Finite Group Databasebeta

← #11905918

Subgroups — #11905918

Order 1152.

3139 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3#10596303C211yesmaximal, characteristic, complemented
4C3×#5833C211yesmaximal, characteristic, complemented
5#10595402C212yesmaximal, complemented
6#10595400C212yesmaximal, complemented
7#10595236C212yesmaximal, complemented
8#10595157C212yesmaximal, complemented
9#10595156C214yesmaximal, complemented
10#10595155C214yesmaximal, complemented
11#10595043C211yesmaximal, characteristic, complemented
12#10595032C211yesmaximal, characteristic, complemented
13#10595006C212yesmaximal, complemented
14#10594900C212yesmaximal, complemented
15#10594830C212yesmaximal, complemented
16C2×#63843C211yesmaximal, characteristic, complemented
17#10594803C212yesmaximal, complemented
18#87291—31nomaximal
19#86367—31nomaximal
20C2×C32×#41C2211yescharacteristic
21C2×#3828C2211yescharacteristic
22C3×#1010—28no—
23C2×C3×D3×Q8C2212yes—
24C2×C3×#237C2214yes—
25C2×C3×#237C2212yes—
26C2×C3×#235C2212yes—
27C2×C3×#235C2211yescharacteristic
28C2×C3×#235C2211yescharacteristic
29C22×C3×Dic6C2212yes—
30C22×C3×Dic6C2211yescharacteristic
31C2×#3804C2214yes—
32C2×#3799C2212yes—
33C2×#3797C2212yes—
34#64297—28no—
35C2×#3796C2212yes—
36C2×D3×Dic6C2212yes—
37#64156C2211yescharacteristic
38#64153C2211yescharacteristic
39#64149C2211yescharacteristic
40#64148C2212yes—
41#64148C2212yes—
42#64145C2211yescharacteristic
43C4×#638C2212yes—
44C4×#638C2212yes—
45C2×C4×C3⋊Dic3C2211yescharacteristic
46C3×#946C2212yes—
47C3×#939C2214yes—
48C3×#938C2212yes—
49C3×#930C2212yes—
50C2×C3×C4⋊Dic3C2211yescharacteristic
51C3×#924C2212yes—
52#63980C2212yes—
53#63980C2212yes—
54#63979C2214yes—
55#63978C2214yes—
56#63978C2214yes—
57Dic3×#67C2214yes—
58#63970C2214yes—
59C2×Dic3⋊Dic3C2212yes—
60#63964C2214yes—
61#63959C2214yes—
62#63958C2214yes—
63C2×Dic32C2212yes—
64#63952C2214yes—
65#63916C2212yes—
66#63914C2211yescharacteristic
67#63909C2212yes—
68#63907C2214yes—
69#63906C2214yes—
70#63904C2214yes—
71C4×#625C2212yes—
72C4×#625C2212yes—
73#63888C2214yes—
74#63887C2214yes—
75#63879C2214yes—
76#63873C2211yescharacteristic
77#63871C2212yes—
78#63863C2211yescharacteristic
79#63863C2211yescharacteristic
80#63857C2212yes—
81#63851C2214yes—
82#63843C2212yes—
83#63843C2212yes—
84#63843C2212yes—
85#63843C2212yes—
86#63839C2214yes—
87C2×C3×2−1+4—31no—
88C2×#1010—31no—
89C2×#1010D311yescharacteristic, complemented
90C2×#1007—31no—
91C3×#537—31no—
92#5834—32no—
93#5834—32no—
94#5833—34no—
95#5833—31no—
96#5833D311yescharacteristic, complemented
97#5832—31no—
98#5832—31no—
99#5832—31no—
100#5832—31no—
101#5832—34no—
102#5832—61no—
103#5831—32no—
104#5831—32no—
105#5817—32no—
106#5817—32no—
107Q8×#67—32no—
