Finite Group Databasebeta

← #11866142

Subgroups — #11866142

Order 1152.

1075 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595432C211yesmaximal, characteristic, complemented
2C2×#63951C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic
4#10594360C211yesmaximal, characteristic, complemented
5#10592501C211yesmaximal, characteristic, complemented
6C3×#4819C211yesmaximal, characteristic, complemented
7C3×#4798C211yesmaximal, characteristic, complemented
8#10591578C211yesmaximal, characteristic, complemented
9#10591567C211yesmaximal, characteristic, complemented
10#10590859C211yesmaximal, characteristic, complemented
11#10590755C211yesmaximal, characteristic, complemented
12#10590666C211yesmaximal, characteristic, complemented
13#10590594C211yesmaximal, characteristic, complemented
14#10590532C211yesmaximal, characteristic, complemented
15#10590530C211yesmaximal, characteristic, complemented
16#80599—31nomaximal
17#80535—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22#64101C2211yescharacteristic
23C3×#947C2211yescharacteristic
24C3×#947C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C2×C3×D24C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C3×#893C2211yescharacteristic, complemented
30C3×#887C2211yescharacteristic, complemented
31#63951—24no—
32#63921—21no—
33#63921—21no—
34#63913—21no—
35#63913—21no—
36#63904—21no—
37Dic3×D12C2211yescharacteristic, complemented
38C4×#624C2211yescharacteristic
39#63880—21no—
40#63878—21no—
41C4×D3×Dic3—21no—
42#63860C2211yescharacteristic
43#63860C2211yescharacteristic
44Dic3×Dic6C2211yescharacteristic, complemented
45C2×#3719C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3712C2211yescharacteristic
50#63798—24no—
51C32×#103C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63563C2211yescharacteristic
62#63563C2211yescharacteristic
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#4819D311yescharacteristic, complemented
86#4802—31no—
87#4802—31no—
88#4802—61no—
89#4798D311yescharacteristic, complemented
90#4787—31no—
91#4770—31no—
92#4770—31no—
93#4767—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96Q8×C3⋊D3—22no—
97Q8×C3⋊D3—22no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634—21no—
101C2×#634C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#625—21no—
109C2×#624D411yescharacteristic
110C2×#624D411yescharacteristic
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113#3802—22no—
114#3802—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×#216—22no—
125C3×#215—22no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
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×D24—22no—
138C3×#204—22no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—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#3713—22no—
152#3712—22no—
153#3040—91noSylow
154C2×#239—31no—
155C2×D3×Q8—31no—
156C2×D3×Q8—31no—
157C2×D3×Q8—61no—
158C2×#237—31no—
159C2×D3×D4—31no—
160C2×D3×D4—31no—
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#947C2×D311yescharacteristic
170#947C2×D311yescharacteristic
171Q8×Dic3—31no—
172C2×#216—31no—
173C2×#216C2×D311yescharacteristic, complemented
174C2×#215—31no—
175C2×#215C2×D311yescharacteristic, complemented
176#936—31no—
177#936—31no—
178D4×Dic3—31no—
179C2×#214—31no—
180C2×#214—31no—
181C2×#213—31no—
182C2×#213—31no—
183C4×#67—61no—
184C2×C4×Dic3—61no—
185#918—64no—
186#915—64no—
187#914—64no—
188#911—64no—
189C2×Dic12—31no—
190C2×D24C2×D311yescharacteristic
191C2×#204—31no—
192C2×#204C2×D311yescharacteristic
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—21no—
226C3×#103C2×D311yescharacteristic, complemented
227C3×#103C2×D311yescharacteristic, complemented
228C3×#102—31no—
229C3×#102—31no—
230#835—31no—
231#835—31no—
232#835—61no—
233#832—31no—
234#832—31no—
235#821—31no—
236#821—31no—
237#816—31no—
238#816—31no—
239#816—61no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8C2×D311yescharacteristic, complemented
243Dic3⋊C8C2×D311yescharacteristic, complemented
244#810—31no—
245#810—31no—
246#810—61no—
247#809C2×D311yescharacteristic
248#809C2×D311yescharacteristic
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—31no—
251C22×C3⋊D3C2×D411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
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⋊Dic3—21no—
265C2×C3⋊Dic3C2×D411yescharacteristic
