Finite Group Databasebeta

← C2×#10595097 #11918813

Subgroups — C2×#10595097 #11918813

Order 1152.

3193 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C2×#64308C211yesmaximal, characteristic, complemented
3C22×#3753C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5C2×#63935C212yesmaximal, complemented
6C2×#63934C212yesmaximal, complemented
7#10595097C2116yesmaximal, direct product factor
8C2×#63925C212yesmaximal, complemented
9C2×D3×#213C212yesmaximal, complemented
10C2×#63825C211yesmaximal, characteristic, complemented
11C2×#63822C211yesmaximal, characteristic, complemented
12C2×#63815C211yesmaximal, characteristic, complemented
13C2×#5835—31nomaximal
14C2×#5774—31nomaximal
15C22×C32×D4C2211yescharacteristic, complemented
16C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
17C22×C3×#67—22no—
18C3×#1004—24no—
19C3×#1004C2218yescomplemented
20C2×C3×#237—21no—
21C2×C3×#237C2212yescomplemented
22C2×C3×D3×D4—21no—
23C2×C3×D3×D4C2212yescomplemented
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic, complemented
26C2×C3×#235C2211yescharacteristic, complemented
27C2×#3811—22no—
28#64308—24no—
29#64308C2218yescomplemented
30C2×D3×D12—21no—
31C2×D3×D12C2212yescomplemented
32C2×#3799—21no—
33C2×#3799C2212yescomplemented
34C2×#3753C2212yescomplemented
35C2×#3753C2212yescomplemented
36C2×#3753C2218yescomplemented
37C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
38C2×C3×#214C2212yescomplemented
39C3×#932C2218yescomplemented
40C2×C3×#213C2212yescomplemented
41C2×C3×#208C2211yescharacteristic, complemented
42#63935C22116yescomplemented
43#63934C22116yescomplemented
44#63925C22116yescomplemented
45D3×#213C22116yescomplemented
46C2×#3718C2211yescharacteristic, complemented
47C2×#3717C2212yescomplemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50#63825C2218yescomplemented
51C2×#3714C2212yescomplemented
52#63822C2218yescomplemented
53C2×#3713C2211yescharacteristic, complemented
54C2×#3711C2212yescomplemented
55#63815C2218yescomplemented
56C2×D3×C3⋊C8C2212yescomplemented
57C2×C3×H(5,𝔽2)—31no—
58C2×#1009—31no—
59C2×#1009—31no—
60C2×#1004D311yescharacteristic, complemented
61C2×C3×AGL(1,ℤ/8)—31no—
62#5835—316no—
63C2×#950—31no—
64C2×#950—31no—
65C2×#950—32no—
66C2×#949—32no—
67C2×#949—31no—
68C2×#948—31no—
69C2×#932—32no—
70C2×#932D311yescharacteristic, complemented
71C22×#213—31no—
72C22×#213—31no—
73C22×#213—32no—
74C22×#213—61no—
75#5774—316no—
76C2×#916—32no—
77C2×#914—32no—
78C2×#911—32no—
79C2×D3×D8—32no—
80C2×#908—31no—
81C2×#907—31no—
82C24×C32—21no—
83C23×C3⋊D3—21no—
84C23×C3×D3—22no—
85C22×D32—22no—
86C2×C32×D4—21no—
87C2×C32×D4—22no—
88C2×C32×D4C2312yes—
89C2×C32×D4C2314yescomplemented
90C22×C32×C4C2311yescharacteristic
91C2×C4⋊(C3⋊D3)—21no—
92C2×C4⋊(C3⋊D3)—22no—
93C2×C4⋊(C3⋊D3)C2312yes—
94C2×C4⋊(C3⋊D3)C2314yescomplemented
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67—22no—
98C2×C3×#67—216no—
99C2×C3×#67—22no—
100C2×C3×#67D412yes—