108Q8×#67—32no—
109C2×Q8×Dic3—31no—
110#5633—32no—
111#5633—32no—
112#5632—32no—
113#5632—32no—
114#5599—32no—
115#5599—32no—
116#5598—32no—
117#5598—32no—
118#5597—34no—
119#5596—34no—
120#5510—31no—
121C2×#887—31no—
122C32×#41—24no—
123C2×C32×Q8C2311yescharacteristic
124C2×C32×D4C2311yescharacteristic
125C2×C32×D4C2312yes—
126C22×C32×C4C2312yes—
127C22×C32×C4C2311yescharacteristic
128C2×#638C2312yes—
129C2×#638C2312yes—
130C2×#638C2312yes—
131C22×C3⋊Dic3C2311yescharacteristic
132C22×C3⋊Dic3C2311yescharacteristic
133#3828—24no—
134C2×C4⋊(C3⋊D3)C2311yescharacteristic
135C2×C4×C3⋊D3C2312yes—
136C2×#634C2311yescharacteristic
137C2×C3×#67C2312yes—
138C2×C3×#67C2314yes—
139C2×C3×#67C2312yes—
140C2×C3×#67C2314yes—
141C22×C3×Dic3C2314yes—
142C22×C3×Dic3C2312yes—
143C22×C3×Dic3C2312yes—
144C3×D3×Q8—28no—
145C3×#237—216no—
146C3×#237—28no—
147C3×#235—24no—
148C3×#235—24no—
149C3×#235—28no—
150C2×C3×D12C2311yescharacteristic
151C2×C3×D12C2311yescharacteristic
152C2×C3×C4×D3C2312yes—
153C2×C3×C4×D3C2314yes—
154C2×C3×C4×D3C2312yes—
155C2×C3×Dic6—28no—
156C2×C3×Dic6D418yescomplemented
157C2×C3×Dic6C2311yescharacteristic
158C2×C3×Dic6C2311yescharacteristic
159C2×C3×Dic6C2314yes—
160C2×C3×Dic6C2312yes—
161C2×C3×Dic6C2312yes—
162C2×#627C2314yes—
163C2×#626C2314yes—
164C2×#626C2314yes—
165C2×#625C2312yes—
166C2×#625C2312yes—
167C2×#624C2314yes—
168#3804—216no—
169C2×D3×Dic3C2314yes—
170#3799—28no—
171#3797—28no—
172#3796—28no—
173D3×Dic6—28no—
174#3757C2312yes—
175#3757C2312yes—
176#3752C2312yes—
177#3752C2312yes—
178#3750C2312yes—
179#3750C2312yes—
180C4×C3⋊Dic3C2311yescharacteristic
181C4×C3⋊Dic3C2311yescharacteristic
182C4×C3⋊Dic3C2311yescharacteristic
183C4×C3⋊Dic3C2311yescharacteristic
184C3×#217C2314yes—
185C3×(C2×D3)⋊C4C2314yes—
186C3×C4⋊Dic3C2312yes—
187C3×C4⋊Dic3C2312yes—
188C3×Dic3⋊C4C2314yes—
189#3724C2312yes—
190#3724C2312yes—
191Dic3⋊Dic3C2314yes—
192Dic3⋊Dic3C2314yes—
193Dic3⋊Dic3C2314yes—
194#3722C2314yes—
195(C2×D3)⋊Dic3C2312yes—
196(C2×D3)⋊Dic3C2314yes—
197(C2×D3)⋊Dic3C2312yes—
198(C2×D3)⋊Dic3C2312yes—
199(C2×D3)⋊Dic3C2312yes—
200Dic32C2314yes—
201Dic32C2314yes—
202#3497—91noSylow
203C3×2−1+4—68no—
204C2×C3×#41—21no—
205C2×C3×#41—32no—
206C2×C3×#41—34no—
207C2×C3×#41—31no—
208C2×C3×#41—32no—
209C2×C3×#41—31no—
210C2×C3×#41C2×D311yescharacteristic
211C2×C3×#41C2×D311yescharacteristic
212C22×C3×Q8—32no—
213C22×C3×Q8—31no—
214C22×C3×Q8—32no—
215#1010—28no—
216#1010—68no—
217#1007—68no—
218C2×#239—32no—
219C2×#239—32no—
220C2×D3×Q8—32no—
221C2×D3×Q8—32no—
222C2×D3×Q8—32no—
223C2×D3×Q8C2×D312yes—
224C2×#237—34no—
225C2×#237—32no—
226C2×#237C2×D314yes—
227C2×#237C2×D312yes—
228C2×#235—31no—
229C2×#235—31no—
230C2×#235—34no—
231C2×#235—32no—
232C2×#235—61no—
