Finite Group Databasebeta

← C2×#10595470 #11918757

Subgroups — C2×#10595470 #11918757

Order 1152.

3117 conjugacy classes of subgroups.

The subgroup lattice has 969 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×#64158C211yesmaximal, characteristic, complemented
4C2×C3×#951C211yesmaximal, characteristic, complemented
5#10595470C2116yesmaximal, direct product factor
6C2×#63949C212yesmaximal, complemented
7C2×#63948C212yesmaximal, complemented
8C2×#63935C212yesmaximal, complemented
9C2×#63934C212yesmaximal, complemented
10C2×#63827C211yesmaximal, characteristic, complemented
11C2×#63825C211yesmaximal, characteristic, complemented
12C2×D3×#208C211yesmaximal, characteristic, complemented
13C2×#5822—31nomaximal
14C2×#5777—31nomaximal
15C2×C32×#41C2211yescharacteristic
16C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
17C3×D3×#41—24no—
18C3×D3×#41C2218yescomplemented
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21C2×C3×#237—21no—
22C2×C3×#237C2211yescharacteristic, complemented
23C2×C3×D3×D4—21no—
24C2×C3×D3×D4C2211yescharacteristic, complemented
25C2×C3×#235—21no—
26C2×C3×#235C2211yescharacteristic
27C22×C3×C4×D3—21no—
28C22×C3×C4×D3C2211yescharacteristic
29C22×C3×Dic6C2211yescharacteristic, complemented
30C22×#626—21no—
31C22×#624—21no—
32C2×#3799—24no—
33C2×#3799—21no—
34C2×#3799—21no—
35C2×#3799C2212yes—
36C2×#3799C2218yescomplemented
37C2×#3799C2212yescomplemented
38#64158C2218yescomplemented
39C2×#3755C2212yescomplemented
40C2×#3753C2212yescomplemented
41C2×#3748C2211yescharacteristic, complemented
42C3×#951C2218yescomplemented
43C2×C3×#216C2212yescomplemented
44C2×C3×#214C2212yescomplemented
45C2×C3×#208C2211yescharacteristic, complemented
46#63949C22116yescomplemented
47#63948C22116yescomplemented
48#63935C22116yescomplemented
49#63934C22116yescomplemented
50C2×#3718C2212yescomplemented
51C2×#3717C2212yescomplemented
52#63827C2218yescomplemented
53C2×#3715C2212yescomplemented
54#63825C2218yescomplemented
55C2×#3714C2212yescomplemented
56C2×#3711C2212yescomplemented
57D3×#208C2218yescomplemented
58C2×D3×C3⋊C8C2212yescomplemented
59C22×C3×#41—31no—
60C2×D3×#41D311yescharacteristic, complemented
61C22×#239—31no—
62C22×#235—31no—
63C2×C3×#137—31no—
64C2×#951—31no—
65C2×#951D311yescharacteristic, complemented
66#5822—316no—
67C2×#950—32no—
68C2×#950—32no—
69C2×#949—31no—
70C2×#949—31no—
71C2×#949—31no—
72C2×#949—61no—
73C2×#942—31no—
74C2×#942—32no—
75C2×#932—32no—
76C22×#208—31no—
77#5777—316no—
78C2×#919—32no—
79C2×#918—32no—
80C2×#916—32no—
81C2×#914—32no—
82C2×#908—31no—
83C2×D3×M16—31no—
84C23×C3⋊D3—21no—
85C23×C3×D3—21no—
86C23×C3×D3D411yescharacteristic
87C32×#41—22no—
88C32×#41C2314yes—
89C2×C32×Q8C2311yescharacteristic
