Finite Group Databasebeta

← #11906232

Subgroups — #11906232

Order 1152.

2303 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595990C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic
3C3×#5517C211yesmaximal, characteristic, complemented
4#10595052C211yesmaximal, characteristic, complemented
5#10595049C211yesmaximal, characteristic, complemented
6#10594982C211yesmaximal, characteristic
7C2×Dic3×D12C211yesmaximal, characteristic
8#10594485C212yesmaximal, complemented
9#10594460C212yesmaximal, complemented
10#10594452C212yesmaximal, complemented
11#10594376C212yesmaximal, complemented
12#10594170C214yesmaximal, complemented
13D3×#878C214yesmaximal, complemented
14#10593960C212yesmaximal, complemented
15#10593929C212yesmaximal, complemented
16#10593929C212yesmaximal, complemented
17Dic6×D12C212yesmaximal, complemented
18#86280—31nomaximal
19#85860—31nomaximal
20C22×C3×D12C2211yescharacteristic
21C22×D3×Dic3C2212yes—
22C2×D3×Dic6C2214yescomplemented
23C32×#117C2211yescharacteristic
24#64135C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26#64099C2212yescomplemented
27#64097C2212yescomplemented
28#64087C2214yes—
29#64079C2212yescomplemented
30#64078C2212yescomplemented
31C3×#926C2211yescharacteristic
32C3×#926C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×#893C2212yes—
35C3×#893C2212yes—
36C3×#890C2211yescharacteristic, complemented
37C3×#890C2211yescharacteristic, complemented
38C3×#888C2211yescharacteristic, complemented
39C3×#888C2211yescharacteristic, complemented
40C3×D3×C22⋊C4C2214yes—
41C3×#878C2212yes—
42C3×#878C2212yes—
43C3×C4×D12C2212yes—
44C3×C4×D12C2212yes—
45C3×C4×Dic6C2212yescomplemented
46C3×C4×Dic6C2212yescomplemented
47#63982C2214yes—
48D3×#217C2214yes—
49#63964C2212yes—
50#63964C2212yes—
51C2×(C2×D3)⋊Dic3C2212yes—
52#63918C2212yescomplemented
53#63918C2211yescharacteristic, complemented
54#63918C2212yescomplemented
55#63918C2211yescharacteristic, complemented
56C4×#627C2212yescomplemented
57C4×#627C2212yescomplemented
58#63899C2214yescomplemented
59#63899C2214yescomplemented
60#63898C2212yes—
61#63898C2212yes—
62#63896C2214yescomplemented
63#63896C2214yescomplemented
64#63893C2214yescomplemented
65#63893C2214yescomplemented
66Dic3×D12C2212yes—
67Dic3×D12C2212yes—
68Dic3×D12C2212yes—
69Dic3×D12C2212yes—
70Dic3×D12C2212yes—
71Dic3×D12C2212yes—
72D3×C4⋊Dic3C2214yescomplemented
73#63887C2214yescomplemented
74#63887C2214yescomplemented
75D3×Dic3⋊C4C2214yescomplemented
76D3×Dic3⋊C4C2214yescomplemented
77#63869C2211yescharacteristic, complemented
78#63869C2212yescomplemented
79#63869C2212yescomplemented
80#63869C2211yescharacteristic, complemented
81#63857C2214yescomplemented
82#63856C2214yescomplemented
83#63851C2214yescomplemented
84#63851C2214yescomplemented
85C3×#533—31no—
86C3×#518—31no—
87#5798—31no—
88C2×D4×Dic3—31no—
89#5730—32no—
90#5727—32no—
91#5690—32no—
92#5690—32no—
93#5634—34no—
94D3×C22⋊Q8—34no—
