Finite Group Databasebeta

← #72222790

Subgroups — #72222790

Order 2304.

1536 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10592607C211yesmaximal, characteristic
2#11861234C211yesmaximal, characteristic, complemented
3#11860704C211yesmaximal, characteristic, complemented
4#11797984C218yesmaximal, complemented
5C3×#71427C211yesmaximal, characteristic, complemented
6C2×#10589128C211yesmaximal, characteristic, complemented
7#11796861C211yesmaximal, characteristic, complemented
8C3×#71425C211yesmaximal, characteristic, complemented
9#10948664—31nomaximal
10#10948661—31nomaximal
11C2×#64113C2211yescharacteristic
12C22×#3745C2211yescharacteristic
13#10594996—21no—
14#10594780—21no—
15C2×C32×M32C2211yescharacteristic
16#10592607C414yescomplemented
17#10592607C2214yes—
18C2×#63627C412yescomplemented
19C2×#63626C412yescomplemented
20C2×C3×#819C2211yescharacteristic
21C3×#5106C2211yescharacteristic
22C3×#5101C2211yescharacteristic
23C2×C3×#812C2211yescharacteristic
24#10591113—21no—
25#10591096—21no—
26#10590918C2214yescomplemented
27#10590917—22no—
28#10590768C2214yescomplemented
29#10590763—22no—
30C3×#4513C2214yescomplemented
31C3×#4512C2214yescomplemented
32#10589128C2214yescomplemented
33#10589125C2214yescomplemented
34C2×#4908—31no—
35C2×#4908—31no—
36C2×#4908—61no—
37#79249—31no—
38#79167—31no—
39#78580—31no—
40#78561—31no—
41C3×#2155—31no—
42C3×#2110—31no—
43#71450—31no—
44C2×#4516—31no—
45#71427D311yescharacteristic, complemented
46#71425D311yescharacteristic, complemented
47C2×#4495—31no—
48#70656—31no—
49#69310—38no—
50#69091—38no—
51C2×#3828—21no—
52C22×C4⋊(C3⋊D3)—21no—
53C22×C32×C8C2311yescharacteristic
54C2×#3746C2×C411yescharacteristic, complemented
55#64113—21no—
56#64113—21no—
57#64113C2×C412yescomplemented
58#64113C2312yes—
59C2×#3745—21no—
60C2×#3745—21no—
61C2×#3745—21no—
62C2×#3745C2×C412yes—
63C2×#3745C2×C412yes—
64C2×#3745C2×C411yescharacteristic, complemented
65C2×#3745C2312yes—
66C2×#3744—21no—
67C3×#926—21no—
68C3×#926D411yescharacteristic
69C2×C3×#208—21no—
70C2×C3×#208D411yescharacteristic
71#63974—42no—
72#63894—24no—
73#63894—42no—
74#63818—42no—
75#63817—24no—
76#63817—42no—
77C32×M32C2×C412yescomplemented
78C32×M32C2312yes—
79C2×C32×C16C2×C412yescomplemented
80#63627C2×C418yescomplemented
81#63626C2×C418yescomplemented
82C3×#819—21no—
83C3×#819C2312yes—
84C3×#818—21no—
85C3×#817C2312yes—
86C3×#815C2312yes—
87C3×C8×Dic3D412yes—
88C3×#812—21no—
89C3×#812C2312yes—
90C2×C3×C3⋊C16—21no—
91#63570—24no—
92#63564—24no—
93#33471—91noSylow
94#5745—61no—
95#5745—61no—
96C2×#904—31no—
97C2×#904—31no—
98C2×#904—61no—
99C22×D24—31no—