90C2×C32×D4—21no—
91C2×C32×D4C2311yescharacteristic
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—22no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2312yes—
97C2×C4⋊(C3⋊D3)C2314yescomplemented
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3D411yescharacteristic
104C3×#239—22no—
105C3×#239C2314yescomplemented
106C3×D3×Q8—22no—
107C3×D3×Q8C2314yescomplemented
108C3×#237—28no—
109C3×#237—22no—
110C3×#237C2314yescomplemented
111C3×D3×D4—28no—
112C3×D3×D4—22no—
113C3×D3×D4C2314yescomplemented
114C3×#235—22no—
115C3×#235—28no—
116C3×#235C2314yes—
117C2×C3×D12—21no—
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—28no—
123C2×C3×C4×D3D411yescharacteristic
124C2×C3×C4×D3D411yescharacteristic
125C2×C3×C4×D3D414yes—
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×C4×D3C2314yes—
129C2×C3×Dic6—22no—
130C2×C3×Dic6—21no—
131C2×C3×Dic6—21no—
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×C3×Dic6C2314yescomplemented
135C2×#626—22no—
136C2×#626—28no—
137C2×#626—22no—
138C2×#624—22no—
139C2×#624—28no—
140C2×#624—22no—
141#3799—24no—
142#3799—28no—
143#3799—28no—
144#3799—24no—
145#3799C2318yes—
146#3799C2318yescomplemented
147#3755C2318yescomplemented
148#3753C2318yescomplemented
149#3748C2314yescomplemented
150C2×C3⋊(C3⋊C8)C2312yes—
151C3×#216C2318yescomplemented
152C3×#214C2318yescomplemented
153C3×#208C2314yescomplemented
154C2×C3×C3⋊C8C2312yes—
155#3718C2318yescomplemented
156#3717C2318yescomplemented
157#3715C2318yescomplemented
158#3714C2318yescomplemented
159#3711C2318yescomplemented
160D3×C3⋊C8C2318yescomplemented
161C2×#575—91noSylow
162C2×C3×#41—21no—
163C2×C3×#41—38no—
164C2×C3×#41—31no—
165C2×C3×#41—31no—
166C2×C3×#41—31no—
167C2×C3×#41—61no—
168C2×C3×#41—61no—
169C2×C3×#41—64no—
170C2×C3×#41C2×D311yescharacteristic
171C2×C3×#41C2×D311yescharacteristic
172C22×C3×Q8—31no—
173C22×C3×Q8—31no—
174C22×C3×D4—31no—
175C22×C3×D4—61no—
176C23×C3×C4—31no—
177C23×C3×C4—61no—
178C22×#67—61no—
179D3×#41—24no—
180D3×#41C2×D318yescomplemented
181C2×#239—32no—
182C2×#239—32no—
183C2×#239—38no—
184C2×#239—61no—
185C2×#239—61no—
186C2×#239—64no—
187C2×#239C2×D311yescharacteristic, complemented
188C2×D3×Q8C2×D311yescharacteristic, complemented
189C2×#237—21no—
190C2×#237C2×D311yescharacteristic, complemented
191C2×D3×D4—21no—
192C2×D3×D4C2×D311yescharacteristic, complemented
193C2×#235—21no—
194C2×#235—32no—
195C2×#235—32no—
196C2×#235—38no—
197C2×#235—61no—
198C2×#235—64no—
199C2×#235—61no—
200C2×#235C2×D311yescharacteristic
201C22×D12—31no—
202C22×D12—31no—
203C22×D12—61no—
204C22×D12—61no—
205C22×C4×D3—21no—
206C22×C4×D3—61no—
207C22×C4×D3—61no—
208C22×C4×D3C2×D311yescharacteristic
