Finite Group Databasebeta

← #11864638

Subgroups — #11864638

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 1045 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64313C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic, complemented
3C2×#63806C211yesmaximal, characteristic, complemented
4#10594523C211yesmaximal, characteristic, complemented
5#10592480C211yesmaximal, characteristic, complemented
6C3×#4776C211yesmaximal, characteristic, complemented
7C3×D3×#102C211yesmaximal, characteristic, complemented
8#10591466C211yesmaximal, characteristic, complemented
9#10591448C211yesmaximal, characteristic, complemented
10#10590968C211yesmaximal, characteristic, complemented
11#10590953C211yesmaximal, characteristic, complemented
12#10590943C211yesmaximal, characteristic, complemented
13#10590614C211yesmaximal, characteristic, complemented
14#10590607C211yesmaximal, characteristic, complemented
15#10590598C211yesmaximal, characteristic, complemented
16#80149—31nomaximal
17#78747—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×#67—21no—
22C2×D3×#67—21no—
23C22×#625—21no—
24C2×#3805—21no—
25#64313—24no—
26#64313—24no—
27C2×#3802C2211yescharacteristic
28C2×#3799C2211yescharacteristic, complemented
29C2×#3798C2211yescharacteristic
30C2×#3795C2211yescharacteristic
31C2×#3795C2211yescharacteristic
32C2×#3753C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34#64104C2211yescharacteristic, complemented
35C2×C3×#214C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×D3×C8C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×D3×C4⋊C4C2211yescharacteristic, complemented
40#63934—24no—
41#63910—21no—
42#63909—21no—
43#63909C2211yescharacteristic, complemented
44#63906—21no—
45#63895—21no—
46#63871C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63806—24no—
53C32×#102C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1004—31no—
66C2×#1004—31no—
67C2×#932—31no—
68C2×#916—31no—
69C2×#914—31no—
70C2×#904—31no—
71#5629—31no—
72#5510—31no—
73C3×#450—31no—
74C2×C3×#102—31no—
75#5217—31no—
76#5173—31no—
77#5169—31no—
78#5110—31no—
79#5047—31no—
80#4966—31no—
81#4783—31no—
82#4783—31no—
83#4781—31no—
84#4781—31no—
85#4781—31no—
86#4781—61no—
87#4776—31no—
88#4776D311yescharacteristic, complemented
89#4773—31no—
90#4773—31no—
91#4773—31no—
92#4771—31no—
93D3×#102D311yescharacteristic, complemented
94#4734—31no—
95#4727—31no—
96C23×C3×D3—21no—
97C23×C3×D3—21no—
98C22×D32—21no—
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101C22×C3⋊Dic3—21no—
102#3830—22no—
103#3830—22no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C3×D3×D4—22no—
111C3×D3×D4—22no—
112C3×D3×D4—22no—
113C3×D3×D4D414yescomplemented
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120D3×#67—28no—
121D3×#67—28no—
122C2×#627D411yescharacteristic
123C2×#626—21no—
124C2×#626—21no—
125C2×#626D411yescharacteristic
126C2×#626D411yescharacteristic
127C2×#625—28no—
128C2×#625—21no—
129C2×#625—21no—
130C2×#625—21no—
131C2×#625D411yescharacteristic
132C2×#624—21no—
133#3805—28no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3—21no—
136#3802—22no—
137#3802—22no—
138#3799—22no—
139#3799—22no—
140#3798—22no—
141#3798—22no—
142#3795—22no—
143#3795—22no—
144#3795—22no—
145#3795D414yescomplemented
146C2×C32×C8C2311yescharacteristic
147C32×C4⋊C4C2311yescharacteristic
148#3753—22no—
149#3752—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151#3744—22no—
152C3×#214—22no—
