Finite Group Databasebeta

← C2×#11797967 #72227376

Subgroups — C2×#11797967 #72227376

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×#10590634C211yesmaximal, characteristic
2C2×#10590920C211yesmaximal, characteristic, complemented
3C2×#10592568C211yesmaximal, characteristic, complemented
4#11797967C218yesmaximal, direct product factor
5C2×C3×#4487C211yesmaximal, characteristic, complemented
6C2×#10589128C211yesmaximal, characteristic, complemented
7C2×C3×#4488C211yesmaximal, characteristic, complemented
8C2×#10589106C211yesmaximal, characteristic, complemented
9C2×#69310—31nomaximal
10C2×#69249—31nomaximal
11C22×#3745C2211yescharacteristic
12C2×#64102—21no—
13C2×C3×#904C2211yescharacteristic
14C2×#63815—21no—
15C2×C32×#106C2211yescharacteristic
16C2×#63642C2211yescharacteristic
17C2×#63636—21no—
18#10592568—22no—
19#10592568C2214yescomplemented
20C2×C3×#819C2211yescharacteristic
21C2×C3×#812C2211yescharacteristic
22C2×C3×#812C2211yescharacteristic
23C2×#63568—21no—
24#10590920—22no—
25#10590920C2214yescomplemented
26C2×#63549C412yescomplemented
27#10590634C414yescomplemented
28#10590634C2214yes—
29C2×#63546C412yescomplemented
30C3×#4488C2214yescomplemented
31C3×#4487C2214yescomplemented
32#10589128C2214yescomplemented
33#10589106C2214yescomplemented
34C2×#5197—31no—
35C2×#5193—31no—
36C2×#4908—31no—
37C2×#4894—31no—
38C2×#4869—31no—
39C2×#4869—31no—
40C2×#4869—61no—
41C2×C3×#365—31no—
42C2×C3×#360—31no—
43C2×#4516—31no—
44C2×#4512—31no—
45C2×#4512—31no—
46C2×#4495—31no—
47C2×#4488D311yescharacteristic, complemented
48C2×#4487D311yescharacteristic, complemented
49#69310—38no—
50#69249—38no—
51C22×C4⋊(C3⋊D3)—21no—
52C22×C4×C3⋊D3—41no—
53C2×C3×#235—21no—
54C22×C32×C8C2311yescharacteristic
55C2×C32×C4⋊C4—21no—
56C2×#3752—41no—
57C2×C4×C3⋊Dic3D411yescharacteristic
58C22×C3⋊(C3⋊C8)D411yescharacteristic
59C2×#3745—21no—
60C2×#3745—21no—
61C2×#3745—21no—
62C2×#3745C2×C412yes—
63C2×#3745C2×C412yes—
64C2×#3745C2312yes—
65#64102—24no—
66#64102—42no—
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—
79C32×#106—21no—
80C32×#106C2312yes—
81#63642D412yes—
82#63642C2312yes—
83#63636—24no—
84C3×#819—21no—
85C3×#819C2312yes—
86C3×#812—21no—
87C3×#812C2×C412yescomplemented
88C3×#812C2312yes—
89C3×#812C2312yes—
90C2×C3×C3⋊C16—21no—
91C2×C3×C3⋊C16C2×C412yescomplemented
92#63568—24no—
93#63549C2×C418yescomplemented
94#63546C2×C418yescomplemented
95C2×AGL(1,ℤ/16)—91noSylow
96C2×C3×#135—31no—
97C2×#948—61no—
98C2×#907—61no—
99C2×#904C2×D311yescharacteristic
100C22×D24—31no—
101C22×D24—31no—
102C22×D24—61no—
103C2×#893—61no—
104C2×#893—61no—
105C2×#893—62no—
