Finite Group Databasebeta

← C2×#10595467 #11918942

Subgroups — C2×#10595467 #11918942

Order 1152.

2945 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3C2×#64160C211yesmaximal, characteristic, complemented
4C2×C3×#950C211yesmaximal, characteristic, complemented
5#10595467C2116yesmaximal, direct product factor
6C2×#63946C212yesmaximal, complemented
7C2×D3×#216C212yesmaximal, complemented
8C2×#63933C212yesmaximal, complemented
9C2×#63929C212yesmaximal, complemented
10C22×#3719C211yesmaximal, characteristic, complemented
11C2×#63827C211yesmaximal, characteristic, complemented
12C2×#63814C211yesmaximal, characteristic, complemented
13C2×#5838—31nomaximal
14C2×#5771—31nomaximal
15C2×C32×#41C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C3×#1010—24no—
18C3×#1010C2218yescomplemented
19C2×C3×D3×Q8C2212yes—
20C2×C3×#237—22no—
21C2×C3×#237C2212yes—
22C2×C3×#235—21no—
23C2×C3×#235C2211yescharacteristic
24C2×C3×#235C2211yescharacteristic
25C22×C3×Dic6—21no—
26C22×C3×Dic6C2211yescharacteristic
27C2×#3805—22no—
28#64298—24no—
29#64298C2218yescomplemented
30C2×#3795—21no—
31C2×#3795C2212yes—
32C2×D3×Dic6—21no—
33C2×D3×Dic6C2212yes—
34#64160C2218yescomplemented
35C2×#3756C2212yes—
36C2×#3754C2212yes—
37C2×#3748C2211yescharacteristic
38C3×#950C2218yescomplemented
39C2×C3×#216C2211yescharacteristic
40C2×C3×#215C2211yescharacteristic
41C2×C3×#214C2211yescharacteristic
42C2×C3×#213C2211yescharacteristic
43C22×C3×C3⋊C8C2211yescharacteristic
44#63946C22116yescomplemented
45D3×#216C22116yescomplemented
46#63933C22116yescomplemented
47#63929C22116yescomplemented
48C2×#3719C2212yes—
49C2×#3719C2212yes—
50C2×#3719C2218yescomplemented
51C2×#3718C2212yes—
52#63827C2218yescomplemented
53C2×#3715C2212yes—
54C2×#3711C2212yes—
55#63814C2218yescomplemented
56C2×D3×C3⋊C8C2212yes—
57C2×C3×2−1+4—31no—
58C2×#1010—31no—
59C2×#1010—31no—
60C2×#1010D311yescharacteristic, complemented
61C2×C3×#135—31no—
62#5838—316no—
63C2×#951—31no—
64C2×#951—31no—
65C2×#951—31no—
66C2×#951—32no—
67C2×#951—61no—
68C2×#950—32no—
69C2×#950D311yescharacteristic, complemented
70C2×#948—31no—
71C22×#216—32no—
72C22×#216—31no—
73C2×#942—31no—
74C2×#942—32no—
75#5771—316no—
76C2×D3×Q16—32no—
77C2×#915—32no—
78C2×#915—32no—
79C2×#912—32no—
80C22×Dic12—31no—
81C2×#901—31no—
82C32×#41—22no—
83C32×#41C2314yes—
84C2×C32×Q8C2311yescharacteristic
85C2×C32×D4—21no—
86C2×C32×D4C2311yescharacteristic
87C22×C32×C4—21no—
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3—21no—
90C2×#634—21no—
91C2×#634—22no—
92C2×#634C2312yes—
93C2×#634C2314yes—
94C2×C3×#67—21no—
95C2×C3×#67—22no—
96C2×C3×#67D412yes—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—22no—
99C3×D3×Q8—24no—
100C3×D3×Q8C2318yes—
101C3×#237—216no—
102C3×#237—24no—
103C3×#237C2318yes—
104C3×#235—22no—
105C3×#235—28no—
106C3×#235D414yes—
107C3×#235C2314yes—
