Finite Group Databasebeta

← #11906236

Subgroups — #11906236

Order 1152.

2321 conjugacy classes of subgroups.

The subgroup lattice has 1223 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596105C211yesmaximal, characteristic, complemented
2C3×#5634C211yesmaximal, characteristic, complemented
3C3×#5622C211yesmaximal, characteristic, complemented
4#10595372C212yesmaximal, complemented
5#10595371C212yesmaximal, complemented
6#10594981C211yesmaximal, characteristic, complemented
7#10594971C211yesmaximal, characteristic, complemented
8C2×#63880C211yesmaximal, characteristic
9#10594808C211yesmaximal, characteristic, complemented
10#10594396C212yesmaximal, complemented
11#10594395C212yesmaximal, complemented
12#10594392C212yesmaximal, complemented
13#10594392C212yesmaximal, complemented
14#10594383C212yesmaximal, complemented
15#10594378C212yesmaximal, complemented
16#10594182C212yesmaximal
17#10594067C212yesmaximal, complemented
18D3×#878C212yesmaximal, complemented
19#10594035C212yesmaximal, complemented
20#86574—31nomaximal
21#86280—31nomaximal
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3797C2212yescomplemented
26C2×D3×Dic6C2212yescomplemented
27C32×C22⋊Q8C2211yescharacteristic
28#64155C2212yescomplemented
29C2×#3752C2211yescharacteristic
30#64133C2211yescharacteristic
31#64106C2212yescomplemented
32#64105C2212yescomplemented
33#64105C2212yescomplemented
34C22⋊C4×C3⋊D3C2212yes—
35#64087C2212yes—
36C3×#946C2212yescomplemented
37C3×Q8×Dic3C2211yescharacteristic, complemented
38C3×#944C2211yescharacteristic, complemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C3×#924C2211yescharacteristic
41C3×#924C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#897C2212yescomplemented
44C3×#896C2212yescomplemented
45C3×#896C2212yescomplemented
46C3×#889C2212yescomplemented
47C3×#888C2211yescharacteristic, complemented
48C3×#887C2212yescomplemented
49C3×#887C2211yescharacteristic, complemented
50C3×D3×C22⋊C4C2212yes—
51C3×#878C2212yes—
52C3×#878C2212yes—
53C3×#877C2212yes—
54#63982C2212yes—
55#63974C2212yes—
56D3×#217C2212yes—
57C2×Dic3⋊Dic3C2211yescharacteristic
58#63964C2212yes—
59#63964C2212yes—
60#63955C2212yes—
61#63918C2212yescomplemented
62#63918C2211yescharacteristic, complemented
63#63904C2212yes—
64#63904C2212yes—
65C4×#626C2212yes—
66C4×#626C2212yes—
67#63900C2212yescomplemented
68#63899C2212yescomplemented
69#63899C2212yescomplemented
70#63896C2212yescomplemented
71#63896C2212yescomplemented
72#63895C2212yescomplemented
73#63895C2212yescomplemented
74#63895C2212yescomplemented
75#63895C2212yescomplemented
76#63893C2212yescomplemented
77#63893C2212yescomplemented
78D3×C4⋊Dic3C2212yescomplemented
79#63888C2212yescomplemented
80#63888C2212yescomplemented
81#63888C2212yescomplemented
82#63888C2212yescomplemented
83#63887C2212yescomplemented
84#63887C2212yescomplemented
85#63883C2212yescomplemented
86#63883C2212yescomplemented
87#63881C2212yes—
88#63881C2212yes—
89#63880C2212yes—
90#63880C2212yes—
91#63880C2212yes—
92#63880C2212yes—
93#63880C2212yes—
94#63880C2212yes—
95D3×Dic3⋊C4C2212yescomplemented
96D3×Dic3⋊C4C2212yescomplemented
97#63867C2212yescomplemented
98#63867C2212yescomplemented
99#63867C2212yescomplemented
100#63866C2212yescomplemented
101#63866C2211yescharacteristic, complemented
102#63846C2212yescomplemented
103#63845C2212yescomplemented
104#63844C2211yescharacteristic, complemented
