Finite Group Databasebeta

← C2×#10594795 #11918769

Subgroups — C2×#10594795 #11918769

Order 1152.

3413 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic, complemented
2C22×C3×#235C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4C2×#63833C212yesmaximal, complemented
5#10594795C2116yesmaximal, direct product factor
6C2×#63831C212yesmaximal, complemented
7C2×#63830C212yesmaximal, complemented
8C2×#63829C214yesmaximal, complemented
9C2×#63825C212yesmaximal, complemented
10C2×#5822—31nomaximal
11C2×#5748—31nomaximal
12C23×C32×C4C2211yescharacteristic
13C22×#638—21no—
14C2×#3828—21no—
15C2×#3828—24no—
16C2×#3828—21no—
17C2×#3828C2212yes—
18C2×#3828C2212yescomplemented
19C2×#3828C2218yescomplemented
20C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
21C22×C4×C3⋊D3—21no—
22C22×#634C2211yescharacteristic, complemented
23C22×C3×#67—21no—
24C2×C3×#235—21no—
25C2×C3×#235—24no—
26C2×C3×#235—21no—
27C2×C3×#235C2212yes—
28C2×C3×#235C2212yescomplemented
29C2×C3×#235C2218yescomplemented
30C22×C3×D12C2211yescharacteristic, complemented
31C22×C3×C4×D3—21no—
32C22×C3×Dic6C2211yescharacteristic, complemented
33C2×C3×#208C2212yescomplemented
34C2×C3×#208C2212yescomplemented
35C2×C3×#208C2218yescomplemented
36C22×C3×C3⋊C8C2212yescomplemented
37C2×#3719C2214yescomplemented
38#63833C22116yescomplemented
39C2×#3717C2214yescomplemented
40#63831C22116yescomplemented
41#63830C22116yescomplemented
42#63829C22132yescomplemented
43C2×#3716C2214yescomplemented
44#63825C22116yescomplemented
45C2×#3714C2214yescomplemented
46C22×C3×#41—31no—
47C22×#235—31no—
48C22×#235—31no—
49C22×#235—61no—
50C22×#235D311yescharacteristic, complemented
51C22×C3×M16—31no—
52C2×#951—32no—
53#5822—316no—
54C2×#950—34no—
55C2×#949—32no—
56C2×#942—32no—
57C2×#932—32no—
58C22×#208D311yescharacteristic, complemented
59#5748—316no—
60C2×#909—32no—
61C2×#909—32no—
62C2×#908—32no—
63C2×#908—32no—
64C2×#904—34no—
65C24×C32D411yescharacteristic
66C23×C3⋊D3—21no—
67C23×C3×D3—21no—
68C22×C32×C4D411yescharacteristic
69C22×C32×C4D411yescharacteristic
70C22×C32×C4D411yescharacteristic
71C22×C32×C4D414yes—
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2314yes—
76C2×#638—22no—
77C2×#638—22no—
78C2×#638—28no—
79C22×C3⋊Dic3—21no—
80#3828—24no—
81#3828—24no—
82#3828—28no—
83#3828—28no—
84#3828C2318yes—
85#3828C2318yescomplemented
86C2×C4⋊(C3⋊D3)—22no—
87C2×C4⋊(C3⋊D3)—21no—
88C2×C4⋊(C3⋊D3)C2312yes—
89C2×C4⋊(C3⋊D3)C2314yescomplemented
90C2×C4×C3⋊D3—22no—
91C2×C4×C3⋊D3—28no—
92C2×C4×C3⋊D3—22no—
93C2×#634—22no—
94C2×#634—21no—
95C2×#634C2312yes—
96C2×#634C2314yescomplemented
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—28no—
100C22×C3×Dic3—21no—
