Finite Group Databasebeta

← C2×#10594755 #11918811

Subgroups — C2×#10594755 #11918811

Order 1152.

3173 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic, complemented
2C2×#64314C211yesmaximal, characteristic, complemented
3C2×#64123C211yesmaximal, characteristic, complemented
4C2×C3×#916C211yesmaximal, characteristic, complemented
5C2×C3×#914C211yesmaximal, characteristic, complemented
6C2×#63950C211yesmaximal, characteristic, complemented
7C2×#63949C211yesmaximal, characteristic, complemented
8C2×#63939C211yesmaximal, characteristic, complemented
9C2×#63926C211yesmaximal, characteristic, complemented
10C2×#63925C211yesmaximal, characteristic, complemented
11C2×D3×#213C211yesmaximal, characteristic, complemented
12#10594755C2116yesmaximal, direct product factor
13C2×#63804C211yesmaximal, characteristic, complemented
14C2×#63798C211yesmaximal, characteristic, complemented
15C2×#63794C211yesmaximal, characteristic, complemented
16C2×D3×D24C211yesmaximal, characteristic, complemented
17C2×#5774—31nomaximal
18C2×#5769—31nomaximal
19C2×#3832C2211yescharacteristic, complemented
20C2×D4×C3⋊D3C2211yescharacteristic, complemented
21C2×C3×#239C2211yescharacteristic, complemented
22C2×C3×#239C2211yescharacteristic, complemented
23C2×C3×#237C2211yescharacteristic, complemented
24C2×C3×D3×D4C2211yescharacteristic, complemented
25C2×#3811—21no—
26C2×D3×#67—21no—
27C22×#626—21no—
28C2×#3804—21no—
29#64320—24no—
30#64320C2218yescomplemented
31#64314—24no—
32#64314C2218yescomplemented
33C2×#3802—21no—
34C2×#3802C2211yescharacteristic, complemented
35C2×D3×D12—21no—
36C2×D3×D12—21no—
37C2×D3×D12C2211yescharacteristic, complemented
38C2×D3×D12C2211yescharacteristic, complemented
39C2×D3×D12C2211yescharacteristic, complemented
40C2×#3799C2211yescharacteristic, complemented
41C2×#3798—21no—
42C2×#3798C2211yescharacteristic
43C2×#3796C2211yescharacteristic, complemented
44C2×C32×SD16C2211yescharacteristic, complemented
45C2×#3755C2211yescharacteristic, complemented
46C2×#3753C2211yescharacteristic, complemented
47#64123C2218yescomplemented
48C2×#3745C2211yescharacteristic, complemented
49C2×#3743C2211yescharacteristic, complemented
50C2×C3×#216C2211yescharacteristic, complemented
51C2×C3×#215C2211yescharacteristic, complemented
52C2×C3×#213C2211yescharacteristic, complemented
53C2×C3×#213C2211yescharacteristic, complemented
54C3×#916C2218yescomplemented
55C3×#914C2218yescomplemented
56C2×C3×D24C2211yescharacteristic, complemented
57C2×C3×#204C2211yescharacteristic, complemented
58C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
59C2×C3×D3×C8C2211yescharacteristic, complemented
60#63950C2218yescomplemented
61#63949C2218yescomplemented
62#63939C2218yescomplemented
63#63926C2218yescomplemented
64#63925C2218yescomplemented
65D3×#213C2218yescomplemented
66C2×#3717C2211yescharacteristic, complemented
67C2×#3715C2211yescharacteristic, complemented
68C2×#3714C2211yescharacteristic, complemented
69C2×#3714C2211yescharacteristic, complemented
70C2×#3714C2211yescharacteristic, complemented
71C2×#3713C2211yescharacteristic, complemented
72C2×#3711C2211yescharacteristic, complemented
73C2×#3710C2211yescharacteristic, complemented
74C2×D3×C3⋊C8C2211yescharacteristic, complemented
75#63804C2218yescomplemented
76#63798C2218yescomplemented
77#63794C2218yescomplemented
78D3×D24C2218yescomplemented
79C2×#1009—31no—
80C2×#1009—31no—
81C2×#1009—31no—
82C2×#1004—31no—
83C2×C3×AGL(1,ℤ/8)—31no—
84C2×C3×#135—31no—
85C2×#950—31no—
86C2×#949—31no—
87C2×#949—31no—
88C22×#213—31no—
89#5774—316no—
90#5769—316no—
91C2×#919—31no—
92C2×#919—31no—
93C2×#916—31no—
94C2×#916D311yescharacteristic, complemented