209C22×Dic6C2×D311yescharacteristic, complemented
210C3×#137—38no—
211C2×C3×Q16—32no—
212C2×C3×SD16—32no—
213C2×C3×M16—31no—
214#951—38no—
215#951C2×D318yescomplemented
216#950—316no—
217#950—316no—
218#949—38no—
219#949—38no—
220#949—38no—
221#949—68no—
222C2×#216—32no—
223C2×#216—32no—
224C2×#216C2×D312yescomplemented
225#942—38no—
226#942—316no—
227C2×#215—32no—
228C2×#215—32no—
229C2×#215—32no—
230C2×#215—32no—
231C2×#215—62no—
232C2×#214—32no—
233C2×#214C2×D312yescomplemented
234#932—316no—
235C2×#213—32no—
236C2×#213—32no—
237C2×#213—32no—
238C2×#213—62no—
239C2×#208—31no—
240C2×#208—31no—
241C2×#208—38no—
242C2×#208—32no—
243C2×#208—61no—
244C2×#208C2×D311yescharacteristic, complemented
245C22×C3⋊C8—32no—
246#919—316no—
247#918—316no—
248#916—316no—
249#914—316no—
250#908—38no—
251D3×M16—38no—
252C2×D24—32no—
253C2×#204—32no—
254C2×ΓL(1,𝔽25)—32no—
255C2×D3×C8—32no—
256C23×C32—21no—
257C23×C32C2×D411yescharacteristic
258C22×C3⋊D3—22no—
259C22×C3⋊D3—24no—
260C22×C3⋊D3—44no—
261C22×C3×D3—21no—
262C22×C3×D3—24no—
263C22×C3×D3—42no—
264C22×C3×D3—44no—
265C22×C3×D3C2×D411yescharacteristic
266C22×C3×D3C2×D411yescharacteristic
267C22×C3×D3C2×D414yes—
268C32×Q8—21no—
269C32×Q8C2412yes—
270C32×D4—24no—
271C32×D4—21no—
272C32×D4C2412yes—
273C2×C32×C4—21no—
274C2×C32×C4—24no—
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2×D412yes—
277C2×C32×C4C2411yescharacteristic
278C2×C32×C4C2412yes—
279C4⋊(C3⋊D3)—22no—
280C4⋊(C3⋊D3)—24no—
281C4⋊(C3⋊D3)C2414yes—
282C3×#67—24no—
283C3×#67—24no—
284C3×#67—24no—
285C2×C3×Dic3—22no—
286C2×C3×Dic3—24no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—24no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D414yes—
292C3×D12—24no—
293C3×D12—21no—
294C3×D12C2412yes—
295C3×C4×D3—24no—
296C3×C4×D3—24no—
297C3×C4×D3—24no—
298C3×C4×D3C2×D414yes—
299C3×C4×D3C2×D414yes—
300C3×C4×D3C2×D412yes—
301C3×C4×D3C2×D412yes—
302C3×C4×D3C2412yes—
303C3×C4×D3C2412yes—
304C3×Dic6—22no—
305C3×Dic6—24no—
306C3×Dic6—21no—
307C3×Dic6—24no—
308C3×Dic6C2414yes—
309C3×Dic6C2412yes—
310#626—28no—
311#626—28no—
312#624—28no—
313#624—28no—
314C3⋊(C3⋊C8)C2414yes—
315C3×C3⋊C8C2414yes—
316C22×#41—31no—
317C22×#41—91no—
318#575—916no—
319C2×#137—31no—
320C2×#137—92no—
321C2×#137—91no—
322C2×AGL(1,ℤ/8)—91no—
323C2×AGL(1,ℤ/8)—92no—
324C2×AGL(1,ℤ/8)—91no—
325C2×#135—92no—
326C2×#135—92no—
327C22×M16—91no—
328C24×C3—31no—
329C24×C3—61no—
330C23×D3—21no—
331C23×D3—61no—
332C23×D3—61no—
333C23×D3—121no—
334C23×D3#6711yescharacteristic
335C3×#41—22no—
336C3×#41—22no—
337C3×#41—24no—
338C3×#41—34no—
339C3×#41—34no—
340C3×#41—34no—
341C3×#41—42no—
342C3×#41—68no—
343C3×#41—68no—
344C3×#41—62no—
345C3×#41—62no—
346C3×#41—62no—
347C3×#41C22×D314yes—