105Dic3×Dic6C2211yescharacteristic, complemented
106#63840C2212yescomplemented
107#63839C2212yescomplemented
108#63837C2212yescomplemented
109C3×#543—31no—
110C3×#533—31no—
111#5730—32no—
112#5727—32no—
113#5690—32no—
114#5690—32no—
115#5636—32no—
116#5636—32no—
117#5636—32no—
118#5636—32no—
119#5635—32no—
120#5635—32no—
121#5634—31no—
122#5634—31no—
123#5634—31no—
124#5634—31no—
125#5634—31no—
126#5634—61no—
127#5634D311yescharacteristic, complemented
128#5632—32no—
129#5632—32no—
130D3×C22⋊Q8—32no—
131D3×C22⋊Q8—32no—
132D3×C22⋊Q8—32no—
133#5623—32no—
134#5622—31no—
135#5622D311yescharacteristic, complemented
136#5579—32no—
137#5579—32no—
138#5579—32no—
139Q8×D12—32no—
140#5521—32no—
141#5519—32no—
142#5486—32no—
143C2×#67⋊C4—31no—
144#5483—31no—
145C2×#878—32no—
146C2×C4×D12—31no—
147#5470—31no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3×D3C2311yescharacteristic
150C2×C32×Q8C2311yescharacteristic
151C22×C32×C4C2311yescharacteristic
152C22×C3⋊Dic3C2311yescharacteristic
153C2×C4×C3⋊D3C2312yes—
154C2×C4×C3⋊D3C2312yes—
155C2×#634C2312yes—
156C2×#634C2311yescharacteristic
157C22×C3×Dic3C2311yescharacteristic
158C22×C3×Dic3C2311yescharacteristic
159C22×C3×Dic3C2311yescharacteristic
160C2×C3×C4×D3C2312yes—
161C2×C3×C4×D3C2312yes—
162C2×C3×Dic6C2312yes—
163C2×C3×Dic6C2312yes—
164C2×C3×Dic6C2311yescharacteristic
165C2×C3×Dic6C2311yescharacteristic
166C2×#627C2312yes—
167C2×#627C2312yes—
168C2×#627C2312yes—
169C2×#626Q818yescomplemented
170C2×#626C2312yes—
171C2×#626C2312yes—
172C2×#624—42no—
173C2×#624C2312yes—
174C2×#624C2312yes—
175C2×#624C2312yes—
176C2×#624C2312yes—
177C2×D3×Dic3—42no—
178C2×D3×Dic3C2312yes—
179C2×D3×Dic3C2312yes—
180C2×D3×Dic3C2312yes—
181C2×D3×Dic3C2312yes—
182#3797—44no—
183D3×Dic6—44no—
184C32×C4⋊C4C2311yescharacteristic
185C32×C4⋊C4C2312yes—
186C32×C22⋊C4C2312yes—
187#3757C2312yes—
188#3752C2312yes—
189#3752C2312yes—
190#3752C2312yes—
191#3752C2312yes—
192C4⋊(C3⋊Dic3)C2312yes—
193C4⋊(C3⋊Dic3)C2311yescharacteristic
194#3750C2312yes—
195#3750C2312yes—
196#3750C2312yes—
197C3×#217C2312yes—
198C3×#217C2312yes—
199C3×(C2×D3)⋊C4C2312yes—
200C3×(C2×D3)⋊C4C2312yes—
201C3×(C2×D3)⋊C4C2312yes—
202C3×(C2×D3)⋊C4C2312yes—
203C3×C4⋊Dic3C2312yes—
204C3×C4⋊Dic3C2312yes—
205C3×C4⋊Dic3C2311yescharacteristic
206C3×C4⋊Dic3C2311yescharacteristic
207C3×Dic3⋊C4C2312yes—
208C3×Dic3⋊C4C2312yes—
209C3×Dic3⋊C4C2312yes—
210C3×Dic3⋊C4C2312yes—
211C3×Dic3⋊C4C2312yes—
212C3×Dic3⋊C4C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×C4×Dic3C2312yes—
216C3×C4×Dic3C2312yes—
217C3×C4×Dic3C2311yescharacteristic
218C3×C4×Dic3C2311yescharacteristic
219C3×C4×Dic3C2311yescharacteristic
220C3×C4×Dic3C2311yescharacteristic
221#3724C2312yes—
222#3724C2312yes—
223#3724C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
228Dic3⋊Dic3C2312yes—
229Dic3⋊Dic3C2312yes—
230Dic3⋊Dic3C2312yes—
231Dic3⋊Dic3C2312yes—
232Dic3⋊Dic3C2312yes—
233Dic3⋊Dic3C2312yes—
234#3722C2312yes—
235#3722C2312yes—
236(C2×D3)⋊Dic3C2312yes—
237(C2×D3)⋊Dic3C2312yes—
238Dic32C2312yes—
239Dic32C2312yes—
240#3501—91noSylow
241C22×#67—31no—
242C23×Dic3—31no—
243C2×D3×Q8—32no—
244C2×D3×Q8—32no—
245C2×D3×Q8—32no—
246C22×D12—31no—
247C22×C4×D3—31no—
248C22×C4×D3—31no—
249C22×C4×D3—31no—
250C22×Dic6—32no—
251C3×C4⋊Q8—31no—
252C3×C4⋊Q8—31no—
253C3×#125—32no—
254C3×C22⋊Q8—21no—
255C3×C22⋊Q8—32no—
256C3×C22⋊Q8—31no—
257C3×C22⋊Q8—31no—
258C3×C22⋊Q8—32no—
