Finite Group Databasebeta

← #11863889

Subgroups — #11863889

Order 1152.

1607 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3C2×#63806C211yesmaximal, characteristic, complemented
4#10594627C211yesmaximal, characteristic, complemented
5#10592505C211yesmaximal, characteristic, complemented
6C3×#4808C211yesmaximal, characteristic, complemented
7C3×#4804C211yesmaximal, characteristic, complemented
8#10591603C211yesmaximal, characteristic, complemented
9#10591588C211yesmaximal, characteristic, complemented
10#10590968C211yesmaximal, characteristic, complemented
11#10590943C211yesmaximal, characteristic, complemented
12D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
13#10590614C211yesmaximal, characteristic, complemented
14#10590608C211yesmaximal, characteristic, complemented
15#10590598C211yesmaximal, characteristic, complemented
16#80226—31nomaximal
17#78833—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21#64319—24no—
22#64319—24no—
23C2×#3802—21no—
24C2×#3802C2211yescharacteristic
25C2×C4×D32—21no—
26C2×C4×D32C2211yescharacteristic
27C2×#3799C2211yescharacteristic, complemented
28C2×#3795—21no—
29C2×#3795—21no—
30C2×#3795C2211yescharacteristic
31C2×#3795C2211yescharacteristic
32C2×#3755C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34#64104C2211yescharacteristic
35C2×C3×#216C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×D3×C8C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×#892C2211yescharacteristic, complemented
40#63949—24no—
41#63923—21no—
42#63909C2211yescharacteristic, complemented
43#63894—21no—
44#63890—21no—
45#63880—21no—
46#63871C2211yescharacteristic
47C2×#3719C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63806—24no—
53C32×#103C2211yescharacteristic, complemented
54#63647C2211yescharacteristic
55#63637C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C2×D3×#41—31no—
67C2×#950—31no—
68C2×#919—31no—
69C2×#916—31no—
70C2×#904—31no—
71#5627—31no—
72#5524—31no—
73C3×#452—31no—
74C3×#416—31no—
75#5238—31no—
76#5186—31no—
77#5169—31no—
78C2×(C2×D3)⋊C8—31no—
79#5047—31no—
80#5002—31no—
81#4810—31no—
82#4809—31no—
83#4808D311yescharacteristic, complemented
84#4806—31no—
85#4806—31no—
86#4806—61no—
87#4804D311yescharacteristic, complemented
88#4783—31no—
89#4781—31no—
90#4776—31no—
91#4773—31no—
92#4773—31no—
93#4772—31no—
94#4734—31no—
95D3×C22⋊C8—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99Q8×C3⋊D3—22no—
100Q8×C3⋊D3—22no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634—21no—
106C2×#634C2311yescharacteristic
107C3×#239—22no—
108C3×#239—22no—
109C3×#239—22no—
110C3×#239D414yescomplemented
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×#626—21no—
121C2×#626—21no—
122C2×#625—21no—
123C2×#625—21no—
124C2×#625—21no—
125C2×#624—21no—
126C2×#624D411yescharacteristic
127C2×D3×Dic3—21no—
128C2×D3×Dic3—21no—
129C2×D3×Dic3D411yescharacteristic
130C2×D3×Dic3D411yescharacteristic
131#3802—28no—
132#3802—22no—
133#3802—22no—
134C4×D32—28no—
135C4×D32—22no—
136C4×D32—22no—
137#3799—22no—
138#3799—22no—
139#3795—28no—
