Finite Group Databasebeta

← C2×#10594717 #11918707

Subgroups — C2×#10594717 #11918707

Order 1152.

3077 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic
2C22×#3797C211yesmaximal, characteristic, complemented
3C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C3×#909C212yesmaximal, complemented
5C2×#63827C212yesmaximal, complemented
6#10594717C2116yesmaximal, direct product factor
7C2×#63811C214yesmaximal, complemented
8C2×#63802C212yesmaximal, complemented
9C2×#63796C212yesmaximal, complemented
10C2×D3×#137—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×C3×#235C2212yes—
13C22×C3×Dic6C2212yescomplemented
14C2×#3811—21no—
15C22×#627—21no—
16C22×#624—21no—
17C2×#3805—21no—
18#64306—24no—
19#64306C2218yes—
20C2×#3802C2211yescharacteristic
21C2×C4×D32—21no—
22C2×#3798—21no—
23C2×#3797—24no—
24C2×#3797—21no—
25C2×#3797—21no—
26C2×#3797C2212yes—
27C2×#3797C2211yescharacteristic
28C2×#3797C2218yescomplemented
29C2×#3797C2212yescomplemented
30C2×#3796C2212yes—
31C2×C32×M16C2211yescharacteristic, complemented
32C2×#3748C2211yescharacteristic, complemented
33M16×C3⋊D3C2218yescomplemented
34C2×#3743C2212yescomplemented
35C2×C8×C3⋊D3C2212yes—
36C3×#909C22116yescomplemented
37C2×C3×Dic12C2214yescomplemented
38C2×C3×#204C2214yescomplemented
39C2×#3718C2214yescomplemented
40#63827C22116yescomplemented
41C2×#3715C2214yescomplemented
42#63811C22132yescomplemented
43#63802C22116yescomplemented
44#63796C22116yescomplemented
45C2×D3×#41—32no—
46C22×D3×Q8—32no—
47C2×C3×#137—32no—
48C2×#951—32no—
49C2×#942—32no—
50D3×#137—332no—
51C2×#918—34no—
52C2×D3×Q16—34no—
53C2×#915—34no—
54C2×D3×SD16—34no—
55C2×#909D312yescomplemented
56C2×D3×M16—32no—
57C2×D3×M16—61no—
58C23×C3⋊D3D411yescharacteristic
59C22×D32—21no—
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3D411yescharacteristic
62C2×C4×C3⋊D3D411yescharacteristic
63C2×C4×C3⋊D3D411yescharacteristic
64C2×C4×C3⋊D3D414yes—
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C4×C3⋊D3C2314yes—
68C2×C3×#67—22no—
69C22×C3×Dic3—22no—
70C3×#235—24no—
71C3×#235C2318yes—
72C2×C3×D12C2312yes—
73C2×C3×C4×D3—22no—
74C2×C3×Dic6—24no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6C2314yes—
77C2×C3×Dic6C2312yes—
78C2×C3×Dic6C2318yescomplemented
79#3811—28no—
80C2×#627—22no—
81C2×#627—28no—
82C2×#627—22no—
83C2×#627—21no—
84C2×#626—22no—
85C2×#625—21no—
86C2×#624—22no—
87C2×#624—28no—
88C2×#624—22no—
89C2×#624—21no—
90#3805—28no—
91C2×D3×Dic3—22no—
92#3802—22no—
93#3802C2314yes—
94C4×D32—28no—
95#3798—28no—
96#3797—24no—
97#3797—28no—
98#3797—28no—
99#3797—24no—
100#3797—22no—
101#3797C2318yes—
102#3797C2314yes—
103#3797C2318yescomplemented
104#3796—24no—
105#3796C2318yes—
106C32×M16C2314yescomplemented
107C2×C32×C8C2312yes—
108#3748C2314yescomplemented