153C3×(C2×D3)⋊C4—21no—
154C3×C4⋊Dic3—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×Dic3⋊C4—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×#204—22no—
160C3×D3×C8—22no—
161Dic3⋊Dic3—21no—
162#3722—21no—
163#3722—21no—
164#3719—22no—
165#3715—22no—
166#3714—22no—
167#3714—22no—
168#3711—22no—
169#3012—91noSylow
170C22×C3×D4—31no—
171C22×C3×D4—31no—
172C22×#67—61no—
173C22×#67—61no—
174C22×#67—61no—
175C22×#67—61no—
176C2×#239—31no—
177#1004—64no—
178#1004—64no—
179#1004—64no—
180#1004—64no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—31no—
185C2×#237—61no—
186C2×#237—61no—
187C2×#237—61no—
188C2×D3×D4—31no—
189C2×D3×D4—31no—
190C2×D3×D4—61no—
191C2×D3×D4—61no—
192C2×D3×D4C2×D311yescharacteristic
193C2×D3×D4C2×D311yescharacteristic
194C2×#235—31no—
195C2×#235—31no—
196C2×#235—31no—
197C2×#235—31no—
198C2×#235—31no—
199C2×C3×SD16—31no—
200C2×C3×SD16—31no—
201C22×C3×C8—31no—
202C3×C22⋊Q8—31no—
203C2×C3×C4⋊C4—31no—
204#946—31no—
205C2×#216—31no—
206C2×#215—31no—
207C2×#214—31no—
208C2×#214C2×D311yescharacteristic, complemented
209#932—64no—
210C2×#213—31no—
211C2×#213—31no—
212C2×#213—31no—
213C2×#213—31no—
214C2×#213—61no—
215#930—31no—
216#930—61no—
217#930—61no—
218C2×#208—31no—
219#916—64no—
220#914—64no—
221C2×Dic12—31no—
222#904—64no—
223C2×D24—31no—
224C2×D24—31no—
225C2×#204—31no—
226C2×#204—31no—
227C2×#204—61no—
228C2×#204C2×D311yescharacteristic, complemented
229C2×ΓL(1,𝔽25)—31no—
230C2×D3×C8C2×D311yescharacteristic, complemented
231#897—31no—
232#897—61no—
233#897C2×D311yescharacteristic, complemented
234#896—61no—
235#895—31no—
236#895—31no—
237#895—31no—
238#895—61no—
239#895—61no—
240#895—61no—
241D3×C4⋊C4C2×D311yescharacteristic, complemented
242#884—61no—
243#884—61no—
244C3×#102—21no—
245C3×#102—31no—
246C3×#102—31no—
247C3×#102—31no—
248C3×#102—31no—
249C3×#102C2×D311yescharacteristic, complemented
250C3×#102C2×D311yescharacteristic, complemented
251C3×C22⋊C8—31no—
252#832—31no—
253#832C2×D311yescharacteristic, complemented
254#830—31no—
255#821C2×D311yescharacteristic, complemented
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—61no—
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816—31no—
264#810—31no—
265#810—31no—
266#810—31no—
267#810—61no—
268#809—31no—
269#809C2×D311yescharacteristic, complemented
270#809C2×D311yescharacteristic, complemented
271C23×C32—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—24no—
277C22×C3×D3—24no—
278C22×C3×D3—81no—
279C22×C3×D3—81no—
280C22×C3×D3—81no—
281C22×C3×D3—81no—
282C22×C3×D3C2×D411yescharacteristic
283C22×C3×D3C2×D411yescharacteristic
284C2×D32—24no—
285C2×D32—81no—
286C2×D32—81no—
287C32×D4—21no—
288C32×D4C2×D412yes—
289C2×C32×C4—21no—
290C2×C32×C4C2411yescharacteristic
291#638—24no—
292C2×C3⋊Dic3—24no—
293C2×C3⋊Dic3—21no—
294C2×C3⋊Dic3C2×D411yescharacteristic
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—81no—
298C4×C3⋊D3—21no—
299C4×C3⋊D3—21no—
300#634—21no—
301#634C2×D412yes—
302C3×#67—24no—
303C3×#67—24no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D411yescharacteristic
307C2×C3×Dic3C2×D411yescharacteristic
308C3×D12—21no—
309C3×D12—21no—
310C3×D12C2×D412yes—
311C3×D12C2×D412yes—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3—81no—
315C3×C4×D3C2×D412yes—
316C3×C4×D3C2×D412yes—
317C3×Dic6—21no—
318C3×Dic6—21no—
319#627—22no—
320#626—22no—
321#626—22no—
322#626—42no—
323#626—81no—
324#625—24no—
325#625—24no—
326#625—24no—
327#625—22no—
