Finite Group Databasebeta

← #11866297

Subgroups — #11866297

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595356C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic
3C2×D3×#204C211yesmaximal, characteristic, complemented
4#10594604C211yesmaximal, characteristic, complemented
5#10592517C211yesmaximal, characteristic, complemented
6C3×#4818C211yesmaximal, characteristic, complemented
7C3×#4804C211yesmaximal, characteristic, complemented
8#10591569C211yesmaximal, characteristic, complemented
9#10591565C211yesmaximal, characteristic, complemented
10#10590860C211yesmaximal, characteristic, complemented
11#10590750C211yesmaximal, characteristic, complemented
12#10590694C211yesmaximal, characteristic, complemented
13#10590600C211yesmaximal, characteristic, complemented
14#10590540C211yesmaximal, characteristic, complemented
15#10590530C211yesmaximal, characteristic, complemented
16#80430—31nomaximal
17#78863—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21#64153C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24#64102C2211yescharacteristic
25C3×#944C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#893C2211yescharacteristic
30C3×#892C2211yescharacteristic
31#63939—24no—
32#63921—21no—
33D3×(C2×D3)⋊C4—21no—
34C4×#626—21no—
35#63898C2211yescharacteristic
36#63894C2211yescharacteristic
37#63884—21no—
38#63884—21no—
39#63880—21no—
40#63863C2211yescharacteristic, complemented
41#63860C2211yescharacteristic, complemented
42#63855C2211yescharacteristic
43#63851—21no—
44#63851—21no—
45C2×#3717C2211yescharacteristic
46C2×#3716C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50D3×#204—24no—
51C32×#103C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63#5825—31no—
64C2×#949—31no—
65C2×#914—31no—
66C2×D3×SD16—31no—
67C22×#204—31no—
68#5724—31no—
69#5545—31no—
70#5521—31no—
71C3×#461—31no—
72C3×#416—31no—
73#5165—31no—
74#5162—31no—
75#5102—31no—
76#5083—31no—
77#5016—31no—
78#5004—31no—
79#4844—31no—
80#4839—31no—
81#4819—31no—
82#4818—31no—
83#4818—31no—
84#4818—31no—
85#4818—31no—
86#4818—61no—
87#4818D311yescharacteristic, complemented
88#4804D311yescharacteristic, complemented
89#4802—31no—
90#4787—31no—
91#4787—31no—
92#4787—31no—
93#4787—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×#634C2311yescharacteristic
99C3×#239—22no—
100C3×#239—22no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#626—21no—
110C2×#624—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113D3×D12—22no—
114D3×D12D414yes—
115D3×Dic6—22no—
116D3×Dic6—22no—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3755—22no—
120#3752—21no—
121#3750—21no—
122#3750—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3744—22no—
126C3×#215—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×#204—22no—
137C3×D3×C8—22no—
138Dic3⋊Dic3D411yescharacteristic
139Dic3⋊Dic3D411yescharacteristic
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3D411yescharacteristic
147(C2×D3)⋊Dic3D411yescharacteristic
148#3717—22no—
149#3716—22no—
150#3714—22no—
151#3713—22no—
152#3711—22no—
153#3042—91noSylow
154C2×C3×#41—31no—
155C2×#239C2×D311yescharacteristic
156C2×D3×Q8—31no—
157C2×D3×D4—31no—
158C22×D12—31no—
159C22×Dic6—31no—
160C2×C3×SD16—31no—
161C2×C3×SD16—31no—
162C22×C3×C8—31no—
163C3×C4⋊Q8—31no—
164C3×C4×D4—31no—
165C3×#117—31no—
166#949—64no—
167#947—31no—
168#944—31no—
169#944—31no—
170#944—61no—
171#944C2×D311yescharacteristic, complemented
172C2×#215—31no—
173C2×#215—31no—
174C2×#215—31no—
175C2×#215—61no—
176C2×#215C2×D311yescharacteristic
177#936—31no—
178#936—31no—
179#935—61no—
180#935—61no—
181D4×Dic3—31no—
182C2×#214—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C4×#67—61no—
187C2×(C2×D3)⋊C4—61no—
188#926—31no—
189#924—61no—
190#924—61no—
191C2×#208—31no—
192#914—64no—
193D3×SD16—64no—
194C2×D24—31no—