140#3795—28no—
141#3795—22no—
142#3795—22no—
143#3795—22no—
144#3795D414yescomplemented
145C2×C32×C8C2311yescharacteristic
146C32×C4⋊C4C2311yescharacteristic
147#3755—22no—
148#3752—21no—
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150#3744—22no—
151C3×#216—22no—
152C3×(C2×D3)⋊C4—21no—
153C3×(C2×D3)⋊C4—21no—
154C3×C4⋊Dic3—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4×Dic3—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—
168D3×C3⋊C8—22no—
169#3002—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172D3×#41—64no—
173D3×#41—64no—
174D3×#41—64no—
175D3×#41—64no—
176C2×#239—31no—
177C2×#239C2×D311yescharacteristic
178C2×#239C2×D311yescharacteristic
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×D3×Q8—61no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—61no—
185C2×#237—61no—
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—61no—
194C2×#235—61no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×C4×D3—61no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C22×C3×C8—31no—
202C3×C22⋊Q8—31no—
203C3×#117—31no—
204#950—64no—
205#946—31no—
206C2×#216—31no—
207C2×#216C2×D311yescharacteristic, complemented
208C2×#215—31no—
209C2×#215—31no—
210C2×#215—31no—
211C2×#215—61no—
212C2×#214—31no—
213C2×#213—31no—
214C2×#213—31no—
215#930—31no—
216C22×C3⋊C8—31no—
217#919—64no—
218#916—64no—
219C2×Dic12—31no—
220#904—64no—
221C2×D24—31no—
222C2×D24—31no—
223C2×#204—31no—
224C2×#204—31no—
225C2×#204—61no—
226C2×#204C2×D311yescharacteristic, complemented
227C2×D3×C8—31no—
228C2×D3×C8C2×D311yescharacteristic, complemented
229#897—31no—
230#897C2×D311yescharacteristic, complemented
231#895—31no—
232#895—31no—
233#895—31no—
234#895—61no—
235#894—61no—
236#893—61no—
237#892C2×D311yescharacteristic, complemented
238#886—61no—
239#882—61no—
240#882—61no—
241#67⋊C4—61no—
242C4×D12—61no—
243C4×D12—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#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
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—22no—
279C2×D32—22no—
280C2×D32—41no—
281C2×D32—42no—
282C2×D32—42no—
283C32×Q8—21no—
284C32×Q8C2×D412yes—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4C2411yescharacteristic
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3C2×D411yescharacteristic
290C4⋊(C3⋊D3)—21no—
291C4⋊(C3⋊D3)—21no—
292C4⋊(C3⋊D3)—42no—
293C4×C3⋊D3—24no—
294C4×C3⋊D3—21no—
295C4×C3⋊D3—21no—
296#634—24no—
297#634—21no—
298#634C2×D412yes—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3C2×D411yescharacteristic
302C2×C3×Dic3C2×D411yescharacteristic
303C3×D12—24no—
304C3×D12—24no—
305C3×D12—21no—
306C3×D12—21no—
307C3×D12C2×D412yes—
308C3×D12C2×D412yes—
309C3×C4×D3—24no—
310C3×C4×D3—21no—
311C3×C4×D3—21no—
312C3×C4×D3—24no—
313C3×C4×D3C2×D412yes—
314C3×C4×D3C2×D412yes—
315C3×Dic6—21no—
316C3×Dic6—21no—
317#626—42no—
318#626—42no—
319#625—24no—
320#625—24no—
321#625—24no—
322#624—22no—
323#624—42no—
324D3×Dic3—24no—
325D3×Dic3—22no—
326D3×Dic3—22no—
327D3×Dic3—24no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C22×#41—91no—