101C22×C3×Dic3—22no—
102C3×#237—24no—
103C3×#237—28no—
104C3×#237C2318yescomplemented
105C3×D3×D4—28no—
106C3×D3×D4—24no—
107C3×D3×D4C2318yescomplemented
108C3×#235—22no—
109C3×#235—22no—
110C3×#235D414yes—
111C3×#235C2314yes—
112C3×#235C2314yescomplemented
113C3×#235C2314yescomplemented
114C2×C3×D12D411yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2312yes—
120C2×C3×Dic6D411yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C2×C3×Dic6C2311yescharacteristic
123#3811—216no—
124C2×#626—22no—
125C2×#626—22no—
126C2×#624—22no—
127D3×D12—28no—
128D3×D12—24no—
129D3×D12C2318yescomplemented
130#3799—24no—
131#3799—28no—
132#3799C2318yescomplemented
133#3753C2318yescomplemented
134#3753C2318yescomplemented
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137C2×C3⋊(C3⋊C8)C2314yescomplemented
138C3×#214C2318yescomplemented
139C3×#213C2318yescomplemented
140C3×#208C2314yescomplemented
141C2×C3×C3⋊C8C2312yes—
142#3718C2314yescomplemented
143#3717C2318yescomplemented
144#3715C2314yescomplemented
145#3715C2314yescomplemented
146#3714C2318yescomplemented
147#3713C2314yescomplemented
148#3711C2318yescomplemented
149D3×C3⋊C8C2318yescomplemented
150C2×#576—91noSylow
151C3×H(5,𝔽2)—38no—
152C3×H(5,𝔽2)—64no—
153C2×C3×#41—31no—
154C2×C3×#41—32no—
155C2×C3×#41—31no—
156C2×C3×#41—31no—
157C2×C3×#41—61no—
158C22×C3×D4—21no—
159C22×C3×D4—32no—
160C22×C3×D4—61no—
161C22×C3×D4—62no—
162C22×C3×D4C2×D311yescharacteristic, complemented
163C22×C3×D4C2×D311yescharacteristic, complemented
164C22×#67—22no—
165#1009—38no—
166#1009—38no—
167#1009—64no—
168#1009—64no—
169C2×#239—32no—
170C2×#239—61no—
171#1004—24no—
172#1004C2×D318yescomplemented
173C2×#237—21no—
174C2×#237C2×D312yescomplemented
175C2×D3×D4—21no—
176C2×D3×D4—32no—
177C2×D3×D4—61no—
178C2×D3×D4—62no—
179C2×D3×D4—62no—
180C2×D3×D4C2×D312yescomplemented
181C2×#235—32no—
182C2×#235—61no—
183C2×#235C2×D311yescharacteristic
184C2×#235C2×D311yescharacteristic, complemented
185C2×#235C2×D311yescharacteristic, complemented
186C22×D12—31no—
187C22×D12—31no—
188C22×D12—32no—
189C22×D12—61no—
190C22×D12—61no—
191C3×AGL(1,ℤ/8)—38no—
192C2×C3×SD16—32no—
193C2×C3×D8—32no—
194C2×C3×M16—31no—
195#950—38no—
196#950—38no—
197#950—316no—
198#949—316no—
199#949—38no—
200#948—38no—
201C2×#216—31no—
202C2×#216—31no—
203C2×#215—31no—
204C2×#215—31no—
205C2×#215—32no—
206C2×#214—31no—
207C2×#214—31no—
208C2×#214C2×D312yescomplemented
209#932—316no—
210#932C2×D318yescomplemented
211C2×#213—32no—
212C2×#213—32no—
213C2×#213—32no—
214C2×#213—32no—
215C2×#213—38no—
216C2×#213—38no—
217C2×#213—31no—
218C2×#213—31no—
219C2×#213—316no—
220C2×#213—32no—
221C2×#213—62no—
222C2×#213—62no—
223C2×#213—68no—
224C2×#213C2×D312yescomplemented
225C2×#208—32no—
226C2×#208C2×D311yescharacteristic, complemented
227C22×C3⋊C8—31no—
228C22×C3⋊C8—31no—
229C22×C3⋊C8—32no—
230C22×C3⋊C8—61no—
231#916—316no—
232#914—316no—
233#911—316no—
234D3×D8—316no—
235#908—38no—
236#907—38no—
