Finite Group Databasebeta

← #11866139

Subgroups — #11866139

Order 1152.

1095 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595170C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic
3C2×#63811C211yesmaximal, characteristic, complemented
4#10594360C211yesmaximal, characteristic, complemented
5#10592469C211yesmaximal, characteristic, complemented
6C3×#4787C211yesmaximal, characteristic, complemented
7C3×#4767C211yesmaximal, characteristic, complemented
8#10591442C211yesmaximal, characteristic, complemented
9#10591431C211yesmaximal, characteristic, complemented
10#10590801C211yesmaximal, characteristic, complemented
11#10590754C211yesmaximal, characteristic, complemented
12#10590666C211yesmaximal, characteristic, complemented
13#10590602C211yesmaximal, characteristic, complemented
14#10590536C211yesmaximal, characteristic, complemented
15#10590534C211yesmaximal, characteristic, complemented
16#80599—31nomaximal
17#80535—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22#64101C2211yescharacteristic
23C3×#936C2211yescharacteristic
24C3×#936C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic, complemented
29C3×#893C2211yescharacteristic, complemented
30C3×#887C2211yescharacteristic, complemented
31#63974—21no—
32#63974—21no—
33#63953—21no—
34#63953—21no—
35#63937—24no—
36#63904—21no—
37Dic3×D12C2211yescharacteristic, complemented
38C4×#624C2211yescharacteristic
39#63880—21no—
40#63878—21no—
41C4×D3×Dic3—21no—
42#63864C2211yescharacteristic
43#63864C2211yescharacteristic
44Dic3×Dic6C2211yescharacteristic, complemented
45C2×#3718C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3712C2211yescharacteristic
50#63811—24no—
51C32×#102C2211yescharacteristic
52#63659C2211yescharacteristic
53#63648C2211yescharacteristic
54#63636C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63566C2211yescharacteristic, complemented
63C2×#918—31no—
64C2×#915—31no—
65C2×#914—31no—
66C2×#911—31no—
67D3×#124—31no—
68D3×#124—31no—
69C4×#239—31no—
70C4×#237—31no—
71C3×#464—31no—
72C3×#463—31no—
73#5185—31no—
74#5166—31no—
75#5165—31no—
76#5153—31no—
77#5057—31no—
78#5054—31no—
79#5028—31no—
80#5016—31no—
81#4845—31no—
82#4844—31no—
83#4837—31no—
84#4837—31no—
85#4819—31no—
86#4802—31no—
87#4802—31no—
88#4798—31no—
89#4787D311yescharacteristic, complemented
90#4770—31no—
91#4770—31no—
92#4770—61no—
93#4767D311yescharacteristic, complemented
94C23×C3⋊D3—21no—
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97D4×C3⋊D3—22no—
98D4×C3⋊D3—22no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#627—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×#624D411yescharacteristic
110C2×#624D411yescharacteristic
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113#3797—22no—
114#3797—22no—
115#3796—22no—
116#3796D414yes—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3752—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4×C3⋊Dic3—21no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3743—22no—
124C3×#217—21no—
125C3×#217—21no—
126C3×#217—21no—
127C3×#217—21no—
128C3×#214—22no—
129C3×#213—22no—
130C3×(C2×D3)⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×Dic12—22no—
138C3×#204—22no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141#3722—21no—
142#3722—21no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145Dic32—21no—