106C2×C3×M32—31no—
107C2×C3×M32—31no—
108C2×C3×#108—31no—
109C2×C3×#106—21no—
110C2×C3×#106C2×D311yescharacteristic
111C2×C3×#106C2×D311yescharacteristic
112C2×#837—61no—
113#5197—34no—
114#5197—62no—
115#5193—34no—
116#5193—34no—
117C2×#828—32no—
118C2×#826—32no—
119C2×#825—61no—
120C2×#819C2×D311yescharacteristic
121C2×#815—31no—
122C2×#815—31no—
123C2×#815—61no—
124C2×#812C2×D311yescharacteristic
125C2×#812C2×D311yescharacteristic
126C2×#809—61no—
127C2×#809—61no—
128C2×#809—62no—
129#4908—34no—
130#4908—34no—
131C2×#800—32no—
132C2×D48—32no—
133#4894—34no—
134#4894—62no—
135#4869—34no—
136#4869—34no—
137#4869—62no—
138#4869—62no—
139#4869—64no—
140#4869—64no—
141C3×#365—34no—
142C3×#360—34no—
143#4516—34no—
144#4512—34no—
145#4512—34no—
146#4495—34no—
147#4488C2×D314yescomplemented
148#4487C2×D314yescomplemented
149C23×C3⋊D3—41no—
150C22×C32×C4—41no—
151C22×C32×C4C2×D411yescharacteristic
152C22×C3⋊Dic3—21no—
153C2×C4⋊(C3⋊D3)—22no—
154C2×C4⋊(C3⋊D3)—22no—
155C2×C4⋊(C3⋊D3)—22no—
156C2×C4⋊(C3⋊D3)—41no—
157C2×C4⋊(C3⋊D3)—41no—
158C2×C4⋊(C3⋊D3)—41no—
159C2×C4×C3⋊D3—44no—
160C2×C4×C3⋊D3—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—
169C2×C32×C8C22×C411yescharacteristic
170C2×C32×C8C22×C411yescharacteristic
171C2×C32×C8C2×D411yescharacteristic
172C2×C32×C8#4111yescharacteristic
173C2×C32×C8#4111yescharacteristic
174C2×C32×C8C2411yescharacteristic
175C32×C4⋊C4—22no—
176C32×C4⋊C4—41no—
177#3752—44no—
178C4×C3⋊Dic3—21no—
179C4×C3⋊Dic3C2×D412yes—
180C2×C3⋊(C3⋊C8)—21no—
181C2×C3⋊(C3⋊C8)—21no—
182C2×C3⋊(C3⋊C8)C2×D412yes—
183#3745—22no—
184#3745—22no—
185#3745—22no—
186#3745C22×C414yes—
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—91no—
201C2×#444—91no—
202C2×#442—91no—
203AGL(1,ℤ/16)—98no—
204C2×#365—31no—
205C2×#361—91no—
206C2×#360—31no—
207C2×#347—91no—
208C2×C3×#41—61no—
209C2×#235—21no—
210C22×D12—62no—
211C22×D12—61no—
212C22×D12—61no—
213C22×C4×D3—122no—
214C22×C4×D3—121no—
215C22×C4×D3—121no—
216C3×#135—32no—
217C3×#135—32no—
218C3×#135—61no—
219C3×#135—61no—
220C2×C3×Q16—31no—
221C2×C3×SD16—61no—
222C2×C3×D8—31no—
223C2×C3×M16—61no—
224C22×C3×C8—21no—
225C22×C3×C8C22×D311yescharacteristic
226C22×C3×C8C22×D311yescharacteristic
227C2×C3×C4⋊C4—22no—
228C2×C3×C4⋊C4—21no—
229C2×C3×C4⋊C4—21no—
230#948—64no—
231#948—122no—
232C2×(C2×D3)⋊C4—122no—
233C2×(C2×D3)⋊C4—121no—
234C2×(C2×D3)⋊C4—121no—
235C2×C4×Dic3—31no—
236C2×C4×Dic3—31no—
237C2×C4×Dic3—61no—
238C2×#208—21no—
239C2×#208—121no—
240C22×C3⋊C8—31no—
241C22×C3⋊C8—31no—
242C22×C3⋊C8—61no—
243C22×C3⋊C8—121no—
244#907—64no—
245#907—122no—
246C2×Dic12C4×D311yescharacteristic, complemented