109C2×C3⋊(C3⋊C8)C2312yes—
110#3743C2318yescomplemented
111C8×C3⋊D3C2318yes—
112C3×Dic12C23116yescomplemented
113C3×#204C23116yescomplemented
114#3718C23116yescomplemented
115#3715C23116yescomplemented
116C22×#137—91noSylow
117C2×C3×#41—32no—
118C22×C3×Q8—32no—
119D3×#41—316no—
120D3×#41—68no—
121C2×#239—32no—
122C2×D3×Q8—34no—
123C2×D3×Q8—32no—
124C2×D3×Q8—34no—
125C2×D3×Q8—316no—
126C2×D3×Q8—62no—
127C2×D3×Q8—62no—
128C2×D3×Q8—68no—
129C2×#237—32no—
130C2×#237—62no—
131C2×D3×D4—32no—
132C2×D3×D4—62no—
133C2×#235—62no—
134C2×#235C2×D312yes—
135C22×C4×D3—32no—
136C22×C4×D3—61no—
137C22×C4×D3—62no—
138C22×C4×D3—62no—
139C22×Dic6—62no—
140C22×Dic6C2×D312yescomplemented
141C3×#137—316no—
142C2×C3×Q16—34no—
143C2×C3×SD16—34no—
144C2×C3×M16—21no—
145C2×C3×M16C2×D312yescomplemented
146#951—316no—
147C2×#216—34no—
148C2×#216—34no—
149#942—316no—
150C2×#215—34no—
151C2×#214—34no—
152C2×#208—32no—
153C2×#208—61no—
154#918—332no—
155D3×Q16—332no—
156#915—332no—
157D3×SD16—332no—
158#909C2×D3116yescomplemented
159D3×M16—316no—
160D3×M16—68no—
161C2×Dic12C2×D314yescomplemented
162C2×#204C2×D314yescomplemented
163C2×ΓL(1,𝔽25)—34no—
164C2×ΓL(1,𝔽25)—62no—
165C2×D3×C8—34no—
166C2×D3×C8—62no—
167C23×C32C2×D411yescharacteristic
168C22×C3⋊D3—24no—
169C22×C3⋊D3C2×D411yescharacteristic
170C22×C3⋊D3C2×D414yes—
171C22×C3⋊D3C2×D411yescharacteristic
172C22×C3×D3—22no—
173C2×D32—24no—
174C2×D32—44no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2411yescharacteristic
178C2×C32×C4C2412yes—
179C2×C3⋊Dic3C2×D411yescharacteristic
180C2×C3⋊Dic3C2×D414yes—
181C2×C3⋊Dic3C2×D411yescharacteristic
182C4×C3⋊D3C2×D412yes—
183C4×C3⋊D3C2×D412yes—
184C4×C3⋊D3C2×D414yes—
185C4×C3⋊D3C2×D414yes—
186C4×C3⋊D3C2412yes—
187C4×C3⋊D3C2412yes—
188C3×#67—28no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—28no—
192C3×D12—22no—
193C3×D12C2414yes—
194C3×C4×D3—28no—
195C3×Dic6—22no—
196C3×Dic6—24no—
197C3×Dic6—28no—
198C3×Dic6C2418yes—
199C3×Dic6C2414yes—
200#627—28no—
201#627—28no—
202#627—24no—
203#626—28no—
204#625—24no—
205#624—28no—
206#624—28no—
207#624—24no—
208D3×Dic3—28no—
209C32×C8C2414yes—
210C3⋊(C3⋊C8)C2414yes—
211C22×#41—91no—
212C23×Q8—91no—
213C2×#137—32no—
214C2×#137—94no—
215C2×#137—916no—
216C2×#137—92no—
217C22×Q16—92no—
218C22×SD16—92no—
219C22×M16—91no—
220C23×D3—32no—
221C23×D3—61no—
222C23×D3—62no—
223C3×#41—38no—
224C3×#41—64no—
225C2×C3×Q8—34no—
226C2×C3×Q8—38no—
227C2×C3×Q8—32no—
228C2×C3×Q8—62no—
229C2×C3×Q8—64no—
230C2×C3×D4—32no—
231C2×C3×D4—62no—
232C22×C3×C4—21no—
233C22×C3×C4—62no—
234C22×C3×C4—62no—
235C22×C3×C4C22×D312yes—
236C2×#67—22no—
237C2×#67—62no—
238C2×#67—62no—
239C22×Dic3—22no—
240C22×Dic3—32no—
241C22×Dic3—61no—
242C22×Dic3—62no—
243#239—38no—
244#239—64no—
245D3×Q8—316no—
