Finite Group Databasebeta

← C2×#10594719 #11918891

Subgroups — C2×#10594719 #11918891

Order 1152.

3053 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C2×#64116C211yesmaximal, characteristic, complemented
4C2×C3×#909C211yesmaximal, characteristic, complemented
5C2×C3×#908C211yesmaximal, characteristic, complemented
6C22×#3715C211yesmaximal, characteristic, complemented
7C2×#63822C211yesmaximal, characteristic, complemented
8#10594719C2116yesmaximal, direct product factor
9C2×#63811C212yesmaximal, complemented
10C2×#63810C212yesmaximal, complemented
11C2×#63798C212yesmaximal, complemented
12C2×#63796C212yesmaximal, complemented
13C2×#5778—31nomaximal
14C2×#5775—31nomaximal
15C2×#3828C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C2×C3×#235C2211yescharacteristic, complemented
18C22×C3×D12C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic, complemented
20C2×D3×#67—22no—
21C2×#3804—22no—
22#64307—24no—
23#64307C2218yescomplemented
24C2×#3802C2212yes—
25C2×D3×D12—21no—
26C2×#3799—21no—
27C2×#3797C2212yescomplemented
28#64297—24no—
29#64297C2218yescomplemented
30C2×#3796C2212yes—
31C2×#3796C2212yescomplemented
32C2×#3795—21no—
33C2×D3×Dic6—21no—
34C2×C32×M16C2211yescharacteristic, complemented
35C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
36#64116C2218yescomplemented
37C2×#3743C2212yescomplemented
38C2×C8×C3⋊D3C2212yescomplemented
39C3×#909C2218yescomplemented
40C3×#908C2218yescomplemented
41C2×C3×Dic12C2212yescomplemented
42C2×C3×D24C2212yescomplemented
43C2×C3×#204C2212yescomplemented
44C2×C3×#204C2212yescomplemented
45C2×#3718C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C2×#3715C2212yescomplemented
48C2×#3715C2212yescomplemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3715C2218yescomplemented
51#63822C2218yescomplemented
52C2×#3713C2211yescharacteristic, complemented
53#63811C22116yescomplemented
54#63810C22116yescomplemented
55#63798C22116yescomplemented
56#63796C22116yescomplemented
57C2×#1010—31no—
58C2×#1009—31no—
59C2×#1007—31no—
60C2×#1004—31no—
61C2×C3×#137—31no—
62C2×C3×AGL(1,ℤ/8)—31no—
63C2×#950—31no—
64C2×#950—31no—
65C22×#215—31no—
66C22×#214—31no—
67#5778—316no—
68#5775—316no—
69C2×#919—32no—
70C2×#918—32no—
71C2×#915—32no—
72C2×#914—32no—
73C2×D3×SD16—32no—
74C2×D3×SD16—32no—
75C2×#912—32no—
76C2×#911—32no—
77C2×#909D311yescharacteristic, complemented
78C2×#908D311yescharacteristic, complemented
79C2×#907—31no—
80C2×#907—31no—
81C2×#907—61no—
82C23×C3×D3—21no—
83C22×D32—22no—
84C22×C32×C4C2311yescharacteristic
85C2×#638D412yes—
86#3828D414yes—
87#3828C2314yes—
88C2×C4⋊(C3⋊D3)D411yescharacteristic
89C2×C4×C3⋊D3C2312yes—
90C2×#634D411yescharacteristic
91C2×C3×#67—21no—
92C2×C3×#67—21no—
93C22×C3×Dic3—21no—
94C3×#235—22no—
95C3×#235—22no—