247#904—21no—
248#904—21no—
249#904C4×D312yescomplemented
250#904C22×D312yes—
251C2×D24—32no—
252C2×D24—32no—
253C2×D24—32no—
254C2×D24—32no—
255C2×D24—32no—
256C2×D24—32no—
257C2×D24—62no—
258C2×D24—62no—
259C2×D24—62no—
260C2×D24—62no—
261C2×D24—62no—
262C2×D24—62no—
263C2×D24—61no—
264C2×D24—61no—
265C2×D24—61no—
266C2×D24—61no—
267C2×D24—61no—
268C2×D24—61no—
269C2×D24C4×D311yescharacteristic, complemented
270C2×#204—21no—
271C2×ΓL(1,𝔽25)—121no—
272C2×D3×C8—121no—
273#893—64no—
274#893—64no—
275#893—68no—
276#893—124no—
277#893—122no—
278#893—122no—
279C3×M32—32no—
280C3×M32—32no—
281C3×M32—32no—
282C3×M32—61no—
283C2×C3×C16—32no—
284C2×C3×C16—61no—
285C3×#108—32no—
286C3×#108—61no—
287C3×#106—22no—
288C3×#106—21no—
289C3×#106—21no—
290C3×#106—22no—
291C3×#106C22×D312yes—
292C3×#106C22×D312yes—
293#837—64no—
294#828—38no—
295#826—38no—
296#825—64no—
297#819—21no—
298#819C22×D312yes—
299#815—32no—
300#815—32no—
301#815—32no—
302#815—32no—
303#815—62no—
304#815—62no—
305#812—21no—
306#812C4×D312yescomplemented
307#812C22×D312yes—
308#812C22×D312yes—
309C2×C3⋊C16—21no—
310C2×C3⋊C16C4×D312yescomplemented
311#809—64no—
312#809—64no—
313#809—68no—
314#800—38no—
315D48—38no—
316C23×C32AGL(1,ℤ/8)11yescharacteristic
317C22×C3⋊D3—42no—
318C22×C3⋊D3—42no—
319C22×C3⋊D3—42no—
320C22×C3⋊D3—82no—
321C22×C3⋊D3—82no—
322C22×C3×D3—41no—
323C2×C32×C4—42no—
324C2×C32×C4—82no—
325C2×C32×C4C4×D411yescharacteristic
326C2×C32×C4C4×D411yescharacteristic
327C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
328C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
329C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
330C2×C32×C4C22×D411yescharacteristic
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3—42no—
333C4⋊(C3⋊D3)—24no—
334C4⋊(C3⋊D3)—42no—
335C4⋊(C3⋊D3)—42no—
336C4⋊(C3⋊D3)—42no—
337C4×C3⋊D3—88no—
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×D8—91no—
355C2×#131—181no—
356C2×C4×D4—181no—
357#509—94no—
358#509—94no—
359C2×SD32—92no—
360C2×D16—92no—
361C2×M32—31no—
362C2×M32—31no—
363#444—94no—
364#444—182no—
365#442—94no—
366#442—182no—
367C2×#108—31no—
368C2×#106D3211yescharacteristic
369C2×#104—181no—
370C2×#102—181no—
371C2×#97—91no—
372#365—34no—
373#361—94no—
374#360—34no—
375#347—94no—
376C23×D3—122no—
377C23×D3—121no—
378C23×D3—121no—
379C3×#41—62no—
380C3×#41—62no—
381C3×#41—121no—
382C3×#41—121no—
383C2×C3×Q8—61no—
384C2×C3×D4—61no—
385C2×C3×D4—121no—
386C22×C3×C4—21no—
387C22×C3×C4—42no—
388C22×C3×C4—41no—
389C22×C3×C4—41no—
390C22×C3×C4—121no—
391C22×C3×C4D3×D411yescharacteristic
392C22×C3×C4D3×D411yescharacteristic
393C2×#67—41no—
