Finite Group Databasebeta

← #11864310

Subgroups — #11864310

Order 1152.

1649 conjugacy classes of subgroups.

The subgroup lattice has 1073 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3C2×D3×D24C211yesmaximal, characteristic, complemented
4#10594628C211yesmaximal, characteristic, complemented
5#10592509C211yesmaximal, characteristic, complemented
6C3×#4810C211yesmaximal, characteristic, complemented
7C3×#4804C211yesmaximal, characteristic, complemented
8#10591593C211yesmaximal, characteristic, complemented
9#10591588C211yesmaximal, characteristic, complemented
10#10590953C211yesmaximal, characteristic, complemented
11#10590947C211yesmaximal, characteristic, complemented
12#10590945C211yesmaximal, characteristic, complemented
13#10590598C211yesmaximal, characteristic, complemented
14#10590595C211yesmaximal, characteristic, complemented
15#10590592C211yesmaximal, characteristic, complemented
16#80085—31nomaximal
17#78834—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic, complemented
21#64320—24no—
22#64320—24no—
23C2×#3802—21no—
24C2×#3802C2211yescharacteristic, complemented
25C2×D3×D12—21no—
26C2×D3×D12—21no—
27C2×D3×D12C2211yescharacteristic
28C2×D3×D12C2211yescharacteristic, complemented
29C2×D3×D12C2211yescharacteristic, complemented
30C2×#3798—21no—
31C2×#3798C2211yescharacteristic
32C2×#3755C2211yescharacteristic, complemented
33C2×#3745C2211yescharacteristic, complemented
34#64104C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×D3×C8C2211yescharacteristic, complemented
38C3×#895C2211yescharacteristic, complemented
39C3×#892C2211yescharacteristic, complemented
40#63939—24no—
41#63923—21no—
42#63922—21no—
43#63916C2211yescharacteristic, complemented
44#63911—21no—
45#63909C2211yescharacteristic, complemented
46#63852—21no—
47C2×#3714C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52D3×D24—24no—
53C32×#103C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1009—31no—
67C2×#949—31no—
68C2×#914—31no—
69C2×D3×D8—31no—
70C22×D24—31no—
71#5607—31no—
72#5525—31no—
73C3×#449—31no—
74C3×#416—31no—
75#5238—31no—
76#5172—31no—
77#5156—31no—
78#5110—31no—
79#5036—31no—
80#5001—31no—
81#4810—31no—
82#4810—31no—
83#4810—31no—
84#4810—31no—
85#4810—61no—
86#4810D311yescharacteristic, complemented
87#4804D311yescharacteristic, complemented
88#4773—31no—
89#4773—31no—
90#4773—31no—
91#4773—31no—
92#4773—31no—
93#4770—31no—
94#4732—31no—
95#4727—31no—
96C22×D32—21no—
97C22×D32—21no—
98C22×D32—21no—
99C22×D32—21no—
100C2×C32×Q8C2311yescharacteristic
101#3832—22no—
102#3832—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4×C3⋊D3—21no—
108C2×C4×C3⋊D3C2311yescharacteristic
109C3×#239—22no—
110C3×#239—22no—
111C3×#239—22no—
112C3×#239D414yescomplemented
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×C4×D3C2311yescharacteristic
123C2×#627D411yescharacteristic
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#626D411yescharacteristic
130C2×#626D411yescharacteristic
131C2×#625—21no—
132C2×#625D411yescharacteristic
