Finite Group Databasebeta

← #11864641

Subgroups — #11864641

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×#64320C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3C2×#63794C211yesmaximal, characteristic, complemented
4#10594523C211yesmaximal, characteristic, complemented
5#10592509C211yesmaximal, characteristic, complemented
6C3×#4808C211yesmaximal, characteristic, complemented
7C3×#4803C211yesmaximal, characteristic, complemented
8#10591602C211yesmaximal, characteristic, complemented
9#10591588C211yesmaximal, characteristic, complemented
10#10590955C211yesmaximal, characteristic, complemented
11#10590947C211yesmaximal, characteristic, complemented
12#10590943C211yesmaximal, characteristic, complemented
13#10590598C211yesmaximal, characteristic, complemented
14#10590596C211yesmaximal, characteristic, complemented
15D3×#809C211yesmaximal, characteristic, complemented
16#80231—31nomaximal
17#78886—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×#3799C2211yescharacteristic, complemented
30C2×#3798—21no—
31C2×#3798C2211yescharacteristic
32C2×#3755C2211yescharacteristic, complemented
33C2×#3745C2211yescharacteristic, complemented
34#64104C2211yescharacteristic, complemented
35C2×C3×#216C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×D3×C4⋊C4C2211yescharacteristic, complemented
40#63949—24no—
41#63910—21no—
42#63909—21no—
43#63909C2211yescharacteristic, complemented
44#63906—21no—
45#63895—21no—
46#63871C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63794—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×#950—31no—
68C2×#919—31no—
69C2×#914—31no—
70C2×#908—31no—
71#5629—31no—
72#5510—31no—
73C3×#452—31no—
74C3×#417—31no—
75#5238—31no—
76#5187—31no—
77#5169—31no—
78#5129—31no—
79#5046—31no—
80C2×#809—31no—
81#4810—31no—
82#4810—31no—
83#4810—31no—
84#4810—61no—
85#4808—31no—
86#4808D311yescharacteristic, complemented
87#4803D311yescharacteristic, complemented
88#4776—31no—
89#4776—31no—
90#4773—31no—
91#4773—31no—
92#4773—31no—
93D3×#102—31no—
94#4732—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)—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C3×#239—22no—
109C3×#239—22no—
110C3×#239—22no—
111C3×#239D414yescomplemented
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C2×#627D411yescharacteristic
123C2×#626—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626D411yescharacteristic
128C2×#626D411yescharacteristic
129C2×#625—21no—
130C2×#625D411yescharacteristic
131C2×#624—21no—
132#3802—28no—
133#3802—22no—
134#3802—22no—
135D3×D12—28no—
136D3×D12—28no—
137D3×D12—22no—
138D3×D12—22no—
139D3×D12—22no—
140D3×D12D414yescomplemented
141#3799—22no—
142#3799—22no—
143#3798—28no—
144#3798—22no—
145#3798—22no—
146C2×C32×C8C2311yescharacteristic
147C32×C4⋊C4C2311yescharacteristic
148#3755—22no—
149#3752—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151#3745—22no—
152C3×#216—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×ΓL(1,𝔽25)—22no—
161Dic3⋊Dic3—21no—
162#3722—21no—
163#3722—21no—
164#3717—22no—
165#3715—22no—
166#3714—22no—
167#3714—22no—
168D3×C3⋊C8—22no—
169#3012—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—31no—
179C2×#239—61no—
180C2×#239C2×D311yescharacteristic
181C2×#239C2×D311yescharacteristic
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—31no—
193C2×#235—61no—
194C2×#235—61no—
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—61no—
198C22×D12—61no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C2×C3×M16—31no—