394C22×Dic3—62no—
395C22×Dic3—61no—
396C22×Dic3—61no—
397#235—22no—
398#235—22no—
399#235—41no—
400#235—41no—
401C2×D12—21no—
402C2×D12—64no—
403C2×D12—64no—
404C2×D12—64no—
405C2×D12—62no—
406C2×D12—62no—
407C2×D12—62no—
408C2×D12—62no—
409C2×D12—62no—
410C2×D12—62no—
411C2×D12—122no—
412C2×D12—122no—
413C2×D12—122no—
414C2×D12—121no—
415C2×D12—121no—
416C2×D12—121no—
417C2×D12—121no—
418C2×D12—121no—
419C2×D12—121no—
420C2×C4×D3—41no—
421C2×C4×D3—128no—
422C2×C4×D3—124no—
423C2×C4×D3—124no—
424C2×C4×D3—248no—
425C2×C4×D3—244no—
426C2×C4×D3—244no—
427C2×Dic6—21no—
428C3×Q16—32no—
429C3×Q16—61no—
430C3×SD16—62no—
431C3×SD16—62no—
432C3×D8—32no—
433C3×D8—61no—
434C3×M16—62no—
435C3×M16—121no—
436C2×C3×C8—21no—
437C2×C3×C8—21no—
438C2×C3×C8—21no—
439C2×C3×C8—21no—
440C2×C3×C8—21no—
441C2×C3×C8—21no—
442C2×C3×C8—121no—
443C2×C3×C8C2×C4×D311yescharacteristic
444C2×C3×C8C2×C4×D311yescharacteristic
445C2×C3×C8C2×C4×D311yescharacteristic
446C2×C3×C8C2×C4×D311yescharacteristic
447C2×C3×C8D3×D411yescharacteristic
448C2×C3×C8D3×D411yescharacteristic
449C2×C3×C8#23711yescharacteristic
450C2×C3×C8#23711yescharacteristic
451C2×C3×C8#23911yescharacteristic
452C2×C3×C8#23911yescharacteristic
453C2×C3×C8C23×D311yescharacteristic
454C2×C3×C8C23×D311yescharacteristic
455C3×C4⋊C4—24no—
456C3×C4⋊C4—22no—
457C3×C4⋊C4—22no—
458C3×C4⋊C4—42no—
459C3×C4⋊C4—41no—
460C3×C4⋊C4—41no—
461(C2×D3)⋊C4—128no—
462(C2×D3)⋊C4—124no—
463(C2×D3)⋊C4—124no—
464C4×Dic3—32no—
465C4×Dic3—32no—
466C4×Dic3—62no—
467C4×Dic3—62no—
468C4×Dic3—61no—
469C4×Dic3—61no—
470#208—22no—
471#208—41no—
472#208—124no—
473C2×C3⋊C8—32no—
474C2×C3⋊C8—32no—
475C2×C3⋊C8—41no—
476C2×C3⋊C8—62no—
477C2×C3⋊C8—61no—
478C2×C3⋊C8—61no—
479C2×C3⋊C8—61no—
480C2×C3⋊C8—61no—
481C2×C3⋊C8—121no—
482C2×C3⋊C8—121no—
483C2×C3⋊C8—124no—
484Dic12—21no—
485Dic12C2×C4×D312yescomplemented
486D24—21no—
487D24—34no—
488D24—34no—
489D24—64no—
490D24—64no—
491D24—64no—
492D24—64no—
493D24—62no—
494D24—62no—
495D24—62no—
496D24—62no—
497D24—62no—
498D24—62no—
499D24C2×C4×D312yescomplemented
500#204—22no—
501#204—22no—
502ΓL(1,𝔽25)—124no—
503D3×C8—124no—
504C3×C16—34no—
505C3×C16—62no—
506C3⋊C16—22no—
507C3⋊C16C2×C4×D314yescomplemented
508C22×C32—22no—
509C22×C32#44211yescharacteristic
510C22×C32#44211yescharacteristic
511C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
512C2×C3⋊D3—44no—
513C2×C3⋊D3—82no—
514C2×C3⋊D3—82no—
515C2×C3⋊D3—84no—
516C2×C3⋊D3—84no—
517C2×C3×D3—42no—
518C2×C3×D3—82no—
519C32×C4—82no—
520C32×C4#44211yescharacteristic
521C32×C4#44211yescharacteristic
522C32×C4C2×C4×D411yescharacteristic
