Finite Group Databasebeta

← #11860744

Subgroups — #11860744

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic
2#10595347C211yesmaximal, characteristic, complemented
3#10595215C211yesmaximal, characteristic
4SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6#10591572C211yesmaximal, characteristic, complemented
7#10591566C211yesmaximal, characteristic, complemented
8#10591557C211yesmaximal, characteristic, complemented
9#10591446C211yesmaximal, characteristic, complemented
10#10591440C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic
12#10590775C211yesmaximal, characteristic, complemented
13Dic3×#204C211yesmaximal, characteristic, complemented
14#10590706C211yesmaximal, characteristic, complemented
15#10590692C211yesmaximal, characteristic, complemented
16#83843—31nomaximal
17#79649—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic, complemented
22D4×C3⋊Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic, complemented
24C2×C3×#215C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C3×D3×SD16C418yescomplemented
28C2×C3×#204C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30#67⋊Dic3—21no—
31Dic3×#67—21no—
32D3×#217—21no—
33C2×(C2×D3)⋊Dic3—21no—
34#63898C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63855—21no—
37#63855C2211yescharacteristic
38#63843—21no—
39#63843C2211yescharacteristic, complemented
40Dic3×Dic6—21no—
41Dic3×Dic6C2211yescharacteristic, complemented
42#63841—21no—
43#63841C2211yescharacteristic
44#63841C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46#63662C2211yescharacteristic, complemented
47#63659C2211yescharacteristic
48#63644C2211yescharacteristic, complemented
49C8×C3⋊Dic3C2211yescharacteristic, complemented
50C3×#835C2211yescharacteristic, complemented
51C3×#832C2211yescharacteristic
52C3×#817C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#63554C2211yescharacteristic, complemented
62C22×C3×SD16—31no—
63#5812—31no—
64#5798—31no—
65C2×D3×SD16D311yescharacteristic
66#5572—31no—
67#5545—31no—
68C3×C4×SD16—31no—
69#5225—31no—
70#5215—31no—
71#5164—31no—
72#5164—31no—
73#5164—31no—
74#5164—31no—
75Dic3×SD16—31no—
76Dic3×SD16—31no—
77Dic3×SD16—31no—
78Dic3×SD16—31no—
79Dic3×SD16—61no—
80Dic3×SD16D311yescharacteristic, complemented
81#5106—31no—
82#5101—31no—
83#5026—31no—
84#5018—31no—
85#4860—31no—
86#4852—31no—
87#4817—31no—
88#4802—31no—
89#4770—31no—
90#4757—31no—
91C4×#204—31no—
92#4689—31no—
93C23×C3×D3—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C3⋊Dic3—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×Q8—22no—
100C3×D3×Q8C2×C414yescomplemented
101C3×D3×D4—22no—
102C3×D3×D4C2×C414yes—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C32×SD16C2×C414yescomplemented
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#215C2×C414yescomplemented
121C3×#214C2×C414yescomplemented
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×#204C2×C414yescomplemented
130C3×D3×C8C2×C414yescomplemented
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134Dic3⋊Dic3D411yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142Dic32—21no—
143Dic32—21no—
144Dic32—21no—
145#3711—22no—
146#2949—91noSylow
147C22×C3×Q8—31no—
148C22×C3×D4—31no—
149C2×D3×Q8C2×D311yescharacteristic
150C2×D3×D4C2×D311yescharacteristic
151C2×C3×SD16—21no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C2×C3×SD16—38no—
155C2×C3×SD16—31no—
156C2×C3×SD16C2×D311yescharacteristic
157C2×C3×SD16C2×D311yescharacteristic
158C22×C3×C8—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161C2×#217—61no—
162C2×#217—61no—
163Q8×Dic3—31no—
164Q8×Dic3—31no—
165Q8×Dic3—31no—