348C3×#41C22×D314yes—
349C2×C3×Q8—21no—
350C2×C3×Q8—34no—
351C2×C3×Q8—31no—
352C2×C3×Q8—32no—
353C2×C3×Q8—34no—
354C2×C3×Q8—61no—
355C2×C3×Q8—62no—
356C2×C3×Q8—61no—
357C2×C3×Q8—62no—
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×D4—21no—
361C2×C3×D4—21no—
362C2×C3×D4—21no—
363C2×C3×D4—34no—
364C2×C3×D4—31no—
365C2×C3×D4—41no—
366C2×C3×D4—61no—
367C2×C3×D4—62no—
368C2×C3×D4—61no—
369C2×C3×D4—68no—
370C2×C3×D4—61no—
371C2×C3×D4—61no—
372C2×C3×D4C22×D311yescharacteristic
373C2×C3×D4C22×D311yescharacteristic
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—21no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—34no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—34no—
384C22×C3×C4—41no—
385C22×C3×C4—61no—
386C22×C3×C4—68no—
387C22×C3×C4—61no—
388C22×C3×C4—61no—
389C22×C3×C4—61no—
390C22×C3×C4—61no—
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C2×#67—21no—
394C2×#67—21no—
395C2×#67—21no—
396C2×#67—62no—
397C2×#67—62no—
398C2×#67—68no—
399C22×Dic3—21no—
400C22×Dic3—21no—
401C22×Dic3#6711yescharacteristic
402#239—22no—
403#239—38no—
404#239—38no—
405#239—68no—
406#239—68no—
407#239—64no—
408#239—64no—
409#239C22×D314yescomplemented
410D3×Q8—22no—
411D3×Q8C22×D314yescomplemented
412#237—28no—
413#237—22no—
414#237C22×D314yescomplemented
415D3×D4—28no—
416D3×D4—22no—
417D3×D4C22×D314yescomplemented
418#235—22no—
419#235—28no—
420#235—38no—
421#235—38no—
422#235—64no—
423#235—64no—
424#235—68no—
425#235—68no—
426#235C22×D314yes—
427C2×D12—21no—
428C2×D12—32no—
429C2×D12—34no—
430C2×D12—32no—
431C2×D12—34no—
432C2×D12—62no—
433C2×D12—64no—
434C2×D12—62no—
435C2×D12—62no—
436C2×D12—68no—
437C2×D12—61no—
438C2×D12—62no—
439C2×D12—61no—
440C2×D12—62no—
441C2×D12—121no—
442C2×D12—122no—
443C2×D12C22×D311yescharacteristic
444C2×C4×D3—21no—
445C2×C4×D3—21no—
446C2×C4×D3—21no—
447C2×C4×D3—28no—
448C2×C4×D3—62no—
449C2×C4×D3—62no—
450C2×C4×D3—68no—
451C2×C4×D3—62no—
452C2×C4×D3—62no—
453C2×C4×D3—68no—
454C2×C4×D3#6711yescharacteristic
455C2×C4×D3#6711yescharacteristic
456C2×C4×D3#6714yes—
457C2×C4×D3C22×D311yescharacteristic
458C2×C4×D3C22×D311yescharacteristic
459C2×C4×D3C22×D314yes—
460C2×Dic6—22no—
461C2×Dic6—21no—
462C2×Dic6—21no—
463C2×Dic6C22×D311yescharacteristic
464C2×Dic6C22×D312yes—
465C2×Dic6C22×D314yescomplemented
466C3×Q16—38no—
467C3×SD16—38no—
468C3×M16—34no—
469C2×C3×C8—32no—
470#216—38no—
471#216—38no—
472#216C22×D318yescomplemented
473#215—38no—
474#215—38no—
475#215—38no—
476#215—38no—
477#215—68no—
478#214—38no—
479#214C22×D318yescomplemented
480#213—38no—
481#213—38no—
482#213—38no—
483#213—68no—
484#208—34no—
485#208—34no—
486#208—38no—
487#208—64no—
488#208C22×D314yescomplemented
489C2×C3⋊C8—32no—
490C2×C3⋊C8—32no—
