Finite Group Databasebeta

← C2×#10595455 #11918886

Subgroups — C2×#10595455 #11918886

Order 1152.

3053 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3C2×#64159C211yesmaximal, characteristic, complemented
4C2×C3×#949C211yesmaximal, characteristic, complemented
5#10595455C2116yesmaximal, direct product factor
6C2×#63946C212yesmaximal, complemented
7C2×D3×#215C212yesmaximal, complemented
8C2×#63933C212yesmaximal, complemented
9C2×#63925C212yesmaximal, complemented
10C2×#63833C211yesmaximal, characteristic, complemented
11C22×#3715C211yesmaximal, characteristic, complemented
12C2×#63815C211yesmaximal, characteristic, complemented
13C2×#5837—31nomaximal
14C2×#5775—31nomaximal
15C2×C32×#41C2211yescharacteristic, complemented
16C2×#3828C2211yescharacteristic
17C3×#1010—24no—
18C3×#1010C2218yescomplemented
19C2×C3×D3×Q8C2212yescomplemented
20C2×C3×#237—22no—
21C2×C3×#237C2212yescomplemented
22C2×C3×#235—21no—
23C2×C3×#235C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic
25C22×C3×Dic6—21no—
26C22×C3×Dic6C2211yescharacteristic, complemented
27C2×D3×#67—22no—
28#64307—24no—
29#64307C2218yescomplemented
30C2×#3802—21no—
31C2×D3×D12C2212yes—
32C2×#3796—21no—
33C2×#3795C2212yes—
34#64159C2218yescomplemented
35C2×#3756C2211yescharacteristic, complemented
36C2×#3755C2211yescharacteristic, complemented
37C2×#3754C2211yescharacteristic, complemented
38C2×#3753C2211yescharacteristic, complemented
39C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
40C3×#949C2218yescomplemented
41C2×C3×#215C2212yescomplemented
42C2×C3×#213C2212yescomplemented
43C2×C3×#208C2211yescharacteristic, complemented
44#63946C22116yescomplemented
45D3×#215C22116yescomplemented
46#63933C22116yescomplemented
47#63925C22116yescomplemented
48C2×#3719C2212yescomplemented
49#63833C2218yescomplemented
50C2×#3717C2212yescomplemented
51C2×#3715C2212yescomplemented
52C2×#3715C2212yescomplemented
53C2×#3715C2218yescomplemented
54C2×#3711C2212yescomplemented
55#63815C2218yescomplemented
56C2×D3×C3⋊C8C2212yescomplemented
57C2×C3×2−1+4—31no—
58C2×#1010D311yescharacteristic, complemented
59C2×#1009—31no—
60C2×#1004—31no—
61C2×C3×AGL(1,ℤ/8)—31no—
62#5837—316no—
63C2×#950—31no—
64C2×#950—31no—
65C2×#950—32no—
66C2×#950—61no—
67C2×#949—32no—
68C2×#949D311yescharacteristic, complemented
69C2×#948—31no—
70C2×#942—32no—
71C2×#942—31no—
72C22×#215—31no—
73C22×#215—32no—
74C22×#214—31no—
75#5775—316no—
76C2×#915—32no—
77C2×D3×SD16—32no—
78C2×#912—32no—
79C2×#911—32no—
80C2×#909—31no—
81C2×#907—31no—
82C23×C3×D3—21no—
83C22×D32—22no—
84C32×#41—22no—
85C32×#41C2314yescomplemented
86C2×C32×Q8C2311yescharacteristic
87C2×C32×D4—21no—
88C2×C32×D4C2311yescharacteristic
89C22×C32×C4—21no—
90C22×C32×C4C2311yescharacteristic
91C2×#638—21no—
92#3828—22no—
93#3828C2314yes—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—22no—