233C2×#235C2×D312yes—
234C2×#235C2×D311yescharacteristic
235C2×#235C2×D311yescharacteristic
236C22×Dic6—32no—
237C22×Dic6C2×D312yes—
238C22×Dic6C2×D311yescharacteristic
239C3×C22⋊Q8—32no—
240C3×C22⋊Q8—32no—
241C3×#121—32no—
242C3×#121—34no—
243C3×#121—32no—
244C2×C3×C4⋊C4—31no—
245#947—31no—
246#947—31no—
247#947—31no—
248#947—31no—
249#947—34no—
250#947—61no—
251#946—34no—
252#946—32no—
253#946—34no—
254#946C2×D312yes—
255Q8×Dic3—32no—
256Q8×Dic3—32no—
257Q8×Dic3—32no—
258Q8×Dic3—32no—
259#944—31no—
260#944—31no—
261#944—31no—
262#944—31no—
263#944—34no—
264#944—61no—
265#940—31no—
266#940—31no—
267#940—34no—
268#940—34no—
269#940—31no—
270#940—31no—
271#940—61no—
272#939—32no—
273#939—32no—
274#939—32no—
275#939—32no—
276#939—32no—
277#939—32no—
278#939—32no—
279#939—32no—
280#939—34no—
281#939—34no—
282#939—34no—
283#939—62no—
284#939—62no—
285#939C2×D314yes—
286#938—34no—
287#938—34no—
288#938—32no—
289#938C2×D312yes—
290#936—31no—
291#936—31no—
292#936—31no—
293#936—31no—
294#936—34no—
295#936—61no—
296D4×Dic3—34no—
297#930—34no—
298#930—34no—
299#930—34no—
300#930—32no—
301#930C2×D312yes—
302C4×#67—32no—
303C4×#67—32no—
304C4×#67—32no—
305C4×#67—32no—
306C4×#67—34no—
307C4×#67—32no—
308C4×#67—32no—
309C4×#67—32no—
310C4×#67—32no—
311C4×#67—34no—
312C4×#67—34no—
313C4×#67—34no—
314C4×#67—62no—
315C4×#67—62no—
316C2×C4⋊Dic3—32no—
317C2×C4⋊Dic3C2×D311yescharacteristic
318#924—34no—
319#924—32no—
320#924—34no—
321#924C2×D312yes—
322C2×Dic3⋊C4—32no—
323C2×C4×Dic3—31no—
324C2×C4×Dic3—31no—
325C2×C4×Dic3—32no—
326C2×C4×Dic3—32no—
327C2×C4×Dic3—61no—
328#897—32no—
329#897—32no—
330#896—34no—
331#896—34no—
332#895—32no—
333#895—32no—
334#893—34no—
335#888—34no—
336#887—32no—
337#887—32no—
338#887—32no—
339#887—32no—
340#885—34no—
341#885—34no—
342#884—34no—
343#884—34no—
344#67⋊C4—34no—
345#67⋊C4—34no—
346#878—34no—
347#878—34no—
348C23×C32C2412yes—
349C23×C32C2411yescharacteristic
350C22×C3⋊D3C2412yes—
351C22×C3×D3C2412yes—
352C22×C3×D3C2412yes—
353C32×Q8—22no—
354C32×D4—24no—
355C32×D4—22no—
356C2×C32×C4—24no—
357C2×C32×C4C2×D414yes—
358C2×C32×C4C2412yes—
359C2×C32×C4C2411yescharacteristic
360C2×C32×C4C2411yescharacteristic
361#638—24no—
362#638—24no—
363#638—42no—
364C2×C3⋊Dic3—22no—
365C2×C3⋊Dic3—41no—
366C2×C3⋊Dic3C2411yescharacteristic
367C2×C3⋊Dic3C2411yescharacteristic
368C2×C3⋊Dic3C2412yes—
369C2×C3⋊Dic3C2411yescharacteristic
370C2×C3⋊Dic3C2411yescharacteristic
371C4⋊(C3⋊D3)—22no—
372C4×C3⋊D3—24no—
373#634—22no—
374C3×#67—24no—
375C3×#67—24no—
376C3×#67—28no—
377C3×#67—44no—
378C2×C3×Dic3—28no—
379C2×C3×Dic3—42no—
380C2×C3×Dic3C2×D418yes—
381C2×C3×Dic3C2414yes—
382C2×C3×Dic3C2412yes—
383C2×C3×Dic3C2412yes—
384C2×C3×Dic3C2414yes—
385C3×D12—22no—