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—61no—
200C2×#204—64no—
201C2×#204C2×D311yescharacteristic
202C2×ΓL(1,𝔽25)—31no—
203C2×D3×C8C2×D311yescharacteristic
204#896—61no—
205#896—61no—
206#894—61no—
207#894—61no—
208#893—31no—
209#893—31no—
210#893—31no—
211#893—31no—
212#893—61no—
213#893C2×D311yescharacteristic
214#892C2×D311yescharacteristic
215#67⋊C4—61no—
216D3×C22⋊C4—61no—
217D3×C22⋊C4—61no—
218D3×C22⋊C4—61no—
219#875—31no—
220C4×D12—31no—
221C4×D12—61no—
222C4×D12—61no—
223#872—31no—
224C3×C4⋊C8—31no—
225C3×#103—21no—
226C3×#103—31no—
227C3×#103—31no—
228C3×#103C2×D311yescharacteristic, complemented
229C3×#103C2×D311yescharacteristic, complemented
230C3×#102—31no—
231C3×#102—31no—
232#835—31no—
233#835C2×D311yescharacteristic, complemented
234#821C2×D311yescharacteristic, complemented
235#816—31no—
236Dic3⋊C8—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—61no—
242Dic3⋊C8C2×D311yescharacteristic, complemented
243#810—31no—
244#810—31no—
245#810—31no—
246#810—31no—
247#810—61no—
248#810C2×D311yescharacteristic, complemented
249#809C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251C22×C3⋊D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C2×D32—24no—
256C2×D32—81no—
257C2×D32—81no—
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)C2×D412yes—
268C4×C3⋊D3—81no—
269#634—21no—
270#634—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—42no—
280C3×D12C2×D412yes—
281C3×C4×D3—42no—
282C3×C4×D3—81no—
283C3×C4×D3C2×D412yes—
284C3×C4×D3#4112yes—
285C3×Dic6—21no—
286C3×Dic6—21no—
287#627—42no—
288#626—24no—
289#624—81no—
290D3×Dic3—42no—
291D3×Dic3—81no—
292C32×C8—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×AGL(1,ℤ/8)—91no—
297C22×SD16—91no—
298#536—91no—
299#518—91no—
300#463—91no—
301#463—91no—
302#463—91no—
303#463—91no—
304#461—31no—
305#461—91no—
306#461—91no—
307#461—91no—
308#424—91no—
309#419—91no—
310#416—31no—
311C23×D3—61no—
312C23×D3—61no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—21no—
316C2×C3×Q8—31no—
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—61no—
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C2×#67—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328#239—22no—
329#239—22no—
330D3×Q8—62no—
331D3×Q8—62no—
332D3×D4—34no—
333D3×D4—62no—
334C2×D12—21no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—34no—
338C2×D12—61no—
339C2×D12—62no—
340C2×D12—61no—
341C2×D12C22×D311yescharacteristic
342C2×D12C22×D311yescharacteristic
343C2×C4×D3—21no—
344C2×C4×D3—21no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—121no—
352C2×C4×D3C22×D311yescharacteristic
353C2×Dic6—31no—
354C2×Dic6—31no—
355C2×Dic6—61no—
356C2×Dic6—62no—
357C2×Dic6—62no—
358C2×Dic6—61no—
359C2×Dic6—61no—
360C2×Dic6C22×D311yescharacteristic
361C3×SD16—62no—
362C3×SD16—62no—
363C2×C3×C8—21no—
364C2×C3×C8—31no—
365C2×C3×C8—31no—
366C2×C3×C8—62no—
367C2×C3×C8C22×D311yescharacteristic
368C2×C3×C8C22×D311yescharacteristic
369C3×C4⋊C4—21no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4C22×D311yescharacteristic
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C42—31no—
378C3×C42—61no—
379#217—31no—
380#217—31no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#215—22no—
387#215—62no—
388#215—62no—
389#215—62no—
390#215—122no—
391#214—62no—
392#213—62no—
393#213—62no—
394#213—62no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
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—121no—
409C4⋊Dic3—31no—
410C4⋊Dic3—31no—
411C4⋊Dic3C22×D311yescharacteristic
412Dic3⋊C4—21no—
413Dic3⋊C4—21no—
414Dic3⋊C4—31no—
415Dic3⋊C4—31no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—121no—
421Dic3⋊C4—121no—
422C4×Dic3—21no—
423C4×Dic3—31no—
424C4×Dic3—31no—
425C4×Dic3—61no—
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
433D24—62no—
434#204—22no—
