Finite Group Databasebeta

← #11872204

Subgroups — #11872204

Order 1152.

860 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic, complemented
2#10594983C211yesmaximal, characteristic, complemented
3#10592695C211yesmaximal, characteristic, complemented
4C3×#5003C211yesmaximal, characteristic, complemented
5#10591172C211yesmaximal, characteristic, complemented
6#10591160C211yesmaximal, characteristic
7#10591056C211yesmaximal, characteristic, complemented
8#10590590C211yesmaximal, characteristic, complemented
9#10590558C211yesmaximal, characteristic, complemented
10#10590555C211yesmaximal, characteristic, complemented
11#10590530C211yesmaximal, characteristic, complemented
12#10590530C211yesmaximal, characteristic, complemented
13#10590479C211yesmaximal, characteristic, complemented
14#10590455C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#82541—31nomaximal
17#81352—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C32×#117C2211yescharacteristic
20#64133C2211yescharacteristic
21C3×#930C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×D3×C22⋊C4—21no—
28C3×D3×C22⋊C4—21no—
29C3×C4×D12—21no—
30C3×C4×D12—21no—
31#63969—21no—
32#63959—21no—
33#63918C2211yescharacteristic, complemented
34#63899—21no—
35Dic3×D12C2211yescharacteristic, complemented
36#63860C2211yescharacteristic, complemented
37#63858—21no—
38#63844C2211yescharacteristic, complemented
39C2×#3716C2211yescharacteristic
40C2×#3716C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63657C2211yescharacteristic
44#63637C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic
49C3×#809C2211yescharacteristic, complemented
50C3×#809C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#518—31no—
62#5603—31no—
63#5534—31no—
64#5521D311yescharacteristic, complemented
65C3×#482—31no—
66#5218—31no—
67#5217—31no—
68#5036—31no—
69#5018—31no—
70C4×#214—31no—
71#5016—31no—
72#5016—31no—
73#5014—31no—
74C4×#213—31no—
75#5008—31no—
76#5007—31no—
77#5003D311yescharacteristic, complemented
78#5000—31no—
79#4996—31no—
80#4996—31no—
81#4996—61no—
82#4890—31no—
83#4889—31no—
84#4870—31no—
85#4852—31no—
86#4787—31no—
87#4787—31no—
88#4785—31no—
89#4756—31no—
90#4731—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×D12—21no—
97C2×C3×D12—22no—
98C2×C3×D12—22no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×#627—21no—
107C2×D3×Dic3—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C42—21no—
112#3757—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217D411yescharacteristic
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137#3716—22no—
138#3716—22no—
139#3713—22no—
140#3713—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C22×D12C2×D311yescharacteristic
144C3×#121—31no—
145C3×C4×D4—31no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4—61no—
150C3×C4×D4—61no—
151C3×#117—21no—
152C3×#117—31no—
153C3×#117C2×D311yescharacteristic
154C3×#117C2×D311yescharacteristic
155C2×C3×C22⋊C4—61no—
156C2×C3×C22⋊C4—61no—
157#936—31no—
158#936—61no—
159#935—61no—
160D4×Dic3—31no—
161C2×#214—31no—
162C2×#214—31no—
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167#930C2×D311yescharacteristic
168#926C2×D311yescharacteristic
169#924—31no—
170#924—31no—
171#924—61no—
172C2×#204—31no—
173C2×#204—31no—
174#898—61no—
175#896—61no—
176#893C2×D311yescharacteristic
177#893C2×D311yescharacteristic
178#893C2×D311yescharacteristic
179#893C2×D311yescharacteristic
180#888—31no—
181#887—31no—
182#885—61no—
183#883—61no—
184D3×C22⋊C4—21no—
185D3×C22⋊C4—21no—
186#879—61no—
187#878—61no—
188#875—31no—
189C4×D12—21no—
190C4×D12—21no—
191C4×D12—31no—
192#869—31no—
193C4×Dic6—31no—
194C3×#107—31no—
195C3×#106—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C22⋊C8—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#830—31no—
204#830—31no—
205#830—61no—
206#830C2×D311yescharacteristic
207#821—31no—
208#821—31no—
209#815—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212C8×Dic3—31no—
213#810—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—61no—
218#810—61no—
219#809—31no—
220#809—31no—
221#809C2×D311yescharacteristic, complemented
222#809C2×D311yescharacteristic, complemented
223#808—31no—