108C3×#235C2314yes—
109C2×C3×D12D411yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2312yes—
114C2×C3×Dic6—21no—
115C2×C3×Dic6—22no—
116C2×C3×Dic6—22no—
117C2×C3×Dic6—28no—
118C2×C3×Dic6D411yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2312yes—
121C2×C3×Dic6C2314yes—
122C2×#627—22no—
123C2×#625—22no—
124#3805—216no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127#3795—28no—
128#3795—24no—
129#3795C2318yes—
130D3×Dic6—24no—
131D3×Dic6—28no—
132D3×Dic6C2318yes—
133#3756C2318yes—
134#3754C2318yes—
135#3748C2314yes—
136C2×C3⋊(C3⋊C8)C2312yes—
137C3×#216C2314yes—
138C3×#215C2314yes—
139C3×#214C2314yes—
140C3×#213C2314yes—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2314yes—
144#3719C2318yes—
145#3719C2318yes—
146#3718C2318yes—
147#3715C2318yes—
148#3711C2318yes—
149D3×C3⋊C8C2318yes—
150C2×#578—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—31no—
157C2×C3×#41—61no—
158C2×C3×#41—62no—
159C2×C3×#41C2×D311yescharacteristic
160C2×C3×#41C2×D311yescharacteristic
161C22×C3×Q8—32no—
162C22×C3×Q8—31no—
163C22×C3×Q8—61no—
164#1010—24no—
165#1010—38no—
166#1010—38no—
167#1010—64no—
168#1010—64no—
169#1010C2×D318yescomplemented
170C2×D3×Q8—32no—
171C2×D3×Q8—61no—
172C2×D3×Q8C2×D312yes—
173C2×#237—22no—
174C2×#237—32no—
175C2×#237—61no—
176C2×#237—62no—
177C2×#237—62no—
178C2×#237C2×D312yes—
179C2×#235—21no—
180C2×#235—32no—
181C2×#235—61no—
182C2×#235C2×D311yescharacteristic
183C2×#235C2×D311yescharacteristic
184C22×Dic6—21no—
185C22×Dic6—31no—
186C22×Dic6—31no—
187C22×Dic6—32no—
188C22×Dic6—61no—
189C22×Dic6—61no—
190C22×Dic6C2×D311yescharacteristic
191C3×#135—38no—
192C2×C3×Q16—31no—
193C2×C3×SD16—31no—
194C2×C3×SD16—31no—
195C2×C3×D8—31no—
196C22×C3×C8—31no—
197#951—38no—
198#951—38no—
199#951—38no—
200#951—316no—
201#951—68no—
202#950—316no—
203#950C2×D318yescomplemented
204#948—38no—
205C2×#216—32no—
206C2×#216—32no—
207C2×#216—32no—
208C2×#216—32no—
209C2×#216—316no—
210C2×#216—32no—
211C2×#216—32no—
212C2×#216—38no—
213C2×#216—62no—
214C2×#216C2×D311yescharacteristic
215#942—38no—
216#942—316no—
217C2×#215—32no—
218C2×#215C2×D311yescharacteristic
219C2×#214—32no—
220C2×#214—32no—
221C2×#214—32no—
222C2×#214—62no—
223C2×#214C2×D311yescharacteristic
224C2×#213C2×D311yescharacteristic
225C2×#208—31no—
226C2×#208—31no—
227C2×#208—32no—
228C2×#208—61no—
229C22×C3⋊C8—32no—
230C22×C3⋊C8C2×D311yescharacteristic
231D3×Q16—316no—
232#915—316no—
233#915—316no—
234#912—316no—
235C2×Dic12—32no—
236C2×Dic12—32no—
237C2×Dic12—38no—
238#901—38no—
239C2×ΓL(1,𝔽25)—32no—
240C2×D3×C8—32no—
241C23×C32—21no—
242C23×C32C2×D411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3C2×D412yes—
245C32×Q8—21no—
246C32×Q8C2412yes—
247C32×D4—24no—
248C32×D4—21no—
249C32×D4C2412yes—
250C2×C32×C4—21no—
251C2×C32×C4—24no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D412yes—
