Finite Group Databasebeta

← C2×#10594736 #11918873

Subgroups — C2×#10594736 #11918873

Order 1152.

3069 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64314C211yesmaximal, characteristic, complemented
2C2×#64309C211yesmaximal, characteristic, complemented
3C2×#64120C211yesmaximal, characteristic, complemented
4C2×C3×#912C211yesmaximal, characteristic, complemented
5C2×C3×#911C211yesmaximal, characteristic, complemented
6C2×#63936C211yesmaximal, characteristic, complemented
7C2×#63935C211yesmaximal, characteristic, complemented
8C2×#63930C211yesmaximal, characteristic, complemented
9C2×#63929C211yesmaximal, characteristic, complemented
10C2×D3×#214C211yesmaximal, characteristic, complemented
11C2×#63925C211yesmaximal, characteristic, complemented
12#10594736C2116yesmaximal, direct product factor
13C2×#63811C211yesmaximal, characteristic, complemented
14C2×#63804C211yesmaximal, characteristic, complemented
15C2×#63801C211yesmaximal, characteristic, complemented
16C2×D3×#204C211yesmaximal, characteristic, complemented
17C2×#5775—31nomaximal
18C2×#5770—31nomaximal
19C2×#3830C2211yescharacteristic, complemented
20C2×D4×C3⋊D3C2211yescharacteristic
21C2×C3×#237C2211yescharacteristic
22C2×C3×#237C2211yescharacteristic, complemented
23C2×C3×#237C2211yescharacteristic, complemented
24C2×C3×D3×D4C2211yescharacteristic
25C2×#3811—21no—
26C2×D3×#67—21no—
27C22×#627—21no—
28C22×#626—21no—
29C2×#3805—21no—
30C2×#3804—21no—
31C2×#3804—21no—
32C2×#3804—21no—
33#64314—24no—
34#64314C2218yescomplemented
35#64309—24no—
36#64309C2218yescomplemented
37C2×D3×D12C2211yescharacteristic
38C2×#3799C2211yescharacteristic
39C2×#3798C2211yescharacteristic
40C2×#3797C2211yescharacteristic, complemented
41C2×#3796C2211yescharacteristic
42C2×D3×Dic6C2211yescharacteristic, complemented
43C2×D3×Dic6C2211yescharacteristic, complemented
44C2×C32×D8C2211yescharacteristic, complemented
45C2×#3754C2211yescharacteristic, complemented
46C2×#3753C2211yescharacteristic, complemented
47#64120C2218yescomplemented
48C2×#3744C2211yescharacteristic, complemented
49C2×#3743C2211yescharacteristic, complemented
50C2×C3×#214C2211yescharacteristic, complemented
51C2×C3×#214C2211yescharacteristic, complemented
52C2×C3×#214C2211yescharacteristic, complemented
53C2×C3×#213C2211yescharacteristic, complemented
54C3×#912C2218yescomplemented
55C3×#911C2218yescomplemented
56C2×C3×Dic12C2211yescharacteristic, complemented
57C2×C3×#204C2211yescharacteristic, complemented
58C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
59C2×C3×D3×C8C2211yescharacteristic, complemented
60#63936C2218yescomplemented
61#63935C2218yescomplemented
62#63930C2218yescomplemented
63#63929C2218yescomplemented
64D3×#214C2218yescomplemented
65#63925C2218yescomplemented
66C2×#3719C2211yescharacteristic, complemented
67C2×#3718C2211yescharacteristic, complemented
68C2×#3717C2211yescharacteristic, complemented
69C2×#3717C2211yescharacteristic, complemented
70C2×#3716C2211yescharacteristic, complemented
71C2×#3715C2211yescharacteristic, complemented
72C2×#3711C2211yescharacteristic, complemented
73C2×#3710C2211yescharacteristic, complemented
74C2×D3×C3⋊C8C2211yescharacteristic, complemented
75#63811C2218yescomplemented
76#63804C2218yescomplemented
77#63801C2218yescomplemented
78D3×#204C2218yescomplemented
79C2×#1010—31no—
80C2×#1010—31no—
81C2×#1009—31no—
82C2×#1004—31no—
83C2×C3×AGL(1,ℤ/8)—31no—
84C2×C3×#135—31no—
85C2×#951—31no—
86C2×#950—31no—
87C2×#949—31no—