146Dic32D411yescharacteristic
147Dic32D411yescharacteristic
148#3718—22no—
149#3717—22no—
150#3715—22no—
151#3714—22no—
152#3712—22no—
153#3040—91noSylow
154C2×#239—31no—
155C2×D3×Q8—31no—
156C2×D3×Q8—31no—
157C2×#237—31no—
158C2×D3×D4—31no—
159C2×D3×D4—31no—
160C2×D3×D4—61no—
161C2×C3×Q16—31no—
162C2×C3×SD16—31no—
163C2×C3×SD16—31no—
164C2×C3×D8—31no—
165C3×#124—31no—
166C3×#124—31no—
167C3×C4×Q8—31no—
168C3×C4×D4—31no—
169#947—31no—
170#947—31no—
171Q8×Dic3—31no—
172C2×#216—31no—
173C2×#216—31no—
174C2×#215—31no—
175C2×#215—31no—
176#936C2×D311yescharacteristic
177#936C2×D311yescharacteristic
178D4×Dic3—31no—
179C2×#214—31no—
180C2×#214C2×D311yescharacteristic
181C2×#213—31no—
182C2×#213C2×D311yescharacteristic
183C4×#67—61no—
184C2×C4×Dic3—61no—
185#918—64no—
186#915—64no—
187#914—64no—
188#911—64no—
189C2×Dic12C2×D311yescharacteristic, complemented
190C2×D24—31no—
191C2×#204—31no—
192C2×#204C2×D311yescharacteristic, complemented
193C2×ΓL(1,𝔽25)—31no—
194C2×ΓL(1,𝔽25)—31no—
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×ΓL(1,𝔽25)—61no—
198#893—61no—
199#893C2×D311yescharacteristic, complemented
200#892—31no—
201#892—31no—
202#892—61no—
203#892—61no—
204#887C2×D311yescharacteristic, complemented
205#885—61no—
206#885—61no—
207#885—61no—
208#885—61no—
209#67⋊C4—61no—
210D3×C22⋊C4—61no—
211D3×C22⋊C4—61no—
212D3×C22⋊C4—61no—
213D3×C22⋊C4—61no—
214#877—61no—
215#875—31no—
216#875—31no—
217C4×D12—31no—
218C4×D12—61no—
219C42×D3—31no—
220C42×D3—31no—
221C42×D3—61no—
222C4×Dic6—31no—
223C3×C4⋊C8—31no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#103—31no—
227C3×#102—21no—
228C3×#102C2×D311yescharacteristic
229C3×#102C2×D311yescharacteristic
230#835—31no—
231#835—31no—
232#832—31no—
233#832—31no—
234#832—61no—
235#821—31no—
236#821—31no—
237#821—61no—
238#816—31no—
239#816—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8C2×D311yescharacteristic, complemented
243Dic3⋊C8C2×D311yescharacteristic, complemented
244#810C2×D311yescharacteristic, complemented
245#810C2×D311yescharacteristic, complemented
246#809—31no—
247#809—31no—
248#809—61no—
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—42no—
254C22×C3⋊D3—42no—
255C22×C3⋊D3—42no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C32×D4—21no—
259C32×D4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C2411yescharacteristic
262#638—42no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3C2×D411yescharacteristic
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—21no—
267C4×C3⋊D3C2×D412yes—
268C4×C3⋊D3#4112yes—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—21no—
277C3×D12C2×D412yes—
278C3×C4×D3—42no—
279C3×Dic6—21no—
280C3×Dic6—21no—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6C2×D412yes—
285#627—42no—
286#626—24no—
287#624—41no—
288#624—41no—
289#624—42no—
290D3×Dic3—24no—
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—31no—
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—91no—
310#418—91no—
311C23×D3—61no—
312C23×D3—61no—
313C23×D3—121no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×Q8—31no—
317C2×C3×D4—21no—
318C2×C3×D4—31no—
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C22×D311yescharacteristic
