Finite Group Databasebeta

← C2×#11797979 #72227378

Subgroups — C2×#11797979 #72227378

Order 2304.

1724 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#5147C211yesmaximal, characteristic
2C2×#10590920C211yesmaximal, characteristic, complemented
3C2×#10592851C211yesmaximal, characteristic, complemented
4#11797979C218yesmaximal, direct product factor
5C2×#10589137C211yesmaximal, characteristic, complemented
6C2×C3×#4563C211yesmaximal, characteristic, complemented
7C2×#10589124C211yesmaximal, characteristic, complemented
8C2×#10589106C211yesmaximal, characteristic, complemented
9C2×#69254—31nomaximal
10C2×#71515—31nomaximal
11C22×C32×D8C2211yescharacteristic
12C2×D4×C3⋊Dic3—21no—
13C2×C3×#904C2211yescharacteristic
14C2×#63815—21no—
15C2×#63659—21no—
16#10592851—22no—
17#10592851C2214yescomplemented
18C2×#63644C2211yescharacteristic
19C2×#63642C2211yescharacteristic
20C2×C3×#827C412yescomplemented
21C3×#5147C414yescomplemented
22C3×#5147C2214yes—
23C2×C3×#826C412yescomplemented
24C2×C3×#819C2211yescharacteristic
25C2×C3×#812C2211yescharacteristic
26C2×C3×#812C2211yescharacteristic
27C2×#63568—21no—
28#10590920—22no—
29#10590920C2214yescomplemented
30C3×#4563C2214yescomplemented
31#10589137C2214yescomplemented
32#10589124C2214yescomplemented
33#10589106C2214yescomplemented
34C2×C3×#509—31no—
35C2×#5197—31no—
36C2×#5152—31no—
37C2×#5152—31no—
38C2×#5152—61no—
39C2×#5147D311yescharacteristic
40C2×#4894—31no—
41C2×C3×#361—31no—
42C2×#4566—31no—
43C2×#4563D311yescharacteristic, complemented
44#71515—38no—
45C2×#4518—31no—
46C2×#4513—31no—
47C2×#4512—31no—
48C2×#4512—31no—
49C2×#4494—31no—
50#69254—38no—
51C22×C32×D4—21no—
52C23×C3⋊Dic3—41no—
53C2×C3×#235—21no—
54C2×C32×D8—21no—
55C2×C32×D8—21no—
56C2×C32×D8—21no—
57C2×C32×D8C2×C412yes—
58C2×C32×D8C2×C412yes—
59C2×C32×D8C2312yes—
60C22×C32×C8C2311yescharacteristic
61C2×#3757—41no—
62D4×C3⋊Dic3—24no—
63D4×C3⋊Dic3—42no—
64C2×C4⋊(C3⋊Dic3)—21no—
65C2×C4×C3⋊Dic3D411yescharacteristic
66C22×C3⋊(C3⋊C8)D411yescharacteristic
67C2×C3×#208—21no—
68C2×C3×Dic12C2×C411yescharacteristic, complemented
69C3×#904—21no—
70C3×#904—21no—
71C3×#904C2×C412yescomplemented
72C3×#904C2312yes—
73C2×C3×D24C2×C411yescharacteristic, complemented
74C2×C3×#204—21no—
75C2×#3711—41no—
76#63815—24no—
77#63815—42no—
78C2×D3×C3⋊C8—41no—
79#63659—24no—
80#63644—21no—
81#63644C2312yes—
82#63642D412yes—
83#63642C2312yes—
84C3×#827C2×C418yescomplemented
85C3×#826C2×C418yescomplemented
86C3×#819—21no—
87C3×#819C2312yes—
88C3×#812—21no—
89C3×#812C2×C412yescomplemented
90C3×#812C2312yes—
91C3×#812C2312yes—
92C2×C3×C3⋊C16—21no—
93C2×C3×C3⋊C16C2×C412yescomplemented
94#63568—24no—
95C2×AGL(1,ℤ/16)—91noSylow
96C2×C3×#135—31no—
97C22×C3×D8—21no—
98C22×C3×D8C2×D311yescharacteristic
99C22×C3×D8C2×D311yescharacteristic
100C2×#948—61no—
101C2×D4×Dic3—61no—