254C2×C32×C4C2411yescharacteristic
255C2×C32×C4C2412yes—
256C2×C3⋊Dic3—22no—
257C2×C3⋊Dic3—24no—
258#634—22no—
259#634—24no—
260#634C2414yes—
261C3×#67—24no—
262C3×#67—28no—
263C3×#67C2×D418yes—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—24no—
267C2×C3×Dic3—28no—
268C2×C3×Dic3C2×D412yes—
269C3×D12—21no—
270C3×D12C2×D414yes—
271C3×D12C2412yes—
272C3×C4×D3—28no—
273C3×C4×D3—24no—
274C3×C4×D3C2×D414yes—
275C3×C4×D3C2414yes—
276C3×Dic6—21no—
277C3×Dic6—24no—
278C3×Dic6—22no—
279C3×Dic6—28no—
280C3×Dic6C2×D414yes—
281C3×Dic6C2414yes—
282C3×Dic6C2412yes—
283#627—28no—
284#625—28no—
285D3×Dic3—28no—
286D3×Dic3—28no—
287C3⋊(C3⋊C8)C2414yes—
288C3×C3⋊C8C2412yes—
289C3×C3⋊C8C2412yes—
290C2×2−1+4—31no—
291C2×2−1+4—91no—
292#578—916no—
293C2×#137—92no—
294C2×#137—92no—
295C2×#137—91no—
296C2×#137—91no—
297C2×#135—31no—
298C2×#135—92no—
299C22×Q16—91no—
300C22×Q16—92no—
301C2×#131—91no—
302C3×#41—22no—
303C3×#41—22no—
304C3×#41—24no—
305C3×#41—34no—
306C3×#41—34no—
307C3×#41—38no—
308C3×#41—34no—
309C3×#41—42no—
310C3×#41—68no—
311C3×#41—64no—
312C3×#41—616no—
313C3×#41—62no—
314C3×#41C22×D314yes—
315C3×#41C22×D314yes—
316C2×C3×Q8—21no—
317C2×C3×Q8—31no—
318C2×C3×Q8—38no—
319C2×C3×Q8—32no—
320C2×C3×Q8—34no—
321C2×C3×Q8—31no—
322C2×C3×Q8—62no—
323C2×C3×Q8—68no—
324C2×C3×Q8—64no—
325C2×C3×Q8—61no—
326C2×C3×Q8—62no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—32no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—41no—
336C2×C3×D4—62no—
337C2×C3×D4—61no—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—32no—
344C22×C3×C4—41no—
345C22×C3×C4—62no—
346C22×C3×C4—62no—
347C22×C3×C4—61no—
348C22×C3×C4—61no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C2×#67—21no—
352C2×#67—22no—
353C2×#67—62no—
354C2×#67—62no—
355C2×#67#6712yes—
356C22×Dic3—21no—
357C22×Dic3—22no—
358C22×Dic3—62no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—62no—
362C22×Dic3—121no—
363D3×Q8—24no—
364D3×Q8—38no—
365D3×Q8—68no—
366D3×Q8—64no—
367D3×Q8C22×D318yes—
368#237—216no—
369#237—24no—
370#237—38no—
371#237—68no—
372#237—616no—
373#237—616no—
374#237—64no—
375#237C22×D318yes—
376#235—22no—
377#235—28no—
378#235—38no—
379#235—64no—
380#235—68no—
381#235#6714yes—
382#235C22×D314yes—
383#235C22×D314yes—
384C2×D12#6711yescharacteristic
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—22no—
387C2×C4×D3—21no—
388C2×C4×D3—62no—
389C2×C4×D3—62no—
390C2×C4×D3C22×D312yes—
391C2×Dic6—21no—
392C2×Dic6—22no—
393C2×Dic6—22no—
394C2×Dic6—28no—
395C2×Dic6—32no—
396C2×Dic6—34no—
397C2×Dic6—32no—
398C2×Dic6—34no—
399C2×Dic6—38no—
400C2×Dic6—62no—
401C2×Dic6—64no—
402C2×Dic6—64no—
403C2×Dic6—62no—
404C2×Dic6—61no—
405C2×Dic6—62no—
406C2×Dic6—61no—
407C2×Dic6—62no—
408C2×Dic6—62no—
409C2×Dic6—68no—
410C2×Dic6—121no—
411C2×Dic6—122no—
412C2×Dic6#6711yescharacteristic
413C2×Dic6C22×D312yes—
414C2×Dic6C22×D314yes—
