Finite Group Databasebeta

← #11860286

Subgroups — #11860286

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64120C211yesmaximal, characteristic
2#10595190C211yesmaximal, characteristic, complemented
3D4×#624C211yesmaximal, characteristic, complemented
4C3×#5152C211yesmaximal, characteristic, complemented
5C3×Dic3×D8C211yesmaximal, characteristic, complemented
6#10591426C211yesmaximal, characteristic, complemented
7#10591418C211yesmaximal, characteristic, complemented
8#10591405C211yesmaximal, characteristic, complemented
9#10591404C211yesmaximal, characteristic, complemented
10#10591401C211yesmaximal, characteristic, complemented
11#10591400C211yesmaximal, characteristic, complemented
12#10590773C211yesmaximal, characteristic, complemented
13#10590758C211yesmaximal, characteristic, complemented
14#10590688C211yesmaximal, characteristic, complemented
15#10590664C211yesmaximal, characteristic, complemented
16#79865—31nomaximal
17C4×#911—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C22×#624—21no—
21C2×C32×D8C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C2×#3753C2211yescharacteristic
24#64120C418yescomplemented
25C2×#3744C2211yescharacteristic
26C2×#3743C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic, complemented
30C3×D4×Dic3C2211yescharacteristic, complemented
31#63974—21no—
32#63957—21no—
33C2×Dic32—21no—
34#63952—21no—
35#63952—21no—
36#63952—21no—
37#63952—21no—
38#63900C2211yescharacteristic
39#63894C2211yescharacteristic
40#63894C2211yescharacteristic
41C4×#624C2211yescharacteristic
42#63849C2211yescharacteristic
43#63844C2211yescharacteristic, complemented
44#63844C2211yescharacteristic, complemented
45C2×#3712C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#818C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×#911—31no—
63C2×#911—31no—
64C2×#911—61no—
65C4×D3×D4—31no—
66C4×D3×D4—31no—
67C4×#237—31no—
68C4×#237—31no—
69C3×#442—31no—
70C3×C4×D8—31no—
71#5152D311yescharacteristic, complemented
72Dic3×D8D311yescharacteristic, complemented
73#5018—31no—
74C4×#214—31no—
75#5014—31no—
76C4×#213—31no—
77#4889—31no—
78#4881—31no—
79#4861—31no—
80#4852—31no—
81#4785—31no—
82#4771—31no—
83#4771—31no—
84#4770—31no—
85#4770—31no—
86#4758—31no—
87#4757—31no—
88#4756—31no—
89#4710—31no—
90#4707—31no—
91C4×#204—31no—
92C4×ΓL(1,𝔽25)—31no—
93C23×C3⋊D3—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98C22×C3⋊Dic3—21no—
99#3830—22no—
100#3830C2×C414yescomplemented
101D4×C3⋊D3—22no—
102D4×C3⋊D3C2×C414yescomplemented
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C2×#624—21no—
111C2×#624—21no—
112C2×#624—21no—
113C2×#624—44no—
114C2×#624D411yescharacteristic
115C2×#624D411yescharacteristic
116C32×D8C2×C414yescomplemented
117C2×C32×C8C2311yescharacteristic
118#3754C2×C414yescomplemented
119#3753C2×C414yescomplemented
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3744C2×C414yescomplemented
122#3743C2×C414yescomplemented
123C3×#217—21no—
124C3×#217—21no—
125C3×#217—21no—
126C3×#217—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3724—21no—
137#3724—21no—
138#3722—21no—
139#3722—21no—
140#3722—21no—
141Dic32—21no—
142Dic32—21no—
143Dic32—21no—
144Dic32D411yescharacteristic
145Dic32D411yescharacteristic
146#3712—22no—
147C4×AGL(1,ℤ/8)—91noSylow
148C2×#237—31no—
149C2×#237—31no—
150C2×#237—61no—
151C2×D3×D4—31no—
152C2×D3×D4—31no—
153C2×D3×D4—61no—
154C22×C4×D3—61no—
155C22×C4×D3—61no—
