Finite Group Databasebeta

← #11901799

Subgroups — #11901799

Order 1152.

2235 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C3×#5832C211yesmaximal, characteristic, complemented
3C3×#5828C211yesmaximal, characteristic, complemented
4#10595396C212yesmaximal, complemented
5#10595349C212yesmaximal, complemented
6#10595267C214yesmaximal, complemented
7#10595220C214yesmaximal, complemented
8#10595217C212yesmaximal, complemented
9#10595126C212yesmaximal, complemented
10#10595049C211yesmaximal, characteristic, complemented
11#10595033C214yesmaximal, complemented
12#10595022C211yesmaximal, characteristic, complemented
13#10594958C211yesmaximal, characteristic, complemented
14#10594934C214yesmaximal, complemented
15C2×#63855C211yesmaximal, characteristic, complemented
16#86236—31nomaximal
17#86019—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21Q8×C3⋊Dic3C2212yescomplemented
22D4×C3⋊Dic3C2214yes—
23D4×C3⋊Dic3C2212yescomplemented
24#64135C2211yescharacteristic
25#64135C2212yescomplemented
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C4×C3⋊Dic3C2212yescomplemented
28C3×#947C2211yescharacteristic, complemented
29C3×#946C2212yes—
30C3×#944C2211yescharacteristic, complemented
31C3×#940C2211yescharacteristic, complemented
32C3×#939C2214yes—
33C3×#938C2212yes—
34C3×#937C2212yes—
35C3×#936C2211yescharacteristic, complemented
36C3×#935C2212yes—
37C3×C4×#67C2214yes—
38C3×C4×#67C2214yescomplemented
39C3×#926C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41#63982C2214yescomplemented
42#63980C2214yes—
43#63976C2212yes—
44#67⋊Dic3C2214yes—
45#63970C2214yes—
46#63969C2214yescomplemented
47C2×Dic3⋊Dic3C2212yes—
48#63964C2214yes—
49#63962C2214yes—
50#63962C2214yescomplemented
51#63961C2212yes—
52C2×(C2×D3)⋊Dic3C2212yes—
53#63959C2214yes—
54#63956C2214yescomplemented
55#63918C2212yescomplemented
56C4×#627C2214yescomplemented
57#63915C2214yes—
58#63908C2212yes—
59C4×#625C2214yes—
60#63898C2212yescomplemented
61#63893C2214yescomplemented
62#63891C2214yes—
63C4×D3×Dic3C2212yescomplemented
64#63870C2214yescomplemented
65#63869C2212yescomplemented
66#63862C2214yes—
67#63862C2214yescomplemented
68#63861C2214yes—
69#63856C2212yes—
70#63855C2212yes—
71#63855C2212yes—
72#63855C2212yes—
73#63855C2212yes—
74#63855C2212yescomplemented
75#63845C2214yescomplemented
76#63843C2212yescomplemented
77C3×#532—31no—
78C3×#525—31no—
79#5832D311yescharacteristic, complemented
80#5828—31no—
81#5828D311yescharacteristic, complemented
82Dic3×#41—31no—
83Dic3×#41—31no—
84Dic3×#41—31no—
85Dic3×#41—61no—
86#5791—31no—
87C2×#926—31no—
88#5731—32no—
89#5719—32no—
90#5682—32no—
91#5682—32no—
92#5665—34no—
93#5643—32no—
94#5625—32no—
95#5619—32no—
96#5617—34no—
97#5603—32no—
98#5602—34no—
99#5593—34no—
100#5557—34no—
101#5538—34no—
102#5538—34no—
103#5538—34no—
104#5522—31no—
105#5517—31no—
106C2×#872—31no—
107#5470—31no—
108C23×C3×D3C2311yescharacteristic
109C32×#41—24no—
110C2×C32×Q8C2311yescharacteristic
111C2×C32×D4C2312yes—
112C2×C32×D4C2311yescharacteristic
113C22×C32×C4C2312yes—
114C22×C32×C4C2311yescharacteristic
115C22×C3⋊Dic3C2312yes—