95C2×#914—31no—
96C2×#914—31no—
97C2×#914—31no—
98C2×#914—31no—
99C2×#914—31no—
100C2×#914—61no—
101C2×#914D311yescharacteristic, complemented
102C2×#911—31no—
103C2×#911—31no—
104C2×D3×D8—31no—
105C2×D3×D8—31no—
106C2×D3×D8—31no—
107C2×D3×D8—31no—
108C2×#908—31no—
109C2×#907—31no—
110C22×D24—31no—
111C2×#901—31no—
112C23×C3⋊D3—21no—
113C23×C3×D3—21no—
114C22×D32—21no—
115C22×D32—21no—
116C22×D32—21no—
117C22×D32—21no—
118C2×C32×Q8C2311yescharacteristic
119C2×C32×D4C2311yescharacteristic
120C2×#638—21no—
121#3832—22no—
122#3832C2314yescomplemented
123D4×C3⋊D3—22no—
124D4×C3⋊D3C2314yescomplemented
125C2×C4⋊(C3⋊D3)—21no—
126C2×C4⋊(C3⋊D3)C2311yescharacteristic
127C2×C4⋊(C3⋊D3)C2311yescharacteristic
128C2×C4×C3⋊D3—21no—
129C2×C4×C3⋊D3C2311yescharacteristic
130C2×C3×#67—21no—
131C2×C3×#67—21no—
132C22×C3×Dic3—21no—
133C3×#239—22no—
134C3×#239—22no—
135C3×#239C2314yescomplemented
136C3×#239C2314yescomplemented
137C3×#237—22no—
138C3×#237C2314yescomplemented
139C3×D3×D4—22no—
140C3×D3×D4C2314yescomplemented
141C2×C3×D12—21no—
142C2×C3×D12—21no—
143C2×C3×D12C2311yescharacteristic
144C2×C3×D12C2311yescharacteristic
145C2×C3×D12C2311yescharacteristic
146C2×C3×C4×D3—21no—
147C2×C3×C4×D3—21no—
148C2×C3×C4×D3C2311yescharacteristic
149C2×C3×C4×D3C2311yescharacteristic
150C2×C3×Dic6C2311yescharacteristic
151#3811—28no—
152D3×#67—28no—
153C2×#627D411yescharacteristic
154C2×#626—21no—
155C2×#626—21no—
156C2×#626—21no—
157C2×#626—21no—
158C2×#626—21no—
159C2×#626—28no—
160C2×#626D411yescharacteristic
161C2×#626D411yescharacteristic
162C2×#625—21no—
163C2×#625D411yescharacteristic
164C2×#624—21no—
165#3804—28no—
166C2×D3×Dic3—21no—
167#3802—22no—
168#3802—28no—
169#3802C2314yescomplemented
170D3×D12—22no—
171D3×D12—22no—
172D3×D12—22no—
173D3×D12—28no—
174D3×D12—28no—
175D3×D12C2314yescomplemented
176D3×D12C2314yescomplemented
177D3×D12C2314yescomplemented
178#3799—22no—
179#3799C2314yescomplemented
180#3798—28no—
181#3798D414yes—
182#3798C2314yes—
183#3796—22no—
184#3796C2314yescomplemented
185C32×SD16C2314yescomplemented
186C2×C32×C8C2311yescharacteristic
187#3755C2314yescomplemented
188#3753C2314yescomplemented
189C2×C3⋊(C3⋊C8)C2311yescharacteristic
190#3745C2314yescomplemented
191#3743C2314yescomplemented
192C3×#216C2314yescomplemented
193C3×#215C2314yescomplemented
194C3×#213C2314yescomplemented
195C3×#213C2314yescomplemented
196C2×C3×C3⋊C8C2311yescharacteristic
197C2×C3×C3⋊C8C2311yescharacteristic
198C3×D24C2314yescomplemented
199C3×#204C2314yescomplemented
200C3×ΓL(1,𝔽25)C2314yescomplemented
201C3×D3×C8C2314yescomplemented
202#3717C2314yescomplemented
203#3715C2314yescomplemented
204#3714C2314yescomplemented
205#3714C2314yescomplemented
206#3714C2314yescomplemented
207#3713C2314yescomplemented
208#3711C2314yescomplemented
209#3710C2314yescomplemented
210D3×C3⋊C8C2314yescomplemented
211C2×#576—91noSylow
212C2×C3×#41—31no—
213C2×C3×#41—31no—
214C2×C3×#41—31no—
215C22×C3×D4—31no—
216C22×#67—61no—
217C22×#67—61no—
218#1009—38no—
219#1009—38no—
220#1009—38no—
221#1009—64no—
222#1009—64no—
223#1009—64no—
224C2×#239—31no—
225C2×#239—31no—
226C2×#239—31no—
227C2×#239—31no—
228C2×#239—61no—
229C2×#239C2×D311yescharacteristic, complemented
230C2×#239C2×D311yescharacteristic, complemented
231#1004—38no—
232#1004—64no—
233C2×#237—31no—
234C2×#237—61no—
235C2×#237C2×D311yescharacteristic, complemented
236C2×D3×D4—31no—
237C2×D3×D4—31no—
238C2×D3×D4—31no—
239C2×D3×D4—31no—
240C2×D3×D4—31no—
241C2×D3×D4—31no—
242C2×D3×D4—31no—
243C2×D3×D4—61no—
244C2×D3×D4—61no—
245C2×D3×D4—61no—
246C2×D3×D4—61no—
247C2×D3×D4—61no—
248C2×D3×D4—61no—
249C2×D3×D4—61no—
250C2×D3×D4—61no—