102C2×D4×Dic3—61no—
103C2×D4×Dic3—62no—
104C2×#907—61no—
105C2×#904C2×D311yescharacteristic
106C3×#509—34no—
107C3×#509—34no—
108C2×C3×SD32—32no—
109C2×C3×D16—32no—
110C2×C3×M32—31no—
111C2×C3×M32—31no—
112C2×C3×#108—31no—
113C2×#837—61no—
114C2×#832—61no—
115C2×#832—61no—
116C2×#832—62no—
117#5197—34no—
118#5197—62no—
119#5152—34no—
120#5152—34no—
121#5152—62no—
122#5152—62no—
123#5152—64no—
124#5152—64no—
125C2×#827Dic312yescomplemented
126#5147Dic314yescomplemented
127#5147C2×D314yes—
128C2×#826Dic312yescomplemented
129C2×#825—61no—
130C2×#819C2×D311yescharacteristic
131C2×#817—31no—
132C2×#817—31no—
133C2×#817—61no—
134C2×#815—31no—
135C2×#815—31no—
136C2×#815—61no—
137C2×#812C2×D311yescharacteristic
138C2×#812C2×D311yescharacteristic
139#4894—34no—
140#4894—62no—
141C3×#361—34no—
142#4566—34no—
143#4563C2×D314yescomplemented
144#4518—34no—
145#4513—34no—
146#4512—34no—
147#4512—34no—
148#4494—34no—
149C24×C32—41no—
150C2×C32×D4—22no—
151C2×C32×D4—22no—
152C2×C32×D4—22no—
153C2×C32×D4—41no—
154C2×C32×D4—41no—
155C2×C32×D4—41no—
156C22×C32×C4C2×D411yescharacteristic
157C22×C3⋊Dic3—21no—
158C22×C3⋊Dic3—44no—
159C22×C3⋊Dic3—41no—
160C22×C3⋊Dic3—84no—
161C2×C3×#67—41no—
162C3×#235—22no—
163C3×#235—22no—
164C3×#235—41no—
165C3×#235—41no—
166C2×C3×D12—21no—
167C2×C3×C4×D3—41no—
168C2×C3×Dic6—21no—
169C32×D8—22no—
170C32×D8—22no—
171C32×D8—22no—
172C32×D8C22×C414yes—
173C2×C32×C8C22×C411yescharacteristic
174C2×C32×C8C22×C411yescharacteristic
175C2×C32×C8C2×D411yescharacteristic
176C2×C32×C8#4111yescharacteristic
177C2×C32×C8#4111yescharacteristic
178C2×C32×C8C2411yescharacteristic
179#3757—44no—
180C4⋊(C3⋊Dic3)—22no—
181C4⋊(C3⋊Dic3)—41no—
182C4×C3⋊Dic3—21no—
183C4×C3⋊Dic3C2×D412yes—
184C2×C3⋊(C3⋊C8)—21no—
185C2×C3⋊(C3⋊C8)—21no—
186C2×C3⋊(C3⋊C8)C2×D412yes—
187C3×#208—22no—
188C3×#208—41no—
189C2×C3×C3⋊C8—41no—
190C3×Dic12—21no—
191C3×Dic12C22×C412yescomplemented
192C3×D24—21no—
193C3×D24C22×C412yescomplemented
194C3×#204—22no—
195C3×#204—22no—
196#3711—44no—
197D3×C3⋊C8—44no—
198C3×C3⋊C16—22no—
199C3×C3⋊C16C22×C414yescomplemented
200C2×#509—31no—
201C2×#444—91no—
202C2×#442—91no—
203AGL(1,ℤ/16)—98no—
204C2×#365—91no—
205C2×#361—31no—
206C2×#360—91no—
207C2×#347—91no—
208C2×C3×#41—61no—
209C22×C3×D4—22no—
210C22×C3×D4—21no—
211C22×C3×D4—21no—
212C23×Dic3—122no—
213C23×Dic3—121no—
214C23×Dic3—121no—
215C2×#235—21no—
216C3×#135—32no—
217C3×#135—32no—
218C3×#135—61no—
219C3×#135—61no—
220C2×C3×Q16—31no—
221C2×C3×SD16—61no—
222C2×C3×D8—22no—
223C2×C3×D8—22no—
224C2×C3×D8—22no—
225C2×C3×D8—21no—
226C2×C3×D8—21no—
227C2×C3×D8—21no—
228C2×C3×D8—21no—
229C2×C3×D8—21no—
230C2×C3×D8—21no—
231C2×C3×D8—22no—
232C2×C3×D8—22no—
233C2×C3×D8—22no—
234C2×C3×D8—31no—
235C2×C3×D8C4×D312yes—
236C2×C3×D8C4×D312yes—
237C2×C3×D8C2×Dic312yes—
238C2×C3×D8C2×Dic312yes—
239C2×C3×D8C22×D312yes—