133#3802—28no—
134#3802—22no—
135#3802—22no—
136D3×D12—28no—
137D3×D12—28no—
138D3×D12—22no—
139D3×D12—22no—
140D3×D12—22no—
141D3×D12—22no—
142D3×D12—22no—
143D3×D12D414yescomplemented
144#3798—28no—
145#3798—22no—
146#3798—22no—
147C2×C32×C8C2311yescharacteristic
148C32×C4⋊C4C2311yescharacteristic
149#3755—22no—
150#3752—21no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152#3745—22no—
153C3×#215—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3C2311yescharacteristic
157C3×C4×Dic3—21no—
158C2×C3×C3⋊C8C2311yescharacteristic
159C2×C3×C3⋊C8C2311yescharacteristic
160C3×D24—22no—
161C3×D3×C8—22no—
162#3722—21no—
163(C2×D3)⋊Dic3—21no—
164#3714—22no—
165#3714—22no—
166#3714—22no—
167#3713—22no—
168#3711—22no—
169#3008—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172#1009—64no—
173#1009—64no—
174#1009—64no—
175#1009—64no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—61no—
179C2×#239C2×D311yescharacteristic
180C2×#239C2×D311yescharacteristic, complemented
181C2×D3×D4—31no—
182C2×D3×D4—31no—
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—61no—
193C2×#235—61no—
194C22×D12—31no—
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—61no—
198C22×D12—61no—
199C2×C3×SD16—31no—
200C2×C3×D8—31no—
201C22×C3×C8—31no—
202C3×#121—31no—
203C3×#117—31no—
204#949—64no—
205C2×#215—31no—
206C2×#215—31no—
207C2×#215—61no—
208C2×#215C2×D311yescharacteristic, complemented
209#940—61no—
210#938—31no—
211#937—61no—
212C2×#213—31no—
213C2×#213—31no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213—31no—
217#930—31no—
218C2×#208—31no—
219#914—64no—
220D3×D8—64no—
221C2×D24—31no—
222C2×D24—31no—
223C2×D24—31no—
224C2×D24—31no—
225C2×D24—31no—
226C2×D24—61no—
227C2×D24—64no—
228C2×D24C2×D311yescharacteristic, complemented
229C2×ΓL(1,𝔽25)—31no—
230C2×D3×C8C2×D311yescharacteristic, complemented
231#895—31no—
232#895—31no—
233#895—31no—
234#895—31no—
235#895—61no—
236#895C2×D311yescharacteristic, complemented
237#892C2×D311yescharacteristic, complemented
238#885—61no—
239#882—61no—
240#882—61no—
241#882—61no—
242#875—61no—
243#874—61no—
244C3×#103—21no—
245C3×#103—31no—
246C3×#103C2×D311yescharacteristic, complemented
247C3×#103C2×D311yescharacteristic, complemented
248C3×#102—31no—
249C3×#102—31no—
250C3×#102—31no—
251C3×C22⋊C8—31no—
252#835C2×D311yescharacteristic, complemented
253#832—31no—
254#830—31no—
255#821—31no—
256#821C2×D311yescharacteristic, complemented
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—61no—
263(C2×D3)⋊C8C2×D311yescharacteristic, complemented
264#809—31no—
265#809—31no—
266#809—31no—
267#809—31no—
268#809—61no—
269#809C2×D311yescharacteristic, complemented
270#809C2×D311yescharacteristic, complemented
271C22×C3⋊D3—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3C2×D411yescharacteristic
278C22×C3×D3C2×D411yescharacteristic
279C2×D32—24no—
280C2×D32—24no—
281C2×D32—24no—
282C2×D32—42no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C2×D32—81no—
287C2×D32—81no—
288C2×D32—81no—
