Finite Group Databasebeta

← #11910732

Subgroups — #11910732

Order 1152.

2244 conjugacy classes of subgroups.

The subgroup lattice has 1261 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596058C211yesmaximal, characteristic, complemented
2C3×#5595C211yesmaximal, characteristic, complemented
3C3×#5589C211yesmaximal, characteristic, complemented
4#10595508C212yesmaximal, complemented
5#10595494C212yesmaximal, complemented
6#10595275C211yesmaximal, characteristic, complemented
7#10595260C212yesmaximal, complemented
8#10595245C212yesmaximal, complemented
9#10595233C211yesmaximal, characteristic, complemented
10#10595200C211yesmaximal, characteristic, complemented
11#10595180C212yesmaximal, complemented
12D3×#935C211yesmaximal, characteristic, complemented
13#10595130C212yesmaximal, complemented
14#10594223C212yesmaximal, complemented
15#10594193C212yesmaximal, complemented
16#10594148C212yesmaximal, complemented
17#10594123C212yesmaximal, complemented
18#10594120C212yesmaximal, complemented
19#10594062C212yesmaximal, complemented
20#87081—31nomaximal
21#86300—31nomaximal
22C22×C3×#67C2211yescharacteristic
23C2×C3×D3×D4C2211yescharacteristic
24C2×#3805C2212yes—
25C22×D3×Dic3C2211yescharacteristic, complemented
26C2×#3795C2211yescharacteristic, complemented
27C32×#120C2211yescharacteristic
28C2×#3757C2212yescomplemented
29#64145C2211yescharacteristic
30#64144C2211yescharacteristic
31#64144C2212yescomplemented
32D4×C3⋊Dic3C2212yescomplemented
33#64088C2212yescomplemented
34#64087C2212yescomplemented
35#64086C2212yescomplemented
36C3×#953C2211yescharacteristic
37C3×#953C2212yescomplemented
38C3×#940C2211yescharacteristic
39C3×#939C2212yescomplemented
40C3×#938C2212yes—
41C3×#938C2212yescomplemented
42C3×#937C2212yes—
43C3×#935C2211yescharacteristic
44C3×#935C2211yescharacteristic
45C3×#886C2211yescharacteristic
46C3×#884C2212yes—
47C3×#884C2212yescomplemented
48C3×#883C2212yes—
49C3×#883C2212yescomplemented
50C3×D3×C22⋊C4C2211yescharacteristic
51C3×#879C2212yescomplemented
52#63982C2212yescomplemented
53#63980C2212yescomplemented
54#63980C2212yescomplemented
55#63976C2212yes—
56#63976C2212yescomplemented
57#67⋊Dic3C2212yes—
58#67⋊Dic3C2212yescomplemented
59#67⋊Dic3C2212yescomplemented
60#67⋊Dic3C2212yescomplemented
61Dic3×#67C2212yescomplemented
62#63970C2212yes—
63#63970C2212yes—
64#63970C2212yescomplemented
65#63970C2212yescomplemented
66#63970C2212yescomplemented
67#63969C2212yes—
68#63969C2212yes—
69#63969C2212yescomplemented
70D3×#217C2212yes—
71D3×#217C2211yescharacteristic, complemented
72#63964C2212yescomplemented
73#63964C2212yescomplemented
74#63962C2211yescharacteristic, complemented
75#63962C2212yescomplemented
76#63961C2211yescharacteristic, complemented
77#63959C2212yescomplemented
78#63959C2212yescomplemented
79#63959C2212yescomplemented
80#63959C2212yescomplemented
81#63956C2212yescomplemented
82#63956C2212yescomplemented
83#63956C2212yescomplemented
84#63914C2211yescharacteristic, complemented
85#63905C2212yescomplemented
86#63905C2212yescomplemented
87#63902C2212yescomplemented
88C4×#625C2212yescomplemented
89#63899C2212yescomplemented
90#63899C2212yescomplemented
91#63893C2212yescomplemented
92#63891C2212yescomplemented
93D3×C4⋊Dic3C2212yescomplemented
94#63884C2212yescomplemented
95#63884C2212yescomplemented
96#63879C2212yescomplemented
97#63878C2212yescomplemented
98D3×Dic3⋊C4C2212yescomplemented