156C2×C3×D8—21no—
157C2×C3×D8C2×D311yescharacteristic
158C2×C3×D8C2×D311yescharacteristic
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163D4×Dic3C2×D311yescharacteristic
164D4×Dic3C2×D311yescharacteristic
165D4×Dic3C2×D311yescharacteristic, complemented
166D4×Dic3C2×D311yescharacteristic, complemented
167C2×#214—31no—
168C2×#214—31no—
169C2×#214—61no—
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—61no—
173C4×#67—61no—
174C4×#67—61no—
175C4×#67—61no—
176C4×#67—61no—
177C2×C4×Dic3—61no—
178C2×C4×Dic3—61no—
179#911—38no—
180#911—38no—
181#911—68no—
182C2×#204—31no—
183C2×#204—31no—
184C2×#204—61no—
185C2×ΓL(1,𝔽25)—31no—
186C2×ΓL(1,𝔽25)—31no—
187C2×ΓL(1,𝔽25)—31no—
188C2×ΓL(1,𝔽25)—31no—
189C2×ΓL(1,𝔽25)—61no—
190#893—31no—
191#893—31no—
192#892—31no—
193#892—31no—
194D3×C4⋊C4—31no—
195D3×C4⋊C4—31no—
196#887—31no—
197#887—31no—
198#67⋊C4—61no—
199#67⋊C4—61no—
200#67⋊C4—61no—
201#67⋊C4—61no—
202D3×C22⋊C4—61no—
203D3×C22⋊C4—61no—
204#877—61no—
205#877—61no—
206C4×D12—31no—
207C4×D12—31no—
208C42×D3—31no—
209C42×D3—31no—
210C4×Dic6—31no—
211C4×Dic6—31no—
212C3×#107—31no—
213C3×#106—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#97—31no—
219C3×C4×C8—31no—
220#832C2×D311yescharacteristic
221#832C2×D311yescharacteristic
222#832C2×D311yescharacteristic, complemented
223#832C2×D311yescharacteristic, complemented
224#821—31no—
225#821—31no—
226#818C2×D311yescharacteristic, complemented
227#817C2×D311yescharacteristic, complemented
228#816—31no—
229#816—31no—
230#815—31no—
231#815C2×D311yescharacteristic, complemented
232C8×Dic3—31no—
233C8×Dic3C2×D311yescharacteristic, complemented
234#810—31no—
235#810—31no—
236#809—31no—
237#809—31no—
238#808—31no—
239#808—31no—
240#807—31no—
241#807—31no—
242#803—31no—
243C4×C3⋊C8—31no—
244C23×C32—21no—
245C23×C32—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—24no—
248C22×C3⋊D3—42no—
249C22×C3⋊D3—42no—
250C22×C3⋊D3C2×D411yescharacteristic
251C32×D4—21no—
252C32×D4—21no—
253C32×D4C22×C412yes—
254C32×D4C22×C412yescomplemented
255C2×C32×C4C2411yescharacteristic
256#638—24no—
257#638—24no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—24no—
260C2×C3⋊Dic3C2×D411yescharacteristic
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)C22×C412yes—
263C4×C3⋊D3C22×C412yes—
264C4×C3⋊D3#4112yes—
265#634—21no—
266#634C22×C412yescomplemented
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—42no—
272C2×C3×Dic3—42no—
273C2×C3×Dic3—42no—
274C2×C3×Dic3—42no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279#624—22no—
280#624—41no—
281#624—42no—
282#624—42no—
283#624—42no—
284C32×C8C22×C412yescomplemented
285C3⋊(C3⋊C8)C22×C412yescomplemented
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288C2×AGL(1,ℤ/8)—91no—
289C4×#41—91no—
290C2×C4×D4—91no—
291#442—31no—
292#442—91no—
293#440—91no—
294#440—91no—
295C4×SD16—91no—
296C4×SD16—91no—
297C4×D8—31no—
298C4×D8—91no—
299#428—91no—
300#418—91no—
301#417—91no—
302C4×M16—91no—
303C23×D3—61no—
304C23×D3—61no—
305C23×D3—121no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—121no—
321C2×#67—121no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—121no—
329#237—34no—
330#237—34no—
331#237—64no—
332#237—62no—
333#237—62no—
334#237—122no—
335D3×D4—34no—
336D3×D4—34no—
337D3×D4—64no—
338D3×D4—62no—
339D3×D4—62no—
340D3×D4—122no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—61no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—124no—