259C3×C22⋊Q8—32no—
260C3×C22⋊Q8—32no—
261C3×C22⋊Q8—32no—
262C3×C22⋊Q8—32no—
263C3×C22⋊Q8C2×D311yescharacteristic
264C3×C22⋊Q8C2×D311yescharacteristic
265C3×C4×Q8—31no—
266C3×C4×Q8—32no—
267C3×C4×Q8—31no—
268C3×#117—32no—
269C2×C3×C22⋊C4—31no—
270C2×C3×C22⋊C4—32no—
271C2×C3×C42—31no—
272C2×#217—32no—
273#946—32no—
274#946—32no—
275#946—32no—
276#946—32no—
277#946—32no—
278#946—32no—
279#946—32no—
280#946—32no—
281#946—62no—
282#946C2×D312yescomplemented
283Q8×Dic3—31no—
284Q8×Dic3C2×D311yescharacteristic, complemented
285#944—32no—
286#944—32no—
287#944—31no—
288#944C2×D311yescharacteristic, complemented
289C4×#67—32no—
290C4×#67—32no—
291C4×#67—32no—
292C4×#67—32no—
293C2×(C2×D3)⋊C4—31no—
294C2×(C2×D3)⋊C4—31no—
295C2×(C2×D3)⋊C4—61no—
296C2×(C2×D3)⋊C4C2×D311yescharacteristic
297#926—32no—
298C2×C4⋊Dic3—31no—
299C2×C4⋊Dic3—32no—
300#924—31no—
301#924—31no—
302#924—32no—
303#924—32no—
304#924—61no—
305#924C2×D311yescharacteristic
306#924C2×D311yescharacteristic
307C2×Dic3⋊C4—31no—
308C2×Dic3⋊C4—32no—
309C2×Dic3⋊C4—32no—
310C2×C4×Dic3C2×D311yescharacteristic
311#897—32no—
312#897—32no—
313#897—32no—
314#897—32no—
315#897—32no—
316#897—32no—
317#897—32no—
318#897—32no—
319#897—62no—
320#897C2×D312yescomplemented
321#896—32no—
322#896—32no—
323#896—32no—
324#896—32no—
325#896—32no—
326#896—32no—
327#896—32no—
328#896—32no—
329#896—32no—
330#896—32no—
331#896—32no—
332#896—32no—
333#896—32no—
334#896—32no—
335#896—32no—
336#896—32no—
337#896—62no—
338#896—62no—
339#896C2×D312yescomplemented
340#896C2×D312yescomplemented
341#893—32no—
342#893—32no—
343#893—32no—
344#893—32no—
345D3×C4⋊C4—32no—
346D3×C4⋊C4—32no—
347D3×C4⋊C4—32no—
348D3×C4⋊C4—32no—
349D3×C4⋊C4—32no—
350D3×C4⋊C4—32no—
351D3×C4⋊C4—32no—
352D3×C4⋊C4—32no—
353D3×C4⋊C4—32no—
354#890—32no—
355#890—32no—
356#889—32no—
357#889—32no—
358#889—32no—
359#889—32no—
360#889—32no—
361#889C2×D312yescomplemented
362#888—32no—
363#888—32no—
364#888—32no—
365#888—31no—
366#888—32no—
367#888C2×D311yescharacteristic, complemented
368#887—32no—
369#887—31no—
370#887C2×D312yescomplemented
371#887C2×D311yescharacteristic, complemented
372#67⋊C4—32no—
373#67⋊C4—32no—
374#67⋊C4—32no—
375#67⋊C4—32no—
376#67⋊C4—32no—
377#67⋊C4—32no—
378#67⋊C4—32no—
379#67⋊C4—32no—
380D3×C22⋊C4—32no—
381D3×C22⋊C4—32no—
382D3×C22⋊C4—32no—
383D3×C22⋊C4—32no—
384D3×C22⋊C4—32no—
385D3×C22⋊C4—62no—
386D3×C22⋊C4C2×D312yes—
387#878—32no—
388#878—32no—
389#878—32no—
390#878—32no—
391#878—32no—
392#878—32no—
393#878—32no—
394#878—32no—
395#878—32no—
396#878—32no—
397#878—32no—
398#878—32no—
399#878—32no—
400#878—32no—
401#878—62no—
402#878C2×D312yes—
403#878C2×D312yes—
404#877—32no—
405#877C2×D312yes—
406C4×D12—32no—
407C4×D12—32no—
408C4×D12—32no—
409C4×D12—32no—
410C4×D12—32no—
411C4×D12—32no—
412C4×D12—32no—
413C4×D12—32no—
414#870—32no—
415#870—32no—
416#870—32no—
417#869—31no—
418#869—32no—
419#869—31no—
420#869—32no—
421C4×Dic6—31no—
422C4×Dic6—31no—
423C4×Dic6—32no—
424C23×C32C2411yescharacteristic
425C22×C3⋊D3—41no—
426C22×C3⋊D3—41no—
427C22×C3⋊D3C2×Q814yescomplemented
428C22×C3⋊D3C2412yes—
429C22×C3×D3—41no—
430C22×C3×D3—41no—
431C22×C3×D3C2×Q814yescomplemented
432C22×C3×D3C2412yes—
433C32×Q8—41no—
434C2×C32×C4—41no—
435C2×C32×C4C2411yescharacteristic
436C2×C32×C4C2411yescharacteristic
437C2×C32×C4C2412yes—
438C2×C32×C4C2412yes—
439C2×C3⋊Dic3—41no—
440C2×C3⋊Dic3C2412yes—
441C2×C3⋊Dic3C2412yes—
442C2×C3⋊Dic3C2412yes—