289C2×D32—81no—
290C2×D32—81no—
291C32×Q8—21no—
292C32×Q8C2×D412yes—
293C2×C32×C4—21no—
294C2×C32×C4—21no—
295C2×C32×C4C2411yescharacteristic
296C2×C3⋊Dic3C2×D411yescharacteristic
297C4⋊(C3⋊D3)—24no—
298C4⋊(C3⋊D3)—21no—
299C4⋊(C3⋊D3)—21no—
300C4⋊(C3⋊D3)—21no—
301C4⋊(C3⋊D3)—81no—
302C4⋊(C3⋊D3)C2×D412yes—
303C4×C3⋊D3—24no—
304C4×C3⋊D3—21no—
305C4×C3⋊D3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3C2×D411yescharacteristic
308C2×C3×Dic3C2×D411yescharacteristic
309C3×D12—24no—
310C3×D12—24no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12—81no—
316C3×D12C2×D412yes—
317C3×D12C2×D412yes—
318C3×C4×D3—24no—
319C3×C4×D3—21no—
320C3×C4×D3—21no—
321C3×C4×D3—24no—
322C3×C4×D3C2×D412yes—
323C3×C4×D3C2×D412yes—
324#627—22no—
325#626—24no—
326#626—22no—
327#626—22no—
328#626—24no—
329#626—42no—
330#626—81no—
331#626—81no—
332#625—24no—
333#625—22no—
334C32×C8—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C2×H(5,𝔽2)—91no—
339C2×AGL(1,ℤ/8)—91no—
340C22×D8—91no—
341#535—91no—
342#449—31no—
343#449—91no—
344#449—91no—
345#449—91no—
346#447—91no—
347#447—91no—
348#447—91no—
349#447—91no—
350#418—91no—
351#416—31no—
352#408—91no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3—61no—
359C23×D3—61no—
360C23×D3—61no—
361C3×#41—34no—
362C3×#41—62no—
363C3×#41—62no—
364C3×#41—62no—
365C2×C3×Q8—21no—
366C2×C3×Q8C22×D311yescharacteristic
367C2×C3×Q8C22×D311yescharacteristic
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—61no—
377C22×C3×C4—61no—
378C2×#67—31no—
379C2×#67—31no—
380C2×#67—31no—
381C2×#67—31no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389#239—22no—
390#239—22no—
391#239—22no—
392#239—62no—
393#239—62no—
394#239—62no—
395#239—62no—
396#239—122no—
397#239—122no—
398#239D1214yescomplemented
399D3×D4—34no—
400D3×D4—62no—
401D3×D4—62no—
402D3×D4—68no—
403D3×D4—68no—
404D3×D4—62no—
405D3×D4—62no—
406D3×D4—68no—
407D3×D4—68no—
408D3×D4—62no—
409D3×D4—62no—
410D3×D4—62no—
411D3×D4—62no—
412D3×D4—62no—
413#235—62no—
414#235—62no—
415#235—68no—
416#235—68no—
417#235—62no—
418#235—62no—
419C2×D12—21no—
420C2×D12—21no—
421C2×D12—21no—
422C2×D12—31no—
423C2×D12—31no—
424C2×D12—34no—
425C2×D12—31no—
426C2×D12—31no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—61no—
430C2×D12—61no—
431C2×D12—62no—
432C2×D12—62no—
433C2×D12—68no—
434C2×D12—68no—
435C2×D12—62no—
436C2×D12—62no—
437C2×D12—61no—
438C2×D12—61no—
439C2×D12—61no—
440C2×D12—61no—
441C2×D12—62no—
442C2×D12—61no—
443C2×D12—61no—
444C2×D12—61no—
445C2×D12—61no—
446C2×D12—61no—
447C2×D12—121no—
448C2×D12—121no—
449C2×D12C22×D311yescharacteristic
450C2×D12C22×D311yescharacteristic
451C2×D12C22×D311yescharacteristic
452C2×C4×D3—21no—
453C2×C4×D3—21no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—61no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3—121no—
460C2×C4×D3C22×D311yescharacteristic
461C2×C4×D3C22×D311yescharacteristic
462C2×Dic6—31no—
463C2×Dic6—31no—
464C3×SD16—62no—
465C3×D8—62no—
466C2×C3×C8—21no—
467C2×C3×C8—31no—