328#624—42no—
329D3×Dic3—24no—
330D3×Dic3—24no—
331C32×C8—21no—
332C3⋊(C3⋊C8)—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—91no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—91no—
338#537—91no—
339#452—91no—
340#452—91no—
341#450—31no—
342#450—91no—
343#449—91no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—91no—
348C2×#102—31no—
349#408—91no—
350C24×C3—61no—
351C24×C3—61no—
352C23×D3—21no—
353C23×D3—21no—
354C23×D3—61no—
355C23×D3—61no—
356C2×C3×Q8—31no—
357C2×C3×D4—21no—
358C2×C3×D4—34no—
359C2×C3×D4—31no—
360C2×C3×D4—31no—
361C2×C3×D4—62no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C2×C3×D4—62no—
365C2×C3×D4—62no—
366C2×C3×D4C22×D311yescharacteristic
367C2×C3×D4C22×D311yescharacteristic
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—61no—
371C2×#67—21no—
372C2×#67—21no—
373C2×#67—31no—
374C2×#67—31no—
375C2×#67—31no—
376C2×#67—31no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—68no—
382C2×#67—68no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—68no—
386C2×#67—68no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—121no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394C22×Dic3—61no—
395C22×Dic3—61no—
396C22×Dic3—121no—
397#239—62no—
398#239—62no—
399#237—34no—
400#237—62no—
401#237—62no—
402#237—62no—
403#237—62no—
404#237—68no—
405#237—68no—
406#237—62no—
407#237—62no—
408#237—62no—
409#237—122no—
410#237—122no—
411D3×D4—22no—
412D3×D4—22no—
413D3×D4—22no—
414D3×D4—62no—
415D3×D4—62no—
416D3×D4—68no—
417D3×D4—68no—
418D3×D4—62no—
419D3×D4—62no—
420D3×D4D1214yescomplemented
421#235—34no—
422#235—62no—
423#235—62no—
424#235—62no—
425#235—62no—
426#235—62no—
427#235—62no—
428#235—62no—
429#235—62no—
430#235—62no—
431C2×D12—31no—
432C2×D12—31no—
433C2×D12—31no—
434C2×D12—31no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—61no—
439C2×D12—61no—
440C2×D12—121no—
441C2×D12C22×D311yescharacteristic
442C2×D12C22×D311yescharacteristic
443C2×C4×D3—21no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—61no—
447C2×C4×D3—61no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3C22×D311yescharacteristic
452C2×C4×D3C22×D311yescharacteristic
453C2×Dic6—31no—
454C2×Dic6—31no—
455C2×Dic6—31no—
456C2×Dic6—31no—
457C2×Dic6—61no—
458C2×Dic6C22×D311yescharacteristic
459C3×SD16—62no—
460C3×SD16—62no—
461C2×C3×C8—21no—
462C2×C3×C8—31no—
463C2×C3×C8—31no—
464C2×C3×C8—62no—
465C2×C3×C8C22×D311yescharacteristic
466C2×C3×C8C22×D311yescharacteristic
467C3×C4⋊C4—21no—
468C3×C4⋊C4—31no—
469C3×C4⋊C4—61no—
470C3×C4⋊C4—61no—
471C3×C4⋊C4C22×D311yescharacteristic
472C3×C4⋊C4C22×D311yescharacteristic
473C3×C22⋊C4—61no—
474#216—62no—
475#215—62no—
476#214—22no—
477#214—62no—
478#213—62no—
479#213—62no—
480#213—62no—
481#213—62no—
482#213—122no—
483(C2×D3)⋊C4—21no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—61no—
488(C2×D3)⋊C4—61no—
489(C2×D3)⋊C4—61no—
490(C2×D3)⋊C4—121no—
491C4⋊Dic3—21no—
492C4⋊Dic3—61no—
493C4⋊Dic3C22×D311yescharacteristic
494Dic3⋊C4—21no—
495Dic3⋊C4—61no—
496#208—62no—
497C2×C3⋊C8—31no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—61no—
500C2×C3⋊C8C22×D311yescharacteristic
501C2×C3⋊C8C22×D311yescharacteristic
502Dic12—62no—
503D24—62no—
504D24—62no—
505#204—22no—
506#204—62no—
507#204—62no—
508#204—122no—
509ΓL(1,𝔽25)—62no—
510D3×C8—22no—
511C22×C32—22no—
512C22×C32—41no—
513C22×C32—41no—
514C22×C32C22×D411yescharacteristic
515C2×C3⋊D3—21no—
516C2×C3⋊D3—21no—
517C2×C3⋊D3—21no—