88C22×#214—31no—
89#5775—316no—
90#5770—316no—
91C2×#918—31no—
92C2×#918—31no—
93C2×#916—31no—
94C2×#916—31no—
95C2×#915—31no—
96C2×#915—31no—
97C2×D3×SD16—31no—
98C2×D3×SD16—31no—
99C2×D3×SD16—31no—
100C2×D3×SD16—31no—
101C2×#912—31no—
102C2×#912D311yescharacteristic, complemented
103C2×#911—31no—
104C2×#911—31no—
105C2×#911—31no—
106C2×#911—61no—
107C2×#911D311yescharacteristic, complemented
108C2×#909—31no—
109C2×#907—31no—
110C22×#204—31no—
111C2×#901—31no—
112C23×C3⋊D3—21no—
113C23×C3×D3—21no—
114C22×D32—21no—
115C2×C32×D4C2311yescharacteristic
116C2×C32×D4C2311yescharacteristic
117C2×#638—21no—
118C2×#638—21no—
119C22×C3⋊Dic3—21no—
120#3830—22no—
121#3830C2314yescomplemented
122D4×C3⋊D3—22no—
123D4×C3⋊D3C2314yes—
124C2×C4⋊(C3⋊D3)C2311yescharacteristic
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×#634C2311yescharacteristic
127C2×C3×#67—21no—
128C2×C3×#67—21no—
129C2×C3×#67—21no—
130C2×C3×#67—21no—
131C22×C3×Dic3—21no—
132C22×C3×Dic3—21no—
133C22×C3×Dic3—21no—
134C3×#237—22no—
135C3×#237—22no—
136C3×#237—22no—
137C3×#237C2314yes—
138C3×#237C2314yescomplemented
139C3×#237C2314yescomplemented
140C3×D3×D4—22no—
141C3×D3×D4C2314yes—
142C2×C3×D12C2311yescharacteristic
143C2×C3×C4×D3C2311yescharacteristic
144C2×C3×C4×D3C2311yescharacteristic
145C2×C3×Dic6C2311yescharacteristic
146C2×C3×Dic6C2311yescharacteristic
147C2×C3×Dic6C2311yescharacteristic
148#3811—28no—
149D3×#67—28no—
150C2×#627—21no—
151C2×#627—21no—
152C2×#627—21no—
153C2×#627—28no—
154C2×#627D411yescharacteristic
155C2×#626—21no—
156C2×#626—21no—
157C2×#626—21no—
158C2×#626—28no—
159C2×#626D411yescharacteristic
160C2×#626D411yescharacteristic
161C2×#625D411yescharacteristic
162C2×#624—21no—
163C2×#624—21no—
164#3805—28no—
165#3804—28no—
166#3804—28no—
167#3804—28no—
168C2×D3×Dic3—21no—
169C2×D3×Dic3—21no—
170C2×D3×Dic3—21no—
171D3×D12—22no—
172D3×D12C2314yes—
173#3799—22no—
174#3799C2314yes—
175#3798D414yes—
176#3798C2314yes—
177#3797—22no—
178#3797C2314yescomplemented
179#3796—22no—
180#3796C2314yes—
181D3×Dic6—22no—
182D3×Dic6—22no—
183D3×Dic6C2314yescomplemented
184D3×Dic6C2314yescomplemented
185C32×D8C2314yescomplemented
186C2×C32×C8C2311yescharacteristic
187#3754C2314yescomplemented
188#3753C2314yescomplemented
189C2×C3⋊(C3⋊C8)C2311yescharacteristic
190#3744C2314yescomplemented
191#3743C2314yescomplemented
192C3×#214C2314yescomplemented
193C3×#214C2314yescomplemented
194C3×#214C2314yescomplemented
195C3×#213C2314yescomplemented
196C2×C3×C3⋊C8C2311yescharacteristic
197C2×C3×C3⋊C8C2311yescharacteristic
198C3×Dic12C2314yescomplemented
199C3×#204C2314yescomplemented
200C3×ΓL(1,𝔽25)C2314yescomplemented
201C3×D3×C8C2314yescomplemented
202#3719C2314yescomplemented
203#3718C2314yescomplemented
204#3717C2314yescomplemented
205#3717C2314yescomplemented
206#3716C2314yescomplemented
207#3715C2314yescomplemented
208#3711C2314yescomplemented
209#3710C2314yescomplemented
210D3×C3⋊C8C2314yescomplemented
211C2×#577—91noSylow
212C2×C3×#41—31no—
213C2×C3×#41—31no—
214C2×C3×#41—31no—
215C22×C3×D4—31no—
216C22×#67—61no—
217C22×#67—61no—
218#1010—38no—
219#1010—38no—
220#1010—64no—
221#1010—64no—
222#1009—38no—
223#1009—64no—
224C2×#239—31no—
225C2×#239—31no—
226C2×D3×Q8—31no—
227C2×D3×Q8—31no—
228C2×D3×Q8—31no—
229C2×D3×Q8—31no—
230#1004—38no—
231#1004—64no—
232C2×#237—31no—
233C2×#237—31no—
234C2×#237—31no—
235C2×#237—61no—
236C2×#237—61no—
237C2×#237—61no—
238C2×#237—61no—
239C2×#237—61no—
240C2×#237—61no—
241C2×#237C2×D311yescharacteristic