98C2×C3×#67D412yes—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—22no—
101C3×D3×Q8—24no—
102C3×D3×Q8C2318yescomplemented
103C3×#237—216no—
104C3×#237—24no—
105C3×#237C2318yescomplemented
106C3×#235—28no—
107C3×#235D414yes—
108C3×#235C2314yes—
109C2×C3×D12—21no—
110C2×C3×D12—22no—
111C2×C3×D12D411yescharacteristic
112C2×C3×D12C2312yes—
113C2×C3×D12C2314yes—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3C2312yes—
116C2×C3×Dic6—21no—
117C2×C3×Dic6—22no—
118C2×C3×Dic6—22no—
119C2×C3×Dic6—28no—
120C2×C3×Dic6D411yescharacteristic
121C2×C3×Dic6C2312yes—
122C2×C3×Dic6C2314yescomplemented
123D3×#67—216no—
124C2×#626—22no—
125C2×#625—22no—
126C2×D3×Dic3—22no—
127#3802—28no—
128D3×D12—24no—
129D3×D12C2318yes—
130#3796—28no—
131#3795—24no—
132#3795C2318yes—
133#3756C2314yescomplemented
134#3755C2314yescomplemented
135#3754C2314yescomplemented
136#3753C2314yescomplemented
137C2×C3⋊(C3⋊C8)C2311yescharacteristic
138C2×C3⋊(C3⋊C8)C2311yescharacteristic
139C2×C3⋊(C3⋊C8)C2314yescomplemented
140C3×#215C2318yescomplemented
141C3×#213C2318yescomplemented
142C3×#208C2314yescomplemented
143C2×C3×C3⋊C8C2312yes—
144#3719C2318yescomplemented
145#3717C2318yescomplemented
146#3715C2318yescomplemented
147#3715C2318yescomplemented
148#3711C2318yescomplemented
149D3×C3⋊C8C2318yescomplemented
150C2×#577—91noSylow
151C3×2−1+4—38no—
152C3×2−1+4—64no—
153C2×C3×#41—21no—
154C2×C3×#41—31no—
155C2×C3×#41—32no—
156C2×C3×#41—61no—
157C2×C3×#41—62no—
158C2×C3×#41C2×D311yescharacteristic, complemented
159C2×C3×#41C2×D311yescharacteristic, complemented
160C22×C3×Q8—32no—
161C22×C3×Q8—31no—
162C22×C3×Q8—61no—
163C22×C3×D4—31no—
164C22×#67—62no—
165#1010—24no—
166#1010C2×D318yescomplemented
167#1009—38no—
168#1009—64no—
169C2×#239—61no—
170C2×D3×Q8C2×D312yescomplemented
171#1004—38no—
172#1004—64no—
173C2×#237—22no—
174C2×#237—32no—
175C2×#237—61no—
176C2×#237C2×D312yescomplemented
177C2×D3×D4—32no—
178C2×D3×D4—61no—
179C2×D3×D4—62no—
180C2×D3×D4—61no—
181C2×#235—21no—
182C2×#235—31no—
183C2×#235—31no—
184C2×#235—32no—
185C2×#235—61no—
186C2×#235C2×D311yescharacteristic
187C22×D12—32no—
188C22×D12C2×D311yescharacteristic
189C22×Dic6—21no—
190C22×Dic6C2×D311yescharacteristic, complemented
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#950—68no—
199#949—316no—
200#949C2×D318yescomplemented
201#948—38no—
202C2×#216—31no—
203C2×#216—31no—
204C2×#216—32no—
205C2×#216—61no—
206#942—316no—
207#942—38no—
208C2×#215—31no—
209C2×#215—31no—
210C2×#215—32no—
211C2×#215—32no—
212C2×#215—38no—
213C2×#215—316no—
214C2×#215—32no—
215C2×#215—61no—
216C2×#215C2×D312yescomplemented
217C2×#214—31no—
218C2×#214—31no—
219C2×#214—32no—
220C2×#214—32no—
221C2×#214—38no—
222C2×#214—61no—
223C2×#213—31no—
224C2×#213—31no—
225C2×#213—61no—
226C2×#213C2×D312yescomplemented
227C2×#208—32no—