96C3×#235C2314yes—
97C3×#235C2314yescomplemented
98C2×C3×D12—21no—
99C2×C3×D12—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2312yes—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2314yes—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6—22no—
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2312yes—
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2314yescomplemented
112D3×#67—216no—
113C2×#627—22no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#625—22no—
117C2×#624—22no—
118#3804—216no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121#3802—24no—
122#3802C2318yes—
123D3×D12—28no—
124#3799—28no—
125#3797—24no—
126#3797C2318yescomplemented
127#3796—24no—
128#3796—24no—
129#3796C2318yes—
130#3796C2318yescomplemented
131#3795—28no—
132D3×Dic6—28no—
133C32×M16C2314yescomplemented
134C2×C32×C8C2312yes—
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137C2×C3⋊(C3⋊C8)C2314yescomplemented
138#3743C2318yescomplemented
139C8×C3⋊D3C2318yescomplemented
140C3×Dic12C2318yescomplemented
141C3×D24C2318yescomplemented
142C3×#204C2318yescomplemented
143C3×#204C2318yescomplemented
144#3718C2314yescomplemented
145#3715C2314yescomplemented
146#3715C2318yescomplemented
147#3715C2318yescomplemented
148#3715C2314yescomplemented
149#3713C2314yescomplemented
150C2×#577—91noSylow
151C2×C3×#41—31no—
152C2×C3×#41—31no—
153C22×C3×Q8—31no—
154C22×C3×D4—31no—
155C22×#67—62no—
156#1010—38no—
157#1010—64no—
158#1009—38no—
159#1009—64no—
160#1007—38no—
161#1007—64no—
162C2×#239—32no—
163C2×#239—32no—
164C2×#239—61no—
165C2×D3×Q8—32no—
166C2×D3×Q8—32no—
167C2×D3×Q8—61no—
168#1004—38no—
169#1004—64no—
170C2×#237—32no—
171C2×#237—32no—
172C2×#237—61no—
173C2×#237—62no—
174C2×D3×D4—32no—
175C2×D3×D4—32no—
176C2×D3×D4—61no—
177C2×D3×D4—62no—
178C2×#235—31no—
179C2×#235—31no—
180C2×#235—61no—
181C2×#235—61no—
182C2×#235—61no—
183C2×#235—62no—
184C2×#235C2×D311yescharacteristic
185C2×#235C2×D311yescharacteristic, complemented
186C22×D12—61no—
187C22×D12C2×D311yescharacteristic
188C22×Dic6—61no—
189C22×Dic6C2×D311yescharacteristic, complemented
190C3×#137—38no—
191C3×AGL(1,ℤ/8)—38no—
192C2×C3×Q16—32no—
193C2×C3×SD16—32no—
194C2×C3×SD16—32no—
195C2×C3×D8—32no—
196C2×C3×M16—21no—
197C2×C3×M16C2×D311yescharacteristic, complemented
198C2×C3×M16C2×D311yescharacteristic, complemented
199#950—38no—
200#950—38no—
201C2×#216—31no—
202C2×#216—31no—
203C2×#215—31no—
204C2×#215—32no—
205C2×#215—32no—
206C2×#215—31no—
207C2×#215—38no—
208C2×#214—32no—
209C2×#214—31no—
210C2×#214—32no—
211C2×#214—31no—
212C2×#214—38no—
213C2×#213—31no—
214C2×#213—31no—
215C22×C3⋊C8—31no—
216C22×C3⋊C8—31no—
217C22×C3⋊C8—61no—
218#919—316no—
219#918—316no—
220#915—316no—
221#914—316no—
222D3×SD16—316no—
223D3×SD16—316no—