518C2×C3⋊D3—41no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—84no—
533C2×C3×D3—84no—
534C2×C3×D3#12012yes—
535D32—84no—
536C32×C4—41no—
537C32×C4C22×D411yescharacteristic
538C32×C4C22×D411yescharacteristic
539C3⋊Dic3—22no—
540C3⋊Dic3—21no—
541C3×Dic3—21no—
542C3×Dic3—41no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—184no—
546H(5,𝔽2)—184no—
547C2×#41—91no—
548C2×#41—91no—
549C2×#41—91no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—181no—
553C22×D4—31no—
554C22×D4—31no—
555C22×D4—91no—
556C22×D4—181no—
557C22×D4—181no—
558C22×D4—181no—
559AGL(1,ℤ/8)—184no—
560#135—184no—
561C2×Q16—91no—
562C2×SD16—31no—
563C2×SD16—31no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—91no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—91no—
570C22×C8—31no—
571C22⋊Q8—31no—
572C22⋊Q8—91no—
573C22⋊Q8—181no—
574#121—91no—
575#121—91no—
576#121—181no—
577#121—181no—
578#121—181no—
579C2×C4⋊C4—31no—
580#103—91no—
581#103—91no—
582#102—31no—
583#102—31no—
584#102—31no—
585#102—31no—
586#102—91no—
587#102D3211yescharacteristic, complemented
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—31no—
595C23×C3—31no—
596C23×C3—41no—
597C23×C3—64no—
598C23×C3—64no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—241no—
602C23×C3—241no—
603C23×C3—241no—
604C23×C3—241no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—24no—
608C22×D3—24no—
609C22×D3—31no—
610C22×D3—31no—
611C22×D3—61no—
612C22×D3—64no—
613C22×D3—64no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—81no—
617C22×D3—81no—
618C22×D3—81no—
619C22×D3—81no—
620C22×D3—121no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3—241no—
625C22×D3D3×D411yescharacteristic
626C22×D3D3×D411yescharacteristic
627C3×Q8—61no—
628C3×Q8—61no—
629C3×D4—21no—
630C3×D4—21no—
631C3×D4—22no—
632C3×D4—32no—
633C3×D4—32no—
634C3×D4—41no—
635C3×D4—64no—
636C3×D4—64no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4C2×D1212yes—
640C3×D4D3×D412yes—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—31no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—31no—
648C2×C3×C4—41no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—241no—
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656#67—24no—
657#67—24no—
658#67—62no—
659#67—64no—
660#67—62no—
661#67—64no—
662#67—64no—
663#67—64no—
664#67—64no—
665#67—64no—
666#67—64no—
667#67—62no—
668#67—64no—
669#67—62no—
670#67—124no—
671#67—122no—
672#67—241no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—61no—
678C2×Dic3—64no—
679C2×Dic3—64no—
680C2×Dic3—64no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—64no—
684C2×Dic3—121no—
685C2×Dic3—124no—
686C2×Dic3D3×D411yescharacteristic
687C2×Dic3D3×D411yescharacteristic
688D12—21no—
689D12—21no—
690D12—62no—
691D12—62no—
692D12—61no—
693D12—61no—
694D12—61no—
695D12—61no—
696D12—121no—
697D12—121no—
698D12—122no—
699D12—241no—
700D12—241no—
701D12—242no—
702D12—241no—
703D12C2×D1212yes—
704D12D3×D412yes—
705C4×D3—21no—
706C4×D3—21no—
707C4×D3—64no—
708C4×D3—64no—
709C4×D3—61no—
710C4×D3—61no—
711C4×D3—61no—
712C4×D3—61no—
713C4×D3—81no—
714C4×D3—121no—
715C4×D3—121no—
716C4×D3—122no—
717C4×D3—122no—
718C4×D3C2×D1212yes—
719C4×D3D3×D412yes—
720Dic6—21no—
721Dic6—21no—
722Dic6—32no—
723Dic6—32no—
724Dic6—62no—
725Dic6—62no—
726Dic6—61no—
727Dic6—61no—
728Dic6—62no—
729Dic6—121no—
730C3×C8—21no—
731C3×C8—21no—
732C3×C8—41no—
733C3×C8—61no—
734C3×C8—61no—
735C3⋊C8—21no—
736C3⋊C8—21no—
737C3⋊C8—61no—
738C3⋊C8—61no—