100C22×D24—31no—
101C22×D24—61no—
102#5521—61no—
103#5521—61no—
104C2×C3×M32—21no—
105C2×C3×M32—31no—
106C2×C3×M32C2×D311yescharacteristic
107C2×C3×M32C2×D311yescharacteristic
108C2×C3×#108—31no—
109C3×#427—31no—
110C3×#405—31no—
111#5139—61no—
112#5131—61no—
113C2×#819C2×D311yescharacteristic
114#5106C2×D311yescharacteristic
115#5101C2×D311yescharacteristic
116C2×#812C2×D311yescharacteristic
117#5005—61no—
118#5001—61no—
119#4908—34no—
120#4908—34no—
121#4908—34no—
122#4908—34no—
123#4908—64no—
124#4908—64no—
125C2×#800—32no—
126C2×#800—32no—
127C2×#800—62no—
128C2×D48—32no—
129C2×D48—32no—
130C2×D48—62no—
131#4895—62no—
132#4894—34no—
133#4872—62no—
134#4869—34no—
135#4717—34no—
136#4711—34no—
137#4700—62no—
138C4×D24—62no—
139C3×#365—34no—
140C3×#347—34no—
141#4518—34no—
142#4516—34no—
143#4513C2×D314yescomplemented
144#4512C2×D314yescomplemented
145#4495—34no—
146#4488—34no—
147C23×C3⋊D3—41no—
148C22×C32×C4C2×D411yescharacteristic
149C2×#638—41no—
150#3828—22no—
151#3828—22no—
152#3828—41no—
153#3828—41no—
154C2×C4⋊(C3⋊D3)—22no—
155C2×C4⋊(C3⋊D3)—22no—
156C2×C4⋊(C3⋊D3)—21no—
157C2×C4⋊(C3⋊D3)—22no—
158C2×C4⋊(C3⋊D3)—41no—
159C2×C4⋊(C3⋊D3)—41no—
160C2×C4⋊(C3⋊D3)—41no—
161C2×C4×C3⋊D3—41no—
162C2×#634—21no—
163C2×#624—44no—
164C2×C32×C8C22×C411yescharacteristic
165C2×C32×C8C22×C411yescharacteristic
166C2×C32×C8C2×D411yescharacteristic
167C2×C32×C8#4111yescharacteristic
168C2×C32×C8#4111yescharacteristic
169C2×C32×C8C2411yescharacteristic
170#3746—21no—
171#3746C22×C412yes—
172#3745—22no—
173#3745—22no—
174#3745—21no—
175#3745—22no—
176#3745C22×C414yes—
177#3745C22×C412yes—
178#3744—22no—
179#3744—22no—
180C3×#217—21no—
181C3×#217—41no—
182C3×C4⋊Dic3—21no—
183C3×C4⋊Dic3—22no—
184C3×C4×Dic3—41no—
185C3×C4×Dic3C2×D412yes—
186C3×#208—21no—
187C3×#208—21no—
188C3×#208—22no—
189C3×#208—41no—
190C2×C3×C3⋊C8—41no—
191C2×C3×C3⋊C8C2×D412yes—
192#3722—44no—
193#3712—44no—
194#3710—44no—
195C32×C16C22×C414yes—
196C3×C3⋊C16—22no—
197C2×#509—91no—
198#2957—91no—
199#2948—91no—
200AGL(1,ℤ/16)—98no—
201#2155—31no—
202C2×#361—91no—
203#2145—91no—
204#2110—31no—
205C2×#235—61no—
206C2×#235—61no—
207C2×#235—121no—
208C22×D12—61no—
209C22×D12—61no—
210C22×D12—121no—
211C2×C3×M16—31no—
212C2×C3×M16—61no—
213C22×C3×C8—21no—
214C22×C3×C8C22×D311yescharacteristic
215C22×C3×C8C22×D311yescharacteristic
216C3×#117—31no—
217C3×#117—61no—
218#926—21no—
219#926D1211yescharacteristic
220C2×#208—21no—
221C2×#208D1211yescharacteristic
222#907—64no—
223#907—122no—
224D3×M16—122no—
225D3×M16—122no—
226C2×Dic12—31no—
227C2×Dic12—31no—
228C2×Dic12—61no—
229#904—32no—
230#904—32no—
231#904—32no—