242C2×#237C2×D311yescharacteristic, complemented
243C2×#237C2×D311yescharacteristic, complemented
244C2×D3×D4—31no—
245C2×D3×D4—31no—
246C2×D3×D4—31no—
247C2×D3×D4—61no—
248C2×D3×D4—61no—
249C2×D3×D4—61no—
250C2×D3×D4—61no—
251C2×D3×D4C2×D311yescharacteristic
252C2×#235—31no—
253C2×#235—31no—
254C2×#235—31no—
255C2×#235—61no—
256C2×#235—61no—
257C2×#235—61no—
258C22×D12—31no—
259C22×D12—61no—
260C22×Dic6—31no—
261C22×Dic6—31no—
262C22×Dic6—61no—
263C22×Dic6—61no—
264C3×AGL(1,ℤ/8)—38no—
265C3×#135—38no—
266C2×C3×Q16—31no—
267C2×C3×SD16—31no—
268C2×C3×SD16—31no—
269C2×C3×SD16—31no—
270C2×C3×SD16—31no—
271C2×C3×D8—21no—
272C2×C3×D8—31no—
273C2×C3×D8C2×D311yescharacteristic, complemented
274C2×C3×D8C2×D311yescharacteristic, complemented
275C2×C3×M16—31no—
276C22×C3×C8—31no—
277#951—38no—
278#950—38no—
279#949—38no—
280C2×#216—31no—
281C2×#216—31no—
282C2×#216—31no—
283C2×#215—31no—
284C2×#215—31no—
285C2×#215—31no—
286C2×#214—31no—
287C2×#214—31no—
288C2×#214—31no—
289C2×#214—38no—
290C2×#214—31no—
291C2×#214—61no—
292C2×#214C2×D311yescharacteristic, complemented
293C2×#214C2×D311yescharacteristic, complemented
294C2×#214C2×D311yescharacteristic, complemented
295C2×#213—31no—
296C2×#213—31no—
297C2×#213—61no—
298C2×#213C2×D311yescharacteristic, complemented
299C2×#208—31no—
300C22×C3⋊C8—31no—
301#918—38no—
302#918—38no—
303#916—38no—
304#916—38no—
305#915—38no—
306#915—38no—
307D3×SD16—38no—
308D3×SD16—38no—
309D3×SD16—38no—
310D3×SD16—38no—
311#912—38no—
312#912C2×D318yescomplemented
313#911—38no—
314#911—38no—
315#911—38no—
316#911—68no—
317#911C2×D318yescomplemented
318#909—38no—
319#907—38no—
320C2×Dic12—31no—
321C2×Dic12C2×D311yescharacteristic, complemented
322C2×#204—31no—
323C2×#204—31no—
324C2×#204—31no—
325C2×#204—31no—
326C2×#204—31no—
327C2×#204—38no—
328C2×#204—61no—
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—
341C23×C32—21no—
342C22×C3⋊D3—21no—
343C22×C3⋊D3—24no—
344C22×C3⋊D3—82no—
345C22×C3⋊D3C2×D411yescharacteristic
346C22×C3×D3—21no—
347C22×C3×D3—24no—
348C22×C3×D3—82no—
349C22×C3×D3C2×D411yescharacteristic
350C22×C3×D3C2×D411yescharacteristic
351C2×D32—24no—
352C2×D32—82no—
353C32×D4—21no—
354C32×D4—21no—
355C32×D4C2412yes—
356C32×D4C2412yes—
357C2×C32×C4C2411yescharacteristic
358#638—24no—
359#638—24no—
360C2×C3⋊Dic3—21no—
361C2×C3⋊Dic3—24no—
362C2×C3⋊Dic3C2×D411yescharacteristic
363C4⋊(C3⋊D3)—21no—
364C4⋊(C3⋊D3)C2412yes—
365C4×C3⋊D3C2×D412yes—
366C4×C3⋊D3C2412yes—
367#634—21no—
368#634C2412yes—
369C3×#67—24no—
370C3×#67—24no—
371C3×#67—24no—
372C3×#67—24no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—24no—
377C2×C3×Dic3—24no—
378C2×C3×Dic3—24no—
379C2×C3×Dic3C2×D411yescharacteristic
380C2×C3×Dic3C2×D411yescharacteristic
381C3×D12—21no—
382C3×D12C2412yes—
383C3×C4×D3C2×D412yes—
384C3×C4×D3C2×D412yes—
385C3×C4×D3C2412yes—
386C3×C4×D3C2412yes—
387C3×Dic6—21no—
388C3×Dic6—21no—
389C3×Dic6—21no—
390C3×Dic6C2412yes—
391C3×Dic6C2412yes—
392C3×Dic6C2412yes—
393#627—24no—
394#627—24no—
395#627—24no—
396#627C2×D414yes—
397#626—24no—
398#626—24no—
399#626—24no—
400#626C2×D414yes—
401#626C2×D414yes—
402#625C2×D414yes—
403#624—24no—
404#624—24no—
405D3×Dic3—24no—
406D3×Dic3—24no—
407D3×Dic3—24no—
408C32×C8C2412yes—
409C3⋊(C3⋊C8)C2412yes—
410C3×C3⋊C8C2412yes—
411C3×C3⋊C8C2412yes—
412C2×2−1+4—91no—
413C2×H(5,𝔽2)—91no—
414#577—916no—
415C2×#137—91no—
416C2×#137—91no—
417C2×#137—91no—
418C2×AGL(1,ℤ/8)—31no—
419C2×AGL(1,ℤ/8)—91no—
420C2×AGL(1,ℤ/8)—91no—
