Finite Group Databasebeta

← #11864387

Subgroups — #11864387

Order 1152.

1580 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic
2C2×#63943C211yesmaximal, characteristic, complemented
3C2×D3×#204C211yesmaximal, characteristic, complemented
4#10594380C211yesmaximal, characteristic, complemented
5#10592507C211yesmaximal, characteristic, complemented
6C3×#4808C211yesmaximal, characteristic, complemented
7C3×#4804C211yesmaximal, characteristic, complemented
8#10591602C211yesmaximal, characteristic, complemented
9#10591599C211yesmaximal, characteristic, complemented
10#10590953C211yesmaximal, characteristic, complemented
11#10590946C211yesmaximal, characteristic, complemented
12#10590943C211yesmaximal, characteristic, complemented
13#10590597C211yesmaximal, characteristic, complemented
14#10590596C211yesmaximal, characteristic, complemented
15#10590592C211yesmaximal, characteristic, complemented
16#80229—31nomaximal
17#78835—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21#64320—24no—
22#64320—24no—
23C2×#3802—21no—
24C2×#3802C2211yescharacteristic
25C2×D3×D12—21no—
26C2×D3×D12—21no—
27C2×D3×D12C2211yescharacteristic
28C2×D3×D12C2211yescharacteristic
29C2×#3798—21no—
30C2×#3798C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic, complemented
32C2×#3756C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34#64106C2211yescharacteristic, complemented
35C2×C3×#216C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×D3×C8C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×#892C2211yescharacteristic, complemented
40#63943—24no—
41#63918—21no—
42#63891—21no—
43#63890—21no—
44#63871C2211yescharacteristic, complemented
45#63857C2211yescharacteristic, complemented
46#63852—21no—
47C2×#3717C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52D3×#204—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×#951—31no—
68C2×#918—31no—
69C2×D3×SD16—31no—
70C22×#204—31no—
71#5628—31no—
72#5526—31no—
73C3×#452—31no—
74C3×#416—31no—
75#5239—31no—
76#5187—31no—
77#5169—31no—
78#5110—31no—
79#5046—31no—
80#5001—31no—
81#4808—31no—
82#4808—31no—
83#4808—31no—
84#4808—31no—
85#4808—61no—
86#4808D311yescharacteristic, complemented
87#4804D311yescharacteristic, complemented
88#4776—31no—
89#4776—31no—
90#4776—31no—
91#4776—31no—
92#4776—31no—
93#4770—31no—
94#4731—31no—
95#4727—31no—
96C22×D32—21no—
97C22×D32—21no—
98C22×D32—21no—
99C2×C32×Q8C2311yescharacteristic
100#3832—22no—
101#3832—22no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×#634C2311yescharacteristic
107C3×#239—22no—
108C3×#239—22no—
109C3×#239—22no—
110C3×#239D414yes—
111C2×C3×D12—21no—
112C2×C3×D12—21no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×#627—21no—
121C2×#627D411yescharacteristic
122C2×#626—21no—
123C2×#626—21no—
124C2×#626D411yescharacteristic
125C2×#626D411yescharacteristic
126C2×#625—21no—
127C2×#625D411yescharacteristic
128C2×D3×Dic3—21no—
129#3802—28no—
130#3802—22no—
131#3802—22no—
132D3×D12—28no—
133D3×D12—28no—
134D3×D12—22no—
135D3×D12—22no—
136D3×D12—22no—
137D3×D12D414yes—
138#3798—28no—
139#3798—22no—
140#3798—22no—
141D3×Dic6—22no—
142D3×Dic6—22no—