491C2×C3⋊C8—38no—
492C2×C3⋊C8—62no—
493C2×C3⋊C8C22×D312yes—
494D24—38no—
495#204—38no—
496ΓL(1,𝔽25)—38no—
497D3×C8—38no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—42no—
501C22×C32C22×D412yes—
502C22×C32C22×D411yescharacteristic
503C2×C3⋊D3—24no—
504C2×C3⋊D3—48no—
505C2×C3⋊D3—44no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—44no—
510C2×C3×D3—48no—
511C2×C3×D3—42no—
512C2×C3×D3C22×D412yes—
513C2×C3×D3C22×D412yes—
514C32×C4—22no—
515C32×C4C22×D411yescharacteristic
516C32×C4C22×D412yes—
517C32×C4C2511yescharacteristic
518C3×Dic3—24no—
519C3×Dic3—22no—
520C3×Dic3C22×D412yes—
521C3×Dic3C22×D412yes—
522C2×#41—38no—
523C2×#41—31no—
524C2×#41—31no—
525C2×#41—31no—
526C2×#41—61no—
527C2×#41—61no—
528C2×#41—64no—
529C2×#41—92no—
530C2×#41—92no—
531C2×#41—98no—
532C2×#41—181no—
533C2×#41—184no—
534C2×#41—181no—
535C2×#41D3211yescharacteristic
536C22×Q8—31no—
537C22×Q8—31no—
538C22×D4—31no—
539C22×D4—61no—
540C22×D4—91no—
541C22×D4—181no—
542C23×C4—31no—
543C23×C4—61no—
544C23×C4—181no—
545#137—38no—
546#137—916no—
547#137—98no—
548AGL(1,ℤ/8)—98no—
549AGL(1,ℤ/8)—916no—
550AGL(1,ℤ/8)—98no—
551#135—916no—
552#135—916no—
553C2×Q16—32no—
554C2×Q16—92no—
555C2×SD16—32no—
556C2×SD16—92no—
557C2×SD16—92no—
558C2×SD16—92no—
559C2×D8—92no—
560C2×D8—92no—
561C2×M16—31no—
562C2×M16—92no—
563C2×M16—98no—
564C2×M16—91no—
565C22×C8—92no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—31no—
570C23×C3—31no—
571C23×C3—34no—
572C23×C3—41no—
573C23×C3—64no—
574C23×C3—61no—
575C23×C3—122no—
576C23×C3—124no—
577C23×C3D3×D411yescharacteristic
578C23×C3C2×#6711yescharacteristic
579C22×D3—21no—
580C22×D3—24no—
581C22×D3—42no—
582C22×D3—44no—
583C22×D3—64no—
584C22×D3—62no—
585C22×D3—64no—
586C22×D3—62no—
587C22×D3—124no—
588C22×D3—122no—
589C22×D3—124no—
590C22×D3—124no—
591C22×D3—244no—
592C22×D3C2×#6711yescharacteristic
593C22×D3C2×#6711yescharacteristic
594C22×D3C2×#6714yes—
595C3×Q8—21no—
596C3×Q8—21no—
597C3×Q8—22no—
598C3×Q8—32no—
599C3×Q8—34no—
600C3×Q8—41no—
601C3×Q8—64no—
602C3×Q8—61no—
603C3×Q8—62no—
604C3×Q8—64no—
605C3×Q8C23×D312yes—
606C3×Q8C23×D312yes—
607C3×D4—24no—
608C3×D4—24no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—22no—
612C3×D4—32no—
613C3×D4—41no—
614C3×D4—44no—
615C3×D4—64no—
616C3×D4—64no—
617C3×D4—64no—
618C3×D4—64no—
619C3×D4—61no—
620C3×D4C23×D312yes—
621C3×D4C23×D312yes—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—24no—
625C2×C3×C4—24no—
626C2×C3×C4—21no—
627C2×C3×C4—22no—
628C2×C3×C4—21no—
629C2×C3×C4—22no—
630C2×C3×C4—31no—
631C2×C3×C4—31no—
632C2×C3×C4—34no—
633C2×C3×C4—34no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—34no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—44no—