266C4×C3⋊D3—42no—
267C4×C3⋊D3C2×D412yes—
268C4×C3⋊D3#4112yes—
269#634—21no—
270#634—21no—
271#634—42no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12C2×D412yes—
283C3×C4×D3—42no—
284C3×Dic6—21no—
285C3×Dic6C2×D412yes—
286#626—24no—
287#625—42no—
288#624—41no—
289#624—41no—
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—
313C2×C3×Q8—21no—
314C2×C3×Q8—31no—
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C22×C3×C4—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326#239—34no—
327#239—62no—
328D3×Q8—62no—
329D3×Q8—62no—
330D3×Q8—62no—
331D3×Q8—62no—
332D3×Q8—64no—
333D3×Q8—122no—
334#237—34no—
335#237—62no—
336D3×D4—62no—
337D3×D4—62no—
338D3×D4—62no—
339D3×D4—62no—
340C2×D12—61no—
341C2×D12C22×D311yescharacteristic
342C2×D12C22×D311yescharacteristic
343C2×D12C22×D311yescharacteristic
344C2×C4×D3—21no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—121no—
357C2×Dic6—31no—
358C2×Dic6—31no—
359C2×Dic6—61no—
360C2×Dic6—61no—
361C2×Dic6—61no—
362C2×Dic6—121no—
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—61no—
386#217—61no—
387#217—61no—
388#217—61no—
389#217—61no—
390#216—22no—
391#216—62no—
392#215—22no—
393#215—62no—
394#214—62no—
395#214—62no—
396#213—62no—
397#213—62no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4—21no—
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—62no—
435D24—22no—
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×C32C22×D411yescharacteristic
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3⋊D3#12112yes—
447C2×C3×D3—22no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456D32—84no—
457C32×C4—41no—
458C32×C4—41no—
459C32×C4C22×D411yescharacteristic
460C32×C4C2×#4111yescharacteristic
461C3⋊Dic3—41no—
462C3⋊Dic3—41no—
463C3⋊Dic3#12112yes—
464C3×Dic3—22no—
465C3×Dic3—21no—
466C3×Dic3—21no—
467C3×Dic3—21no—
468C3×Dic3—21no—
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—91no—
507#103—91no—
508#103—91no—
509#103D3211yescharacteristic, complemented
510#102—31no—
511#102—31no—
512#102—91no—
513#102—91no—
514C23×C3—61no—
515C23×C3—61no—
516C23×C3—61no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—31no—
521C22×D3—31no—
522C22×D3—61no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—122no—
528C22×D3—122no—
529C3×Q8—22no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—21no—
534C3×Q8—32no—
535C3×Q8—41no—
536C3×Q8—61no—
537C3×D4—32no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—61no—
542C3×D4—61no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—61no—
555C2×C3×C4—122no—
556C2×C3×C4C23×D311yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558#67—64no—
559#67—122no—
560#67—122no—
561C2×Dic3—21no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—61no—
565C2×Dic3—64no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—121no—
571C2×Dic3—121no—
572C2×Dic3—122no—
573C2×Dic3D3×D411yescharacteristic
574C2×Dic3D3×D411yescharacteristic
575C2×Dic3D3×D411yescharacteristic
576C2×Dic3D3×D411yescharacteristic
577D12—21no—
578D12—21no—
579D12—21no—
580D12—21no—
581D12—21no—
582D12—64no—
583D12D3×D412yes—
584C4×D3—32no—
585C4×D3—32no—
586C4×D3—32no—
587C4×D3—32no—
588C4×D3—42no—
589C4×D3—62no—
590C4×D3—62no—
591C4×D3—64no—
592C4×D3—121no—
593C4×D3—121no—
594C4×D3—121no—
595C4×D3—121no—
596C4×D3—122no—
597C4×D3—122no—
598C4×D3—124no—
599C4×D3—122no—
600Dic6—21no—
601Dic6—62no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—61no—
606Dic6—121no—
607Dic6—122no—
608Dic6—122no—
609Dic6—124no—
610Dic6D3×D412yes—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—41no—
614C3×C8—61no—
615C3×C8—61no—
616C3⋊C8—21no—
617C3⋊C8—21no—
618C3⋊C8—61no—
619C3⋊C8—61no—
620C3⋊C8—121no—
621C2×C32C2×#12111yescharacteristic
622C2×C32#57511yescharacteristic
623C2×C32#57511yescharacteristic
624C3⋊D3—22no—
625C3×D3—42no—
626C3×D3—81no—
627C3×D3—81no—
628C24—181no—
629#41—94no—
630#41—182no—
631C2×Q8—31no—
632C2×Q8—91no—
633C2×Q8—181no—
634C2×Q8—182no—
635C2×Q8—182no—
636C2×Q8C2×D3211yescharacteristic
637C2×D4—31no—
638C2×D4—31no—
639C2×D4—31no—
640C2×D4—181no—
641C2×D4—182no—
642C2×D4—182no—
643C2×D4—181no—
644C22×C4—61no—
645C22×C4—91no—
646C22×C4—91no—
647C22×C4—91no—
648C22×C4—181no—
649C22×C4—181no—
650C22×C4—181no—
651Q16—62no—
652Q16—182no—
653SD16—62no—
654SD16—62no—
655SD16—182no—
656SD16—182no—
657D8—62no—
658D8—182no—
659M16—182no—
660M16—182no—