202C3×C22⋊Q8—31no—
203C2×C3×C4⋊C4—31no—
204#950—64no—
205#946—31no—
206C2×#216C2×D311yescharacteristic, complemented
207C2×#215—31no—
208C2×#215—31no—
209C2×#215—31no—
210C2×#215—31no—
211C2×#215—61no—
212C2×#214—31no—
213C2×#213—31no—
214C2×#213—31no—
215#930—31no—
216#930—61no—
217#930—61no—
218C22×C3⋊C8—31no—
219#919—64no—
220#914—64no—
221#908—64no—
222C2×D24—31no—
223C2×D24—31no—
224C2×D24—31no—
225C2×D24—31no—
226C2×D24—61no—
227C2×#204—31no—
228C2×#204C2×D311yescharacteristic, complemented
229C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
230C2×D3×C8—31no—
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×#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×D3C2×D411yescharacteristic
277C22×C3×D3C2×D411yescharacteristic
278C2×D32—24no—
279C2×D32—24no—
280C2×D32—24no—
281C2×D32—81no—
282C2×D32—81no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C2×D32—81no—
287C32×Q8—21no—
288C32×Q8C2×D412yes—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4C2411yescharacteristic
292C2×C3⋊Dic3C2×D411yescharacteristic
293C4⋊(C3⋊D3)—24no—
294C4⋊(C3⋊D3)—21no—
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—81no—
298C4⋊(C3⋊D3)C2×D412yes—
299C4×C3⋊D3—24no—
300C4×C3⋊D3—21no—
301C4×C3⋊D3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3C2×D411yescharacteristic
305C2×C3×Dic3C2×D411yescharacteristic
306C3×D12—24no—
307C3×D12—24no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12C2×D412yes—
311C3×D12C2×D412yes—
312C3×C4×D3—24no—
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×C4×D3—24no—
316C3×C4×D3—81no—
317C3×C4×D3C2×D412yes—
318C3×C4×D3C2×D412yes—
319C3×Dic6—21no—
320C3×Dic6—21no—
321#627—22no—
322#626—24no—
323#626—22no—
324#626—22no—
325#626—24no—
326#626—42no—
327#626—81no—
328#625—24no—
329#625—22no—
330#624—42no—
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—31no—
340#452—91no—
341#450—91no—
342#450—91no—
343#449—91no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—31no—
348C2×#102—91no—
349#408—91no—
350C23×D3—61no—
351C23×D3—61no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C3×#41—34no—
357C3×#41—62no—
358C3×#41—62no—
359C3×#41—62no—
360C2×C3×Q8—21no—
361C2×C3×Q8—31no—
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×Q8C22×D311yescharacteristic
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—61no—
367C2×C3×D4—61no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—61no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
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—61no—
382C2×#67—61no—
383#239—22no—
384#239—22no—
385#239—22no—
386#239—62no—
387#239—62no—
388#239—62no—
389#239—62no—
390#239—62no—
391#239—62no—
392#239—122no—
393#239—122no—
394#239D1214yescomplemented
395D3×D4—34no—
396D3×D4—62no—
397D3×D4—62no—
398D3×D4—68no—
399D3×D4—68no—
400D3×D4—62no—
401D3×D4—62no—
402D3×D4—68no—
403D3×D4—68no—
404D3×D4—62no—
405D3×D4—62no—
406D3×D4—62no—
407#235—62no—
408#235—62no—
409#235—62no—
410#235—62no—
411#235—68no—
412#235—68no—
413#235—62no—
414#235—62no—
415C2×D12—21no—
416C2×D12—21no—
417C2×D12—31no—
418C2×D12—31no—
419C2×D12—34no—
420C2×D12—31no—
421C2×D12—31no—
422C2×D12—31no—
423C2×D12—31no—
424C2×D12—61no—
425C2×D12—61no—
426C2×D12—62no—
427C2×D12—62no—
428C2×D12—68no—
429C2×D12—68no—
430C2×D12—61no—
431C2×D12—61no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—62no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—61no—
439C2×D12—121no—
440C2×D12—121no—
441C2×D12C22×D311yescharacteristic