640C2×C3×C4—41no—
641C2×C3×C4—64no—
642C2×C3×C4—64no—
643C2×C3×C4—64no—
644C2×C3×C4—61no—
645C2×C3×C4—64no—
646C2×C3×C4—62no—
647C2×C3×C4—64no—
648C2×C3×C4D3×D411yescharacteristic
649C2×C3×C4D3×D412yes—
650C2×C3×C4C2×#6711yescharacteristic
651C2×C3×C4C2×#6712yes—
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D312yes—
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D312yes—
656#67—24no—
657#67—24no—
658#67—24no—
659#67—68no—
660#67—68no—
661C2×Dic3—22no—
662C2×Dic3—24no—
663C2×Dic3—21no—
664C2×Dic3—24no—
665C2×Dic3C2×#6711yescharacteristic
666C2×Dic3C2×#6711yescharacteristic
667C2×Dic3C2×#6714yes—
668D12—24no—
669D12—21no—
670D12—34no—
671D12—34no—
672D12—64no—
673D12—68no—
674D12—68no—
675D12—64no—
676D12—62no—
677D12—62no—
678D12—64no—
679D12—124no—
680D12—122no—
681D12C23×D312yes—
682C4×D3—24no—
683C4×D3—24no—
684C4×D3—24no—
685C4×D3—68no—
686C4×D3—68no—
687C4×D3—68no—
688C4×D3—68no—
689C4×D3C2×#6714yes—
690C4×D3C2×#6714yes—
691C4×D3C2×#6712yes—
692C4×D3C2×#6712yes—
693C4×D3C23×D312yes—
694C4×D3C23×D312yes—
695Dic6—22no—
696Dic6—24no—
697Dic6—21no—
698Dic6—24no—
699Dic6C23×D312yes—
700Dic6C23×D314yes—
701C3×C8—34no—
702C3⋊C8—34no—
703C3⋊C8—34no—
704C3⋊C8—64no—
705C3⋊C8C23×D314yes—
706C2×C32—22no—
707C2×C32—42no—
708C2×C32#57512yescomplemented
709C2×C32C23×D411yescharacteristic
710C3⋊D3—44no—
711C3×D3—22no—
712C3×D3—22no—
713C3×D3—42no—
714C24—31no—
715C24—61no—
716C24—181no—
717#41—22no—
718#41—34no—
719#41—34no—
720#41—34no—
721#41—68no—
722#41—68no—
723#41—62no—
724#41—62no—
725#41—62no—
726#41—98no—
727#41—98no—
728#41—188no—
729#41—184no—
730#41—184no—
731#41—188no—
732#41C2×D3214yes—
733C2×Q8—34no—
734C2×Q8—32no—
735C2×Q8—31no—
736C2×Q8—34no—
737C2×Q8—61no—
738C2×Q8—62no—
739C2×Q8—62no—
740C2×Q8—61no—
741C2×Q8C2×D3211yescharacteristic
742C2×D4—21no—
743C2×D4—34no—
744C2×D4—31no—
745C2×D4—61no—
746C2×D4—62no—
747C2×D4—61no—
748C2×D4—68no—
749C2×D4—61no—
750C2×D4—61no—
751C2×D4—92no—
752C2×D4—94no—
753C2×D4—188no—
754C2×D4—182no—
755C2×D4—182no—
756C2×D4—182no—
757C2×D4—181no—
758C2×D4C2×D3211yescharacteristic
759C22×C4—21no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—34no—
764C22×C4—31no—
765C22×C4—34no—
766C22×C4—31no—
767C22×C4—61no—
768C22×C4—68no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—188no—
774C22×C4—182no—
775C22×C4—182no—
776C22×C4C2×D3211yescharacteristic
777Q16—38no—
778Q16—98no—
779SD16—38no—
780SD16—98no—
781SD16—98no—
782SD16—98no—
783D8—98no—
784D8—98no—
785M16—34no—
786M16—98no—
787M16—94no—
788C2×C8—32no—
789C2×C8—98no—
790C2×C8—92no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—21no—
797C22×C3—32no—
798C22×C3—32no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—82no—