95#5579—32no—
96#5579—32no—
97#5579—32no—
98Q8×D12—32no—
99#5543—32no—
100#5543—32no—
101#5539—32no—
102#5539—32no—
103#5539—32no—
104#5539—32no—
105D4×Dic6—32no—
106D4×Dic6—32no—
107#5521—31no—
108#5521D311yescharacteristic
109#5519—31no—
110#5519—31no—
111#5519—31no—
112#5519—31no—
113#5519—61no—
114#5517—31no—
115#5517D311yescharacteristic, complemented
116#5483—34no—
117C2×#878—34no—
118C2×C4×D12—31no—
119#5470—31no—
120C23×C3×D3C2312yes—
121C22×C32×C4C2311yescharacteristic
122C22×C3⋊Dic3C2312yes—
123C2×#634C2314yes—
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C2×C3×D12Q818yescomplemented
127C2×C3×D12C2312yes—
128C2×C3×D12C2312yes—
129C2×C3×C4×D3C2314yes—
130C2×C3×C4×D3C2314yes—
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2312yes—
133C2×#627C2312yes—
134C2×#627C2314yes—
135C2×#627C2312yes—
136C2×D3×Dic3—44no—
137C2×D3×Dic3C2314yes—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141D3×Dic6—48no—
142C32×C4⋊C4C2311yescharacteristic
143C32×C4⋊C4C2311yescharacteristic
144C32×C22⋊C4C2312yes—
145C32×C42C2312yes—
146#3757C2312yes—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2312yes—
149C4⋊(C3⋊Dic3)C2314yes—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C4⋊(C3⋊Dic3)C2312yes—
152#3750C2314yes—
153#3750C2314yes—
154C4×C3⋊Dic3C2312yes—
155C3×#217C2312yes—
156C3×#217C2312yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×C4⋊Dic3C2312yes—
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2311yescharacteristic
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2311yescharacteristic
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2312yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2312yes—
175#3724C2312yes—
176#3724C2314yes—
177#3724C2312yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2312yes—
183Dic3⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2314yes—
188#3501—91noSylow
189C22×C3×D4—31no—
190C23×Dic3—32no—
191C2×D3×Q8—34no—
192C22×D12C2×D311yescharacteristic
193C22×C4×D3—32no—
194C22×Dic6—34no—
195C3×C4⋊Q8—31no—
196C3×C4⋊Q8—31no—
197C3×#125—31no—
198C3×#125—31no—
199C3×C22⋊Q8—32no—
200C3×C22⋊Q8—32no—
201C3×C4×Q8—32no—
202C3×C4×Q8—32no—
203C3×C4×D4—32no—
204C3×C4×D4—32no—
205C3×C4×D4—32no—
206C3×C4×D4—32no—
207C3×#117—21no—
208C3×#117—31no—
209C3×#117—31no—
210C3×#117C2×D311yescharacteristic
211C3×#117C2×D311yescharacteristic
212C2×C3×C22⋊C4—34no—
213C2×C3×C42—31no—
214C2×#217—32no—
215C2×#217—34no—
216#946—34no—
217#946—34no—
218#946—34no—
219D4×Dic3—32no—
220D4×Dic3—32no—
221D4×Dic3—32no—
222D4×Dic3—32no—
223D4×Dic3—32no—
224D4×Dic3—32no—
225D4×Dic3—32no—
226D4×Dic3—32no—
227C2×(C2×D3)⋊C4—32no—
228#926—31no—
229#926—31no—
230#926—61no—
231#926C2×D311yescharacteristic
232#926C2×D311yescharacteristic
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3—31no—
235C2×C4⋊Dic3—34no—
236C2×C4⋊Dic3—61no—
237#924—34no—
238#924—32no—
239#924—32no—
240#924—34no—
241#924—34no—
242#924—34no—