251C2×D3×D4C2×D311yescharacteristic, complemented
252C2×#235—31no—
253C2×#235—31no—
254C2×#235—31no—
255C2×#235—61no—
256C2×#235—61no—
257C2×#235—61no—
258C22×D12—31no—
259C22×D12—31no—
260C22×D12—31no—
261C22×D12—61no—
262C22×D12—61no—
263C22×D12—61no—
264C3×AGL(1,ℤ/8)—38no—
265C3×#135—38no—
266C2×C3×Q16—31no—
267C2×C3×SD16—21no—
268C2×C3×SD16—31no—
269C2×C3×SD16—31no—
270C2×C3×SD16C2×D311yescharacteristic, complemented
271C2×C3×SD16C2×D311yescharacteristic, complemented
272C2×C3×D8—31no—
273C2×C3×D8—31no—
274C2×C3×D8—31no—
275C2×C3×M16—31no—
276C22×C3×C8—31no—
277#950—38no—
278#949—38no—
279#949—38no—
280C2×#216C2×D311yescharacteristic, complemented
281C2×#215—31no—
282C2×#215—31no—
283C2×#215—31no—
284C2×#215—31no—
285C2×#215—61no—
286C2×#215C2×D311yescharacteristic, complemented
287C2×#214—31no—
288C2×#213—31no—
289C2×#213—31no—
290C2×#213—31no—
291C2×#213—31no—
292C2×#213—38no—
293C2×#213—31no—
294C2×#213—31no—
295C2×#213—31no—
296C2×#213—61no—
297C2×#213C2×D311yescharacteristic, complemented
298C2×#213C2×D311yescharacteristic, complemented
299C2×#208—31no—
300C22×C3⋊C8—31no—
301#919—38no—
302#919—38no—
303#916—38no—
304#916C2×D318yescomplemented
305#914—38no—
306#914—38no—
307#914—38no—
308#914—38no—
309#914—38no—
310#914—68no—
311#914C2×D318yescomplemented
312#911—38no—
313#911—38no—
314D3×D8—38no—
315D3×D8—38no—
316D3×D8—38no—
317D3×D8—38no—
318#908—38no—
319#907—38no—
320C2×D24—31no—
321C2×D24—31no—
322C2×D24—31no—
323C2×D24—31no—
324C2×D24—31no—
325C2×D24—38no—
326C2×D24—61no—
327C2×D24C2×D311yescharacteristic, complemented
328C2×#204—31no—
329C2×#204C2×D311yescharacteristic, complemented
330#901—38no—
331C2×ΓL(1,𝔽25)—31no—
332C2×ΓL(1,𝔽25)—31no—
333C2×ΓL(1,𝔽25)—31no—
334C2×ΓL(1,𝔽25)—61no—
335C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
336C2×D3×C8—31no—
337C2×D3×C8—31no—
338C2×D3×C8—31no—
339C2×D3×C8C2×D311yescharacteristic, complemented
340C23×C32—21no—
341C22×C3⋊D3—21no—
342C22×C3⋊D3—21no—
343C22×C3⋊D3—24no—
344C22×C3⋊D3—82no—
345C22×C3⋊D3C2×D411yescharacteristic
346C22×C3×D3—21no—
347C22×C3×D3—21no—
348C22×C3×D3—21no—
349C22×C3×D3—24no—
350C22×C3×D3—82no—
351C22×C3×D3C2×D411yescharacteristic
352C22×C3×D3C2×D411yescharacteristic
353C2×D32—24no—
354C2×D32—24no—
355C2×D32—24no—
356C2×D32—24no—
357C2×D32—82no—
358C2×D32—82no—
359C2×D32—82no—
360C2×D32—82no—
361C32×Q8—21no—
362C32×Q8C2412yes—
363C32×D4—21no—
364C32×D4C2412yes—
365C2×C32×C4—21no—
366C2×C32×C4C2411yescharacteristic
367#638—24no—
368C2×C3⋊Dic3C2×D411yescharacteristic
369C4⋊(C3⋊D3)—24no—
370C4⋊(C3⋊D3)—21no—
371C4⋊(C3⋊D3)—21no—
372C4⋊(C3⋊D3)C2412yes—
373C4⋊(C3⋊D3)C2412yes—
374C4×C3⋊D3—24no—
375C4×C3⋊D3C2×D412yes—
376C4×C3⋊D3C2412yes—
377C3×#67—24no—
378C3×#67—24no—
379C2×C3×Dic3—21no—
380C2×C3×Dic3—24no—
381C2×C3×Dic3C2×D411yescharacteristic
382C2×C3×Dic3C2×D411yescharacteristic
383C3×D12—24no—
384C3×D12—24no—
385C3×D12—21no—
386C3×D12—21no—
387C3×D12—21no—
388C3×D12C2412yes—
389C3×D12C2412yes—
390C3×D12C2412yes—
391C3×C4×D3—24no—
392C3×C4×D3—24no—
393C3×C4×D3C2×D412yes—
394C3×C4×D3C2×D412yes—
395C3×C4×D3C2412yes—
396C3×C4×D3C2412yes—
397C3×Dic6—21no—
398C3×Dic6C2412yes—
399#627C2×D414yes—
400#626—24no—
401#626—24no—
402#626—24no—
403#626—24no—
404#626—24no—
405#626C2×D414yes—
406#626C2×D414yes—
407#625—24no—
408#625C2×D414yes—
409#624—24no—
410D3×Dic3—24no—
411C32×C8C2412yes—
412C3⋊(C3⋊C8)C2412yes—
413C3×C3⋊C8C2412yes—
414C3×C3⋊C8C2412yes—
415C2×H(5,𝔽2)—91no—
416C2×H(5,𝔽2)—91no—
417#576—916no—
418C2×AGL(1,ℤ/8)—31no—
419C2×AGL(1,ℤ/8)—91no—
420C2×AGL(1,ℤ/8)—91no—
421C2×AGL(1,ℤ/8)—91no—
422C2×AGL(1,ℤ/8)—91no—
423C2×AGL(1,ℤ/8)—91no—
424C2×#135—31no—
425C2×#135—91no—
426C2×#135—91no—
427C22×D8—91no—
428C22×D8—91no—