246D3×Q8—316no—
247D3×Q8—38no—
248D3×Q8—68no—
249D3×Q8—68no—
250D3×Q8—616no—
251D3×Q8—616no—
252D3×Q8—64no—
253#237—38no—
254#237—64no—
255#237—616no—
256D3×D4—38no—
257D3×D4—64no—
258D3×D4—616no—
259#235—24no—
260#235—616no—
261#235C22×D318yes—
262C2×D12—62no—
263C2×D12C22×D312yes—
264C2×C4×D3—22no—
265C2×C4×D3—32no—
266C2×C4×D3—32no—
267C2×C4×D3—38no—
268C2×C4×D3—32no—
269C2×C4×D3—32no—
270C2×C4×D3—38no—
271C2×C4×D3—61no—
272C2×C4×D3—61no—
273C2×C4×D3—64no—
274C2×C4×D3—61no—
275C2×C4×D3—61no—
276C2×C4×D3—64no—
277C2×C4×D3—616no—
278C2×C4×D3—62no—
279C2×C4×D3—64no—
280C2×C4×D3—64no—
281C2×C4×D3—616no—
282C2×C4×D3—62no—
283C2×Dic6—24no—
284C2×Dic6—22no—
285C2×Dic6—64no—
286C2×Dic6—64no—
287C2×Dic6—616no—
288C2×Dic6—62no—
289C2×Dic6C22×D314yes—
290C2×Dic6C22×D312yes—
291C2×Dic6C22×D318yescomplemented
292C3×Q16—316no—
293C3×SD16—316no—
294C3×M16—24no—
295C3×M16C22×D318yescomplemented
296C2×C3×C8—22no—
297C2×C3×C8C22×D314yes—
298#216—316no—
299#216—316no—
300#215—316no—
301#214—316no—
302#208—38no—
303#208—64no—
304C2×C3⋊C8—34no—
305C2×C3⋊C8—62no—
306Dic12C22×D3116yescomplemented
307#204C22×D3116yescomplemented
308ΓL(1,𝔽25)—316no—
309ΓL(1,𝔽25)—68no—
310D3×C8—316no—
311D3×C8—68no—
312C22×C32—22no—
313C22×C32C22×D412yes—
314C22×C32C22×D411yescharacteristic
315C2×C3⋊D3—22no—
316C2×C3⋊D3—28no—
317C2×C3⋊D3#13714yescomplemented
318C2×C3⋊D3C22×D412yes—
319C2×C3⋊D3C22×D412yes—
320C2×C3×D3—24no—
321C2×C3×D3—44no—
322D32—48no—
323C32×C4C22×D411yescharacteristic
324C32×C4C22×D412yes—
325C32×C4C2511yescharacteristic
326C3⋊Dic3C22×D412yes—
327C3⋊Dic3C22×D412yes—
328C3×Dic3—24no—
329C3×Dic3—28no—
330C2×#41—32no—
331C2×#41—92no—
332C2×#41—98no—
333C2×#41—181no—
334C2×#41—181no—
335C2×#41—184no—
336C22×Q8—32no—
337C22×Q8—92no—
338C22×Q8—91no—
339C22×Q8—92no—
340C22×Q8—98no—
341C22×Q8—181no—
342C22×Q8—181no—
343C22×Q8—184no—
344C22×Q8—181no—
345C22×D4—91no—
346C22×D4—181no—
347C23×C4—91no—
348C23×C4—181no—
349C23×C4—181no—
350#137—316no—
351#137—932no—
352#137—916no—
353C2×Q16—34no—
354C2×Q16—916no—
355C2×Q16—94no—
356C2×SD16—34no—
357C2×SD16—916no—
358C2×SD16—94no—
359C2×M16—91no—
360C2×M16—98no—
361C2×M16—92no—
362C2×M16D3211yescharacteristic, complemented
363C22×C8—92no—
364C23×C3—21no—
365C23×C3—62no—
366C23×C3D3×D412yes—
367C22×D3—22no—
368C22×D3—32no—
369C22×D3—32no—
370C22×D3—38no—
371C22×D3—61no—
372C22×D3—64no—
373C22×D3—61no—
374C22×D3—68no—
375C22×D3—68no—
376C22×D3—124no—
377C22×D3—128no—
378C3×Q8—38no—
379C3×Q8—34no—
380C3×Q8—64no—
381C3×Q8—68no—
382C3×Q8—62no—
383C3×D4—34no—
384C3×D4—68no—
385C3×D4—62no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—68no—
391C2×C3×C4—64no—
392C2×C3×C4—62no—
393C2×C3×C4—68no—
394C2×C3×C4D3×D412yes—
395C2×C3×C4D3×D414yes—
396C2×C3×C4C23×D312yes—
397C2×C3×C4C23×D314yes—