358C2×C4×D3—124no—
359C2×Dic6—31no—
360C2×Dic6—31no—
361C2×Dic6—61no—
362C3×D8—24no—
363C3×D8C4×D314yescomplemented
364C3×D8C4×D314yescomplemented
365C2×C3×C8—21no—
366C2×C3×C8—31no—
367C2×C3×C8—31no—
368C2×C3×C8C22×D311yescharacteristic
369C2×C3×C8C22×D311yescharacteristic
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—31no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C42—31no—
379C3×C42—31no—
380#217—21no—
381#217—21no—
382#217—21no—
383#217—21no—
384#214—34no—
385#214—34no—
386#214—64no—
387#213—34no—
388#213—34no—
389#213—64no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396C4⋊Dic3C22×D311yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406C4×Dic3—31no—
407C4×Dic3—31no—
408C4×Dic3—31no—
409C4×Dic3—31no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C4×Dic3—61no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416C4×Dic3C22×D311yescharacteristic
417C4×Dic3C22×D311yescharacteristic
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—61no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423#204—34no—
424#204—34no—
425#204—64no—
426ΓL(1,𝔽25)—34no—
427ΓL(1,𝔽25)—34no—
428ΓL(1,𝔽25)—64no—
429ΓL(1,𝔽25)—62no—
430ΓL(1,𝔽25)—62no—
431C22×C32—22no—
432C22×C32—22no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32C22×D411yescharacteristic
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—22no—
441C2×C3⋊D3—48no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3C4×D412yes—
445C32×C4C23×C411yescharacteristic
446C32×C4C2×#4111yescharacteristic
447C3⋊Dic3—22no—
448C3⋊Dic3C4×D412yes—
449C3×Dic3—21no—
450C3×Dic3—21no—
451C3×Dic3—21no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3AGL(1,ℤ/8)12yescomplemented
457C2×#41—91no—
458C22×D4—91no—
459C23×C4—181no—
460AGL(1,ℤ/8)—98no—
461C2×SD16—91no—
462C2×SD16—91no—
463C2×D8—91no—
464C2×D8D3211yescharacteristic
465C2×M16—91no—
466C2×M16—91no—
467C4×Q8—91no—
468C4×Q8—91no—
469C4×D4—31no—
470C4×D4—31no—
471C4×D4—31no—
472C4×D4—31no—
473C4×D4—91no—
474C4×D4—91no—
475C4×D4—181no—
476C4×D4—181no—
477C4×D4—181no—
478C4×D4—181no—
479#117—91no—
480#117—181no—
481C2×C4⋊C4—91no—
482C2×C22⋊C4—181no—
483C2×C42—91no—
484C2×C42—181no—
485#107—31no—
486#107—91no—
487#106—31no—
488#106—91no—
489#103—91no—
490#103—91no—
491#102—31no—
492#102—31no—
493#102—31no—
494#102—31no—
495#102—91no—
496#102—91no—
497#97—31no—
498#97—91no—
499C4×C8—31no—
500C4×C8—91no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—41no—
506C23×C3—41no—
507C22×D3—31no—
508C22×D3—31no—
509C22×D3—61no—
510C22×D3—64no—
511C22×D3—64no—
512C22×D3—61no—
513C22×D3—61no—
514C22×D3—124no—
515C22×D3—121no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—242no—
521C22×D3—242no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—22no—
527C3×D4—22no—
528C3×D4—41no—
529C3×D4—41no—
530C3×D4C2×C4×D312yes—
531C3×D4C2×C4×D312yes—
532C3×D4C2×C4×D312yescomplemented
533C3×D4C2×C4×D312yescomplemented
534C2×C3×C4—21no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—122no—
544C2×C3×C4—122no—
545C2×C3×C4—122no—
546C2×C3×C4—122no—
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549#67—64no—
550#67—64no—
551#67—64no—
552#67—64no—
553#67—124no—
554#67—124no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—42no—
562C2×Dic3—42no—
563C2×Dic3—42no—
564C2×Dic3—42no—
565C2×Dic3—61no—
566C2×Dic3—64no—
567C2×Dic3—64no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—124no—