99#63872C2212yescomplemented
100#63870C2212yescomplemented
101#63860C2211yescharacteristic, complemented
102#63858C2212yescomplemented
103#63855C2211yescharacteristic, complemented
104#63851C2212yescomplemented
105#63847C2212yescomplemented
106#63841C2212yescomplemented
107#63840C2212yescomplemented
108#63837C2212yescomplemented
109C3×#560—31no—
110C3×#534—31no—
111#5806—32no—
112#5805—31no—
113C2×#935—31no—
114#5715—31no—
115#5713—31no—
116#5710—32no—
117#5708—32no—
118#5665—32no—
119#5664—31no—
120#5660—32no—
121#5659—32no—
122#5655—32no—
123D3×#123—31no—
124#5651—31no—
125#5651—31no—
126#5650—32no—
127#5621—32no—
128#5621—32no—
129#5618—32no—
130#5615—32no—
131#5615—32no—
132#5614—32no—
133#5613—32no—
134#5611—32no—
135#5606—32no—
136#5603—32no—
137#5595D311yescharacteristic, complemented
138#5593—32no—
139#5593—32no—
140#5593—32no—
141#5591—32no—
142#5589D311yescharacteristic, complemented
143#5587—31no—
144#5587—31no—
145#5587—61no—
146#5586—32no—
147#5495—32no—
148C24×C32C2311yescharacteristic
149C23×C3×D3C2311yescharacteristic
150C23×C3×D3C2311yescharacteristic
151C2×C32×D4C2311yescharacteristic
152C2×C32×D4C2312yes—
153C22×C3⋊Dic3C2311yescharacteristic
154C22×C3⋊Dic3C2312yes—
155C22×C3⋊Dic3C2312yes—
156C2×#634C2311yescharacteristic
157C2×C3×#67—42no—
158C2×C3×#67C2312yes—
159C2×C3×#67C2312yes—
160C2×C3×#67C2312yes—
161C2×C3×#67C2312yes—
162C2×C3×#67C2312yes—
163C2×C3×#67C2312yes—
164C2×C3×#67C2311yescharacteristic
165C2×C3×#67C2311yescharacteristic
166C2×C3×#67C2312yes—
167C22×C3×Dic3C2311yescharacteristic
168C22×C3×Dic3C2311yescharacteristic
169C3×D3×D4—42no—
170C2×C3×D12C2311yescharacteristic
171C2×C3×D12C2311yescharacteristic
172C2×C3×C4×D3C2311yescharacteristic
173C2×C3×C4×D3C2312yes—
174C2×C3×C4×D3C2312yes—
175C2×#627C2312yes—
176C2×#627C2312yes—
177C2×#625C2312yes—
178C2×#625C2312yes—
179C2×#625C2312yes—
180#3805—44no—
181C2×D3×Dic3—42no—
182C2×D3×Dic3C2312yes—
183C2×D3×Dic3C2312yes—
184C2×D3×Dic3C2312yes—
185C2×D3×Dic3C2312yes—
186C2×D3×Dic3C2312yes—
187#3795—42no—
188C32×C22⋊C4C2312yes—
189C32×C22⋊C4C2311yescharacteristic
190#3757C2312yes—
191#3757C2312yes—
192#3757C2312yes—
193#3757C2312yes—
194#3757C2312yes—
195#3757C2311yescharacteristic
196C4⋊(C3⋊Dic3)C2312yes—
197#3750C2312yes—
198#3750C2312yes—
199#3750C2312yes—
200C4×C3⋊Dic3C2311yescharacteristic
201C4×C3⋊Dic3C2312yes—
202C3×#217C2312yes—
203C3×#217C2312yes—
204C3×#217C2311yescharacteristic
205C3×#217C2312yes—
206C3×#217C2312yes—
207C3×#217C2312yes—
208C3×#217C2311yescharacteristic
209C3×(C2×D3)⋊C4C2312yes—
210C3×(C2×D3)⋊C4C2312yes—
211C3×(C2×D3)⋊C4C2312yes—
212C3×C4⋊Dic3C2312yes—
213C3×C4⋊Dic3C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×Dic3⋊C4C2312yes—
216C3×Dic3⋊C4C2312yes—
217C3×C4×Dic3C2311yescharacteristic
218#3724C2312yes—
219#3724C2312yes—
220#3724C2312yes—
221Dic3⋊Dic3C2312yes—
222Dic3⋊Dic3C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229(C2×D3)⋊Dic3C2312yes—
230(C2×D3)⋊Dic3C2312yes—
231(C2×D3)⋊Dic3C2312yes—
232(C2×D3)⋊Dic3C2312yes—
233(C2×D3)⋊Dic3C2312yes—
234(C2×D3)⋊Dic3C2312yes—
235(C2×D3)⋊Dic3C2312yes—
236(C2×D3)⋊Dic3C2312yes—
237Dic32C2312yes—
238Dic32C2312yes—
239Dic32C2312yes—
240#3533—91noSylow
241C22×C3×D4—31no—
242C22×C3×D4—31no—
243C22×#67C2×D311yescharacteristic
244C23×Dic3—31no—
245C2×#237—32no—
246C2×#237—32no—
247C2×#237—31no—
248C2×D3×D4C2×D311yescharacteristic
249C2×#235—31no—
250C22×C4×D3—31no—
251C3×#127—31no—
252C3×#126—32no—