143C2×C32×C8C2311yescharacteristic
144C32×C4⋊C4C2311yescharacteristic
145#3756—22no—
146#3752—21no—
147C4⋊(C3⋊Dic3)—21no—
148C2×C3⋊(C3⋊C8)C2311yescharacteristic
149#3744—22no—
150C3×#216—22no—
151C3×(C2×D3)⋊C4—21no—
152C3×(C2×D3)⋊C4—21no—
153C3×C4⋊Dic3—21no—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×C4×Dic3—21no—
156C2×C3×C3⋊C8C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158C3×#204—22no—
159C3×D3×C8—22no—
160Dic3⋊Dic3—21no—
161Dic3⋊Dic3—21no—
162#3722—21no—
163(C2×D3)⋊Dic3—21no—
164#3717—22no—
165#3716—22no—
166#3716—22no—
167#3715—22no—
168#3711—22no—
169#3009—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
181C2×D3×Q8—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—61no—
197C22×D12—61no—
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C22×C3×C8—31no—
202C3×C22⋊Q8—31no—
203C3×#117—31no—
204#951—64no—
205#946—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#216—61no—
209C2×#216C2×D311yescharacteristic, complemented
210C2×#215—31no—
211C2×#215—31no—
212C2×#214—31no—
213C2×#214—31no—
214C2×#214—31no—
215#924—31no—
216C2×#208—31no—
217#918—64no—
218D3×SD16—64no—
219C2×#204—31no—
220C2×#204—31no—
221C2×#204—31no—
222C2×#204—31no—
223C2×#204—31no—
224C2×#204—61no—
225C2×#204—64no—
226C2×#204C2×D311yescharacteristic, complemented
227C2×ΓL(1,𝔽25)—31no—
228C2×D3×C8C2×D311yescharacteristic, complemented
229#897—31no—
230#897—31no—
231#897—31no—
232#897—31no—
233#897—61no—
234#897C2×D311yescharacteristic, complemented
235#894—61no—
236#892C2×D311yescharacteristic, complemented
237#888—61no—
238#886—61no—
239#886—61no—
240#885—61no—
241#883—61no—
242#875—61no—
243#869—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⋊D3C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3C2×D411yescharacteristic
276C22×C3×D3C2×D411yescharacteristic
277C2×D32—24no—
278C2×D32—24no—
279C2×D32—24no—
280C2×D32—81no—
281C2×D32—81no—
282C2×D32—81no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C32×Q8—21no—
287C32×Q8C2×D412yes—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4C2411yescharacteristic
291C2×C3⋊Dic3—21no—
292C2×C3⋊Dic3C2×D411yescharacteristic
293C4⋊(C3⋊D3)—24no—
294C4⋊(C3⋊D3)—21no—
295C4⋊(C3⋊D3)C2×D412yes—
296C4×C3⋊D3—24no—
297C4×C3⋊D3—21no—
298C4×C3⋊D3—21no—
299#634—21no—
300#634—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C2×D411yescharacteristic
304C2×C3×Dic3C2×D411yescharacteristic
305C3×D12—24no—
306C3×D12—24no—
307C3×D12—21no—
308C3×D12—21no—
309C3×D12C2×D412yes—
310C3×D12C2×D412yes—
311C3×C4×D3—24no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3—24no—
315C3×C4×D3C2×D412yes—
316C3×C4×D3C2×D412yes—
317C3×Dic6—21no—
318C3×Dic6—21no—
319#627—22no—
320#627—42no—
321#626—24no—
322#626—22no—
323#626—22no—
324#626—24no—
325#625—24no—
326#625—22no—
327D3×Dic3—42no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C2×H(5,𝔽2)—91no—
333C2×#137—91no—
334C22×SD16—91no—
335#536—91no—
336#452—31no—
337#452—91no—
338#452—91no—
339#452—91no—
340#450—91no—
341#450—91no—
342#450—91no—
343#450—91no—
344#418—91no—
345#416—31no—
346#408—91no—
347C23×D3—61no—
348C23×D3—61no—
349C23×D3—61no—
350C23×D3—61no—
351C23×D3—61no—