166Q8×Dic3—31no—
167Q8×Dic3—61no—
168Q8×Dic3—61no—
169Q8×Dic3—61no—
170Q8×Dic3C2×D311yescharacteristic, complemented
171C2×#215C2×D311yescharacteristic
172D4×Dic3—31no—
173D4×Dic3—31no—
174D4×Dic3—31no—
175D4×Dic3—31no—
176D4×Dic3—61no—
177D4×Dic3—61no—
178D4×Dic3—61no—
179D4×Dic3C2×D311yescharacteristic
180C2×#214C2×D311yescharacteristic
181C4×#67—61no—
182C2×(C2×D3)⋊C4—61no—
183#926—31no—
184#926—31no—
185#926—31no—
186#926—61no—
187#926—61no—
188C2×#208—31no—
189D3×SD16Dic318yescomplemented
190C2×#204C2×D311yescharacteristic
191C2×ΓL(1,𝔽25)—31no—
192C2×D3×C8C2×D311yescharacteristic
193#893—31no—
194#892—31no—
195#892—31no—
196#892—61no—
197#887—31no—
198#887—61no—
199#67⋊C4—61no—
200D3×C22⋊C4—61no—
201C4×D12—31no—
202#872—31no—
203#872—61no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×C4×C8—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—61no—
215#835C2×D311yescharacteristic, complemented
216#832—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—61no—
221#832C2×D311yescharacteristic
222#821—31no—
223#818—31no—
224#818—31no—
225#817—31no—
226#817—31no—
227#817—61no—
228#817C2×D311yescharacteristic, complemented
229#816—31no—
230#815—31no—
231#815—31no—
232#815—31no—
233C8×Dic3—31no—
234C8×Dic3—31no—
235C8×Dic3—61no—
236C8×Dic3C2×D311yescharacteristic, complemented
237#810—31no—
238#809—31no—
239#807—31no—
240#807—31no—
241#803—31no—
242C23×C32—21no—
243C22×C3×D3—21no—
244C22×C3×D3—24no—
245C22×C3×D3—81no—
246C22×C3×D3—81no—
247C22×C3×D3C2×D411yescharacteristic
248C32×Q8—21no—
249C32×Q8C22×C412yes—
250C32×D4—21no—
251C32×D4C22×C412yes—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—81no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C3×#67—24no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12C22×C412yes—
269C3×C4×D3—24no—
270C3×C4×D3C22×C412yes—
271C3×C4×D3#4112yes—
272C3×Dic6—21no—
273C3×Dic6—24no—
274C3×Dic6C22×C412yes—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8C22×C412yes—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C22×SD16—31no—
282#519—91no—
283#518—91no—
284#440—91no—
285#440—91no—
286#440—91no—
287#440—91no—
288C4×SD16—31no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292#427—91no—
293#419—91no—
294#418—91no—
295#405—91no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—34no—
300C2×C3×Q8—31no—
301C2×C3×Q8—61no—
302C2×C3×Q8—62no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×D4—21no—
306C2×C3×D4—34no—
307C2×C3×D4—31no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C2×#67—21no—
316C22×Dic3—21no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—121no—
322D3×Q8—22no—
323D3×Q8C2×Dic314yescomplemented
324D3×D4—22no—
325D3×D4C2×Dic314yes—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6C22×D311yescharacteristic
333C3×SD16—24no—
334C3×SD16—34no—
335C3×SD16—34no—
336C3×SD16—34no—
337C3×SD16C4×D314yescomplemented
338C3×SD16C2×Dic314yescomplemented
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—34no—
342C2×C3×C8—31no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—31no—
350C3×C42—61no—
351#217—21no—
352#217—31no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—121no—
361#215C2×Dic314yescomplemented
362#214C2×Dic314yescomplemented
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369C4⋊Dic3—21no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—121no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389C4×Dic3—21no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—121no—
404C4×Dic3C22×D311yescharacteristic
405#208—62no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204C2×Dic314yescomplemented
