
806Dic3—121no—
807Dic3—121no—
808Dic3—241no—
809Dic3—241no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—21no—
812C23—31no—
813C23—61no—
814C23—61no—
815C23—61no—
816C23—122no—
817C23—122no—
818C23—122no—
819C23—122no—
820C23—241no—
821C23—241no—
822C23D3×#6711yescharacteristic
823Q8—32no—
824Q8—61no—
825Q8—181no—
826Q8—181no—
827Q8—362no—
828D4—21no—
829D4—21no—
830D4—32no—
831D4—42no—
832D4—62no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—61no—
837D4—61no—
838D4—122no—
839D4—122no—
840D4—122no—
841D4—122no—
842D4—122no—
843D4—241no—
844D4—362no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—31no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—122no—
855C2×C4—122no—
856C2×C4—181no—
857C2×C4—181no—
858C2×C4—362no—
859C2×C4D3×#6711yescharacteristic
860C2×C4C22×D3211yescharacteristic
861C8—61no—
862C8—61no—
863C8—92no—
864C8—181no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—41no—
869C2×C3—41no—
870C2×C3—62no—
871C2×C3—81no—
872C2×C3—81no—
873C2×C3—81no—
874C2×C3—122no—
875C2×C3—161no—
876C2×C3—241no—
877C2×C3—241no—
878C2×C3#559011yescharacteristic
879C2×C3#577011yescharacteristic
880C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
881C2×C3C2×#93211yescharacteristic
882C2×C3D4×#6711yescharacteristic
883C2×C3#583611yescharacteristic
884D3—22no—
885D3—42no—
886D3—81no—
887D3—81no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—32no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—61no—
896C22—61no—
897C22—62no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—244no—
907C22—244no—
908C22C2×D3×#6711yescharacteristic
909C4—21no—
910C4—41no—
911C4—61no—
912C4—61no—
913C4—61no—
914C4—62no—
915C4—361no—
916C4—361no—
917C4D32×D411yescharacteristic
918C4#6431311yescharacteristic
919C3—21no—
920C3#8012111yescharacteristic, complemented
921C3#8349111yescharacteristic, complemented
922C2—41no—
923C2—62no—
924C2—81no—
925C2—122no—
926C2—241no—
927C2—241no—
928C2D3×#93211yescharacteristic
929C2#1059528711yescharacteristic
930C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5609C2semidirect
2. C2×D3×#214C2semidirect
3. #10594899C2semidirect
4. C2×#63823C2semidirect
5. #10592741C2semidirect
6. C3×#5037C2semidirect
7. #10591469C2semidirect
8. #10591447C2semidirect
9. #10591438C2semidirect
10. #10591172C2semidirect
11. #10591151C2semidirect
12. #10590603C2semidirect
13. #10590530C2semidirect
14. #10590499C2semidirect
15. #10590478C2semidirect
20. C2×C3×#235C22semidirect
22. C2×D3×Dic6C22semidirect
24. C2×#3754C22semidirect
25. #64133C22semidirect
26. C2×#3748C22semidirect
29. C2×C3×#214C22semidirect
30. C2×C3×#213C22semidirect
39. #63908C22semidirect
41. #63860C22semidirect
43. Dic3×Dic6C22semidirect
45. C2×#3716C22semidirect
47. C2×#3715C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63659C22semidirect
53. #63637C22semidirect
54. #63634C22semidirect
55. C3×#830C22semidirect
56. C3×#810C22semidirect
57. C3×#809C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
60. #63563C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
69. #5609D3semidirect
84. #5037D3semidirect
153. #3715D4semidirect
165. C2×#235C2×D3semidirect
199. C2×#214C2×D3semidirect
205. C2×#213C2×D3semidirect
239. #830C2×D3semidirect
248. #810C2×D3semidirect
249. #809C2×D3semidirect
301. C3×Dic6C2×D4semidirect
306. C3⋊(C3⋊C8)C2×D4semidirect
483. C2×C3×D3AGL(1,ℤ/8)semidirect
652. Dic6D3×D4semidirect
783. C2×D3#932semidirect
810. C32#3265semidirect
920. C3#80121semidirect
921. C3#83491semidirect

Maximal subgroups

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

subgroupindex
C3×#56092
C2×D3×#2142
#105948992
C2×#638232
#105927412
C3×#50372
#105914692
#105914472
#105914382
#105911722
#105911512
#105906032
#105905302
#105904992
#105904782
#834913
#801213