429C22×D8—91no—
430C2×#131—91no—
431C24×C3—61no—
432C23×D3—21no—
433C23×D3—61no—
434C23×D3—61no—
435C23×D3—61no—
436C23×D3—61no—
437C23×D3—61no—
438C23×D3—61no—
439C23×D3—61no—
440C23×D3—61no—
441C23×D3—61no—
442C23×D3—61no—
443C23×D3—121no—
444C3×#41—34no—
445C3×#41—34no—
446C3×#41—34no—
447C3×#41—62no—
448C3×#41—62no—
449C3×#41—62no—
450C2×C3×Q8—21no—
451C2×C3×Q8—31no—
452C2×C3×Q8C22×D311yescharacteristic
453C2×C3×Q8C22×D311yescharacteristic
454C2×C3×D4—21no—
455C2×C3×D4—34no—
456C2×C3×D4—31no—
457C2×C3×D4—31no—
458C2×C3×D4—31no—
459C2×C3×D4—61no—
460C2×C3×D4—61no—
461C2×C3×D4—62no—
462C2×C3×D4—61no—
463C2×C3×D4—61no—
464C2×C3×D4C22×D311yescharacteristic
465C2×C3×D4C22×D311yescharacteristic
466C22×C3×C4—31no—
467C22×C3×C4—31no—
468C22×C3×C4—61no—
469C22×C3×C4—61no—
470C22×C3×C4—61no—
471C2×#67—21no—
472C2×#67—21no—
473C2×#67—31no—
474C2×#67—31no—
475C2×#67—31no—
476C2×#67—31no—
477C2×#67—68no—
478C2×#67—61no—
479C2×#67—61no—
480C2×#67—61no—
481C2×#67—61no—
482C2×#67—61no—
483C2×#67—61no—
484C2×#67—68no—
485C2×#67—61no—
486C2×#67—61no—
487C2×#67—61no—
488C2×#67—121no—
489C22×Dic3—21no—
490C22×Dic3—61no—
491#239—22no—
492#239—22no—
493#239—34no—
494#239—34no—
495#239—34no—
496#239—34no—
497#239—64no—
498#239—62no—
499#239—62no—
500#239—62no—
501#239—62no—
502#239—122no—
503#239C22×D314yescomplemented
504#239C22×D314yescomplemented
505#237—22no—
506#237—34no—
507#237—62no—
508#237—68no—
509#237C22×D314yescomplemented
510D3×D4—22no—
511D3×D4—34no—
512D3×D4—34no—
513D3×D4—34no—
514D3×D4—34no—
515D3×D4—34no—
516D3×D4—34no—
517D3×D4—34no—
518D3×D4—64no—
519D3×D4—68no—
520D3×D4—68no—
521D3×D4—62no—
522D3×D4—62no—
523D3×D4—62no—
524D3×D4—62no—
525D3×D4—68no—
526D3×D4—68no—
527D3×D4—68no—
528D3×D4—68no—
529D3×D4—68no—
530D3×D4—62no—
531D3×D4—62no—
532D3×D4—62no—
533D3×D4—122no—
534D3×D4C22×D314yescomplemented
535#235—34no—
536#235—34no—
537#235—34no—
538#235—34no—
539#235—34no—
540#235—62no—
541#235—68no—
542#235—68no—
543#235—68no—
544C2×D12—21no—
545C2×D12—21no—
546C2×D12—31no—
547C2×D12—31no—
548C2×D12—31no—
549C2×D12—31no—
550C2×D12—31no—
551C2×D12—31no—
552C2×D12—34no—
553C2×D12—34no—
554C2×D12—34no—
555C2×D12—61no—
556C2×D12—61no—
557C2×D12—68no—
558C2×D12—68no—
559C2×D12—62no—
560C2×D12—62no—
561C2×D12—62no—
562C2×D12—68no—
563C2×D12—61no—
564C2×D12—61no—
565C2×D12—61no—
566C2×D12—61no—
567C2×D12—61no—
568C2×D12—61no—
569C2×D12—61no—
570C2×D12—121no—
571C2×D12C22×D311yescharacteristic
572C2×D12C22×D311yescharacteristic
573C2×D12C22×D311yescharacteristic
574C2×C4×D3—21no—
575C2×C4×D3—21no—
576C2×C4×D3—31no—
577C2×C4×D3—31no—
578C2×C4×D3—61no—
579C2×C4×D3—61no—
580C2×C4×D3—61no—
581C2×C4×D3—61no—
582C2×C4×D3—61no—
583C2×C4×D3—61no—
584C2×C4×D3—121no—
585C2×C4×D3C22×D311yescharacteristic
586C2×C4×D3C22×D311yescharacteristic
587C2×Dic6—31no—
588C2×Dic6—31no—
589C2×Dic6C22×D311yescharacteristic
590C3×Q16—34no—
591C3×SD16—24no—
592C3×SD16—34no—
593C3×SD16—34no—
594C3×SD16C22×D314yescomplemented
595C3×SD16C22×D314yescomplemented
596C3×D8—34no—
597C3×D8—34no—
598C3×D8—34no—
599C3×M16—34no—
600C2×C3×C8—21no—
601C2×C3×C8—31no—
602C2×C3×C8—31no—
603C2×C3×C8—34no—
604C2×C3×C8C22×D311yescharacteristic
605C2×C3×C8C22×D311yescharacteristic
606#216C22×D314yescomplemented
607#215—34no—
608#215—34no—
609#215—34no—
610#215—34no—
611#215—64no—
612#215C22×D314yescomplemented
613#214—34no—
614#213—34no—
615#213—34no—
616#213—34no—
617#213—34no—
618#213—34no—
619#213—34no—
620#213—34no—
621#213—64no—
622#213C22×D314yescomplemented
623#213C22×D314yescomplemented
624#208—34no—
625C2×C3⋊C8—31no—
626C2×C3⋊C8—31no—
627C2×C3⋊C8—34no—
628C2×C3⋊C8—61no—
629C2×C3⋊C8C22×D311yescharacteristic
