Finite Group Databasebeta

← #11866143

Subgroups — #11866143

Order 1152.

1056 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
1D3×#947C211yesmaximal, characteristic, complemented
2C2×#63946C211yesmaximal, characteristic, complemented
3C2×#63795C211yesmaximal, characteristic
4#10594358C211yesmaximal, characteristic, complemented
5#10592497C211yesmaximal, characteristic, complemented
6C3×#4819C211yesmaximal, characteristic, complemented
7C3×#4802C211yesmaximal, characteristic, complemented
8#10591577C211yesmaximal, characteristic, complemented
9#10591570C211yesmaximal, characteristic, complemented
10#10590813C211yesmaximal, characteristic, complemented
11#10590751C211yesmaximal, characteristic, complemented
12#10590663C211yesmaximal, characteristic, complemented
13#10590592C211yesmaximal, characteristic, complemented
14#10590538C211yesmaximal, characteristic, complemented
15#10590534C211yesmaximal, characteristic, complemented
16#80535—31nomaximal
17#78975—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21#64156C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic
24#64096C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic, complemented
27C2×C3×D24C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C3×#893C2211yescharacteristic, complemented
30C3×#892C2211yescharacteristic
31#63946—24no—
32D3×(C2×D3)⋊C4—21no—
33D3×(C2×D3)⋊C4—21no—
34#63907—21no—
35#63907—21no—
36#63902—21no—
37#63898C2211yescharacteristic, complemented
38#63879—21no—
39#63877—21no—
40C4×D3×Dic3—21no—
41C4×D3×Dic3C2211yescharacteristic
42#63864C2211yescharacteristic
43#63863C2211yescharacteristic
44#63844C2211yescharacteristic, complemented
45C2×#3719C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50#63795—24no—
51C32×#103C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54C3×#835C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63564C2211yescharacteristic
62#63562C2211yescharacteristic
63C2×#947—31no—
64C2×#942—31no—
65C2×#915—31no—
66C2×#911—31no—
67C2×#908—31no—
68D3×#124—31no—
69C4×#237—31no—
70#5522—31no—
71C3×#463—31no—
72C3×#419—31no—
73#5165—31no—
74#5153—31no—
75#5118—31no—
76#5054—31no—
77#5016—31no—
78#5001—31no—
79#4845—31no—
80#4837—31no—
81#4819—31no—
82#4819—31no—
83#4819—31no—
84#4819D311yescharacteristic, complemented
85#4802D311yescharacteristic, complemented
86#4798—31no—
87#4798—31no—
88#4798—31no—
89#4798—31no—
90#4798—31no—
91#4798—61no—
92#4770—31no—
93#4767—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C3×D3×Q8—22no—
99C3×D3×Q8—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#625—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3D411yescharacteristic
112C2×D3×Dic3D411yescharacteristic
113D3×D12—22no—
114D3×D12—22no—
115#3795—22no—
116#3795D414yes—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3756—22no—
120#3752—21no—
121#3752—21no—
122#3750—21no—
123C4×C3⋊Dic3—21no—
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3744—22no—
127C3×#215—22no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×D24—22no—
138C3×ΓL(1,𝔽25)—22no—
139#3724—21no—
140#3722—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145Dic32—21no—
146Dic32D411yescharacteristic
147Dic32D411yescharacteristic
148#3719—22no—
149#3716—22no—
150#3715—22no—
151#3714—22no—
152#3711—22no—
153#3040—91noSylow
154C22×C3×Q8—31no—
155C2×D3×Q8C2×D311yescharacteristic
156C2×#237—31no—
157C2×D3×D4—31no—
158C2×#235—31no—
159C22×D12—31no—
160C2×C3×SD16—31no—
161C2×C3×D8—31no—
162C2×C3×M16—31no—
163C3×#124—31no—
164C3×C4×D4—31no—
165C3×#117—31no—
166#947—31no—
167#947—31no—
168#947—31no—
169#947—31no—
170#947—61no—
171#947—61no—
172#947—61no—
173#947C2×D311yescharacteristic
174C2×#216—31no—
175C2×#216—31no—
176C2×#216—31no—
177C2×#216—61no—
178#942—64no—
179C2×#215—31no—
180C2×#215C2×D311yescharacteristic, complemented
181#936—31no—
182D4×Dic3—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#213—31no—
186C4×#67—61no—