352C23×D3—61no—
353C3×#41—34no—
354C3×#41—62no—
355C3×#41—62no—
356C3×#41—62no—
357C2×C3×Q8—21no—
358C2×C3×Q8—31no—
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×Q8C22×D311yescharacteristic
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C2×C3×D4—61no—
364C2×C3×D4—61no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—61no—
368C22×C3×C4—61no—
369C2×#67—31no—
370C2×#67—31no—
371C2×#67—31no—
372C2×#67—31no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—61no—
377C22×Dic3—61no—
378#239—22no—
379#239—22no—
380#239—22no—
381#239—62no—
382#239—62no—
383#239—62no—
384#239—62no—
385#239—122no—
386#239—122no—
387#239D1214yes—
388D3×Q8—62no—
389D3×Q8—62no—
390D3×D4—34no—
391D3×D4—62no—
392D3×D4—62no—
393D3×D4—68no—
394D3×D4—68no—
395D3×D4—62no—
396D3×D4—62no—
397D3×D4—68no—
398D3×D4—68no—
399D3×D4—62no—
400D3×D4—62no—
401D3×D4—62no—
402#235—62no—
403#235—62no—
404#235—68no—
405#235—68no—
406#235—62no—
407#235—62no—
408C2×D12—21no—
409C2×D12—21no—
410C2×D12—31no—
411C2×D12—31no—
412C2×D12—34no—
413C2×D12—31no—
414C2×D12—31no—
415C2×D12—61no—
416C2×D12—62no—
417C2×D12—62no—
418C2×D12—68no—
419C2×D12—68no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12—61no—
423C2×D12—61no—
424C2×D12—62no—
425C2×D12—121no—
426C2×D12C22×D311yescharacteristic
427C2×D12C22×D311yescharacteristic
428C2×C4×D3—21no—
429C2×C4×D3—21no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—61no—
433C2×C4×D3—61no—
434C2×C4×D3—61no—
435C2×C4×D3—61no—
436C2×C4×D3—121no—
437C2×C4×D3C22×D311yescharacteristic
438C2×C4×D3C22×D311yescharacteristic
439C2×Dic6—31no—
440C2×Dic6—31no—
441C2×Dic6—31no—
442C2×Dic6—31no—
443C2×Dic6—61no—
444C2×Dic6—62no—
445C2×Dic6—62no—
446C2×Dic6—61no—
447C2×Dic6—61no—
448C2×Dic6C22×D311yescharacteristic
449C3×Q16—62no—
450C3×SD16—62no—
451C2×C3×C8—21no—
452C2×C3×C8—31no—
453C2×C3×C8—31no—
454C2×C3×C8—62no—
455C2×C3×C8C22×D311yescharacteristic
456C2×C3×C8C22×D311yescharacteristic
457C3×C4⋊C4—21no—
458C3×C4⋊C4—31no—
459C3×C4⋊C4—61no—
460C3×C4⋊C4C22×D311yescharacteristic
461C3×C4⋊C4C22×D311yescharacteristic
462C3×C22⋊C4—61no—
463C3×C22⋊C4—61no—
464C3×C42—61no—
465#217—61no—
466#216—22no—
467#216—62no—
468#216—62no—
469#216—122no—
470#215—62no—
471#215—62no—
472#214—62no—
473#214—62no—
474#214—62no—
475(C2×D3)⋊C4—21no—
476(C2×D3)⋊C4—21no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—121no—
483C4⋊Dic3—21no—
484C4⋊Dic3—61no—
485C4⋊Dic3—61no—
486C4⋊Dic3—61no—
487C4⋊Dic3—61no—
488C4⋊Dic3—121no—
489C4⋊Dic3C22×D311yescharacteristic
490Dic3⋊C4—61no—
491Dic3⋊C4—61no—
492C4×Dic3—21no—
493#208—62no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—61no—
497C2×C3⋊C8C22×D311yescharacteristic
498C2×C3⋊C8C22×D311yescharacteristic
499#204—22no—
500#204—62no—
501#204—62no—
502#204—62no—
503#204—62no—
504#204—62no—
505#204—122no—
506ΓL(1,𝔽25)—62no—
507D3×C8—22no—
508C22×C32C22×D411yescharacteristic
509C2×C3⋊D3—21no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—41no—
514C2×C3⋊D3—41no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3#12012yes—
527D32—84no—
528D32—84no—
529D32—84no—
530C32×C4—22no—
531C32×C4—41no—
532C32×C4C22×D411yescharacteristic