442C2×D12C22×D311yescharacteristic
443C2×C4×D3—21no—
444C2×C4×D3—21no—
445C2×C4×D3—21no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3—121no—
454C2×C4×D3C22×D311yescharacteristic
455C2×C4×D3C22×D311yescharacteristic
456C2×Dic6—31no—
457C2×Dic6—31no—
458C2×Dic6C22×D311yescharacteristic
459C3×Q16—62no—
460C3×SD16—62no—
461C3×M16—62no—
462C2×C3×C8—21no—
463C2×C3×C8—31no—
464C2×C3×C8—31no—
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—22no—
475#215—62no—
476#215—62no—
477#215—62no—
478#215—62no—
479#215—122no—
480#214—62no—
481#213—62no—
482#213—62no—
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—
496C2×C3⋊C8—31no—
497C2×C3⋊C8—31no—
498C2×C3⋊C8—61no—
499C2×C3⋊C8—62no—
500C2×C3⋊C8C22×D311yescharacteristic
501C2×C3⋊C8C22×D311yescharacteristic
502D24—62no—
503D24—62no—
504D24—62no—
505D24—62no—
506D24—122no—
507#204—22no—
508#204—62no—
509ΓL(1,𝔽25)—22no—
510D3×C8—62no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—21no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3—41no—
518C2×C3⋊D3—41no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
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#12012yes—
533D32—84no—
534D32—84no—
535D32—84no—
536C32×C4—22no—
537C32×C4—41no—
538C32×C4C22×D411yescharacteristic
539C32×C4C22×D411yescharacteristic
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—31no—
548C2×#41—31no—
549C2×#41—91no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—181no—
553C22×D4—91no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—181no—
557C22×D4—181no—
558C22×D4—181no—
559AGL(1,ℤ/8)—184no—
560#135—184no—
561C2×Q16—31no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—91no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—31no—
570C22×C8—91no—
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—31no—
581#103D3211yescharacteristic, complemented
582#102—31no—
583#102—31no—
584#102—31no—
585#102—91no—
586#102—91no—
587#102—91no—
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—31no—
593C23×C3—31no—
594C23×C3—61no—
595C23×C3—61no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—31no—
599C22×D3—31no—
600C22×D3—61no—
601C22×D3—64no—
602C22×D3—64no—
603C22×D3—64no—
604C22×D3—64no—
605C22×D3—64no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—64no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—241no—
614C22×D3—241no—
615C22×D3—241no—
616C22×D3—241no—
617C22×D3—241no—
618C22×D3—241no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3—241no—
625C22×D3D3×D411yescharacteristic
626C22×D3D3×D411yescharacteristic
627C3×Q8—21no—
628C3×Q8—21no—
629C3×Q8—22no—
630C3×Q8—41no—
631C3×Q8—61no—
632C3×Q8—61no—
633C3×Q8C2×D1212yes—
634C3×Q8D3×D412yes—
635C3×D4—32no—
636C3×D4—32no—
637C3×D4—64no—
638C3×D4—64no—
639C3×D4—61no—
640C3×D4—61no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—31no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—31no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—64no—
653C2×C3×C4—64no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—241no—
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661#67—62no—
662#67—64no—
663#67—62no—
664#67—64no—
665#67—64no—
666#67—62no—
667#67—64no—
668#67—62no—
669#67—122no—
670#67—241no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—31no—
674C2×Dic3—31no—
675C2×Dic3—61no—
676C2×Dic3D3×D411yescharacteristic
677C2×Dic3D3×D411yescharacteristic
678D12—24no—
679D12—24no—
680D12—21no—
681D12—21no—
682D12—32no—
683D12—32no—
684D12—62no—