435#204—62no—
436#204—62no—
437#204—62no—
438#204—62no—
439#204—122no—
440ΓL(1,𝔽25)—62no—
441D3×C8—22no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—22no—
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—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3—41no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—31no—
469C22×Q8—91no—
470C22×D4—91no—
471AGL(1,ℤ/8)—184no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—184no—
479C2×D8—91no—
480C2×D8—91no—
481C2×M16—91no—
482C22×C8—31no—
483C4⋊Q8—31no—
484C4⋊Q8—91no—
485#124—91no—
486#124—91no—
487#123—181no—
488#123—181no—
489C22⋊Q8—181no—
490C22⋊Q8—181no—
491C4×D4—31no—
492C4×D4—91no—
493C4×D4—91no—
494C4×D4—91no—
495C4×D4—181no—
496C4×D4—181no—
497#117—31no—
498#117—91no—
499C2×C22⋊C4—181no—
500C2×C22⋊C4—181no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—31no—
506#103—31no—
507#103—91no—
508#103—91no—
509#103—91no—
510#103D3211yescharacteristic, complemented
511#102—31no—
512#102—31no—
513C23×C3—31no—
514C23×C3—61no—
515C23×C3—61no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—64no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—64no—
522C22×D3—121no—
523C22×D3—241no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
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×D4—32no—
537C3×D4—61no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—122no—
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—241no—
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559#67—64no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—121no—
571C2×Dic3—122no—
572C2×Dic3—241no—
573C2×Dic3D3×D411yescharacteristic
574C2×Dic3D3×D411yescharacteristic
575C2×Dic3D3×D411yescharacteristic
576D12—21no—
577D12—21no—
578D12—21no—
579D12—32no—
580D12—32no—
581D12—42no—
582D12—62no—
583D12—64no—
584D12—61no—
585D12—61no—
586D12—121no—
587D12D3×D412yes—
588C4×D3—42no—
589C4×D3—81no—
590C4×D3—122no—
591C4×D3—241no—
592C4×D3—241no—
593C4×D3—241no—
594C4×D3—241no—
595C4×D3—242no—
596C4×D3—241no—
597C4×D3#23512yes—
598C4×D3D3×D412yes—
599Dic6—21no—
600Dic6—21no—
601Dic6—61no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—121no—
606Dic6—121no—
607Dic6—122no—
608Dic6—122no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—41no—
612C3×C8—61no—
613C3×C8—61no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C3⋊C8—61no—
617C3⋊C8—61no—
618C3⋊C8—121no—
619C2×C32C2×#12111yescharacteristic
620C2×C32#57711yescharacteristic
621C2×C32#57711yescharacteristic
622C3⋊D3—42no—
623C3×D3—22no—
624C3×D3—42no—
625C3×D3—81no—
626C24—181no—
627#41—62no—
628#41—62no—
629C2×Q8—31no—
630C2×Q8—91no—
631C2×Q8—181no—
632C2×Q8—182no—
633C2×Q8—182no—
634C2×Q8C2×D3211yescharacteristic
635C2×D4—31no—
636C2×D4—31no—
637C2×D4—61no—
638C2×D4—94no—
639C2×D4—91no—
640C2×D4—182no—
641C2×D4—181no—
642C22×C4—31no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—181no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4—181no—
649SD16—62no—
650SD16—62no—
651SD16—182no—
652SD16—182no—
653SD16—182no—
654SD16—182no—
655D8—182no—
656D8—182no—
657M16—182no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—62no—
661C2×C8—91no—
662C2×C8C2×D3211yescharacteristic
663C4⋊C4—31no—
664C4⋊C4—61no—
665C4⋊C4—61no—
666C4⋊C4—91no—
667C4⋊C4—91no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C4⋊C4C2×D3211yescharacteristic
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—91no—
674C22⋊C4—91no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C42—61no—
684C42—91no—
685C22×C3—21no—
686C22×C3—32no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—62no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3C2×D3×D411yescharacteristic
696C22×C3C2×D3×D411yescharacteristic
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—22no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—62no—