253C3×#123—31no—
254C3×#123—31no—
255C3×#123—32no—
256C3×#123—32no—
257C3×#123—31no—
258C3×#121—32no—
259C3×#121—32no—
260C3×#121—32no—
261C3×#121—32no—
262C3×#121—32no—
263C3×#120—21no—
264C3×#120—32no—
265C3×#120—31no—
266C3×#120—32no—
267C3×#120C2×D311yescharacteristic
268C3×#120C2×D311yescharacteristic
269C2×C3×C22⋊C4—31no—
270#953—32no—
271#953—32no—
272#953C2×D311yescharacteristic
273#953C2×D312yescomplemented
274C2×#217—32no—
275C2×#217—32no—
276C2×#217—32no—
277C2×#217—31no—
278C2×#217—62no—
279#940—31no—
280#940—31no—
281#940C2×D311yescharacteristic
282#939—32no—
283#939—32no—
284#939—32no—
285#939—32no—
286#939—32no—
287#939—32no—
288#939—32no—
289#939—32no—
290#939—32no—
291#939C2×D312yescomplemented
292#938—32no—
293#938—32no—
294#938—32no—
295#938—32no—
296#938—32no—
297#938C2×D312yes—
298#938C2×D312yescomplemented
299#937—32no—
300#937—32no—
301#937C2×D312yes—
302#936—31no—
303#936—31no—
304#936—32no—
305#936—32no—
306#936—32no—
307#936—32no—
308#936—31no—
309#936—61no—
310#935—31no—
311#935—31no—
312#935—32no—
313#935—32no—
314#935—31no—
315#935—32no—
316#935—32no—
317#935—31no—
318#935—32no—
319#935—32no—
320#935—32no—
321#935—32no—
322#935—61no—
323#935—62no—
324#935C2×D311yescharacteristic
325#935C2×D311yescharacteristic
326D4×Dic3—32no—
327D4×Dic3—32no—
328D4×Dic3—32no—
329D4×Dic3—32no—
330D4×Dic3—32no—
331D4×Dic3—32no—
332D4×Dic3—32no—
333D4×Dic3—62no—
334#929—31no—
335#929—32no—
336#929—32no—
337C4×#67—32no—
338C4×#67—32no—
339C4×#67—32no—
340C4×#67—32no—
341#926—32no—
342#926—31no—
343C2×C4⋊Dic3—32no—
344#924—32no—
345#924—32no—
346#924—32no—
347C2×Dic3⋊C4—32no—
348#898—32no—
349#897—32no—
350#896—32no—
351#896—32no—
352#896—32no—
353#894—32no—
354#894—32no—
355#892—32no—
356#892—32no—
357D3×C4⋊C4—32no—
358D3×C4⋊C4—32no—
359#890—32no—
360#890—32no—
361#889—32no—
362#889—32no—
363#889—32no—
364#889—32no—
365#888—32no—
366#888—32no—
367#887—32no—
368#886—31no—
369#886—32no—
370#886—32no—
371#886C2×D311yescharacteristic
372#885—32no—
373#885—32no—
374#885—32no—
375#885—32no—
376#884C2×D312yes—
377#884C2×D312yescomplemented
378#883—32no—
379#883—32no—
380#883—32no—
381#883—32no—
382#883—32no—
383#883—32no—
384#883C2×D312yes—
385#883C2×D312yescomplemented
386#67⋊C4—32no—
387#67⋊C4—32no—
388#67⋊C4—32no—
389#67⋊C4—32no—
390#67⋊C4—32no—
391#67⋊C4—32no—
392#67⋊C4—32no—
393D3×C22⋊C4—32no—
394D3×C22⋊C4—31no—
395D3×C22⋊C4C2×D311yescharacteristic
396#879—32no—
397#879—32no—
398#879—32no—
399#879—32no—
400#879—32no—
401#879—32no—
402#879—32no—
403#879—32no—
404#879—32no—
405#879—62no—
406#879C2×D312yescomplemented
407#878—32no—
408#878—32no—
409#878—32no—
410#878—32no—
411#878—32no—
412#878—32no—
413#878—32no—
414#878—32no—
415#878—32no—
416#878—62no—
417#877—32no—
418#877—32no—
419#877—32no—
420#877—62no—
421#875—31no—
422#872—31no—
423C4×Dic6—32no—
424C23×C32—42no—
425C23×C32—41no—
426C23×C32C2411yescharacteristic
427C23×C32C2411yescharacteristic
428C23×C32C2412yes—
429C22×C3×D3—22no—
430C22×C3×D3—22no—
431C22×C3×D3—42no—
432C22×C3×D3—42no—
433C22×C3×D3C2411yescharacteristic
434C22×C3×D3C2411yescharacteristic
435C22×C3×D3C2412yes—
436C22×C3×D3C2411yescharacteristic
437C32×D4—42no—
438C32×D4—41no—
439C2×C32×C4C2411yescharacteristic
440C2×C32×C4C2412yes—
441C2×C3⋊Dic3—42no—
442C2×C3⋊Dic3—41no—
443C2×C3⋊Dic3—42no—
444C2×C3⋊Dic3C2412yes—
445C2×C3⋊Dic3C2412yes—
446C2×C3⋊Dic3C2412yes—
447C2×C3⋊Dic3C2412yes—
448#634—41no—