412ΓL(1,𝔽25)—62no—
413D3×C8C2×Dic314yescomplemented
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—84no—
424C2×C3×D3C4×D412yes—
425C32×C4—22no—
426C32×C4C23×C411yescharacteristic
427C32×C4C2×#4111yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3C4×D412yes—
438C22×Q8—31no—
439C22×D4—31no—
440C2×SD16—31no—
441C2×SD16—31no—
442C2×SD16—38no—
443C2×SD16—31no—
444C2×SD16D3211yescharacteristic
445C2×M16—91no—
446C22×C8—31no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×Q8—181no—
452C4×Q8—181no—
453C4×D4—31no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—181no—
458C4×D4—181no—
459#117—91no—
460#117—91no—
461#117—91no—
462#117—181no—
463#117—181no—
464C2×C22⋊C4—181no—
465C2×C22⋊C4—181no—
466#107—91no—
467#107—91no—
468#106—31no—
469#106—91no—
470#103—31no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#97—91no—
479#97—91no—
480C4×C8—31no—
481C4×C8—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3—64no—
487C23×C3—61no—
488C23×C3—241no—
489C23×C3—241no—
490C22×D3—21no—
491C22×D3—24no—
492C22×D3—81no—
493C22×D3—81no—
494C22×D3D3×D411yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—22no—
498C3×Q8—32no—
499C3×Q8—41no—
500C3×Q8—64no—
501C3×Q8—61no—
502C3×Q8C2×C4×D312yes—
503C3×Q8C22×Dic312yes—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—32no—
508C3×D4—41no—
509C3×D4—64no—
510C3×D4—61no—
511C3×D4C2×C4×D312yes—
512C3×D4C22×Dic312yes—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—64no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—241no—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—24no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—81no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—241no—
547C2×Dic3—241no—
548C2×Dic3—241no—
549C2×Dic3—241no—
550C2×Dic3—242no—
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553C2×Dic3D3×D411yescharacteristic
554D12—21no—
555D12C22×Dic312yes—
556C4×D3—24no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3#23712yes—
560C4×D3C22×Dic312yes—
561Dic6—21no—
562Dic6—24no—
563Dic6C22×Dic312yes—
564C3×C8—22no—
565C3×C8—32no—
566C3×C8—61no—
567C3×C8C2×C4×D312yes—
568C3×C8C22×Dic312yes—
569C3⋊C8—21no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C3⋊C8C22×Dic312yes—
574C2×C32—42no—
575C2×C32C2×C4×D411yescharacteristic
576C2×C32#57711yescharacteristic
577C2×C32#57711yescharacteristic
578C3×D3—22no—
579C3×D3—42no—
580C24—61no—
581C2×Q8—34no—
582C2×Q8—31no—
583C2×Q8—61no—
584C2×Q8—62no—
585C2×Q8C2×D3211yescharacteristic
586C2×D4—34no—
587C2×D4—31no—
588C2×D4—62no—
589C2×D4—61no—
590C2×D4C2×D3211yescharacteristic
591C22×C4—31no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597SD16—34no—
598SD16—34no—
599SD16—34no—
600SD16D3×Dic314yescomplemented
601M16—182no—
602C2×C8—31no—
603C2×C8—34no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C22⋊C4—61no—
618C22⋊C4—91no—
619C22⋊C4—91no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—61no—
627C42—91no—
628C42—181no—
629C42—181no—
630C42—181no—
631C42—181no—
632C42—181no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—32no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—62no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—244no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—22no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—84no—
658C2×D3D4×Dic312yes—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—32no—
664C3×C4—42no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—62no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4C22×C4×D311yescharacteristic
671C3×C4C2×#23711yescharacteristic
672C3×C4D3×#4111yescharacteristic