240C2×C3×D8C22×D312yes—
241C2×C3×M16—61no—
242C22×C3×C8—21no—
243C22×C3×C8C22×D311yescharacteristic
244C22×C3×C8C22×D311yescharacteristic
245C2×#217—122no—
246C2×#217—121no—
247C2×#217—121no—
248#948—64no—
249#948—122no—
250D4×Dic3—64no—
251D4×Dic3—64no—
252D4×Dic3—68no—
253D4×Dic3—124no—
254D4×Dic3—122no—
255D4×Dic3—122no—
256C2×C4⋊Dic3—62no—
257C2×C4⋊Dic3—61no—
258C2×C4⋊Dic3—61no—
259C2×C4×Dic3—31no—
260C2×C4×Dic3—31no—
261C2×C4×Dic3—61no—
262C2×#208—21no—
263C2×#208—121no—
264C22×C3⋊C8—31no—
265C22×C3⋊C8—31no—
266C22×C3⋊C8—61no—
267C22×C3⋊C8—121no—
268#907—64no—
269#907—122no—
270C2×Dic12C2×Dic311yescharacteristic, complemented
271#904—21no—
272#904—21no—
273#904C2×Dic312yescomplemented
274#904C22×D312yes—
275C2×D24C2×Dic311yescharacteristic, complemented
276C2×#204—21no—
277C2×ΓL(1,𝔽25)—121no—
278C2×D3×C8—121no—
279C3×SD32—38no—
280C3×D16—38no—
281C3×M32—32no—
282C3×M32—32no—
283C3×M32—32no—
284C3×M32—61no—
285C2×C3×C16—32no—
286C2×C3×C16—61no—
287C3×#108—32no—
288C3×#108—61no—
289#837—64no—
290#832—64no—
291#832—64no—
292#832—68no—
293#827C2×Dic318yescomplemented
294#826C2×Dic318yescomplemented
295#825—64no—
296#819—21no—
297#819C22×D312yes—
298#817—32no—
299#817—32no—
300#817—62no—
301#817—62no—
302#817—61no—
303#817—61no—
304#815—32no—
305#815—32no—
306#815—32no—
307#815—32no—
308#815—62no—
309#815—62no—
310#812—21no—
311#812C2×Dic312yescomplemented
312#812C22×D312yes—
313#812C22×D312yes—
314C2×C3⋊C16—21no—
315C2×C3⋊C16C2×Dic312yescomplemented
316C23×C32—42no—
317C23×C32—42no—
318C23×C32—42no—
319C23×C32—82no—
320C23×C32—82no—
321C23×C32AGL(1,ℤ/8)11yescharacteristic
322C22×C3×D3—41no—
323C32×D4—24no—
324C32×D4—42no—
325C32×D4—42no—
326C32×D4—42no—
327C2×C32×C4C4×D411yescharacteristic
328C2×C32×C4C4×D411yescharacteristic
329C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
330C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
331C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
332C2×C32×C4C22×D411yescharacteristic
333C2×C3⋊Dic3—22no—
334C2×C3⋊Dic3—42no—
335C2×C3⋊Dic3—42no—
336C2×C3⋊Dic3—88no—
337C2×C3⋊Dic3—82no—
338C3×#67—42no—
339C3×#67—42no—
340C2×C3×Dic3—41no—
341C3×D12—22no—
342C3×D12—41no—
343C3×C4×D3—42no—
344C3×C4×D3—42no—
345C3×Dic6—22no—
346C3×Dic6—41no—
347C32×C8C4×D411yescharacteristic
348C32×C8C4×D411yescharacteristic
349C32×C8C23×C411yescharacteristic
350C32×C8C2×#4111yescharacteristic
351C3⋊(C3⋊C8)—22no—
352C3×C3⋊C8—42no—
353C2×#135—31no—
354C22×D8D3211yescharacteristic
355C2×#131—181no—
356C2×C4×D4—181no—
357#509—34no—
358#509—34no—
359C2×SD32—32no—
360C2×D16—32no—
361C2×M32—31no—
362C2×M32—31no—
363#444—94no—
364#444—182no—
365#442—94no—
366#442—182no—
367C2×#108—31no—
368C2×#106—91no—
369C2×#104—181no—
370C2×#102—181no—
371C2×#97—91no—
372#365—94no—
373#361—34no—
374#360—94no—
375#347—94no—
376C24×C3—42no—