421C2×#135—31no—
422C2×#135—91no—
423C2×#135—91no—
424C22×SD16—91no—
425C22×SD16—91no—
426C22×SD16—91no—
427C2×#131—91no—
428C24×C3—61no—
429C23×D3—21no—
430C23×D3—61no—
431C23×D3—61no—
432C23×D3—61no—
433C23×D3—61no—
434C23×D3—121no—
435C3×#41—34no—
436C3×#41—34no—
437C3×#41—34no—
438C3×#41—62no—
439C3×#41—62no—
440C3×#41—62no—
441C2×C3×Q8—31no—
442C2×C3×Q8—31no—
443C2×C3×Q8—31no—
444C2×C3×D4—21no—
445C2×C3×D4—21no—
446C2×C3×D4—34no—
447C2×C3×D4—31no—
448C2×C3×D4—62no—
449C2×C3×D4—61no—
450C2×C3×D4—61no—
451C2×C3×D4—61no—
452C2×C3×D4—61no—
453C2×C3×D4C22×D311yescharacteristic
454C2×C3×D4C22×D311yescharacteristic
455C2×C3×D4C22×D311yescharacteristic
456C2×C3×D4C22×D311yescharacteristic
457C22×C3×C4—31no—
458C22×C3×C4—31no—
459C22×C3×C4—61no—
460C22×C3×C4—61no—
461C22×C3×C4—61no—
462C2×#67—21no—
463C2×#67—21no—
464C2×#67—21no—
465C2×#67—21no—
466C2×#67—31no—
467C2×#67—31no—
468C2×#67—31no—
469C2×#67—31no—
470C2×#67—68no—
471C2×#67—61no—
472C2×#67—61no—
473C2×#67—61no—
474C2×#67—61no—
475C2×#67—68no—
476C2×#67—61no—
477C2×#67—61no—
478C2×#67—61no—
479C2×#67—121no—
480C2×#67—121no—
481C22×Dic3—21no—
482C22×Dic3—21no—
483C22×Dic3—21no—
484C22×Dic3—61no—
485C22×Dic3—61no—
486C22×Dic3—61no—
487C22×Dic3—61no—
488C22×Dic3—61no—
489C22×Dic3—121no—
490#239—34no—
491#239—34no—
492#239—62no—
493#239—62no—
494D3×Q8—34no—
495D3×Q8—34no—
496D3×Q8—34no—
497D3×Q8—34no—
498D3×Q8—62no—
499D3×Q8—62no—
500D3×Q8—62no—
501D3×Q8—62no—
502#237—22no—
503#237—22no—
504#237—22no—
505#237—34no—
506#237—34no—
507#237—34no—
508#237—64no—
509#237—62no—
510#237—68no—
511#237—62no—
512#237—62no—
513#237—68no—
514#237—68no—
515#237—68no—
516#237—68no—
517#237—122no—
518#237C22×D314yes—
519#237C22×D314yescomplemented
520#237C22×D314yescomplemented
521D3×D4—22no—
522D3×D4—34no—
523D3×D4—34no—
524D3×D4—34no—
525D3×D4—64no—
526D3×D4—62no—
527D3×D4—62no—
528D3×D4—68no—
529D3×D4—68no—
530D3×D4—68no—
531D3×D4—62no—
532D3×D4—122no—
533D3×D4C22×D314yes—
534#235—34no—
535#235—34no—
536#235—34no—
537#235—34no—
538#235—34no—
539#235—62no—
540#235—68no—
541#235—68no—
542#235—68no—
543C2×D12—31no—
544C2×D12—31no—
545C2×D12—31no—
546C2×D12—31no—
547C2×D12—34no—
548C2×D12—61no—
549C2×D12—62no—
550C2×D12—68no—
551C2×D12—61no—
552C2×D12—61no—
553C2×D12—61no—
554C2×D12C22×D311yescharacteristic
555C2×C4×D3—31no—
556C2×C4×D3—31no—
557C2×C4×D3—61no—
558C2×C4×D3—61no—
559C2×C4×D3—61no—
560C2×C4×D3—61no—
561C2×C4×D3—61no—
562C2×C4×D3—61no—
563C2×C4×D3—61no—
564C2×C4×D3—61no—
565C2×C4×D3C22×D311yescharacteristic
566C2×C4×D3C22×D311yescharacteristic
567C2×Dic6—31no—
568C2×Dic6—31no—
569C2×Dic6—31no—
570C2×Dic6—31no—
571C2×Dic6—34no—
572C2×Dic6—34no—
573C2×Dic6—61no—
574C2×Dic6—62no—
575C2×Dic6—62no—
576C2×Dic6—68no—
577C2×Dic6—68no—
578C2×Dic6—61no—
579C2×Dic6—61no—
580C2×Dic6—61no—
581C2×Dic6—61no—
582C2×Dic6—61no—
583C2×Dic6—61no—
584C2×Dic6C22×D311yescharacteristic
585C2×Dic6C22×D311yescharacteristic
586C2×Dic6C22×D311yescharacteristic
587C3×Q16—34no—
588C3×SD16—34no—
589C3×SD16—34no—
590C3×SD16—34no—
591C3×SD16—34no—
592C3×D8—24no—
593C3×D8—34no—
594C3×D8C22×D314yescomplemented
595C3×D8C22×D314yescomplemented
596C3×M16—34no—
597C2×C3×C8—21no—
598C2×C3×C8—31no—
599C2×C3×C8—31no—
600C2×C3×C8—34no—
601C2×C3×C8C22×D311yescharacteristic
602C2×C3×C8C22×D311yescharacteristic
603#216—34no—
604#216—34no—
605#216—34no—
606#215—34no—
607#215—34no—
608#215—34no—
609#214—34no—
610#214—34no—
611#214—34no—
612#214—34no—
613#214—64no—