386C3×D12—22no—
387C3×C4×D3—24no—
388C3×C4×D3—24no—
389C3×C4×D3—28no—
390C3×Dic6—22no—
391C3×Dic6—22no—
392C3×Dic6—28no—
393C3×Dic6C2×D418yes—
394C3×Dic6C2×D418yes—
395#627—28no—
396#626—28no—
397#626—44no—
398#625—24no—
399#625—42no—
400#624—28no—
401D3×Dic3—28no—
402C2×2−1+4—31no—
403C2×2−1+4—91no—
404#550—92no—
405#550—92no—
406D4×Q8—92no—
407D4×Q8—92no—
408#548—92no—
409#548—92no—
410#548—92no—
411#548—92no—
412#537—31no—
413#537—91no—
414#537—94no—
415#532—94no—
416#532—91no—
417#532—91no—
418C2×C4×Q8—91no—
419C3×#41—24no—
420C3×#41—24no—
421C3×#41—44no—
422C3×#41—68no—
423C3×#41—616no—
424C3×#41—68no—
425C3×#41—64no—
426C3×#41—64no—
427C2×C3×Q8—21no—
428C2×C3×Q8—38no—
429C2×C3×Q8—32no—
430C2×C3×Q8—32no—
431C2×C3×Q8—34no—
432C2×C3×Q8—31no—
433C2×C3×Q8—31no—
434C2×C3×Q8—68no—
435C2×C3×Q8—68no—
436C2×C3×Q8C22×D311yescharacteristic
437C2×C3×Q8C22×D311yescharacteristic
438C2×C3×D4—21no—
439C2×C3×D4—22no—
440C2×C3×D4—34no—
441C2×C3×D4—32no—
442C2×C3×D4—32no—
443C2×C3×D4—34no—
444C2×C3×D4—31no—
445C2×C3×D4—31no—
446C2×C3×D4C22×D311yescharacteristic
447C2×C3×D4C22×D311yescharacteristic
448C2×C3×D4C22×D312yes—
449C2×C3×D4C22×D312yes—
450C22×C3×C4—21no—
451C22×C3×C4—22no—
452C22×C3×C4—32no—
453C22×C3×C4—34no—
454C22×C3×C4—32no—
455C22×C3×C4—34no—
456C22×C3×C4—32no—
457C22×C3×C4—32no—
458C22×C3×C4C22×D312yes—
459C22×C3×C4C22×D312yes—
460C22×C3×C4C22×D311yescharacteristic
461C22×C3×C4C22×D311yescharacteristic
462C2×#67—32no—
463C2×#67—32no—
464C2×#67—32no—
465C2×#67—32no—
466C2×#67—32no—
467C2×#67—32no—
468C2×#67—32no—
469C2×#67—32no—
470C2×#67—32no—
471C2×#67—32no—
472C2×#67—34no—
473C2×#67—34no—
474C2×#67—62no—
475C2×#67—62no—
476C2×#67—62no—
477C2×#67C22×D314yes—
478C2×#67C22×D312yes—
479C2×#67C22×D312yes—
480C2×#67C22×D314yes—
481C22×Dic3—31no—
482C22×Dic3—31no—
483C22×Dic3—31no—
484C22×Dic3—31no—
485C22×Dic3—34no—
486C22×Dic3—61no—
487C22×Dic3—61no—
488C22×Dic3C22×D314yes—
489C22×Dic3C22×D312yes—
490C22×Dic3C22×D312yes—
491#239—68no—
492#239—68no—
493D3×Q8—28no—
494D3×Q8—68no—
495D3×Q8—68no—
496D3×Q8—68no—
497#237—216no—
498#237—28no—
499#237—616no—
500#237—68no—
501#235—24no—
502#235—24no—
503#235—28no—
504#235—616no—
505#235—64no—
506#235—64no—
507#235—68no—
508#235—124no—
509C2×D12—34no—
510C2×D12—31no—
511C2×D12—31no—
512C2×D12—34no—
513C2×D12—61no—
514C2×D12C22×D311yescharacteristic
515C2×D12C22×D311yescharacteristic
516C2×C4×D3—34no—
517C2×C4×D3—32no—
518C2×C4×D3—32no—
519C2×C4×D3—34no—
520C2×C4×D3—34no—
521C2×C4×D3—62no—
522C2×C4×D3C22×D314yes—
523C2×C4×D3C22×D312yes—
524C2×C4×D3C22×D312yes—
525C2×Dic6—28no—
526C2×Dic6—31no—
527C2×Dic6—31no—
528C2×Dic6—34no—
529C2×Dic6—34no—
530C2×Dic6—61no—
531C2×Dic6—68no—
532C2×Dic6#6718yescomplemented
533C2×Dic6C22×D314yes—