807C22×C3—124no—
808C22×C3—128no—
809C22×C3—122no—
810C22×C3C2×D3×D412yes—
811C22×C3C2×D3×D411yescharacteristic
812C22×C3C22×#6712yes—
813C22×C3C22×#6711yescharacteristic
814C2×D3—22no—
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—44no—
818C2×D3—48no—
819C2×D3—42no—
820C2×D3—64no—
821C2×D3—64no—
822C2×D3—124no—
823C2×D3—128no—
824C2×D3—128no—
825C2×D3—124no—
826C2×D3—124no—
827C2×D3—244no—
828C2×D3—248no—
829C2×D3C22×#6712yes—
830C2×D3C22×#6712yes—
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—22no—
834C3×C4—21no—
835C3×C4—21no—
836C3×C4—32no—
837C3×C4—32no—
838C3×C4—42no—
839C3×C4—62no—
840C3×C4—64no—
841C3×C4C2×D3×D412yes—
842C3×C4C2×D3×D411yescharacteristic
843C3×C4C22×#6711yescharacteristic
844C3×C4C22×#6712yes—
845C3×C4C24×D311yescharacteristic
846C3×C4C24×D311yescharacteristic
847Dic3—24no—
848Dic3—22no—
849Dic3C22×#6712yes—
850Dic3C22×#6712yes—
851C32C2×#57511yescharacteristic, complemented, Sylow
852C23—21no—
853C23—31no—
854C23—31no—
855C23—34no—
856C23—64no—
857C23—61no—
858C23—122no—
859C23—124no—
860C23—184no—
861C23—182no—
862C23—364no—
863C23D3×#6711yescharacteristic
864Q8—21no—
865Q8—34no—
866Q8—32no—
867Q8—64no—
868Q8—61no—
869Q8—64no—
870Q8—62no—
871Q8C22×D3212yes—
872D4—24no—
873D4—21no—
874D4—32no—
875D4—64no—
876D4—64no—
877D4—64no—
878D4—64no—
879D4—61no—
880D4—94no—
881D4—188no—
882D4—188no—
883D4—184no—
884D4—182no—
885D4C22×D3212yes—
886C2×C4—21no—
887C2×C4—24no—
888C2×C4—34no—
889C2×C4—31no—
890C2×C4—31no—
891C2×C4—34no—
892C2×C4—32no—
893C2×C4—32no—
894C2×C4—34no—
895C2×C4—32no—
896C2×C4—32no—
897C2×C4—64no—
898C2×C4—64no—
899C2×C4—64no—
900C2×C4—64no—
901C2×C4—61no—
902C2×C4—62no—
903C2×C4—64no—
904C2×C4—188no—
905C2×C4—188no—
906C2×C4D3×#6712yes—
907C2×C4D3×#6711yescharacteristic
908C2×C4C22×D3212yes—
909C2×C4C22×D3211yescharacteristic
910C8—34no—
911C8—94no—
912C2×C3—22no—
913C2×C3—22no—
914C2×C3—21no—
915C2×C3—22no—
916C2×C3—42no—
917C2×C3—42no—
918C2×C3—42no—
919C2×C3—62no—
920C2×C3—62no—
921C2×C3—82no—
922C2×C3—122no—
923C2×C3#577712yescomplemented
924C2×C3#582212yescomplemented
925C2×C3C22×D3×D411yescharacteristic
926C2×C3C23×#6711yescharacteristic
927D3—22no—
928D3—22no—
929D3—42no—
930D3—124no—
931D3—124no—
932D3—244no—
933C22—22no—
934C22—22no—
935C22—32no—
936C22—32no—
937C22—42no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—124no—
942C22—128no—
943C22—122no—
944C22—184no—
945C22—368no—
946C22—364no—
947C22C2×D3×#6712yes—
948C22C2×D3×#6711yescharacteristic
949C4—22no—
950C4—32no—
951C4—32no—
952C4—62no—
953C4—64no—
954C4C2×D3×#6712yes—
955C4C2×D3×#6711yescharacteristic
956C4C23×D3211yescharacteristic
957C3—21no—
958C3C2×#577711yescharacteristic, complemented