232#904—32no—
233#904—62no—
234#904—62no—
235#904—61no—
236#904—61no—
237#904—61no—
238#904—61no—
239#904—121no—
240#904—121no—
241C2×D24—31no—
242C2×D24—31no—
243C2×D24—32no—
244C2×D24—32no—
245C2×D24—32no—
246C2×D24—32no—
247C2×D24—32no—
248C2×D24—32no—
249C2×D24—61no—
250C2×D24—62no—
251C2×D24—62no—
252C2×D24—62no—
253C2×D24—61no—
254C2×D24—61no—
255C2×D24—61no—
256C2×D24—61no—
257C2×D24—61no—
258C2×D24—61no—
259C2×D24—121no—
260C2×D24—121no—
261C2×D24—121no—
262C2×#204—61no—
263C2×#204—61no—
264C2×#204—121no—
265#901—64no—
266#901—122no—
267#893—64no—
268#893—122no—
269D3×C22⋊C4—122no—
270D3×C22⋊C4—122no—
271C4×D12—64no—
272C4×D12—122no—
273C3×M32—22no—
274C3×M32—22no—
275C3×M32—32no—
276C3×M32—61no—
277C3×M32C4×D312yescomplemented
278C3×M32C4×D312yescomplemented
279C3×M32C22×D312yes—
280C3×M32C22×D312yes—
281C2×C3×C16—22no—
282C2×C3×C16—61no—
283C2×C3×C16C4×D312yescomplemented
284C2×C3×C16C4×D312yescomplemented
285C3×#108—32no—
286C3×#108—61no—
287C3×#107—61no—
288C3×#106—32no—
289C3×#97—32no—
290C3×C4×C8—32no—
291#825—64no—
292#821—64no—
293#819—21no—
294#819C22×D312yes—
295#818—21no—
296#817C22×D312yes—
297#815C22×D312yes—
298C8×Dic3D1212yes—
299#812—21no—
300#812C22×D312yes—
301C2×C3⋊C16—21no—
302#809—64no—
303#805—64no—
304#800—38no—
305#800—38no—
306#800—68no—
307D48—38no—
308D48—38no—
309D48—68no—
310C23×C32AGL(1,ℤ/8)11yescharacteristic
311C22×C3⋊D3—42no—
312C22×C3⋊D3—42no—
313C22×C3⋊D3—42no—
314C22×C3⋊D3—41no—
315C22×C3⋊D3—162no—
316C2×C32×C4C4×D411yescharacteristic
317C2×C32×C4C4×D411yescharacteristic
318C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
319C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
320C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
321C2×C32×C4C22×D411yescharacteristic
322#638—42no—
323#638—42no—
324C2×C3⋊Dic3—41no—
325C4⋊(C3⋊D3)—22no—
326C4⋊(C3⋊D3)—24no—
327C4⋊(C3⋊D3)—42no—
328C4⋊(C3⋊D3)—42no—
329C4⋊(C3⋊D3)—42no—
330C4⋊(C3⋊D3)—41no—
331C4×C3⋊D3—42no—
332C4×C3⋊D3—42no—
333#634—22no—
334#634—41no—
335C2×C3×Dic3—22no—
336C2×C3×Dic3—42no—
337#624—164no—
338C32×C8C4×D411yescharacteristic
339C32×C8C4×D411yescharacteristic
340C32×C8C23×C411yescharacteristic
341C32×C8C2×#4111yescharacteristic
342C3×C3⋊C8—22no—
343C3×C3⋊C8—42no—
344C2×#135—91no—
345C22×D8—91no—
346#568—181no—
347#518—181no—
348#509—94no—
349#509—94no—
350C2×SD32—92no—
351C2×D16—92no—
352C2×M32—31no—
353C2×M32D3211yescharacteristic
354#444—94no—
355#443—182no—
356#442—94no—
357C4×D8—182no—
358C2×#108—31no—
359#427—31no—
360#421—181no—
361#418—181no—
362#405—31no—
363#365—34no—
364#361—94no—
365#360—94no—
366#347—34no—
367C23×D3—121no—
368C23×D3—121no—