534C2×Dic6C22×D311yescharacteristic
535C2×Dic6C22×D311yescharacteristic
536C2×Dic6C22×D312yes—
537C2×Dic6C22×D312yes—
538C3×C4⋊C4—32no—
539C3×C4⋊C4—32no—
540C3×C4⋊C4—34no—
541C3×C22⋊C4—34no—
542C3×C22⋊C4—34no—
543#217—32no—
544#217—32no—
545#217—32no—
546#217—32no—
547#217—32no—
548#217—32no—
549#217—32no—
550#217—34no—
551#217—32no—
552#217—62no—
553#217—62no—
554#217C22×D314yes—
555(C2×D3)⋊C4—34no—
556(C2×D3)⋊C4—32no—
557(C2×D3)⋊C4—32no—
558(C2×D3)⋊C4—32no—
559(C2×D3)⋊C4—32no—
560(C2×D3)⋊C4—32no—
561(C2×D3)⋊C4—32no—
562(C2×D3)⋊C4—32no—
563(C2×D3)⋊C4—32no—
564(C2×D3)⋊C4—34no—
565(C2×D3)⋊C4—34no—
566(C2×D3)⋊C4—62no—
567(C2×D3)⋊C4—62no—
568(C2×D3)⋊C4C22×D314yes—
569C4⋊Dic3—34no—
570C4⋊Dic3—34no—
571C4⋊Dic3—34no—
572C4⋊Dic3C22×D312yes—
573C4⋊Dic3C22×D312yes—
574Dic3⋊C4—32no—
575Dic3⋊C4—32no—
576Dic3⋊C4—32no—
577Dic3⋊C4—32no—
578Dic3⋊C4—32no—
579Dic3⋊C4—34no—
580Dic3⋊C4—34no—
581Dic3⋊C4—32no—
582Dic3⋊C4—34no—
583Dic3⋊C4—32no—
584Dic3⋊C4—32no—
585Dic3⋊C4—62no—
586Dic3⋊C4—62no—
587Dic3⋊C4C22×D314yes—
588C4×Dic3—31no—
589C4×Dic3—31no—
590C4×Dic3—31no—
591C4×Dic3—31no—
592C4×Dic3—31no—
593C4×Dic3—31no—
594C4×Dic3—31no—
595C4×Dic3—31no—
596C4×Dic3—34no—
597C4×Dic3—34no—
598C4×Dic3—34no—
599C4×Dic3—34no—
600C4×Dic3—61no—
601C4×Dic3—61no—
602C4×Dic3—61no—
603C4×Dic3—61no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—22no—
607C22×C32—22no—
608C22×C32—22no—
609C22×C32C22×D412yes—
610C22×C32C2511yescharacteristic
611C2×C3⋊D3—22no—
612C2×C3⋊D3—22no—
613C2×C3⋊D3—22no—
614C2×C3×D3—22no—
615C2×C3×D3—22no—
616C2×C3×D3—22no—
617C2×C3×D3—22no—
618C2×C3×D3—22no—
619C2×C3×D3—22no—
620C32×C4—22no—
621C32×C4C22×D412yes—
622C32×C4C22×D412yes—
623C3⋊Dic3—21no—
624C3⋊Dic3—22no—
625C3⋊Dic3—21no—
626C3⋊Dic3—21no—
627C3⋊Dic32−1+412yescomplemented
628C3×Dic3—22no—
629C3×Dic3—22no—
630C3×Dic3—24no—
631C3×Dic3C22×D418yes—
6322−1+4—68no—
6332−1+4—188no—
634C2×#41—34no—
635C2×#41—32no—
636C2×#41—31no—
637C2×#41—31no—
638C2×#41—32no—
639C2×#41—94no—
640C2×#41—92no—
641C2×#41—92no—
642C2×#41—91no—
643C2×#41D3211yescharacteristic
644C22×Q8—32no—
645C22×Q8—31no—
646C22×Q8—32no—
647C22×Q8—92no—
648C22×Q8—92no—
649C4⋊Q8—94no—
650C4⋊Q8—91no—
651C4⋊Q8—91no—
652#127—94no—
653#127—91no—
654#127—91no—
655#124—94no—
656#124—94no—
657#124—91no—
658#124—91no—
659#124—91no—
660#124—91no—
661C22⋊Q8—32no—
662C22⋊Q8—32no—
663C22⋊Q8—94no—
664C22⋊Q8—94no—
665C22⋊Q8—94no—
666C22⋊Q8—92no—
667C22⋊Q8—94no—
668C22⋊Q8—92no—
669#121—34no—
670#121—32no—
671#121—32no—
672#121—94no—
673#121—94no—
674#121—92no—
675#121—92no—
676#121—94no—
677#121—94no—
678#121—92no—
679#121—92no—
680#121—94no—
681#121—92no—
682#121—92no—
683C4×Q8—92no—
684C4×Q8—92no—
685C4×Q8—92no—
686C4×Q8—92no—
687C4×D4—94no—
688C4×D4—94no—