116C22×C3⋊Dic3C2314yes—
117C2×C3×#67C2312yes—
118C2×C3×#67C2314yes—
119C2×C3×#67C2314yes—
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2312yes—
122C3×#235—24no—
123C2×C3×D12C2311yescharacteristic
124C2×C3×C4×D3—24no—
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2312yes—
127C2×C3×C4×D3C2312yes—
128C2×C3×Dic6C2311yescharacteristic
129C2×#627C2314yes—
130C2×#625C2314yes—
131C2×D3×Dic3C2314yes—
132#3757C2312yes—
133#3757C2314yes—
134C4⋊(C3⋊Dic3)C2314yes—
135C4⋊(C3⋊Dic3)C2312yes—
136C4×C3⋊Dic3C2312yes—
137C4×C3⋊Dic3C2311yescharacteristic
138C4×C3⋊Dic3C2311yescharacteristic
139C4×C3⋊Dic3C2314yes—
140C4×C3⋊Dic3C2312yes—
141C3×#217C2312yes—
142C3×#217C2314yes—
143C3×#217C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×C4⋊Dic3C2312yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×C4×Dic3C2312yes—
150C3×C4×Dic3C2311yescharacteristic
151C3×C4×Dic3C2311yescharacteristic
152C3×C4×Dic3C2312yes—
153#3724C2314yes—
154#3724C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2312yes—
157Dic3⋊Dic3C2314yes—
158Dic3⋊Dic3C2312yes—
159Dic3⋊Dic3C2312yes—
160Dic3⋊Dic3C2312yes—
161Dic3⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2312yes—
163(C2×D3)⋊Dic3C2312yes—
164(C2×D3)⋊Dic3C2312yes—
165(C2×D3)⋊Dic3C2312yes—
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169Dic32C2314yes—
170#3455—91noSylow
171C2×C3×#41—21no—
172C2×C3×#41—31no—
173C2×C3×#41C2×D311yescharacteristic
174C2×C3×#41C2×D311yescharacteristic
175C23×C3×C4—31no—
176C2×#235C2×D311yescharacteristic
177C22×C4×D3C2×D311yescharacteristic
178C3×C4⋊Q8—31no—
179C3×#127—31no—
180C3×#124—31no—
181C3×#124—31no—
182C3×#123—32no—
183C3×C22⋊Q8—32no—
184C3×#121—32no—
185C3×#121—34no—
186C3×#120—32no—
187C3×C4×D4—34no—
188C3×C4×D4—34no—
189C3×#117—31no—
190C2×C3×C42—31no—
191#953—32no—
192C2×#217—32no—
193#947C2×D311yescharacteristic, complemented
194#946—32no—
195#946C2×D312yes—
196Q8×Dic3—32no—
197Q8×Dic3—32no—
198Q8×Dic3—32no—
199Q8×Dic3—62no—
200#944C2×D311yescharacteristic, complemented
201#940C2×D311yescharacteristic, complemented
202#939—34no—
203#939—34no—
204#939—34no—
205#939C2×D314yes—
206#938—34no—
207#938—32no—
208#938C2×D312yes—
209#937—32no—
210#937C2×D312yes—
211#936—34no—
212#936C2×D311yescharacteristic, complemented
213#935—32no—
214#935—34no—
215#935—34no—
216#935—34no—
217#935C2×D312yes—
218D4×Dic3—34no—
219D4×Dic3—32no—
220D4×Dic3—34no—
221D4×Dic3—32no—
222D4×Dic3—34no—
223D4×Dic3—32no—
224D4×Dic3—64no—
225D4×Dic3—62no—
226#930—32no—
227#929—32no—
228C4×#67—34no—
229C4×#67—34no—
230C4×#67C2×D314yes—
231C4×#67C2×D314yescomplemented
232C2×(C2×D3)⋊C4—32no—
233#926—31no—
234#926—31no—
235#926—32no—
236#926—32no—
237#926—32no—
238#926—32no—
239#926—32no—
240#926—32no—
241#926—32no—
242#926—61no—
243#926—62no—
244#926C2×D311yescharacteristic
245C2×C4⋊Dic3—32no—
246#924—32no—
247#924—34no—
248C2×Dic3⋊C4—32no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3—31no—
251C2×C4×Dic3—32no—
252C2×C4×Dic3—32no—
253C2×C4×Dic3—32no—
254C2×C4×Dic3—61no—
255C2×C4×Dic3—62no—
256C2×C4×Dic3C2×D311yescharacteristic
257#898—34no—
258#898—34no—