333C2×#135—91no—
334C2×#135—91no—
335#525—91no—
336#452—31no—
337#452—91no—
338#451—91no—
339#450—91no—
340#449—91no—
341#449—91no—
342#448—91no—
343#447—91no—
344#416—31no—
345#416—91no—
346C2×C22⋊C8—91no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—61no—
350C23×D3—61no—
351C3×#41—34no—
352C3×#41—62no—
353C3×#41—62no—
354C3×#41—62no—
355C2×C3×Q8—21no—
356C2×C3×Q8—31no—
357C2×C3×Q8C22×D311yescharacteristic
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×D4—31no—
360C2×C3×D4—31no—
361C2×C3×D4—61no—
362C2×C3×D4—61no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—61no—
366C22×C3×C4—61no—
367C2×#67—61no—
368C2×#67—61no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—61no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379#239—22no—
380#239—22no—
381#239—22no—
382#239—62no—
383#239—62no—
384#239D1214yescomplemented
385D3×Q8—62no—
386D3×Q8—62no—
387D3×Q8—62no—
388D3×Q8—62no—
389D3×Q8—122no—
390D3×Q8—122no—
391#237—34no—
392#237—62no—
393#237—62no—
394#237—68no—
395#237—68no—
396#237—62no—
397D3×D4—62no—
398D3×D4—62no—
399D3×D4—68no—
400D3×D4—68no—
401D3×D4—62no—
402D3×D4—62no—
403#235—34no—
404#235—62no—
405#235—62no—
406#235—62no—
407#235—62no—
408#235—68no—
409#235—68no—
410#235—62no—
411C2×D12—21no—
412C2×D12—21no—
413C2×D12—31no—
414C2×D12—31no—
415C2×D12—61no—
416C2×D12—61no—
417C2×D12—61no—
418C2×D12—61no—
419C2×D12—61no—
420C2×D12—121no—
421C2×D12C22×D311yescharacteristic
422C2×D12C22×D311yescharacteristic
423C2×C4×D3—21no—
424C2×C4×D3—21no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—61no—
432C2×C4×D3—62no—
433C2×C4×D3—62no—
434C2×C4×D3—68no—
435C2×C4×D3—68no—
436C2×C4×D3—61no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—62no—
441C2×C4×D3—62no—
442C2×C4×D3—61no—
443C2×C4×D3—61no—
444C2×C4×D3—121no—
445C2×C4×D3C22×D311yescharacteristic
446C2×C4×D3C22×D311yescharacteristic
447C2×Dic6—31no—
448C2×Dic6—31no—
449C2×Dic6—61no—
450C2×Dic6—61no—
451C2×Dic6—61no—
452C2×Dic6—121no—
453C2×Dic6C22×D311yescharacteristic
454C3×Q16—62no—
455C3×SD16—62no—
456C2×C3×C8—21no—
457C2×C3×C8—31no—
458C2×C3×C8—31no—
459C2×C3×C8—62no—
460C2×C3×C8C22×D311yescharacteristic
461C2×C3×C8C22×D311yescharacteristic
462C3×C4⋊C4—21no—
463C3×C4⋊C4—31no—
464C3×C4⋊C4—61no—
465C3×C4⋊C4C22×D311yescharacteristic
466C3×C4⋊C4C22×D311yescharacteristic
467C3×C22⋊C4—61no—
468C3×C22⋊C4—61no—
469C3×C42—61no—
470#216—22no—
471#216—62no—
472#215—62no—
473#215—62no—
474#215—62no—
475#215—122no—
476#214—62no—
477#213—62no—
478#213—62no—
479(C2×D3)⋊C4—21no—
480(C2×D3)⋊C4—21no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—121no—
488C4⋊Dic3—21no—
489C4⋊Dic3—61no—
490C4⋊Dic3C22×D311yescharacteristic
491Dic3⋊C4—61no—
492C4×Dic3—21no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—61no—
496C2×C3⋊C8—62no—
497C2×C3⋊C8C22×D311yescharacteristic
498C2×C3⋊C8C22×D311yescharacteristic
499Dic12—62no—
500D24—62no—
501D24—62no—
502#204—22no—
503#204—62no—
504#204—62no—
505#204—122no—
506D3×C8—22no—
507D3×C8—62no—
508C22×C32C22×D411yescharacteristic
509C2×C3⋊D3—21no—
510C2×C3⋊D3—21no—