443C4×C3⋊D3—42no—
444C4×C3⋊D3—42no—
445#634—42no—
446#634—41no—
447C2×C3×Dic3—22no—
448C2×C3×Dic3—41no—
449C2×C3×Dic3C2×Q814yescomplemented
450C2×C3×Dic3C2412yes—
451C2×C3×Dic3C2412yes—
452C2×C3×Dic3C2412yes—
453C2×C3×Dic3C2412yes—
454C2×C3×Dic3C2412yes—
455C2×C3×Dic3C2411yescharacteristic
456C2×C3×Dic3C2411yescharacteristic
457C2×C3×Dic3C2411yescharacteristic
458C2×C3×Dic3C2411yescharacteristic
459C3×C4×D3—42no—
460C3×C4×D3—42no—
461C3×Dic6—24no—
462C3×Dic6—42no—
463C3×Dic6—41no—
464C3×Dic6—41no—
465#627—24no—
466#627—42no—
467#627—42no—
468#626C2×Q818yescomplemented
469#626C2×Q818yescomplemented
470#624—24no—
471#624—42no—
472#624—42no—
473#624—42no—
474D3×Dic3—24no—
475D3×Dic3—42no—
476D3×Dic3—42no—
477D3×Dic3—42no—
478#554—92no—
479#554—92no—
480#554—92no—
481#554—92no—
482#554—92no—
483#554—92no—
484D4×Q8—92no—
485D4×Q8—92no—
486#544—92no—
487#543—31no—
488#543—91no—
489#543—91no—
490#543—91no—
491#533—31no—
492#533—91no—
493C2×C22⋊Q8—92no—
494C2×C22⋊Q8—92no—
495#518—92no—
496C2×C4×D4—91no—
497C24×C3—31no—
498C23×D3—31no—
499C23×D3—31no—
500C23×D3—61no—
501C23×D3C22×D311yescharacteristic
502C2×C3×Q8—21no—
503C2×C3×Q8—32no—
504C2×C3×Q8—32no—
505C2×C3×Q8—31no—
506C2×C3×Q8—31no—
507C2×C3×Q8C22×D311yescharacteristic
508C2×C3×Q8C22×D311yescharacteristic
509C22×C3×C4—21no—
510C22×C3×C4—31no—
511C22×C3×C4—31no—
512C22×C3×C4—31no—
513C22×C3×C4—32no—
514C22×C3×C4—32no—
515C22×C3×C4C22×D311yescharacteristic
516C22×C3×C4C22×D311yescharacteristic
517C2×#67—38no—
518C2×#67—32no—
519C2×#67—32no—
520C22×Dic3—31no—
521C22×Dic3—31no—
522C22×Dic3—32no—
523C22×Dic3—32no—
524C22×Dic3—32no—
525C22×Dic3—32no—
526C22×Dic3—61no—
527C22×Dic3—122no—
528C22×Dic3C22×D311yescharacteristic
529C22×Dic3C22×D311yescharacteristic
530C22×Dic3C22×D311yescharacteristic
531D3×Q8—124no—
532D3×Q8—124no—
533D3×Q8—124no—
534C2×D12—38no—
535C2×D12—32no—
536C2×D12—32no—
537C2×C4×D3—32no—
538C2×C4×D3—32no—
539C2×C4×D3—32no—
540C2×C4×D3—32no—
541C2×C4×D3—32no—
542C2×C4×D3—32no—
543C2×C4×D3—32no—
544C2×C4×D3—32no—
545C2×C4×D3—32no—
546C2×C4×D3—32no—
547C2×C4×D3—32no—
548C2×C4×D3—32no—
549C2×C4×D3—32no—
550C2×C4×D3—32no—
551C2×C4×D3—32no—
552C2×C4×D3—32no—
553C2×C4×D3—62no—
554C2×C4×D3—62no—
555C2×C4×D3—122no—
556C2×C4×D3—122no—
557C2×C4×D3—122no—
558C2×C4×D3C22×D312yes—
559C2×C4×D3C22×D312yes—
560C2×Dic6—32no—
561C2×Dic6—32no—
562C2×Dic6—31no—
563C2×Dic6—32no—
564C2×Dic6—31no—
565C2×Dic6—32no—
566C2×Dic6—32no—
567C2×Dic6—32no—
568C2×Dic6—32no—
569C2×Dic6—32no—
570C2×Dic6—62no—
571C2×Dic6—61no—
572C2×Dic6—124no—
573C2×Dic6C22×D312yes—
574C2×Dic6C22×D311yescharacteristic
575C2×Dic6C22×D312yes—
576C2×Dic6C22×D311yescharacteristic
577C3×C4⋊C4—21no—
578C3×C4⋊C4—22no—
579C3×C4⋊C4—31no—
580C3×C4⋊C4—32no—
581C3×C4⋊C4—32no—
582C3×C4⋊C4—32no—
583C3×C4⋊C4—32no—
584C3×C4⋊C4—32no—
585C3×C4⋊C4—32no—
586C3×C4⋊C4—32no—
587C3×C4⋊C4—32no—
588C3×C4⋊C4—32no—
589C3×C4⋊C4—31no—
590C3×C4⋊C4—32no—
591C3×C4⋊C4C22×D311yescharacteristic
592C3×C4⋊C4C22×D312yes—
593C3×C4⋊C4C22×D311yescharacteristic
594C3×C4⋊C4C22×D312yes—
595C3×C22⋊C4—22no—
596C3×C22⋊C4—32no—
597C3×C22⋊C4—32no—
598C3×C22⋊C4—32no—
599C3×C22⋊C4—32no—
600C3×C22⋊C4—32no—
601C3×C22⋊C4—32no—
602C3×C22⋊C4C22×D312yes—
603C3×C22⋊C4C22×D312yes—
604C3×C42—31no—
605C3×C42—31no—
606C3×C42—31no—
607C3×C42—32no—
608C3×C42—32no—
609C3×C42—31no—
610#217—32no—
611#217—32no—
612#217—32no—
613#217—32no—
614#217—62no—