689C4×D4—94no—
690C4×D4—92no—
691C4×D4—92no—
692C4×D4—94no—
693C4×D4—92no—
694C4×D4—92no—
695C2×C4⋊C4—31no—
696C2×C4⋊C4—92no—
697C2×C42—92no—
698C2×C42—91no—
699C23×C3—21no—
700C23×C3—22no—
701C23×C3—32no—
702C23×C3—32no—
703C23×C3C23×D312yes—
704C23×C3C23×D312yes—
705C23×C3C23×D311yescharacteristic
706C23×C3C23×D311yescharacteristic
707C22×D3—32no—
708C22×D3—32no—
709C22×D3—62no—
710C22×D3C23×D312yes—
711C22×D3C23×D312yes—
712C3×Q8—22no—
713C3×Q8—22no—
714C3×Q8—38no—
715C3×Q8—38no—
716C3×Q8—42no—
717C3×Q8—68no—
718C3×Q8—62no—
719C3×Q8—62no—
720C3×D4—24no—
721C3×D4—24no—
722C3×D4—22no—
723C3×D4—22no—
724C3×D4—42no—
725C3×D4—44no—
726C3×D4—68no—
727C3×D4—64no—
728C3×D4—64no—
729C3×D4—62no—
730C3×D4—62no—
731C3×D4—124no—
732C2×C3×C4—24no—
733C2×C3×C4—24no—
734C2×C3×C4—21no—
735C2×C3×C4—21no—
736C2×C3×C4—22no—
737C2×C3×C4—24no—
738C2×C3×C4—38no—
739C2×C3×C4—34no—
740C2×C3×C4—34no—
741C2×C3×C4—32no—
742C2×C3×C4—32no—
743C2×C3×C4—44no—
744C2×C3×C4—68no—
745C2×C3×C4—68no—
746C2×C3×C4—64no—
747C2×C3×C4—64no—
748C2×C3×C4—122no—
749C2×C3×C4D3×D414yes—
750C2×C3×C4C2×#6714yes—
751C2×C3×C4C23×D312yes—
752C2×C3×C4C23×D312yes—
753C2×C3×C4C23×D311yescharacteristic
754C2×C3×C4C23×D311yescharacteristic
755C2×C3×C4C23×D311yescharacteristic
756C2×C3×C4C23×D311yescharacteristic
757#67—24no—
758#67—24no—
759#67—28no—
760#67—44no—
761#67—64no—
762#67—64no—
763#67—64no—
764#67—64no—
765#67—64no—
766#67—64no—
767#67—68no—
768#67—124no—
769#67—124no—
770#67—124no—
771#67—122no—
772#67—122no—
773#67—122no—
774#67—122no—
775#67—124no—
776C2×Dic3—28no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—31no—
781C2×Dic3—31no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—31no—
785C2×Dic3—32no—
786C2×Dic3—32no—
787C2×Dic3—42no—
788C2×Dic3—61no—
789C2×Dic3—61no—
790C2×Dic3—61no—
791C2×Dic3—61no—
792C2×Dic3—62no—
793C2×Dic3—62no—
794C2×Dic3—62no—
795C2×Dic3—68no—
796C2×Dic3—122no—
797C2×Dic3—121no—
798C2×Dic3—121no—
799C2×Dic3—122no—
800C2×Dic3C2×#6718yes—
801C2×Dic3C23×D314yes—
802C2×Dic3C23×D312yes—
803C2×Dic3C23×D312yes—
804C2×Dic3C23×D314yes—
805D12—22no—
806D12—22no—
807D12—68no—
808D12—62no—
809D12—62no—
810D12—122no—
811D12—124no—
812C4×D3—24no—
813C4×D3—24no—
814C4×D3—28no—
815C4×D3—68no—
816C4×D3—68no—
817C4×D3—64no—
818C4×D3—64no—
819C4×D3—68no—
820C4×D3—124no—
821Dic6—22no—
822Dic6—22no—
823Dic6—28no—
824Dic6—68no—
825Dic6—62no—
826Dic6—62no—
827Dic6—68no—
828Dic6—122no—
829Dic6C2×#6718yes—
830Dic6C2×#6718yes—
831C2×C32—22no—
832C2×C32—42no—
833C2×C32C23×D411yescharacteristic
834C2×C32C2×2−1+411yescharacteristic
835C2×C32#58511yescharacteristic
836C3⋊D3—42no—
837C3×D3—42no—
838C3×D3—42no—
839#41—24no—
840#41—68no—
841#41—616no—
842#41—68no—
843#41—64no—
844#41—64no—
845#41—1816no—