243C2×Dic3⋊C4—34no—
244C2×Dic3⋊C4—34no—
245C2×C4×Dic3C2×D311yescharacteristic
246#897—34no—
247#897—34no—
248#897—34no—
249#896—34no—
250#896—34no—
251#896—34no—
252#896—34no—
253#896—34no—
254#896—34no—
255#893—32no—
256#893—32no—
257#893C2×D312yes—
258#893C2×D312yes—
259D3×C4⋊C4—34no—
260D3×C4⋊C4—34no—
261D3×C4⋊C4—34no—
262#890—32no—
263#890—32no—
264#890—32no—
265#890—31no—
266#890—31no—
267#890—32no—
268#890—62no—
269#890C2×D311yescharacteristic, complemented
270#890C2×D311yescharacteristic, complemented
271#888—32no—
272#888—32no—
273#888—32no—
274#888—31no—
275#888—31no—
276#888—32no—
277#888—62no—
278#888C2×D311yescharacteristic, complemented
279#888C2×D311yescharacteristic, complemented
280D3×C22⋊C4—34no—
281D3×C22⋊C4C2×D314yes—
282#878—32no—
283#878—32no—
284#878—34no—
285#878—34no—
286#878—34no—
287#878—34no—
288#878—34no—
289#878—34no—
290#878—34no—
291#878—34no—
292#878—34no—
293#878—34no—
294#878—34no—
295#878—34no—
296#878—64no—
297#878C2×D312yes—
298#878C2×D312yes—
299C4×D12—32no—
300C4×D12—32no—
301C4×D12—32no—
302C4×D12—32no—
303C4×D12—32no—
304C4×D12—32no—
305C4×D12C2×D312yes—
306C4×D12C2×D312yes—
307#870—32no—
308#870—32no—
309#870—31no—
310#870—31no—
311#870—32no—
312#870—32no—
313#870—62no—
314#869—32no—
315#869—32no—
316#869—31no—
317#869—31no—
318#869—32no—
319#869—32no—
320#869—62no—
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6C2×D312yescomplemented
326C4×Dic6C2×D312yescomplemented
327C23×C32C2411yescharacteristic
328C22×C3×D3—42no—
329C22×C3×D3—42no—
330C22×C3×D3C2×Q818yescomplemented
331C22×C3×D3C2414yes—
332C2×C32×C4C2×Q814yescomplemented
333C2×C32×C4C2412yes—
334C2×C32×C4C2412yes—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3—42no—
338C2×C3⋊Dic3C2412yes—
339C2×C3⋊Dic3C2412yes—
340C2×C3⋊Dic3C2414yes—
341#634—44no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—41no—
344C2×C3×Dic3C2411yescharacteristic
345C2×C3×Dic3C2411yescharacteristic
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2411yescharacteristic
351C2×C3×Dic3C2411yescharacteristic
352C3×D12C2×Q818yescomplemented
353C3×D12C2×Q818yescomplemented
354C3×C4×D3—44no—
355C3×C4×D3—44no—
356C3×Dic6—24no—
357C3×Dic6—42no—
358#627—24no—
359#627—44no—
360#627—42no—
361D3×Dic3—28no—
362D3×Dic3—44no—
363D3×Dic3—44no—
364D3×Dic3—44no—
365#554—92no—
366#554—92no—
367#554—92no—
368#554—92no—
369#554—92no—
370#554—92no—
371D4×Q8—92no—
372D4×Q8—92no—
373#544—91no—
374#544—91no—
375#543—94no—
376#533—31no—
377#533—91no—
378C2×C22⋊Q8—94no—
379#518—31no—
380#518—91no—
381C2×C4×D4—91no—
382C24×C3—32no—
383C23×D3C22×D312yes—
384C2×C3×Q8—32no—
385C2×C3×Q8—32no—
386C2×C3×D4—38no—
387C2×C3×D4—32no—
388C2×C3×D4—32no—
389C22×C3×C4—21no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—34no—
393C22×C3×C4—34no—
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C22×Dic3—32no—
397C22×Dic3—32no—
398C22×Dic3—34no—
399C22×Dic3—34no—
400C22×Dic3—34no—
401C22×Dic3—34no—