511C2×C3⋊D3—41no—
512C2×C3⋊D3—41no—
513C2×C3⋊D3—41no—
514C2×C3⋊D3#13512yescomplemented
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—44no—
528D32—48no—
529C32×C4—22no—
530C32×C4—41no—
531C32×C4C22×D411yescharacteristic
532C32×C4C22×D411yescharacteristic
533C3⋊Dic3—21no—
534C3⋊Dic3—22no—
535C3×Dic3—21no—
536C3×Dic3—41no—
537C3×Dic3—41no—
538C3×Dic3#12012yes—
539C2×#41—31no—
540C2×#41—31no—
541C2×#41—91no—
542C2×#41—91no—
543C2×#41—91no—
544C2×#41—181no—
545C2×#41—181no—
546C2×#41—184no—
547C2×#41—184no—
548C22×Q8—91no—
549C22×D4—91no—
550C22×D4—181no—
551C23×C4—91no—
552C23×C4—181no—
553#135—184no—
554#135—184no—
555C2×Q16—31no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×D8—91no—
562C2×D8—91no—
563C22×C8—31no—
564C22×C8—91no—
565#123—181no—
566C22⋊Q8—31no—
567C22⋊Q8—91no—
568#121—91no—
569#121—91no—
570#120—181no—
571C4×D4—181no—
572C4×D4—181no—
573#117—31no—
574#103—31no—
575#103—91no—
576#103—91no—
577#103D3211yescharacteristic, complemented
578#102—31no—
579#102—31no—
580#102—31no—
581#102—91no—
582C22⋊C8—31no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C23×C3—31no—
587C23×C3—31no—
588C23×C3—61no—
589C23×C3—61no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—31no—
593C22×D3—31no—
594C22×D3—61no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—64no—
599C22×D3—64no—
600C22×D3—62no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3D3×D411yescharacteristic
611C22×D3D3×D411yescharacteristic
612C3×Q8—21no—
613C3×Q8—21no—
614C3×Q8—22no—
615C3×Q8—41no—
616C3×Q8—61no—
617C3×Q8—61no—
618C3×Q8C2×D1212yes—
619C3×Q8D3×D412yes—
620C3×D4—32no—
621C3×D4—32no—
622C3×D4—64no—
623C3×D4—64no—
624C3×D4—61no—
625C3×D4—61no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—31no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—31no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—64no—
638C2×C3×C4—64no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4C23×D311yescharacteristic
644C2×C3×C4C23×D311yescharacteristic
645#67—64no—
646#67—64no—
647#67—64no—
648#67—64no—
649#67—64no—
650#67—64no—
651#67—122no—
652#67—122no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—31no—
656C2×Dic3—31no—
657C2×Dic3—61no—
658C2×Dic3—62no—
659C2×Dic3—64no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—64no—
663C2×Dic3—62no—
664C2×Dic3—121no—
665C2×Dic3D3×D411yescharacteristic
666C2×Dic3D3×D411yescharacteristic
667D12—24no—
668D12—24no—
669D12—21no—
670D12—21no—
671D12—61no—
672D12—61no—
673D12—61no—
674D12—61no—
675D12—121no—
676D12—121no—
677D12—122no—
678D12—122no—
679D12—122no—
680D12—122no—
681D12—242no—
682D12C2×D1212yes—
683D12D3×D412yes—
684C4×D3—24no—
685C4×D3—21no—
686C4×D3—21no—
687C4×D3—24no—
688C4×D3—62no—
689C4×D3—64no—
690C4×D3—64no—
691C4×D3—62no—
692C4×D3—64no—
693C4×D3—64no—
694C4×D3—62no—
695C4×D3—61no—
696C4×D3—61no—
697C4×D3—61no—
698C4×D3—61no—
699C4×D3—62no—
700C4×D3—121no—
701C4×D3—121no—
702C4×D3—124no—
703C4×D3—122no—
704C4×D3—122no—
705C4×D3C2×D1212yes—
706C4×D3D3×D412yes—
707Dic6—21no—
708Dic6—21no—
709Dic6—32no—
710Dic6—32no—