398#67—28no—
399#67—68no—
400#67—68no—
401C2×Dic3—24no—
402C2×Dic3—28no—
403C2×Dic3—22no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—38no—
407C2×Dic3—64no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—68no—
411D12—22no—
412D12—68no—
413D12C23×D314yes—
414C4×D3—28no—
415C4×D3—38no—
416C4×D3—38no—
417C4×D3—34no—
418C4×D3—34no—
419C4×D3—34no—
420C4×D3—34no—
421C4×D3—64no—
422C4×D3—62no—
423C4×D3—62no—
424C4×D3—64no—
425C4×D3—62no—
426C4×D3—62no—
427C4×D3—68no—
428C4×D3—616no—
429C4×D3—616no—
430C4×D3—68no—
431Dic6—24no—
432Dic6—28no—
433Dic6—22no—
434Dic6—616no—
435Dic6—616no—
436Dic6—68no—
437Dic6C23×D318yes—
438Dic6C23×D314yes—
439C3×C8—24no—
440C3×C8C23×D318yes—
441C3⋊C8—38no—
442C3⋊C8—64no—
443C2×C32—22no—
444C2×C32C2×#13712yescomplemented
445C2×C32C23×D411yescharacteristic
446C3⋊D3—22no—
447C3⋊D3C2×#13714yescomplemented
448C3×D3—44no—
449C24—91no—
450C24—181no—
451#41—38no—
452#41—64no—
453#41—98no—
454#41—188no—
455#41—188no—
456#41—184no—
457C2×Q8—34no—
458C2×Q8—32no—
459C2×Q8—38no—
460C2×Q8—64no—
461C2×Q8—62no—
462C2×Q8—98no—
463C2×Q8—94no—
464C2×Q8—98no—
465C2×Q8—188no—
466C2×Q8—182no—
467C2×Q8—182no—
468C2×Q8—181no—
469C2×Q8—188no—
470C2×Q8—184no—
471C2×Q8—184no—
472C2×Q8—188no—
473C2×Q8—182no—
474C2×D4—32no—
475C2×D4—62no—
476C2×D4—94no—
477C2×D4—182no—
478C2×D4—182no—
479C2×D4—181no—
480C2×D4—188no—
481C22×C4—62no—
482C22×C4—62no—
483C22×C4—91no—
484C22×C4—91no—
485C22×C4—94no—
486C22×C4—91no—
487C22×C4—91no—
488C22×C4—94no—
489C22×C4—91no—
490C22×C4—188no—
491C22×C4—181no—
492C22×C4—188no—
493C22×C4—182no—
494C22×C4—182no—
495C22×C4—182no—
496C22×C4C2×D3211yescharacteristic
497Q16—316no—
498Q16—916no—
499SD16—316no—
500SD16—916no—
501M16—94no—
502M16—98no—
503M16C2×D3214yescomplemented
504C2×C8—92no—
505C2×C8—98no—
506C2×C8C2×D3212yes—
507C22×C3—24no—
508C22×C3—22no—
509C22×C3—21no—
510C22×C3—42no—
511C22×C3—64no—
512C22×C3—124no—
513C22×C3C2×D3×D414yes—
514C22×C3C2×D3×D412yes—
515C2×D3—24no—
516C2×D3—34no—
517C2×D3—38no—
518C2×D3—34no—
519C2×D3—44no—
520C2×D3—62no—
521C2×D3—64no—
522C2×D3—62no—
523C2×D3—616no—
524C2×D3—64no—
525C2×D3—128no—
526C2×D3—122no—
527C2×D3—1216no—
528C3×C4—22no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—68no—
532C3×C4—64no—
533C3×C4C2×D3×D412yes—
534C3×C4C2×D3×D414yes—
535C3×C4C24×D312yes—
536Dic3—28no—
537Dic3—24no—
538Dic3—34no—
539Dic3—34no—
540Dic3—62no—
541Dic3—62no—
542C32C22×#13711yescharacteristic, complemented, Sylow
543C23—62no—
544C23—91no—
545C23—94no—
546C23—91no—
547C23—184no—
548C23—184no—
549C23—364no—
550C23#380211yescharacteristic
551Q8—38no—
552Q8—34no—
553Q8—68no—
554Q8—64no—
555Q8—62no—
556Q8—188no—
557Q8—188no—
558Q8—184no—
559D4—34no—
560D4—68no—
561D4—62no—
562D4—188no—
563D4—184no—
564C2×C4—68no—