228C2×#208C2×D311yescharacteristic, complemented
229C22×C3⋊C8—31no—
230C22×C3⋊C8—31no—
231C22×C3⋊C8—32no—
232C22×C3⋊C8—61no—
233#915—316no—
234D3×SD16—316no—
235#912—316no—
236#911—316no—
237#909—38no—
238#907—38no—
239C2×Dic12—32no—
240C2×#204—32no—
241C2×ΓL(1,𝔽25)—32no—
242C2×D3×C8—32no—
243C23×C32—21no—
244C23×C32C2×D411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3×D3—22no—
247C22×C3×D3—24no—
248C22×C3×D3—82no—
249C22×C3×D3C2×D412yes—
250C2×D32—28no—
251C2×D32—84no—
252C32×Q8—21no—
253C32×Q8C2412yes—
254C32×D4—24no—
255C32×D4—21no—
256C32×D4C2412yes—
257C2×C32×C4—21no—
258C2×C32×C4—24no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2×D412yes—
261C2×C32×C4C2411yescharacteristic
262C2×C32×C4C2412yes—
263#638—24no—
264C2×C3⋊Dic3—21no—
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)C2412yes—
267C4×C3⋊D3—24no—
268#634—21no—
269#634C2412yes—
270C3×#67—28no—
271C3×#67C2×D418yes—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—24no—
274C2×C3×Dic3—28no—
275C2×C3×Dic3C2×D412yes—
276C3×D12—22no—
277C3×D12—24no—
278C3×D12C2×D414yes—
279C3×D12C2414yes—
280C3×C4×D3—28no—
281C3×C4×D3C2×D414yes—
282C3×C4×D3C2414yes—
283C3×Dic6—24no—
284C3×Dic6—22no—
285C3×Dic6—28no—
286C3×Dic6C2×D414yes—
287C3×Dic6C2414yes—
288#626—28no—
289#625—28no—
290D3×Dic3—28no—
291C3⋊(C3⋊C8)C2412yes—
292C3⋊(C3⋊C8)C2412yes—
293C3×C3⋊C8C2414yes—
294C2×2−1+4—31no—
295C2×H(5,𝔽2)—91no—
296#577—916no—
297C2×#137—91no—
298C2×#137—92no—
299C2×AGL(1,ℤ/8)—31no—
300C2×AGL(1,ℤ/8)—92no—
301C2×#135—92no—
302C2×#135—91no—
303C22×SD16—92no—
304C22×SD16—91no—
305C2×#131—91no—
306C24×C3—61no—
307C23×D3—21no—
308C23×D3—62no—
309C23×D3—62no—
310C3×#41—22no—
311C3×#41—22no—
312C3×#41—24no—
313C3×#41—34no—
314C3×#41—34no—
315C3×#41—38no—
316C3×#41—42no—
317C3×#41—68no—
318C3×#41—64no—
319C3×#41—616no—
320C3×#41C22×D314yescomplemented
321C3×#41C22×D314yescomplemented
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8—38no—
325C2×C3×Q8—32no—
326C2×C3×Q8—34no—
327C2×C3×Q8—62no—
328C2×C3×Q8—68no—
329C2×C3×Q8—64no—
330C2×C3×Q8—61no—
331C2×C3×Q8—62no—
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—32no—
338C2×C3×D4—31no—
339C2×C3×D4—32no—
340C2×C3×D4—34no—
341C2×C3×D4—41no—
342C2×C3×D4—62no—
343C2×C3×D4—61no—
344C2×C3×D4—62no—
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—32no—
351C22×C3×C4—41no—
352C22×C3×C4—62no—
353C22×C3×C4—62no—
354C22×C3×C4—61no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C2×#67—22no—
358C2×#67—62no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—62no—
362C2×#67—616no—
363C2×#67—62no—
364C2×#67—121no—
365C2×#67#6712yes—
366C22×Dic3—21no—
367C22×Dic3—22no—
368C22×Dic3—62no—
369#239—68no—
370D3×Q8—24no—
371D3×Q8C22×D318yescomplemented
372#237—216no—
373#237—24no—
374#237—38no—
375#237—64no—
376#237—68no—
377#237C22×D318yescomplemented
378D3×D4—38no—
379D3×D4—68no—