630C2×C3⋊C8C22×D311yescharacteristic
631D24—34no—
632D24—34no—
633D24—34no—
634D24—34no—
635D24—34no—
636D24—64no—
637D24C22×D314yescomplemented
638#204—34no—
639#204C22×D314yescomplemented
640ΓL(1,𝔽25)—34no—
641ΓL(1,𝔽25)—34no—
642ΓL(1,𝔽25)—34no—
643ΓL(1,𝔽25)—64no—
644ΓL(1,𝔽25)C22×D314yescomplemented
645D3×C8—34no—
646D3×C8—34no—
647D3×C8—34no—
648D3×C8C22×D314yescomplemented
649C22×C32—22no—
650C22×C32—42no—
651C22×C32C22×D411yescharacteristic
652C2×C3⋊D3—22no—
653C2×C3⋊D3—22no—
654C2×C3⋊D3—22no—
655C2×C3⋊D3—42no—
656C2×C3⋊D3—42no—
657C2×C3⋊D3—84no—
658C2×C3⋊D3C22×D412yes—
659C2×C3×D3—22no—
660C2×C3×D3—22no—
661C2×C3×D3—22no—
662C2×C3×D3—22no—
663C2×C3×D3—22no—
664C2×C3×D3—42no—
665C2×C3×D3—42no—
666C2×C3×D3—42no—
667C2×C3×D3—84no—
668C2×C3×D3C22×D412yes—
669C2×C3×D3C22×D412yes—
670D32—84no—
671D32—84no—
672D32—84no—
673D32—84no—
674C32×C4—22no—
675C32×C4C22×D411yescharacteristic
676C32×C4C2511yescharacteristic
677C3⋊Dic3C22×D412yes—
678C3×Dic3—22no—
679C3×Dic3C22×D412yes—
680C3×Dic3C22×D412yes—
681H(5,𝔽2)—98no—
682H(5,𝔽2)—98no—
683H(5,𝔽2)—184no—
684H(5,𝔽2)—184no—
685C2×#41—31no—
686C2×#41—31no—
687C2×#41—31no—
688C2×#41—91no—
689C2×#41—91no—
690C2×#41—91no—
691C2×#41—91no—
692C2×#41—181no—
693C2×#41—181no—
694C22×D4—31no—
695C22×D4—91no—
696C22×D4—91no—
697C22×D4—91no—
698C22×D4—91no—
699C22×D4—91no—
700C22×D4—181no—
701C22×D4—181no—
702C22×D4—181no—
703C22×D4—181no—
704C22×D4—181no—
705C22×D4—181no—
706AGL(1,ℤ/8)—38no—
707AGL(1,ℤ/8)—98no—
708AGL(1,ℤ/8)—98no—
709AGL(1,ℤ/8)—98no—
710AGL(1,ℤ/8)—98no—
711AGL(1,ℤ/8)—98no—
712#135—38no—
713#135—98no—
714#135—98no—
715C2×Q16—31no—
716C2×SD16—31no—
717C2×SD16—31no—
718C2×SD16—91no—
719C2×SD16—91no—
720C2×SD16—91no—
721C2×SD16D3211yescharacteristic, complemented
722C2×D8—31no—
723C2×D8—31no—
724C2×D8—31no—
725C2×D8—98no—
726C2×D8—91no—
727C2×D8—91no—
728C2×D8—91no—
729C2×D8—98no—
730C2×D8—98no—
731C2×D8—91no—
732C2×D8—91no—
733C2×D8—91no—
734#131—98no—
735C2×M16—31no—
736C2×M16—91no—
737C2×M16—91no—
738C22×C8—31no—
739C22×C8—91no—
740C22×C8—91no—
741C23×C3—21no—
742C23×C3—21no—
743C23×C3—31no—
744C23×C3—31no—
745C23×C3—41no—
746C23×C3—64no—
747C23×C3—61no—
748C23×C3—61no—
749C23×C3—61no—
750C23×C3—242no—
751C22×D3—21no—
752C22×D3—21no—
753C22×D3—21no—
754C22×D3—24no—
755C22×D3—31no—
756C22×D3—31no—
757C22×D3—61no—
758C22×D3—64no—
759C22×D3—64no—
760C22×D3—64no—
761C22×D3—64no—
762C22×D3—64no—
763C22×D3—64no—
764C22×D3—64no—
765C22×D3—61no—
766C22×D3—61no—
767C22×D3—61no—
768C22×D3—61no—
769C22×D3—64no—
770C22×D3—64no—
771C22×D3—64no—
772C22×D3—82no—
773C22×D3—124no—
774C22×D3—121no—
775C22×D3—121no—
776C22×D3—242no—
777C22×D3—242no—
778C22×D3—242no—
779C22×D3—242no—
780C22×D3—242no—
781C22×D3—242no—
782C22×D3—242no—
783C22×D3—242no—
784C22×D3—242no—
785C22×D3—242no—
786C22×D3—244no—
787C22×D3D3×D411yescharacteristic
788C22×D3D3×D411yescharacteristic
789C3×Q8—21no—
790C3×Q8—21no—
791C3×Q8—22no—
792C3×Q8—32no—
793C3×Q8—41no—
794C3×Q8—61no—
795C3×Q8C23×D312yes—
796C3×Q8C23×D312yes—
797C3×D4—21no—
798C3×D4—21no—
799C3×D4—22no—
800C3×D4—32no—
801C3×D4—32no—
802C3×D4—32no—
803C3×D4—41no—
804C3×D4—64no—
805C3×D4—64no—
806C3×D4—64no—
807C3×D4—64no—
808C3×D4—61no—
809C3×D4—61no—
810C3×D4—61no—
811C3×D4C23×D312yes—
812C3×D4C23×D312yes—
813C2×C3×C4—21no—
814C2×C3×C4—21no—
815C2×C3×C4—21no—
816C2×C3×C4—31no—
817C2×C3×C4—31no—
818C2×C3×C4—32no—
819C2×C3×C4—32no—
820C2×C3×C4—32no—
821C2×C3×C4—32no—
822C2×C3×C4—41no—
823C2×C3×C4—64no—
824C2×C3×C4—64no—
825C2×C3×C4—64no—
826C2×C3×C4—61no—
827C2×C3×C4C23×D311yescharacteristic
828C2×C3×C4C23×D311yescharacteristic
829#67—24no—
830#67—24no—
831#67—34no—
832#67—34no—
833#67—34no—
834#67—34no—
835#67—64no—