615#217C22×D312yes—
616#217C22×D312yes—
617(C2×D3)⋊C4—32no—
618(C2×D3)⋊C4—32no—
619(C2×D3)⋊C4—32no—
620(C2×D3)⋊C4—32no—
621(C2×D3)⋊C4—32no—
622(C2×D3)⋊C4—32no—
623(C2×D3)⋊C4—32no—
624(C2×D3)⋊C4—32no—
625(C2×D3)⋊C4—32no—
626(C2×D3)⋊C4—32no—
627(C2×D3)⋊C4—32no—
628(C2×D3)⋊C4—32no—
629(C2×D3)⋊C4—32no—
630(C2×D3)⋊C4—32no—
631(C2×D3)⋊C4—62no—
632(C2×D3)⋊C4—62no—
633(C2×D3)⋊C4—62no—
634(C2×D3)⋊C4—62no—
635(C2×D3)⋊C4C22×D312yes—
636(C2×D3)⋊C4C22×D312yes—
637(C2×D3)⋊C4C22×D312yes—
638(C2×D3)⋊C4C22×D312yes—
639C4⋊Dic3—31no—
640C4⋊Dic3—32no—
641C4⋊Dic3—32no—
642C4⋊Dic3—31no—
643C4⋊Dic3—32no—
644C4⋊Dic3—32no—
645C4⋊Dic3—32no—
646C4⋊Dic3—32no—
647C4⋊Dic3—32no—
648C4⋊Dic3—32no—
649C4⋊Dic3—32no—
650C4⋊Dic3—32no—
651C4⋊Dic3—32no—
652C4⋊Dic3—32no—
653C4⋊Dic3—62no—
654C4⋊Dic3—61no—
655C4⋊Dic3C22×D311yescharacteristic
656C4⋊Dic3C22×D312yes—
657C4⋊Dic3C22×D311yescharacteristic
658C4⋊Dic3C22×D312yes—
659Dic3⋊C4—32no—
660Dic3⋊C4—32no—
661Dic3⋊C4—32no—
662Dic3⋊C4—32no—
663Dic3⋊C4—32no—
664Dic3⋊C4—32no—
665Dic3⋊C4—32no—
666Dic3⋊C4—32no—
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—62no—
682Dic3⋊C4—62no—
683Dic3⋊C4—62no—
684Dic3⋊C4C22×D312yes—
685Dic3⋊C4C22×D312yes—
686Dic3⋊C4C22×D312yes—
687Dic3⋊C4C22×D312yes—
688Dic3⋊C4C22×D312yes—
689Dic3⋊C4C22×D312yes—
690Dic3⋊C4C22×D312yes—
691Dic3⋊C4C22×D312yes—
692C4×Dic3—32no—
693C4×Dic3—32no—
694C4×Dic3—32no—
695C4×Dic3—32no—
696C4×Dic3C22×D312yes—
697C4×Dic3C22×D312yes—
698C4×Dic3C22×D311yescharacteristic
699C4×Dic3C22×D311yescharacteristic
700C4×Dic3C22×D311yescharacteristic
701C4×Dic3C22×D311yescharacteristic
702C22×C32—21no—
703C22×C32—21no—
704C22×C32C22×Q812yes—
705C22×C32C2511yescharacteristic
706C2×C3⋊D3—22no—
707C2×C3⋊D3—22no—
708C2×C3⋊D3—44no—
709C2×C3⋊D3C22×Q814yes—
710C2×C3×D3—22no—
711C2×C3×D3—22no—
712C2×C3×D3—44no—
713C2×C3×D3C22×Q814yes—
714C32×C4—22no—
715C32×C4—21no—
716C32×C4—21no—
717C32×C4—22no—
718C3⋊Dic3—22no—
719C3⋊Dic3—22no—
720C3⋊Dic3—22no—
721C3×Dic3—21no—
722C3×Dic3—22no—
723C3×Dic3—22no—
724C3×Dic3—22no—
725C3×Dic3—22no—
726C3×Dic3—22no—
727C3×Dic3C22×Q812yes—
728C3×Dic3C22×Q812yes—
729C3×Dic3H(5,𝔽2)12yes—
730C22×Q8—92no—
731C22×Q8—92no—
732C22×D4—91no—
733C23×C4—91no—
734C23×C4—91no—
735C4⋊Q8—31no—
736C4⋊Q8—31no—
737C4⋊Q8—91no—
738C4⋊Q8—92no—
739C4⋊Q8—91no—
740C4⋊Q8—92no—
741C4⋊Q8—92no—
742C4⋊Q8—92no—
743#125—32no—
744#125—92no—
745#125—92no—
746#125—92no—
747#125—92no—
748#125—92no—
749C22⋊Q8—32no—
750C22⋊Q8—31no—
751C22⋊Q8—31no—
752C22⋊Q8—32no—
753C22⋊Q8—32no—
754C22⋊Q8—32no—
755C22⋊Q8—32no—
756C22⋊Q8—32no—
757C22⋊Q8—92no—
758C22⋊Q8—92no—
759C22⋊Q8—92no—
760C22⋊Q8—92no—
761C22⋊Q8—92no—
762C22⋊Q8—92no—
763C22⋊Q8—92no—
764C22⋊Q8—92no—
765C22⋊Q8—92no—
766C22⋊Q8—92no—
767C22⋊Q8—92no—
768C22⋊Q8—92no—
769C22⋊Q8—92no—
770C22⋊Q8—92no—
771C22⋊Q8—92no—
772C22⋊Q8—92no—
773C22⋊Q8—92no—
774C22⋊Q8—92no—
775C22⋊Q8—92no—
776C22⋊Q8—92no—
777C22⋊Q8—91no—
778C22⋊Q8—92no—
779C22⋊Q8—92no—
780C22⋊Q8—92no—
781C22⋊Q8—92no—
782C22⋊Q8D3211yescharacteristic
783C4×Q8—31no—
784C4×Q8—32no—
785C4×Q8—31no—
786C4×Q8—92no—
787C4×Q8—91no—
788C4×Q8—91no—
789C4×D4—92no—
790C4×D4—92no—
791C4×D4—92no—
792C4×D4—92no—
793C4×D4—92no—
794C4×D4—92no—
795C4×D4—92no—
796C4×D4—92no—
797C4×D4—92no—
798C4×D4—92no—
799C4×D4—92no—
800C4×D4—92no—
801#117—32no—
802#117—92no—
803C2×C4⋊C4—92no—
804C2×C4⋊C4—92no—
805C2×C4⋊C4—92no—
806C2×C4⋊C4—92no—
807C2×C4⋊C4—92no—
808C2×C4⋊C4—92no—
809C2×C4⋊C4—91no—
810C2×C22⋊C4—31no—