259#898—34no—
260#897—34no—
261#893—32no—
262#890—34no—
263#890—32no—
264#889—34no—
265#889—34no—
266#889—34no—
267#888—32no—
268#887—32no—
269#886—34no—
270#886—34no—
271#886—34no—
272#885—34no—
273#885—34no—
274#885—34no—
275#883—34no—
276#883—34no—
277#67⋊C4—34no—
278#879—34no—
279#879—34no—
280#879—34no—
281#879—34no—
282#879—34no—
283#878—34no—
284#878—34no—
285#878—34no—
286#878—34no—
287#872—32no—
288#872—32no—
289#872—32no—
290#872—32no—
291#872—32no—
292C42×D3—32no—
293#870—32no—
294#869—32no—
295C4×Dic6—34no—
296C4×Dic6—34no—
297C23×C32C2412yes—
298C23×C32C2411yescharacteristic
299C22×C3×D3—22no—
300C22×C3×D3—42no—
301C22×C3×D3C2412yes—
302C22×C3×D3C2412yes—
303C32×Q8—22no—
304C32×D4—24no—
305C32×D4—22no—
306C2×C32×C4—24no—
307C2×C32×C4#4114yes—
308C2×C32×C4C2412yes—
309C2×C32×C4C2411yescharacteristic
310C2×C32×C4C2411yescharacteristic
311C2×C3⋊Dic3—42no—
312C2×C3⋊Dic3—44no—
313C2×C3⋊Dic3C2412yes—
314C2×C3⋊Dic3C2412yes—
315C2×C3⋊Dic3C2414yes—
316C3×#67—24no—
317C3×#67—44no—
318C3×#67—44no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—42no—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2414yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C3×D12—22no—
327C3×C4×D3—24no—
328C3×C4×D3—24no—
329C3×C4×D3—24no—
330C3×Dic6—22no—
331#627—44no—
332#625—44no—
333D3×Dic3—44no—
334#542—92no—
335#542—92no—
336#541—92no—
337#540—92no—
338#539—94no—
339#538—94no—
340#533—91no—
341#532—31no—
342#529—94no—
343#529—94no—
344#525—31no—
345#525—91no—
346C4×#41—91no—
347C4×#41—91no—
348C2×#117—91no—
349C24×C3—31no—
350C23×D3C22×D311yescharacteristic
351C3×#41—28no—
352C3×#41—24no—
353C3×#41—24no—
354C3×#41—64no—
355C2×C3×Q8—21no—
356C2×C3×Q8—31no—
357C2×C3×Q8C22×D311yescharacteristic
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×D4—22no—
360C2×C3×D4—21no—
361C2×C3×D4—32no—
362C2×C3×D4—34no—
363C2×C3×D4—34no—
364C2×C3×D4—31no—
365C2×C3×D4C22×D312yes—
366C2×C3×D4C22×D311yescharacteristic
367C2×C3×D4C22×D311yescharacteristic
368C2×C3×D4C22×D312yes—
369C22×C3×C4—22no—
370C22×C3×C4—21no—
371C22×C3×C4—31no—
372C22×C3×C4—32no—
373C22×C3×C4—32no—
374C22×C3×C4—32no—
375C22×C3×C4—32no—
376C22×C3×C4—64no—
377C22×C3×C4C22×D312yes—
378C22×C3×C4C22×D312yes—
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C2×#67—34no—
382C2×#67—34no—
383C2×#67C22×D312yes—
384C2×#67C22×D314yes—
385C2×#67C22×D314yes—
386C22×Dic3—34no—
387C22×Dic3—34no—
388C22×Dic3—32no—
389C22×Dic3—32no—
390C22×Dic3—34no—
391C22×Dic3—62no—
392C22×Dic3—64no—
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D312yes—
395#235—24no—
396C2×D12C22×D311yescharacteristic
397C2×C4×D3—24no—
398C2×C4×D3—34no—
399C2×C4×D3C22×D312yes—
400C2×C4×D3C22×D312yes—
401C2×C4×D3C22×D312yes—
402C2×Dic6—34no—
403C2×Dic6—34no—
404C2×Dic6C22×D311yescharacteristic
405C3×C4⋊C4—32no—
406C3×C4⋊C4—34no—
407C3×C4⋊C4—34no—
408C3×C22⋊C4—32no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—34no—
412C3×C22⋊C4—34no—
413C3×C42—32no—
414C3×C42—32no—
415C3×C42—31no—
416C3×C42—31no—
417#217—32no—
418#217—34no—
419#217—34no—
420#217—32no—
421#217—34no—
422#217—34no—
423#217—32no—
424#217—32no—