836#67—64no—
837#67—64no—
838#67—64no—
839#67—64no—
840#67—64no—
841#67—64no—
842#67—64no—
843#67—64no—
844#67—124no—
845C2×Dic3—21no—
846C2×Dic3—24no—
847C2×Dic3—31no—
848C2×Dic3—31no—
849C2×Dic3—61no—
850C2×Dic3—64no—
851C2×Dic3D3×D411yescharacteristic
852C2×Dic3D3×D411yescharacteristic
853D12—24no—
854D12—24no—
855D12—21no—
856D12—21no—
857D12—21no—
858D12—34no—
859D12—34no—
860D12—32no—
861D12—32no—
862D12—32no—
863D12—32no—
864D12—62no—
865D12—62no—
866D12—64no—
867D12—64no—
868D12—64no—
869D12—64no—
870D12—64no—
871D12—64no—
872D12—64no—
873D12—61no—
874D12—61no—
875D12—61no—
876D12—61no—
877D12—121no—
878D12—121no—
879D12—124no—
880D12C23×D312yes—
881D12C23×D312yes—
882D12C23×D312yes—
883C4×D3—24no—
884C4×D3—24no—
885C4×D3—32no—
886C4×D3—32no—
887C4×D3—32no—
888C4×D3—32no—
889C4×D3—62no—
890C4×D3—62no—
891C4×D3—64no—
892C4×D3—64no—
893C4×D3—64no—
894C4×D3—64no—
895C4×D3—64no—
896C4×D3—124no—
897C4×D3D3×D412yes—
898C4×D3D3×D412yes—
899C4×D3C23×D312yes—
900C4×D3C23×D312yes—
901Dic6—21no—
902Dic6—34no—
903Dic6—34no—
904Dic6C23×D312yes—
905C3×C8—22no—
906C3×C8—32no—
907C3×C8—32no—
908C3×C8C23×D312yes—
909C3×C8C23×D312yes—
910C3⋊C8—32no—
911C3⋊C8—32no—
912C3⋊C8—62no—
913C3⋊C8C23×D312yes—
914C3⋊C8C23×D312yes—
915C2×C32—42no—
916C2×C32#57612yescomplemented
917C2×C32C23×D411yescharacteristic
918C3⋊D3—22no—
919C3⋊D3—42no—
920C3⋊D3—42no—
921C3×D3—22no—
922C3×D3—22no—
923C3×D3—42no—
924C3×D3—42no—
925C3×D3—42no—
926C24—61no—
927C24—181no—
928C24—181no—
929C24—181no—
930C24—181no—
931C24—181no—
932#41—34no—
933#41—34no—
934#41—34no—
935#41—62no—
936#41—62no—
937#41—62no—
938#41—94no—
939#41—94no—
940#41—94no—
941#41—94no—
942#41—94no—
943#41—182no—
944#41—188no—
945#41—188no—
946#41—182no—
947#41—182no—
948C2×Q8—31no—
949C2×Q8—91no—
950C2×Q8C2×D3211yescharacteristic
951C2×D4—34no—
952C2×D4—31no—
953C2×D4—31no—
954C2×D4—31no—
955C2×D4—61no—
956C2×D4—61no—
957C2×D4—62no—
958C2×D4—61no—
959C2×D4—61no—
960C2×D4—94no—
961C2×D4—94no—
962C2×D4—94no—
963C2×D4—91no—
964C2×D4—91no—
965C2×D4—94no—
966C2×D4—91no—
967C2×D4—94no—
968C2×D4—91no—
969C2×D4—91no—
970C2×D4—181no—
971C2×D4—182no—
972C2×D4—182no—
973C2×D4—182no—
974C2×D4—181no—
975C2×D4—181no—
976C2×D4—181no—
977C2×D4—188no—
978C2×D4—188no—
979C2×D4—188no—
980C2×D4—181no—
981C2×D4—181no—
982C2×D4—182no—
983C2×D4—182no—
984C2×D4—181no—
985C2×D4—181no—
986C2×D4—188no—
987C2×D4—188no—
988C2×D4—188no—
989C2×D4C2×D3211yescharacteristic
990C22×C4—31no—
991C22×C4—31no—
992C22×C4—61no—
993C22×C4—61no—
994C22×C4—61no—
995C22×C4—91no—
996C22×C4—181no—
997C22×C4—181no—
998C22×C4—181no—
999Q16—34no—
1000SD16—34no—
1001SD16—34no—
1002SD16—94no—
1003SD16—94no—
1004SD16—94no—
1005SD16C2×D3214yescomplemented
1006D8—34no—
1007D8—34no—
1008D8—34no—
1009D8—94no—
1010D8—94no—
1011D8—94no—
1012D8—94no—
1013D8—94no—
1014D8—94no—
1015M16—34no—
1016M16—94no—
1017M16—94no—
1018C2×C8—31no—
1019C2×C8—31no—
1020C2×C8—34no—
1021C2×C8—94no—
1022C2×C8—94no—
1023C2×C8—91no—
1024C2×C8C2×D3211yescharacteristic
1025C22×C3—22no—
1026C22×C3—22no—
1027C22×C3—21no—
1028C22×C3—32no—
1029C22×C3—32no—
1030C22×C3—42no—
1031C22×C3—42no—
1032C22×C3—42no—
1033C22×C3—62no—
1034C22×C3—62no—
1035C22×C3—62no—
1036C22×C3—62no—
1037C22×C3—62no—
1038C22×C3—82no—
1039C22×C3—122no—
1040C22×C3—122no—
1041C22×C3—122no—
1042C22×C3—244no—
1043C22×C3C2×D3×D411yescharacteristic
1044C22×C3C2×D3×D411yescharacteristic
1045C2×D3—22no—
1046C2×D3—22no—
1047C2×D3—22no—
1048C2×D3—22no—
1049C2×D3—22no—
1050C2×D3—32no—
1051C2×D3—32no—
1052C2×D3—42no—
1053C2×D3—42no—
1054C2×D3—42no—
1055C2×D3—62no—
1056C2×D3—62no—
1057C2×D3—62no—
1058C2×D3—62no—
1059C2×D3—62no—
1060C2×D3—62no—
1061C2×D3—62no—