811C2×C22⋊C4—32no—
812C2×C22⋊C4—92no—
813C2×C22⋊C4—92no—
814C2×C22⋊C4—91no—
815C2×C22⋊C4—92no—
816C2×C42—31no—
817C23×C3—21no—
818C23×C3—32no—
819C23×C3—34no—
820C23×C3—121no—
821C23×C3—121no—
822C23×C3C23×D311yescharacteristic
823C23×C3C23×D311yescharacteristic
824C22×D3—32no—
825C22×D3—32no—
826C22×D3—34no—
827C22×D3—34no—
828C22×D3—41no—
829C22×D3—41no—
830C22×D3—62no—
831C22×D3—64no—
832C22×D3—121no—
833C22×D3—121no—
834C22×D3—121no—
835C22×D3—121no—
836C22×D3—241no—
837C22×D3—241no—
838C22×D3D3×Q814yescomplemented
839C22×D3C23×D312yes—
840C3×Q8—41no—
841C3×Q8—41no—
842C3×Q8—64no—
843C3×Q8—81no—
844C3×Q8—122no—
845C3×Q8—121no—
846C3×Q8—121no—
847C2×C3×C4—21no—
848C2×C3×C4—22no—
849C2×C3×C4—22no—
850C2×C3×C4—21no—
851C2×C3×C4—34no—
852C2×C3×C4—31no—
853C2×C3×C4—31no—
854C2×C3×C4—31no—
855C2×C3×C4—32no—
856C2×C3×C4—32no—
857C2×C3×C4—32no—
858C2×C3×C4—31no—
859C2×C3×C4—32no—
860C2×C3×C4—32no—
861C2×C3×C4—41no—
862C2×C3×C4—41no—
863C2×C3×C4—62no—
864C2×C3×C4—81no—
865C2×C3×C4—122no—
866C2×C3×C4—122no—
867C2×C3×C4—121no—
868C2×C3×C4C23×D311yescharacteristic
869C2×C3×C4C23×D311yescharacteristic
870C2×C3×C4C23×D312yes—
871C2×C3×C4C23×D312yes—
872C2×C3×C4C23×D311yescharacteristic
873C2×C3×C4C23×D312yes—
874C2×C3×C4C23×D312yes—
875C2×C3×C4C23×D311yescharacteristic
876#67—38no—
877#67—38no—
878C2×Dic3—22no—
879C2×Dic3—32no—
880C2×Dic3—32no—
881C2×Dic3—32no—
882C2×Dic3—32no—
883C2×Dic3—32no—
884C2×Dic3—32no—
885C2×Dic3—41no—
886C2×Dic3—62no—
887C2×Dic3—62no—
888C2×Dic3—62no—
889C2×Dic3—64no—
890C2×Dic3—122no—
891C2×Dic3—122no—
892C2×Dic3—122no—
893C2×Dic3—121no—
894C2×Dic3—121no—
895C2×Dic3—241no—
896C2×Dic3D3×Q814yescomplemented
897C2×Dic3C23×D312yes—
898C2×Dic3C23×D312yes—
899C2×Dic3C23×D311yescharacteristic
900C2×Dic3C23×D312yes—
901C2×Dic3C23×D312yes—
902C2×Dic3C23×D312yes—
903C2×Dic3C23×D311yescharacteristic
904C2×Dic3C23×D311yescharacteristic
905C2×Dic3C23×D311yescharacteristic
906D12—38no—
907D12—38no—
908C4×D3—42no—
909C4×D3—42no—
910C4×D3—64no—
911C4×D3—64no—
912C4×D3—64no—
913C4×D3—122no—
914C4×D3—122no—
915C4×D3—122no—
916C4×D3—122no—
917C4×D3—122no—
918C4×D3—122no—
919C4×D3—122no—
920C4×D3—122no—
921C4×D3—122no—
922C4×D3—122no—
923C4×D3—122no—
924C4×D3—122no—
925C4×D3—122no—
926C4×D3—242no—
927C4×D3—242no—
928Dic6—24no—
929Dic6—41no—
930Dic6—41no—
931Dic6—42no—
932Dic6—64no—
933Dic6—64no—
934Dic6—122no—
935Dic6—122no—
936Dic6—122no—
937Dic6—122no—
938Dic6—121no—
939Dic6—121no—
940Dic6—122no—
941Dic6—122no—
942Dic6—242no—
943Dic6—241no—
944C2×C32—22no—
945C2×C32C23×Q811yescharacteristic
946C2×C32C2×H(5,𝔽2)11yescharacteristic
947C2×C32#58511yescharacteristic
948C3⋊D3—24no—
949C3×D3—24no—
950C24—31no—
951C24—91no—
952C2×Q8—32no—
953C2×Q8—31no—
954C2×Q8—31no—
955C2×Q8—32no—
956C2×Q8—92no—
957C2×Q8—92no—
958C2×Q8—92no—
959C2×Q8—91no—
960C2×Q8—92no—
961C2×Q8—364no—
962C2×Q8—364no—
963C2×Q8C2×D3211yescharacteristic
964C2×D4—92no—
965C2×D4—92no—
966C2×D4—98no—
967C22×C4—31no—
968C22×C4—31no—
969C22×C4—31no—
970C22×C4—32no—
971C22×C4—32no—
972C22×C4—92no—
973C22×C4—92no—
974C22×C4—92no—
975C22×C4—92no—
976C22×C4—92no—
977C22×C4—92no—
978C22×C4—92no—
979C22×C4—92no—
980C22×C4—91no—
981C22×C4—92no—
982C22×C4—92no—
983C22×C4—362no—
984C22×C4—362no—
985C22×C4C2×D3211yescharacteristic
986C4⋊C4—32no—
987C4⋊C4—32no—
988C4⋊C4—32no—
989C4⋊C4—32no—
990C4⋊C4—32no—
991C4⋊C4—32no—
992C4⋊C4—32no—
993C4⋊C4—32no—
994C4⋊C4—32no—