685D12—64no—
686D12—64no—
687D12—62no—
688D12—64no—
689D12—64no—
690D12—62no—
691D12—61no—
692D12—61no—
693D12—61no—
694D12—61no—
695D12—61no—
696D12—61no—
697D12—121no—
698D12—121no—
699D12—121no—
700D12—124no—
701D12—122no—
702D12—241no—
703D12—241no—
704D12—242no—
705D12—241no—
706D12C2×D1212yes—
707D12D3×D412yes—
708C4×D3—24no—
709C4×D3—21no—
710C4×D3—21no—
711C4×D3—24no—
712C4×D3—64no—
713C4×D3—64no—
714C4×D3—61no—
715C4×D3—61no—
716C4×D3—61no—
717C4×D3—61no—
718C4×D3—81no—
719C4×D3—121no—
720C4×D3—121no—
721C4×D3—124no—
722C4×D3—122no—
723C4×D3—122no—
724C4×D3C2×D1212yes—
725C4×D3D3×D412yes—
726Dic6—21no—
727Dic6—21no—
728Dic6—62no—
729Dic6—62no—
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×C32C2×#12011yescharacteristic
741C2×C32#57611yescharacteristic
742C2×C32#57711yescharacteristic
743C3⋊D3—41no—
744C3⋊D3—42no—
745C3⋊D3—81no—
746C3×D3—22no—
747C3×D3—41no—
748C3×D3—42no—
749C3×D3—42no—
750C24—181no—
751C24—181no—
752C24—181no—
753#41—34no—
754#41—62no—
755#41—62no—
756#41—62no—
757#41—182no—
758#41—182no—
759#41—182no—
760#41—182no—
761#41—188no—
762#41—182no—
763#41—182no—
764C2×Q8—31no—
765C2×Q8—91no—
766C2×Q8C2×D3211yescharacteristic
767C2×D4—31no—
768C2×D4—31no—
769C2×D4—61no—
770C2×D4—61no—
771C2×D4—94no—
772C2×D4—91no—
773C2×D4—91no—
774C2×D4—91no—
775C2×D4—91no—
776C2×D4—91no—
777C2×D4—181no—
778C2×D4—181no—
779C2×D4—182no—
780C2×D4—181no—
781C2×D4—181no—
782C2×D4—182no—
783C2×D4—182no—
784C2×D4—188no—
785C2×D4—188no—
786C2×D4—181no—
787C2×D4—181no—
788C2×D4—181no—
789C2×D4—182no—
790C2×D4—182no—
791C2×D4—188no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—91no—
798C22×C4—181no—
799C22×C4—181no—
800Q16—62no—
801SD16—62no—
802SD16—182no—
803SD16—182no—
804SD16—182no—
805D8—182no—
806D8—182no—
807D8—182no—
808M16—62no—
809C2×C8—31no—
810C2×C8—31no—
811C2×C8—91no—
812C2×C8—182no—
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—21no—
824C22×C3—32no—
825C22×C3—61no—
826C22×C3—61no—
827C22×C3—62no—
828C22×C3—61no—
829C22×C3—61no—
830C22×C3—61no—
831C22×C3—62no—
832C22×C3—121no—
833C22×C3—121no—
834C22×C3—121no—
835C22×C3—121no—
836C22×C3C2×D3×D411yescharacteristic
837C22×C3C2×D3×D411yescharacteristic
838C2×D3—21no—
839C2×D3—21no—
840C2×D3—22no—
841C2×D3—21no—
842C2×D3—21no—
843C2×D3—21no—
844C2×D3—22no—
845C2×D3—41no—
846C2×D3—41no—
847C2×D3—41no—
848C2×D3—41no—
849C2×D3—62no—
850C2×D3—61no—
851C2×D3—61no—
852C2×D3—61no—
853C2×D3—61no—
854C2×D3—61no—
855C2×D3—62no—
856C2×D3—61no—
857C2×D3—122no—
858C2×D3—121no—
859C2×D3—121no—
860C2×D3—121no—
861C2×D3—121no—
862C2×D3—121no—
863C2×D3—121no—
864C2×D3—121no—
865C2×D3—121no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—241no—
872C2×D3—241no—
873C2×D3—241no—
874C2×D3—241no—
875C2×D3—241no—
876C2×D3—244no—
877C2×D3—244no—
878C2×D3—244no—
879C2×D3—244no—
880C2×D3—244no—
881C2×D3—244no—
882C2×D3#88212yes—
883C3×C4—22no—
884C3×C4—22no—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—32no—
888C3×C4—42no—
889C3×C4—41no—
890C3×C4—41no—
891C3×C4—61no—
892C3×C4—81no—
893C3×C4—121no—
894C3×C4—121no—
895C3×C4C22×D1211yescharacteristic
896C3×C4C2×D3×D411yescharacteristic
897C3×C4C2×D3×D411yescharacteristic
898C3×C4C2×D3×D411yescharacteristic
899Dic3—21no—
900Dic3—41no—
901Dic3—41no—
902Dic3—61no—
903Dic3—61no—
904Dic3—121no—
905Dic3#88212yes—
906C32#301211yescharacteristic, complemented, Sylow
907C23—31no—
908C23—31no—
909C23—61no—
910C23—61no—
911C23—91no—
912C23—184no—
913C23—184no—
914C23—184no—
915C23—181no—