224#808—31no—
225#808—61no—
226#808C2×D311yescharacteristic, complemented
227#807—31no—
228#807—31no—
229#807—61no—
230#807C2×D311yescharacteristic, complemented
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250#634—21no—
251#634—21no—
252C3×#67—81no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—24no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12#4112yes—
264C3×D12#4112yes—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269#627—81no—
270D3×Dic3—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—31no—
277#485—91no—
278#482—31no—
279#476—91no—
280#474—91no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×D4—31no—
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—62no—
296C2×C3×D4—62no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C22×C3×C4—21no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—21no—
307C22×Dic3—61no—
308C2×D12—21no—
309C2×D12—22no—
310C2×D12—22no—
311C2×D12C22×D311yescharacteristic
312C2×D12C22×D311yescharacteristic
313C2×D12C22×D311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—61no—
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—61no—
322C2×Dic6—61no—
323C2×Dic6—61no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4C22×D311yescharacteristic
332C3×C4⋊C4C22×D311yescharacteristic
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C22⋊C4—21no—
336C3×C22⋊C4—21no—
337C3×C22⋊C4—31no—
338C3×C22⋊C4—31no—
339C3×C22⋊C4—41no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C42—21no—
346C3×C42—21no—
347C3×C42—31no—
348C3×C42—31no—
349C3×C42—41no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—121no—
356#217#6711yescharacteristic
357#217#6711yescharacteristic
358#214—62no—
359#214—62no—
360#213—62no—
361#213—62no—
362#213—62no—
363#213—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3#6711yescharacteristic
377C4⋊Dic3#6711yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—121no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3C22×D311yescharacteristic
388C4×Dic3C22×D311yescharacteristic
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397#204—62no—
398#204—62no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32C22×D411yescharacteristic
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
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×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C22×D4—31no—
426C2×SD16—91no—
427C2×SD16—91no—
428C2×D8—91no—
429C2×D8—91no—
430C4⋊Q8—91no—
431#126—181no—
432#124—91no—
433#124—181no—
434#123—181no—
435C22⋊Q8—91no—
436C22⋊Q8—181no—
437#121—31no—
438C4×Q8—91no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—61no—
444C4×D4—61no—
445C4×D4—91no—
446#117—31no—
447#117D3211yescharacteristic
448C2×C22⋊C4—61no—
449C2×C22⋊C4—61no—
450#107—31no—
451#107—91no—
452#106—31no—
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—64no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3—241no—
474C23×C3—241no—
475C23×C3D3×D411yescharacteristic
476C23×C3C2×#6711yescharacteristic
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—24no—
480C22×D3—21no—
481C22×D3—81no—
482C22×D3—81no—
483C3×D4—32no—
484C3×D4—32no—
485C3×D4—64no—
486C3×D4—61no—
487C3×D4—61no—
488C3×D4—61no—
489C3×D4—61no—
490C3×D4—241no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—61no—
510C2×C3×C4—241no—
511C2×C3×C4—241no—
512C2×C3×C4—241no—
513C2×C3×C4—241no—
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—81no—
519C2×Dic3—21no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—241no—
527C2×Dic3C2×#6711yescharacteristic
528C2×Dic3C2×#6711yescharacteristic
529C2×Dic3C2×#6711yescharacteristic
530C2×Dic3C2×#6711yescharacteristic
531D12—24no—
532D12—21no—
533D12—21no—
534D12—21no—
535D12—21no—
536D12#23512yes—
537D12#23512yes—
538C4×D3—81no—
539C4×D3—81no—
540C4×D3—81no—
541C4×D3—81no—
542C4×D3—241no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—61no—
547Dic6—121no—
548Dic6—121no—
549Dic6—241no—
550Dic6—241no—
551C3×C8—61no—
552C3×C8—61no—
553C3⋊C8—21no—
554C3⋊C8—21no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—121no—
560C3⋊C8—121no—
561C2×C32—41no—
562C2×C32#52511yescharacteristic
563C2×C32#57611yescharacteristic
564C2×C32#57711yescharacteristic