224#912—316no—
225#911—316no—
226#909C2×D318yescomplemented
227#908C2×D318yescomplemented
228#907—38no—
229#907—38no—
230#907—68no—
231C2×Dic12C2×D312yescomplemented
232C2×D24C2×D312yescomplemented
233C2×#204C2×D312yescomplemented
234C2×#204C2×D312yescomplemented
235C2×ΓL(1,𝔽25)—32no—
236C2×ΓL(1,𝔽25)—32no—
237C2×ΓL(1,𝔽25)—62no—
238C2×D3×C8—32no—
239C2×D3×C8—32no—
240C2×D3×C8—62no—
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3C2×D412yes—
243C22×C3×D3—21no—
244C22×C3×D3—22no—
245C22×C3×D3—21no—
246C22×C3×D3—24no—
247C22×C3×D3—82no—
248C2×D32—28no—
249C2×D32—84no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D412yes—
252C2×C32×C4C2411yescharacteristic
253C2×C32×C4C2412yes—
254#638C2×D418yes—
255C2×C3⋊Dic3C2×D412yes—
256C4⋊(C3⋊D3)C2×D414yes—
257C4×C3⋊D3C2×D414yes—
258C4×C3⋊D3C2414yes—
259#634C2×D414yes—
260C3×#67—24no—
261C3×#67—24no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—24no—
265C2×C3×Dic3—21no—
266C3×D12—24no—
267C3×D12—21no—
268C3×D12—22no—
269C3×D12—21no—
270C3×D12C2412yes—
271C3×D12C2412yes—
272C3×D12C2414yes—
273C3×C4×D3—24no—
274C3×C4×D3—24no—
275C3×Dic6—24no—
276C3×Dic6—21no—
277C3×Dic6—22no—
278C3×Dic6—21no—
279C3×Dic6C2414yes—
280C3×Dic6C2412yes—
281C3×Dic6C2412yes—
282#627—28no—
283#626—28no—
284#626—28no—
285#625—28no—
286#624—28no—
287D3×Dic3—28no—
288D3×Dic3—28no—
289C32×C8C2414yes—
290C3⋊(C3⋊C8)C2412yes—
291C3⋊(C3⋊C8)C2412yes—
292C2×2−1+4—91no—
293C2×H(5,𝔽2)—91no—
294#577—916no—
295C2×#137—31no—
296C2×#137—92no—
297C2×AGL(1,ℤ/8)—31no—
298C2×AGL(1,ℤ/8)—92no—
299C2×#135—92no—
300C2×#135—91no—
301C22×SD16—92no—
302C22×SD16—91no—
303C2×#131—91no—
304C24×C3—61no—
305C23×D3—21no—
306C23×D3—62no—
307C23×D3—62no—
308C3×#41—34no—
309C3×#41—34no—
310C3×#41—62no—
311C3×#41—62no—
312C2×C3×Q8—32no—
313C2×C3×Q8—34no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×Q8—61no—
317C2×C3×Q8—62no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C2×C3×D4—32no—
321C2×C3×D4—34no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—62no—
326C22×C3×C4—21no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—21no—
333C2×#67—21no—
334C2×#67—32no—
335C2×#67—32no—
336C2×#67—62no—
337C2×#67—62no—
338C2×#67—62no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—616no—
342C22×Dic3—21no—
343C22×Dic3—62no—
344C22×Dic3—62no—
345#239—38no—
346#239—38no—
347#239—68no—
348#239—64no—
349#239—64no—
350D3×Q8—38no—
351D3×Q8—38no—
352D3×Q8—64no—
353D3×Q8—64no—
354D3×Q8—68no—
355#237—38no—
356#237—38no—
357#237—64no—
358#237—64no—
359#237—68no—
360#237—616no—
361D3×D4—38no—
362D3×D4—38no—
363D3×D4—68no—
364D3×D4—64no—
365D3×D4—64no—
366D3×D4—616no—
367#235—22no—
368#235—22no—
369#235—34no—
370#235—34no—
371#235—34no—
372#235—34no—
373#235—64no—
374#235—64no—
375#235—68no—
376#235—68no—