614#214C22×D314yescomplemented
615#214C22×D314yescomplemented
616#214C22×D314yescomplemented
617#213—34no—
618#213—34no—
619#213—64no—
620#213C22×D314yescomplemented
621#208—34no—
622C2×C3⋊C8—31no—
623C2×C3⋊C8—31no—
624C2×C3⋊C8—34no—
625C2×C3⋊C8—61no—
626C2×C3⋊C8C22×D311yescharacteristic
627C2×C3⋊C8C22×D311yescharacteristic
628Dic12—34no—
629Dic12C22×D314yescomplemented
630#204—34no—
631#204—34no—
632#204—34no—
633#204—34no—
634#204—34no—
635#204—64no—
636#204C22×D314yescomplemented
637ΓL(1,𝔽25)—34no—
638ΓL(1,𝔽25)—34no—
639ΓL(1,𝔽25)—34no—
640ΓL(1,𝔽25)—64no—
641ΓL(1,𝔽25)C22×D314yescomplemented
642D3×C8—34no—
643D3×C8—34no—
644D3×C8—34no—
645D3×C8C22×D314yescomplemented
646C22×C32—22no—
647C22×C32—22no—
648C22×C32—42no—
649C22×C32—42no—
650C22×C32C22×D411yescharacteristic
651C2×C3⋊D3—22no—
652C2×C3⋊D3—22no—
653C2×C3⋊D3—42no—
654C2×C3⋊D3—84no—
655C2×C3⋊D3C22×D412yes—
656C2×C3×D3—22no—
657C2×C3×D3—22no—
658C2×C3×D3—22no—
659C2×C3×D3—42no—
660C2×C3×D3—84no—
661C2×C3×D3C22×D412yes—
662C2×C3×D3C22×D412yes—
663D32—84no—
664C32×C4C22×D411yescharacteristic
665C32×C4C2511yescharacteristic
666C3⋊Dic3—22no—
667C3⋊Dic3C22×D412yes—
668C3×Dic3—22no—
669C3×Dic3—22no—
670C3×Dic3—22no—
671C3×Dic3C22×D412yes—
672C3×Dic3C22×D412yes—
6732−1+4—98no—
6742−1+4—184no—
675H(5,𝔽2)—98no—
676H(5,𝔽2)—184no—
677C2×#41—31no—
678C2×#41—31no—
679C2×#41—31no—
680C2×#41—91no—
681C2×#41—91no—
682C2×#41—91no—
683C2×#41—91no—
684C2×#41—181no—
685C2×#41—181no—
686C2×#41—181no—
687C2×#41—181no—
688C22×Q8—91no—
689C22×Q8—91no—
690C22×Q8—91no—
691C22×Q8—181no—
692C22×D4—31no—
693C22×D4—91no—
694C22×D4—91no—
695C22×D4—181no—
696C22×D4—181no—
697C22×D4—181no—
698#137—98no—
699#137—98no—
700#137—98no—
701AGL(1,ℤ/8)—38no—
702AGL(1,ℤ/8)—98no—
703AGL(1,ℤ/8)—98no—
704#135—38no—
705#135—98no—
706#135—98no—
707C2×Q16—31no—
708C2×Q16—91no—
709C2×Q16—91no—
710C2×SD16—31no—
711C2×SD16—31no—
712C2×SD16—31no—
713C2×SD16—31no—
714C2×SD16—98no—
715C2×SD16—91no—
716C2×SD16—91no—
717C2×SD16—91no—
718C2×SD16—98no—
719C2×SD16—98no—
720C2×SD16—91no—
721C2×SD16—91no—
722C2×SD16—91no—
723C2×D8—31no—
724C2×D8—91no—
725C2×D8D3211yescharacteristic, complemented
726#131—98no—
727C2×M16—31no—
728C2×M16—91no—
729C2×M16—91no—
730C22×C8—31no—
731C22×C8—91no—
732C22×C8—91no—
733C23×C3—21no—
734C23×C3—21no—
735C23×C3—21no—
736C23×C3—21no—
737C23×C3—31no—
738C23×C3—31no—
739C23×C3—41no—
740C23×C3—41no—
741C23×C3—64no—
742C23×C3—61no—
743C23×C3—242no—
744C22×D3—21no—
745C22×D3—24no—
746C22×D3—31no—
747C22×D3—31no—
748C22×D3—61no—
749C22×D3—64no—
750C22×D3—64no—
751C22×D3—64no—
752C22×D3—61no—
753C22×D3—61no—
754C22×D3—64no—
755C22×D3—82no—
756C22×D3—124no—
757C22×D3—121no—
758C22×D3—242no—
759C22×D3—242no—
760C22×D3—242no—
761C22×D3—242no—
762C22×D3—244no—
763C22×D3D3×D411yescharacteristic
764C22×D3D3×D411yescharacteristic
765C3×Q8—32no—
766C3×Q8—32no—
767C3×Q8—32no—
768C3×Q8—61no—
769C3×Q8—61no—
770C3×Q8—61no—
771C3×D4—21no—
772C3×D4—21no—
773C3×D4—21no—
774C3×D4—21no—
775C3×D4—22no—
776C3×D4—22no—
777C3×D4—32no—
778C3×D4—41no—
779C3×D4—41no—
780C3×D4—64no—
781C3×D4—64no—
782C3×D4—64no—
783C3×D4—64no—
784C3×D4—61no—
785C3×D4C23×D312yes—
786C3×D4C23×D312yes—
787C3×D4C23×D312yes—
788C3×D4C23×D312yes—
789C2×C3×C4—21no—
790C2×C3×C4—31no—
791C2×C3×C4—31no—
792C2×C3×C4—32no—
793C2×C3×C4—32no—
794C2×C3×C4—32no—
795C2×C3×C4—32no—
796C2×C3×C4—64no—
797C2×C3×C4—64no—
798C2×C3×C4—64no—
799C2×C3×C4—61no—
800C2×C3×C4—61no—
801C2×C3×C4—61no—
802C2×C3×C4C23×D311yescharacteristic