565C3×D3—42no—
566C3×D3—42no—
567C3×D3—81no—
568C24—61no—
569C2×Q8—91no—
570C2×Q8—181no—
571C2×D4—31no—
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—62no—
575C2×D4—62no—
576C2×D4—61no—
577C2×D4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—181no—
583C22×C4C2×D3211yescharacteristic
584SD16—182no—
585SD16—182no—
586D8—182no—
587D8—182no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—91no—
591C2×C8—91no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—91no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4C2×D3211yescharacteristic
600C4⋊C4C2×D3211yescharacteristic
601C22⋊C4—21no—
602C22⋊C4—31no—
603C22⋊C4—31no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C42—21no—
614C42—31no—
615C42—31no—
616C42—181no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—62no—
628C22×C3—62no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—244no—
637C22×C3C2×D3×D411yescharacteristic
638C22×C3C22×#6711yescharacteristic
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—84no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—81no—
663C3×C4—81no—
664C3×C4—121no—
665C3×C4C2×#23511yescharacteristic
666C3×C4C2×#23511yescharacteristic
667C3×C4D3×#4111yescharacteristic
668C3×C4D3×#4111yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—21no—
672Dic3—21no—
673Dic3—41no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—241no—
679Dic3—241no—
680C32#311811yescharacteristic, complemented, Sylow
681C23—64no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—241no—
686C23—241no—
687C23D3×#6711yescharacteristic
688Q8—181no—
689Q8—181no—
690Q8—721no—
691D4—32no—
692D4—32no—
693D4—64no—
694D4—61no—
695D4—61no—
696D4—61no—
697D4—61no—
698D4—241no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—61no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—241no—
711C2×C4—241no—
712C2×C4—241no—
713C2×C4—241no—
714C2×C4—721no—
715C2×C4D3×#6711yescharacteristic
716C2×C4C22×D3211yescharacteristic
717C8—61no—
718C8—61no—
719C8—181no—
720C8—181no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—41no—
725C2×C3—41no—
726C2×C3—81no—
727C2×C3—122no—
728C2×C3—122no—
729C2×C3—241no—
730C2×C3#565611yescharacteristic
731C2×C3#577011yescharacteristic
732C2×C3#577411yescharacteristic
733C2×C3#579111yescharacteristic
734C2×C3#583511yescharacteristic
735C2×C3#583611yescharacteristic
736D3—42no—
737D3—42no—
738D3—81no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—62no—
743C22—62no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—244no—
752C22C2×D3×#6711yescharacteristic
753C4—21no—
754C4—41no—
755C4—41no—
756C4—61no—
757C4—61no—
758C4—61no—
759C4—61no—
760C4—121no—
761C4—361no—
762C4—361no—
763C4D3×#23511yescharacteristic
764C4D3×#23511yescharacteristic
765C3—21no—
766C3#8135211yescharacteristic, complemented
767C3#8254111yescharacteristic, complemented
768C2—41no—
769C2—122no—
770C2—122no—
771C2—241no—
772C2#1059489611yescharacteristic
773C2#1059545411yescharacteristic
774C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10591160C2
hypercenter#117D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5521C2semidirect
2. #10594983C2semidirect
3. #10592695C2semidirect
4. C3×#5003C2semidirect
5. #10591172C2semidirect
7. #10591056C2semidirect
8. #10590590C2semidirect
9. #10590558C2semidirect
10. #10590555C2semidirect
11. #10590530C2semidirect
12. #10590530C2semidirect
13. #10590479C2semidirect
14. #10590455C2semidirect
15. #10590452C2semidirect
33. #63918C22semidirect
35. Dic3×D12C22semidirect
36. #63860C22semidirect
38. #63844C22semidirect
44. #63637C22semidirect
45. #63637C22semidirect
46. #63635C22semidirect
47. #63634C22semidirect
49. C3×#809C22semidirect
50. C3×#809C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
64. #5521D3semidirect
77. #5003D3semidirect
221. #809C2×D3semidirect
222. #809C2×D3semidirect
226. #808C2×D3semidirect
230. #807C2×D3semidirect
680. C32#3118semidirect
766. C3#81352semidirect
767. C3#82541semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105949832
#105926952
C3×#50032
#105911722
#105911602
#105910562
#105905902
#105905582
#105905552
#105905302
#105904792
#105904552
#105904522
#825413
#813523