377#235—616no—
378#235C22×D314yes—
379#235C22×D314yescomplemented
380C2×D12—21no—
381C2×D12—22no—
382C2×D12—31no—
383C2×D12—31no—
384C2×D12—61no—
385C2×D12—68no—
386C2×D12—62no—
387C2×D12—62no—
388C2×D12C22×D311yescharacteristic
389C2×D12C22×D312yes—
390C2×D12C22×D311yescharacteristic
391C2×D12C22×D314yes—
392C2×C4×D3—21no—
393C2×C4×D3—21no—
394C2×C4×D3—32no—
395C2×C4×D3—32no—
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C2×C4×D3—62no—
399C2×C4×D3—62no—
400C2×C4×D3—62no—
401C2×Dic6—21no—
402C2×Dic6—22no—
403C2×Dic6—31no—
404C2×Dic6—31no—
405C2×Dic6—61no—
406C2×Dic6—68no—
407C2×Dic6—62no—
408C2×Dic6—62no—
409C2×Dic6C22×D311yescharacteristic
410C2×Dic6C22×D312yes—
411C2×Dic6C22×D311yescharacteristic
412C2×Dic6C22×D314yescomplemented
413C3×Q16—38no—
414C3×SD16—38no—
415C3×SD16—38no—
416C3×D8—38no—
417C3×M16—24no—
418C3×M16C22×D314yescomplemented
419C3×M16C22×D314yescomplemented
420C2×C3×C8—22no—
421C2×C3×C8C22×D312yes—
422C2×C3×C8C22×D312yes—
423#216—34no—
424#216—34no—
425#215—34no—
426#215—38no—
427#215—38no—
428#215—34no—
429#214—38no—
430#214—34no—
431#214—38no—
432#214—34no—
433#213—34no—
434#213—34no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—34no—
440C2×C3⋊C8—34no—
441C2×C3⋊C8—61no—
442C2×C3⋊C8—61no—
443C2×C3⋊C8—64no—
444Dic12C22×D318yescomplemented
445D24C22×D318yescomplemented
446#204C22×D318yescomplemented
447#204C22×D318yescomplemented
448ΓL(1,𝔽25)—38no—
449ΓL(1,𝔽25)—38no—
450ΓL(1,𝔽25)—68no—
451D3×C8—38no—
452D3×C8—38no—
453D3×C8—68no—
454C22×C32—22no—
455C22×C32C22×D412yes—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—24no—
458C2×C3⋊D3C22×D414yes—
459C2×C3×D3—22no—
460C2×C3×D3—24no—
461C2×C3×D3—22no—
462C2×C3×D3—42no—
463C2×C3×D3—44no—
464C2×C3×D3—42no—
465C2×C3×D3—84no—
466D32—88no—
467C32×C4C22×D411yescharacteristic
468C32×C4C22×D412yes—
469C32×C4C2511yescharacteristic
470C3⋊Dic3C22×D414yes—
471C3×Dic3—22no—
472C3×Dic3—24no—
473C3×Dic3—22no—
4742−1+4—98no—
4752−1+4—184no—
476H(5,𝔽2)—98no—
477H(5,𝔽2)—184no—
478C2×#41—31no—
479C2×#41—31no—
480C2×#41—91no—
481C2×#41—92no—
482C2×#41—92no—
483C2×#41—182no—
484C2×#41—181no—
485C2×#41—181no—
486C22×Q8—31no—
487C22×Q8—92no—
488C22×Q8—181no—
489C22×D4—31no—
490C22×D4—92no—
491C22×D4—181no—
492C22×D4—182no—
493#137—38no—
494#137—916no—
495AGL(1,ℤ/8)—38no—
496AGL(1,ℤ/8)—916no—
497#135—916no—
498#135—98no—
499C2×Q16—32no—
500C2×Q16—91no—
501C2×SD16—32no—
502C2×SD16—32no—
503C2×SD16—916no—
504C2×SD16—92no—
505C2×SD16—91no—
506C2×SD16—92no—
507C2×SD16—98no—
508C2×SD16—91no—
509C2×D8—32no—
510C2×D8—91no—
511#131—98no—
512C2×M16—92no—
513C2×M16D3211yescharacteristic, complemented
514C22×C8—91no—
515C22×C8—92no—
516C23×C3—21no—
517C23×C3—61no—
518C23×C3—62no—
519C23×C3—61no—
520C23×C3—64no—
521C23×C3—242no—