321C22×C3×C4—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—121no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328#239—34no—
329#239—62no—
330D3×Q8—62no—
331D3×Q8—62no—
332D3×Q8—62no—
333D3×Q8—62no—
334#237—34no—
335#237—62no—
336D3×D4—62no—
337D3×D4—62no—
338D3×D4—62no—
339D3×D4—62no—
340D3×D4—64no—
341D3×D4—122no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12C22×D311yescharacteristic
347C2×C4×D3—21no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×C4×D3—31no—
353C2×C4×D3—31no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×Dic6—61no—
360C2×Dic6—61no—
361C2×Dic6C22×D311yescharacteristic
362C2×Dic6C22×D311yescharacteristic
363C2×Dic6C22×D311yescharacteristic
364C3×Q16—62no—
365C3×SD16—62no—
366C3×SD16—62no—
367C3×D8—62no—
368C2×C3×C8—21no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C3×C4⋊C4—21no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C42—31no—
383C3×C42—31no—
384C3×C42—61no—
385#217—21no—
386#217—21no—
387#217—21no—
388#217—21no—
389#217—61no—
390#216—62no—
391#216—62no—
392#215—62no—
393#215—62no—
394#214—22no—
395#214—62no—
396#213—22no—
397#213—62no—
398(C2×D3)⋊C4—21no—
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—61no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—121no—
411C4⋊Dic3—31no—
412C4⋊Dic3—31no—
413C4⋊Dic3—61no—
414C4⋊Dic3—61no—
415Dic3⋊C4—21no—
416Dic3⋊C4—61no—
417C4×Dic3—21no—
418C4×Dic3—31no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—121no—
427C4×Dic3C22×D311yescharacteristic
428C4×Dic3C22×D311yescharacteristic
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—61no—
432C2×C3⋊C8C22×D311yescharacteristic
433C2×C3⋊C8C22×D311yescharacteristic
434Dic12—22no—
435D24—62no—
436#204—22no—
437#204—62no—
438ΓL(1,𝔽25)—62no—
439ΓL(1,𝔽25)—62no—
440ΓL(1,𝔽25)—62no—
441ΓL(1,𝔽25)—62no—
442ΓL(1,𝔽25)—122no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32C22×D411yescharacteristic
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3⋊D3—41no—
450C2×C3⋊D3—41no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—84no—
453C2×C3⋊D3#12112yes—
454C2×C3×D3—22no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C32×C4—41no—
458C32×C4C22×D411yescharacteristic
459C32×C4C2×#4111yescharacteristic
460C3⋊Dic3—41no—
461C3⋊Dic3#12112yes—
462C3×Dic3—22no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—21no—
467C3×Dic3—41no—
468C3×Dic3—41no—
469C2×#41—91no—
470C22×Q8—91no—
471C22×D4—91no—
472#137—184no—
473AGL(1,ℤ/8)—184no—
474C2×Q16—31no—
475C2×Q16—91no—
476C2×SD16—31no—
477C2×SD16—31no—
478C2×SD16—91no—
479C2×SD16—91no—
480C2×D8—31no—
481C2×D8—91no—
482C2×M16—91no—
483C2×M16—91no—
484#124—31no—
485#124—31no—
486#124—91no—
487#124—91no—
488#124—181no—
489#124—181no—
490C4×Q8—31no—
491C4×Q8—91no—
492C4×D4—31no—
493C4×D4—91no—
494C4×D4—181no—
495C4×D4—181no—
496#117—91no—
497#117—181no—
498C2×C22⋊C4—181no—
499C2×C22⋊C4—181no—
500C2×C42—91no—
501C2×C42—181no—
502C4⋊C8—31no—
503C4⋊C8—31no—
504C4⋊C8—91no—
505C4⋊C8—91no—
506#103—31no—
507#103—31no—
508#103—91no—
509#103—91no—
510#102—91no—
511#102—91no—
512#102—91no—
513#102D3211yescharacteristic
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—41no—
517C23×C3—61no—
518C22×D3—21no—
519C22×D3—31no—
520C22×D3—31no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—61no—
524C22×D3—121no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—124no—