468C2×C3×C8—31no—
469C2×C3×C8—62no—
470C2×C3×C8C22×D311yescharacteristic
471C2×C3×C8C22×D311yescharacteristic
472C3×C4⋊C4—21no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4C22×D311yescharacteristic
475C3×C4⋊C4C22×D311yescharacteristic
476C3×C22⋊C4—61no—
477C3×C22⋊C4—61no—
478C3×C42—61no—
479#217—61no—
480#215—22no—
481#215—62no—
482#215—62no—
483#215—122no—
484#213—62no—
485#213—62no—
486#213—62no—
487#213—62no—
488#213—62no—
489(C2×D3)⋊C4—21no—
490(C2×D3)⋊C4—21no—
491(C2×D3)⋊C4—61no—
492(C2×D3)⋊C4—61no—
493(C2×D3)⋊C4—61no—
494(C2×D3)⋊C4—61no—
495(C2×D3)⋊C4—61no—
496(C2×D3)⋊C4—121no—
497C4⋊Dic3C22×D311yescharacteristic
498C4×Dic3—21no—
499#208—62no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—61no—
503C2×C3⋊C8C22×D311yescharacteristic
504C2×C3⋊C8C22×D311yescharacteristic
505D24—22no—
506D24—62no—
507D24—62no—
508D24—62no—
509D24—62no—
510D24—62no—
511D24—122no—
512ΓL(1,𝔽25)—62no—
513D3×C8—22no—
514C22×C32C22×D411yescharacteristic
515C2×C3⋊D3—21no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—21no—
518C2×C3⋊D3—21no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3⋊D3—41no—
522C2×C3⋊D3—41no—
523C2×C3⋊D3—41no—
524C2×C3×D3—21no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3—21no—
530C2×C3×D3—21no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3—41no—
538C2×C3×D3#12012yes—
539D32—84no—
540D32—84no—
541D32—84no—
542D32—84no—
543C32×C4—22no—
544C32×C4—41no—
545C32×C4C22×D411yescharacteristic
546C32×C4C22×D411yescharacteristic
547C3⋊Dic3—21no—
548C3×Dic3—21no—
549C3×Dic3—41no—
550C3×Dic3#12012yes—
551H(5,𝔽2)—184no—
552H(5,𝔽2)—184no—
553C2×#41—31no—
554C2×#41—31no—
555C2×#41—91no—
556C2×#41—91no—
557C2×#41—181no—
558C22×D4—91no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4—91no—
562C22×D4—181no—
563C22×D4—181no—
564C22×D4—181no—
565AGL(1,ℤ/8)—184no—
566C2×SD16—31no—
567C2×SD16—91no—
568C2×D8—31no—
569C2×D8—91no—
570C2×D8—91no—
571C2×D8—91no—
572C2×D8—91no—
573C2×D8—91no—
574C2×D8—184no—
575C2×M16—91no—
576C22×C8—31no—
577#127—181no—
578#124—181no—
579#121—31no—
580#121—91no—
581#121—91no—
582#121—91no—
583#120—181no—
584#120—181no—
585#117—31no—
586#103—31no—
587#103D3211yescharacteristic, complemented
588#102—31no—
589#102—31no—
590#102—31no—
591#102—91no—
592#102—91no—
593#102—91no—
594C22⋊C8—31no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C22⋊C8—91no—
598C23×C3—31no—
599C23×C3—31no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—31no—
607C22×D3—31no—
608C22×D3—61no—
609C22×D3—64no—
610C22×D3—64no—
611C22×D3—64no—
612C22×D3—64no—
613C22×D3—64no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—64no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—121no—
620C22×D3—121no—
621C22×D3—122no—
622C22×D3—122no—
623C22×D3—241no—
624C22×D3—241no—
625C22×D3—241no—
626C22×D3—241no—
627C22×D3—241no—
628C22×D3—241no—
629C22×D3—241no—
630C22×D3—241no—
631C22×D3—241no—
632C22×D3—241no—
633C22×D3—241no—
634C22×D3—241no—
635C22×D3—241no—
636C22×D3—241no—
637C22×D3—241no—
638C22×D3—241no—