187C2×(C2×D3)⋊C4—61no—
188C2×(C2×D3)⋊C4—61no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—61no—
191C2×#208—31no—
192#915—64no—
193#911—64no—
194#908—64no—
195C2×Dic12—31no—
196C2×D24—31no—
197C2×D24C2×D311yescharacteristic
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—61no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)C2×D311yescharacteristic
204#893—31no—
205#893C2×D311yescharacteristic, complemented
206#892C2×D311yescharacteristic
207#887—31no—
208#887—31no—
209#887—31no—
210#887—61no—
211#885—61no—
212#885—61no—
213#67⋊C4—61no—
214#67⋊C4—61no—
215#67⋊C4—61no—
216D3×C22⋊C4—61no—
217D3×C22⋊C4—61no—
218#877—61no—
219#875—31no—
220#872—61no—
221C42×D3—31no—
222C42×D3—61no—
223C4×Dic6—31no—
224C3×C4⋊C8—31no—
225C3×#103—21no—
226C3×#103—31no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103C2×D311yescharacteristic, complemented
230C3×#103C2×D311yescharacteristic, complemented
231C3×#102—31no—
232#835C2×D311yescharacteristic, complemented
233#832—31no—
234#821—31no—
235#816C2×D311yescharacteristic, complemented
236Dic3⋊C8—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—61no—
242Dic3⋊C8C2×D311yescharacteristic, complemented
243#810C2×D311yescharacteristic, complemented
244#809—31no—
245#809—31no—
246#809—31no—
247#809—31no—
248#809—61no—
249#809C2×D311yescharacteristic
250C4⋊(C3⋊C8)—31no—
251C22×C3⋊D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C2×D32—42no—
256C2×D32—42no—
257C2×D32—42no—
258C32×Q8—21no—
259C32×Q8—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4C2411yescharacteristic
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3C2×D411yescharacteristic
265C2×C3⋊Dic3C2×D411yescharacteristic
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)—21no—
268#634—21no—
269#634C2×D412yes—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12C2×D412yes—
279C3×C4×D3—42no—
280C3×C4×D3—42no—
281C3×C4×D3C2×D412yes—
282C3×C4×D3#4112yes—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6—42no—
286#626—42no—
287#625—24no—
288D3×Dic3—24no—
289D3×Dic3—41no—
290D3×Dic3—41no—
291D3×Dic3—42no—
292C32×C8—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#137—91no—
297C2×AGL(1,ℤ/8)—91no—
298C2×#124—91no—
299C4×#41—91no—
300#464—91no—
301#464—91no—
302#464—91no—
303#464—91no—
304#463—31no—
305#463—91no—
306#463—91no—
307#463—91no—
308#423—91no—
309#419—31no—
310#418—91no—
311C23×D3—61no—
312C23×D3—61no—
313C2×C3×Q8—21no—
314C2×C3×Q8—31no—
315C2×C3×Q8—61no—
316C2×C3×Q8—62no—
317C2×C3×Q8—62no—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332D3×Q8—22no—
333D3×Q8—22no—
334#237—34no—
335#237—62no—
336D3×D4—62no—
337D3×D4—62no—
338#235—34no—
339#235—62no—
340C2×D12—31no—
341C2×D12—31no—
342C2×D12—61no—
343C2×D12—62no—
344C2×D12—62no—
345C2×D12—61no—
346C2×D12C22×D311yescharacteristic
347C2×D12C22×D311yescharacteristic
348C2×C4×D3—21no—
349C2×C4×D3—21no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3C22×D311yescharacteristic
355C2×Dic6—21no—
356C2×Dic6—31no—
357C2×Dic6—31no—
358C2×Dic6—61no—
359C2×Dic6C22×D311yescharacteristic
360C3×SD16—62no—
361C3×D8—62no—
362C3×M16—62no—
363C2×C3×C8—21no—
364C2×C3×C8—31no—
365C2×C3×C8—31no—
366C2×C3×C8C22×D311yescharacteristic
367C2×C3×C8C22×D311yescharacteristic
368C3×C4⋊C4—21no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C42—31no—
377C3×C42—61no—
378#217—61no—
379#217—61no—
380#217—61no—
381#216—62no—
382#216—62no—
383#216—62no—
384#216—122no—
385#215—22no—
386#215—62no—
387#214—62no—
388#214—62no—
389#213—62no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—121no—
406(C2×D3)⋊C4—121no—
407C4⋊Dic3C22×D311yescharacteristic
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—121no—
413C4×Dic3—21no—
414C4×Dic3—31no—
415C4×Dic3—31no—
416C4×Dic3—31no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—31no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—121no—
426C4×Dic3C22×D311yescharacteristic
427#208—62no—