739C3⋊C8—121no—
740C2×C32—42no—
741C2×C32C2×#12011yescharacteristic
742C2×C32#57611yescharacteristic
743C2×C32#57711yescharacteristic
744C3⋊D3—41no—
745C3⋊D3—81no—
746C3×D3—22no—
747C3×D3—42no—
748C3×D3—42no—
749C3×D3—41no—
750C24—61no—
751C24—61no—
752C24—181no—
753#41—94no—
754#41—182no—
755#41—182no—
756#41—182no—
757#41—182no—
758#41—182no—
759#41—182no—
760#41—182no—
761#41—182no—
762#41—188no—
763#41—182no—
764C2×Q8—31no—
765C2×Q8—91no—
766C2×Q8—91no—
767C2×D4—34no—
768C2×D4—31no—
769C2×D4—31no—
770C2×D4—62no—
771C2×D4—61no—
772C2×D4—61no—
773C2×D4—62no—
774C2×D4—62no—
775C2×D4—91no—
776C2×D4—91no—
777C2×D4—91no—
778C2×D4—91no—
779C2×D4—181no—
780C2×D4—181no—
781C2×D4—181no—
782C2×D4—181no—
783C2×D4—182no—
784C2×D4—182no—
785C2×D4—188no—
786C2×D4—188no—
787C2×D4—181no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—188no—
791C2×D4C2×D3211yescharacteristic
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—61no—
795C22×C4—91no—
796C22×C4—181no—
797C22×C4—181no—
798C22×C4—181no—
799C22×C4—181no—
800Q16—182no—
801SD16—62no—
802SD16—62no—
803SD16—182no—
804SD16—182no—
805D8—182no—
806D8—182no—
807D8—182no—
808M16—182no—
809C2×C8—31no—
810C2×C8—31no—
811C2×C8—62no—
812C2×C8—91no—
813C2×C8C2×D3211yescharacteristic
814C4⋊C4—31no—
815C4⋊C4—61no—
816C4⋊C4—61no—
817C4⋊C4—181no—
818C4⋊C4C2×D3211yescharacteristic
819C22⋊C4—61no—
820C22⋊C4—181no—
821C22⋊C4—181no—
822C22⋊C4—181no—
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—21no—
826C22×C3—32no—
827C22×C3—42no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—61no—
833C22×C3—61no—
834C22×C3—62no—
835C22×C3—61no—
836C22×C3—61no—
837C22×C3—61no—
838C22×C3—62no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—244no—
846C22×C3—244no—
847C22×C3C2×D3×D411yescharacteristic
848C22×C3C2×D3×D411yescharacteristic
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—22no—
852C2×D3—21no—
853C2×D3—21no—
854C2×D3—21no—
855C2×D3—22no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—61no—
861C2×D3—61no—
862C2×D3—61no—
863C2×D3—61no—
864C2×D3—61no—
865C2×D3—61no—
866C2×D3—84no—
867C2×D3—84no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—241no—
878C2×D3—241no—
879C2×D3—241no—
880C2×D3—244no—
881C2×D3—244no—
882C2×D3#88212yes—
883C3×C4—21no—
884C3×C4—21no—
885C3×C4—32no—
886C3×C4—41no—
887C3×C4—41no—
888C3×C4—61no—
889C3×C4—81no—
890C3×C4—121no—
891C3×C4—121no—
892C3×C4C22×D1211yescharacteristic
893C3×C4C2×D3×D411yescharacteristic
894C3×C4C2×D3×D411yescharacteristic
895C3×C4C2×D3×D411yescharacteristic
896Dic3—21no—
897Dic3—41no—
898Dic3—41no—
899Dic3—62no—
900Dic3—61no—
901Dic3—62no—
902Dic3—61no—
903Dic3—122no—
904Dic3—121no—
905Dic3#88212yes—
906C32#301211yescharacteristic, complemented, Sylow
907C23—21no—
908C23—31no—
909C23—31no—
910C23—64no—
911C23—64no—
912C23—61no—
913C23—61no—
914C23—91no—
915C23—184no—
916C23—181no—
917C23—241no—
918C23—241no—
919C23—241no—
920C23—241no—
921C23—721no—
922C23—721no—
923Q8—61no—
924Q8—61no—
925Q8—92no—
926Q8—182no—
927Q8—181no—
928D4—21no—
929D4—32no—
930D4—32no—
931D4—64no—
932D4—64no—
933D4—61no—
934D4—61no—
935D4—182no—
936D4—182no—
937D4—184no—
938D4—182no—
939D4—184no—
940D4—184no—
941D4—184no—
942D4—181no—
943D4—181no—
944D4—362no—
945D4—721no—
946D4—721no—
947D4D3×D1212yes—
948C2×C4—21no—
949C2×C4—31no—
950C2×C4—32no—
951C2×C4—32no—
952C2×C4—31no—
953C2×C4—61no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—91no—
958C2×C4—184no—
959C2×C4—184no—