380D3×D4—616no—
381D3×D4—68no—
382D3×D4—64no—
383#235—28no—
384#235—34no—
385#235—34no—
386#235—38no—
387#235—64no—
388#235—64no—
389#235—62no—
390#235—62no—
391#235—122no—
392#235#6714yes—
393#235C22×D314yes—
394C2×D12—21no—
395C2×D12—22no—
396C2×D12—31no—
397C2×D12—31no—
398C2×D12—38no—
399C2×D12—61no—
400C2×D12—64no—
401C2×D12—62no—
402C2×D12#6711yescharacteristic
403C2×D12C22×D312yes—
404C2×D12C22×D314yes—
405C2×C4×D3—22no—
406C2×C4×D3—62no—
407C2×C4×D3—61no—
408C2×C4×D3—61no—
409C2×C4×D3—121no—
410C2×C4×D3C22×D312yes—
411C2×Dic6—21no—
412C2×Dic6—22no—
413C2×Dic6—22no—
414C2×Dic6—28no—
415C2×Dic6—31no—
416C2×Dic6—31no—
417C2×Dic6—61no—
418C2×Dic6#6711yescharacteristic
419C2×Dic6C22×D312yes—
420C2×Dic6C22×D314yescomplemented
421C3×SD16—38no—
422C3×D8—38no—
423C3×M16—34no—
424C2×C3×C8—32no—
425#216—34no—
426#216—34no—
427#216—38no—
428#216—64no—
429#215—34no—
430#215—34no—
431#215—38no—
432#215—38no—
433#215—38no—
434#215—64no—
435#215C22×D318yescomplemented
436#214—34no—
437#214—34no—
438#214—38no—
439#214—38no—
440#214—64no—
441#213—34no—
442#213—34no—
443#213—64no—
444#213C22×D318yescomplemented
445#208—38no—
446#208C22×D314yescomplemented
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—34no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—34no—
453C2×C3⋊C8—38no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—64no—
457C2×C3⋊C8C22×D312yes—
458Dic12—38no—
459#204—38no—
460ΓL(1,𝔽25)—38no—
461D3×C8—38no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—42no—
465C22×C32C22×D412yes—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—22no—
468C2×C3⋊D3—42no—
469C2×C3×D3—24no—
470C2×C3×D3—24no—
471C2×C3×D3—44no—
472C2×C3×D3—84no—
473C2×C3×D3C22×D414yes—
474D32—88no—
475C32×C4—22no—
476C32×C4C22×D412yes—
477C32×C4C22×D411yescharacteristic
478C32×C4C2511yescharacteristic
479C3⋊Dic3—22no—
480C3×Dic3—24no—
481C3×Dic3C22×D414yes—
4822−1+4—38no—
4832−1+4—64no—
484H(5,𝔽2)—98no—
485H(5,𝔽2)—184no—
486C2×#41—31no—
487C2×#41—32no—
488C2×#41—61no—
489C2×#41—62no—
490C2×#41—92no—
491C2×#41—91no—
492C2×#41—181no—
493C2×#41D3211yescharacteristic, complemented
494C22×Q8—32no—
495C22×Q8—31no—
496C22×Q8—61no—
497C22×D4—31no—
498C22×D4—92no—
499C22×D4—181no—
500C22×D4—182no—
501#137—98no—
502#137—916no—
503AGL(1,ℤ/8)—38no—
504AGL(1,ℤ/8)—916no—
505#135—916no—
506#135—98no—
507C2×Q16—92no—
508C2×Q16—91no—
509C2×SD16—32no—
510C2×SD16—92no—
511C2×SD16—916no—
512C2×SD16—92no—
513C2×SD16—92no—
514C2×SD16—98no—
515C2×SD16—91no—
516C2×SD16—91no—
517C2×D8—32no—
518C2×D8—91no—
519#131—98no—
520C2×M16—31no—
521C2×M16—92no—
522C22×C8—92no—
523C22×C8—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—32no—
528C23×C3—41no—
529C23×C3—62no—
530C23×C3—64no—
531C23×C3—242no—
532C23×C3D3×D411yescharacteristic
533C23×C3C2×#6711yescharacteristic
534C22×D3—22no—
535C22×D3—24no—