377C24×C3—41no—
378C24×C3—41no—
379C3×#41—62no—
380C3×#41—62no—
381C3×#41—121no—
382C3×#41—121no—
383C2×C3×Q8—61no—
384C2×C3×D4—24no—
385C2×C3×D4—24no—
386C2×C3×D4—24no—
387C2×C3×D4—22no—
388C2×C3×D4—22no—
389C2×C3×D4—22no—
390C2×C3×D4—22no—
391C2×C3×D4—22no—
392C2×C3×D4—22no—
393C2×C3×D4—42no—
394C2×C3×D4—42no—
395C2×C3×D4—42no—
396C2×C3×D4—41no—
397C2×C3×D4—41no—
398C2×C3×D4—41no—
399C2×C3×D4—41no—
400C2×C3×D4—41no—
401C2×C3×D4—41no—
402C2×C3×D4—61no—
403C2×C3×D4—121no—
404C22×C3×C4—21no—
405C22×C3×C4—121no—
406C22×C3×C4D3×D411yescharacteristic
407C22×C3×C4D3×D411yescharacteristic
408C2×#67—41no—
409C22×Dic3—62no—
410C22×Dic3—61no—
411C22×Dic3—61no—
412C22×Dic3—128no—
413C22×Dic3—124no—
414C22×Dic3—124no—
415C22×Dic3—122no—
416C22×Dic3—121no—
417C22×Dic3—121no—
418C22×Dic3—248no—
419C22×Dic3—244no—
420C22×Dic3—244no—
421#235—22no—
422#235—22no—
423#235—41no—
424#235—41no—
425C2×D12—21no—
426C2×C4×D3—41no—
427C2×Dic6—21no—
428C3×Q16—32no—
429C3×Q16—61no—
430C3×SD16—62no—
431C3×SD16—62no—
432C3×D8—24no—
433C3×D8—24no—
434C3×D8—24no—
435C3×D8—22no—
436C3×D8—22no—
437C3×D8—22no—
438C3×D8—22no—
439C3×D8—22no—
440C3×D8—22no—
441C3×D8—24no—
442C3×D8—32no—
443C3×D8—61no—
444C3×D8C2×C4×D314yes—
445C3×D8C22×Dic314yes—
446C3×M16—62no—
447C3×M16—121no—
448C2×C3×C8—21no—
449C2×C3×C8—21no—
450C2×C3×C8—21no—
451C2×C3×C8—21no—
452C2×C3×C8—21no—
453C2×C3×C8—21no—
454C2×C3×C8—121no—
455C2×C3×C8C2×C4×D311yescharacteristic
456C2×C3×C8C2×C4×D311yescharacteristic
457C2×C3×C8D3×D411yescharacteristic
458C2×C3×C8D3×D411yescharacteristic
459C2×C3×C8#23711yescharacteristic
460C2×C3×C8#23711yescharacteristic
461C2×C3×C8#23711yescharacteristic
462C2×C3×C8#23711yescharacteristic
463C2×C3×C8C22×Dic311yescharacteristic
464C2×C3×C8C22×Dic311yescharacteristic
465C2×C3×C8C23×D311yescharacteristic
466C2×C3×C8C23×D311yescharacteristic
467#217—128no—
468#217—124no—
469#217—124no—
470C4⋊Dic3—64no—
471C4⋊Dic3—62no—
472C4⋊Dic3—62no—
473C4⋊Dic3—122no—
474C4⋊Dic3—121no—
475C4⋊Dic3—121no—
476C4×Dic3—32no—
477C4×Dic3—32no—
478C4×Dic3—62no—
479C4×Dic3—62no—
480C4×Dic3—61no—
481C4×Dic3—61no—
482#208—22no—
483#208—41no—
484#208—124no—
485C2×C3⋊C8—32no—
486C2×C3⋊C8—32no—
487C2×C3⋊C8—41no—
488C2×C3⋊C8—62no—
489C2×C3⋊C8—61no—
490C2×C3⋊C8—61no—
491C2×C3⋊C8—61no—
492C2×C3⋊C8—61no—
493C2×C3⋊C8—121no—
494C2×C3⋊C8—121no—
495C2×C3⋊C8—124no—
496Dic12—21no—
497Dic12C22×Dic312yescomplemented
498D24—21no—
499D24C22×Dic312yescomplemented
500#204—22no—
501#204—22no—
502ΓL(1,𝔽25)—124no—
503D3×C8—124no—
504C3×C16—34no—
505C3×C16—62no—
506C3⋊C16—22no—
507C3⋊C16C22×Dic314yescomplemented
508C22×C32—22no—
509C22×C32—44no—
510C22×C32—82no—
511C22×C32—82no—
512C22×C32—84no—
513C22×C32—84no—
514C22×C32#44211yescharacteristic
515C22×C32#44211yescharacteristic
516C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
517C2×C3×D3—42no—