237C2×D24—32no—
238C2×#204—32no—
239C2×ΓL(1,𝔽25)—32no—
240C2×D3×C8—32no—
241C23×C32—22no—
242C23×C32—24no—
243C23×C32—82no—
244C23×C32C2×D411yescharacteristic
245C22×C3⋊D3—22no—
246C22×C3⋊D3—24no—
247C22×C3⋊D3—82no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—28no—
251C22×C3×D3—84no—
252C22×C3×D3C2×D412yes—
253C2×D32—28no—
254C2×D32—84no—
255C32×D4—22no—
256C32×D4—24no—
257C32×D4C2414yes—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D412yes—
260C2×C32×C4C2411yescharacteristic
261C2×C32×C4C2412yes—
262C4⋊(C3⋊D3)—22no—
263C4⋊(C3⋊D3)—24no—
264C4⋊(C3⋊D3)C2414yes—
265C3×#67—24no—
266C3×#67—24no—
267C3×#67—28no—
268C3×#67—28no—
269C3×#67C2×D418yes—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—28no—
273C2×C3×Dic3C2×D412yes—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12C2×D414yes—
277C3×D12C2412yes—
278C3×D12C2412yes—
279C3×C4×D3—24no—
280C3×C4×D3—24no—
281C3×C4×D3C2×D414yes—
282C3×C4×D3C2414yes—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6C2×D414yes—
286C3×Dic6C2412yes—
287C3×Dic6C2412yes—
288#626—28no—
289#626—28no—
290#624—28no—
291C3⋊(C3⋊C8)C2412yes—
292C3⋊(C3⋊C8)C2412yes—
293C3×C3⋊C8C2414yes—
294C2×H(5,𝔽2)—31no—
295C2×H(5,𝔽2)—91no—
296#576—916no—
297C2×AGL(1,ℤ/8)—31no—
298C2×AGL(1,ℤ/8)—91no—
299C2×AGL(1,ℤ/8)—92no—
300C2×AGL(1,ℤ/8)—92no—
301C2×#135—92no—
302C2×#135—91no—
303C22×D8—92no—
304C22×D8—91no—
305C2×#131—91no—
306C24×C3—21no—
307C24×C3—21no—
308C24×C3—41no—
309C24×C3—62no—
310C23×D3—22no—
311C23×D3—62no—
312C23×D3—61no—
313C23×D3—61no—
314C23×D3—62no—
315C23×D3—121no—
316C3×#41—34no—
317C3×#41—34no—
318C3×#41—38no—
319C3×#41—34no—
320C3×#41—34no—
321C3×#41—64no—
322C3×#41—68no—
323C3×#41—62no—
324C3×#41—62no—
325C2×C3×Q8—31no—
326C2×C3×Q8—31no—
327C2×C3×Q8—31no—
328C2×C3×D4—21no—
329C2×C3×D4—22no—
330C2×C3×D4—21no—
331C2×C3×D4—22no—
332C2×C3×D4—22no—
333C2×C3×D4—24no—
334C2×C3×D4—32no—
335C2×C3×D4—38no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—41no—
340C2×C3×D4—42no—
341C2×C3×D4—64no—
342C2×C3×D4—62no—
343C2×C3×D4—68no—
344C2×C3×D4—616no—
345C2×C3×D4—62no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4C22×D312yes—
349C2×C3×D4C22×D312yes—
350C2×C3×D4C22×D314yescomplemented
351C2×C3×D4C22×D314yescomplemented
352C22×C3×C4—21no—
353C22×C3×C4—32no—
354C22×C3×C4—62no—
355C22×C3×C4—61no—
356C22×C3×C4—61no—
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—21no—
360C2×#67—21no—
361C2×#67—22no—
362C2×#67—216no—
363C2×#67—22no—
364C2×#67—62no—
365C2×#67—62no—
366C2×#67#6712yes—
367C22×Dic3—22no—
368#239—38no—
369#239—68no—
370#239—64no—
371#237—24no—
372#237—28no—
373#237C22×D318yescomplemented
374D3×D4—28no—
375D3×D4—24no—
376D3×D4—38no—
377D3×D4—68no—
378D3×D4—616no—
379D3×D4—616no—
380D3×D4—64no—
381D3×D4C22×D318yescomplemented
382#235—22no—
383#235—22no—
384#235—38no—
385#235—64no—
386#235—68no—
387#235#6714yes—
388#235C22×D314yes—
389#235C22×D314yescomplemented
390#235C22×D314yescomplemented
391C2×D12—32no—