1062C2×D3—84no—
1063C2×D3—122no—
1064C2×D3—122no—
1065C2×D3—122no—
1066C2×D3—122no—
1067C2×D3—122no—
1068C2×D3—122no—
1069C2×D3—122no—
1070C2×D3—242no—
1071C2×D3—242no—
1072C2×D3—244no—
1073C2×D3—244no—
1074C2×D3—244no—
1075C2×D3—244no—
1076C2×D3—244no—
1077C2×D3—244no—
1078C2×D3—244no—
1079C2×D3—244no—
1080C2×D3—244no—
1081C2×D3—244no—
1082C2×D3—248no—
1083C2×D3C2×D3×D412yes—
1084C2×D3C2×D3×D412yes—
1085C3×C4—22no—
1086C3×C4—22no—
1087C3×C4—21no—
1088C3×C4—21no—
1089C3×C4—32no—
1090C3×C4—32no—
1091C3×C4—42no—
1092C3×C4—62no—
1093C3×C4C2×D3×D411yescharacteristic
1094C3×C4C2×D3×D411yescharacteristic
1095C3×C4C24×D311yescharacteristic
1096C3×C4C24×D311yescharacteristic
1097Dic3—22no—
1098Dic3—32no—
1099Dic3—32no—
1100Dic3—62no—
1101Dic3C2×D3×D412yes—
1102Dic3C2×D3×D412yes—
1103C32C2×#57611yescharacteristic, complemented, Sylow
1104C23—21no—
1105C23—31no—
1106C23—31no—
1107C23—64no—
1108C23—61no—
1109C23—61no—
1110C23—61no—
1111C23—91no—
1112C23—184no—
1113C23—184no—
1114C23—184no—
1115C23—184no—
1116C23—184no—
1117C23—181no—
1118C23—181no—
1119C23—242no—
1120C23—722no—
1121C23—722no—
1122C23—722no—
1123C23—722no—
1124C23—722no—
1125Q8—21no—
1126Q8—32no—
1127Q8—61no—
1128Q8—94no—
1129Q8C22×D3212yes—
1130D4—21no—
1131D4—32no—
1132D4—32no—
1133D4—32no—
1134D4—64no—
1135D4—64no—
1136D4—64no—
1137D4—64no—
1138D4—61no—
1139D4—61no—
1140D4—61no—
1141D4—94no—
1142D4—94no—
1143D4—94no—
1144D4—92no—
1145D4—92no—
1146D4—184no—
1147D4—184no—
1148D4—184no—
1149D4—184no—
1150D4—184no—
1151D4—184no—
1152D4—184no—
1153D4—184no—
1154D4—181no—
1155D4—181no—
1156D4C22×D3212yes—
1157C2×C4—21no—
1158C2×C4—31no—
1159C2×C4—31no—
1160C2×C4—32no—
1161C2×C4—32no—
1162C2×C4—32no—
1163C2×C4—32no—
1164C2×C4—64no—
1165C2×C4—64no—
1166C2×C4—64no—
1167C2×C4—61no—
1168C2×C4—91no—
1169C2×C4—92no—
1170C2×C4—92no—
1171C2×C4—184no—
1172C2×C4—184no—
1173C2×C4—184no—
1174C2×C4C22×D3211yescharacteristic
1175C8—32no—
1176C8—32no—
1177C8—92no—
1178C8C22×D3212yes—
1179C2×C3—21no—
1180C2×C3—22no—
1181C2×C3—42no—
1182C2×C3—42no—
1183C2×C3—62no—
1184C2×C3—62no—
1185C2×C3—82no—
1186C2×C3—122no—
1187C2×C3—122no—
1188C2×C3—122no—
1189C2×C3#576912yescomplemented
1190C2×C3#577412yescomplemented
1191C2×C3C22×D3×D411yescharacteristic
1192C2×C3C22×D3×D411yescharacteristic
1193D3—22no—
1194D3—22no—
1195D3—42no—
1196D3—42no—
1197D3—42no—
1198D3—62no—
1199D3—62no—
1200D3—122no—
1201D3—122no—
1202D3—122no—
1203D3—122no—
1204D3—122no—
1205D3—242no—
1206D3—242no—
1207C22—22no—
1208C22—32no—
1209C22—32no—
1210C22—42no—
1211C22—62no—
1212C22—62no—
1213C22—62no—
1214C22—62no—
1215C22—62no—
1216C22—92no—
1217C22—122no—
1218C22—122no—
1219C22—122no—
1220C22—182no—
1221C22—182no—
1222C22—182no—
1223C22—244no—
1224C22—362no—
1225C22—362no—
1226C22—724no—
1227C22—724no—
1228C22—724no—
1229C22—724no—
1230C22—724no—
1231C22D32×D411yescharacteristic
1232C4—22no—
1233C4—32no—
1234C4—32no—
1235C4—62no—
1236C4—92no—
1237C4D32×D411yescharacteristic
1238C4C23×D3211yescharacteristic
1239C3—21no—
1240C3C2×#576911yescharacteristic, complemented
1241C3C2×#577411yescharacteristic, complemented
1242C2—42no—
1243C2—62no—
1244C2—62no—
1245C2—122no—
1246C2—122no—
1247C2—122no—
1248C2—182no—
1249C2—362no—
1250C2—362no—
1251C2#1059475512yesdirect product factor
1252C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32C2×#576
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#64320C2semidirect
2. C2×#64314C2semidirect
3. C2×#64123C2semidirect
4. C2×C3×#916C2semidirect
5. C2×C3×#914C2semidirect
6. C2×#63950C2semidirect
7. C2×#63949C2semidirect
8. C2×#63939C2semidirect
9. C2×#63926C2semidirect
10. C2×#63925C2semidirect
11. C2×D3×#213C2semidirect