846#41—188no—
847#41—188no—
848#41—184no—
849C2×Q8—32no—
850C2×Q8—32no—
851C2×Q8—31no—
852C2×Q8—34no—
853C2×Q8—31no—
854C2×Q8—38no—
855C2×Q8—68no—
856C2×Q8—68no—
857C2×Q8—94no—
858C2×Q8—91no—
859C2×Q8—188no—
860C2×Q8—188no—
861C2×Q8C2×D3211yescharacteristic
862C2×D4—32no—
863C2×D4—32no—
864C2×D4—34no—
865C2×D4—34no—
866C2×D4—31no—
867C2×D4—31no—
868C2×D4—94no—
869C2×D4—94no—
870C2×D4—92no—
871C2×D4—92no—
872C2×D4—92no—
873C2×D4—92no—
874C2×D4—92no—
875C2×D4—91no—
876C2×D4C2×D3212yes—
877C2×D4C2×D3211yescharacteristic
878C22×C4—32no—
879C22×C4—34no—
880C22×C4—32no—
881C22×C4—32no—
882C22×C4—34no—
883C22×C4—32no—
884C22×C4—94no—
885C22×C4—94no—
886C22×C4—91no—
887C22×C4—91no—
888C22×C4—92no—
889C22×C4C2×D3212yes—
890C22×C4C2×D3211yescharacteristic
891C4⋊C4—32no—
892C4⋊C4—32no—
893C4⋊C4—34no—
894C4⋊C4—94no—
895C4⋊C4—94no—
896C4⋊C4—92no—
897C4⋊C4—92no—
898C4⋊C4—94no—
899C4⋊C4—92no—
900C4⋊C4—92no—
901C22⋊C4—34no—
902C22⋊C4—34no—
903C22⋊C4—94no—
904C22⋊C4—92no—
905C22⋊C4—92no—
906C22⋊C4—94no—
907C22⋊C4—92no—
908C22⋊C4—92no—
909C22⋊C4—92no—
910C22⋊C4—92no—
911C22⋊C4—92no—
912C22⋊C4—92no—
913C42—94no—
914C42—94no—
915C42—91no—
916C42—91no—
917C42—91no—
918C42—91no—
919C22×C3—21no—
920C22×C3—21no—
921C22×C3—21no—
922C22×C3—21no—
923C22×C3—22no—
924C22×C3—22no—
925C22×C3—22no—
926C22×C3—22no—
927C22×C3—22no—
928C22×C3—22no—
929C22×C3—22no—
930C22×C3—21no—
931C22×C3—41no—
932C22×C3—41no—
933C22×C3—42no—
934C22×C3—42no—
935C22×C3—42no—
936C22×C3—62no—
937C22×C3—62no—
938C22×C3—62no—
939C22×C3—62no—
940C22×C3—62no—
941C22×C3—62no—
942C22×C3C2×D3×D412yes—
943C22×C3C22×#6712yes—
944C22×C3C24×D311yescharacteristic
945C22×C3C24×D311yescharacteristic
946C2×D3—22no—
947C2×D3—22no—
948C2×D3—22no—
949C2×D3—22no—
950C2×D3—22no—
951C2×D3—22no—
952C2×D3—62no—
953C2×D3—62no—
954C2×D3—62no—
955C2×D3—62no—
956C2×D3—62no—
957C2×D3—62no—
958C2×D3—122no—
959C2×D3—122no—
960C2×D3—122no—
961C3×C4—22no—
962C3×C4—22no—
963C3×C4—22no—
964C3×C4—22no—
965C3×C4—38no—
966C3×C4—42no—
967C3×C4—62no—
968C3×C4—64no—
969C3×C4—62no—
970C3×C4C2×D3×D412yes—
971C3×C4C2×D3×D412yes—
972C3×C4C22×#6712yes—
973C3×C4C22×#6712yes—
974Dic3—22no—
975Dic3—24no—
976Dic3—22no—
977Dic3—32no—
978Dic3—32no—
979Dic3—62no—
980Dic3—62no—
981Dic3—62no—
982Dic3—61no—
983Dic3—61no—
984Dic3—61no—
985Dic3—61no—
986Dic3—61no—
987Dic3—61no—
988Dic3—62no—
989Dic3—122no—
990Dic3—121no—
991Dic3—121no—
992Dic3C22×#6718yes—
993C32#349711yescharacteristic, complemented, Sylow
994C23—32no—
995C23—32no—
996C23—92no—
997C23C22×D3212yes—
998C23C22×D3211yescharacteristic
999Q8—22no—
1000Q8—38no—
1001Q8—38no—
1002Q8—68no—
1003Q8—62no—
1004Q8—62no—
1005Q8—188no—
1006Q8—182no—
1007D4—24no—
1008D4—22no—
1009D4—68no—
1010D4—64no—
1011D4—64no—