392C2×D12—34no—
393C2×D12—32no—
394C2×D12—34no—
395C2×D12—38no—
396C2×D12—62no—
397C2×D12—64no—
398C2×D12—64no—
399C2×D12—62no—
400C2×D12—62no—
401C2×D12—61no—
402C2×D12—62no—
403C2×D12—61no—
404C2×D12—62no—
405C2×D12—68no—
406C2×D12—121no—
407C2×D12—122no—
408C2×D12#6711yescharacteristic
409C2×D12C22×D311yescharacteristic
410C2×D12C22×D311yescharacteristic
411C2×C4×D3—21no—
412C2×C4×D3—21no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3C22×D312yes—
416C2×Dic6#6711yescharacteristic
417C2×Dic6C22×D311yescharacteristic
418C2×Dic6C22×D311yescharacteristic
419C3×SD16—38no—
420C3×D8—38no—
421C3×M16—34no—
422C2×C3×C8—32no—
423#216—34no—
424#216—34no—
425#215—34no—
426#215—34no—
427#215—38no—
428#214—34no—
429#214—34no—
430#214C22×D318yescomplemented
431#213—38no—
432#213—38no—
433#213—38no—
434#213—38no—
435#213—34no—
436#213—34no—
437#213—38no—
438#213—68no—
439#213—68no—
440#213C22×D318yescomplemented
441#208—38no—
442#208C22×D314yescomplemented
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—34no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—34no—
449C2×C3⋊C8—38no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—64no—
453C2×C3⋊C8C22×D312yes—
454D24—38no—
455#204—38no—
456ΓL(1,𝔽25)—38no—
457D3×C8—38no—
458C22×C32—22no—
459C22×C32—24no—
460C22×C32—44no—
461C22×C32—84no—
462C22×C32C22×D412yes—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—24no—
465C2×C3⋊D3—44no—
466C2×C3⋊D3—84no—
467C2×C3×D3—24no—
468C2×C3×D3—22no—
469C2×C3×D3—22no—
470C2×C3×D3—42no—
471C2×C3×D3—42no—
472C2×C3×D3—88no—
473C2×C3×D3C22×D414yes—
474D32—88no—
475C32×C4C22×D411yescharacteristic
476C32×C4C22×D412yes—
477C32×C4C2511yescharacteristic
478C3×Dic3—22no—
479C3×Dic3—22no—
480C3×Dic3C22×D414yes—
481H(5,𝔽2)—38no—
482H(5,𝔽2)—64no—
483H(5,𝔽2)—98no—
484H(5,𝔽2)—184no—
485C2×#41—31no—
486C2×#41—32no—
487C2×#41—31no—
488C2×#41—31no—
489C2×#41—61no—
490C2×#41—92no—
491C2×#41—181no—
492C22×D4—32no—
493C22×D4—61no—
494C22×D4—62no—
495C22×D4—92no—
496C22×D4—91no—
497C22×D4—181no—
498C22×D4—182no—
499C22×D4D3211yescharacteristic, complemented
500AGL(1,ℤ/8)—38no—
501AGL(1,ℤ/8)—98no—
502AGL(1,ℤ/8)—916no—
503AGL(1,ℤ/8)—916no—
504#135—916no—
505#135—98no—
506C2×Q16—91no—
507C2×SD16—32no—
508C2×SD16—92no—
509C2×SD16—91no—
510C2×SD16—91no—
511C2×D8—32no—
512C2×D8—92no—
513C2×D8—916no—
514C2×D8—91no—
515C2×D8—92no—
516C2×D8—92no—
517C2×D8—98no—
518#131—98no—
519C2×M16—31no—
520C2×M16—92no—
521C22×C8—92no—
522C22×C8—91no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—24no—
526C23×C3—24no—
527C23×C3—21no—
528C23×C3—32no—
529C23×C3—42no—
530C23×C3—44no—
531C23×C3—68no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—82no—
535C23×C3—82no—
536C23×C3—84no—
537C23×C3—244no—
538C23×C3D3×D411yescharacteristic
539C23×C3C2×#6711yescharacteristic
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—28no—
543C22×D3—68no—
544C22×D3—62no—
545C22×D3—62no—
546C22×D3—64no—
547C22×D3—64no—