12. #10594755C2direct (N × H)
13. C2×#63804C2semidirect
14. C2×#63798C2semidirect
15. C2×#63794C2semidirect
16. C2×D3×D24C2semidirect
19. C2×#3832C22semidirect
20. C2×D4×C3⋊D3C22semidirect
21. C2×C3×#239C22semidirect
22. C2×C3×#239C22semidirect
23. C2×C3×#237C22semidirect
24. C2×C3×D3×D4C22semidirect
30. #64320C22semidirect
32. #64314C22semidirect
34. C2×#3802C22semidirect
37. C2×D3×D12C22semidirect
38. C2×D3×D12C22semidirect
39. C2×D3×D12C22semidirect
40. C2×#3799C22semidirect
43. C2×#3796C22semidirect
44. C2×C32×SD16C22semidirect
45. C2×#3755C22semidirect
46. C2×#3753C22semidirect
47. #64123C22semidirect
48. C2×#3745C22semidirect
49. C2×#3743C22semidirect
50. C2×C3×#216C22semidirect
51. C2×C3×#215C22semidirect
52. C2×C3×#213C22semidirect
53. C2×C3×#213C22semidirect
54. C3×#916C22semidirect
55. C3×#914C22semidirect
56. C2×C3×D24C22semidirect
57. C2×C3×#204C22semidirect
58. C2×C3×ΓL(1,𝔽25)C22semidirect
59. C2×C3×D3×C8C22semidirect
60. #63950C22semidirect
61. #63949C22semidirect
62. #63939C22semidirect
63. #63926C22semidirect
64. #63925C22semidirect
65. D3×#213C22semidirect
66. C2×#3717C22semidirect
67. C2×#3715C22semidirect
68. C2×#3714C22semidirect
69. C2×#3714C22semidirect
70. C2×#3714C22semidirect
71. C2×#3713C22semidirect
72. C2×#3711C22semidirect
73. C2×#3710C22semidirect
74. C2×D3×C3⋊C8C22semidirect
75. #63804C22semidirect
76. #63798C22semidirect
77. #63794C22semidirect
78. D3×D24C22semidirect
94. C2×#916D3semidirect
101. C2×#914D3semidirect
122. #3832C23semidirect
124. D4×C3⋊D3C23semidirect
135. C3×#239C23semidirect
136. C3×#239C23semidirect
138. C3×#237C23semidirect
140. C3×D3×D4C23semidirect
169. #3802C23semidirect
175. D3×D12C23semidirect
176. D3×D12C23semidirect
177. D3×D12C23semidirect
179. #3799C23semidirect
184. #3796C23semidirect
185. C32×SD16C23semidirect
187. #3755C23semidirect
188. #3753C23semidirect
190. #3745C23semidirect
191. #3743C23semidirect
192. C3×#216C23semidirect
193. C3×#215C23semidirect
194. C3×#213C23semidirect
195. C3×#213C23semidirect
198. C3×D24C23semidirect
199. C3×#204C23semidirect
200. C3×ΓL(1,𝔽25)C23semidirect
201. C3×D3×C8C23semidirect
202. #3717C23semidirect
203. #3715C23semidirect
204. #3714C23semidirect
205. #3714C23semidirect
206. #3714C23semidirect
207. #3713C23semidirect
208. #3711C23semidirect
209. #3710C23semidirect
210. D3×C3⋊C8C23semidirect
229. C2×#239C2×D3semidirect
230. C2×#239C2×D3semidirect
235. C2×#237C2×D3semidirect
251. C2×D3×D4C2×D3semidirect
270. C2×C3×SD16C2×D3semidirect
271. C2×C3×SD16C2×D3semidirect
280. C2×#216C2×D3semidirect
286. C2×#215C2×D3semidirect
297. C2×#213C2×D3semidirect
298. C2×#213C2×D3semidirect
304. #916C2×D3semidirect
311. #914C2×D3semidirect
327. C2×D24C2×D3semidirect
329. C2×#204C2×D3semidirect
335. C2×ΓL(1,𝔽25)C2×D3semidirect
339. C2×D3×C8C2×D3semidirect
503. #239C22×D3semidirect
504. #239C22×D3semidirect
509. #237C22×D3semidirect
534. D3×D4C22×D3semidirect
594. C3×SD16C22×D3semidirect
595. C3×SD16C22×D3semidirect
606. #216C22×D3semidirect
612. #215C22×D3semidirect
622. #213C22×D3semidirect
623. #213C22×D3semidirect
637. D24C22×D3semidirect
639. #204C22×D3semidirect
644. ΓL(1,𝔽25)C22×D3semidirect
648. D3×C8C22×D3semidirect
721. C2×SD16D32semidirect
916. C2×C32#576semidirect
1005. SD16C2×D32semidirect
1103. C32C2×#576semidirect
1189. C2×C3#5769semidirect
1190. C2×C3#5774semidirect
1240. C3C2×#5769semidirect
1241. C3C2×#5774semidirect
1251. C2#10594755direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643202
C2×#643142
C2×#641232
C2×C3×#9162
C2×C3×#9142
C2×#639502
C2×#639492
C2×#639392
C2×#639262
C2×#639252
C2×D3×#2132
#105947552
C2×#638042
C2×#637982
C2×#637942
C2×D3×D242
C2×#57743
C2×#57693