Finite Group Databasebeta

← #11906361

Subgroups — #11906361

Order 1152.

2231 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595988C211yesmaximal, characteristic, complemented
2C3×#5523C211yesmaximal, characteristic
3C3×#5519C211yesmaximal, characteristic, complemented
4#10595051C211yesmaximal, characteristic, complemented
5C2×#63919C211yesmaximal, characteristic, complemented
6#10594986C211yesmaximal, characteristic
7#10594958C211yesmaximal, characteristic
8#10594505C212yesmaximal, complemented
9#10594477C212yesmaximal, complemented
10D3×#888C212yesmaximal, complemented
11#10594342C212yesmaximal, complemented
12#10594156C214yesmaximal, complemented
13#10594071C214yesmaximal, complemented
14#10593941C212yesmaximal, complemented
15#10593904C212yesmaximal, complemented
16#10593856C212yesmaximal, complemented
17#10593853C212yesmaximal, complemented
18#86586—31nomaximal
19#85889—31nomaximal
20C2×C3×#235C2211yescharacteristic
21C22×#627C2212yes—
22C2×D3×Dic6C2214yes—
23C32×#117C2211yescharacteristic
24#64135C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64099C2211yescharacteristic
27#64099C2211yescharacteristic
28#64097C2211yescharacteristic
29#64097C2211yescharacteristic
30#64087C2212yes—
31#64087C2212yes—
32C4×#634C2212yes—
33C4×#634C2212yes—
34C3×#926C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C3×#892C2212yes—
38C3×D3×C4⋊C4C2212yes—
39C3×#890C2212yes—
40C3×#888C2212yes—
41C3×#67⋊C4C2214yes—
42C3×#878C2214yes—
43C3×C4×D12C2212yes—
44C3×#870C2212yes—
45C3×#869C2212yes—
46C3×C4×Dic6C2212yes—
47#67⋊Dic3C2212yes—
48#67⋊Dic3C2212yes—
49Dic3×#67C2214yes—
50C2×#3724C2212yes—
51#63964C2214yes—
52#63919C2212yes—
53#63919C2212yes—
54#63919C2212yes—
55#63919C2212yes—
56#63919C2212yes—
57#63918C2214yes—
58#63918C2212yes—
59#63899C2214yes—
60#63899C2214yes—
61#63898C2211yescharacteristic
62#63898C2212yes—
63#63898C2211yescharacteristic
64#63896C2214yes—
65#63893C2214yes—
66D3×C4⋊Dic3C2212yes—
67D3×Dic3⋊C4C2214yes—
68C4×D3×Dic3C2212yes—
69#63872C2212yes—
70#63869C2212yes—
71#63867C2214yes—
72#63856C2214yes—
73#63855C2212yes—
74#63851C2214yes—
75#63845C2214yes—
76#63844C2214yes—
77#63843C2211yescharacteristic
78#63843C2212yes—
79#63843C2211yescharacteristic
80#63841C2212yes—
81#63840C2214yes—
82#63839C2214yes—
83#63839C2214yes—
84#63837C2214yes—
85C3×#544—31no—
86C3×#520—31no—
87#5827—31no—
88Dic3×#41—31no—
89#5729—32no—
90#5727—32no—
91D3×C4⋊Q8—32no—
92#5722—32no—
93#5690—32no—
94#5689—32no—
95#5688—32no—
96#5685—32no—
97#5636—34no—
98#5632—34no—
99#5569—32no—
100Q8×Dic6—32no—
101#5539—34no—
102#5539—32no—
103D4×Dic6—34no—
104D4×Dic6—32no—
105#5523D311yescharacteristic
106#5522—31no—
107#5519—31no—
108#5519—32no—
109#5519D311yescharacteristic, complemented
110#5517—31no—
111#5517—31no—
112#5517—32no—
113#5517—61no—
114#5504—31no—
115#5500—31no—
116#5500—32no—
117C2×#888—31no—
118C2×#888—31no—
119C2×#888—32no—
120C22×C32×C4C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C22×C3⋊Dic3C2311yescharacteristic
123C2×#634C2312yes—
124C2×#634C2312yes—
125C2×C3×#67C2312yes—
126C22×C3×Dic3C2312yes—
127C22×C3×Dic3C2312yes—
128C3×#235Q818yescomplemented
129C2×C3×D12C2311yescharacteristic
130C2×C3×C4×D3C2314yes—
131C2×C3×C4×D3C2312yes—
132C2×C3×Dic6C2314yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×#627—44no—
135C2×#627C2314yes—
136C2×#627C2314yes—
137C2×#627C2314yes—
138C2×D3×Dic3C2312yes—