803C2×C3×C4C23×D311yescharacteristic
804#67—24no—
805#67—24no—
806#67—24no—
807#67—24no—
808#67—34no—
809#67—34no—
810#67—34no—
811#67—34no—
812#67—64no—
813#67—64no—
814#67—64no—
815#67—64no—
816#67—64no—
817#67—64no—
818#67—64no—
819#67—124no—
820#67—124no—
821C2×Dic3—21no—
822C2×Dic3—21no—
823C2×Dic3—21no—
824C2×Dic3—24no—
825C2×Dic3—24no—
826C2×Dic3—24no—
827C2×Dic3—31no—
828C2×Dic3—31no—
829C2×Dic3—61no—
830C2×Dic3—64no—
831C2×Dic3—64no—
832C2×Dic3—64no—
833C2×Dic3—64no—
834C2×Dic3—64no—
835C2×Dic3—61no—
836C2×Dic3—61no—
837C2×Dic3—124no—
838C2×Dic3—121no—
839C2×Dic3D3×D411yescharacteristic
840C2×Dic3D3×D411yescharacteristic
841D12—21no—
842D12—34no—
843D12—34no—
844D12—32no—
845D12—32no—
846D12—62no—
847D12—64no—
848D12—64no—
849D12—64no—
850D12—61no—
851D12—61no—
852D12—121no—
853D12C23×D312yes—
854C4×D3—32no—
855C4×D3—32no—
856C4×D3—32no—
857C4×D3—32no—
858C4×D3—62no—
859C4×D3—62no—
860C4×D3—64no—
861C4×D3—64no—
862C4×D3—64no—
863C4×D3—64no—
864C4×D3—64no—
865C4×D3—64no—
866C4×D3—64no—
867C4×D3D3×D412yes—
868C4×D3D3×D412yes—
869C4×D3C23×D312yes—
870C4×D3C23×D312yes—
871Dic6—21no—
872Dic6—21no—
873Dic6—21no—
874Dic6—34no—
875Dic6—34no—
876Dic6—32no—
877Dic6—32no—
878Dic6—62no—
879Dic6—64no—
880Dic6—64no—
881Dic6—64no—
882Dic6—64no—
883Dic6—61no—
884Dic6—61no—
885Dic6—64no—
886Dic6—64no—
887Dic6—121no—
888Dic6C23×D312yes—
889Dic6C23×D312yes—
890Dic6C23×D312yes—
891C3×C8—22no—
892C3×C8—32no—
893C3×C8—32no—
894C3×C8C23×D312yes—
895C3×C8C23×D312yes—
896C3⋊C8—32no—
897C3⋊C8—32no—
898C3⋊C8—62no—
899C3⋊C8C23×D312yes—
900C3⋊C8C23×D312yes—
901C2×C32—42no—
902C2×C32—42no—
903C2×C32#57712yescomplemented
904C2×C32C23×D411yescharacteristic
905C3⋊D3—22no—
906C3⋊D3—42no—
907C3×D3—22no—
908C3×D3—22no—
909C3×D3—42no—
910C24—61no—
911C24—181no—
912C24—181no—
913#41—34no—
914#41—34no—
915#41—34no—
916#41—62no—
917#41—62no—
918#41—62no—
919#41—94no—
920#41—94no—
921#41—94no—
922#41—94no—
923#41—94no—
924#41—182no—
925#41—188no—
926#41—188no—
927#41—188no—
928#41—182no—
929#41—182no—
930#41—188no—
931C2×Q8—31no—
932C2×Q8—31no—
933C2×Q8—31no—
934C2×Q8—91no—
935C2×Q8—94no—
936C2×Q8—94no—
937C2×Q8—94no—
938C2×Q8—91no—
939C2×Q8—181no—
940C2×Q8—181no—
941C2×Q8—182no—
942C2×Q8—182no—
943C2×Q8—181no—
944C2×Q8—188no—
945C2×Q8—182no—
946C2×D4—34no—
947C2×D4—31no—
948C2×D4—62no—
949C2×D4—61no—
950C2×D4—61no—
951C2×D4—61no—
952C2×D4—61no—
953C2×D4—94no—
954C2×D4—91no—
955C2×D4—91no—
956C2×D4—91no—
957C2×D4—94no—
958C2×D4—91no—
959C2×D4—182no—
960C2×D4—181no—
961C2×D4—188no—
962C2×D4—181no—
963C2×D4—181no—
964C2×D4—182no—
965C2×D4—181no—
966C2×D4—188no—
967C2×D4—188no—
968C2×D4—181no—
969C2×D4C2×D3211yescharacteristic
970C2×D4C2×D3211yescharacteristic
971C22×C4—31no—
972C22×C4—31no—
973C22×C4—61no—
974C22×C4—61no—
975C22×C4—61no—
976C22×C4—91no—
977C22×C4—181no—
978C22×C4—181no—
979C22×C4—181no—
980C22×C4—181no—
981C22×C4—181no—
982C22×C4—181no—
983Q16—34no—
984Q16—94no—
985Q16—94no—
986SD16—34no—
987SD16—34no—
988SD16—34no—
989SD16—34no—
990SD16—94no—
991SD16—94no—
992SD16—94no—
993SD16—94no—
994SD16—94no—
995SD16—94no—
996D8—34no—
997D8—94no—
998D8C2×D3214yescomplemented
999M16—34no—
1000M16—94no—
1001M16—94no—
1002C2×C8—31no—
1003C2×C8—31no—
1004C2×C8—34no—
1005C2×C8—94no—
1006C2×C8—94no—
1007C2×C8—91no—
1008C2×C8C2×D3211yescharacteristic
1009C22×C3—22no—
1010C22×C3—22no—
1011C22×C3—22no—
1012C22×C3—22no—
1013C22×C3—21no—
1014C22×C3—32no—
1015C22×C3—32no—
1016C22×C3—42no—
1017C22×C3—42no—
1018C22×C3—42no—