101C3×#235—24no—
102C3×#235—24no—
103C3×#235—28no—
104C3×#235—28no—
105C3×#235C2318yes—
106C3×#235C2318yescomplemented
107C2×C3×D12—22no—
108C2×C3×D12—21no—
109C2×C3×D12C2312yes—
110C2×C3×D12C2314yescomplemented
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—28no—
113C2×C3×C4×D3—22no—
114C2×C3×Dic6—22no—
115C2×C3×Dic6—21no—
116C2×C3×Dic6C2312yes—
117C2×C3×Dic6C2314yescomplemented
118C3×#208C2318yescomplemented
119C3×#208C2318yescomplemented
120C2×C3×C3⋊C8C2314yes—
121C2×C3×C3⋊C8C2318yescomplemented
122#3719C23116yescomplemented
123#3717C23116yescomplemented
124#3716C23116yescomplemented
125#3714C23116yescomplemented
126C2×#575—91noSylow
127C2×C3×#41—32no—
128C2×C3×#41—32no—
129C2×C3×#41—38no—
130C2×C3×#41—61no—
131C2×C3×#41—61no—
132C2×C3×#41—64no—
133C22×C3×Q8—31no—
134C22×C3×D4—31no—
135C22×C3×D4—61no—
136C23×C3×C4—21no—
137C23×C3×C4—61no—
138C23×C3×C4C2×D311yescharacteristic
139C23×C3×C4C2×D311yescharacteristic
140C22×#67—21no—
141C22×#67—62no—
142C22×#67—61no—
143C22×#67—61no—
144C2×#235—21no—
145C2×#235—24no—
146C2×#235—21no—
147C2×#235—32no—
148C2×#235—32no—
149C2×#235—32no—
150C2×#235—38no—
151C2×#235—32no—
152C2×#235—38no—
153C2×#235—62no—
154C2×#235—62no—
155C2×#235—68no—
156C2×#235—62no—
157C2×#235—68no—
158C2×#235—62no—
159C2×#235—61no—
160C2×#235—61no—
161C2×#235—64no—
162C2×#235—61no—
163C2×#235—61no—
164C2×#235—64no—
165C2×#235C2×D312yes—
166C2×#235C2×D312yescomplemented
167C2×#235C2×D318yescomplemented
168C22×D12—31no—
169C22×D12—31no—
170C22×D12—61no—
171C22×D12C2×D311yescharacteristic, complemented
172C22×C4×D3—21no—
173C22×C4×D3—62no—
174C22×C4×D3—61no—
175C22×C4×D3—61no—
176C22×Dic6—31no—
177C22×Dic6—31no—
178C22×Dic6—61no—
179C22×Dic6C2×D311yescharacteristic, complemented
180C2×C3×M16—32no—
181C2×C3×M16—32no—
182C2×C3×M16—38no—
183C22×C3×C8—32no—
184#951—316no—
185#950—332no—
186#949—316no—
187C2×#216—34no—
188#942—316no—
189C2×#215—34no—
190C2×#214—34no—
191#932—316no—
192C2×#213—34no—
193C2×#208C2×D312yescomplemented
194C2×#208C2×D312yescomplemented
195C2×#208C2×D318yescomplemented
196C22×C3⋊C8C2×D312yescomplemented
197#909—316no—
198#909—316no—
199#908—316no—
200#908—316no—
201C2×Dic12—34no—
202#904—332no—
203C2×D24—34no—
204C2×#204—34no—
205C2×#204—34no—
206C23×C32—42no—
207C23×C32C2×D411yescharacteristic
208C23×C32C2×D411yescharacteristic
209C23×C32C2×D411yescharacteristic
210C23×C32C2×D414yes—
211C22×C3⋊D3—22no—
212C22×C3⋊D3—24no—
213C22×C3⋊D3—44no—
214C22×C3×D3—22no—
215C22×C3×D3—24no—
216C22×C3×D3—44no—
217C2×C32×C4C2×D411yescharacteristic
218C2×C32×C4C2×D412yes—
219C2×C32×C4C2×D411yescharacteristic
220C2×C32×C4C2×D411yescharacteristic
221C2×C32×C4C2×D414yes—
222C2×C32×C4C2×D412yes—