522C23×C3D3×D411yescharacteristic
523C23×C3D3×D411yescharacteristic
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—22no—
527C22×D3—24no—
528C22×D3—32no—
529C22×D3—32no—
530C22×D3—62no—
531C22×D3—68no—
532C22×D3—68no—
533C22×D3—82no—
534C22×D3—244no—
535C22×D3—244no—
536C3×Q8—34no—
537C3×Q8—32no—
538C3×Q8—32no—
539C3×Q8—61no—
540C3×Q8—62no—
541C3×Q8—64no—
542C3×Q8—61no—
543C3×D4—32no—
544C3×D4—32no—
545C3×D4—34no—
546C3×D4—64no—
547C3×D4—64no—
548C3×D4—61no—
549C3×D4—62no—
550C3×D4—64no—
551C3×D4—61no—
552C2×C3×C4—21no—
553C2×C3×C4—22no—
554C2×C3×C4—21no—
555C2×C3×C4—22no—
556C2×C3×C4—61no—
557C2×C3×C4—62no—
558C2×C3×C4—61no—
559C2×C3×C4—64no—
560C2×C3×C4—64no—
561C2×C3×C4—64no—
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4D3×D412yes—
564C2×C3×C4D3×D411yescharacteristic
565C2×C3×C4D3×D412yes—
566C2×C3×C4C23×D311yescharacteristic
567C2×C3×C4C23×D311yescharacteristic
568C2×C3×C4C23×D312yes—
569C2×C3×C4C23×D312yes—
570#67—24no—
571#67—24no—
572#67—38no—
573#67—38no—
574#67—68no—
575#67—68no—
576#67—68no—
577#67—68no—
578#67—68no—
579C2×Dic3—22no—
580C2×Dic3—24no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—32no—
584C2×Dic3—32no—
585C2×Dic3—62no—
586C2×Dic3—68no—
587C2×Dic3—68no—
588D12—24no—
589D12—22no—
590D12—21no—
591D12—21no—
592D12—34no—
593D12—34no—
594D12—64no—
595D12—68no—
596D12—68no—
597D12C23×D312yes—
598D12C23×D314yes—
599D12C23×D312yes—
600C4×D3—24no—
601C4×D3—24no—
602C4×D3—34no—
603C4×D3—34no—
604C4×D3—34no—
605C4×D3—34no—
606C4×D3—64no—
607C4×D3—64no—
608C4×D3—68no—
609C4×D3—68no—
610C4×D3—68no—
611C4×D3—68no—
612Dic6—24no—
613Dic6—22no—
614Dic6—21no—
615Dic6—21no—
616Dic6—34no—
617Dic6—34no—
618Dic6—64no—
619Dic6—68no—
620Dic6—68no—
621Dic6C23×D312yes—
622Dic6C23×D314yes—
623Dic6C23×D312yes—
624C3×C8—24no—
625C3×C8C23×D314yes—
626C3×C8C23×D314yes—
627C3⋊C8—32no—
628C3⋊C8—32no—
629C3⋊C8—32no—
630C3⋊C8—32no—
631C3⋊C8—62no—
632C3⋊C8—62no—
633C2×C32—22no—
634C2×C32#57712yescomplemented
635C2×C32C23×D411yescharacteristic
636C3⋊D3—24no—
637C3×D3—42no—
638C3×D3—44no—
639C3×D3—42no—
640C24—61no—
641C24—182no—
642#41—34no—
643#41—34no—
644#41—62no—
645#41—62no—
646#41—94no—
647#41—94no—
648#41—98no—
649#41—98no—
650#41—1816no—
651#41—188no—
652#41—188no—
653#41—184no—
654#41—184no—
655C2×Q8—31no—
656C2×Q8—32no—
657C2×Q8—34no—
658C2×Q8—31no—
659C2×Q8—61no—
660C2×Q8—62no—
661C2×Q8—91no—
662C2×Q8—98no—
663C2×Q8—182no—
664C2×Q8—188no—
665C2×Q8—184no—
666C2×D4—31no—
667C2×D4—32no—
668C2×D4—31no—
669C2×D4—34no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—62no—
674C2×D4—98no—
675C2×D4—92no—
676C2×D4—91no—
677C2×D4—188no—
678C2×D4—182no—
679C2×D4—182no—
680C2×D4—184no—
681C2×D4—182no—
682C2×D4—1816no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—92no—
687C22×C4—182no—