402C22×Dic3—62no—
403C22×Dic3—124no—
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406D3×Q8—128no—
407C2×D12Dic618yescomplemented
408C2×D12C22×D312yes—
409C2×D12C22×D312yes—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—124no—
415C2×C4×D3C22×D314yes—
416C2×C4×D3C22×D314yes—
417C2×Dic6—32no—
418C2×Dic6—32no—
419C2×Dic6—34no—
420C2×Dic6—34no—
421C2×Dic6—32no—
422C2×Dic6—32no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—64no—
426C2×Dic6—128no—
427C2×Dic6C22×D312yes—
428C2×Dic6C22×D312yes—
429C3×C4⋊C4—21no—
430C3×C4⋊C4—21no—
431C3×C4⋊C4—31no—
432C3×C4⋊C4—31no—
433C3×C4⋊C4—31no—
434C3×C4⋊C4—31no—
435C3×C4⋊C4—32no—
436C3×C4⋊C4—32no—
437C3×C4⋊C4—32no—
438C3×C4⋊C4—32no—
439C3×C4⋊C4—32no—
440C3×C4⋊C4—32no—
441C3×C4⋊C4C22×D311yescharacteristic
442C3×C4⋊C4C22×D311yescharacteristic
443C3×C4⋊C4C22×D311yescharacteristic
444C3×C4⋊C4C22×D311yescharacteristic
445C3×C22⋊C4—22no—
446C3×C22⋊C4—32no—
447C3×C22⋊C4—32no—
448C3×C22⋊C4—34no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4C22×D312yes—
451C3×C22⋊C4C22×D312yes—
452C3×C42—22no—
453C3×C42—32no—
454C3×C42—31no—
455C3×C42—31no—
456C3×C42—31no—
457C3×C42—32no—
458C3×C42—31no—
459C3×C42C22×D312yes—
460C3×C42C22×D312yes—
461#217—32no—
462#217—32no—
463#217—34no—
464#217—34no—
465#217—34no—
466#217—34no—
467#217—62no—
468#217C22×D312yes—
469#217C22×D312yes—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4C22×D314yes—
475(C2×D3)⋊C4C22×D314yes—
476C4⋊Dic3—31no—
477C4⋊Dic3—32no—
478C4⋊Dic3—31no—
479C4⋊Dic3—31no—
480C4⋊Dic3—32no—
481C4⋊Dic3—32no—
482C4⋊Dic3—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3—31no—
485C4⋊Dic3—32no—
486C4⋊Dic3—32no—
487C4⋊Dic3—32no—
488C4⋊Dic3—32no—
489C4⋊Dic3—32no—
490C4⋊Dic3—34no—
491C4⋊Dic3—34no—
492C4⋊Dic3—61no—
493C4⋊Dic3—62no—
494C4⋊Dic3—64no—
495C4⋊Dic3—61no—
496C4⋊Dic3—62no—
497C4⋊Dic3C22×D312yes—
498C4⋊Dic3C22×D312yes—
499C4⋊Dic3C22×D311yescharacteristic
500C4⋊Dic3C22×D311yescharacteristic
501C4⋊Dic3C22×D311yescharacteristic
502C4⋊Dic3C22×D311yescharacteristic
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—32no—
508Dic3⋊C4—32no—
509Dic3⋊C4—32no—
510Dic3⋊C4—32no—
511Dic3⋊C4—32no—
512Dic3⋊C4—32no—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4—64no—
520Dic3⋊C4—64no—
521Dic3⋊C4C22×D312yes—
522Dic3⋊C4C22×D312yes—
523Dic3⋊C4C22×D312yes—
524Dic3⋊C4C22×D312yes—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—62no—
528C4×Dic3C22×D312yes—
529C4×Dic3C22×D311yescharacteristic
530C4×Dic3C22×D311yescharacteristic
531C4×Dic3C22×D311yescharacteristic
532C4×Dic3C22×D312yes—
533C4×Dic3C22×D311yescharacteristic
534C22×C32—21no—
535C22×C32—21no—
536C22×C32C22×Q812yes—
537C22×C32C2511yescharacteristic
538C2×C3×D3—24no—
539C2×C3×D3—24no—
540C2×C3×D3—48no—
541C2×C3×D3C22×Q818yes—
542C32×C4—22no—
543C32×C4—22no—
544C32×C4C22×Q812yes—
545C32×C4C22×Q812yes—
546C3⋊Dic3—24no—
547C3⋊Dic3—22no—
548C3⋊Dic3—22no—
549C3×Dic3—21no—
550C3×Dic3—22no—
551C3×Dic3—22no—