523C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
524C3⋊Dic3—42no—
525C3×Dic3—42no—
526C2×#41—61no—
527C22×D4—181no—
528C23×C4—361no—
529#135—32no—
530#135—32no—
531#135—61no—
532#135—61no—
533C2×Q16—31no—
534C2×SD16—61no—
535C2×D8—31no—
536C2×D8—92no—
537C2×D8—92no—
538C2×D8—92no—
539C2×D8—181no—
540C2×D8—181no—
541C2×D8—181no—
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—21no—
552C2×C22⋊C4—361no—
553C2×C42—91no—
554SD32—98no—
555D16—98no—
556M32—32no—
557M32—32no—
558M32—32no—
559M32—61no—
560C2×C16—32no—
561C2×C16—61no—
562#108—32no—
563#108—61no—
564#106—21no—
565#106C2×D3212yes—
566#104—184no—
567#102—184no—
568#97—92no—
569#97—92no—
570C23×C3—21no—
571C23×C3—121no—
572C23×C3#91111yescharacteristic
573C23×C3#91411yescharacteristic
574C22×D3—41no—
575C22×D3—124no—
576C22×D3—124no—
577C22×D3—124no—
578C22×D3—122no—
579C22×D3—122no—
580C22×D3—122no—
581C22×D3—122no—
582C22×D3—122no—
583C22×D3—122no—
584C22×D3—244no—
585C22×D3—242no—
586C22×D3—242no—
587C22×D3—244no—
588C22×D3—242no—
589C22×D3—242no—
590C3×Q8—62no—
591C3×Q8—121no—
592C3×D4—62no—
593C3×D4—122no—
594C3×D4—122no—
595C3×D4—121no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—44no—
603C2×C3×C4—42no—
604C2×C3×C4—42no—
605C2×C3×C4—84no—
606C2×C3×C4—82no—
607C2×C3×C4—82no—
608C2×C3×C4—121no—
609C2×C3×C4—122no—
610C2×C3×C4—122no—
611C2×C3×C4#67⋊C411yescharacteristic
612C2×C3×C4#67⋊C411yescharacteristic
613C2×C3×C4#89311yescharacteristic
614C2×C3×C4#89311yescharacteristic
615C2×C3×C4#91111yescharacteristic
616C2×C3×C4#91411yescharacteristic
617C2×C3×C4#91411yescharacteristic
618C2×C3×C4#91411yescharacteristic
619C2×C3×C4#91411yescharacteristic
620C2×C3×C4#91411yescharacteristic
621C2×C3×C4C2×D3×D411yescharacteristic
622C2×C3×C4C2×D3×D411yescharacteristic
623#67—42no—
624#67—42no—
625C2×Dic3—41no—
626C2×Dic3—64no—
627C2×Dic3—62no—
628C2×Dic3—62no—
629C2×Dic3—124no—
630C2×Dic3—122no—
631C2×Dic3—122no—
632D12—22no—
633D12—41no—
634D12—68no—
635D12—64no—
636D12—64no—
637D12—124no—
638D12—124no—
639D12—124no—
640D12—122no—
641D12—122no—
642D12—122no—
643D12—122no—
644D12—122no—
645D12—122no—
646C4×D3—42no—
647C4×D3—42no—
648C4×D3—2416no—
649C4×D3—248no—
650C4×D3—248no—
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×C8#89311yescharacteristic
661C3×C8#89311yescharacteristic
662C3×C8C22×C4×D311yescharacteristic
663C3×C8C22×C4×D311yescharacteristic
664C3×C8C2×#23711yescharacteristic
665C3×C8C2×#23911yescharacteristic
666C3⋊C8—42no—
667C3⋊C8—62no—
668C3⋊C8—62no—
669C3⋊C8—122no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32AGL(1,ℤ/16)12yescomplemented
673C2×C32C2×#44211yescharacteristic