369C23×D3—241no—
370C22×C3×C4—21no—
371C22×C3×C4C2×D1211yescharacteristic
372C22×C3×C4D3×D411yescharacteristic
373C2×#67—121no—
374C2×#67—121no—
375C2×#67—241no—
376#235—62no—
377#235—62no—
378#235—62no—
379#235—62no—
380#235—122no—
381#235—122no—
382#235—121no—
383#235—121no—
384#235—121no—
385#235—121no—
386#235—241no—
387#235—241no—
388C2×D12—61no—
389C2×D12—62no—
390C2×D12—62no—
391C2×D12—61no—
392C2×D12—62no—
393C2×D12—62no—
394C2×D12—62no—
395C2×D12—62no—
396C2×D12—121no—
397C2×D12—122no—
398C2×D12—122no—
399C2×D12—122no—
400C2×D12—121no—
401C2×D12—121no—
402C2×D12—121no—
403C2×D12—121no—
404C2×D12—121no—
405C2×D12—121no—
406C2×D12—241no—
407C2×D12—241no—
408C2×D12—241no—
409C2×C4×D3—121no—
410C2×C4×D3—121no—
411C2×C4×D3—124no—
412C2×C4×D3—124no—
413C2×C4×D3—241no—
414C2×Dic6—61no—
415C2×Dic6—61no—
416C2×Dic6—121no—
417C3×M16—61no—
418C3×M16—61no—
419C3×M16—62no—
420C3×M16—121no—
421C2×C3×C8—21no—
422C2×C3×C8—21no—
423C2×C3×C8—21no—
424C2×C3×C8—21no—
425C2×C3×C8—21no—
426C2×C3×C8—21no—
427C2×C3×C8—32no—
428C2×C3×C8—121no—
429C2×C3×C8C2×C4×D311yescharacteristic
430C2×C3×C8C2×C4×D311yescharacteristic
431C2×C3×C8C2×C4×D311yescharacteristic
432C2×C3×C8C2×C4×D311yescharacteristic
433C2×C3×C8C2×D1211yescharacteristic
434C2×C3×C8#23511yescharacteristic
435C2×C3×C8#23511yescharacteristic
436C2×C3×C8D3×D411yescharacteristic
437C2×C3×C8#23911yescharacteristic
438C2×C3×C8#23911yescharacteristic
439C2×C3×C8C23×D311yescharacteristic
440C2×C3×C8C23×D311yescharacteristic
441C3×C4⋊C4—61no—
442C3×C4⋊C4—62no—
443C3×C22⋊C4—61no—
444C3×C22⋊C4—121no—
445C3×C42—32no—
446C3×C42—121no—
447#217—21no—
448#217—41no—
449(C2×D3)⋊C4—124no—
450(C2×D3)⋊C4—124no—
451C4⋊Dic3—21no—
452C4⋊Dic3—22no—
453C4×Dic3—41no—
454C4×Dic3C2×D1212yes—
455#208—21no—
456#208—21no—
457#208—22no—
458#208—41no—
459C2×C3⋊C8—41no—
460C2×C3⋊C8C2×D1212yes—
461Dic12—32no—
462Dic12—32no—
463Dic12—62no—
464Dic12—61no—
465Dic12—61no—
466Dic12—121no—
467D24—32no—
468D24—32no—
469D24—34no—
470D24—34no—
471D24—62no—
472D24—64no—
473D24—62no—
474D24—62no—
475D24—61no—
476D24—62no—
477D24—62no—
478D24—61no—
479D24—62no—
480D24—62no—
481D24—122no—
482D24—122no—
483D24—122no—
484D24—121no—
485#204—62no—
486#204—62no—
487#204—62no—
488#204—62no—
489#204—122no—
490#204—122no—
491ΓL(1,𝔽25)—124no—
492ΓL(1,𝔽25)—124no—
493D3×C8—124no—
494D3×C8—124no—
495C3×C16—24no—
496C3×C16—62no—
497C3×C16C2×C4×D314yes—
498C3×C16C2×C4×D314yes—
499C3⋊C16—22no—
500C22×C32—41no—
501C22×C32#44211yescharacteristic
502C22×C32#44211yescharacteristic
503C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
504C2×C3⋊D3—42no—
505C2×C3⋊D3—44no—