415C2×Dic6C22×D311yescharacteristic
416C3×Q16—34no—
417C3×SD16—34no—
418C3×SD16—34no—
419C3×D8—34no—
420C2×C3×C8—31no—
421C2×C3×C8—31no—
422C2×C3×C8—34no—
423#216—38no—
424#216—38no—
425#216—38no—
426#216—38no—
427#216—38no—
428#216—38no—
429#216—68no—
430#216C22×D314yes—
431#215—38no—
432#215C22×D314yes—
433#214—38no—
434#214—38no—
435#214—38no—
436#214—68no—
437#214C22×D314yes—
438#213C22×D314yes—
439#208—34no—
440#208—34no—
441#208—38no—
442#208—64no—
443C2×C3⋊C8—32no—
444C2×C3⋊C8—32no—
445C2×C3⋊C8—38no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D314yes—
450Dic12—38no—
451Dic12—38no—
452ΓL(1,𝔽25)—38no—
453D3×C8—38no—
454C22×C32—22no—
455C22×C32—22no—
456C22×C32—42no—
457C22×C32C22×D412yes—
458C22×C32C22×D411yescharacteristic
459C2×C3×D3—24no—
460C2×C3×D3—22no—
461C2×C3×D3—42no—
462C2×C3×D3C22×D414yes—
463C32×C4—22no—
464C32×C4C22×D411yescharacteristic
465C32×C4C22×D412yes—
466C32×C4C2511yescharacteristic
467C3⋊Dic3—24no—
468C3×Dic3—22no—
469C3×Dic3—24no—
470C3×Dic3C22×D414yes—
4712−1+4—38no—
4722−1+4—64no—
4732−1+4—98no—
4742−1+4—184no—
475C2×#41—31no—
476C2×#41—32no—
477C2×#41—31no—
478C2×#41—61no—
479C2×#41—62no—
480C2×#41—92no—
481C2×#41—181no—
482C2×#41—182no—
483C2×#41D3211yescharacteristic
484C22×Q8—32no—
485C22×Q8—31no—
486C22×Q8—61no—
487C22×Q8—92no—
488C22×Q8—91no—
489C22×Q8—181no—
490#137—916no—
491#137—916no—
492#137—98no—
493#137—98no—
494#135—38no—
495#135—916no—
496C2×Q16—31no—
497C2×Q16—92no—
498C2×Q16—92no—
499C2×Q16—98no—
500C2×Q16—916no—
501C2×Q16—92no—
502C2×Q16—92no—
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—92no—
506C2×SD16—92no—
507C2×D8—31no—
508#131—98no—
509C2×M16—92no—
510C2×M16—91no—
511C22×C8—31no—
512C22×C8—92no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—32no—
517C23×C3—41no—
518C23×C3—61no—
519C23×C3D3×D411yescharacteristic
520C23×C3C2×#6711yescharacteristic
521C22×D3—21no—
522C22×D3C2×#6712yes—
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—22no—
526C3×Q8—34no—
527C3×Q8—34no—
528C3×Q8—32no—
529C3×Q8—41no—
530C3×Q8—68no—
531C3×Q8—62no—
532C3×Q8—64no—
533C3×Q8—61no—
534C3×Q8C23×D312yes—
535C3×Q8C23×D312yes—
536C3×D4—24no—
537C3×D4—24no—
538C3×D4—21no—
539C3×D4—21no—
540C3×D4—22no—
541C3×D4—38no—
542C3×D4—34no—
543C3×D4—32no—
544C3×D4—41no—
545C3×D4—44no—
546C3×D4—68no—
547C3×D4—64no—
548C3×D4—61no—
549C3×D4C23×D312yes—
550C3×D4C23×D312yes—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—24no—
554C2×C3×C4—24no—
555C2×C3×C4—21no—
556C2×C3×C4—22no—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—32no—
560C2×C3×C4—34no—
561C2×C3×C4—34no—
562C2×C3×C4—44no—
563C2×C3×C4—41no—
564C2×C3×C4—68no—
565C2×C3×C4—68no—
566C2×C3×C4—62no—
567C2×C3×C4—64no—
568C2×C3×C4—61no—
569C2×C3×C4—64no—
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4D3×D412yes—
572C2×C3×C4C2×#6711yescharacteristic