223C2×C32×C4C2×D414yes—
224C2×C32×C4C2×D412yes—
225C2×C32×C4C2×D414yes—
226C2×C32×C4C2411yescharacteristic
227C2×C32×C4C2412yes—
228C2×C32×C4C2412yes—
229C2×C32×C4C2412yes—
230#638—28no—
231#638—28no—
232C2×C3⋊Dic3—22no—
233C2×C3⋊Dic3—24no—
234C4⋊(C3⋊D3)—22no—
235C4⋊(C3⋊D3)—24no—
236C4⋊(C3⋊D3)C2414yes—
237C4×C3⋊D3—28no—
238C4×C3⋊D3—28no—
239#634—22no—
240#634—24no—
241#634C2414yes—
242C3×#67—28no—
243C3×#67—28no—
244C2×C3×Dic3—22no—
245C2×C3×Dic3—24no—
246C3×D12—22no—
247C3×D12—24no—
248C3×D12C2414yes—
249C3×C4×D3—28no—
250C3×C4×D3—28no—
251C3×Dic6—22no—
252C3×Dic6—24no—
253C3×Dic6C2414yes—
254C3×C3⋊C8C2418yes—
255C22×#41—31no—
256C22×#41—91no—
257#575—916no—
258C2×#137—92no—
259C2×#137—92no—
260C2×AGL(1,ℤ/8)—92no—
261C2×AGL(1,ℤ/8)—92no—
262C2×#135—94no—
263C22×M16—31no—
264C24×C3—21no—
265C24×C3—61no—
266C24×C3D1211yescharacteristic
267C24×C3#6711yescharacteristic
268C23×D3—21no—
269C23×D3—62no—
270C23×D3—61no—
271C23×D3—61no—
272C3×#41—38no—
273C3×#41—38no—
274C3×#41—64no—
275C3×#41—68no—
276C3×#41—64no—
277C3×#41—68no—
278C2×C3×Q8—32no—
279C2×C3×Q8—34no—
280C2×C3×Q8—61no—
281C2×C3×Q8—62no—
282C2×C3×D4—32no—
283C2×C3×D4—34no—
284C2×C3×D4—62no—
285C2×C3×D4—62no—
286C2×C3×D4—68no—
287C2×C3×D4—61no—
288C2×C3×D4—62no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—24no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—24no—
296C22×C3×C4—21no—
297C22×C3×C4—61no—
298C22×C3×C4—62no—
299C22×C3×C4—68no—
300C22×C3×C4—62no—
301C22×C3×C4D1211yescharacteristic
302C22×C3×C4D1211yescharacteristic
303C22×C3×C4D1211yescharacteristic
304C22×C3×C4D1214yes—
305C22×C3×C4#6711yescharacteristic
306C22×C3×C4#6711yescharacteristic
307C22×C3×C4#6711yescharacteristic
308C22×C3×C4#6714yes—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D314yes—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D314yes—
317C2×#67—22no—
318C2×#67—22no—
319C2×#67—28no—
320C2×#67—64no—
321C2×#67—64no—
322C2×#67—616no—
323C2×#67—62no—
324C2×#67—62no—
325C2×#67—68no—
326C2×#67—62no—
327C2×#67—62no—
328C2×#67—68no—
329C22×Dic3—21no—
330C22×Dic3—62no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333#235—24no—
334#235—24no—
335#235—28no—
336#235—28no—
337#235—38no—
338#235—38no—
339#235—38no—
340#235—38no—
341#235—68no—
342#235—68no—
343#235—68no—
344#235—616no—
345#235—68no—
346#235—616no—
347#235—68no—
348#235—64no—
349#235—64no—
350#235—68no—
351#235—64no—
352#235—68no—
353#235—64no—
354#235—68no—
355#235C22×D318yes—
356#235C22×D318yescomplemented
357C2×D12—22no—
358C2×D12—21no—
359C2×D12—32no—
360C2×D12—34no—
361C2×D12—32no—
362C2×D12—34no—
363C2×D12—62no—
364C2×D12—64no—
365C2×D12—62no—
366C2×D12—64no—
367C2×D12—61no—