518C2×C3×D3—82no—
519C32×C4#44211yescharacteristic
520C32×C4#44211yescharacteristic
521C32×C4C2×C4×D411yescharacteristic
522C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
523C3⋊Dic3—42no—
524C3⋊Dic3—82no—
525C3×Dic3—42no—
526C2×#41—61no—
527C22×D4—21no—
528C23×C4—361no—
529#135—32no—
530#135—32no—
531#135—61no—
532#135—61no—
533C2×Q16—31no—
534C2×SD16—61no—
535C2×D8—21no—
536C2×D8—21no—
537C2×D8—21no—
538C2×D8—31no—
539C2×D8D3×Dic312yes—
540C2×D8D3×Dic312yes—
541C2×D8C2×D3212yes—
542#131—184no—
543#131—362no—
544C2×M16—61no—
545C2×M16—361no—
546C22×C8—91no—
547C22×C8—361no—
548C22×C8C2×D3211yescharacteristic
549C4×D4—184no—
550C4×D4—362no—
551C2×C4⋊C4—181no—
552C2×C22⋊C4—361no—
553C2×C42—91no—
554SD32—38no—
555D16—38no—
556M32—32no—
557M32—32no—
558M32—32no—
559M32—61no—
560C2×C16—32no—
561C2×C16—61no—
562#108—32no—
563#108—61no—
564#106—92no—
565#106—181no—
566#104—184no—
567#102—184no—
568#97—92no—
569#97—92no—
570C23×C3—21no—
571C23×C3—44no—
572C23×C3—44no—
573C23×C3—44no—
574C23×C3—42no—
575C23×C3—42no—
576C23×C3—42no—
577C23×C3—42no—
578C23×C3—42no—
579C23×C3—42no—
580C23×C3—84no—
581C23×C3—82no—
582C23×C3—82no—
583C23×C3—84no—
584C23×C3—82no—
585C23×C3—82no—
586C23×C3—121no—
587C23×C3#91111yescharacteristic
588C23×C3#91411yescharacteristic
589C22×D3—41no—
590C3×Q8—62no—
591C3×Q8—121no—
592C3×D4—28no—
593C3×D4—24no—
594C3×D4—24no—
595C3×D4—44no—
596C3×D4—44no—
597C3×D4—44no—
598C3×D4—42no—
599C3×D4—42no—
600C3×D4—42no—
601C3×D4—42no—
602C3×D4—42no—
603C3×D4—42no—
604C3×D4—62no—
605C3×D4—122no—
606C3×D4—122no—
607C3×D4—121no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—121no—
615C2×C3×C4—122no—
616C2×C3×C4—122no—
617C2×C3×C4#67⋊C411yescharacteristic
618C2×C3×C4#67⋊C411yescharacteristic
619C2×C3×C4#91111yescharacteristic
620C2×C3×C4#91111yescharacteristic
621C2×C3×C4#91111yescharacteristic
622C2×C3×C4#91111yescharacteristic
623C2×C3×C4#91111yescharacteristic
624C2×C3×C4#91411yescharacteristic
625C2×C3×C4D4×Dic311yescharacteristic
626C2×C3×C4D4×Dic311yescharacteristic
627C2×C3×C4C2×D3×D411yescharacteristic
628C2×C3×C4C2×D3×D411yescharacteristic
629#67—42no—
630#67—42no—
631C2×Dic3—41no—
632C2×Dic3—64no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—124no—
636C2×Dic3—122no—
637C2×Dic3—122no—
638C2×Dic3—124no—
639C2×Dic3—122no—
640C2×Dic3—122no—
641C2×Dic3—2416no—
642C2×Dic3—248no—
643C2×Dic3—248no—
644C2×Dic3—244no—
645C2×Dic3—242no—
646C2×Dic3—242no—
647D12—22no—
648D12—41no—
649C4×D3—42no—
650C4×D3—42no—
651Dic6—22no—
652Dic6—41no—
653C3×C8—21no—
654C3×C8—21no—
655C3×C8—21no—
656C3×C8—21no—
657C3×C8—122no—
658C3×C8#67⋊C411yescharacteristic
659C3×C8#67⋊C411yescharacteristic
660C3×C8D4×Dic311yescharacteristic
661C3×C8D4×Dic311yescharacteristic
662C3×C8C22×C4×D311yescharacteristic
663C3×C8C2×#23711yescharacteristic