533C32×C4C22×D411yescharacteristic
534C3⋊Dic3—21no—
535C3⋊Dic3—41no—
536C3×Dic3—21no—
537C3×Dic3—41no—
538C3×Dic3—41no—
539C3×Dic3#12012yes—
540H(5,𝔽2)—184no—
541H(5,𝔽2)—184no—
542C2×#41—31no—
543C2×#41—31no—
544C2×#41—91no—
545C2×#41—91no—
546C2×#41—181no—
547C22×Q8—91no—
548C22×D4—91no—
549C22×D4—91no—
550C22×D4—91no—
551C22×D4—181no—
552C22×D4—181no—
553C22×D4—181no—
554#137—184no—
555C2×Q16—31no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×SD16—91no—
562C2×SD16—91no—
563C2×SD16—184no—
564C2×M16—91no—
565C22×C8—31no—
566C4⋊Q8—181no—
567#124—181no—
568#123—181no—
569#123—181no—
570C22⋊Q8—31no—
571C22⋊Q8—91no—
572C22⋊Q8—91no—
573C22⋊Q8—91no—
574#117—31no—
575#103—31no—
576#103D3211yescharacteristic, complemented
577#102—31no—
578#102—31no—
579#102—31no—
580#102—91no—
581#102—91no—
582#102—91no—
583C22⋊C8—31no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C22⋊C8—91no—
587C23×C3—31no—
588C23×C3—31no—
589C23×C3—61no—
590C23×C3—61no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—31no—
594C22×D3—31no—
595C22×D3—61no—
596C22×D3—64no—
597C22×D3—64no—
598C22×D3—64no—
599C22×D3—64no—
600C22×D3—64no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—64no—
604C22×D3—121no—
605C22×D3—241no—
606C22×D3—241no—
607C22×D3—241no—
608C22×D3—241no—
609C22×D3—241no—
610C22×D3—241no—
611C22×D3—241no—
612C22×D3—241no—
613C22×D3—241no—
614C22×D3—241no—
615C22×D3—241no—
616C22×D3—241no—
617C22×D3D3×D411yescharacteristic
618C22×D3D3×D411yescharacteristic
619C3×Q8—21no—
620C3×Q8—21no—
621C3×Q8—22no—
622C3×Q8—41no—
623C3×Q8—61no—
624C3×Q8—61no—
625C3×Q8C2×D1212yes—
626C3×Q8D3×D412yes—
627C3×D4—32no—
628C3×D4—32no—
629C3×D4—64no—
630C3×D4—64no—
631C3×D4—61no—
632C3×D4—61no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—31no—
639C2×C3×C4—32no—
640C2×C3×C4—32no—
641C2×C3×C4—31no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—64no—
645C2×C3×C4—64no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652#67—62no—
653#67—64no—
654#67—62no—
655#67—64no—
656#67—64no—
657#67—62no—
658#67—64no—
659#67—62no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—31no—
663C2×Dic3—31no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—121no—
668C2×Dic3—122no—
669C2×Dic3D3×D411yescharacteristic
670C2×Dic3D3×D411yescharacteristic
671D12—24no—
672D12—24no—
673D12—21no—
674D12—21no—
675D12—32no—
676D12—32no—
677D12—62no—
678D12—64no—
679D12—64no—
680D12—62no—
681D12—64no—
682D12—64no—
683D12—62no—
684D12—61no—
685D12—61no—
686D12—121no—
687D12—124no—
688D12C2×D1212yes—
689D12D3×D412yes—
690C4×D3—24no—
691C4×D3—21no—
692C4×D3—21no—
693C4×D3—24no—
694C4×D3—64no—
695C4×D3—64no—
696C4×D3—61no—
697C4×D3—61no—
698C4×D3—61no—
699C4×D3—61no—
700C4×D3—121no—
701C4×D3—121no—
702C4×D3—124no—
703C4×D3—122no—
704C4×D3C2×D1212yes—
705C4×D3D3×D412yes—
706Dic6—21no—
707Dic6—21no—
708Dic6—62no—
709Dic6—62no—
710Dic6—61no—
711Dic6—61no—
712Dic6—61no—
713Dic6—61no—
714Dic6—121no—
715Dic6—121no—
716Dic6—122no—
717Dic6—122no—
718C3×C8—21no—
719C3×C8—21no—
720C3×C8—41no—
721C3×C8—61no—
722C3×C8—61no—
723C3⋊C8—21no—
724C3⋊C8—21no—
725C3⋊C8—61no—
726C3⋊C8—61no—
727C3⋊C8—121no—
728C2×C32C2×#12011yescharacteristic