565C2×C4—62no—
566C2×C4—64no—
567C2×C4—68no—
568C2×C4—94no—
569C2×C4—91no—
570C2×C4—91no—
571C2×C4—94no—
572C2×C4—92no—
573C2×C4—92no—
574C2×C4—94no—
575C2×C4—92no—
576C2×C4—92no—
577C2×C4—184no—
578C2×C4—188no—
579C2×C4—188no—
580C2×C4—188no—
581C2×C4#380212yes—
582C2×C4#380211yescharacteristic
583C2×C4C22×D3212yes—
584C2×C4C22×D3211yescharacteristic
585C8—94no—
586C8C22×D3214yes—
587C2×C3—24no—
588C2×C3—21no—
589C2×C3—22no—
590C2×C3—42no—
591C2×C3—124no—
592C2×C3D3×#13714yescomplemented
593C2×C3C22×D3×D412yes—
594D3—38no—
595D3—44no—
596D3—64no—
597D3—64no—
598D3—122no—
599C22—22no—
600C22—64no—
601C22—92no—
602C22—94no—
603C22—92no—
604C22—124no—
605C22—188no—
606C22—182no—
607C22—368no—
608C22C2×#380212yes—
609C22C2×#380211yescharacteristic
610C4—64no—
611C4—68no—
612C4—92no—
613C4—92no—
614C4C2×#380212yes—
615C4C2×#380211yescharacteristic
616C4C23×D3211yescharacteristic
617C3—21no—
618C3C2×D3×#13712yescomplemented
619C2—22no—
620C2—94no—
621C2—124no—
622C2—182no—
623C2#1059471712yesdirect product factor
624C2C22×#380211yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#64306C2
hypercenterC2×M16D32
hypocenterC32C22×#137
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
2. C22×#3797C2semidirect
3. C2×M16×C3⋊D3C2semidirect
4. C2×C3×#909C2semidirect
5. C2×#63827C2semidirect
6. #10594717C2direct (N × H)
7. C2×#63811C2semidirect
8. C2×#63802C2semidirect
9. C2×#63796C2semidirect
13. C22×C3×Dic6C22semidirect
28. C2×#3797C22semidirect
29. C2×#3797C22semidirect
31. C2×C32×M16C22semidirect
32. C2×#3748C22semidirect
33. M16×C3⋊D3C22semidirect
34. C2×#3743C22semidirect
36. C3×#909C22semidirect
37. C2×C3×Dic12C22semidirect
38. C2×C3×#204C22semidirect
39. C2×#3718C22semidirect
40. #63827C22semidirect
41. C2×#3715C22semidirect
42. #63811C22semidirect
43. #63802C22semidirect
44. #63796C22semidirect
55. C2×#909D3semidirect
78. C2×C3×Dic6C23semidirect
103. #3797C23semidirect
106. C32×M16C23semidirect
108. #3748C23semidirect
110. #3743C23semidirect
112. C3×Dic12C23semidirect
113. C3×#204C23semidirect
114. #3718C23semidirect
115. #3715C23semidirect
140. C22×Dic6C2×D3semidirect
145. C2×C3×M16C2×D3semidirect
158. #909C2×D3semidirect
161. C2×Dic12C2×D3semidirect
162. C2×#204C2×D3semidirect
291. C2×Dic6C22×D3semidirect
295. C3×M16C22×D3semidirect
306. Dic12C22×D3semidirect
307. #204C22×D3semidirect
317. C2×C3⋊D3#137semidirect
362. C2×M16D32semidirect
444. C2×C32C2×#137semidirect
447. C3⋊D3C2×#137semidirect
503. M16C2×D32semidirect
542. C32C22×#137semidirect
592. C2×C3D3×#137semidirect
618. C3C2×D3×#137semidirect
623. C2#10594717direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643062
C22×#37972
C2×M16×C3⋊D32
C2×C3×#9092
C2×#638272
#105947172
C2×#638112
C2×#638022
C2×#637962
C2×D3×#1373