528C22×D3—122no—
529C22×D3—122no—
530C22×D3—122no—
531C22×D3—122no—
532C22×D3—242no—
533C22×D3—242no—
534C3×Q8—32no—
535C3×Q8—61no—
536C3×Q8—61no—
537C3×Q8—61no—
538C3×Q8—61no—
539C3×Q8—61no—
540C3×D4—22no—
541C3×D4—21no—
542C3×D4—21no—
543C3×D4—21no—
544C3×D4—21no—
545C3×D4—32no—
546C3×D4—41no—
547C3×D4—61no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—31no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—41no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—122no—
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—64no—
563#67—122no—
564#67—122no—
565#67—124no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—61no—
572C2×Dic3—64no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—121no—
576C2×Dic3—122no—
577C2×Dic3D3×D411yescharacteristic
578C2×Dic3D3×D411yescharacteristic
579C2×Dic3D3×D411yescharacteristic
580C2×Dic3D3×D411yescharacteristic
581D12—21no—
582D12—62no—
583D12—64no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—61no—
588D12—121no—
589D12D3×D412yes—
590C4×D3—32no—
591C4×D3—32no—
592C4×D3—32no—
593C4×D3—32no—
594C4×D3—42no—
595C4×D3—62no—
596C4×D3—62no—
597C4×D3—64no—
598C4×D3—121no—
599C4×D3—121no—
600C4×D3—121no—
601C4×D3—121no—
602C4×D3—122no—
603C4×D3—122no—
604C4×D3—122no—
605Dic6—21no—
606Dic6—21no—
607Dic6—21no—
608Dic6—21no—
609Dic6—21no—
610Dic6—122no—
611Dic6—122no—
612Dic6D3×D412yes—
613C3×C8—21no—
614C3×C8—21no—
615C3×C8—41no—
616C3×C8—61no—
617C3×C8—61no—
618C3⋊C8—21no—
619C3⋊C8—21no—
620C3⋊C8—61no—
621C3⋊C8—61no—
622C3⋊C8—121no—
623C2×C32—81no—
624C2×C32C2×#12111yescharacteristic
625C2×C32#57511yescharacteristic
626C2×C32#57511yescharacteristic
627C3⋊D3—22no—
628C3⋊D3—81no—
629C3×D3—42no—
630C24—181no—
631#41—94no—
632#41—182no—
633C2×Q8—31no—
634C2×Q8—31no—
635C2×Q8—31no—
636C2×Q8—181no—
637C2×Q8—182no—
638C2×Q8—182no—
639C2×D4—31no—
640C2×D4—91no—
641C2×D4—181no—
642C2×D4—182no—
643C2×D4—182no—
644C2×D4—181no—
645C2×D4C2×D3211yescharacteristic
646C22×C4—61no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—181no—
651C22×C4—181no—
652C22×C4—181no—
653Q16—62no—
654Q16—182no—
655SD16—62no—
656SD16—62no—
657SD16—182no—
658SD16—182no—
659D8—62no—
660D8—182no—
661M16—182no—
662M16—182no—
663C2×C8—31no—
664C2×C8—31no—
665C2×C8—91no—
666C2×C8C2×D3211yescharacteristic
667C4⋊C4—61no—
668C4⋊C4—91no—
669C4⋊C4—181no—
670C4⋊C4C2×D3211yescharacteristic
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C42—31no—
684C42—61no—
685C42—91no—
686C42—91no—
687C42—181no—
688C42—181no—
689C22×C3—21no—
690C22×C3—42no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—62no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C2×D3—22no—
705C2×D3—32no—
706C2×D3—32no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—62no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—122no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—241no—
724C2×D3—241no—
725C2×D3—244no—
726C2×D3—244no—
727C2×D3—248no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—41no—
731C3×C4—41no—
732C3×C4—61no—
733C3×C4—61no—
734C3×C4—61no—
735C3×C4—61no—
736C3×C4—62no—
737C3×C4—81no—
738C3×C4—121no—
739C3×C4—121no—
740C3×C4C2×D3×D411yescharacteristic
741C3×C4C2×D3×D411yescharacteristic
742C3×C4D3×#4111yescharacteristic
743C3×C4D3×#4111yescharacteristic
744Dic3—21no—
745Dic3—21no—
746Dic3—21no—