688C22×C4—182no—
689C22×C4—182no—
690C22×C4C2×D3211yescharacteristic
691Q16—38no—
692Q16—94no—
693SD16—38no—
694SD16—38no—
695SD16—98no—
696SD16—94no—
697SD16—98no—
698SD16—94no—
699D8—38no—
700D8—94no—
701M16—98no—
702M16C2×D3214yescomplemented
703C2×C8—91no—
704C2×C8—91no—
705C2×C8—94no—
706C2×C8—98no—
707C2×C8C2×D3212yes—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—21no—
712C22×C3—42no—
713C22×C3—62no—
714C22×C3—64no—
715C22×C3—62no—
716C22×C3—122no—
717C22×C3—124no—
718C22×C3—122no—
719C22×C3—244no—
720C22×C3C2×D3×D412yes—
721C22×C3C2×D3×D412yes—
722C22×C3C2×D3×D411yescharacteristic
723C22×C3C2×D3×D411yescharacteristic
724C2×D3—22no—
725C2×D3—22no—
726C2×D3—24no—
727C2×D3—34no—
728C2×D3—34no—
729C2×D3—44no—
730C2×D3—42no—
731C2×D3—42no—
732C2×D3—64no—
733C2×D3—64no—
734C2×D3—64no—
735C2×D3—84no—
736C2×D3—124no—
737C2×D3—248no—
738C2×D3—248no—
739C3×C4—22no—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—62no—
743C3×C4—64no—
744C3×C4—62no—
745C3×C4C2×D3×D411yescharacteristic
746C3×C4C2×D3×D412yes—
747C3×C4C2×D3×D411yescharacteristic
748C3×C4C2×D3×D412yes—
749C3×C4C24×D311yescharacteristic
750C3×C4C24×D311yescharacteristic
751Dic3—24no—
752Dic3—22no—
753Dic3—22no—
754Dic3—34no—
755Dic3—34no—
756Dic3—64no—
757C32C2×#57711yescharacteristic, complemented, Sylow
758C23—61no—
759C23—61no—
760C23—62no—
761C23—64no—
762C23—92no—
763C23—188no—
764C23—242no—
765C23—724no—
766C23#380211yescharacteristic
767Q8—32no—
768Q8—34no—
769Q8—32no—
770Q8—64no—
771Q8—62no—
772Q8—61no—
773Q8—61no—
774Q8—94no—
775Q8—188no—
776D4—32no—
777D4—34no—
778D4—32no—
779D4—64no—
780D4—64no—
781D4—64no—
782D4—62no—
783D4—61no—
784D4—61no—
785D4—98no—
786D4—94no—
787D4—188no—
788D4—188no—
789D4—188no—
790C2×C4—64no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—62no—
794C2×C4—64no—
795C2×C4—64no—
796C2×C4—92no—
797C2×C4—94no—
798C2×C4—94no—
799C2×C4—188no—
800C2×C4—188no—
801C2×C4—188no—
802C2×C4#380212yes—
803C2×C4#380211yescharacteristic
804C2×C4C22×D3212yes—
805C2×C4C22×D3211yescharacteristic
806C8—92no—
807C8—92no—
808C8C22×D3214yes—
809C2×C3—22no—
810C2×C3—22no—
811C2×C3—21no—
812C2×C3—22no—
813C2×C3—42no—
814C2×C3—122no—
815C2×C3—124no—
816C2×C3—122no—
817C2×C3#577512yescomplemented
818C2×C3#577812yescomplemented
819C2×C3C22×D3×D411yescharacteristic
820C2×C3C22×D3×D411yescharacteristic
821D3—44no—
822D3—42no—
823D3—42no—
824D3—64no—
825D3—64no—
826D3—124no—
827C22—22no—
828C22—62no—
829C22—62no—
830C22—64no—
831C22—94no—
832C22—124no—
833C22—122no—
834C22—122no—
835C22—184no—
836C22—244no—
837C22—728no—
838C22C2×#380212yes—
839C22C2×#380211yescharacteristic
840C4—62no—
841C4—62no—
842C4—64no—
843C4—94no—
844C4C2×#380212yes—
845C4C2×#380211yescharacteristic
846C4C23×D3211yescharacteristic
847C3—21no—
