Finite Group Databasebeta

← #11872126

Subgroups — #11872126

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5603C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic, complemented
3#10592734C211yesmaximal, characteristic, complemented
4C3×#5036C211yesmaximal, characteristic
5#10591431C211yesmaximal, characteristic, complemented
6#10591431C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10591169C211yesmaximal, characteristic, complemented
10#10591127C211yesmaximal, characteristic, complemented
11#10591056C211yesmaximal, characteristic, complemented
12#10590465C211yesmaximal, characteristic, complemented
13#10590463C211yesmaximal, characteristic, complemented
14#10590454C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16#83460—31nomaximal
17#79992—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C32×#121C2211yescharacteristic
20#64135C2211yescharacteristic
21C3×#936—21no—
22C3×#936C2211yescharacteristic, complemented
23C3×#935—21no—
24C3×D4×Dic3C2211yescharacteristic, complemented
25C2×C3×#213C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C3×#888C2211yescharacteristic, complemented
30C3×#887C2211yescharacteristic, complemented
31C3×#879—21no—
32C3×#878—21no—
33D3×#217—21no—
34D3×#217—21no—
35#63898—21no—
36#63898—21no—
37Dic3×D12C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40Dic3×D12C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43#63659C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63657C2211yescharacteristic
46#63635C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#542—31no—
62#5798—31no—
63#5603D311yescharacteristic, complemented
64#5521—31no—
65C3×#447—31no—
66#5218—31no—
67#5153—31no—
68#5153—31no—
69#5152—31no—
70Dic3×D8—31no—
71#5087—31no—
72#5084—31no—
73#5057—31no—
74#5057—31no—
75#5046—31no—
76#5045—31no—
77#5036D311yescharacteristic
78#5035—31no—
79#5035—31no—
80#5035—61no—
81#5026—31no—
82C4×#215—31no—
83#5014—31no—
84C4×#213—31no—
85#5000—31no—
86#4761—31no—
87#4759—31no—
88#4758—31no—
89#4757—31no—
90#4723—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3×Dic3—21no—
97C2×C3×D12—21no—
98C2×C3×D12—22no—
99C2×C3×D12—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110#3757—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4×C3⋊Dic3—21no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×#217D411yescharacteristic
122C3×#213—22no—
123C3×#213—22no—
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3715—22no—
140#3715—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C22×D12C2×D311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×C4⋊Q8—31no—
147C3×#126—61no—
148C3×#124—31no—
149C3×#124—61no—
150C3×#123—61no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—61no—
153C3×#121—21no—
154C3×#121C2×D311yescharacteristic
155C3×#121C2×D311yescharacteristic
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C3×#117—31no—
159C2×#217—61no—
160C2×#217—61no—
161C2×#215—31no—
162C2×#215—31no—
163#936—21no—
164#936C2×D311yescharacteristic, complemented
165#935—21no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170D4×Dic3—61no—
171D4×Dic3—61no—
172D4×Dic3C2×D311yescharacteristic, complemented
173C2×#214—31no—
174C2×#214—31no—
175C2×#213C2×D311yescharacteristic
176C2×#213C2×D311yescharacteristic
177#926—31no—
178#926—31no—
179#926—61no—
180#926C2×D311yescharacteristic
181#924C2×D311yescharacteristic
182#893—61no—
183#893—61no—
184#888C2×D311yescharacteristic, complemented
185#887C2×D311yescharacteristic, complemented
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188#879—21no—
189#878—21no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194C3×#102—31no—
195C3×#102—31no—
196C3×C22⋊C8—31no—
197#835—31no—
198#835—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832—61no—
207#830—31no—
208#830—31no—
209#830—61no—
210#830C2×D311yescharacteristic
211#818—31no—
212#817—31no—
213#816—31no—
214#816—31no—
215#815—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218C8×Dic3—31no—
219#809—31no—
220#809—31no—
221#809C2×D311yescharacteristic
222#809C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808—31no—