573C2×C3×C4C2×#6712yes—
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D312yes—
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D312yes—
578#67—24no—
579#67—28no—
580#67—68no—
581#67—68no—
582#67C2×#6718yes—
583C2×Dic3—21no—
584C2×Dic3—22no—
585C2×Dic3—24no—
586C2×Dic3—28no—
587C2×Dic3—68no—
588C2×Dic3—62no—
589C2×Dic3—64no—
590C2×Dic3—62no—
591C2×Dic3—64no—
592C2×Dic3—68no—
593C2×Dic3—124no—
594C2×Dic3—122no—
595C2×Dic3C2×#6712yes—
596D12—21no—
597D12C2×#6714yes—
598D12C23×D312yes—
599C4×D3—28no—
600C4×D3—24no—
601C4×D3—68no—
602C4×D3—68no—
603C4×D3C2×#6714yes—
604C4×D3C23×D314yes—
605Dic6—21no—
606Dic6—24no—
607Dic6—22no—
608Dic6—28no—
609Dic6—34no—
610Dic6—34no—
611Dic6—64no—
612Dic6—68no—
613Dic6—62no—
614Dic6—64no—
615Dic6—64no—
616Dic6—62no—
617Dic6—68no—
618Dic6—124no—
619Dic6—122no—
620Dic6C2×#6714yes—
621Dic6C23×D314yes—
622Dic6C23×D312yes—
623C3×C8—32no—
624C3×C8—32no—
625C3⋊C8—34no—
626C3⋊C8—34no—
627C3⋊C8—64no—
628C3⋊C8C23×D312yes—
629C3⋊C8C23×D312yes—
630C2×C32—22no—
631C2×C32—42no—
632C2×C32#57812yescomplemented
633C2×C32C23×D411yescharacteristic
634C3×D3—24no—
635C3×D3—42no—
636#41—22no—
637#41—34no—
638#41—34no—
639#41—38no—
640#41—34no—
641#41—68no—
642#41—64no—
643#41—616no—
644#41—62no—
645#41—98no—
646#41—184no—
647#41—188no—
648#41—1816no—
649#41C2×D3214yes—
650C2×Q8—31no—
651C2×Q8—38no—
652C2×Q8—31no—
653C2×Q8—32no—
654C2×Q8—34no—
655C2×Q8—62no—
656C2×Q8—68no—
657C2×Q8—64no—
658C2×Q8—61no—
659C2×Q8—62no—
660C2×Q8—98no—
661C2×Q8—92no—
662C2×Q8—94no—
663C2×Q8—182no—
664C2×Q8—184no—
665C2×Q8—188no—
666C2×Q8—181no—
667C2×Q8—182no—
668C2×Q8C2×D3211yescharacteristic
669C2×D4—21no—
670C2×D4—32no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—62no—
674C2×D4—61no—
675C2×D4—182no—
676C2×D4C2×D3211yescharacteristic
677C22×C4—21no—
678C22×C4—32no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—182no—
684C22×C4—182no—
685C22×C4—181no—
686C22×C4C2×D3211yescharacteristic
687Q16—34no—
688Q16—98no—
689Q16—98no—
690Q16—98no—
691Q16—98no—
692SD16—34no—
693SD16—34no—
694SD16—98no—
695SD16—98no—
696D8—34no—
697M16—98no—
698M16—94no—
699C2×C8—31no—
700C2×C8—31no—
701C2×C8—34no—
702C2×C8—98no—
703C2×C8—92no—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—21no—
710C22×C3—34no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—64no—
716C22×C3—62no—
717C22×C3—82no—
718C22×C3—122no—
719C22×C3C2×D3×D412yes—
720C22×C3C2×D3×D411yescharacteristic
721C22×C3C22×#6712yes—
722C22×C3C22×#6711yescharacteristic
723C2×D3—24no—
724C2×D3—22no—
725C2×D3—42no—
726C2×D3C22×#6714yes—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—34no—
733C3×C4—42no—
734C3×C4—64no—
735C3×C4—62no—
736C3×C4C2×D3×D411yescharacteristic
737C3×C4C2×D3×D412yes—
738C3×C4C22×#6712yes—
739C3×C4C22×#6711yescharacteristic
740C3×C4C24×D311yescharacteristic
741C3×C4C24×D311yescharacteristic