571C2×Dic3—121no—
572C2×Dic3D3×D411yescharacteristic
573C2×Dic3D3×D411yescharacteristic
574C2×Dic3D3×D411yescharacteristic
575C2×Dic3D3×D411yescharacteristic
576D12—32no—
577D12—32no—
578D12—62no—
579D12—61no—
580D12—61no—
581D12—121no—
582C4×D3—32no—
583C4×D3—32no—
584C4×D3—32no—
585C4×D3—32no—
586C4×D3—62no—
587C4×D3—62no—
588C4×D3—62no—
589C4×D3—62no—
590C4×D3—121no—
591C4×D3—121no—
592C4×D3—122no—
593C4×D3—122no—
594C4×D3—122no—
595C4×D3—122no—
596C4×D3—122no—
597C4×D3—122no—
598Dic6—32no—
599Dic6—32no—
600Dic6—62no—
601Dic6—61no—
602Dic6—61no—
603Dic6—121no—
604C3×C8—22no—
605C3×C8—61no—
606C3×C8—61no—
607C3×C8C2×C4×D312yescomplemented
608C3×C8C2×C4×D312yescomplemented
609C3⋊C8—21no—
610C3⋊C8—21no—
611C3⋊C8—32no—
612C3⋊C8—32no—
613C3⋊C8—62no—
614C2×C32—42no—
615C2×C32—42no—
616C2×C32C2×C4×D411yescharacteristic
617C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
618C2×C32#57511yescharacteristic
619C3⋊D3—22no—
620C3⋊D3—42no—
621C24—181no—
622#41—94no—
623#41—182no—
624C2×Q8—91no—
625C2×D4—94no—
626C2×D4—91no—
627C2×D4—182no—
628C2×D4—181no—
629C2×D4—181no—
630C2×D4C2×D3211yescharacteristic
631C2×D4C2×D3211yescharacteristic
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—91no—
637C22×C4—91no—
638C22×C4—91no—
639C22×C4—181no—
640C22×C4—181no—
641C22×C4—181no—
642C22×C4—181no—
643C22×C4—364no—
644SD16—94no—
645SD16—94no—
646D8—94no—
647D8#62414yescomplemented
648M16—94no—
649M16—182no—
650C2×C8—31no—
651C2×C8—31no—
652C2×C8—91no—
653C2×C8C2×D3211yescharacteristic
654C4⋊C4—31no—
655C4⋊C4—31no—
656C4⋊C4—31no—
657C4⋊C4—31no—
658C4⋊C4—181no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C22⋊C4—61no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—61no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C42—31no—
669C42—31no—
670C42—91no—
671C42—91no—
672C42—181no—
673C42—181no—
674C42—181no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—21no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3C2×D3×D411yescharacteristic
695C22×C3C2×D3×D411yescharacteristic
696C2×D3—32no—
697C2×D3—32no—
698C2×D3—62no—
699C2×D3—61no—
700C2×D3—61no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—62no—
704C2×D3—62no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—122no—
708C2×D3—128no—
709C2×D3—128no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—248no—
715C2×D3—241no—
716C2×D3—241no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—32no—
720C3×C4—61no—
721C3×C4—61no—
722C3×C4—61no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4C22×C4×D311yescharacteristic
728C3×C4C22×C4×D311yescharacteristic
729C3×C4D3×#4111yescharacteristic
730C3×C4D3×#4111yescharacteristic
731Dic3—21no—
732Dic3—21no—
733Dic3—21no—
734Dic3—32no—
735Dic3—32no—
736Dic3—41no—
737Dic3—41no—
738Dic3—41no—
739Dic3—41no—
740Dic3—62no—
741Dic3—62no—
742Dic3—62no—
743Dic3—122no—
744Dic3#91112yescomplemented
745C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
746C23—21no—
747C23—21no—
748C23—91no—
749C23—184no—
750C23—181no—
751C23—362no—
752C23—362no—
753Q8—92no—
754Q8—181no—
755D4—21no—
756D4—21no—
757D4—92no—
758D4—184no—
759D4—184no—
760D4—181no—
761D4C2×#62412yes—
762D4C2×#62412yescomplemented
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—31no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—91no—
772C2×C4—92no—
773C2×C4—92no—
774C2×C4—122no—
775C2×C4—122no—
776C2×C4—122no—
777C2×C4—122no—
778C2×C4—182no—