139C2×D3×Dic3C2312yes—
140C2×D3×Dic3C2314yes—
141D3×Dic6—48no—
142C32×C4⋊C4C2311yescharacteristic
143C32×C4⋊C4C2311yescharacteristic
144C32×C22⋊C4C2312yes—
145C32×C42C2312yes—
146#3757C2312yes—
147C4⋊(C3⋊Dic3)C2312yes—
148C4⋊(C3⋊Dic3)C2312yes—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151#3750C2312yes—
152#3750C2312yes—
153#3750C2312yes—
154#3750C2312yes—
155C4×C3⋊Dic3C2312yes—
156C4×C3⋊Dic3C2311yescharacteristic
157C4×C3⋊Dic3C2311yescharacteristic
158C4×C3⋊Dic3C2311yescharacteristic
159C4×C3⋊Dic3C2311yescharacteristic
160C3×#217C2312yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×C4⋊Dic3C2314yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2312yes—
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2311yescharacteristic
169C3×Dic3⋊C4C2314yes—
170C3×Dic3⋊C4C2314yes—
171C3×Dic3⋊C4C2314yes—
172C3×C4×Dic3C2314yes—
173C3×C4×Dic3C2312yes—
174#3724C2314yes—
175#3724C2314yes—
176#3724C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2312yes—
188#3503—91noSylow
189C2×C3×#41—31no—
190C2×D3×Q8—34no—
191C2×#235C2×D311yescharacteristic
192C22×Dic6—32no—
193C22×Dic6—32no—
194C22×Dic6—34no—
195C3×C4⋊Q8—32no—
196C3×C4⋊Q8—32no—
197C3×#125—32no—
198C3×#125—32no—
199C3×C22⋊Q8—34no—
200C3×C4×Q8—32no—
201C3×C4×D4—34no—
202C3×C4×D4—32no—
203C3×#117—21no—
204C3×#117—31no—
205C3×#117—32no—
206C3×#117C2×D311yescharacteristic
207C3×#117C2×D311yescharacteristic
208C2×C3×C4⋊C4—31no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—32no—
211#946—34no—
212Q8×Dic3—31no—
213Q8×Dic3—32no—
214Q8×Dic3—31no—
215#944—34no—
216#944—34no—
217D4×Dic3—34no—
218D4×Dic3—32no—
219D4×Dic3—32no—
220D4×Dic3—31no—
221D4×Dic3—32no—
222D4×Dic3—31no—
223C4×#67—34no—
224#926—31no—
225#926—31no—
226#926—32no—
227#926—32no—
228#926—61no—
229#926C2×D311yescharacteristic
230C2×C4⋊Dic3—32no—
231C2×C4⋊Dic3C2×D311yescharacteristic
232C2×C4⋊Dic3C2×D311yescharacteristic
233#924—34no—
234#924—34no—
235#924—34no—
236C2×Dic3⋊C4—32no—
237C2×Dic3⋊C4—32no—
238C2×Dic3⋊C4—34no—
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3—32no—
242C2×C4×Dic3—61no—
243#897—34no—
244#896—34no—
245#896—34no—
246#896—34no—
247#896—34no—
248#893—31no—
249#893—32no—
250#893—31no—
251#892—32no—
252#892C2×D312yes—
253D3×C4⋊C4—34no—
254D3×C4⋊C4—32no—
255D3×C4⋊C4C2×D312yes—
256#890—31no—
257#890—31no—
258#890—31no—
259#890—31no—
260#890—32no—
261#890—32no—
262#890—34no—
263#890—32no—
264#890—61no—
265#890—61no—
266#890C2×D312yes—
267#889—34no—
268#889—34no—
269#888—34no—
270#888—34no—
271#888—31no—
272#888—31no—
273#888—31no—
274#888—31no—
275#888—32no—
276#888—32no—
277#888—32no—
278#888—32no—
279#888—32no—
280#888—32no—
281#888—32no—
282#888—32no—
283#888—32no—
284#888—32no—
285#888—34no—
286#888—34no—
287#888—34no—
288#888—32no—
289#888—61no—
290#888—61no—
291#888C2×D312yes—
292#887—31no—
293#887—32no—
294#887—31no—
295#887—34no—
296#887—34no—
297#67⋊C4—32no—
298#67⋊C4—32no—
299#67⋊C4C2×D314yes—
300#878—34no—
301#878—32no—
302#878—32no—
303#878—32no—
304#878—32no—
305#878—34no—
306#878—34no—
307#878—34no—
308#878—34no—
309#878—62no—
310#878—62no—
311#878C2×D314yes—
312C4×D12C2×D312yes—
313#872—32no—
314C42×D3—32no—
315#870—32no—
316#870—34no—
317#870C2×D312yes—
318#869—32no—
319#869—34no—
320#869C2×D312yes—
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—34no—
326C4×Dic6—34no—
327C4×Dic6—62no—
328C4×Dic6—62no—
329C4×Dic6C2×D312yes—