664C3×C8C2×#23711yescharacteristic
665C3×C8C23×Dic311yescharacteristic
666C3⋊C8—42no—
667C3⋊C8—62no—
668C3⋊C8—62no—
669C3⋊C8—122no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32—84no—
673C2×C32AGL(1,ℤ/16)12yescomplemented
674C2×C32C2×#44211yescharacteristic
675C3×D3—82no—
676C24—41no—
677#41—62no—
678#41—62no—
679#41—121no—
680#41—121no—
681C2×Q8—61no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—61no—
689C2×D4—121no—
690C22×C4—121no—
691C22×C4—181no—
692C22×C4—364no—
693C22×C4—361no—
694C22×C4—724no—
695C22×C4#381111yescharacteristic
696Q16—32no—
697Q16—61no—
698SD16—62no—
699SD16—62no—
700D8—22no—
701D8—22no—
702D8—22no—
703D8—32no—
704D8—61no—
705D8C2×D3×Dic314yes—
706M16—62no—
707M16—121no—
708M16—364no—
709C2×C8—92no—
710C2×C8—121no—
711C2×C8—181no—
712C2×C8—181no—
713C2×C8—364no—
714C2×C8C2×D3×Dic311yescharacteristic
715C2×C8C2×D3×Dic311yescharacteristic
716C2×C8#380511yescharacteristic
717C2×C8#380511yescharacteristic
718C2×C8#381111yescharacteristic
719C2×C8C22×D3211yescharacteristic
720C4⋊C4—182no—
721C4⋊C4—361no—
722C22⋊C4—364no—
723C42—92no—
724C42—181no—
725C16—34no—
726C16—62no—
727C22×C3—24no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—48no—
734C22×C3—44no—
735C22×C3—44no—
736C22×C3—84no—
737C22×C3—82no—
738C22×C3—82no—
739C22×C3—84no—
740C22×C3—88no—
741C22×C3—82no—
742C22×C3—84no—
743C22×C3—82no—
744C22×C3—84no—
745C22×C3—88no—
746C22×C3—84no—
747C22×C3—84no—
748C22×C3—122no—
749C22×C3—242no—
750C22×C3#478511yescharacteristic
751C22×C3#478511yescharacteristic
752C22×C3#515211yescharacteristic
753C22×C3#515211yescharacteristic
754C22×C3C2×#91111yescharacteristic
755C22×C3C2×#91411yescharacteristic
756C2×D3—42no—
757C2×D3—82no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—122no—
763C3×C4#478511yescharacteristic
764C3×C4#478511yescharacteristic
765C3×C4#515211yescharacteristic
766C3×C4#515211yescharacteristic
767C3×C4C2×#67⋊C411yescharacteristic
768C3×C4C2×#91111yescharacteristic
769C3×C4C2×#91111yescharacteristic
770C3×C4C2×D4×Dic311yescharacteristic
771Dic3—42no—
772Dic3—124no—
773Dic3—122no—
774Dic3—122no—
775Dic3—244no—
776Dic3—242no—
777Dic3—242no—
778C32C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
779C23—42no—
780C23—42no—
781C23—42no—
782C23—82no—
783C23—82no—
784C23—121no—
785C23#6393711yescharacteristic
786Q8—62no—
787Q8—121no—
788D4—24no—
789D4—42no—
790D4—42no—
791D4—42no—
792D4—62no—
793D4—122no—
794D4—122no—
795D4—121no—
796C2×C4—121no—
797C2×C4—122no—
798C2×C4—122no—
799C2×C4—182no—
800C2×C4—362no—
801C2×C4—362no—
802C2×C4—728no—
803C2×C4—722no—
804C2×C4#6392711yescharacteristic
805C2×C4#6392711yescharacteristic
806C2×C4#6393711yescharacteristic
807C2×C4#67⋊Dic311yescharacteristic
808C2×C4#67⋊Dic311yescharacteristic
809C2×C4C2×#381111yescharacteristic
810C8—122no—
811C8—182no—
812C8#67⋊Dic311yescharacteristic