368C2×D12—62no—
369C2×D12—61no—
370C2×D12—62no—
371C2×D12C22×D312yes—
372C2×D12C22×D314yescomplemented
373C2×C4×D3—22no—
374C2×C4×D3—28no—
375C2×C4×D3—22no—
376C2×C4×D3—64no—
377C2×C4×D3—616no—
378C2×C4×D3—64no—
379C2×C4×D3—62no—
380C2×C4×D3—68no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—68no—
384C2×C4×D3—62no—
385C2×Dic6—22no—
386C2×Dic6—21no—
387C2×Dic6—32no—
388C2×Dic6—34no—
389C2×Dic6—32no—
390C2×Dic6—34no—
391C2×Dic6—62no—
392C2×Dic6—64no—
393C2×Dic6—62no—
394C2×Dic6—64no—
395C2×Dic6—61no—
396C2×Dic6—62no—
397C2×Dic6—61no—
398C2×Dic6—62no—
399C2×Dic6C22×D312yes—
400C2×Dic6C22×D314yescomplemented
401C3×M16—38no—
402C3×M16—38no—
403C2×C3×C8—34no—
404C2×C3×C8—38no—
405#216—316no—
406#215—316no—
407#214—316no—
408#213—316no—
409#208C22×D318yescomplemented
410#208C22×D318yescomplemented
411C2×C3⋊C8C22×D314yes—
412C2×C3⋊C8C22×D318yescomplemented
413Dic12—316no—
414D24—316no—
415#204—316no—
416#204—316no—
417C22×C32—22no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—44no—
421C22×C32C22×D412yes—
422C22×C32C22×D412yes—
423C22×C32C22×D412yes—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—24no—
426C2×C3⋊D3—48no—
427C2×C3⋊D3—44no—
428C2×C3×D3—24no—
429C2×C3×D3—48no—
430C2×C3×D3—44no—
431C32×C4C22×D411yescharacteristic
432C32×C4C22×D412yes—
433C32×C4C22×D412yes—
434C32×C4C22×D412yes—
435C32×C4C2511yescharacteristic
436C3⋊Dic3—24no—
437C3×Dic3—24no—
438C2×#41—32no—
439C2×#41—32no—
440C2×#41—38no—
441C2×#41—61no—
442C2×#41—64no—
443C2×#41—61no—
444C2×#41—92no—
445C2×#41—92no—
446C2×#41—98no—
447C2×#41—181no—
448C2×#41—184no—
449C2×#41—181no—
450C22×Q8—31no—
451C22×Q8—91no—
452C22×D4—31no—
453C22×D4—61no—
454C22×D4—91no—
455C22×D4—181no—
456C23×C4—61no—
457C23×C4—181no—
458C23×C4D3211yescharacteristic
459#137—916no—
460#137—916no—
461AGL(1,ℤ/8)—916no—
462AGL(1,ℤ/8)—916no—
463#135—932no—
464C2×Q16—94no—
465C2×SD16—94no—
466C2×SD16—94no—
467C2×D8—94no—
468C2×M16—32no—
469C2×M16—32no—
470C2×M16—38no—
471C22×C8—32no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—24no—
476C23×C3—42no—
477C23×C3—42no—
478C23×C3—44no—
479C23×C3—64no—
480C23×C3—62no—
481C23×C3—124no—
482C23×C3C2×D1211yescharacteristic
483C23×C3C2×D1211yescharacteristic
484C23×C3C2×D1211yescharacteristic
485C23×C3C2×D1214yes—
486C23×C3C2×#6711yescharacteristic
487C23×C3C2×#6711yescharacteristic
488C23×C3C2×#6711yescharacteristic
489C23×C3C2×#6714yes—
490C22×D3—22no—
491C22×D3—24no—
492C22×D3—44no—
493C22×D3—64no—
494C22×D3—68no—
495C22×D3—64no—
496C22×D3—62no—
497C22×D3—64no—
498C22×D3—62no—
499C22×D3—128no—
500C22×D3—124no—
501C22×D3—124no—
502C3×Q8—34no—
503C3×Q8—62no—
504C3×Q8—64no—
505C3×D4—34no—
506C3×D4—68no—
507C3×D4—68no—