506C2×C3⋊D3—84no—
507C2×C3⋊D3—161no—
508C2×C3⋊D3—162no—
509C2×C3⋊D3—162no—
510C32×C4#44211yescharacteristic
511C32×C4#44211yescharacteristic
512C32×C4C2×C4×D411yescharacteristic
513C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
514C3⋊Dic3—42no—
515C3×Dic3—42no—
516C3×Dic3—82no—
517C2×#41—181no—
518C22×D4—181no—
519#135—92no—
520#135—92no—
521#135—181no—
522#135—181no—
523C2×Q16—91no—
524C2×SD16—181no—
525C2×D8—92no—
526C2×D8—92no—
527C2×D8—92no—
528C2×D8—91no—
529C2×D8—181no—
530C2×D8—181no—
531C2×D8—181no—
532#131—184no—
533#131—362no—
534C2×M16—31no—
535C2×M16—61no—
536C2×M16—362no—
537C22×C8C2×D3211yescharacteristic
538C4×D4—184no—
539C4×D4—362no—
540#117—31no—
541#117—61no—
542C2×C22⋊C4—362no—
543SD32—98no—
544D16—98no—
545M32—32no—
546M32—61no—
547M32#62412yescomplemented
548M32C2×D3212yes—
549C2×C16—61no—
550C2×C16#62412yescomplemented
551#108—32no—
552#108—61no—
553#107—61no—
554#106—32no—
555#104—184no—
556#102—184no—
557#97—32no—
558C4×C8—32no—
559C23×C3—21no—
560C23×C3#90811yescharacteristic
561C23×C3#91411yescharacteristic
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—121no—
565C22×D3—122no—
566C22×D3—122no—
567C22×D3—121no—
568C22×D3—122no—
569C22×D3—122no—
570C22×D3—241no—
571C22×D3—242no—
572C22×D3—242no—
573C22×D3—242no—
574C22×D3—482no—
575C22×D3—482no—
576C22×D3—484no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—62no—
584C2×C3×C4—122no—
585C2×C3×C4C4×D1211yescharacteristic
586C2×C3×C4C4×D1211yescharacteristic
587C2×C3×C4#89311yescharacteristic
588C2×C3×C4#89311yescharacteristic
589C2×C3×C4#90811yescharacteristic
590C2×C3×C4#90811yescharacteristic
591C2×C3×C4#90811yescharacteristic
592C2×C3×C4#91411yescharacteristic
593C2×C3×C4#91411yescharacteristic
594C2×C3×C4#91411yescharacteristic
595C2×C3×C4C22×D1211yescharacteristic
596C2×C3×C4C2×D3×D411yescharacteristic
597#67—122no—
598#67—122no—
599#67—122no—
600#67—122no—
601#67—242no—
602#67—242no—
603C2×Dic3—22no—
604C2×Dic3—42no—
605C2×Dic3—121no—
606C2×Dic3—121no—
607C2×Dic3—241no—
608D12—62no—
609D12—64no—
610D12—62no—
611D12—64no—
612D12—122no—
613D12—124no—
614D12—122no—
615D12—122no—
616D12—121no—
617D12—122no—
618D12—122no—
619D12—121no—
620D12—122no—
621D12—122no—
622D12—242no—
623D12—242no—
624D12—242no—
625D12—241no—
626C4×D3—122no—
627C4×D3—122no—
628C4×D3—122no—
629C4×D3—122no—
630C4×D3—242no—
631C4×D3—242no—
632C4×D3—484no—
633C4×D3—484no—
634Dic6—62no—
635Dic6—62no—
636Dic6—122no—
637Dic6—121no—
638Dic6—121no—
639Dic6—241no—
640C3×C8—21no—
641C3×C8—21no—
642C3×C8—21no—
643C3×C8—21no—
644C3×C8—62no—
645C3×C8—122no—
646C3×C8C4×D1211yescharacteristic