711Dic6—62no—
712Dic6—64no—
713Dic6—64no—
714Dic6—61no—
715Dic6—61no—
716Dic6—121no—
717Dic6—124no—
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×C32C2×#13511yescharacteristic
730C2×C32#57511yescharacteristic
731C3⋊D3—22no—
732C3⋊D3—81no—
733C3×D3—22no—
734C3×D3—41no—
735C3×D3—42no—
736C3×D3—42no—
737C24—91no—
738C24—181no—
739#41—34no—
740#41—62no—
741#41—62no—
742#41—62no—
743#41—94no—
744#41—182no—
745#41—182no—
746#41—182no—
747#41—182no—
748#41—182no—
749#41—188no—
750#41—188no—
751C2×Q8—31no—
752C2×Q8—91no—
753C2×Q8—181no—
754C2×Q8—182no—
755C2×Q8—182no—
756C2×Q8C2×D3211yescharacteristic
757C2×D4—31no—
758C2×D4—31no—
759C2×D4—61no—
760C2×D4—61no—
761C2×D4—91no—
762C2×D4—181no—
763C2×D4—181no—
764C2×D4—181no—
765C2×D4—181no—
766C2×D4—182no—
767C2×D4—182no—
768C2×D4—188no—
769C2×D4—181no—
770C2×D4—181no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—91no—
779C22×C4—181no—
780C22×C4—182no—
781C22×C4—182no—
782C22×C4—181no—
783C22×C4—181no—
784C22×C4—181no—
785C22×C4—188no—
786Q16—62no—
787Q16—182no—
788SD16—62no—
789SD16—182no—
790SD16—182no—
791SD16—182no—
792D8—182no—
793D8—182no—
794C2×C8—31no—
795C2×C8—31no—
796C2×C8—62no—
797C2×C8—91no—
798C2×C8—182no—
799C2×C8C2×D3211yescharacteristic
800C4⋊C4—31no—
801C4⋊C4—61no—
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—32no—
833C2×D3—32no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—62no—
839C2×D3—61no—
840C2×D3—61no—
841C2×D3—61no—
842C2×D3—61no—
843C2×D3—121no—
844C2×D3—121no—
845C2×D3—124no—
846C2×D3—124no—
847C2×D3—128no—
848C2×D3—128no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—241no—
856C2×D3—241no—
857C2×D3—241no—
858C2×D3#88212yes—
859C3×C4—22no—
860C3×C4—22no—
861C3×C4—21no—
862C3×C4—21no—
863C3×C4—32no—
864C3×C4—42no—
865C3×C4—41no—
866C3×C4—41no—
867C3×C4—61no—
868C3×C4—81no—
869C3×C4—121no—
870C3×C4—121no—
871C3×C4C22×D1211yescharacteristic
872C3×C4C2×D3×D411yescharacteristic
873C3×C4C2×D3×D411yescharacteristic
874C3×C4C2×D3×D411yescharacteristic
875Dic3—21no—
876Dic3—41no—
877Dic3—41no—
878Dic3—62no—
879Dic3—61no—
880Dic3—62no—
881Dic3—61no—
882Dic3—122no—
883Dic3—121no—
884Dic3#88212yes—
885C32#300211yescharacteristic, complemented, Sylow
886C23—31no—
887C23—31no—
888C23—61no—
889C23—61no—
890C23—91no—
891C23—182no—
892C23—182no—
893C23—184no—
894C23—181no—
895C23—361no—
896C23—362no—
897C23—362no—
898Q8—21no—
899Q8—61no—
900Q8—61no—
901Q8—92no—
902Q8—184no—
903Q8—181no—
904Q8D3×D1212yes—
905D4—32no—
906D4—32no—
907D4—64no—
908D4—64no—
909D4—61no—
910D4—61no—
911D4—184no—
912D4—184no—
913D4—184no—
914D4—181no—
915D4—181no—
916D4—362no—
917D4—362no—
918D4—362no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—31no—
922C2×C4—32no—
923C2×C4—32no—
924C2×C4—31no—
925C2×C4—64no—
926C2×C4—64no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—91no—
932C2×C4—184no—
933C2×C4—182no—
934C2×C4—182no—
935C2×C4—184no—
936C2×C4—182no—
937C2×C4—184no—
938C2×C4—181no—
939C2×C4—181no—
940C2×C4—181no—
941C2×C4—362no—
942C2×C4C22×D3211yescharacteristic
943C8—21no—
944C8—61no—
945C8—61no—