661C2×C8—31no—
662C2×C8—31no—
663C2×C8—91no—
664C2×C8C2×D3211yescharacteristic
665C4⋊C4—61no—
666C4⋊C4—91no—
667C4⋊C4—181no—
668C4⋊C4C2×D3211yescharacteristic
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C42—31no—
681C42—31no—
682C42—61no—
683C42—91no—
684C42—91no—
685C42—181no—
686C42—181no—
687C22×C3—21no—
688C22×C3—62no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3C2×D3×D411yescharacteristic
698C22×C3C2×D3×D411yescharacteristic
699C2×D3—22no—
700C2×D3—32no—
701C2×D3—32no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—62no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—61no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—244no—
718C2×D3—244no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—42no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—61no—
727C3×C4—61no—
728C3×C4—61no—
729C3×C4—61no—
730C3×C4—62no—
731C3×C4—81no—
732C3×C4C2×D3×D411yescharacteristic
733C3×C4C2×D3×D411yescharacteristic
734C3×C4D3×#4111yescharacteristic
735C3×C4D3×#4111yescharacteristic
736Dic3—21no—
737Dic3—21no—
738Dic3—21no—
739Dic3—21no—
740Dic3—22no—
741Dic3—32no—
742Dic3—32no—
743Dic3—62no—
744Dic3—122no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749Dic3—241no—
750C32#304011yescharacteristic, complemented, Sylow
751C23—61no—
752C23—61no—
753C23—61no—
754C23—91no—
755C23—362no—
756C23—362no—
757C23—362no—
758Q8—21no—
759Q8—21no—
760Q8—32no—
761Q8—61no—
762Q8—181no—
763Q8—181no—
764Q8—362no—
765D4—32no—
766D4—61no—
767D4—61no—
768D4—61no—
769D4—61no—
770D4—61no—
771D4—184no—
772D4—362no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—31no—
778C2×C4—31no—
779C2×C4—61no—
780C2×C4—91no—
781C2×C4—92no—
782C2×C4—92no—
783C2×C4—122no—
784C2×C4—184no—
785C2×C4—181no—
786C2×C4—181no—
787C2×C4—362no—
788C2×C4—361no—
789C2×C4—361no—
790C2×C4—362no—
791C2×C4C22×D3211yescharacteristic
792C8—21no—
793C8—61no—
794C8—61no—
795C8—181no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—122no—
800C2×C3—241no—
801C2×C3—241no—
802C2×C3D3×#12111yescharacteristic
803C2×C3D3×#12111yescharacteristic
804C2×C3#576811yescharacteristic
805C2×C3#576811yescharacteristic
806C2×C3#577311yescharacteristic
807C2×C3#577711yescharacteristic
808D3—42no—
809D3—62no—
810D3—62no—
811D3—81no—
812D3—81no—
813D3—122no—
814C22—62no—
815C22—92no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—181no—
825C22—181no—
826C22—724no—
827C22D32×D411yescharacteristic
828C4—41no—
829C4—41no—
830C4—61no—
831C4—61no—
832C4—61no—
833C4—61no—
834C4—62no—
835C4—92no—
836C4—361no—
837C4—361no—
838C4#6430611yescharacteristic
839C4D32×D411yescharacteristic
840C3—21no—
841C3#8053511yescharacteristic, complemented
842C3#8059911yescharacteristic, complemented
843C2—122no—
844C2—182no—
845C2—241no—
846C2—241no—
847C2#1059426511yescharacteristic
848C2#1059474511yescharacteristic
849C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#63798C2
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. #10595432C2semidirect
2. C2×#63951C2semidirect
4. #10594360C2semidirect
5. #10592501C2semidirect
6. C3×#4819C2semidirect
7. C3×#4798C2semidirect
8. #10591578C2semidirect
9. #10591567C2semidirect
10. #10590859C2semidirect
11. #10590755C2semidirect
12. #10590666C2semidirect
13. #10590594C2semidirect
14. #10590532C2semidirect
15. #10590530C2semidirect
25. C2×C3×#216C22semidirect
26. C2×C3×#215C22semidirect
29. C3×#893C22semidirect
30. C3×#887C22semidirect
37. Dic3×D12C22semidirect
44. Dic3×Dic6C22semidirect
45. C2×#3719C22semidirect
46. C2×#3716C22semidirect
51. C32×#103C22semidirect
52. #63662C22semidirect
53. #63643C22semidirect
54. #63637C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
59. Dic3⋊(C3⋊C8)C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
85. #4819D3semidirect
89. #4798D3semidirect
173. C2×#216C2×D3semidirect
175. C2×#215C2×D3semidirect
199. #893C2×D3semidirect
204. #887C2×D3semidirect
226. C3×#103C2×D3semidirect
227. C3×#103C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
509. #103D32semidirect
750. C32#3040semidirect
841. C3#80535semidirect
842. C3#80599semidirect

Maximal subgroups

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

subgroupindex
#105954322
C2×#639512
C2×#637982
#105943602
#105925012
C3×#48192
C3×#47982
#105915782
#105915672
#105908592
#105907552
#105906662
#105905942
#105905322
#105905302
#805993
#805353