647C3×C8C4×D1211yescharacteristic
648C3×C8#89311yescharacteristic
649C3×C8#89311yescharacteristic
650C3×C8C22×C4×D311yescharacteristic
651C3×C8C22×C4×D311yescharacteristic
652C3×C8C2×#23511yescharacteristic
653C3×C8C2×#23911yescharacteristic
654C3⋊C8—22no—
655C3⋊C8—42no—
656C2×C32—21no—
657C2×C32—21no—
658C2×C32—21no—
659C2×C32C2×#44211yescharacteristic
660C3⋊D3—84no—
661C3⋊D3—82no—
662C24—361no—
663#41—182no—
664#41—182no—
665#41—361no—
666#41—361no—
667C2×Q8—181no—
668C2×D4—182no—
669C2×D4—182no—
670C2×D4—182no—
671C2×D4—181no—
672C2×D4—361no—
673C2×D4—361no—
674C2×D4—361no—
675C2×D4—361no—
676C22×C4—364no—
677C22×C4—361no—
678C22×C4D3×D1211yescharacteristic
679Q16—92no—
680Q16—181no—
681SD16—182no—
682SD16—182no—
683D8—92no—
684D8—94no—
685D8—182no—
686D8—182no—
687D8—182no—
688D8—181no—
689M16—61no—
690M16—61no—
691M16—62no—
692M16—121no—
693M16—364no—
694C2×C8—32no—
695C2×C8—121no—
696C2×C8—364no—
697C2×C8#379911yescharacteristic
698C2×C8#379911yescharacteristic
699C2×C8D3×D1211yescharacteristic
700C2×C8C2×#62411yescharacteristic
701C2×C8C2×#62411yescharacteristic
702C2×C8C22×D3211yescharacteristic
703C4⋊C4—61no—
704C4⋊C4—62no—
705C22⋊C4—61no—
706C22⋊C4—121no—
707C22⋊C4—364no—
708C42—32no—
709C42—121no—
710C16—62no—
711C16C2×#62414yes—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—42no—
718C22×C3#471111yescharacteristic
719C22×C3#471111yescharacteristic
720C22×C3#486911yescharacteristic
721C22×C3#486911yescharacteristic
722C22×C3C2×#90811yescharacteristic
723C22×C3C2×#91411yescharacteristic
724C2×D3—122no—
725C2×D3—124no—
726C2×D3—122no—
727C2×D3—124no—
728C2×D3—242no—
729C2×D3—244no—
730C2×D3—244no—
731C2×D3—244no—
732C2×D3—484no—
733C2×D3—482no—
734C2×D3—482no—
735C2×D3—482no—
736C2×D3—482no—
737C2×D3—481no—
738C2×D3—481no—
739C2×D3—484no—
740C2×D3—482no—
741C2×D3—484no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—122no—
747C3×C4—242no—
748C3×C4#471111yescharacteristic
749C3×C4#471111yescharacteristic
750C3×C4#486911yescharacteristic
751C3×C4#486911yescharacteristic
752C3×C4C2×C4×D1211yescharacteristic
753C3×C4C2×#89311yescharacteristic
754C3×C4C2×#90811yescharacteristic
755C3×C4C2×#91411yescharacteristic
756Dic3—42no—
757Dic3—82no—
758Dic3—122no—
759Dic3—122no—
760Dic3—242no—
761C32#3347111yescharacteristic, complemented, Sylow
762C23—362no—
763C23—361no—
764C23—362no—
765C23—362no—
766C23—1442no—
767C23#6379411yescharacteristic
768Q8—182no—
769Q8—361no—
770D4—184no—
771D4—182no—
772D4—362no—
773D4—362no—
774D4—362no—
775D4—362no—
776D4—361no—
777D4—362no—
778C2×C4—62no—
779C2×C4—122no—
780C2×C4—361no—
781C2×C4—362no—
782C2×C4—362no—
783C2×C4—1444no—