1019C22×C3—42no—
1020C22×C3—42no—
1021C22×C3—42no—
1022C22×C3—62no—
1023C22×C3—62no—
1024C22×C3—62no—
1025C22×C3—82no—
1026C22×C3—82no—
1027C22×C3—122no—
1028C22×C3—244no—
1029C22×C3C2×D3×D411yescharacteristic
1030C22×C3C2×D3×D411yescharacteristic
1031C2×D3—22no—
1032C2×D3—22no—
1033C2×D3—22no—
1034C2×D3—32no—
1035C2×D3—32no—
1036C2×D3—42no—
1037C2×D3—62no—
1038C2×D3—62no—
1039C2×D3—62no—
1040C2×D3—62no—
1041C2×D3—62no—
1042C2×D3—84no—
1043C2×D3—122no—
1044C2×D3—122no—
1045C2×D3—122no—
1046C2×D3—122no—
1047C2×D3—242no—
1048C2×D3—244no—
1049C2×D3—244no—
1050C2×D3—244no—
1051C2×D3—244no—
1052C2×D3—248no—
1053C2×D3C2×D3×D412yes—
1054C2×D3C2×D3×D412yes—
1055C3×C4—21no—
1056C3×C4—21no—
1057C3×C4—32no—
1058C3×C4—32no—
1059C3×C4—62no—
1060C3×C4—62no—
1061C3×C4—62no—
1062C3×C4C2×D3×D411yescharacteristic
1063C3×C4C2×D3×D411yescharacteristic
1064C3×C4C24×D311yescharacteristic
1065C3×C4C24×D311yescharacteristic
1066Dic3—22no—
1067Dic3—22no—
1068Dic3—22no—
1069Dic3—32no—
1070Dic3—32no—
1071Dic3—62no—
1072Dic3—62no—
1073Dic3—62no—
1074Dic3—122no—
1075Dic3C2×D3×D412yes—
1076Dic3C2×D3×D412yes—
1077C32C2×#57711yescharacteristic, complemented, Sylow
1078C23—21no—
1079C23—21no—
1080C23—31no—
1081C23—31no—
1082C23—64no—
1083C23—61no—
1084C23—91no—
1085C23—184no—
1086C23—184no—
1087C23—181no—
1088C23—242no—
1089C23—722no—
1090C23—722no—
1091Q8—32no—
1092Q8—32no—
1093Q8—32no—
1094Q8—61no—
1095Q8—61no—
1096Q8—61no—
1097Q8—94no—
1098Q8—92no—
1099Q8—184no—
1100Q8—184no—
1101Q8—184no—
1102Q8—181no—
1103D4—21no—
1104D4—21no—
1105D4—32no—
1106D4—64no—
1107D4—64no—
1108D4—64no—
1109D4—64no—
1110D4—61no—
1111D4—94no—
1112D4—94no—
1113D4—94no—
1114D4—92no—
1115D4—184no—
1116D4—184no—
1117D4—184no—
1118D4—184no—
1119D4—184no—
1120D4—181no—
1121D4C22×D3212yes—
1122D4C22×D3212yes—
1123C2×C4—31no—
1124C2×C4—31no—
1125C2×C4—32no—
1126C2×C4—32no—
1127C2×C4—32no—
1128C2×C4—32no—
1129C2×C4—64no—
1130C2×C4—64no—
1131C2×C4—64no—
1132C2×C4—61no—
1133C2×C4—61no—
1134C2×C4—61no—
1135C2×C4—91no—
1136C2×C4—92no—
1137C2×C4—92no—
1138C2×C4—184no—
1139C2×C4—184no—
1140C2×C4—184no—
1141C2×C4—184no—
1142C2×C4—184no—
1143C2×C4—184no—
1144C2×C4—181no—
1145C2×C4C22×D3211yescharacteristic
1146C8—32no—
1147C8—32no—
1148C8—92no—
1149C8C22×D3212yes—
1150C2×C3—21no—
1151C2×C3—22no—
1152C2×C3—42no—
1153C2×C3—42no—
1154C2×C3—42no—
1155C2×C3—42no—
1156C2×C3—62no—
1157C2×C3—62no—
1158C2×C3—82no—
1159C2×C3—82no—
1160C2×C3—122no—
1161C2×C3#577012yescomplemented
1162C2×C3#577512yescomplemented
1163C2×C3C22×D3×D411yescharacteristic
1164C2×C3C22×D3×D411yescharacteristic
1165D3—22no—
1166D3—22no—
1167D3—42no—
1168D3—62no—
1169D3—62no—
1170D3—122no—
1171D3—122no—
1172D3—122no—
1173D3—242no—
1174C22—22no—
1175C22—22no—
1176C22—32no—
1177C22—32no—
1178C22—42no—
1179C22—42no—
1180C22—62no—
1181C22—62no—
1182C22—62no—
1183C22—92no—
1184C22—122no—
1185C22—182no—
1186C22—182no—
1187C22—244no—
1188C22—362no—
1189C22—724no—
1190C22—724no—
1191C22D32×D411yescharacteristic
1192C4—32no—
1193C4—32no—
1194C4—62no—
1195C4—62no—
1196C4—62no—
1197C4—92no—
1198C4—182no—
1199C4D32×D411yescharacteristic
1200C4C23×D3211yescharacteristic
1201C3—21no—
1202C3C2×#577011yescharacteristic, complemented
1203C3C2×#577511yescharacteristic, complemented
1204C2—42no—
1205C2—42no—
1206C2—62no—
1207C2—62no—
1208C2—122no—
1209C2—182no—
1210C2—362no—
1211C2#1059473612yesdirect product factor
1212C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#64314C2semidirect
2. C2×#64309C2semidirect