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—61no—
431C2×C3⋊C8C22×D311yescharacteristic
432C2×C3⋊C8C22×D311yescharacteristic
433Dic12—62no—
434D24—22no—
435D24—62no—
436#204—62no—
437#204—62no—
438#204—62no—
439#204—122no—
440ΓL(1,𝔽25)—22no—
441ΓL(1,𝔽25)—62no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—22no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455D32—84no—
456C32×C4—41no—
457C32×C4—41no—
458C32×C4C22×D411yescharacteristic
459C32×C4C2×#4111yescharacteristic
460C3⋊Dic3—22no—
461C3⋊Dic3—21no—
462C3⋊Dic3—21no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—91no—
469C22×Q8—31no—
470C22×D4—91no—
471#137—184no—
472AGL(1,ℤ/8)—184no—
473C2×Q16—91no—
474C2×Q16—91no—
475C2×SD16—31no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×D8—31no—
480C2×D8—91no—
481C2×M16—31no—
482C2×M16—91no—
483#124—31no—
484#124—91no—
485#124—91no—
486#124—91no—
487#124—181no—
488#124—181no—
489C4×Q8—91no—
490C4×Q8—91no—
491C4×D4—31no—
492C4×D4—91no—
493C4×D4—181no—
494C4×D4—181no—
495#117—31no—
496#117—181no—
497C2×C22⋊C4—181no—
498C2×C22⋊C4—181no—
499C2×C42—91no—
500C2×C42—181no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—31no—
506#103—31no—
507#103—31no—
508#103D3211yescharacteristic, complemented
509#102—31no—
510#102—91no—
511#102—91no—
512#102—91no—
513C23×C3—31no—
514C23×C3—61no—
515C23×C3—61no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—121no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3D3×D411yescharacteristic
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—41no—
533C3×Q8—41no—
534C3×Q8—61no—
535C3×Q8—61no—
536C3×Q8—122no—
537C3×D4—32no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—61no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—31no—
547C2×C3×C4—32no—
548C2×C3×C4—32no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—122no—
556C2×C3×C4—122no—
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559#67—64no—
560#67—64no—
561#67—122no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—64no—
573C2×Dic3—121no—
574C2×Dic3—121no—
575C2×Dic3—121no—
576C2×Dic3—122no—
577C2×Dic3D3×D411yescharacteristic
578C2×Dic3D3×D411yescharacteristic
579C2×Dic3D3×D411yescharacteristic
580D12—21no—
581D12—21no—
582D12—21no—
583D12—61no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—121no—
588D12—121no—
589D12—122no—
590D12D3×D412yes—
591C4×D3—42no—
592C4×D3—42no—
593C4×D3—64no—
594C4×D3—121no—
595C4×D3—121no—
596C4×D3—122no—
597C4×D3#23512yes—
598C4×D3D3×D412yes—
599Dic6—21no—
600Dic6—21no—
601Dic6—32no—
602Dic6—32no—
603Dic6—42no—
604Dic6—62no—
605Dic6—61no—
606Dic6—61no—
607Dic6—121no—
608C3×C8—21no—
609C3×C8—21no—
610C3×C8—41no—
611C3×C8—61no—
612C3×C8—61no—
613C3⋊C8—21no—
614C3⋊C8—21no—
615C3⋊C8—61no—
616C3⋊C8—61no—
617C3⋊C8—121no—
618C2×C32C2×#12111yescharacteristic
619C2×C32#57511yescharacteristic
620C2×C32#57511yescharacteristic
621C3⋊D3—81no—
622C3×D3—22no—
623C3×D3—42no—
624C3×D3—81no—
625C24—181no—
626#41—94no—
627#41—182no—
628C2×Q8—31no—
629C2×Q8—61no—
630C2×Q8—62no—
631C2×Q8—62no—
632C2×Q8—91no—
633C2×Q8C2×D3211yescharacteristic
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—91no—
637C2×D4—182no—
638C2×D4—182no—
639C2×D4—181no—
640C2×D4—181no—
641C22×C4—31no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—91no—
645C22×C4—91no—
646C22×C4—181no—
647C22×C4—181no—
648Q16—182no—
649Q16—182no—
650SD16—62no—
651SD16—182no—
652SD16—182no—
653SD16—182no—
654D8—62no—
655D8—182no—
656M16—62no—
657M16—182no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—91no—
661C2×C8C2×D3211yescharacteristic
662C4⋊C4—31no—
663C4⋊C4—181no—
664C4⋊C4—181no—
665C4⋊C4C2×D3211yescharacteristic
666C22⋊C4—61no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C42—31no—
678C42—61no—
679C42—91no—
680C42—91no—
681C42—91no—
682C42—181no—
683C42—181no—
684C22×C3—21no—
685C22×C3—32no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—62no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3C2×D3×D411yescharacteristic