995C4⋊C4—31no—
996C4⋊C4—32no—
997C4⋊C4—31no—
998C4⋊C4—92no—
999C4⋊C4—92no—
1000C4⋊C4—92no—
1001C4⋊C4—92no—
1002C4⋊C4—92no—
1003C4⋊C4—92no—
1004C4⋊C4—92no—
1005C4⋊C4—92no—
1006C4⋊C4—92no—
1007C4⋊C4—92no—
1008C4⋊C4—92no—
1009C4⋊C4—92no—
1010C4⋊C4—92no—
1011C4⋊C4—92no—
1012C4⋊C4—92no—
1013C4⋊C4—92no—
1014C4⋊C4—92no—
1015C4⋊C4—91no—
1016C4⋊C4C2×D3212yes—
1017C4⋊C4C2×D3211yescharacteristic
1018C22⋊C4—32no—
1019C22⋊C4—32no—
1020C22⋊C4—32no—
1021C22⋊C4—32no—
1022C22⋊C4—32no—
1023C22⋊C4—32no—
1024C22⋊C4—92no—
1025C22⋊C4—92no—
1026C22⋊C4—92no—
1027C22⋊C4—92no—
1028C22⋊C4—92no—
1029C22⋊C4—92no—
1030C22⋊C4—92no—
1031C22⋊C4—92no—
1032C22⋊C4—92no—
1033C22⋊C4C2×D3212yes—
1034C42—31no—
1035C42—31no—
1036C42—31no—
1037C42—31no—
1038C42—32no—
1039C42—32no—
1040C42—92no—
1041C42—92no—
1042C22×C3—21no—
1043C22×C3—21no—
1044C22×C3—21no—
1045C22×C3—21no—
1046C22×C3—22no—
1047C22×C3—21no—
1048C22×C3—34no—
1049C22×C3—41no—
1050C22×C3—41no—
1051C22×C3—62no—
1052C22×C3—62no—
1053C22×C3—124no—
1054C22×C3C2×D3×Q812yes—
1055C22×C3C2×D3×Q812yes—
1056C22×C3C24×D311yescharacteristic
1057C22×C3C24×D311yescharacteristic
1058C2×D3—22no—
1059C2×D3—22no—
1060C2×D3—34no—
1061C2×D3—34no—
1062C2×D3—44no—
1063C2×D3—64no—
1064C2×D3—62no—
1065C2×D3—62no—
1066C2×D3—62no—
1067C2×D3—62no—
1068C2×D3—122no—
1069C2×D3—122no—
1070C2×D3—124no—
1071C2×D3—124no—
1072C2×D3—244no—
1073C2×D3C2×D3×Q814yes—
1074C3×C4—22no—
1075C3×C4—21no—
1076C3×C4—21no—
1077C3×C4—22no—
1078C3×C4—22no—
1079C3×C4—21no—
1080C3×C4—22no—
1081C3×C4—21no—
1082C3×C4—32no—
1083C3×C4—32no—
1084C3×C4—32no—
1085C3×C4—42no—
1086C3×C4—41no—
1087C3×C4—42no—
1088C3×C4—41no—
1089C3×C4—62no—
1090C3×C4—62no—
1091C3×C4—62no—
1092C3×C4—62no—
1093C3×C4—61no—
1094C3×C4—62no—
1095Dic3—22no—
1096Dic3—21no—
1097Dic3—22no—
1098Dic3—22no—
1099Dic3—22no—
1100Dic3—22no—
1101Dic3—62no—
1102Dic3—62no—
1103Dic3—62no—
1104Dic3—62no—
1105Dic3—62no—
1106Dic3—62no—
1107Dic3—122no—
1108Dic3—122no—
1109Dic3—122no—
1110Dic3C2×D3×Q812yes—
1111Dic3C2×D3×Q812yes—
1112Dic3#100912yes—
1113C32#350111yescharacteristic, complemented, Sylow
1114C23—32no—
1115C23—34no—
1116C23—92no—
1117C23—94no—
1118C23—121no—
1119C23—121no—
1120C23—361no—
1121C23—361no—
1122C23C22×D3211yescharacteristic
1123Q8—41no—
1124Q8—64no—
1125Q8—122no—
1126Q8—121no—
1127Q8—121no—
1128Q8—184no—
1129Q8—362no—
1130Q8—361no—
1131Q8—362no—
1132Q8—362no—
1133D4—98no—
1134D4—98no—
1135C2×C4—34no—
1136C2×C4—31no—
1137C2×C4—31no—
1138C2×C4—31no—
1139C2×C4—31no—
1140C2×C4—32no—
1141C2×C4—32no—
1142C2×C4—32no—
1143C2×C4—32no—
1144C2×C4—32no—
1145C2×C4—41no—
1146C2×C4—62no—
1147C2×C4—92no—
1148C2×C4—92no—
1149C2×C4—92no—
1150C2×C4—122no—
1151C2×C4—122no—
1152C2×C4—121no—
1153C2×C4—184no—
1154C2×C4—184no—
1155C2×C4—362no—
1156C2×C4—362no—
1157C2×C4—362no—
1158C2×C4—362no—
1159C2×C4—362no—
1160C2×C4—362no—
1161C2×C4—362no—
1162C2×C4—362no—
1163C2×C4—361no—
1164C2×C4C22×D3211yescharacteristic
1165C2×C4C22×D3211yescharacteristic
1166C2×C4C22×D3212yes—
1167C2×C4C22×D3212yes—
1168C2×C3—22no—
1169C2×C3—22no—
1170C2×C3—21no—
1171C2×C3—21no—
1172C2×C3—21no—
1173C2×C3—42no—
1174C2×C3—64no—
1175C2×C3C22×D3×Q811yescharacteristic
1176C2×C3C22×D3×Q811yescharacteristic
1177C2×C3C2×#100911yescharacteristic
1178C2×C3#596411yescharacteristic
1179C2×C3D3×H(5,𝔽2)11yescharacteristic
1180C2×C3#596611yescharacteristic
1181D3—24no—
1182D3—64no—
1183D3—64no—
1184D3—124no—
1185C22—21no—