548C22×D3—68no—
549C22×D3—84no—
550C22×D3—122no—
551C22×D3—124no—
552C22×D3—244no—
553C22×D3—244no—
554C22×D3—242no—
555C22×D3—242no—
556C22×D3—244no—
557C22×D3C2×#6712yes—
558C3×Q8—34no—
559C3×Q8—32no—
560C3×Q8—32no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×D4—22no—
564C3×D4—24no—
565C3×D4—22no—
566C3×D4—24no—
567C3×D4—24no—
568C3×D4—38no—
569C3×D4—34no—
570C3×D4—32no—
571C3×D4—32no—
572C3×D4—42no—
573C3×D4—44no—
574C3×D4—68no—
575C3×D4—68no—
576C3×D4—64no—
577C3×D4—64no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4C23×D314yes—
581C3×D4C23×D314yes—
582C2×C3×C4—22no—
583C2×C3×C4—21no—
584C2×C3×C4—22no—
585C2×C3×C4—21no—
586C2×C3×C4—32no—
587C2×C3×C4—34no—
588C2×C3×C4—34no—
589C2×C3×C4—68no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—64no—
593C2×C3×C4—64no—
594C2×C3×C4D3×D411yescharacteristic
595C2×C3×C4D3×D412yes—
596C2×C3×C4C2×#6711yescharacteristic
597C2×C3×C4C2×#6712yes—
598C2×C3×C4C23×D311yescharacteristic
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C23×D312yes—
602#67—24no—
603#67—24no—
604#67—28no—
605#67—28no—
606#67—68no—
607#67—68no—
608#67C2×#6718yes—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—28no—
612C2×Dic3C2×#6712yes—
613D12—21no—
614D12—21no—
615D12—34no—
616D12—34no—
617D12—64no—
618D12—68no—
619D12—68no—
620D12—62no—
621D12—64no—
622D12—64no—
623D12—62no—
624D12—122no—
625D12—124no—
626D12C2×#6714yes—
627D12C23×D312yes—
628D12C23×D312yes—
629C4×D3—24no—
630C4×D3—24no—
631C4×D3—68no—
632C4×D3—68no—
633C4×D3C2×#6714yes—
634C4×D3C23×D314yes—
635Dic6—21no—
636Dic6—21no—
637Dic6C2×#6714yes—
638Dic6C23×D312yes—
639Dic6C23×D312yes—
640C3×C8—34no—
641C3⋊C8—32no—
642C3⋊C8—32no—
643C3⋊C8—32no—
644C3⋊C8—32no—
645C3⋊C8—62no—
646C3⋊C8—62no—
647C3⋊C8C23×D314yes—
648C2×C32—22no—
649C2×C32—44no—
650C2×C32#57612yescomplemented
651C2×C32C23×D411yescharacteristic
652C3⋊D3—44no—
653C3×D3—24no—
654C3×D3—42no—
655C3×D3—42no—
656C24—21no—
657C24—62no—
658C24—182no—
659C24—181no—
660#41—34no—
661#41—34no—
662#41—38no—
663#41—34no—
664#41—34no—
665#41—64no—
666#41—68no—
667#41—62no—
668#41—62no—
669#41—98no—
670#41—184no—
671#41—188no—
672C2×Q8—31no—
673C2×Q8—31no—
674C2×Q8—31no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—32no—
678C2×D4—38no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—31no—
682C2×D4—64no—
683C2×D4—62no—
684C2×D4—68no—
685C2×D4—616no—
686C2×D4—62no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—98no—
690C2×D4—92no—
691C2×D4—94no—
692C2×D4—184no—
693C2×D4—182no—
694C2×D4—188no—
695C2×D4—182no—
696C2×D4—1816no—
697C2×D4—181no—
698C2×D4—182no—
699C2×D4C2×D3212yes—
700C2×D4C2×D3214yescomplemented
701C22×C4—32no—
702C22×C4—62no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—182no—
706C22×C4C2×D3211yescharacteristic
707Q16—94no—
708SD16—38no—
709SD16—98no—
710SD16—94no—
711SD16—94no—
712D8—38no—
713D8—98no—
714D8—94no—
715D8—98no—
716D8—98no—
717M16—34no—
718M16—98no—
719C2×C8—32no—
720C2×C8—98no—