508C3×D4—62no—
509C3×D4—64no—
510C2×C3×C4—21no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—22no—
516C2×C3×C4—21no—
517C2×C3×C4—24no—
518C2×C3×C4—24no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—24no—
522C2×C3×C4—21no—
523C2×C3×C4—64no—
524C2×C3×C4—62no—
525C2×C3×C4—68no—
526C2×C3×C4—68no—
527C2×C3×C4C2×D1211yescharacteristic
528C2×C3×C4C2×D1212yes—
529C2×C3×C4C2×D1211yescharacteristic
530C2×C3×C4C2×D1214yes—
531C2×C3×C4C2×D1214yes—
532C2×C3×C4C2×D1212yes—
533C2×C3×C4C2×D1214yes—
534C2×C3×C4C2×D1212yes—
535C2×C3×C4C2×D1211yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C2×#6712yes—
538C2×C3×C4C2×#6711yescharacteristic
539C2×C3×C4C2×#6712yes—
540C2×C3×C4C2×#6714yes—
541C2×C3×C4C2×#6714yes—
542C2×C3×C4C2×#6712yes—
543C2×C3×C4C2×#6714yes—
544C2×C3×C4C2×#6711yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546C2×C3×C4C23×D312yes—
547C2×C3×C4C23×D312yes—
548C2×C3×C4C23×D312yes—
549C2×C3×C4C23×D311yescharacteristic
550C2×C3×C4C23×D312yes—
551C2×C3×C4C23×D312yes—
552C2×C3×C4C23×D312yes—
553#67—28no—
554#67—28no—
555#67—616no—
556#67—616no—
557#67—68no—
558#67—68no—
559#67—68no—
560#67—68no—
561C2×Dic3—22no—
562C2×Dic3—24no—
563C2×Dic3—64no—
564C2×Dic3—68no—
565C2×Dic3—64no—
566C2×Dic3—62no—
567C2×Dic3—64no—
568C2×Dic3—62no—
569D12—22no—
570D12—24no—
571D12—34no—
572D12—34no—
573D12—64no—
574D12—64no—
575D12—68no—
576D12—64no—
577D12—62no—
578D12—62no—
579D12—64no—
580D12C23×D314yes—
581C4×D3—28no—
582C4×D3—28no—
583C4×D3—616no—
584C4×D3—616no—
585C4×D3—68no—
586C4×D3—68no—
587C4×D3—68no—
588C4×D3—68no—
589Dic6—22no—
590Dic6—24no—
591Dic6—34no—
592Dic6—34no—
593Dic6—64no—
594Dic6—64no—
595Dic6—68no—
596Dic6—64no—
597Dic6—62no—
598Dic6—62no—
599Dic6—64no—
600Dic6C23×D314yes—
601C3×C8—38no—
602C3⋊C8C23×D318yes—
603C2×C32—22no—
604C2×C32—22no—
605C2×C32—22no—
606C2×C32#57512yescomplemented
607C2×C32C23×D411yescharacteristic
608C3⋊D3—44no—
609C3×D3—44no—
610C24—61no—
611C24—181no—
612C24#62611yescharacteristic
613#41—38no—
614#41—38no—
615#41—68no—
616#41—64no—
617#41—64no—
618#41—68no—
619#41—98no—
620#41—98no—
621#41—188no—
622#41—184no—
623#41—184no—
624#41—188no—
625C2×Q8—32no—
626C2×Q8—34no—
627C2×Q8—61no—
628C2×Q8—62no—
629C2×Q8—92no—
630C2×Q8—94no—
631C2×Q8—181no—
632C2×Q8—182no—
633C2×D4—32no—
634C2×D4—34no—
635C2×D4—62no—
636C2×D4—62no—
637C2×D4—68no—
638C2×D4—61no—
639C2×D4—62no—
640C2×D4—92no—
641C2×D4—94no—
642C2×D4—182no—
643C2×D4—182no—
644C2×D4—188no—
645C2×D4—181no—
646C2×D4—182no—
647C22×C4—61no—
648C22×C4—62no—
649C22×C4—68no—
650C22×C4—62no—
651C22×C4—181no—
652C22×C4—182no—
653C22×C4—188no—
654C22×C4—182no—
655C22×C4#62611yescharacteristic
656C22×C4#62614yes—
657C22×C4#62611yescharacteristic