742Dic3—22no—
743Dic3—24no—
744Dic3—64no—
745Dic3—64no—
746Dic3—124no—
747Dic3C22×#6714yes—
748C32C2×#57811yescharacteristic, complemented, Sylow
749C23—21no—
750C23—32no—
751C23—61no—
752C23D3×#6711yescharacteristic
753Q8—21no—
754Q8—34no—
755Q8—32no—
756Q8—34no—
757Q8—68no—
758Q8—64no—
759Q8—62no—
760Q8—61no—
761Q8—94no—
762Q8—188no—
763Q8—184no—
764Q8—182no—
765Q8C22×D3212yes—
766D4—24no—
767D4—21no—
768D4—38no—
769D4—34no—
770D4—32no—
771D4—68no—
772D4—64no—
773D4—61no—
774D4—188no—
775D4C22×D3212yes—
776C2×C4—21no—
777C2×C4—24no—
778C2×C4—32no—
779C2×C4—34no—
780C2×C4—34no—
781C2×C4—68no—
782C2×C4—68no—
783C2×C4—64no—
784C2×C4—62no—
785C2×C4—61no—
786C2×C4—64no—
787C2×C4—188no—
788C2×C4—188no—
789C2×C4—184no—
790C2×C4—182no—
791C2×C4D3×#6712yes—
792C2×C4D3×#6711yescharacteristic
793C2×C4C22×D3212yes—
794C2×C4C22×D3211yescharacteristic
795C8—32no—
796C8—32no—
797C8—94no—
798C2×C3—22no—
799C2×C3—22no—
800C2×C3—21no—
801C2×C3—22no—
802C2×C3—42no—
803C2×C3—42no—
804C2×C3—42no—
805C2×C3—64no—
806C2×C3—82no—
807C2×C3—122no—
808C2×C3#577112yescomplemented
809C2×C3#583812yescomplemented
810C2×C3C22×D3×D411yescharacteristic
811C2×C3C23×#6711yescharacteristic
812D3—24no—
813D3—42no—
814C22—22no—
815C22—22no—
816C22—34no—
817C22—42no—
818C22—64no—
819C22—62no—
820C22—122no—
821C22C2×D3×#6712yes—
822C22C2×D3×#6711yescharacteristic
823C4—22no—
824C4—34no—
825C4—64no—
826C4—62no—
827C4—184no—
828C4C2×D3×#6712yes—
829C4C2×D3×#6711yescharacteristic
830C4C23×D3211yescharacteristic
831C3—21no—
832C3C2×#577111yescharacteristic, complemented
833C3C2×#583811yescharacteristic, complemented
834C2—22no—
835C2—42no—
836C2—64no—
837C2—122no—
838C2#1059546712yesdirect product factor
839C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#578
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×#64298C2semidirect
3. C2×#64160C2semidirect
4. C2×C3×#950C2semidirect
5. #10595467C2direct (N × H)
6. C2×#63946C2semidirect
7. C2×D3×#216C2semidirect
8. C2×#63933C2semidirect
9. C2×#63929C2semidirect
10. C22×#3719C2semidirect
11. C2×#63827C2semidirect
12. C2×#63814C2semidirect
18. C3×#1010C22semidirect
29. #64298C22semidirect
34. #64160C22semidirect
38. C3×#950C22semidirect
44. #63946C22semidirect
45. D3×#216C22semidirect
46. #63933C22semidirect
47. #63929C22semidirect
50. C2×#3719C22semidirect
52. #63827C22semidirect
55. #63814C22semidirect
60. C2×#1010D3semidirect
69. C2×#950D3semidirect
169. #1010C2×D3semidirect
203. #950C2×D3semidirect
632. C2×C32#578semidirect
748. C32C2×#578semidirect
808. C2×C3#5771semidirect
809. C2×C3#5838semidirect
832. C3C2×#5771semidirect
833. C3C2×#5838semidirect
838. C2#10595467direct (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×#642982
C2×#641602
C2×C3×#9502
#105954672
C2×#639462
C2×D3×#2162
C2×#639332
C2×#639292
C22×#37192
C2×#638272
C2×#638142
C2×#58383
C2×#57713