721C2×C8—91no—
722C2×C8—91no—
723C2×C8—94no—
724C22×C3—24no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—24no—
728C22×C3—24no—
729C22×C3—22no—
730C22×C3—21no—
731C22×C3—34no—
732C22×C3—44no—
733C22×C3—44no—
734C22×C3—44no—
735C22×C3—64no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—84no—
739C22×C3—84no—
740C22×C3—84no—
741C22×C3—88no—
742C22×C3—122no—
743C22×C3—122no—
744C22×C3—248no—
745C22×C3C2×D3×D412yes—
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C22×#6712yes—
748C22×C3C22×#6711yescharacteristic
749C2×D3—24no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—42no—
753C2×D3—42no—
754C2×D3—64no—
755C2×D3—64no—
756C2×D3—88no—
757C2×D3—124no—
758C2×D3—124no—
759C2×D3—124no—
760C2×D3—244no—
761C2×D3—248no—
762C2×D3—248no—
763C2×D3—244no—
764C2×D3—244no—
765C2×D3—248no—
766C2×D3C22×#6714yes—
767C3×C4—21no—
768C3×C4—22no—
769C3×C4—21no—
770C3×C4—34no—
771C3×C4—62no—
772C3×C4—62no—
773C3×C4C2×D3×D411yescharacteristic
774C3×C4C2×D3×D412yes—
775C3×C4C22×#6711yescharacteristic
776C3×C4C22×#6712yes—
777C3×C4C24×D311yescharacteristic
778C3×C4C24×D311yescharacteristic
779Dic3—22no—
780Dic3—22no—
781Dic3C22×#6714yes—
782C32C2×#57611yescharacteristic, complemented, Sylow
783C23—22no—
784C23—24no—
785C23—32no—
786C23—68no—
787C23—61no—
788C23—61no—
789C23—82no—
790C23—188no—
791C23—182no—
792C23—184no—
793C23—244no—
794C23—722no—
795C23—724no—
796C23D3×#6711yescharacteristic
797Q8—34no—
798Q8—32no—
799Q8—32no—
800Q8—61no—
801Q8—61no—
802D4—22no—
803D4—24no—
804D4—38no—
805D4—34no—
806D4—32no—
807D4—32no—
808D4—68no—
809D4—68no—
810D4—64no—
811D4—64no—
812D4—61no—
813D4—61no—
814D4—94no—
815D4—188no—
816D4—188no—
817D4—182no—
818D4—184no—
819D4C22×D3214yes—
820C2×C4—32no—
821C2×C4—34no—
822C2×C4—34no—
823C2×C4—68no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—64no—
827C2×C4—64no—
828C2×C4—188no—
829C2×C4D3×#6712yes—
830C2×C4D3×#6711yescharacteristic
831C2×C4C22×D3212yes—
832C2×C4C22×D3211yescharacteristic
833C8—34no—
834C8—92no—
835C8—92no—
836C2×C3—24no—
837C2×C3—22no—
838C2×C3—22no—
839C2×C3—22no—
840C2×C3—21no—
841C2×C3—44no—
842C2×C3—44no—
843C2×C3—64no—
844C2×C3—84no—
845C2×C3—122no—
846C2×C3—122no—
847C2×C3#577412yescomplemented
848C2×C3#583512yescomplemented
849C2×C3C22×D3×D411yescharacteristic
850C2×C3C23×#6711yescharacteristic
851D3—24no—
852D3—42no—
853D3—42no—
854D3—124no—
855D3—124no—
856D3—244no—
857C22—22no—
858C22—24no—
859C22—34no—
860C22—44no—
861C22—64no—
862C22—62no—
863C22—62no—
864C22—84no—
865C22—122no—
866C22—122no—
867C22—184no—
868C22—248no—
869C22—364no—
870C22—724no—
871C22—728no—
872C22C2×D3×#6712yes—
873C22C2×D3×#6711yescharacteristic
874C4—34no—
875C4—62no—
876C4—62no—
877C4C2×D3×#6711yescharacteristic
878C4C2×D3×#6712yes—
879C4C23×D3211yescharacteristic
880C3—21no—
881C3C2×#577411yescharacteristic, complemented
882C3C2×#583511yescharacteristic, complemented
883C2—22no—
884C2—44no—
885C2—64no—
886C2—122no—
887C2—122no—