3. C2×#64120C2semidirect
4. C2×C3×#912C2semidirect
5. C2×C3×#911C2semidirect
6. C2×#63936C2semidirect
7. C2×#63935C2semidirect
8. C2×#63930C2semidirect
9. C2×#63929C2semidirect
10. C2×D3×#214C2semidirect
11. C2×#63925C2semidirect
12. #10594736C2direct (N × H)
13. C2×#63811C2semidirect
14. C2×#63804C2semidirect
15. C2×#63801C2semidirect
16. C2×D3×#204C2semidirect
19. C2×#3830C22semidirect
22. C2×C3×#237C22semidirect
23. C2×C3×#237C22semidirect
34. #64314C22semidirect
36. #64309C22semidirect
40. C2×#3797C22semidirect
42. C2×D3×Dic6C22semidirect
43. C2×D3×Dic6C22semidirect
44. C2×C32×D8C22semidirect
45. C2×#3754C22semidirect
46. C2×#3753C22semidirect
47. #64120C22semidirect
48. C2×#3744C22semidirect
49. C2×#3743C22semidirect
50. C2×C3×#214C22semidirect
51. C2×C3×#214C22semidirect
52. C2×C3×#214C22semidirect
53. C2×C3×#213C22semidirect
54. C3×#912C22semidirect
55. C3×#911C22semidirect
56. C2×C3×Dic12C22semidirect
57. C2×C3×#204C22semidirect
58. C2×C3×ΓL(1,𝔽25)C22semidirect
59. C2×C3×D3×C8C22semidirect
60. #63936C22semidirect
61. #63935C22semidirect
62. #63930C22semidirect
63. #63929C22semidirect
64. D3×#214C22semidirect
65. #63925C22semidirect
66. C2×#3719C22semidirect
67. C2×#3718C22semidirect
68. C2×#3717C22semidirect
69. C2×#3717C22semidirect
70. C2×#3716C22semidirect
71. C2×#3715C22semidirect
72. C2×#3711C22semidirect
73. C2×#3710C22semidirect
74. C2×D3×C3⋊C8C22semidirect
75. #63811C22semidirect
76. #63804C22semidirect
77. #63801C22semidirect
78. D3×#204C22semidirect
102. C2×#912D3semidirect
107. C2×#911D3semidirect
121. #3830C23semidirect
138. C3×#237C23semidirect
139. C3×#237C23semidirect
178. #3797C23semidirect
183. D3×Dic6C23semidirect
184. D3×Dic6C23semidirect
185. C32×D8C23semidirect
187. #3754C23semidirect
188. #3753C23semidirect
190. #3744C23semidirect
191. #3743C23semidirect
192. C3×#214C23semidirect
193. C3×#214C23semidirect
194. C3×#214C23semidirect
195. C3×#213C23semidirect
198. C3×Dic12C23semidirect
199. C3×#204C23semidirect
200. C3×ΓL(1,𝔽25)C23semidirect
201. C3×D3×C8C23semidirect
202. #3719C23semidirect
203. #3718C23semidirect
204. #3717C23semidirect
205. #3717C23semidirect
206. #3716C23semidirect
207. #3715C23semidirect
208. #3711C23semidirect
209. #3710C23semidirect
210. D3×C3⋊C8C23semidirect
242. C2×#237C2×D3semidirect
243. C2×#237C2×D3semidirect
273. C2×C3×D8C2×D3semidirect
274. C2×C3×D8C2×D3semidirect
292. C2×#214C2×D3semidirect
293. C2×#214C2×D3semidirect
294. C2×#214C2×D3semidirect
298. C2×#213C2×D3semidirect
312. #912C2×D3semidirect
317. #911C2×D3semidirect
321. C2×Dic12C2×D3semidirect
329. C2×#204C2×D3semidirect
335. C2×ΓL(1,𝔽25)C2×D3semidirect
339. C2×D3×C8C2×D3semidirect
519. #237C22×D3semidirect
520. #237C22×D3semidirect
594. C3×D8C22×D3semidirect
595. C3×D8C22×D3semidirect
614. #214C22×D3semidirect
615. #214C22×D3semidirect
616. #214C22×D3semidirect
620. #213C22×D3semidirect
629. Dic12C22×D3semidirect
636. #204C22×D3semidirect
641. ΓL(1,𝔽25)C22×D3semidirect
645. D3×C8C22×D3semidirect
725. C2×D8D32semidirect
903. C2×C32#577semidirect
998. D8C2×D32semidirect
1077. C32C2×#577semidirect
1161. C2×C3#5770semidirect
1162. C2×C3#5775semidirect
1202. C3C2×#5770semidirect
1203. C3C2×#5775semidirect
1211. C2#10594736direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643142
C2×#643092
C2×#641202
C2×C3×#9122
C2×C3×#9112
C2×#639362
C2×#639352
C2×#639302
C2×#639292
C2×D3×#2142
C2×#639252
#105947362
C2×#638112
C2×#638042
C2×#638012
C2×D3×#2042
C2×#57753
C2×#57703