1012D4—62no—
1013D4—62no—
1014D4—124no—
1015D4—188no—
1016D4—184no—
1017D4—184no—
1018D4—184no—
1019D4—182no—
1020D4—364no—
1021D4—362no—
1022D4—362no—
1023C2×C4—24no—
1024C2×C4—38no—
1025C2×C4—34no—
1026C2×C4—34no—
1027C2×C4—32no—
1028C2×C4—32no—
1029C2×C4—68no—
1030C2×C4—68no—
1031C2×C4—64no—
1032C2×C4—64no—
1033C2×C4—91no—
1034C2×C4—91no—
1035C2×C4—91no—
1036C2×C4—91no—
1037C2×C4—92no—
1038C2×C4—122no—
1039C2×C4—188no—
1040C2×C4—188no—
1041C2×C4—182no—
1042C2×C4—184no—
1043C2×C4—361no—
1044C2×C4D3×#6714yes—
1045C2×C4C22×D3212yes—
1046C2×C4C22×D3211yescharacteristic
1047C2×C4C22×D3211yescharacteristic
1048C2×C3—22no—
1049C2×C3—22no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—42no—
1054C2×C3—42no—
1055C2×C3—42no—
1056C2×C3—82no—
1057C2×C3—122no—
1058C2×C3—122no—
1059C2×C3C22×D3×D411yescharacteristic
1060C2×C3#596611yescharacteristic
1061C2×C3D3×2−1+411yescharacteristic
1062C2×C3D3×2−1+411yescharacteristic
1063C2×C3#596811yescharacteristic
1064C2×C3C23×#6711yescharacteristic
1065D3—42no—
1066D3—42no—
1067D3—122no—
1068D3—122no—
1069D3—242no—
1070C22—21no—
1071C22—21no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—62no—
1076C22—62no—
1077C22—62no—
1078C22—62no—
1079C22—62no—
1080C22—62no—
1081C22—182no—
1082C22—182no—
1083C22—182no—
1084C22C2×D3×#6712yes—
1085C22C23×D3211yescharacteristic
1086C4—22no—
1087C4—38no—
1088C4—64no—
1089C4—62no—
1090C4—62no—
1091C4—92no—
1092C4—181no—
1093C4—181no—
1094C4—181no—
1095C4—182no—
1096C4C2×D3×#6712yes—
1097C4C2×D3×#6712yes—
1098C3—21no—
1099C3#8636711yescharacteristic, complemented
1100C3#8729111yescharacteristic, complemented
1101C2—22no—
1102C2—42no—
1103C2—122no—
1104C2—122no—
1105C2—362no—
1106C2#1059669411yescharacteristic
1107C2#1059669811yescharacteristic
1108C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3497
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×#64297C2semidirect
3. #10596303C2semidirect
4. C3×#5833C2semidirect
5. #10595402C2semidirect
6. #10595400C2semidirect
7. #10595236C2semidirect
8. #10595157C2semidirect
9. #10595156C2semidirect
10. #10595155C2semidirect
11. #10595043C2semidirect
12. #10595032C2semidirect
13. #10595006C2semidirect
14. #10594900C2semidirect
15. #10594830C2semidirect
16. C2×#63843C2semidirect
17. #10594803C2semidirect
89. C2×#1010D3semidirect
96. #5833D3semidirect
156. C2×C3×Dic6D4semidirect
532. C2×Dic6#67semidirect
627. C3⋊Dic32−1+4semidirect
993. C32#3497semidirect
1099. C3#86367semidirect
1100. C3#87291semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×#642972
#105963032
C3×#58332
#105954022
#105954002
#105952362
#105951572
#105951562
#105951552
#105950432
#105950322
#105950062
#105949002
#105948302
C2×#638432
#105948032
#872913
#863673