960C2×C4—184no—
961C2×C4—181no—
962C2×C4—181no—
963C2×C4—181no—
964C2×C4—241no—
965C2×C4—362no—
966C2×C4C22×D3211yescharacteristic
967C8—21no—
968C8—61no—
969C8—61no—
970C8—181no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—42no—
975C2×C3—42no—
976C2×C3—62no—
977C2×C3—82no—
978C2×C3—122no—
979C2×C3—122no—
980C2×C3—121no—
981C2×C3C2×#88211yescharacteristic
982C2×C3D3×#12011yescharacteristic
983C2×C3#575711yescharacteristic
984C2×C3#576211yescharacteristic
985C2×C3#576211yescharacteristic
986C2×C3#577411yescharacteristic
987D3—22no—
988D3—41no—
989D3—42no—
990D3—42no—
991D3—121no—
992D3—121no—
993D3—241no—
994D3—241no—
995D3—241no—
996D3—481no—
997C22—22no—
998C22—32no—
999C22—41no—
1000C22—41no—
1001C22—61no—
1002C22—61no—
1003C22—61no—
1004C22—61no—
1005C22—61no—
1006C22—62no—
1007C22—62no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—181no—
1013C22—181no—
1014C22—181no—
1015C22—244no—
1016C22—244no—
1017C22—361no—
1018C22—361no—
1019C22—361no—
1020C22—724no—
1021C22D32×D411yescharacteristic
1022C4—32no—
1023C4—41no—
1024C4—61no—
1025C4—121no—
1026C4—121no—
1027C4—181no—
1028C4—182no—
1029C4C2×D3×D1211yescharacteristic
1030C4D32×D411yescharacteristic
1031C3—21no—
1032C3#7874711yescharacteristic, complemented
1033C3#8014911yescharacteristic, complemented
1034C2—42no—
1035C2—62no—
1036C2—121no—
1037C2—122no—
1038C2—122no—
1039C2—361no—
1040C2—721no—
1041C2D3×#88211yescharacteristic
1042C2#1059473211yescharacteristic
1043C2#1059474811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3012
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. C2×#64313C2semidirect
2. C2×#63934C2semidirect
3. C2×#63806C2semidirect
4. #10594523C2semidirect
5. #10592480C2semidirect
6. C3×#4776C2semidirect
7. C3×D3×#102C2semidirect
8. #10591466C2semidirect
9. #10591448C2semidirect
10. #10590968C2semidirect
11. #10590953C2semidirect
12. #10590943C2semidirect
13. #10590614C2semidirect
14. #10590607C2semidirect
15. #10590598C2semidirect
28. C2×#3799C22semidirect
32. C2×#3753C22semidirect
33. C2×#3744C22semidirect
34. #64104C22semidirect
35. C2×C3×#214C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×D3×C8C22semidirect
38. C3×#897C22semidirect
39. C3×D3×C4⋊C4C22semidirect
43. #63909C22semidirect
46. #63871C22semidirect
47. C2×#3719C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
51. C2×#3711C22semidirect
53. C32×#102C22semidirect
54. #63647C22semidirect
55. #63637C22semidirect
56. C3×#832C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#809C22semidirect
60. C3×#809C22semidirect
61. #63567C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
88. #4776D3semidirect
93. D3×#102D3semidirect
113. C3×D3×D4D4semidirect
145. #3795D4semidirect
208. C2×#214C2×D3semidirect
228. C2×#204C2×D3semidirect
230. C2×D3×C8C2×D3semidirect
233. #897C2×D3semidirect
241. D3×C4⋊C4C2×D3semidirect
249. C3×#102C2×D3semidirect
250. C3×#102C2×D3semidirect
253. #832C2×D3semidirect
255. #821C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
269. #809C2×D3semidirect
270. #809C2×D3semidirect
420. D3×D4D12semidirect
587. #102D32semidirect
906. C32#3012semidirect
1032. C3#78747semidirect
1033. C3#80149semidirect

Maximal subgroups

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

subgroupindex
C2×#643132
C2×#639342
C2×#638062
#105945232
#105924802
C3×#47762
C3×D3×#1022
#105914662
#105914482
#105909682
#105909532
#105909432
#105906142
#105906072
#105905982
#801493
#787473