673C3×C4C23×Dic311yescharacteristic
674Dic3—21no—
675Dic3—21no—
676Dic3—22no—
677Dic3—41no—
678Dic3—41no—
679Dic3—62no—
680Dic3—61no—
681Dic3—61no—
682Dic3—61no—
683Dic3—61no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—241no—
690Dic3—241no—
691Dic3D4×Dic312yes—
692C32#294911yescharacteristic, complemented, Sylow
693C23—21no—
694C23—31no—
695C23—64no—
696C23—61no—
697C23—241no—
698C23—241no—
699Q8—21no—
700Q8—32no—
701Q8—64no—
702Q8—61no—
703Q8C2×D3×Dic312yes—
704D4—21no—
705D4—32no—
706D4—64no—
707D4—61no—
708D4C2×D3×Dic312yes—
709C2×C4—21no—
710C2×C4—31no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—64no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—91no—
720C2×C4—91no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—241no—
724C2×C4—721no—
725C2×C4—721no—
726C2×C4—721no—
727C2×C4C22×D3211yescharacteristic
728C8—32no—
729C8—61no—
730C8—181no—
731C8C2×D3×Dic312yes—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—42no—
736C2×C3—42no—
737C2×C3—62no—
738C2×C3—82no—
739C2×C3—122no—
740C2×C3C4×D3×D411yescharacteristic
741C2×C3#576211yescharacteristic
742C2×C3#576211yescharacteristic
743C2×C3#576211yescharacteristic
744C2×C3#577011yescharacteristic
745C2×C3C2×D4×Dic311yescharacteristic
746D3—22no—
747D3—42no—
748C22—22no—
749C22—32no—
750C22—41no—
751C22—41no—
752C22—61no—
753C22—61no—
754C22—62no—
755C22—121no—
756C22—121no—
757C22—244no—
758C22D32×D411yescharacteristic
759C4—22no—
760C4—32no—
761C4—62no—
762C4—61no—
763C4—61no—
764C4—121no—
765C4—121no—
766C4—181no—
767C4—181no—
768C4—361no—
769C4—361no—
770C4D3×#23711yescharacteristic
771C4C22×D3×Dic311yescharacteristic
772C3—21no—
773C3#7964911yescharacteristic, complemented
774C3#8384311yescharacteristic, complemented
775C2—42no—
776C2—62no—
777C2—122no—
778C2#1059474811yescharacteristic
779C2#1059475311yescharacteristic
780C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
cosocleC2×C32×C4C24
hypercenterC2×SD16D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. #10595347C2semidirect
4. SD16×C3⋊Dic3C2semidirect
5. C3×Dic3×SD16C2semidirect
6. #10591572C2semidirect
7. #10591566C2semidirect
8. #10591557C2semidirect
9. #10591446C2semidirect
10. #10591440C2semidirect
12. #10590775C2semidirect
13. Dic3×#204C2semidirect
14. #10590706C2semidirect
15. #10590692C2semidirect
21. Q8×C3⋊Dic3C22semidirect
23. C3×Q8×Dic3C22semidirect
27. C3×D3×SD16C4semidirect
39. #63843C22semidirect
41. Dic3×Dic6C22semidirect
46. #63662C22semidirect
48. #63644C22semidirect
49. C8×C3⋊Dic3C22semidirect
50. C3×#835C22semidirect
52. C3×#817C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63575C22semidirect
55. #63575C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
60. #63555C22semidirect
61. #63554C22semidirect
80. Dic3×SD16D3semidirect
100. C3×D3×Q8C2×C4semidirect
110. C32×SD16C2×C4semidirect
120. C3×#215C2×C4semidirect
121. C3×#214C2×C4semidirect
129. C3×#204C2×C4semidirect
130. C3×D3×C8C2×C4semidirect
170. Q8×Dic3C2×D3semidirect
189. D3×SD16Dic3semidirect
215. #835C2×D3semidirect
228. #817C2×D3semidirect
236. C8×Dic3C2×D3semidirect
323. D3×Q8C2×Dic3semidirect
337. C3×SD16C4×D3semidirect
338. C3×SD16C2×Dic3semidirect
361. #215C2×Dic3semidirect
362. #214C2×Dic3semidirect
411. #204C2×Dic3semidirect
413. D3×C8C2×Dic3semidirect
600. SD16D3×Dic3semidirect
692. C32#2949semidirect
773. C3#79649semidirect
774. C3#83843semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
#105953472
#105952152
SD16×C3⋊Dic32
C3×Dic3×SD162
#105915722
#105915662
#105915572
#105914462
#105914402
#105914212
#105907752
Dic3×#2042
#105907062
#105906922
#838433
#796493