552C3×Dic3—22no—
553C3×Dic3—21no—
554C3×Dic3—22no—
555C3×Dic3—21no—
556C3×Dic3H(5,𝔽2)12yes—
557C22×Q8—94no—
558C22×D4—31no—
559C23×C4—92no—
560C4⋊Q8—31no—
561C4⋊Q8—31no—
562C4⋊Q8—91no—
563C4⋊Q8—91no—
564C4⋊Q8—92no—
565C4⋊Q8—92no—
566C4⋊Q8—92no—
567C4⋊Q8—92no—
568#125—31no—
569#125—31no—
570#125—91no—
571#125—91no—
572#125—92no—
573#125—92no—
574#125—92no—
575#125—92no—
576C22⋊Q8—32no—
577C22⋊Q8—32no—
578C22⋊Q8—94no—
579C22⋊Q8—94no—
580C22⋊Q8—94no—
581C22⋊Q8—94no—
582C22⋊Q8—94no—
583C22⋊Q8—94no—
584C22⋊Q8—94no—
585C22⋊Q8—92no—
586C22⋊Q8—92no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—94no—
594C4×Q8—32no—
595C4×Q8—32no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×D4—32no—
599C4×D4—32no—
600C4×D4—32no—
601C4×D4—32no—
602C4×D4—92no—
603C4×D4—92no—
604C4×D4—92no—
605C4×D4—92no—
606C4×D4—92no—
607C4×D4—92no—
608C4×D4—92no—
609C4×D4—92no—
610#117—31no—
611#117—31no—
612#117—91no—
613#117D3211yescharacteristic
614C2×C4⋊C4—94no—
615C2×C4⋊C4—94no—
616C2×C4⋊C4—94no—
617C2×C4⋊C4—91no—
618C2×C22⋊C4—34no—
619C2×C22⋊C4—94no—
620C2×C22⋊C4—92no—
621C2×C42—31no—
622C23×C3—21no—
623C23×C3—34no—
624C23×C3—38no—
625C23×C3—122no—
626C23×C3—122no—
627C23×C3C23×D311yescharacteristic
628C23×C3C23×D311yescharacteristic
629C22×D3—42no—
630C22×D3—42no—
631C22×D3C2×Dic618yescomplemented
632C22×D3C23×D314yes—
633C3×Q8—64no—
634C3×Q8—122no—
635C3×D4—38no—
636C3×D4—38no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—24no—
642C2×C3×C4—31no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—31no—
646C2×C3×C4—31no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—31no—
650C2×C3×C4—62no—
651C2×C3×C4—124no—
652C2×C3×C4—124no—
653C2×C3×C4—121no—
654C2×C3×C4C2×Dic614yescomplemented
655C2×C3×C4D3×Q814yescomplemented
656C2×C3×C4C23×D312yes—
657C2×C3×C4C23×D312yes—
658C2×C3×C4C23×D312yes—
659C2×C3×C4C23×D312yes—
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664C2×Dic3—22no—
665C2×Dic3—32no—
666C2×Dic3—32no—
667C2×Dic3—32no—
668C2×Dic3—32no—
669C2×Dic3—34no—
670C2×Dic3—34no—
671C2×Dic3—41no—
672C2×Dic3—62no—
673C2×Dic3—62no—
674C2×Dic3—64no—
675C2×Dic3—68no—
676C2×Dic3—124no—
677C2×Dic3—124no—
678C2×Dic3—124no—
679C2×Dic3—122no—
680C2×Dic3—122no—
681C2×Dic3—242no—
682C2×Dic3C23×D311yescharacteristic
683C2×Dic3C23×D311yescharacteristic
684C2×Dic3C23×D311yescharacteristic
685C2×Dic3C23×D312yes—
686C2×Dic3C23×D312yes—
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D311yescharacteristic
690D12C2×Dic618yescomplemented
691D12C2×Dic618yescomplemented
692C4×D3—44no—
693C4×D3—44no—
694C4×D3—68no—
695C4×D3—124no—
696C4×D3—124no—
697C4×D3—124no—
698Dic6—24no—
699Dic6—42no—
700Dic6—64no—
701Dic6—64no—
702Dic6—122no—
703Dic6—122no—
704Dic6—124no—
705Dic6—124no—
706Dic6—124no—
707Dic6—124no—
708Dic6—244no—
709C2×C32—22no—
710C2×C32C23×Q811yescharacteristic
711C2×C32C2×H(5,𝔽2)11yescharacteristic
712C2×C32#58511yescharacteristic
713C3×D3—28no—
714C24—32no—