729C2×C32#57711yescharacteristic
730C2×C32#57711yescharacteristic
731C3⋊D3—41no—
732C3⋊D3—42no—
733C3×D3—22no—
734C3×D3—41no—
735C3×D3—42no—
736C3×D3—42no—
737C24—181no—
738C24—181no—
739C24—181no—
740#41—34no—
741#41—62no—
742#41—62no—
743#41—62no—
744#41—182no—
745#41—182no—
746#41—188no—
747#41—182no—
748#41—182no—
749C2×Q8—31no—
750C2×Q8—91no—
751C2×Q8—91no—
752C2×Q8—181no—
753C2×Q8—182no—
754C2×Q8—182no—
755C2×Q8C2×D3211yescharacteristic
756C2×D4—31no—
757C2×D4—31no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—94no—
761C2×D4—91no—
762C2×D4—91no—
763C2×D4—91no—
764C2×D4—91no—
765C2×D4—181no—
766C2×D4—182no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4—182no—
770C2×D4—182no—
771C2×D4—188no—
772C2×D4—188no—
773C2×D4—181no—
774C2×D4—182no—
775C2×D4—182no—
776C2×D4—188no—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—91no—
782C22×C4—181no—
783C22×C4—181no—
784Q16—62no—
785Q16—182no—
786SD16—62no—
787SD16—182no—
788SD16—182no—
789SD16—182no—
790SD16—182no—
791SD16—182no—
792M16—182no—
793C2×C8—31no—
794C2×C8—31no—
795C2×C8—62no—
796C2×C8—91no—
797C2×C8C2×D3211yescharacteristic
798C4⋊C4—31no—
799C4⋊C4—61no—
800C4⋊C4—181no—
801C4⋊C4—181no—
802C4⋊C4—181no—
803C4⋊C4C2×D3211yescharacteristic
804C22⋊C4—61no—
805C22⋊C4—61no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C22⋊C4—181no—
809C42—61no—
810C22×C3—21no—
811C22×C3—32no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—62no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—62no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3C2×D3×D411yescharacteristic
824C22×C3C2×D3×D411yescharacteristic
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—22no—
828C2×D3—21no—
829C2×D3—21no—
830C2×D3—21no—
831C2×D3—22no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—62no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—61no—
840C2×D3—61no—
841C2×D3—61no—
842C2×D3—62no—
843C2×D3—61no—
844C2×D3—122no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—241no—
853C2×D3—241no—
854C2×D3—244no—
855C2×D3—244no—
856C2×D3—244no—
857C2×D3—244no—
858C2×D3—244no—
859C2×D3—244no—
860C2×D3#88212yes—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—21no—
864C3×C4—21no—
865C3×C4—32no—
866C3×C4—42no—
867C3×C4—41no—
868C3×C4—41no—
869C3×C4—61no—
870C3×C4—81no—
871C3×C4—121no—
872C3×C4—121no—
873C3×C4C22×D1211yescharacteristic
874C3×C4C2×D3×D411yescharacteristic
875C3×C4C2×D3×D411yescharacteristic
876C3×C4C2×D3×D411yescharacteristic
877Dic3—21no—
878Dic3—41no—
879Dic3—41no—
880Dic3—61no—
881Dic3—61no—
882Dic3—121no—
883Dic3—121no—
884Dic3—121no—
885Dic3—241no—
886Dic3#88212yes—
887C32#300911yescharacteristic, complemented, Sylow
888C23—31no—
889C23—31no—
890C23—61no—
891C23—61no—
892C23—91no—
893C23—184no—
894C23—184no—
895C23—184no—
896C23—181no—
897C23—721no—
898C23—721no—
899C23—721no—
900C23—721no—
901C23—721no—
902C23—721no—
903Q8—21no—
904Q8—61no—
905Q8—61no—
906Q8—182no—
907Q8—181no—
908Q8—181no—
909Q8—362no—
910Q8D3×D1212yes—
911D4—32no—
912D4—32no—
913D4—64no—
914D4—64no—
915D4—61no—
916D4—61no—
917D4—92no—
918D4—184no—
919D4—184no—
920D4—182no—
921D4—182no—
922D4—184no—