425#217—34no—
426#217—32no—
427#217—32no—
428#217—62no—
429#217—64no—
430#217C22×D314yes—
431#217C22×D314yes—
432#217C22×D312yes—
433(C2×D3)⋊C4—32no—
434(C2×D3)⋊C4—32no—
435(C2×D3)⋊C4—32no—
436(C2×D3)⋊C4—32no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4C22×D314yes—
441(C2×D3)⋊C4C22×D314yes—
442C4⋊Dic3—32no—
443C4⋊Dic3—34no—
444C4⋊Dic3—34no—
445C4⋊Dic3—32no—
446C4⋊Dic3—34no—
447C4⋊Dic3—34no—
448C4⋊Dic3—32no—
449C4⋊Dic3—34no—
450C4⋊Dic3—32no—
451C4⋊Dic3—32no—
452C4⋊Dic3—32no—
453C4⋊Dic3—62no—
454C4⋊Dic3—64no—
455C4⋊Dic3C22×D312yes—
456Dic3⋊C4—34no—
457Dic3⋊C4—34no—
458Dic3⋊C4—34no—
459Dic3⋊C4—34no—
460Dic3⋊C4—32no—
461Dic3⋊C4—32no—
462Dic3⋊C4—32no—
463Dic3⋊C4—32no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4C22×D314yes—
468Dic3⋊C4C22×D314yes—
469C4×Dic3—32no—
470C4×Dic3—32no—
471C4×Dic3—31no—
472C4×Dic3—31no—
473C4×Dic3—31no—
474C4×Dic3—31no—
475C4×Dic3—32no—
476C4×Dic3—34no—
477C4×Dic3—34no—
478C4×Dic3—32no—
479C4×Dic3—34no—
480C4×Dic3—34no—
481C4×Dic3—61no—
482C4×Dic3—61no—
483C4×Dic3—62no—
484C4×Dic3—62no—
485C4×Dic3—64no—
486C4×Dic3C22×D312yes—
487C4×Dic3C22×D312yes—
488C4×Dic3C22×D311yescharacteristic
489C4×Dic3C22×D311yescharacteristic
490C22×C32—22no—
491C22×C32—22no—
492C22×C32—24no—
493C22×C32C2×#4112yes—
494C22×C32C2511yescharacteristic
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—24no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—44no—
501C32×C4—22no—
502C32×C4C2×#4112yes—
503C32×C4C2×#4112yes—
504C3⋊Dic3—22no—
505C3⋊Dic3—22no—
506C3⋊Dic3—24no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—24no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C2×#41—31no—
513C2×#41D3211yescharacteristic
514C23×C4—31no—
515C4⋊Q8—31no—
516C4⋊Q8—92no—
517#127—31no—
518#126—94no—
519#126—94no—
520#126—94no—
521#126—94no—
522#125—92no—
523#125—94no—
524#125—94no—
525#124—31no—
526#124—31no—
527#124—94no—
528#124—94no—
529#123—32no—
530#123—94no—
531#123—94no—
532#123—94no—
533#123—94no—
534#123—92no—
535C22⋊Q8—32no—
536C22⋊Q8—94no—
537C22⋊Q8—94no—
538C22⋊Q8—94no—
539C22⋊Q8—92no—
540#121—32no—
541#121—34no—
542#121—92no—
543#121—94no—
544#121—94no—
545#120—32no—
546#120—92no—
547C4×Q8—94no—
548C4×Q8—92no—
549C4×Q8—92no—
550C4×D4—34no—
551C4×D4—34no—
552C4×D4—94no—
553C4×D4—92no—
554C4×D4—94no—
555C4×D4—94no—
556C4×D4—92no—
557#117—31no—
558#117—92no—
559#117—92no—
560#117—92no—
561#117—92no—
562#117—92no—
563#117—91no—
564#117—92no—
565C2×C4⋊C4—92no—
566C2×C22⋊C4—92no—
567C2×C42—31no—
568C2×C42—92no—
569C2×C42—91no—
570C2×C42—92no—
571C23×C3—22no—
572C23×C3—21no—
573C23×C3—32no—
574C23×C3—32no—
575C23×C3—62no—
576C23×C3—122no—
577C23×C3C23×D312yes—
578C23×C3C23×D312yes—
579C23×C3C23×D311yescharacteristic
580C23×C3C23×D311yescharacteristic
581C22×D3—22no—
582C22×D3—42no—
583C22×D3C23×D312yes—
584C22×D3C23×D312yes—
585C3×Q8—24no—
586C3×Q8—22no—
587C3×Q8—22no—
588C3×Q8—62no—
589C3×D4—28no—
590C3×D4—24no—
591C3×D4—24no—
592C3×D4—24no—
593C3×D4—22no—
594C3×D4—22no—
595C3×D4—64no—
596C3×D4—62no—
597C3×D4—124no—
598C3×D4—124no—
599C2×C3×C4—28no—
600C2×C3×C4—24no—
601C2×C3×C4—24no—