639C22×D3D3×D411yescharacteristic
640C22×D3D3×D411yescharacteristic
641C3×Q8—21no—
642C3×Q8—21no—
643C3×Q8—22no—
644C3×Q8—41no—
645C3×Q8C2×D1212yes—
646C3×Q8D3×D412yes—
647C3×D4—32no—
648C3×D4—32no—
649C3×D4—64no—
650C3×D4—64no—
651C3×D4—61no—
652C3×D4—61no—
653C3×D4—61no—
654C3×D4—61no—
655C3×D4—241no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—31no—
662C2×C3×C4—32no—
663C2×C3×C4—32no—
664C2×C3×C4—31no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—64no—
668C2×C3×C4—64no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4C23×D311yescharacteristic
673C2×C3×C4C23×D311yescharacteristic
674#67—62no—
675#67—64no—
676#67—62no—
677#67—64no—
678#67—64no—
679#67—62no—
680#67—64no—
681#67—62no—
682#67—122no—
683#67—241no—
684#67—241no—
685C2×Dic3—21no—
686C2×Dic3—31no—
687C2×Dic3—31no—
688C2×Dic3—61no—
689C2×Dic3D3×D411yescharacteristic
690C2×Dic3D3×D411yescharacteristic
691D12—24no—
692D12—24no—
693D12—21no—
694D12—21no—
695D12—21no—
696D12—21no—
697D12—32no—
698D12—32no—
699D12—62no—
700D12—64no—
701D12—64no—
702D12—62no—
703D12—64no—
704D12—64no—
705D12—62no—
706D12—61no—
707D12—61no—
708D12—61no—
709D12—61no—
710D12—61no—
711D12—61no—
712D12—81no—
713D12—121no—
714D12—121no—
715D12—121no—
716D12—124no—
717D12—122no—
718D12—241no—
719D12—241no—
720D12—242no—
721D12—241no—
722D12—241no—
723D12C2×D1212yes—
724D12D3×D412yes—
725C4×D3—24no—
726C4×D3—21no—
727C4×D3—21no—
728C4×D3—24no—
729C4×D3—64no—
730C4×D3—64no—
731C4×D3—61no—
732C4×D3—61no—
733C4×D3—61no—
734C4×D3—61no—
735C4×D3—121no—
736C4×D3—121no—
737C4×D3—124no—
738C4×D3C2×D1212yes—
739C4×D3D3×D412yes—
740Dic6—62no—
741Dic6—62no—
742C3×C8—21no—
743C3×C8—21no—
744C3×C8—41no—
745C3×C8—61no—
746C3×C8—61no—
747C3⋊C8—21no—
748C3⋊C8—21no—
749C3⋊C8—61no—
750C3⋊C8—61no—
751C3⋊C8—121no—
752C2×C32C2×#12011yescharacteristic
753C2×C32#57611yescharacteristic
754C2×C32#57611yescharacteristic
755C3⋊D3—41no—
756C3⋊D3—42no—
757C3⋊D3—81no—
758C3×D3—22no—
759C3×D3—41no—
760C3×D3—42no—
761C3×D3—42no—
762C3×D3—81no—
763C24—181no—
764C24—181no—
765C24—181no—
766C24—181no—
767#41—34no—
768#41—62no—
769#41—62no—
770#41—62no—
771#41—182no—
772#41—182no—
773#41—188no—
774#41—182no—
775#41—182no—
776C2×Q8—91no—
777C2×Q8C2×D3211yescharacteristic
778C2×D4—31no—
779C2×D4—31no—
780C2×D4—31no—
781C2×D4—61no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—94no—
785C2×D4—91no—
786C2×D4—91no—
787C2×D4—91no—
788C2×D4—91no—
789C2×D4—91no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4—182no—
793C2×D4—182no—
794C2×D4—182no—
795C2×D4—181no—
796C2×D4—181no—
797C2×D4—181no—
798C2×D4—182no—
799C2×D4—182no—
800C2×D4—188no—
801C2×D4—188no—
802C2×D4—181no—
803C2×D4—181no—
804C2×D4—181no—
805C2×D4—182no—
806C2×D4—182no—
807C2×D4—188no—
808C22×C4—31no—
809C22×C4—31no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—91no—
813C22×C4—181no—
814SD16—62no—
815SD16—182no—
816D8—62no—
817D8—182no—
818D8—182no—
819D8—182no—
820D8—182no—
821D8—182no—
822M16—182no—
823C2×C8—31no—
824C2×C8—31no—
825C2×C8—62no—