715C2×Q8—32no—
716C2×Q8—32no—
717C2×Q8—92no—
718C2×Q8—92no—
719C2×Q8—94no—
720C2×Q8—94no—
721C2×Q8—368no—
722C2×D4—32no—
723C2×D4—32no—
724C2×D4—38no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—34no—
728C22×C4—34no—
729C22×C4—94no—
730C22×C4—94no—
731C22×C4—94no—
732C22×C4—94no—
733C22×C4—92no—
734C22×C4—364no—
735C22×C4C2×D3211yescharacteristic
736C4⋊C4—32no—
737C4⋊C4—32no—
738C4⋊C4—32no—
739C4⋊C4—31no—
740C4⋊C4—31no—
741C4⋊C4—31no—
742C4⋊C4—31no—
743C4⋊C4—32no—
744C4⋊C4—32no—
745C4⋊C4—32no—
746C4⋊C4—92no—
747C4⋊C4—92no—
748C4⋊C4—92no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4—92no—
753C4⋊C4—92no—
754C4⋊C4—92no—
755C4⋊C4—92no—
756C4⋊C4—92no—
757C4⋊C4—94no—
758C4⋊C4—94no—
759C4⋊C4—94no—
760C4⋊C4—91no—
761C4⋊C4—91no—
762C4⋊C4C2×D3211yescharacteristic
763C4⋊C4C2×D3211yescharacteristic
764C22⋊C4—32no—
765C22⋊C4—32no—
766C22⋊C4—34no—
767C22⋊C4—34no—
768C22⋊C4—94no—
769C22⋊C4—94no—
770C22⋊C4—94no—
771C22⋊C4—94no—
772C22⋊C4—92no—
773C22⋊C4C2×D3212yes—
774C42—31no—
775C42—31no—
776C42—31no—
777C42—31no—
778C42—32no—
779C42—32no—
780C42—92no—
781C42C2×D3212yes—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—22no—
787C22×C3—21no—
788C22×C3—38no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—64no—
792C22×C3—64no—
793C22×C3—128no—
794C22×C3C22×Dic612yes—
795C22×C3C2×D3×Q812yes—
796C22×C3C24×D311yescharacteristic
797C22×C3C24×D311yescharacteristic
798C2×D3—24no—
799C2×D3—24no—
800C2×D3—48no—
801C2×D3C22×Dic618yes—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—32no—
809C3×C4—42no—
810C3×C4—42no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—62no—
814C3×C4—61no—
815C3×C4—61no—
816C3×C4—62no—
817C3×C4—61no—
818C3×C4C22×Dic612yes—
819C3×C4C22×Dic612yes—
820C3×C4C2×D3×Q812yes—
821C3×C4C2×D3×Q812yes—
822Dic3—22no—
823Dic3—21no—
824Dic3—21no—
825Dic3—22no—
826Dic3—21no—
827Dic3—22no—
828Dic3—22no—
829Dic3—62no—
830Dic3—64no—
831Dic3—62no—
832Dic3—62no—
833Dic3—64no—
834Dic3—62no—
835Dic3—122no—
836Dic3—124no—
837Dic3—122no—
838Dic3#100912yes—
839C32#350111yescharacteristic, complemented, Sylow
840C23—34no—
841C23—38no—
842C23—122no—
843C23—122no—
844C23C22×D3211yescharacteristic
845Q8—64no—
846Q8—122no—
847Q8—184no—
848Q8—364no—
849Q8—364no—
850Q8—362no—
851D4—38no—
852D4—38no—
853C2×C4—31no—
854C2×C4—31no—
855C2×C4—31no—
856C2×C4—31no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—62no—
862C2×C4—92no—
863C2×C4—92no—
864C2×C4—94no—
865C2×C4—124no—
866C2×C4—124no—
867C2×C4—121no—
868C2×C4—188no—
869C2×C4—364no—
870C2×C4—364no—
871C2×C4—364no—
872C2×C4—362no—
873C2×C4D3×Dic614yescomplemented
874C2×C4C22×D3212yes—
875C2×C4C22×D3212yes—
876C2×C4C22×D3211yescharacteristic
877C2×C4C22×D3211yescharacteristic
878C2×C3—22no—
879C2×C3—22no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—42no—
884C2×C3—68no—
885C2×C3C23×Dic611yescharacteristic
886C2×C3C22×D3×Q811yescharacteristic
887C2×C3C2×#100911yescharacteristic