706C2×D3—62no—
707C2×D3—122no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—241no—
713C2×D3—241no—
714C2×D3—244no—
715C2×D3—244no—
716C2×D3#88412yes—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—32no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—81no—
727C3×C4—81no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4C2×#23511yescharacteristic
731C3×C4C2×D3×D411yescharacteristic
732C3×C4C2×D3×D411yescharacteristic
733C3×C4D3×#4111yescharacteristic
734Dic3—21no—
735Dic3—21no—
736Dic3—41no—
737Dic3—41no—
738Dic3—62no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—121no—
744Dic3—121no—
745Dic3—121no—
746Dic3—241no—
747Dic3#88412yes—
748C32#304211yescharacteristic, complemented, Sylow
749C23—31no—
750C23—61no—
751C23—61no—
752C23—184no—
753C23—181no—
754C23—721no—
755C23—721no—
756Q8—21no—
757Q8—21no—
758Q8—61no—
759Q8—61no—
760Q8—181no—
761Q8—181no—
762Q8—362no—
763D4—32no—
764D4—61no—
765D4—61no—
766D4—61no—
767D4—92no—
768D4—122no—
769D4—184no—
770D4—181no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—31no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—31no—
777C2×C4—31no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—91no—
781C2×C4—91no—
782C2×C4—122no—
783C2×C4—181no—
784C2×C4—241no—
785C2×C4—362no—
786C2×C4—721no—
787C2×C4—721no—
788C2×C4—721no—
789C2×C4C22×D3211yescharacteristic
790C8—21no—
791C8—61no—
792C8—61no—
793C8—181no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—62no—
798C2×C3—122no—
799C2×C3—241no—
800C2×C3C2×#88411yescharacteristic
801C2×C3D3×#12111yescharacteristic
802C2×C3#576211yescharacteristic
803C2×C3#577011yescharacteristic
804C2×C3#577011yescharacteristic
805C2×C3#577811yescharacteristic
806D3—22no—
807D3—42no—
808D3—81no—
809D3—122no—
810D3—122no—
811D3—242no—
812C22—32no—
813C22—61no—
814C22—61no—
815C22—62no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—182no—
822C22—361no—
823C22—361no—
824C22—724no—
825C22D32×D411yescharacteristic
826C4—32no—
827C4—41no—
828C4—41no—
829C4—61no—
830C4—61no—
831C4—121no—
832C4—121no—
833C4—181no—
834C4—181no—
835C4—361no—
836C4D3×#23511yescharacteristic
837C4D32×D411yescharacteristic
838C3—21no—
839C3#7886311yescharacteristic, complemented
840C3#8043011yescharacteristic, complemented
841C2—62no—
842C2—122no—
843C2—241no—
844C2—362no—
845C2D3×#88411yescharacteristic
846C2#1059475311yescharacteristic
847C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#63939C2
hypercenter#103D32
hypocenterC32#3042
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. #10595356C2semidirect
3. C2×D3×#204C2semidirect
4. #10594604C2semidirect
5. #10592517C2semidirect
6. C3×#4818C2semidirect
7. C3×#4804C2semidirect
8. #10591569C2semidirect
9. #10591565C2semidirect
10. #10590860C2semidirect
11. #10590750C2semidirect
12. #10590694C2semidirect
13. #10590600C2semidirect
14. #10590540C2semidirect
15. #10590530C2semidirect
21. #64153C22semidirect
25. C3×#944C22semidirect
40. #63863C22semidirect
41. #63860C22semidirect
51. C32×#103C22semidirect
52. #63641C22semidirect
53. #63637C22semidirect
54. C3×#835C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63567C22semidirect
62. #63565C22semidirect
87. #4818D3semidirect
88. #4804D3semidirect
171. #944C2×D3semidirect
228. C3×#103C2×D3semidirect
229. C3×#103C2×D3semidirect
233. #835C2×D3semidirect
234. #821C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
248. #810C2×D3semidirect
249. #809C2×D3semidirect
510. #103D32semidirect
748. C32#3042semidirect
839. C3#78863semidirect
840. C3#80430semidirect

Maximal subgroups

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

subgroupindex
#105953562
C2×#639392
C2×D3×#2042
#105946042
#105925172
C3×#48182
C3×#48042
#105915692
#105915652
#105908602
#105907502
#105906942
#105906002
#105905402
#105905302
#804303
#788633