784C2×C4#6379411yescharacteristic
785C2×C4#6379411yescharacteristic
786C2×C4#6379411yescharacteristic
787C2×C4#6389411yescharacteristic
788C2×C4#6389411yescharacteristic
789C2×C4C2×D3×D1211yescharacteristic
790C8—62no—
791C8—122no—
792C8#6389411yescharacteristic
793C8#6389411yescharacteristic
794C8C2×#379911yescharacteristic
795C8C22×#62411yescharacteristic
796C2×C3—22no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—41no—
805C2×C3—41no—
806C2×C3C2×#471111yescharacteristic
807C2×C3C2×#486911yescharacteristic
808D3—244no—
809D3—242no—
810D3—244no—
811D3—242no—
812D3—484no—
813D3—482no—
814C22—41no—
815C22—362no—
816C22—364no—
817C22—724no—
818C22—1442no—
819C22—1442no—
820C22—1441no—
821C22#1059076811yescharacteristic
822C22#1059076811yescharacteristic
823C22C2×#6379411yescharacteristic
824C4—122no—
825C4—242no—
826C4—362no—
827C4#1059076811yescharacteristic
828C4#1059076811yescharacteristic
829C4C2×#6379411yescharacteristic
830C4C2×#6389411yescharacteristic
831C3—21no—
832C3#1094866111yescharacteristic, complemented
833C3#1094866411yescharacteristic, complemented
834C2—21no—
835C2—21no—
836C2—21no—
837C2—724no—
838C2—722no—
839C2C2×#1059076811yescharacteristic
subgroupG/H
centerC2C2×#10590768
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC2×C32×M32C22
socleC2×C32C2×#442
prime radicalC2×#10592607C2
cosocleC2×C32×C8C24
hypercenterC2×M32D32
hypocenterC32#33471
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
2. #11861234C2semidirect
3. #11860704C2semidirect
4. #11797984C2semidirect
5. C3×#71427C2semidirect
6. C2×#10589128C2semidirect
7. #11796861C2semidirect
8. C3×#71425C2semidirect
16. #10592607C4semidirect
18. C2×#63627C4semidirect
19. C2×#63626C4semidirect
26. #10590918C22semidirect
28. #10590768C22semidirect
30. C3×#4513C22semidirect
31. C3×#4512C22semidirect
32. #10589128C22semidirect
33. #10589125C22semidirect
45. #71427D3semidirect
46. #71425D3semidirect
54. C2×#3746C2×C4semidirect
57. #64113C2×C4semidirect
64. C2×#3745C2×C4semidirect
77. C32×M32C2×C4semidirect
79. C2×C32×C16C2×C4semidirect
80. #63627C2×C4semidirect
81. #63626C2×C4semidirect
143. #4513C2×D3semidirect
144. #4512C2×D3semidirect
277. C3×M32C4×D3semidirect
278. C3×M32C4×D3semidirect
283. C2×C3×C16C4×D3semidirect
284. C2×C3×C16C4×D3semidirect
547. M32#624semidirect
550. C2×C16#624semidirect
761. C32#33471semidirect
832. C3#10948661semidirect
833. C3#10948664semidirect

Maximal subgroups

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

subgroupindex
C2×#105926072
#118612342
#118607042
#117979842
C3×#714272
C2×#105891282
#117968612
C3×#714252
#109486643
#109486613