888C2—364no—
889C2#1059509712yesdirect product factor
890C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32C2×#576
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C2×#64308C2semidirect
3. C22×#3753C2semidirect
4. C2×C3×#932C2semidirect
5. C2×#63935C2semidirect
6. C2×#63934C2semidirect
7. #10595097C2direct (N × H)
8. C2×#63925C2semidirect
9. C2×D3×#213C2semidirect
10. C2×#63825C2semidirect
11. C2×#63822C2semidirect
12. C2×#63815C2semidirect
15. C22×C32×D4C22semidirect
16. C22×C4⋊(C3⋊D3)C22semidirect
19. C3×#1004C22semidirect
21. C2×C3×#237C22semidirect
23. C2×C3×D3×D4C22semidirect
25. C2×C3×#235C22semidirect
26. C2×C3×#235C22semidirect
29. #64308C22semidirect
31. C2×D3×D12C22semidirect
33. C2×#3799C22semidirect
34. C2×#3753C22semidirect
35. C2×#3753C22semidirect
36. C2×#3753C22semidirect
37. C22×C3⋊(C3⋊C8)C22semidirect
38. C2×C3×#214C22semidirect
39. C3×#932C22semidirect
40. C2×C3×#213C22semidirect
41. C2×C3×#208C22semidirect
42. #63935C22semidirect
43. #63934C22semidirect
44. #63925C22semidirect
45. D3×#213C22semidirect
46. C2×#3718C22semidirect
47. C2×#3717C22semidirect
48. C2×#3715C22semidirect
49. C2×#3715C22semidirect
50. #63825C22semidirect
51. C2×#3714C22semidirect
52. #63822C22semidirect
53. C2×#3713C22semidirect
54. C2×#3711C22semidirect
55. #63815C22semidirect
56. C2×D3×C3⋊C8C22semidirect
60. C2×#1004D3semidirect
70. C2×#932D3semidirect
89. C2×C32×D4C23semidirect
94. C2×C4⋊(C3⋊D3)C23semidirect
104. C3×#237C23semidirect
107. C3×D3×D4C23semidirect
112. C3×#235C23semidirect
113. C3×#235C23semidirect
129. D3×D12C23semidirect
132. #3799C23semidirect
133. #3753C23semidirect
134. #3753C23semidirect
137. C2×C3⋊(C3⋊C8)C23semidirect
138. C3×#214C23semidirect
139. C3×#213C23semidirect
140. C3×#208C23semidirect
142. #3718C23semidirect
143. #3717C23semidirect
144. #3715C23semidirect
145. #3715C23semidirect
146. #3714C23semidirect
147. #3713C23semidirect
148. #3711C23semidirect
149. D3×C3⋊C8C23semidirect
162. C22×C3×D4C2×D3semidirect
163. C22×C3×D4C2×D3semidirect
172. #1004C2×D3semidirect
174. C2×#237C2×D3semidirect
180. C2×D3×D4C2×D3semidirect
184. C2×#235C2×D3semidirect
185. C2×#235C2×D3semidirect
208. C2×#214C2×D3semidirect
210. #932C2×D3semidirect
224. C2×#213C2×D3semidirect
226. C2×#208C2×D3semidirect
350. C2×C3×D4C22×D3semidirect
351. C2×C3×D4C22×D3semidirect
373. #237C22×D3semidirect
381. D3×D4C22×D3semidirect
389. #235C22×D3semidirect
390. #235C22×D3semidirect
430. #214C22×D3semidirect
440. #213C22×D3semidirect
442. #208C22×D3semidirect
499. C22×D4D32semidirect
650. C2×C32#576semidirect
700. C2×D4C2×D32semidirect
782. C32C2×#576semidirect
847. C2×C3#5774semidirect
848. C2×C3#5835semidirect
881. C3C2×#5774semidirect
882. C3C2×#5835semidirect
889. C2#10595097direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×#643082
C22×#37532
C2×C3×#9322
C2×#639352
C2×#639342
#105950972
C2×#639252
C2×D3×#2132
C2×#638252
C2×#638222
C2×#638152
C2×#58353
C2×#57743