674C3⋊D3—84no—
675C3×D3—82no—
676C24—361no—
677#41—62no—
678#41—62no—
679#41—121no—
680#41—121no—
681C2×Q8—61no—
682C2×D4—61no—
683C2×D4—121no—
684C2×D4—182no—
685C2×D4—182no—
686C2×D4—182no—
687C2×D4—361no—
688C2×D4—361no—
689C2×D4—361no—
690C22×C4—41no—
691C22×C4—121no—
692C22×C4—181no—
693C22×C4—364no—
694C22×C4—724no—
695C22×C4#381111yescharacteristic
696Q16—32no—
697Q16—61no—
698SD16—62no—
699SD16—62no—
700D8—32no—
701D8—61no—
702D8—94no—
703D8—182no—
704D8—182no—
705D8—182no—
706M16—62no—
707M16—121no—
708M16—364no—
709C2×C8—92no—
710C2×C8—121no—
711C2×C8—181no—
712C2×C8—181no—
713C2×C8—364no—
714C2×C8#379611yescharacteristic
715C2×C8#379611yescharacteristic
716C2×C8C4×D3211yescharacteristic
717C2×C8C4×D3211yescharacteristic
718C2×C8#381111yescharacteristic
719C2×C8C22×D3211yescharacteristic
720C4⋊C4—22no—
721C4⋊C4—41no—
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—122no—
734C22×C3—242no—
735C22×C3#478511yescharacteristic
736C22×C3#478511yescharacteristic
737C22×C3#486911yescharacteristic
738C22×C3#486911yescharacteristic
739C22×C3C2×#91111yescharacteristic
740C22×C3C2×#91411yescharacteristic
741C2×D3—42no—
742C2×D3—82no—
743C2×D3—128no—
744C2×D3—124no—
745C2×D3—124no—
746C2×D3—244no—
747C2×D3—242no—
748C2×D3—242no—
749C2×D3—244no—
750C2×D3—248no—
751C2×D3—242no—
752C2×D3—244no—
753C2×D3—242no—
754C2×D3—244no—
755C2×D3—248no—
756C2×D3—244no—
757C2×D3—244no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—84no—
763C3×C4—82no—
764C3×C4—82no—
765C3×C4—122no—
766C3×C4#478511yescharacteristic
767C3×C4#478511yescharacteristic
768C3×C4#486911yescharacteristic
769C3×C4#486911yescharacteristic
770C3×C4C2×#67⋊C411yescharacteristic
771C3×C4C2×#89311yescharacteristic
772C3×C4C2×#91411yescharacteristic
773C3×C4C2×#91411yescharacteristic
774Dic3—42no—
775Dic3—124no—
776Dic3—122no—
777Dic3—122no—
778C32C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
779C23—121no—
780C23—362no—
781C23—362no—
782C23—362no—
783C23—722no—
784C23—722no—
785C23#6393711yescharacteristic
786Q8—62no—
787Q8—121no—
788D4—62no—
789D4—122no—
790D4—122no—
791D4—121no—
792D4—184no—
793D4—362no—
794D4—362no—
795D4—362no—
796C2×C4—42no—
797C2×C4—82no—
798C2×C4—121no—
799C2×C4—122no—
800C2×C4—122no—
801C2×C4—182no—
802C2×C4—362no—
803C2×C4—728no—
804C2×C4#6388111yescharacteristic
805C2×C4#6388111yescharacteristic
806C2×C4#6393711yescharacteristic
807C2×C4#6394111yescharacteristic
808C2×C4#6394111yescharacteristic
809C2×C4C2×#381111yescharacteristic
810C8—122no—
811C8—182no—
812C8#6388111yescharacteristic
813C8#6388111yescharacteristic
814C8C2×#379611yescharacteristic