888C2×C3#596411yescharacteristic
889C2×C3D3×H(5,𝔽2)11yescharacteristic
890C2×C3#596611yescharacteristic
891D3—28no—
892C22—21no—
893C22—21no—
894C22—38no—
895C22—64no—
896C22—64no—
897C22—128no—
898C22C2×D3×Dic612yes—
899C22C23×D3211yescharacteristic
900C4—22no—
901C4—22no—
902C4—32no—
903C4—61no—
904C4—62no—
905C4—62no—
906C4—62no—
907C4—61no—
908C4—61no—
909C4—62no—
910C4—184no—
911C4—182no—
912C4—182no—
913C4C2×D3×Dic612yes—
914C4C2×D3×Dic612yes—
915C3—21no—
916C3#8586011yescharacteristic, complemented
917C3#8628011yescharacteristic, complemented
918C2—22no—
919C2—68no—
920C2C22×D3×Dic611yescharacteristic
921C2D3×#100911yescharacteristic
922C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
prime radicalC22×C3×D12C22
hypercenter#117D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595990C2semidirect
3. C3×#5517C2semidirect
4. #10595052C2semidirect
5. #10595049C2semidirect
8. #10594485C2semidirect
9. #10594460C2semidirect
10. #10594452C2semidirect
11. #10594376C2semidirect
12. #10594170C2semidirect
13. D3×#878C2semidirect
14. #10593960C2semidirect
15. #10593929C2semidirect
16. #10593929C2semidirect
17. Dic6×D12C2semidirect
22. C2×D3×Dic6C22semidirect
26. #64099C22semidirect
27. #64097C22semidirect
29. #64079C22semidirect
30. #64078C22semidirect
36. C3×#890C22semidirect
37. C3×#890C22semidirect
38. C3×#888C22semidirect
39. C3×#888C22semidirect
45. C3×C4×Dic6C22semidirect
46. C3×C4×Dic6C22semidirect
52. #63918C22semidirect
53. #63918C22semidirect
54. #63918C22semidirect
55. #63918C22semidirect
56. C4×#627C22semidirect
57. C4×#627C22semidirect
58. #63899C22semidirect
59. #63899C22semidirect
62. #63896C22semidirect
63. #63896C22semidirect
64. #63893C22semidirect
65. #63893C22semidirect
72. D3×C4⋊Dic3C22semidirect
73. #63887C22semidirect
74. #63887C22semidirect
75. D3×Dic3⋊C4C22semidirect
76. D3×Dic3⋊C4C22semidirect
77. #63869C22semidirect
78. #63869C22semidirect
79. #63869C22semidirect
80. #63869C22semidirect
81. #63857C22semidirect
82. #63856C22semidirect
83. #63851C22semidirect
84. #63851C22semidirect
115. #5517D3semidirect
126. C2×C3×D12Q8semidirect
269. #890C2×D3semidirect
270. #890C2×D3semidirect
278. #888C2×D3semidirect
279. #888C2×D3semidirect
325. C4×Dic6C2×D3semidirect
326. C4×Dic6C2×D3semidirect
330. C22×C3×D3C2×Q8semidirect
332. C2×C32×C4C2×Q8semidirect
352. C3×D12C2×Q8semidirect
353. C3×D12C2×Q8semidirect
407. C2×D12Dic6semidirect
631. C22×D3C2×Dic6semidirect
654. C2×C3×C4C2×Dic6semidirect
655. C2×C3×C4D3×Q8semidirect
690. D12C2×Dic6semidirect
691. D12C2×Dic6semidirect
839. C32#3501semidirect
873. C2×C4D3×Dic6semidirect
916. C3#85860semidirect
917. C3#86280semidirect

Maximal subgroups

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

subgroupindex
#105959902
C3×#55212
C3×#55172
#105950522
#105950492
#105949822
C2×Dic3×D122
#105944852
#105944602
#105944522
#105943762
#105941702
D3×#8782
#105939602
#105939292
Dic6×D122
#862803
#858603