536C22×D3—68no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—68no—
540C22×D3—82no—
541C22×D3—121no—
542C22×D3—244no—
543C22×D3—244no—
544C22×D3C2×#6712yes—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—22no—
548C3×Q8—34no—
549C3×Q8—34no—
550C3×Q8—41no—
551C3×Q8—68no—
552C3×Q8—62no—
553C3×Q8—64no—
554C3×Q8C23×D312yes—
555C3×Q8C23×D312yes—
556C3×D4—24no—
557C3×D4—24no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—22no—
561C3×D4—38no—
562C3×D4—34no—
563C3×D4—34no—
564C3×D4—41no—
565C3×D4—44no—
566C3×D4—68no—
567C3×D4—62no—
568C3×D4—64no—
569C3×D4C23×D312yes—
570C3×D4C23×D312yes—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—24no—
574C2×C3×C4—24no—
575C2×C3×C4—21no—
576C2×C3×C4—22no—
577C2×C3×C4—21no—
578C2×C3×C4—22no—
579C2×C3×C4—32no—
580C2×C3×C4—34no—
581C2×C3×C4—34no—
582C2×C3×C4—44no—
583C2×C3×C4—41no—
584C2×C3×C4—68no—
585C2×C3×C4—68no—
586C2×C3×C4—62no—
587C2×C3×C4—64no—
588C2×C3×C4D3×D411yescharacteristic
589C2×C3×C4D3×D412yes—
590C2×C3×C4C2×#6711yescharacteristic
591C2×C3×C4C2×#6712yes—
592C2×C3×C4C23×D311yescharacteristic
593C2×C3×C4C23×D312yes—
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D312yes—
596#67—28no—
597#67—68no—
598#67—64no—
599#67—64no—
600#67—68no—
601#67—68no—
602#67—124no—
603#67C2×#6718yes—
604C2×Dic3—22no—
605C2×Dic3—24no—
606C2×Dic3—28no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—68no—
610C2×Dic3—121no—
611C2×Dic3C2×#6712yes—
612D12—22no—
613D12—24no—
614D12—32no—
615D12—32no—
616D12—62no—
617D12—68no—
618D12—61no—
619D12—61no—
620D12—121no—
621D12C2×#6714yes—
622D12C23×D314yes—
623C4×D3—28no—
624C4×D3—68no—
625C4×D3—64no—
626C4×D3—64no—
627C4×D3—124no—
628C4×D3C2×#6714yes—
629C4×D3C23×D314yes—
630Dic6—24no—
631Dic6—22no—
632Dic6—28no—
633Dic6—32no—
634Dic6—32no—
635Dic6—62no—
636Dic6—61no—
637Dic6—61no—
638Dic6—121no—
639Dic6C2×#6714yes—
640Dic6C23×D314yes—
641C3×C8—34no—
642C3⋊C8—32no—
643C3⋊C8—32no—
644C3⋊C8—32no—
645C3⋊C8—32no—
646C3⋊C8—62no—
647C3⋊C8—62no—
648C3⋊C8C23×D314yes—
649C2×C32—22no—
650C2×C32—42no—
651C2×C32#57712yescomplemented
652C2×C32C23×D411yescharacteristic
653C3⋊D3—42no—
654C3×D3—24no—
655C3×D3—44no—
656C24—61no—
657C24—182no—
658#41—22no—
659#41—34no—
660#41—34no—
661#41—38no—
662#41—68no—
663#41—64no—
664#41—616no—
665#41—98no—
666#41—94no—
667#41—184no—
668#41—188no—
669#41—182no—
670#41C2×D3214yescomplemented
671C2×Q8—31no—
672C2×Q8—38no—
673C2×Q8—32no—
674C2×Q8—34no—
675C2×Q8—62no—
676C2×Q8—68no—
677C2×Q8—64no—
678C2×Q8—61no—
679C2×Q8—62no—
680C2×Q8—91no—
681C2×Q8C2×D3211yescharacteristic
682C2×D4—21no—
683C2×D4—32no—
684C2×D4—32no—
685C2×D4—34no—
686C2×D4—31no—
687C2×D4—62no—
688C2×D4—61no—
689C2×D4—62no—
690C2×D4—98no—
691C2×D4—91no—
692C2×D4—184no—
693C2×D4—182no—
694C2×D4—188no—
695C2×D4—1816no—
696C2×D4—182no—
697C2×D4—181no—
698C2×D4C2×D3211yescharacteristic
699C22×C4—21no—