848C3C2×#577511yescharacteristic, complemented
849C3C2×#577811yescharacteristic, complemented
850C2—22no—
851C2—124no—
852C2—122no—
853C2—122no—
854C2—184no—
855C2#1059471912yesdirect product factor
856C2C22×#380211yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C2×#64297C2semidirect
3. C2×#64116C2semidirect
4. C2×C3×#909C2semidirect
5. C2×C3×#908C2semidirect
6. C22×#3715C2semidirect
7. C2×#63822C2semidirect
8. #10594719C2direct (N × H)
9. C2×#63811C2semidirect
10. C2×#63810C2semidirect
11. C2×#63798C2semidirect
12. C2×#63796C2semidirect
17. C2×C3×#235C22semidirect
19. C22×C3×Dic6C22semidirect
23. #64307C22semidirect
27. C2×#3797C22semidirect
29. #64297C22semidirect
31. C2×#3796C22semidirect
34. C2×C32×M16C22semidirect
35. C22×C3⋊(C3⋊C8)C22semidirect
36. #64116C22semidirect
37. C2×#3743C22semidirect
38. C2×C8×C3⋊D3C22semidirect
39. C3×#909C22semidirect
40. C3×#908C22semidirect
41. C2×C3×Dic12C22semidirect
42. C2×C3×D24C22semidirect
43. C2×C3×#204C22semidirect
44. C2×C3×#204C22semidirect
45. C2×#3718C22semidirect
46. C2×#3715C22semidirect
47. C2×#3715C22semidirect
48. C2×#3715C22semidirect
49. C2×#3715C22semidirect
50. C2×#3715C22semidirect
51. #63822C22semidirect
52. C2×#3713C22semidirect
53. #63811C22semidirect
54. #63810C22semidirect
55. #63798C22semidirect
56. #63796C22semidirect
77. C2×#909D3semidirect
78. C2×#908D3semidirect
97. C3×#235C23semidirect
111. C2×C3×Dic6C23semidirect
126. #3797C23semidirect
130. #3796C23semidirect
133. C32×M16C23semidirect
137. C2×C3⋊(C3⋊C8)C23semidirect
138. #3743C23semidirect
139. C8×C3⋊D3C23semidirect
140. C3×Dic12C23semidirect
141. C3×D24C23semidirect
142. C3×#204C23semidirect
143. C3×#204C23semidirect
144. #3718C23semidirect
145. #3715C23semidirect
146. #3715C23semidirect
147. #3715C23semidirect
148. #3715C23semidirect
149. #3713C23semidirect
185. C2×#235C2×D3semidirect
189. C22×Dic6C2×D3semidirect
197. C2×C3×M16C2×D3semidirect
198. C2×C3×M16C2×D3semidirect
226. #909C2×D3semidirect
227. #908C2×D3semidirect
231. C2×Dic12C2×D3semidirect
232. C2×D24C2×D3semidirect
233. C2×#204C2×D3semidirect
234. C2×#204C2×D3semidirect
379. #235C22×D3semidirect
412. C2×Dic6C22×D3semidirect
418. C3×M16C22×D3semidirect
419. C3×M16C22×D3semidirect
444. Dic12C22×D3semidirect
445. D24C22×D3semidirect
446. #204C22×D3semidirect
447. #204C22×D3semidirect
513. C2×M16D32semidirect
634. C2×C32#577semidirect
702. M16C2×D32semidirect
757. C32C2×#577semidirect
817. C2×C3#5775semidirect
818. C2×C3#5778semidirect
848. C3C2×#5775semidirect
849. C3C2×#5778semidirect
855. C2#10594719direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643072
C2×#642972
C2×#641162
C2×C3×#9092
C2×C3×#9082
C22×#37152
C2×#638222
#105947192
C2×#638112
C2×#638102
C2×#637982
C2×#637962
C2×#57783
C2×#57753