658C22×C4#62611yescharacteristic
659C22×C4C2×D3211yescharacteristic
660C22×C4C2×D3211yescharacteristic
661C22×C4C2×D3214yes—
662C22×C4C2×D3211yescharacteristic
663Q16—916no—
664SD16—916no—
665SD16—916no—
666D8—916no—
667M16—38no—
668M16—38no—
669C2×C8—34no—
670C2×C8—38no—
671C22×C3—24no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—21no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—44no—
685C22×C3—44no—
686C22×C3—48no—
687C22×C3—64no—
688C22×C3—128no—
689C22×C3—124no—
690C22×C3C22×D1212yes—
691C22×C3C22×D1212yes—
692C22×C3C22×D1212yes—
693C22×C3C22×D1211yescharacteristic
694C22×C3C22×#6712yes—
695C22×C3C22×#6712yes—
696C22×C3C22×#6712yes—
697C22×C3C22×#6711yescharacteristic
698C2×D3—24no—
699C2×D3—48no—
700C2×D3—44no—
701C2×D3—68no—
702C2×D3—64no—
703C2×D3—64no—
704C2×D3—1216no—
705C2×D3—128no—
706C2×D3—128no—
707C2×D3—128no—
708C2×D3—124no—
709C2×D3—124no—
710C3×C4—22no—
711C3×C4—21no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—21no—
715C3×C4—64no—
716C3×C4C22×D1212yes—
717C3×C4C22×D1211yescharacteristic
718C3×C4C22×D1212yes—
719C3×C4C22×D1212yes—
720C3×C4C22×#6711yescharacteristic
721C3×C4C22×#6712yes—
722C3×C4C22×#6712yes—
723C3×C4C22×#6712yes—
724C3×C4C24×D311yescharacteristic
725C3×C4C24×D311yescharacteristic
726Dic3—24no—
727Dic3—68no—
728Dic3—64no—
729Dic3—64no—
730C32C2×#57511yescharacteristic, complemented, Sylow
731C23—42no—
732C23—64no—
733C23—62no—
734C23—124no—
735C23—184no—
736C23—182no—
737C23—364no—
738C23C2×#62611yescharacteristic
739C23C2×#62611yescharacteristic
740C23C2×#62611yescharacteristic
741C23C2×#62614yes—
742Q8—34no—
743Q8—64no—
744Q8—62no—
745Q8—94no—
746Q8—184no—
747Q8—182no—
748D4—34no—
749D4—68no—
750D4—68no—
751D4—64no—
752D4—62no—
753D4—94no—
754D4—188no—
755D4—188no—
756D4—184no—
757D4—182no—
758C2×C4—64no—
759C2×C4—62no—
760C2×C4—68no—
761C2×C4—68no—
762C2×C4—184no—
763C2×C4—182no—
764C2×C4—188no—
765C2×C4—188no—
766C2×C4C2×#62611yescharacteristic
767C2×C4C2×#62614yes—
768C2×C4C2×#62611yescharacteristic
769C2×C4C2×#62614yes—
770C2×C4C2×#62612yes—
771C2×C4C2×#62612yes—
772C2×C4C2×#62612yes—
773C2×C4C2×#62614yes—
774C2×C4C2×#62611yescharacteristic
775C2×C4C22×D3211yescharacteristic
776C2×C4C22×D3212yes—
777C2×C4C22×D3212yes—
778C2×C4C22×D3212yes—
779C8—38no—
780C2×C3—24no—
781C2×C3—22no—
782C2×C3—22no—
783C2×C3—22no—
784C2×C3—22no—
785C2×C3—22no—
786C2×C3—22no—
787C2×C3—21no—
788C2×C3—22no—
789C2×C3—42no—
790C2×C3—42no—
791C2×C3—124no—
792C2×C3#574812yescomplemented
793C2×C3#582212yescomplemented
794C2×C3C23×D1211yescharacteristic
795C2×C3C23×#6711yescharacteristic
796D3—44no—
797D3—128no—
798D3—124no—