226#808—61no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807—61no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C23×C32C2×D411yescharacteristic
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—24no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—24no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12#4112yes—
263C3×D12#4112yes—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—81no—
267D3×Dic3—81no—
268D3×Dic3—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—31no—
276#518—91no—
277#485—91no—
278#482—91no—
279#476—91no—
280#474—91no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—31no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—41no—
300C2×C3×D4—62no—
301C2×C3×D4—62no—
302C2×C3×D4—61no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C22×Dic3—21no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C2×D12—21no—
315C2×D12—22no—
316C2×D12—22no—
317C2×D12C22×D311yescharacteristic
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×Dic6—21no—
324C2×Dic6C22×D311yescharacteristic
325C3×D8—62no—
326C3×D8—62no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C22⋊C4—21no—
339C3×C22⋊C4—21no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—31no—
342C3×C22⋊C4—41no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—31no—
348C3×C42—31no—
349C3×C42—61no—
350#217—21no—
351#217—21no—
352#217—21no—
353#217—21no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—121no—
361#217#6711yescharacteristic
362#217#6711yescharacteristic
363#215—62no—
364#215—62no—
365#214—62no—
366#214—62no—
367#213—22no—
368#213—22no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3#6711yescharacteristic
380C4⋊Dic3#6711yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385C4×Dic3—21no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—121no—
389C4×Dic3C22×D311yescharacteristic
390C4×Dic3C22×D311yescharacteristic
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8C22×D311yescharacteristic
398C2×C3⋊C8C22×D311yescharacteristic
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32C22×D411yescharacteristic
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—84no—
413C32×C4—21no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—21no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—31no—
426C2×SD16—91no—
427C2×SD16—91no—
428C2×D8—31no—
429C2×D8—31no—
430C4⋊Q8—31no—
431#126—61no—
432#124—31no—
433#124—61no—
434#123—61no—
435C22⋊Q8—31no—
436C22⋊Q8—61no—
437#121D3211yescharacteristic
438C4×Q8—31no—
439C4×D4—31no—
440C4×D4—91no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—181no—
445C4×D4—181no—
446#117—31no—
447#117—91no—
448C2×C22⋊C4—181no—
449C2×C22⋊C4—181no—
450#107—91no—
451#107—91no—
452#106—91no—
453#106—91no—
454C4⋊C8—91no—
455C4⋊C8—91no—
456#103—91no—
457#103—91no—
458#102—31no—
459#102—31no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—31no—
465C22⋊C8—91no—
466#97—91no—
467C4×C8—91no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—41no—
472C23×C3—64no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3—241no—
476C23×C3—241no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×#6711yescharacteristic
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—24no—
482C22×D3—81no—
483C22×D3—81no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—241no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—32no—
492C3×D4—32no—
493C3×D4—41no—
494C3×D4—41no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—81no—
499C3×D4—81no—
500C3×D4—82no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—241no—
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—81no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—241no—
533C2×Dic3—241no—
534C2×Dic3—241no—
535C2×Dic3—241no—
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538C2×Dic3C2×#6711yescharacteristic
539C2×Dic3C2×#6711yescharacteristic
540D12—24no—
541D12—21no—
542D12—21no—
543D12#23712yes—
544D12#23712yes—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549Dic6—21no—
550Dic6—21no—
551Dic6—81no—
552C3×C8—61no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—121no—