946C8—181no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—62no—
951C2×C3—122no—
952C2×C3—121no—
953C2×C3—122no—
954C2×C3C2×#88211yescharacteristic
955C2×C3D3×#12011yescharacteristic
956C2×C3D3×#13511yescharacteristic
957C2×C3D3×#13511yescharacteristic
958C2×C3#576811yescharacteristic
959C2×C3#577711yescharacteristic
960D3—22no—
961D3—41no—
962D3—42no—
963D3—42no—
964D3—62no—
965D3—62no—
966D3—122no—
967D3—241no—
968D3—241no—
969D3—481no—
970C22—32no—
971C22—61no—
972C22—61no—
973C22—61no—
974C22—61no—
975C22—62no—
976C22—62no—
977C22—61no—
978C22—92no—
979C22—121no—
980C22—121no—
981C22—121no—
982C22—121no—
983C22—181no—
984C22—181no—
985C22—364no—
986C22—368no—
987C22—361no—
988C22—361no—
989C22—361no—
990C22D32×D411yescharacteristic
991C4—22no—
992C4—32no—
993C4—41no—
994C4—61no—
995C4—121no—
996C4—121no—
997C4—181no—
998C4—182no—
999C4C2×D3×D1211yescharacteristic
1000C4D32×D411yescharacteristic
1001C3—21no—
1002C3#7883311yescharacteristic, complemented
1003C3#8022611yescharacteristic, complemented
1004C2—62no—
1005C2—121no—
1006C2—122no—
1007C2—122no—
1008C2—182no—
1009C2—721no—
1010C2D3×#88211yescharacteristic
1011C2#1059474711yescharacteristic
1012C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3002
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×#64319C2semidirect
2. C2×#63949C2semidirect
3. C2×#63806C2semidirect
4. #10594627C2semidirect
5. #10592505C2semidirect
6. C3×#4808C2semidirect
7. C3×#4804C2semidirect
8. #10591603C2semidirect
9. #10591588C2semidirect
10. #10590968C2semidirect
11. #10590943C2semidirect
12. D3×(C2×D3)⋊C8C2semidirect
13. #10590614C2semidirect
14. #10590608C2semidirect
15. #10590598C2semidirect
27. C2×#3799C22semidirect
32. C2×#3755C22semidirect
33. C2×#3744C22semidirect
35. C2×C3×#216C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×D3×C8C22semidirect
38. C3×#897C22semidirect
39. C3×#892C22semidirect
42. #63909C22semidirect
47. C2×#3719C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. C32×#103C22semidirect
55. #63637C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#809C22semidirect
60. C3×#809C22semidirect
61. #63567C22semidirect
62. #63562C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
83. #4808D3semidirect
87. #4804D3semidirect
110. C3×#239D4semidirect
144. #3795D4semidirect
207. C2×#216C2×D3semidirect
226. C2×#204C2×D3semidirect
228. C2×D3×C8C2×D3semidirect
230. #897C2×D3semidirect
237. #892C2×D3semidirect
246. C3×#103C2×D3semidirect
247. C3×#103C2×D3semidirect
252. #835C2×D3semidirect
255. #821C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
269. #809C2×D3semidirect
270. #809C2×D3semidirect
384. #239D12semidirect
514. C2×C3⋊D3#135semidirect
577. #103D32semidirect
885. C32#3002semidirect
1002. C3#78833semidirect
1003. C3#80226semidirect

Maximal subgroups

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

subgroupindex
C2×#643192
C2×#639492
C2×#638062
#105946272
#105925052
C3×#48082
C3×#48042
#105916032
#105915882
#105909682
#105909432
D3×(C2×D3)⋊C82
#105906142
#105906082
#105905982
#802263
#788333