815C8C2×C4×D3211yescharacteristic
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—242no—
825C2×C3#6924912yescomplemented
826C2×C3#6931012yescomplemented
827C2×C3C2×#478511yescharacteristic
828C2×C3C2×#486911yescharacteristic
829D3—82no—
830D3—248no—
831D3—244no—
832D3—244no—
833C22—22no—
834C22—122no—
835C22—242no—
836C22—364no—
837C22—722no—
838C22—722no—
839C22—724no—
840C22—724no—
841C22#1059046211yescharacteristic
842C22#1059046211yescharacteristic
843C22C2×#6393711yescharacteristic
844C4—82no—
845C4—122no—
846C4—362no—
847C4#1059046211yescharacteristic
848C4#1059046211yescharacteristic
849C4C2×#6388111yescharacteristic
850C4C2×#6394111yescharacteristic
851C3—21no—
852C3C2×#6924911yescharacteristic, complemented
853C3C2×#6931011yescharacteristic, complemented
854C2—21no—
855C2—21no—
856C2—242no—
857C2—724no—
858C2#1179796712yesdirect product factor
859C2C2×#1059046211yescharacteristic
subgroupG/H
centerC22#10590462
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC2×C32×#106C22
socleC22×C32#442
prime radicalC2×#10590634C2
cosocleC2×C32×C8C24
hypercenterC2×#106D32
hypocenterC32C2×AGL(1,ℤ/16)
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#10590920C2semidirect
3. C2×#10592568C2semidirect
4. #11797967C2direct (N × H)
5. C2×C3×#4487C2semidirect
6. C2×#10589128C2semidirect
7. C2×C3×#4488C2semidirect
8. C2×#10589106C2semidirect
19. #10592568C22semidirect
25. #10590920C22semidirect
26. C2×#63549C4semidirect
27. #10590634C4semidirect
29. C2×#63546C4semidirect
30. C3×#4488C22semidirect
31. C3×#4487C22semidirect
32. #10589128C22semidirect
33. #10589106C22semidirect
47. C2×#4488D3semidirect
48. C2×#4487D3semidirect
68. C2×C3×Dic12C2×C4semidirect
71. C3×#904C2×C4semidirect
73. C2×C3×D24C2×C4semidirect
87. C3×#812C2×C4semidirect
91. C2×C3×C3⋊C16C2×C4semidirect
93. #63549C2×C4semidirect
94. #63546C2×C4semidirect
147. #4488C2×D3semidirect
148. #4487C2×D3semidirect
191. C3×Dic12C22×C4semidirect
193. C3×D24C22×C4semidirect
199. C3×C3⋊C16C22×C4semidirect
246. C2×Dic12C4×D3semidirect
249. #904C4×D3semidirect
269. C2×D24C4×D3semidirect
306. #812C4×D3semidirect
310. C2×C3⋊C16C4×D3semidirect
485. Dic12C2×C4×D3semidirect
499. D24C2×C4×D3semidirect
507. C3⋊C16C2×C4×D3semidirect
672. C2×C32AGL(1,ℤ/16)semidirect
778. C32C2×AGL(1,ℤ/16)semidirect
825. C2×C3#69249semidirect
826. C2×C3#69310semidirect
852. C3C2×#69249semidirect
853. C3C2×#69310semidirect
858. C2#11797967direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#105906342
C2×#105909202
C2×#105925682
#117979672
C2×C3×#44872
C2×#105891282
C2×C3×#44882
C2×#105891062
C2×#693103
C2×#692493