449C3×#67—24no—
450C3×#67—42no—
451C3×#67—41no—
452C3×#67—41no—
453C3×#67—42no—
454C3×#67—42no—
455C3×#67—42no—
456C3×#67—42no—
457C3×#67—42no—
458C2×C3×Dic3—41no—
459C2×C3×Dic3—41no—
460C2×C3×Dic3C2412yes—
461C2×C3×Dic3C2412yes—
462C2×C3×Dic3C2412yes—
463C2×C3×Dic3C2412yes—
464C2×C3×Dic3C2412yes—
465C2×C3×Dic3C2411yescharacteristic
466C3×D12—41no—
467C3×D12—41no—
468C3×C4×D3—22no—
469C3×C4×D3—42no—
470C3×C4×D3—42no—
471#627—42no—
472#627—42no—
473#625—24no—
474#625—42no—
475#625—42no—
476D3×Dic3—24no—
477D3×Dic3—42no—
478D3×Dic3—42no—
479D3×Dic3—42no—
480D3×Dic3—42no—
481#563—91no—
482#562—92no—
483#560—31no—
484#559—91no—
485#553—92no—
486#552—92no—
487#551—92no—
488#551—91no—
489#547—92no—
490#546—92no—
491#542—92no—
492#540—92no—
493#539—92no—
494#538—92no—
495#538—92no—
496#535—91no—
497#534—31no—
498#525—92no—
499C2×#123—91no—
500C24×C3—21no—
501C24×C3—31no—
502C24×C3—31no—
503C24×C3C22×D311yescharacteristic
504C24×C3C22×D311yescharacteristic
505C23×D3C22×D311yescharacteristic
506C23×D3C22×D311yescharacteristic
507C2×C3×D4—22no—
508C2×C3×D4—21no—
509C2×C3×D4—32no—
510C2×C3×D4—32no—
511C2×C3×D4—32no—
512C2×C3×D4—32no—
513C2×C3×D4—32no—
514C2×C3×D4—31no—
515C2×C3×D4—31no—
516C2×C3×D4—32no—
517C2×C3×D4—32no—
518C2×C3×D4—31no—
519C2×C3×D4—31no—
520C2×C3×D4—122no—
521C2×C3×D4—122no—
522C2×C3×D4C22×D312yes—
523C2×C3×D4C22×D312yes—
524C2×C3×D4C22×D311yescharacteristic
525C2×C3×D4C22×D311yescharacteristic
526C22×C3×C4—31no—
527C22×C3×C4—31no—
528C22×C3×C4—31no—
529C22×C3×C4—32no—
530C22×C3×C4—32no—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—32no—
534C2×#67—32no—
535C2×#67—32no—
536C2×#67—32no—
537C2×#67—42no—
538C2×#67C22×D312yes—
539C2×#67C22×D312yes—
540C2×#67C22×D312yes—
541C2×#67C22×D312yes—
542C2×#67C22×D311yescharacteristic
543C2×#67C22×D312yes—
544C2×#67C22×D312yes—
545C2×#67C22×D312yes—
546C2×#67C22×D311yescharacteristic
547C22×Dic3—32no—
548C22×Dic3—32no—
549C22×Dic3—32no—
550C22×Dic3—32no—
551C22×Dic3—31no—
552C22×Dic3—31no—
553C22×Dic3—32no—
554C22×Dic3—32no—
555C22×Dic3—32no—
556C22×Dic3—32no—
557C22×Dic3—32no—
558C22×Dic3—62no—
559C22×Dic3—62no—
560C22×Dic3—61no—
561C22×Dic3—122no—
562C22×Dic3C22×D311yescharacteristic
563C22×Dic3C22×D311yescharacteristic
564#237—122no—
565#237—124no—
566#237—124no—
567D3×D4—42no—
568#235—122no—
569C2×D12C22×D311yescharacteristic
570C2×D12C22×D311yescharacteristic
571C2×C4×D3—32no—
572C2×C4×D3—32no—
573C2×C4×D3—32no—
574C2×C4×D3—32no—
575C2×C4×D3—32no—
576C2×C4×D3—122no—
577C2×C4×D3C22×D311yescharacteristic
578C2×C4×D3C22×D312yes—
579C2×C4×D3C22×D312yes—
580C2×Dic6—31no—
581C2×Dic6—31no—
582C2×Dic6—32no—
583C2×Dic6—32no—
584C2×Dic6—32no—
585C2×Dic6—32no—
586C2×Dic6—61no—
587C3×C4⋊C4—32no—
588C3×C4⋊C4—32no—
589C3×C4⋊C4—32no—
590C3×C4⋊C4—32no—
591C3×C4⋊C4—32no—
592C3×C22⋊C4—22no—
593C3×C22⋊C4—21no—
594C3×C22⋊C4—32no—
595C3×C22⋊C4—32no—
596C3×C22⋊C4—32no—
597C3×C22⋊C4—32no—
598C3×C22⋊C4—31no—
599C3×C22⋊C4—31no—
600C3×C22⋊C4—32no—
601C3×C22⋊C4—32no—
602C3×C22⋊C4—32no—
603C3×C22⋊C4—32no—
604C3×C22⋊C4C22×D312yes—
605C3×C22⋊C4C22×D312yes—
606C3×C22⋊C4C22×D311yescharacteristic
607C3×C22⋊C4C22×D311yescharacteristic
608C3×C42—31no—
609#217—32no—
610#217—32no—
611#217—32no—
612#217—32no—
613#217—32no—
614#217—32no—
615#217—32no—
616#217—32no—
617#217—32no—
618#217—32no—
619#217—31no—
620#217—31no—
621#217—32no—
622#217—32no—
623#217—32no—
624#217—32no—
625#217—32no—
626#217—32no—
627#217—32no—