959C3C2×#582211yescharacteristic, complemented
960C2—22no—
961C2—42no—
962C2—62no—
963C2—62no—
964C2—122no—
965C2—364no—
966C2#1059547012yesdirect product factor
967C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. C22×#3799C2semidirect
3. C2×#64158C2semidirect
4. C2×C3×#951C2semidirect
5. #10595470C2direct (N × H)
6. C2×#63949C2semidirect
7. C2×#63948C2semidirect
8. C2×#63935C2semidirect
9. C2×#63934C2semidirect
10. C2×#63827C2semidirect
11. C2×#63825C2semidirect
12. C2×D3×#208C2semidirect
16. C22×C4⋊(C3⋊D3)C22semidirect
18. C3×D3×#41C22semidirect
19. C2×C3×#239C22semidirect
20. C2×C3×D3×Q8C22semidirect
22. C2×C3×#237C22semidirect
24. C2×C3×D3×D4C22semidirect
29. C22×C3×Dic6C22semidirect
36. C2×#3799C22semidirect
37. C2×#3799C22semidirect
38. #64158C22semidirect
39. C2×#3755C22semidirect
40. C2×#3753C22semidirect
41. C2×#3748C22semidirect
42. C3×#951C22semidirect
43. C2×C3×#216C22semidirect
44. C2×C3×#214C22semidirect
45. C2×C3×#208C22semidirect
46. #63949C22semidirect
47. #63948C22semidirect
48. #63935C22semidirect
49. #63934C22semidirect
50. C2×#3718C22semidirect
51. C2×#3717C22semidirect
52. #63827C22semidirect
53. C2×#3715C22semidirect
54. #63825C22semidirect
55. C2×#3714C22semidirect
56. C2×#3711C22semidirect
57. D3×#208C22semidirect
58. C2×D3×C3⋊C8C22semidirect
60. C2×D3×#41D3semidirect
65. C2×#951D3semidirect
97. C2×C4⋊(C3⋊D3)C23semidirect
105. C3×#239C23semidirect
107. C3×D3×Q8C23semidirect
110. C3×#237C23semidirect
113. C3×D3×D4C23semidirect
134. C2×C3×Dic6C23semidirect
146. #3799C23semidirect
147. #3755C23semidirect
148. #3753C23semidirect
149. #3748C23semidirect
151. C3×#216C23semidirect
152. C3×#214C23semidirect
153. C3×#208C23semidirect
155. #3718C23semidirect
156. #3717C23semidirect
157. #3715C23semidirect
158. #3714C23semidirect
159. #3711C23semidirect
160. D3×C3⋊C8C23semidirect
180. D3×#41C2×D3semidirect
187. C2×#239C2×D3semidirect
188. C2×D3×Q8C2×D3semidirect
190. C2×#237C2×D3semidirect
192. C2×D3×D4C2×D3semidirect
209. C22×Dic6C2×D3semidirect
215. #951C2×D3semidirect
224. C2×#216C2×D3semidirect
233. C2×#214C2×D3semidirect
244. C2×#208C2×D3semidirect
409. #239C22×D3semidirect
411. D3×Q8C22×D3semidirect
414. #237C22×D3semidirect
417. D3×D4C22×D3semidirect
465. C2×Dic6C22×D3semidirect
472. #216C22×D3semidirect
479. #214C22×D3semidirect
488. #208C22×D3semidirect
708. C2×C32#575semidirect
851. C32C2×#575semidirect
923. C2×C3#5777semidirect
924. C2×C3#5822semidirect
958. C3C2×#5777semidirect
959. C3C2×#5822semidirect
966. C2#10595470direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C22×#37992
C2×#641582
C2×C3×#9512
#105954702
C2×#639492
C2×#639482
C2×#639352
C2×#639342
C2×#638272
C2×#638252
C2×D3×#2082
C2×#58223
C2×#57773