799D3—124no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—44no—
804C22—64no—
805C22—128no—
806C22—124no—
807C22—184no—
808C22—368no—
809C22—364no—
810C22C22×#62612yes—
811C22C22×#62612yes—
812C22C22×#62612yes—
813C22C22×#62611yescharacteristic
814C4—64no—
815C4—184no—
816C4C22×#62612yes—
817C4C22×#62612yes—
818C4C22×#62612yes—
819C4C22×#62611yescharacteristic
820C4C23×D3211yescharacteristic
821C3—21no—
822C3C2×#574811yescharacteristic, complemented
823C3C2×#582211yescharacteristic, complemented
824C2—22no—
825C2—22no—
826C2—22no—
827C2—124no—
828C2—364no—
829C2#1059479512yesdirect product factor
830C2C23×#62611yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC23×C32×C4C22
socleC22×C32C22×D4
hypercenterC23×C4D32
hypocenterC32C2×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C22×C3×#235C2semidirect
3. C22×C3×#208C2semidirect
4. C2×#63833C2semidirect
5. #10594795C2direct (N × H)
6. C2×#63831C2semidirect
7. C2×#63830C2semidirect
8. C2×#63829C2semidirect
9. C2×#63825C2semidirect
18. C2×#3828C22semidirect
19. C2×#3828C22semidirect
20. C22×C4⋊(C3⋊D3)C22semidirect
22. C22×#634C22semidirect
28. C2×C3×#235C22semidirect
29. C2×C3×#235C22semidirect
30. C22×C3×D12C22semidirect
32. C22×C3×Dic6C22semidirect
33. C2×C3×#208C22semidirect
34. C2×C3×#208C22semidirect
35. C2×C3×#208C22semidirect
36. C22×C3×C3⋊C8C22semidirect
37. C2×#3719C22semidirect
38. #63833C22semidirect
39. C2×#3717C22semidirect
40. #63831C22semidirect
41. #63830C22semidirect
42. #63829C22semidirect
43. C2×#3716C22semidirect
44. #63825C22semidirect
45. C2×#3714C22semidirect
50. C22×#235D3semidirect
58. C22×#208D3semidirect
85. #3828C23semidirect
89. C2×C4⋊(C3⋊D3)C23semidirect
96. C2×#634C23semidirect
106. C3×#235C23semidirect
110. C2×C3×D12C23semidirect
117. C2×C3×Dic6C23semidirect
118. C3×#208C23semidirect
119. C3×#208C23semidirect
121. C2×C3×C3⋊C8C23semidirect
122. #3719C23semidirect
123. #3717C23semidirect
124. #3716C23semidirect
125. #3714C23semidirect
166. C2×#235C2×D3semidirect
167. C2×#235C2×D3semidirect
171. C22×D12C2×D3semidirect
179. C22×Dic6C2×D3semidirect
193. C2×#208C2×D3semidirect
194. C2×#208C2×D3semidirect
195. C2×#208C2×D3semidirect
196. C22×C3⋊C8C2×D3semidirect
356. #235C22×D3semidirect
372. C2×D12C22×D3semidirect
400. C2×Dic6C22×D3semidirect
409. #208C22×D3semidirect
410. #208C22×D3semidirect
412. C2×C3⋊C8C22×D3semidirect
606. C2×C32#575semidirect
730. C32C2×#575semidirect
792. C2×C3#5748semidirect
793. C2×C3#5822semidirect
822. C3C2×#5748semidirect
823. C3C2×#5822semidirect
829. C2#10594795direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C22×C3×#2352
C22×C3×#2082
C2×#638332
#105947952
C2×#638312
C2×#638302
C2×#638292
C2×#638252
C2×#58223
C2×#57483