628#217—32no—
629#217—32no—
630#217—62no—
631#217—62no—
632#217—62no—
633#217—62no—
634#217—62no—
635#217—61no—
636#217C22×D312yes—
637#217C22×D312yes—
638#217C22×D311yescharacteristic
639#217C22×D311yescharacteristic
640#217C22×D312yes—
641#217C22×D312yes—
642#217C22×D312yes—
643(C2×D3)⋊C4—32no—
644(C2×D3)⋊C4—32no—
645(C2×D3)⋊C4—32no—
646(C2×D3)⋊C4—32no—
647(C2×D3)⋊C4—32no—
648(C2×D3)⋊C4—32no—
649(C2×D3)⋊C4—32no—
650(C2×D3)⋊C4—32no—
651(C2×D3)⋊C4—32no—
652(C2×D3)⋊C4C22×D312yes—
653(C2×D3)⋊C4C22×D312yes—
654(C2×D3)⋊C4C22×D312yes—
655C4⋊Dic3—32no—
656C4⋊Dic3—32no—
657C4⋊Dic3—32no—
658C4⋊Dic3—32no—
659C4⋊Dic3—32no—
660C4⋊Dic3—32no—
661C4⋊Dic3—32no—
662C4⋊Dic3—32no—
663C4⋊Dic3—32no—
664C4⋊Dic3—62no—
665C4⋊Dic3C22×D312yes—
666C4⋊Dic3C22×D312yes—
667Dic3⋊C4—32no—
668Dic3⋊C4—32no—
669Dic3⋊C4—32no—
670Dic3⋊C4—32no—
671Dic3⋊C4—32no—
672Dic3⋊C4—32no—
673Dic3⋊C4—32no—
674Dic3⋊C4—32no—
675Dic3⋊C4—32no—
676Dic3⋊C4—32no—
677Dic3⋊C4—32no—
678Dic3⋊C4—32no—
679Dic3⋊C4—32no—
680Dic3⋊C4—32no—
681Dic3⋊C4—32no—
682Dic3⋊C4—32no—
683Dic3⋊C4—32no—
684Dic3⋊C4—32no—
685Dic3⋊C4—32no—
686Dic3⋊C4—62no—
687Dic3⋊C4—62no—
688Dic3⋊C4—62no—
689Dic3⋊C4C22×D312yes—
690Dic3⋊C4C22×D312yes—
691Dic3⋊C4C22×D312yes—
692C4×Dic3—31no—
693C4×Dic3—32no—
694C4×Dic3—31no—
695C4×Dic3—32no—
696C4×Dic3—32no—
697C4×Dic3—32no—
698C4×Dic3—32no—
699C4×Dic3—32no—
700C4×Dic3—32no—
701C4×Dic3—32no—
702C4×Dic3—61no—
703C4×Dic3—62no—
704C4×Dic3C22×D311yescharacteristic
705C22×C32—22no—
706C22×C32—21no—
707C22×C32—21no—
708C22×C32—22no—
709C22×C32—22no—
710C22×C32—22no—
711C22×C32—22no—
712C22×C32—82no—
713C22×C32C2511yescharacteristic
714C2×C3×D3—22no—
715C2×C3×D3—22no—
716C2×C3×D3—21no—
717C2×C3×D3—21no—
718C2×C3×D3—22no—
719C2×C3×D3—22no—
720C2×C3×D3—22no—
721C2×C3×D3—22no—
722C2×C3×D3—44no—
723C2×C3×D3—82no—
724C2×C3×D3H(5,𝔽2)12yes—
725C32×C4—21no—
726C32×C4—22no—
727C3⋊Dic3—22no—
728C3⋊Dic3—22no—
729C3⋊Dic3—22no—
730C3⋊Dic3—22no—
731C3×Dic3—22no—
732C3×Dic3—21no—
733C3×Dic3—22no—
734C3×Dic3—22no—
735C3×Dic3—22no—
736C3×Dic3—22no—
737C2×#41—91no—
738C2×#41—92no—
739C22×D4—31no—
740C22×D4—31no—
741C23×C4—91no—
742C4⋊Q8—92no—
743#127—31no—
744#127—91no—
745#126—32no—
746#126—92no—
747#126—92no—
748#126—92no—
749#126—92no—
750#126—92no—
751#125—92no—
752#125—92no—
753#125—92no—
754#124—91no—
755#124—92no—
756#124—92no—
757#124—92no—
758#124—92no—
759#124—91no—
760#123—31no—
761#123—31no—
762#123—31no—
763#123—32no—
764#123—32no—
765#123—92no—
766#123—92no—
767#123—92no—
768#123—92no—
769#123—91no—
770#123—92no—
771#123—92no—
772#123—92no—
773#123—92no—
774#123—92no—
775#123—91no—
776#123—91no—
777#123—92no—
778C22⋊Q8—92no—
779C22⋊Q8—92no—
780C22⋊Q8—92no—
781C22⋊Q8—92no—
782C22⋊Q8—92no—
783C22⋊Q8—92no—
784C22⋊Q8—92no—
785C22⋊Q8—92no—
786#121—32no—
787#121—32no—
788#121—32no—
789#121—32no—
790#121—32no—
791#121—92no—
792#121—92no—
793#121—92no—
794#121—92no—
795#121—92no—
796#121—92no—
797#121—92no—
798#120—31no—
799#120—32no—
800#120—32no—
801#120—92no—
802#120—92no—
803#120D3211yescharacteristic
804C4×Q8—92no—
805C4×D4—92no—
806C4×D4—92no—
807C4×D4—92no—
808C4×D4—92no—
809C4×D4—92no—
810C4×D4—92no—
811C4×D4—92no—
812C4×D4—92no—
813C4×D4—92no—
814#117—91no—
815#117—92no—
816#117—92no—
817#117—92no—
818C2×C4⋊C4—92no—
819C2×C4⋊C4—92no—
820C2×C22⋊C4—31no—
821C2×C22⋊C4—91no—
822C2×C22⋊C4—92no—
823C2×C22⋊C4—92no—
824C23×C3—22no—
825C23×C3—21no—
826C23×C3—21no—
827C23×C3—31no—
828C23×C3—31no—