779C2×C4—184no—
780C2×C4—181no—
781C2×C4—362no—
782C2×C4—361no—
783C2×C4—362no—
784C2×C4—362no—
785C2×C4C22×D3211yescharacteristic
786C8—61no—
787C8—61no—
788C8—92no—
789C8C2×#62412yescomplemented
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—42no—
794C2×C3—42no—
795C2×C3—42no—
796C2×C3—42no—
797C2×C3—82no—
798C2×C3—82no—
799C2×C3C4×D3×D411yescharacteristic
800C2×C3C4×D3×D411yescharacteristic
801C2×C3C2×#91111yescharacteristic
802C2×C3#576811yescharacteristic
803C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
804C2×C3#577311yescharacteristic
805D3—62no—
806D3—62no—
807D3—122no—
808D3—122no—
809D3—122no—
810D3—242no—
811C22—22no—
812C22—22no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—92no—
818C22—181no—
819C22—181no—
820C22—182no—
821C22—368no—
822C22—361no—
823C22—361no—
824C22D32×D411yescharacteristic
825C4—32no—
826C4—61no—
827C4—61no—
828C4—61no—
829C4—92no—
830C4—121no—
831C4—121no—
832C4—121no—
833C4—121no—
834C4—182no—
835C4#6431211yescharacteristic
836C4C22×#62411yescharacteristic
837C3—21no—
838C3C4×#91111yescharacteristic, complemented
839C3#7986511yescharacteristic, complemented
840C2—42no—
841C2—42no—
842C2—182no—
843C2—362no—
844C2D3×#91111yescharacteristic
845C2#1059472911yescharacteristic
846C2D4×#62411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC2×#64120C2
cosocleC2×C32×C4C24
hypercenterC2×D8D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10595190C2semidirect
3. D4×#624C2semidirect
4. C3×#5152C2semidirect
5. C3×Dic3×D8C2semidirect
6. #10591426C2semidirect
7. #10591418C2semidirect
8. #10591405C2semidirect
9. #10591404C2semidirect
10. #10591401C2semidirect
11. #10591400C2semidirect
12. #10590773C2semidirect
13. #10590758C2semidirect
14. #10590688C2semidirect
15. #10590664C2semidirect
24. #64120C4semidirect
29. C3×D4×Dic3C22semidirect
30. C3×D4×Dic3C22semidirect
43. #63844C22semidirect
44. #63844C22semidirect
48. C3×#832C22semidirect
49. C3×#832C22semidirect
50. C3×#818C22semidirect
51. C3×#817C22semidirect
52. C3×#815C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63576C22semidirect
55. #63574C22semidirect
56. #63567C22semidirect
57. #63567C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
71. #5152D3semidirect
72. Dic3×D8D3semidirect
100. #3830C2×C4semidirect
102. D4×C3⋊D3C2×C4semidirect
116. C32×D8C2×C4semidirect
118. #3754C2×C4semidirect
119. #3753C2×C4semidirect
121. #3744C2×C4semidirect
122. #3743C2×C4semidirect
165. D4×Dic3C2×D3semidirect
166. D4×Dic3C2×D3semidirect
222. #832C2×D3semidirect
223. #832C2×D3semidirect
226. #818C2×D3semidirect
227. #817C2×D3semidirect
231. #815C2×D3semidirect
233. C8×Dic3C2×D3semidirect
254. C32×D4C22×C4semidirect
266. #634C22×C4semidirect
284. C32×C8C22×C4semidirect
285. C3⋊(C3⋊C8)C22×C4semidirect
363. C3×D8C4×D3semidirect
364. C3×D8C4×D3semidirect
456. C3×Dic3AGL(1,ℤ/8)semidirect
532. C3×D4C2×C4×D3semidirect
533. C3×D4C2×C4×D3semidirect
607. C3×C8C2×C4×D3semidirect
608. C3×C8C2×C4×D3semidirect
647. D8#624semidirect
744. Dic3#911semidirect
745. C32C4×AGL(1,ℤ/8)semidirect
762. D4C2×#624semidirect
789. C8C2×#624semidirect
838. C3C4×#911semidirect
839. C3#79865semidirect

Maximal subgroups

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

subgroupindex
C2×#641202
#105951902
D4×#6242
C3×#51522
C3×Dic3×D82
#105914262
#105914182
#105914052
#105914042
#105914012
#105914002
#105907732
#105907582
#105906882
#105906642
#798653
C4×#9113