826C2×C8—91no—
827C2×C8C2×D3211yescharacteristic
828C4⋊C4—31no—
829C4⋊C4C2×D3211yescharacteristic
830C22⋊C4—61no—
831C22⋊C4—61no—
832C22⋊C4—181no—
833C22⋊C4—181no—
834C22⋊C4—181no—
835C42—61no—
836C22×C3—21no—
837C22×C3—32no—
838C22×C3—61no—
839C22×C3—61no—
840C22×C3—62no—
841C22×C3—61no—
842C22×C3—61no—
843C22×C3—61no—
844C22×C3—62no—
845C22×C3—121no—
846C22×C3—121no—
847C22×C3—121no—
848C22×C3—121no—
849C22×C3—121no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3C2×D3×D411yescharacteristic
853C22×C3C2×D3×D411yescharacteristic
854C2×D3—21no—
855C2×D3—21no—
856C2×D3—22no—
857C2×D3—21no—
858C2×D3—21no—
859C2×D3—21no—
860C2×D3—22no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—41no—
864C2×D3—41no—
865C2×D3—41no—
866C2×D3—41no—
867C2×D3—41no—
868C2×D3—62no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3—61no—
873C2×D3—61no—
874C2×D3—62no—
875C2×D3—61no—
876C2×D3—122no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—241no—
891C2×D3—241no—
892C2×D3—241no—
893C2×D3—241no—
894C2×D3—241no—
895C2×D3—244no—
896C2×D3—244no—
897C2×D3—244no—
898C2×D3—244no—
899C2×D3—244no—
900C2×D3—244no—
901C2×D3—244no—
902C2×D3—244no—
903C2×D3#88212yes—
904C3×C4—22no—
905C3×C4—22no—
906C3×C4—21no—
907C3×C4—21no—
908C3×C4—32no—
909C3×C4—42no—
910C3×C4—41no—
911C3×C4—41no—
912C3×C4—61no—
913C3×C4—81no—
914C3×C4—121no—
915C3×C4C22×D1211yescharacteristic
916C3×C4C2×D3×D411yescharacteristic
917C3×C4C2×D3×D411yescharacteristic
918C3×C4C2×D3×D411yescharacteristic
919Dic3—21no—
920Dic3—41no—
921Dic3—61no—
922Dic3—61no—
923Dic3—121no—
924Dic3#88212yes—
925C32#300811yescharacteristic, complemented, Sylow
926C23—31no—
927C23—31no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—91no—
932C23—184no—
933C23—184no—
934C23—184no—
935C23—181no—
936C23—181no—
937C23—362no—
938C23—721no—
939C23—721no—
940C23—721no—
941C23—721no—
942C23—721no—
943C23—721no—
944C23—721no—
945C23—721no—
946Q8—21no—
947Q8—182no—
948Q8D3×D1212yes—
949D4—32no—
950D4—32no—
951D4—64no—
952D4—64no—
953D4—61no—
954D4—61no—
955D4—61no—
956D4—61no—
957D4—92no—
958D4—184no—
959D4—184no—
960D4—182no—
961D4—182no—
962D4—184no—
963D4—182no—
964D4—184no—
965D4—181no—
966D4—181no—
967D4—181no—
968D4—241no—
969D4—362no—
970D4—721no—
971D4—721no—
972D4—721no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—31no—
976C2×C4—32no—
977C2×C4—32no—
978C2×C4—31no—
979C2×C4—64no—
980C2×C4—64no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—91no—
985C2×C4—184no—
986C2×C4—181no—
987C2×C4—181no—
988C2×C4C22×D3211yescharacteristic
989C8—21no—
990C8—61no—
991C8—61no—
992C8—181no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—62no—
997C2×C3—122no—
998C2×C3—121no—
999C2×C3—122no—
1000C2×C3—241no—
1001C2×C3C2×#88211yescharacteristic
1002C2×C3D3×#12011yescharacteristic
1003C2×C3#576911yescharacteristic
1004C2×C3#576911yescharacteristic
1005C2×C3#576911yescharacteristic
1006C2×C3#577411yescharacteristic
1007D3—22no—
1008D3—41no—
1009D3—42no—
1010D3—42no—
1011D3—81no—
1012D3—121no—