829C23×C3—31no—
830C23×C3—32no—
831C23×C3—41no—
832C23×C3—41no—
833C23×C3—42no—
834C23×C3—42no—
835C23×C3—44no—
836C23×C3—62no—
837C23×C3—62no—
838C23×C3—81no—
839C23×C3—122no—
840C23×C3—122no—
841C23×C3C23×D311yescharacteristic
842C23×C3C23×D311yescharacteristic
843C23×C3C23×D311yescharacteristic
844C23×C3C23×D311yescharacteristic
845C23×C3C23×D312yes—
846C23×C3C23×D312yes—
847C22×D3—22no—
848C22×D3—22no—
849C22×D3—42no—
850C22×D3—42no—
851C22×D3C23×D311yescharacteristic
852C22×D3C23×D311yescharacteristic
853C22×D3C23×D312yes—
854C22×D3C23×D311yescharacteristic
855C3×D4—41no—
856C3×D4—41no—
857C3×D4—42no—
858C3×D4—42no—
859C3×D4—44no—
860C3×D4—64no—
861C3×D4—81no—
862C3×D4—121no—
863C3×D4—121no—
864C3×D4—122no—
865C3×D4—122no—
866C3×D4—122no—
867C3×D4—122no—
868C3×D4—122no—
869C3×D4—122no—
870C3×D4—121no—
871C3×D4—121no—
872C2×C3×C4—22no—
873C2×C3×C4—21no—
874C2×C3×C4—32no—
875C2×C3×C4—32no—
876C2×C3×C4—32no—
877C2×C3×C4—32no—
878C2×C3×C4—31no—
879C2×C3×C4—32no—
880C2×C3×C4—62no—
881C2×C3×C4—122no—
882C2×C3×C4—122no—
883C2×C3×C4—121no—
884C2×C3×C4—121no—
885C2×C3×C4C23×D311yescharacteristic
886C2×C3×C4C23×D311yescharacteristic
887C2×C3×C4C23×D312yes—
888C2×C3×C4C23×D312yes—
889#67—24no—
890#67—41no—
891#67—41no—
892#67—42no—
893#67—42no—
894#67—42no—
895#67—42no—
896#67—42no—
897#67—42no—
898#67—64no—
899#67—64no—
900#67—122no—
901#67—122no—
902#67—122no—
903#67—122no—
904C2×Dic3—32no—
905C2×Dic3—32no—
906C2×Dic3—32no—
907C2×Dic3—32no—
908C2×Dic3—32no—
909C2×Dic3—32no—
910C2×Dic3—32no—
911C2×Dic3—32no—
912C2×Dic3—41no—
913C2×Dic3—41no—
914C2×Dic3—62no—
915C2×Dic3—62no—
916C2×Dic3—62no—
917C2×Dic3—62no—
918C2×Dic3—64no—
919C2×Dic3—122no—
920C2×Dic3—122no—
921C2×Dic3—122no—
922C2×Dic3—122no—
923C2×Dic3—121no—
924C2×Dic3—122no—
925C2×Dic3—122no—
926C2×Dic3—122no—
927C2×Dic3—122no—
928C2×Dic3—121no—
929C2×Dic3—124no—
930C2×Dic3—241no—
931C2×Dic3—242no—
932C2×Dic3C23×D312yes—
933C2×Dic3C23×D312yes—
934C2×Dic3C23×D312yes—
935C2×Dic3C23×D312yes—
936C2×Dic3C23×D311yescharacteristic
937C2×Dic3C23×D312yes—
938D12—41no—
939D12—41no—
940C4×D3—22no—
941C4×D3—42no—
942C4×D3—42no—
943C4×D3—64no—
944C4×D3—122no—
945C4×D3—122no—
946C4×D3—122no—
947C4×D3—122no—
948Dic6—122no—
949Dic6—122no—
950Dic6—122no—
951Dic6—122no—
952Dic6—121no—
953Dic6—121no—
954Dic6—241no—
955C2×C32—42no—
956C2×C32—41no—
957C2×C32—41no—
958C2×C32C2×H(5,𝔽2)11yescharacteristic
959C2×C32#58512yes—
960C3×D3—22no—
961C3×D3—42no—
962C3×D3—41no—
963C3×D3—41no—
964C24—31no—
965C24—31no—
966C24C2×D3211yescharacteristic
967#41—362no—
968#41—364no—
969C2×Q8—92no—
970C2×Q8—92no—
971C2×Q8—91no—
972C2×D4—32no—
973C2×D4—32no—
974C2×D4—32no—
975C2×D4—32no—
976C2×D4—32no—
977C2×D4—32no—
978C2×D4—31no—
979C2×D4—31no—
980C2×D4—32no—
981C2×D4—31no—
982C2×D4—31no—
983C2×D4—92no—
984C2×D4—92no—
985C2×D4—92no—
986C2×D4—122no—
987C2×D4—122no—
988C2×D4C2×D3212yes—
989C2×D4C2×D3211yescharacteristic
990C22×C4—31no—
991C22×C4—31no—
992C22×C4—31no—
993C22×C4—32no—
994C22×C4—32no—
995C22×C4—92no—
996C22×C4—92no—
997C22×C4—92no—
998C22×C4—92no—
999C22×C4—92no—
1000C22×C4—92no—
1001C22×C4—92no—
1002C22×C4—91no—
1003C22×C4—362no—
1004C4⋊C4—32no—
1005C4⋊C4—32no—
1006C4⋊C4—32no—
1007C4⋊C4—32no—
1008C4⋊C4—32no—
1009C4⋊C4—92no—
1010C4⋊C4—92no—
1011C4⋊C4—92no—
1012C4⋊C4—92no—
1013C4⋊C4—92no—
1014C4⋊C4—92no—
1015C4⋊C4—92no—
1016C4⋊C4—92no—
1017C4⋊C4—92no—
1018C4⋊C4—92no—
1019C4⋊C4—92no—
1020C4⋊C4—92no—
1021C4⋊C4—92no—