916C23—181no—
917C23—721no—
918C23—721no—
919C23—721no—
920C23—721no—
921C23—721no—
922C23—721no—
923Q8—21no—
924Q8—61no—
925Q8—61no—
926Q8—182no—
927Q8D3×D1212yes—
928D4—32no—
929D4—32no—
930D4—64no—
931D4—64no—
932D4—61no—
933D4—61no—
934D4—92no—
935D4—184no—
936D4—184no—
937D4—182no—
938D4—182no—
939D4—184no—
940D4—182no—
941D4—184no—
942D4—181no—
943D4—181no—
944D4—181no—
945D4—362no—
946D4—721no—
947D4—721no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—31no—
951C2×C4—32no—
952C2×C4—32no—
953C2×C4—31no—
954C2×C4—64no—
955C2×C4—64no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—91no—
961C2×C4—184no—
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—62no—
975C2×C3—121no—
976C2×C3—122no—
977C2×C3—122no—
978C2×C3C2×#88211yescharacteristic
979C2×C3D3×#12011yescharacteristic
980C2×C3#576911yescharacteristic
981C2×C3#577411yescharacteristic
982C2×C3#577811yescharacteristic
983C2×C3#577811yescharacteristic
984D3—22no—
985D3—42no—
986D3—41no—
987D3—42no—
988D3—121no—
989D3—122no—
990D3—121no—
991D3—122no—
992D3—241no—
993D3—242no—
994D3—241no—
995D3—241no—
996D3—481no—
997C22—32no—
998C22—61no—
999C22—61no—
1000C22—61no—
1001C22—61no—
1002C22—62no—
1003C22—62no—
1004C22—61no—
1005C22—121no—
1006C22—121no—
1007C22—121no—
1008C22—121no—
1009C22—181no—
1010C22—181no—
1011C22—182no—
1012C22—181no—
1013C22—361no—
1014C22—361no—
1015C22—361no—
1016C22—361no—
1017C22—361no—
1018C22—724no—
1019C22—724no—
1020C22—724no—
1021C22D32×D411yescharacteristic
1022C4—22no—
1023C4—32no—
1024C4—41no—
1025C4—61no—
1026C4—121no—
1027C4—121no—
1028C4—181no—
1029C4C2×D3×D1211yescharacteristic
1030C4D32×D411yescharacteristic
1031C3—21no—
1032C3#7888611yescharacteristic, complemented
1033C3#8023111yescharacteristic, complemented
1034C2—62no—
1035C2—121no—
1036C2—122no—
1037C2—122no—
1038C2—361no—
1039C2—362no—
1040C2—721no—
1041C2D3×#88211yescharacteristic
1042C2#1059475511yescharacteristic
1043C2#1059476711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3012
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×#63949C2semidirect
3. C2×#63794C2semidirect
4. #10594523C2semidirect
5. #10592509C2semidirect
6. C3×#4808C2semidirect
7. C3×#4803C2semidirect
8. #10591602C2semidirect
9. #10591588C2semidirect
10. #10590955C2semidirect
11. #10590947C2semidirect
12. #10590943C2semidirect
13. #10590598C2semidirect
14. #10590596C2semidirect
15. D3×#809C2semidirect
29. C2×#3799C22semidirect
32. C2×#3755C22semidirect
33. C2×#3745C22semidirect
34. #64104C22semidirect
35. C2×C3×#216C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
38. C3×#897C22semidirect
39. C3×D3×C4⋊C4C22semidirect
43. #63909C22semidirect
46. #63871C22semidirect
47. C2×#3717C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
51. C2×D3×C3⋊C8C22semidirect
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. #4803D3semidirect
111. C3×#239D4semidirect
140. D3×D12D4semidirect
206. C2×#216C2×D3semidirect
228. C2×#204C2×D3semidirect
229. C2×ΓL(1,𝔽25)C2×D3semidirect
233. #897C2×D3semidirect
241. D3×C4⋊C4C2×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
394. #239D12semidirect
581. #103D32semidirect
906. C32#3012semidirect
1032. C3#78886semidirect
1033. C3#80231semidirect

Maximal subgroups

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

subgroupindex
C2×#643202
C2×#639492
C2×#637942
#105945232
#105925092
C3×#48082
C3×#48032
#105916022
#105915882
#105909552
#105909472
#105909432
#105905982
#105905962
D3×#8092
#802313
#788863