700C22×C4—32no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—61no—
704C22×C4—182no—
705C22×C4—181no—
706C22×C4C2×D3211yescharacteristic
707Q16—98no—
708Q16—94no—
709SD16—38no—
710SD16—98no—
711SD16—98no—
712SD16—98no—
713SD16—94no—
714SD16—94no—
715D8—38no—
716D8—94no—
717M16—34no—
718M16—98no—
719C2×C8—32no—
720C2×C8—98no—
721C2×C8—91no—
722C2×C8—91no—
723C2×C8—94no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—21no—
730C22×C3—34no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—64no—
736C22×C3—64no—
737C22×C3—82no—
738C22×C3—124no—
739C22×C3—244no—
740C22×C3C2×D3×D412yes—
741C22×C3C2×D3×D411yescharacteristic
742C22×C3C22×#6712yes—
743C22×C3C22×#6711yescharacteristic
744C2×D3—24no—
745C2×D3—24no—
746C2×D3—44no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—84no—
750C2×D3—122no—
751C2×D3—122no—
752C2×D3—122no—
753C2×D3—242no—
754C2×D3—248no—
755C2×D3—248no—
756C2×D3C22×#6714yes—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—21no—
760C3×C4—22no—
761C3×C4—21no—
762C3×C4—34no—
763C3×C4—42no—
764C3×C4—64no—
765C3×C4C2×D3×D411yescharacteristic
766C3×C4C2×D3×D412yes—
767C3×C4C22×#6711yescharacteristic
768C3×C4C22×#6712yes—
769C3×C4C24×D311yescharacteristic
770C3×C4C24×D311yescharacteristic
771Dic3—24no—
772Dic3—62no—
773Dic3—62no—
774Dic3—122no—
775Dic3C22×#6714yes—
776C32C2×#57711yescharacteristic, complemented, Sylow
777C23—21no—
778C23—32no—
779C23—62no—
780C23—64no—
781C23—188no—
782C23—181no—
783C23—242no—
784C23—724no—
785C23D3×#6711yescharacteristic
786Q8—21no—
787Q8—34no—
788Q8—34no—
789Q8—68no—
790Q8—64no—
791Q8—62no—
792Q8—92no—
793Q8—181no—
794Q8C22×D3212yes—
795D4—24no—
796D4—21no—
797D4—38no—
798D4—34no—
799D4—34no—
800D4—68no—
801D4—64no—
802D4—62no—
803D4—92no—
804D4—188no—
805D4—188no—
806D4—184no—
807D4—181no—
808D4C22×D3212yes—
809C2×C4—21no—
810C2×C4—24no—
811C2×C4—32no—
812C2×C4—34no—
813C2×C4—34no—
814C2×C4—68no—
815C2×C4—68no—
816C2×C4—64no—
817C2×C4—62no—
818C2×C4—188no—
819C2×C4—181no—
820C2×C4—184no—
821C2×C4D3×#6712yes—
822C2×C4D3×#6711yescharacteristic
823C2×C4C22×D3212yes—
824C2×C4C22×D3211yescharacteristic
825C8—34no—
826C8—92no—
827C8—92no—
828C2×C3—22no—
829C2×C3—22no—
830C2×C3—21no—
831C2×C3—22no—
832C2×C3—42no—
833C2×C3—42no—
834C2×C3—42no—
835C2×C3—64no—
836C2×C3—82no—
837C2×C3—124no—
838C2×C3#577512yescomplemented
839C2×C3#583712yescomplemented
840C2×C3C22×D3×D411yescharacteristic
841C2×C3C23×#6711yescharacteristic
842D3—24no—
843D3—44no—
844D3—122no—
845D3—122no—
846D3—242no—
847C22—22no—
848C22—22no—
849C22—34no—
850C22—42no—
851C22—64no—
852C22—64no—
853C22—124no—
854C22—182no—
855C22—244no—
856C22—362no—
857C22—728no—
858C22C2×D3×#6712yes—
859C22C2×D3×#6711yescharacteristic
860C4—22no—
861C4—34no—
862C4—64no—
863C4—182no—
864C4C2×D3×#6712yes—
865C4C2×D3×#6711yescharacteristic
866C4C23×D3211yescharacteristic