747Dic3—21no—
748Dic3—22no—
749Dic3—32no—
750Dic3—32no—
751Dic3—41no—
752Dic3—41no—
753Dic3—62no—
754Dic3—121no—
755Dic3—121no—
756Dic3—241no—
757C32#304011yescharacteristic, complemented, Sylow
758C23—21no—
759C23—61no—
760C23—91no—
761C23—181no—
762C23—362no—
763C23—362no—
764C23—362no—
765Q8—32no—
766Q8—61no—
767Q8—61no—
768Q8—61no—
769Q8—61no—
770Q8—61no—
771Q8—362no—
772D4—21no—
773D4—21no—
774D4—32no—
775D4—61no—
776D4—184no—
777D4—181no—
778D4—181no—
779D4—362no—
780C2×C4—21no—
781C2×C4—31no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—91no—
789C2×C4—92no—
790C2×C4—92no—
791C2×C4—122no—
792C2×C4—184no—
793C2×C4—181no—
794C2×C4—361no—
795C2×C4—361no—
796C2×C4—362no—
797C2×C4—362no—
798C2×C4C22×D3211yescharacteristic
799C8—21no—
800C8—61no—
801C8—61no—
802C8—181no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—82no—
807C2×C3—81no—
808C2×C3—81no—
809C2×C3—122no—
810C2×C3D3×#12111yescharacteristic
811C2×C3D3×#12111yescharacteristic
812C2×C3#576811yescharacteristic
813C2×C3#576811yescharacteristic
814C2×C3#577311yescharacteristic
815C2×C3#577711yescharacteristic
816D3—42no—
817D3—62no—
818D3—62no—
819D3—122no—
820D3—242no—
821D3—241no—
822D3—241no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—62no—
827C22—92no—
828C22—121no—
829C22—121no—
830C22—181no—
831C22—181no—
832C22—361no—
833C22—361no—
834C22—361no—
835C22—724no—
836C22D32×D411yescharacteristic
837C4—41no—
838C4—61no—
839C4—61no—
840C4—61no—
841C4—61no—
842C4—62no—
843C4—92no—
844C4—121no—
845C4—121no—
846C4—361no—
847C4#6430611yescharacteristic
848C4D32×D411yescharacteristic
849C3—21no—
850C3#8053511yescharacteristic, complemented
851C3#8059911yescharacteristic, complemented
852C2—81no—
853C2—122no—
854C2—182no—
855C2—721no—
856C2#1059426511yescharacteristic
857C2#1059472911yescharacteristic
858C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63937C2
hypercenter#102D32
hypocenterC32#3040
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595170C2semidirect
3. C2×#63811C2semidirect
4. #10594360C2semidirect
5. #10592469C2semidirect
6. C3×#4787C2semidirect
7. C3×#4767C2semidirect
8. #10591442C2semidirect
9. #10591431C2semidirect
10. #10590801C2semidirect
11. #10590754C2semidirect
12. #10590666C2semidirect
13. #10590602C2semidirect
14. #10590536C2semidirect
15. #10590534C2semidirect
27. C2×C3×Dic12C22semidirect
28. C2×C3×#204C22semidirect
29. C3×#893C22semidirect
30. C3×#887C22semidirect
37. Dic3×D12C22semidirect
44. Dic3×Dic6C22semidirect
45. C2×#3718C22semidirect
47. C2×#3715C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#810C22semidirect
59. Dic3⋊(C3⋊C8)C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63566C22semidirect
62. #63566C22semidirect
89. #4787D3semidirect
93. #4767D3semidirect
189. C2×Dic12C2×D3semidirect
192. C2×#204C2×D3semidirect
199. #893C2×D3semidirect
204. #887C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
244. #810C2×D3semidirect
245. #810C2×D3semidirect
757. C32#3040semidirect
850. C3#80535semidirect
851. C3#80599semidirect

Maximal subgroups

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

subgroupindex
#105951702
C2×#639372
C2×#638112
#105943602
#105924692
C3×#47872
C3×#47672
#105914422
#105914312
#105908012
#105907542
#105906662
#105906022
#105905362
#105905342
#805993
#805353