1022C4⋊C4—92no—
1023C22⋊C4—31no—
1024C22⋊C4—32no—
1025C22⋊C4—31no—
1026C22⋊C4—32no—
1027C22⋊C4—32no—
1028C22⋊C4—32no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—32no—
1033C22⋊C4—92no—
1034C22⋊C4—92no—
1035C22⋊C4—92no—
1036C22⋊C4—92no—
1037C22⋊C4—92no—
1038C22⋊C4—92no—
1039C22⋊C4—92no—
1040C22⋊C4—92no—
1041C22⋊C4—92no—
1042C22⋊C4—92no—
1043C22⋊C4—92no—
1044C22⋊C4—92no—
1045C22⋊C4—92no—
1046C22⋊C4—91no—
1047C22⋊C4—92no—
1048C22⋊C4C2×D3211yescharacteristic
1049C22⋊C4C2×D3212yes—
1050C42—31no—
1051C42—92no—
1052C42—92no—
1053C42—92no—
1054C42—91no—
1055C42—92no—
1056C22×C3—24no—
1057C22×C3—21no—
1058C22×C3—22no—
1059C22×C3—21no—
1060C22×C3—21no—
1061C22×C3—22no—
1062C22×C3—21no—
1063C22×C3—22no—
1064C22×C3—22no—
1065C22×C3—22no—
1066C22×C3—22no—
1067C22×C3—22no—
1068C22×C3—22no—
1069C22×C3—22no—
1070C22×C3—22no—
1071C22×C3—21no—
1072C22×C3—32no—
1073C22×C3—42no—
1074C22×C3—42no—
1075C22×C3—41no—
1076C22×C3—42no—
1077C22×C3—41no—
1078C22×C3—42no—
1079C22×C3—62no—
1080C22×C3—62no—
1081C22×C3—61no—
1082C22×C3—61no—
1083C22×C3—62no—
1084C22×C3—62no—
1085C22×C3—62no—
1086C22×C3—62no—
1087C22×C3—82no—
1088C22×C3—82no—
1089C22×C3—84no—
1090C22×C3—124no—
1091C22×C3—242no—
1092C22×C3C24×D311yescharacteristic
1093C22×C3C24×D311yescharacteristic
1094C2×D3—22no—
1095C2×D3—21no—
1096C2×D3—21no—
1097C2×D3—22no—
1098C2×D3—22no—
1099C2×D3—22no—
1100C2×D3—22no—
1101C2×D3—22no—
1102C2×D3—44no—
1103C2×D3—82no—
1104C2×D3#100412yes—
1105C3×C4—21no—
1106C3×C4—21no—
1107C3×C4—22no—
1108C3×C4—22no—
1109C3×C4—41no—
1110C3×C4—42no—
1111C3×C4—62no—
1112C3×C4—62no—
1113C3×C4—61no—
1114C3×C4—62no—
1115C3×C4—62no—
1116C3×C4—62no—
1117Dic3—22no—
1118Dic3—21no—
1119Dic3—22no—
1120Dic3—22no—
1121Dic3—22no—
1122Dic3—22no—
1123Dic3—62no—
1124Dic3—62no—
1125Dic3—62no—
1126Dic3—62no—
1127Dic3—62no—
1128Dic3—62no—
1129Dic3—62no—
1130Dic3—62no—
1131Dic3—122no—
1132Dic3—122no—
1133Dic3—122no—
1134Dic3—122no—
1135C32#353311yescharacteristic, complemented, Sylow
1136C23—31no—
1137C23—31no—
1138C23—32no—
1139C23—31no—
1140C23—41no—
1141C23—42no—
1142C23—62no—
1143C23—62no—
1144C23—122no—
1145C23—122no—
1146C23C22×D3211yescharacteristic
1147C23C22×D3211yescharacteristic
1148C23C22×D3212yes—
1149Q8—361no—
1150Q8—362no—
1151Q8—362no—
1152D4—41no—
1153D4—42no—
1154D4—64no—
1155D4—121no—
1156D4—121no—
1157D4—121no—
1158D4—121no—
1159D4—122no—
1160D4—122no—
1161D4—122no—
1162D4—122no—
1163D4—122no—
1164D4—122no—
1165D4—184no—
1166D4—362no—
1167D4—362no—
1168C2×C4—32no—
1169C2×C4—32no—
1170C2×C4—32no—
1171C2×C4—32no—
1172C2×C4—32no—
1173C2×C4—31no—
1174C2×C4—62no—
1175C2×C4—92no—
1176C2×C4—92no—
1177C2×C4—92no—
1178C2×C4—92no—
1179C2×C4—122no—
1180C2×C4—122no—
1181C2×C4—121no—
1182C2×C4—121no—
1183C2×C4—184no—
1184C2×C4—362no—
1185C2×C4—362no—
1186C2×C4—362no—
1187C2×C4—362no—
1188C2×C4—361no—
1189C2×C4—362no—
1190C2×C4—362no—
1191C2×C4C22×D3211yescharacteristic
1192C2×C4C22×D3212yes—
1193C2×C3—21no—
1194C2×C3—22no—
1195C2×C3—44no—
1196C2×C3—41no—
1197C2×C3—41no—
1198C2×C3—42no—
1199C2×C3—41no—
1200C2×C3—42no—
1201C2×C3—41no—
1202C2×C3—62no—
1203C2×C3—81no—
1204C2×C3—81no—
1205C2×C3—122no—
1206C2×C3—121no—
1207C2×C3—121no—
1208C2×C3C2×#100411yescharacteristic
1209C2×C3D3×H(5,𝔽2)11yescharacteristic
1210C2×C3#596612yes—
1211C2×C3#596612yes—
1212D3—22no—
1213D3—41no—
1214D3—41no—
1215D3—42no—
1216C22—21no—
1217C22—21no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—32no—