561C3⋊C8—121no—
562C2×C32—41no—
563C2×C32—81no—
564C2×C32#52511yescharacteristic
565C2×C32#57611yescharacteristic
566C2×C32#57711yescharacteristic
567C3×D3—42no—
568C3×D3—42no—
569C24—61no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×D4—21no—
573C2×D4—31no—
574C2×D4—31no—
575C2×D4—62no—
576C2×D4—62no—
577C2×D4—61no—
578C2×D4C2×D3211yescharacteristic
579C22×C4—61no—
580C22×C4—181no—
581C22×C4—181no—
582C22×C4—181no—
583C22×C4—181no—
584C22×C4C2×D3211yescharacteristic
585SD16—182no—
586SD16—182no—
587D8—62no—
588D8—62no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8—91no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4C2×D3211yescharacteristic
602C22⋊C4—21no—
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—31no—
615C42—31no—
616C42—61no—
617C42—181no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—244no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C22×#6711yescharacteristic
646C2×D3—22no—
647C2×D3—22no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—84no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4C2×#23711yescharacteristic
668C3×C4C2×#23711yescharacteristic
669C3×C4D3×#4111yescharacteristic
670C3×C4D3×#4111yescharacteristic
671Dic3—21no—
672Dic3—21no—
673Dic3—21no—
674Dic3—21no—
675Dic3—41no—
676Dic3—41no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682Dic3—241no—
683C32#311811yescharacteristic, complemented, Sylow
684C23—21no—
685C23—64no—
686C23—61no—
687C23—61no—
688C23—241no—
689C23—241no—
690C23D3×#6711yescharacteristic
691Q8—61no—
692Q8—61no—
693Q8—241no—
694D4—21no—
695D4—21no—
696D4—32no—
697D4—32no—
698D4—64no—
699D4—61no—
700D4—61no—
701D4—81no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—241no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4—721no—
717C2×C4—721no—
718C2×C4D3×#6711yescharacteristic
719C2×C4C22×D3211yescharacteristic
720C8—61no—
721C8—61no—
722C8—181no—
723C8—181no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—41no—
728C2×C3—41no—
729C2×C3—81no—
730C2×C3—81no—
731C2×C3—81no—
732C2×C3—122no—
733C2×C3—122no—
734C2×C3—161no—
735C2×C3#558611yescharacteristic
736C2×C3#575711yescharacteristic
737C2×C3#577511yescharacteristic
738C2×C3#582811yescharacteristic
739C2×C3#583511yescharacteristic
740C2×C3#583711yescharacteristic
741D3—42no—
742D3—42no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—62no—
750C22—62no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—244no—
756C22C2×D3×#6711yescharacteristic
757C4—21no—
758C4—41no—
759C4—61no—
760C4—61no—
761C4—61no—
762C4—61no—
763C4—121no—
764C4—121no—
765C4—361no—
766C4—361no—
767C4D3×#23711yescharacteristic
768C4D3×#23711yescharacteristic
769C3—21no—
770C3#7999211yescharacteristic, complemented
771C3#8346011yescharacteristic, complemented
772C2—41no—
773C2—81no—
774C2—122no—
775C2—122no—
776C2#1059509611yescharacteristic
777C2#1059515411yescharacteristic
778C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5036C2
hypercenter#121D32
hypocenterC32#3118
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×#5603C2semidirect
2. #10594982C2semidirect
3. #10592734C2semidirect
5. #10591431C2semidirect
6. #10591431C2semidirect
7. #10591430C2semidirect
8. Dic3×#213C2semidirect
9. #10591169C2semidirect
10. #10591127C2semidirect
11. #10591056C2semidirect
12. #10590465C2semidirect
13. #10590463C2semidirect
14. #10590454C2semidirect
15. #10590453C2semidirect
22. C3×#936C22semidirect
24. C3×D4×Dic3C22semidirect
29. C3×#888C22semidirect
30. C3×#887C22semidirect
43. #63659C22semidirect
44. #63659C22semidirect
46. #63635C22semidirect
47. #63634C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5603D3semidirect
164. #936C2×D3semidirect
172. D4×Dic3C2×D3semidirect
184. #888C2×D3semidirect
185. #887C2×D3semidirect
683. C32#3118semidirect
770. C3#79992semidirect
771. C3#83460semidirect

Maximal subgroups

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

subgroupindex
C3×#56032
#105949822
#105927342
C3×#50362
#105914312
#105914302
Dic3×#2132
#105911692
#105911272
#105910562
#105904652
#105904632
#105904542
#105904532
#834603
#799923