923D4—182no—
924D4—184no—
925D4—181no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—31no—
929C2×C4—32no—
930C2×C4—32no—
931C2×C4—31no—
932C2×C4—64no—
933C2×C4—64no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—91no—
939C2×C4—184no—
940C2×C4—181no—
941C2×C4—181no—
942C2×C4—181no—
943C2×C4—362no—
944C2×C4C22×D3211yescharacteristic
945C8—21no—
946C8—61no—
947C8—61no—
948C8—181no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—62no—
953C2×C3—122no—
954C2×C3—121no—
955C2×C3—122no—
956C2×C3C2×#88211yescharacteristic
957C2×C3D3×#12011yescharacteristic
958C2×C3#577011yescharacteristic
959C2×C3#577011yescharacteristic
960C2×C3#577011yescharacteristic
961C2×C3#577811yescharacteristic
962D3—22no—
963D3—41no—
964D3—42no—
965D3—42no—
966D3—121no—
967D3—122no—
968D3—121no—
969D3—122no—
970D3—241no—
971D3—242no—
972C22—32no—
973C22—61no—
974C22—61no—
975C22—61no—
976C22—62no—
977C22—62no—
978C22—61no—
979C22—61no—
980C22—121no—
981C22—121no—
982C22—121no—
983C22—121no—
984C22—181no—
985C22—182no—
986C22—181no—
987C22—181no—
988C22—361no—
989C22—361no—
990C22—724no—
991C22—724no—
992C22—724no—
993C22D32×D411yescharacteristic
994C4—22no—
995C4—32no—
996C4—41no—
997C4—61no—
998C4—121no—
999C4—121no—
1000C4—181no—
1001C4—361no—
1002C4C2×D3×D1211yescharacteristic
1003C4D32×D411yescharacteristic
1004C3—21no—
1005C3#7883511yescharacteristic, complemented
1006C3#8022911yescharacteristic, complemented
1007C2—62no—
1008C2—121no—
1009C2—122no—
1010C2—122no—
1011C2—361no—
1012C2—362no—
1013C2D3×#88211yescharacteristic
1014C2#1059475711yescharacteristic
1015C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#64320C2
hypercenter#103D32
hypocenterC32#3009
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
2. C2×#63943C2semidirect
3. C2×D3×#204C2semidirect
4. #10594380C2semidirect
5. #10592507C2semidirect
6. C3×#4808C2semidirect
7. C3×#4804C2semidirect
8. #10591602C2semidirect
9. #10591599C2semidirect
10. #10590953C2semidirect
11. #10590946C2semidirect
12. #10590943C2semidirect
13. #10590597C2semidirect
14. #10590596C2semidirect
15. #10590592C2semidirect
31. C2×D3×Dic6C22semidirect
32. C2×#3756C22semidirect
33. C2×#3744C22semidirect
34. #64106C22semidirect
35. C2×C3×#216C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×D3×C8C22semidirect
38. C3×#897C22semidirect
39. C3×#892C22semidirect
44. #63871C22semidirect
45. #63857C22semidirect
47. C2×#3717C22semidirect
48. C2×#3716C22semidirect
49. C2×#3716C22semidirect
50. C2×#3715C22semidirect
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. #4808D3semidirect
87. #4804D3semidirect
209. C2×#216C2×D3semidirect
226. C2×#204C2×D3semidirect
228. C2×D3×C8C2×D3semidirect
234. #897C2×D3semidirect
236. #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
576. #103D32semidirect
887. C32#3009semidirect
1005. C3#78835semidirect
1006. C3#80229semidirect

Maximal subgroups

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

subgroupindex
C2×#643202
C2×#639432
C2×D3×#2042
#105943802
#105925072
C3×#48082
C3×#48042
#105916022
#105915992
#105909532
#105909462
#105909432
#105905972
#105905962
#105905922
#802293
#788353