1224C22—62no—
1225C22—62no—
1226C22—61no—
1227C22—61no—
1228C22—62no—
1229C22—62no—
1230C22—62no—
1231C22—62no—
1232C22—82no—
1233C22—124no—
1234C22—242no—
1235C22C23×D3211yescharacteristic
1236C4—21no—
1237C4—22no—
1238C4—61no—
1239C4—62no—
1240C4—62no—
1241C4—62no—
1242C4—62no—
1243C4—62no—
1244C4—182no—
1245C4—182no—
1246C4—182no—
1247C4—182no—
1248C3—21no—
1249C3#8630011yescharacteristic, complemented
1250C3#8708111yescharacteristic, complemented
1251C2—41no—
1252C2—42no—
1253C2—41no—
1254C2—62no—
1255C2—121no—
1256C2—121no—
1257C2—122no—
1258C2D3×#100411yescharacteristic
1259C2#1059667912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#120C22
hypercenter#120D32
hypocenterC32#3533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #10596058C2semidirect
2. C3×#5595C2semidirect
3. C3×#5589C2semidirect
4. #10595508C2semidirect
5. #10595494C2semidirect
6. #10595275C2semidirect
7. #10595260C2semidirect
8. #10595245C2semidirect
9. #10595233C2semidirect
10. #10595200C2semidirect
11. #10595180C2semidirect
12. D3×#935C2semidirect
13. #10595130C2semidirect
14. #10594223C2semidirect
15. #10594193C2semidirect
16. #10594148C2semidirect
17. #10594123C2semidirect
18. #10594120C2semidirect
19. #10594062C2semidirect
25. C22×D3×Dic3C22semidirect
26. C2×#3795C22semidirect
28. C2×#3757C22semidirect
31. #64144C22semidirect
32. D4×C3⋊Dic3C22semidirect
33. #64088C22semidirect
34. #64087C22semidirect
35. #64086C22semidirect
37. C3×#953C22semidirect
39. C3×#939C22semidirect
41. C3×#938C22semidirect
47. C3×#884C22semidirect
49. C3×#883C22semidirect
51. C3×#879C22semidirect
52. #63982C22semidirect
53. #63980C22semidirect
54. #63980C22semidirect
56. #63976C22semidirect
58. #67⋊Dic3C22semidirect
59. #67⋊Dic3C22semidirect
60. #67⋊Dic3C22semidirect
61. Dic3×#67C22semidirect
64. #63970C22semidirect
65. #63970C22semidirect
66. #63970C22semidirect
69. #63969C22semidirect
71. D3×#217C22semidirect
72. #63964C22semidirect
73. #63964C22semidirect
74. #63962C22semidirect
75. #63962C22semidirect
76. #63961C22semidirect
77. #63959C22semidirect
78. #63959C22semidirect
79. #63959C22semidirect
80. #63959C22semidirect
81. #63956C22semidirect
82. #63956C22semidirect
83. #63956C22semidirect
84. #63914C22semidirect
85. #63905C22semidirect
86. #63905C22semidirect
87. #63902C22semidirect
88. C4×#625C22semidirect
89. #63899C22semidirect
90. #63899C22semidirect
91. #63893C22semidirect
92. #63891C22semidirect
93. D3×C4⋊Dic3C22semidirect
94. #63884C22semidirect
95. #63884C22semidirect
96. #63879C22semidirect
97. #63878C22semidirect
98. D3×Dic3⋊C4C22semidirect
99. #63872C22semidirect
100. #63870C22semidirect
101. #63860C22semidirect
102. #63858C22semidirect
103. #63855C22semidirect
104. #63851C22semidirect
105. #63847C22semidirect
106. #63841C22semidirect
107. #63840C22semidirect
108. #63837C22semidirect
137. #5595D3semidirect
142. #5589D3semidirect
273. #953C2×D3semidirect
291. #939C2×D3semidirect
298. #938C2×D3semidirect
377. #884C2×D3semidirect
385. #883C2×D3semidirect
406. #879C2×D3semidirect
1135. C32#3533semidirect
1249. C3#86300semidirect
1250. C3#87081semidirect

Maximal subgroups

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

subgroupindex
#105960582
C3×#55952
C3×#55892
#105955082
#105954942
#105952752
#105952602
#105952452
#105952332
#105952002
#105951802
D3×#9352
#105951302
#105942232
#105941932
#105941482
#105941232
#105941202
#105940622
#870813
#863003