602C2×C3×C4—22no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—24no—
606C2×C3×C4—32no—
607C2×C3×C4—34no—
608C2×C3×C4—32no—
609C2×C3×C4—32no—
610C2×C3×C4—32no—
611C2×C3×C4—62no—
612C2×C3×C4—64no—
613C2×C3×C4—64no—
614C2×C3×C4—64no—
615C2×C3×C4—122no—
616C2×C3×C4#23714yes—
617C2×C3×C4#23714yes—
618C2×C3×C4C23×D312yes—
619C2×C3×C4C23×D312yes—
620C2×C3×C4C23×D311yescharacteristic
621C2×C3×C4C23×D311yescharacteristic
622C2×C3×C4C23×D311yescharacteristic
623C2×C3×C4C23×D311yescharacteristic
624#67—24no—
625#67—44no—
626#67—44no—
627#67—124no—
628#67—124no—
629C2×Dic3—22no—
630C2×Dic3—32no—
631C2×Dic3—32no—
632C2×Dic3—32no—
633C2×Dic3—32no—
634C2×Dic3—34no—
635C2×Dic3—34no—
636C2×Dic3—42no—
637C2×Dic3—62no—
638C2×Dic3—62no—
639C2×Dic3—64no—
640C2×Dic3—124no—
641C2×Dic3—124no—
642C2×Dic3—124no—
643C2×Dic3—122no—
644C2×Dic3—122no—
645C2×Dic3—124no—
646C2×Dic3—128no—
647C2×Dic3C23×D312yes—
648C2×Dic3C23×D314yes—
649C2×Dic3C23×D312yes—
650C2×Dic3C23×D312yes—
651C2×Dic3C23×D312yes—
652D12—22no—
653C4×D3—24no—
654C4×D3—24no—
655C4×D3—24no—
656C4×D3—124no—
657Dic6—22no—
658Dic6—124no—
659Dic6—124no—
660C2×C32—22no—
661C2×C32—42no—
662C2×C32C22×#4111yescharacteristic
663C2×C32#58512yes—
664C3×D3—42no—
665C3×D3—42no—
666C24—31no—
667#41—24no—
668#41—64no—
669C2×Q8—31no—
670C2×Q8—94no—
671C2×Q8C2×D3211yescharacteristic
672C2×D4—32no—
673C2×D4—34no—
674C2×D4—34no—
675C2×D4—31no—
676C2×D4—94no—
677C2×D4C2×D3212yes—
678C2×D4C2×D3211yescharacteristic
679C22×C4—31no—
680C22×C4—32no—
681C22×C4—32no—
682C22×C4—32no—
683C22×C4—32no—
684C22×C4—64no—
685C22×C4—94no—
686C22×C4—92no—
687C22×C4—94no—
688C22×C4C2×D3212yes—
689C22×C4C2×D3211yescharacteristic
690C4⋊C4—32no—
691C4⋊C4—34no—
692C4⋊C4—34no—
693C4⋊C4—92no—
694C4⋊C4—92no—
695C4⋊C4—92no—
696C4⋊C4—92no—
697C4⋊C4—94no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C4⋊C4—94no—
702C4⋊C4—92no—
703C4⋊C4—94no—
704C22⋊C4—32no—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—34no—
708C22⋊C4—34no—
709C22⋊C4—92no—
710C22⋊C4—92no—
711C22⋊C4—92no—
712C22⋊C4—92no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4—92no—
717C22⋊C4—94no—
718C42—31no—
719C42—31no—
720C42—32no—
721C42—32no—
722C42—94no—
723C42—92no—
724C42—94no—
725C42—91no—
726C42—91no—
727C42—92no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—24no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—24no—
734C22×C3—24no—
735C22×C3—22no—
736C22×C3—21no—
737C22×C3—42no—
738C22×C3—44no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—64no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3—124no—
745C22×C3C2×#23712yes—
746C22×C3C2×#23712yes—
747C22×C3C24×D311yescharacteristic
748C22×C3C24×D311yescharacteristic
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—24no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—44no—
755C3×C4—24no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—62no—
761C3×C4—62no—
762C3×C4—62no—
763C3×C4—64no—
764C3×C4—62no—
765C3×C4C2×#23712yes—
766C3×C4C2×#23712yes—
767C3×C4C2×#23712yes—
768C3×C4C2×#23712yes—
769Dic3—22no—
770Dic3—22no—
771Dic3—22no—
772Dic3—24no—
773Dic3—22no—