867C3—21no—
868C3C2×#577511yescharacteristic, complemented
869C3C2×#583711yescharacteristic, complemented
870C2—22no—
871C2—42no—
872C2—64no—
873C2—124no—
874C2—362no—
875C2#1059545512yesdirect product factor
876C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#577
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×#1010C2semidirect
2. C2×#64307C2semidirect
3. C2×#64159C2semidirect
4. C2×C3×#949C2semidirect
5. #10595455C2direct (N × H)
6. C2×#63946C2semidirect
7. C2×D3×#215C2semidirect
8. C2×#63933C2semidirect
9. C2×#63925C2semidirect
10. C2×#63833C2semidirect
11. C22×#3715C2semidirect
12. C2×#63815C2semidirect
15. C2×C32×#41C22semidirect
18. C3×#1010C22semidirect
19. C2×C3×D3×Q8C22semidirect
21. C2×C3×#237C22semidirect
26. C22×C3×Dic6C22semidirect
29. #64307C22semidirect
34. #64159C22semidirect
35. C2×#3756C22semidirect
36. C2×#3755C22semidirect
37. C2×#3754C22semidirect
38. C2×#3753C22semidirect
39. C22×C3⋊(C3⋊C8)C22semidirect
40. C3×#949C22semidirect
41. C2×C3×#215C22semidirect
42. C2×C3×#213C22semidirect
43. C2×C3×#208C22semidirect
44. #63946C22semidirect
45. D3×#215C22semidirect
46. #63933C22semidirect
47. #63925C22semidirect
48. C2×#3719C22semidirect
49. #63833C22semidirect
50. C2×#3717C22semidirect
51. C2×#3715C22semidirect
52. C2×#3715C22semidirect
53. C2×#3715C22semidirect
54. C2×#3711C22semidirect
55. #63815C22semidirect
56. C2×D3×C3⋊C8C22semidirect
58. C2×#1010D3semidirect
68. C2×#949D3semidirect
85. C32×#41C23semidirect
102. C3×D3×Q8C23semidirect
105. C3×#237C23semidirect
122. C2×C3×Dic6C23semidirect
133. #3756C23semidirect
134. #3755C23semidirect
135. #3754C23semidirect
136. #3753C23semidirect
139. C2×C3⋊(C3⋊C8)C23semidirect
140. C3×#215C23semidirect
141. C3×#213C23semidirect
142. C3×#208C23semidirect
144. #3719C23semidirect
145. #3717C23semidirect
146. #3715C23semidirect
147. #3715C23semidirect
148. #3711C23semidirect
149. D3×C3⋊C8C23semidirect
158. C2×C3×#41C2×D3semidirect
159. C2×C3×#41C2×D3semidirect
166. #1010C2×D3semidirect
170. C2×D3×Q8C2×D3semidirect
176. C2×#237C2×D3semidirect
190. C22×Dic6C2×D3semidirect
200. #949C2×D3semidirect
216. C2×#215C2×D3semidirect
226. C2×#213C2×D3semidirect
228. C2×#208C2×D3semidirect
320. C3×#41C22×D3semidirect
321. C3×#41C22×D3semidirect
371. D3×Q8C22×D3semidirect
377. #237C22×D3semidirect
420. C2×Dic6C22×D3semidirect
435. #215C22×D3semidirect
444. #213C22×D3semidirect
446. #208C22×D3semidirect
493. C2×#41D32semidirect
651. C2×C32#577semidirect
670. #41C2×D32semidirect
776. C32C2×#577semidirect
838. C2×C3#5775semidirect
839. C2×C3#5837semidirect
868. C3C2×#5775semidirect
869. C3C2×#5837semidirect
875. C2#10595455direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×#643072
C2×#641592
C2×C3×#9492
#105954552
C2×#639462
C2×D3×#2152
C2×#639332
C2×#639252
C2×#638332
C22×#37152
C2×#638152
C2×#58373
C2×#57753