813C8#67⋊Dic311yescharacteristic
814C8C22×D3×Dic311yescharacteristic
815C8C2×#380511yescharacteristic
816C2×C3—22no—
817C2×C3—22no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—22no—
824C2×C3—88no—
825C2×C3—84no—
826C2×C3—84no—
827C2×C3—242no—
828C2×C3#6925412yescomplemented
829C2×C3#7151512yescomplemented
830C2×C3C2×#478511yescharacteristic
831C2×C3C2×#515211yescharacteristic
832D3—82no—
833C22—22no—
834C22—44no—
835C22—82no—
836C22—82no—
837C22—84no—
838C22—84no—
839C22—122no—
840C22—242no—
841C22#1059143611yescharacteristic
842C22#1059143611yescharacteristic
843C22C2×#6393711yescharacteristic
844C4—122no—
845C4—362no—
846C4—722no—
847C4#1059143611yescharacteristic
848C4#1059143611yescharacteristic
849C4C2×#6392711yescharacteristic
850C4C2×#67⋊Dic311yescharacteristic
851C3—21no—
852C3C2×#7151511yescharacteristic, complemented
853C3C2×#6925411yescharacteristic, complemented
854C2—21no—
855C2—21no—
856C2—84no—
857C2—242no—
858C2#1179797912yesdirect product factor
859C2C2×#1059143611yescharacteristic
subgroupG/H
centerC22#10591436
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC22×C32×D8C22
socleC22×C32#442
prime radicalC2×C3×#5147C2
cosocleC2×C32×C8C24
hypercenterC22×D8D32
hypocenterC32C2×AGL(1,ℤ/16)
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
2. C2×#10590920C2semidirect
3. C2×#10592851C2semidirect
4. #11797979C2direct (N × H)
5. C2×#10589137C2semidirect
6. C2×C3×#4563C2semidirect
7. C2×#10589124C2semidirect
8. C2×#10589106C2semidirect
17. #10592851C22semidirect
20. C2×C3×#827C4semidirect
21. C3×#5147C4semidirect
23. C2×C3×#826C4semidirect
29. #10590920C22semidirect
30. C3×#4563C22semidirect
31. #10589137C22semidirect
32. #10589124C22semidirect
33. #10589106C22semidirect
43. C2×#4563D3semidirect
68. C2×C3×Dic12C2×C4semidirect
71. C3×#904C2×C4semidirect
73. C2×C3×D24C2×C4semidirect
84. C3×#827C2×C4semidirect
85. C3×#826C2×C4semidirect
89. C3×#812C2×C4semidirect
93. C2×C3×C3⋊C16C2×C4semidirect
125. C2×#827Dic3semidirect
126. #5147Dic3semidirect
128. C2×#826Dic3semidirect
143. #4563C2×D3semidirect
191. C3×Dic12C22×C4semidirect
193. C3×D24C22×C4semidirect
199. C3×C3⋊C16C22×C4semidirect
270. C2×Dic12C2×Dic3semidirect
273. #904C2×Dic3semidirect
275. C2×D24C2×Dic3semidirect
293. #827C2×Dic3semidirect
294. #826C2×Dic3semidirect
311. #812C2×Dic3semidirect
315. C2×C3⋊C16C2×Dic3semidirect
497. Dic12C22×Dic3semidirect
499. D24C22×Dic3semidirect
507. C3⋊C16C22×Dic3semidirect
673. C2×C32AGL(1,ℤ/16)semidirect
778. C32C2×AGL(1,ℤ/16)semidirect
828. C2×C3#69254semidirect
829. C2×C3#71515semidirect
852. C3C2×#71515semidirect
853. C3C2×#69254semidirect
858. C2#11797979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#51472
C2×#105909202
C2×#105928512
#117979792
C2×#105891372
C2×C3×#45632
C2×#105891242
C2×#105891062
C2×#692543
C2×#715153