774Dic3—64no—
775Dic3—64no—
776Dic3—64no—
777Dic3—62no—
778Dic3—62no—
779Dic3—62no—
780Dic3—62no—
781Dic3—122no—
782Dic3—124no—
783C32#345511yescharacteristic, complemented, Sylow
784C23—32no—
785C23—32no—
786C23—62no—
787C23—122no—
788C23C22×D3212yes—
789C23C22×D3211yescharacteristic
790Q8—22no—
791Q8—62no—
792Q8—364no—
793D4—24no—
794D4—22no—
795D4—64no—
796D4—62no—
797D4—124no—
798D4—124no—
799D4—364no—
800C2×C4—24no—
801C2×C4—32no—
802C2×C4—32no—
803C2×C4—34no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—62no—
807C2×C4—64no—
808C2×C4—64no—
809C2×C4—64no—
810C2×C4—92no—
811C2×C4—92no—
812C2×C4—94no—
813C2×C4—122no—
814C2×C4—364no—
815C2×C4—362no—
816C2×C4—364no—
817C2×C4#380514yes—
818C2×C4C22×D3212yes—
819C2×C4C22×D3211yescharacteristic
820C2×C4C22×D3211yescharacteristic
821C2×C3—22no—
822C2×C3—22no—
823C2×C3—22no—
824C2×C3—21no—
825C2×C3—42no—
826C2×C3—44no—
827C2×C3—42no—
828C2×C3—42no—
829C2×C3—122no—
830C2×C3—122no—
831C2×C3C22×#23711yescharacteristic
832C2×C3C22×#23711yescharacteristic
833C2×C3#596412yes—
834C2×C3#596412yes—
835D3—42no—
836D3—42no—
837C22—22no—
838C22—24no—
839C22—22no—
840C22—64no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—124no—
846C22C2×#380512yes—
847C22C23×D3211yescharacteristic
848C4—22no—
849C4—62no—
850C4—62no—
851C4—64no—
852C4—62no—
853C4—62no—
854C4—182no—
855C4—182no—
856C4—184no—
857C4C2×#380512yes—
858C4C2×#380512yes—
859C3—21no—
860C3#8601911yescharacteristic, complemented
861C3#8623611yescharacteristic, complemented
862C2—22no—
863C2—42no—
864C2—122no—
865C2—122no—
866C2#1059669512yes—
867C2C22×#380511yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊Dic3C2semidirect
2. C3×#5832C2semidirect
3. C3×#5828C2semidirect
4. #10595396C2semidirect
5. #10595349C2semidirect
6. #10595267C2semidirect
7. #10595220C2semidirect
8. #10595217C2semidirect
9. #10595126C2semidirect
10. #10595049C2semidirect
11. #10595033C2semidirect
12. #10595022C2semidirect
13. #10594958C2semidirect
14. #10594934C2semidirect
15. C2×#63855C2semidirect
21. Q8×C3⋊Dic3C22semidirect
23. D4×C3⋊Dic3C22semidirect
25. #64135C22semidirect
27. C2×C4×C3⋊Dic3C22semidirect
28. C3×#947C22semidirect
30. C3×#944C22semidirect
31. C3×#940C22semidirect
35. C3×#936C22semidirect
38. C3×C4×#67C22semidirect
41. #63982C22semidirect
46. #63969C22semidirect
50. #63962C22semidirect
54. #63956C22semidirect
55. #63918C22semidirect
56. C4×#627C22semidirect
60. #63898C22semidirect
61. #63893C22semidirect
63. C4×D3×Dic3C22semidirect
64. #63870C22semidirect
65. #63869C22semidirect
67. #63862C22semidirect
74. #63855C22semidirect
75. #63845C22semidirect
76. #63843C22semidirect
79. #5832D3semidirect
81. #5828D3semidirect
193. #947C2×D3semidirect
200. #944C2×D3semidirect
201. #940C2×D3semidirect
212. #936C2×D3semidirect
231. C4×#67C2×D3semidirect
783. C32#3455semidirect
860. C3#86019semidirect
861. C3#86236semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
C3×#58322
C3×#58282
#105953962
#105953492
#105952672
#105952202
#105952172
#105951262
#105950492
#105950332
#105950222
#105949582
#105949342
C2×#638552
#862363
#860193