1013D3—122no—
1014D3—121no—
1015D3—122no—
1016D3—241no—
1017D3—242no—
1018D3—241no—
1019D3—241no—
1020D3—481no—
1021C22—32no—
1022C22—61no—
1023C22—61no—
1024C22—61no—
1025C22—62no—
1026C22—62no—
1027C22—61no—
1028C22—61no—
1029C22—121no—
1030C22—121no—
1031C22—121no—
1032C22—121no—
1033C22—121no—
1034C22—121no—
1035C22—121no—
1036C22—181no—
1037C22—182no—
1038C22—181no—
1039C22—181no—
1040C22—361no—
1041C22—361no—
1042C22—361no—
1043C22—361no—
1044C22—361no—
1045C22—724no—
1046C22—724no—
1047C22—724no—
1048C22—724no—
1049C22D32×D411yescharacteristic
1050C4—22no—
1051C4—32no—
1052C4—41no—
1053C4—61no—
1054C4—121no—
1055C4—181no—
1056C4C2×D3×D1211yescharacteristic
1057C4D32×D411yescharacteristic
1058C3—21no—
1059C3#7883411yescharacteristic, complemented
1060C3#8008511yescharacteristic, complemented
1061C2—62no—
1062C2—121no—
1063C2—122no—
1064C2—122no—
1065C2—241no—
1066C2—361no—
1067C2—362no—
1068C2—721no—
1069C2D3×#88211yescharacteristic
1070C2#1059475511yescharacteristic
1071C2#1059477111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3008
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. C2×#64320C2semidirect
2. C2×#63939C2semidirect
3. C2×D3×D24C2semidirect
4. #10594628C2semidirect
5. #10592509C2semidirect
6. C3×#4810C2semidirect
7. C3×#4804C2semidirect
8. #10591593C2semidirect
9. #10591588C2semidirect
10. #10590953C2semidirect
11. #10590947C2semidirect
12. #10590945C2semidirect
13. #10590598C2semidirect
14. #10590595C2semidirect
15. #10590592C2semidirect
18. C2×#3832C22semidirect
20. C2×C3×#239C22semidirect
24. C2×#3802C22semidirect
28. C2×D3×D12C22semidirect
29. C2×D3×D12C22semidirect
32. C2×#3755C22semidirect
33. C2×#3745C22semidirect
34. #64104C22semidirect
35. C2×C3×#215C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×D3×C8C22semidirect
38. C3×#895C22semidirect
39. C3×#892C22semidirect
43. #63916C22semidirect
45. #63909C22semidirect
47. C2×#3714C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
53. C32×#103C22semidirect
54. #63647C22semidirect
55. #63636C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#809C22semidirect
60. C3×#809C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
86. #4810D3semidirect
87. #4804D3semidirect
112. C3×#239D4semidirect
143. D3×D12D4semidirect
180. C2×#239C2×D3semidirect
208. C2×#215C2×D3semidirect
228. C2×D24C2×D3semidirect
230. C2×D3×C8C2×D3semidirect
236. #895C2×D3semidirect
237. #892C2×D3semidirect
246. C3×#103C2×D3semidirect
247. C3×#103C2×D3semidirect
252. #835C2×D3semidirect
256. #821C2×D3semidirect
263. (C2×D3)⋊C8C2×D3semidirect
269. #809C2×D3semidirect
270. #809C2×D3semidirect
398. #239D12semidirect
587. #103D32semidirect
925. C32#3008semidirect
1059. C3#78834semidirect
1060. C3#80085semidirect

Maximal subgroups

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

subgroupindex
C2×#643202
C2×#639392
C2×D3×D242
#105946282
#105925092
C3×#48102
C3×#48042
#105915932
#105915882
#105909532
#105909472
#105909452
#105905982
#105905952
#105905922
#800853
#788343