1186C22—21no—
1187C22—34no—
1188C22—62no—
1189C22—62no—
1190C22—94no—
1191C22—124no—
1192C22—182no—
1193C22—182no—
1194C22—364no—
1195C22D32×Q812yes—
1196C22C23×D3211yescharacteristic
1197C4—21no—
1198C4—21no—
1199C4—22no—
1200C4—22no—
1201C4—32no—
1202C4—32no—
1203C4—32no—
1204C4—62no—
1205C4—62no—
1206C4—61no—
1207C4—62no—
1208C4—62no—
1209C4—62no—
1210C4—182no—
1211C4—182no—
1212C4—182no—
1213C3—21no—
1214C3#8628011yescharacteristic, complemented
1215C3#8657411yescharacteristic, complemented
1216C2—22no—
1217C2—64no—
1218C2—184no—
1219C2#1059667811yescharacteristic
1220C2C2×D32×Q811yescharacteristic
1221C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
prime radicalC22×#626C22
hypercenterC22⋊Q8D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596105C2semidirect
2. C3×#5634C2semidirect
3. C3×#5622C2semidirect
4. #10595372C2semidirect
5. #10595371C2semidirect
6. #10594981C2semidirect
7. #10594971C2semidirect
9. #10594808C2semidirect
10. #10594396C2semidirect
11. #10594395C2semidirect
12. #10594392C2semidirect
13. #10594392C2semidirect
14. #10594383C2semidirect
15. #10594378C2semidirect
17. #10594067C2semidirect
18. D3×#878C2semidirect
19. #10594035C2semidirect
25. C2×#3797C22semidirect
26. C2×D3×Dic6C22semidirect
28. #64155C22semidirect
31. #64106C22semidirect
32. #64105C22semidirect
33. #64105C22semidirect
36. C3×#946C22semidirect
37. C3×Q8×Dic3C22semidirect
38. C3×#944C22semidirect
43. C3×#897C22semidirect
44. C3×#896C22semidirect
45. C3×#896C22semidirect
46. C3×#889C22semidirect
47. C3×#888C22semidirect
48. C3×#887C22semidirect
49. C3×#887C22semidirect
61. #63918C22semidirect
62. #63918C22semidirect
67. #63900C22semidirect
68. #63899C22semidirect
69. #63899C22semidirect
70. #63896C22semidirect
71. #63896C22semidirect
72. #63895C22semidirect
73. #63895C22semidirect
74. #63895C22semidirect
75. #63895C22semidirect
76. #63893C22semidirect
77. #63893C22semidirect
78. D3×C4⋊Dic3C22semidirect
79. #63888C22semidirect
80. #63888C22semidirect
81. #63888C22semidirect
82. #63888C22semidirect
83. #63887C22semidirect
84. #63887C22semidirect
85. #63883C22semidirect
86. #63883C22semidirect
95. D3×Dic3⋊C4C22semidirect
96. D3×Dic3⋊C4C22semidirect
97. #63867C22semidirect
98. #63867C22semidirect
99. #63867C22semidirect
100. #63866C22semidirect
101. #63866C22semidirect
102. #63846C22semidirect
103. #63845C22semidirect
104. #63844C22semidirect
105. Dic3×Dic6C22semidirect
106. #63840C22semidirect
107. #63839C22semidirect
108. #63837C22semidirect
127. #5634D3semidirect
135. #5622D3semidirect
169. C2×#626Q8semidirect
282. #946C2×D3semidirect
284. Q8×Dic3C2×D3semidirect
288. #944C2×D3semidirect
320. #897C2×D3semidirect
339. #896C2×D3semidirect
340. #896C2×D3semidirect
361. #889C2×D3semidirect
367. #888C2×D3semidirect
370. #887C2×D3semidirect
371. #887C2×D3semidirect
427. C22×C3⋊D3C2×Q8semidirect
431. C22×C3×D3C2×Q8semidirect
449. C2×C3×Dic3C2×Q8semidirect
468. #626C2×Q8semidirect
469. #626C2×Q8semidirect
838. C22×D3D3×Q8semidirect
896. C2×Dic3D3×Q8semidirect
1113. C32#3501semidirect
1214. C3#86280semidirect
1215. C3#86574semidirect

Maximal subgroups

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

subgroupindex
#105961052
C3×#56342
C3×#56222
#105953722
#105953712
#105949812
#105949712
C2×#638802
#105948082
#105943962
#105943952
#105943922
#105943832
#105943782
#105941822
#105940672
D3×#8782
#105940352
#865743
#862803