695C22×C3C2×D3×D411yescharacteristic
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—22no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—241no—
711C2×D3—241no—
712C2×D3—241no—
713C2×D3—244no—
714C2×D3—244no—
715C2×D3#88412yes—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—32no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—61no—
724C3×C4—61no—
725C3×C4—81no—
726C3×C4—81no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4C2×#23511yescharacteristic
730C3×C4C2×D3×D411yescharacteristic
731C3×C4C2×D3×D411yescharacteristic
732C3×C4D3×#4111yescharacteristic
733Dic3—21no—
734Dic3—21no—
735Dic3—41no—
736Dic3—41no—
737Dic3—62no—
738Dic3—61no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—62no—
743Dic3—122no—
744Dic3—121no—
745Dic3—121no—
746Dic3#88412yes—
747C32#304011yescharacteristic, complemented, Sylow
748C23—31no—
749C23—61no—
750C23—61no—
751C23—181no—
752C23—362no—
753C23—362no—
754C23—362no—
755Q8—21no—
756Q8—21no—
757Q8—61no—
758Q8—61no—
759Q8—92no—
760Q8—122no—
761Q8—181no—
762D4—32no—
763D4—61no—
764D4—61no—
765D4—61no—
766D4—184no—
767D4—181no—
768D4—181no—
769D4—362no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—31no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—91no—
780C2×C4—91no—
781C2×C4—122no—
782C2×C4—122no—
783C2×C4—184no—
784C2×C4—181no—
785C2×C4—361no—
786C2×C4—361no—
787C2×C4—362no—
788C2×C4C22×D3211yescharacteristic
789C8—21no—
790C8—61no—
791C8—61no—
792C8—181no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—62no—
797C2×C3—122no—
798C2×C3—241no—
799C2×C3C2×#88411yescharacteristic
800C2×C3D3×#12111yescharacteristic
801C2×C3#576811yescharacteristic
802C2×C3#577311yescharacteristic
803C2×C3#577711yescharacteristic
804C2×C3#577711yescharacteristic
805D3—22no—
806D3—42no—
807D3—81no—
808D3—241no—
809D3—241no—
810D3—481no—
811C22—32no—
812C22—61no—
813C22—61no—
814C22—62no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—361no—
821C22—361no—
822C22—361no—
823C22—724no—
824C22D32×D411yescharacteristic
825C4—32no—
826C4—41no—
827C4—41no—
828C4—61no—
829C4—61no—
830C4—121no—
831C4—121no—
832C4—181no—
833C4—181no—
834C4—182no—
835C4D3×#23511yescharacteristic
836C4D32×D411yescharacteristic
837C3—21no—
838C3#7897511yescharacteristic, complemented
839C3#8053511yescharacteristic, complemented
840C2—62no—
841C2—122no—
842C2—241no—
843C2—721no—
844C2D3×#88411yescharacteristic
845C2#1059474411yescharacteristic
846C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#63795C2
hypercenter#103D32
hypocenterC32#3040
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. D3×#947C2semidirect
2. C2×#63946C2semidirect
4. #10594358C2semidirect
5. #10592497C2semidirect
6. C3×#4819C2semidirect
7. C3×#4802C2semidirect
8. #10591577C2semidirect
9. #10591570C2semidirect
10. #10590813C2semidirect
11. #10590751C2semidirect
12. #10590663C2semidirect
13. #10590592C2semidirect
14. #10590538C2semidirect
15. #10590534C2semidirect
22. C2×#3756C22semidirect
24. #64096C22semidirect
26. C2×C3×#215C22semidirect
29. C3×#893C22semidirect
37. #63898C22semidirect
44. #63844C22semidirect
45. C2×#3719C22semidirect
47. C2×#3715C22semidirect
51. C32×#103C22semidirect
52. #63641C22semidirect
54. C3×#835C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
84. #4819D3semidirect
85. #4802D3semidirect
180. C2×#215C2×D3semidirect
205. #893C2×D3semidirect
229. C3×#103C2×D3semidirect
230. C3×#103C2×D3semidirect
232. #835C2×D3semidirect
235. #816C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
243. #810C2×D3semidirect
508. #103D32semidirect
747. C32#3040semidirect
838. C3#78975semidirect
839. C3#80535semidirect

Maximal subgroups

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

subgroupindex
D3×#9472
C2×#639462
C2×#637952
#105943582
#105924972
C3×#48192
C3×#48022
#105915772
#105915702
#105908132
#105907512
#105906632
#105905922
#105905382
#105905342
#805353
#789753