330C23×C32C2411yescharacteristic
331C22×C3×D3C2412yes—
332C2×C32×C4C2×Q814yescomplemented
333C2×C32×C4C2412yes—
334C2×C32×C4C2412yes—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3—22no—
338C2×C3⋊Dic3—22no—
339C2×C3⋊Dic3C2412yes—
340C2×C3⋊Dic3C2411yescharacteristic
341C2×C3⋊Dic3C2411yescharacteristic
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2411yescharacteristic
344C2×C3⋊Dic3C2411yescharacteristic
345#634—24no—
346#634—24no—
347C3×#67C2×Q818yescomplemented
348C2×C3×Dic3—42no—
349C2×C3×Dic3—42no—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2414yes—
353C2×C3×Dic3C2414yes—
354C2×C3×Dic3C2412yes—
355C3×D12C2×Q814yescomplemented
356C3×C4×D3—44no—
357C3×C4×D3C2×Q818yescomplemented
358C3×Dic6—44no—
359C3×Dic6C2×Q814yescomplemented
360#627—28no—
361#627—44no—
362#627—44no—
363D3×Dic3—24no—
364D3×Dic3—24no—
365D3×Dic3—44no—
366Q82—92no—
367#557—92no—
368#554—94no—
369#554—92no—
370D4×Q8—94no—
371D4×Q8—92no—
372#544—31no—
373#544—91no—
374#544—92no—
375#544—92no—
376#533—92no—
377#533—91no—
378C2×C4⋊Q8—91no—
379C2×C4⋊Q8—92no—
380#520—31no—
381#520—91no—
382C4×#41—91no—
383C3×#41—38no—
384C2×C3×Q8—31no—
385C2×C3×Q8—34no—
386C2×C3×D4—32no—
387C2×C3×D4—31no—
388C22×C3×C4—21no—
389C22×C3×C4—32no—
390C22×C3×C4—32no—
391C22×C3×C4—32no—
392C22×C3×C4—34no—
393C22×C3×C4C22×D311yescharacteristic
394C22×C3×C4C22×D311yescharacteristic
395C2×#67C22×D312yes—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—31no—
400C22×Dic3—32no—
401C22×Dic3—32no—
402C22×Dic3—34no—
403C22×Dic3—61no—
404C22×Dic3—61no—
405C22×Dic3C22×D312yes—
406C22×Dic3C22×D312yes—
407D3×Q8—128no—
408#235Dic618yescomplemented
409C2×D12C22×D311yescharacteristic
410C2×C4×D3—32no—
411C2×C4×D3—32no—
412C2×C4×D3—34no—
413C2×C4×D3C22×D314yes—
414C2×C4×D3C22×D312yes—
415C2×Dic6—32no—
416C2×Dic6—32no—
417C2×Dic6—32no—
418C2×Dic6—32no—
419C2×Dic6—34no—
420C2×Dic6—34no—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—62no—
426C2×Dic6—62no—
427C2×Dic6—128no—
428C2×Dic6—124no—
429C2×Dic6—124no—
430C2×Dic6C22×D314yes—
431C2×Dic6C22×D311yescharacteristic
432C3×C4⋊C4—21no—
433C3×C4⋊C4—21no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4—31no—
436C3×C4⋊C4—34no—
437C3×C4⋊C4—34no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—34no—
440C3×C4⋊C4—32no—
441C3×C4⋊C4—32no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—34no—
444C3×C4⋊C4C22×D311yescharacteristic
445C3×C4⋊C4C22×D311yescharacteristic
446C3×C4⋊C4C22×D311yescharacteristic
447C3×C4⋊C4C22×D311yescharacteristic
448C3×C22⋊C4—22no—
449C3×C22⋊C4—32no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4C22×D312yes—
452C3×C22⋊C4C22×D312yes—
453C3×C42—22no—
454C3×C42—34no—
455C3×C42—32no—
456C3×C42C22×D312yes—
457C3×C42C22×D312yes—
458#217—32no—
459#217—32no—
460#217—34no—
461#217—32no—
462#217—32no—
463#217—62no—
464#217C22×D312yes—
465(C2×D3)⋊C4—32no—
466(C2×D3)⋊C4—32no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4C22×D314yes—
469C4⋊Dic3—32no—
470C4⋊Dic3—32no—
471C4⋊Dic3—32no—
472C4⋊Dic3—32no—
473C4⋊Dic3—31no—
474C4⋊Dic3—31no—
475C4⋊Dic3—31no—
476C4⋊Dic3—31no—
477C4⋊Dic3—34no—
478C4⋊Dic3—32no—
479C4⋊Dic3—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3—32no—
482C4⋊Dic3—62no—
483C4⋊Dic3—62no—
484C4⋊Dic3—61no—
485C4⋊Dic3—61no—
486C4⋊Dic3C22×D314yes—
487C4⋊Dic3C22×D312yes—
488C4⋊Dic3C22×D312yes—
489C4⋊Dic3C22×D311yescharacteristic
490C4⋊Dic3C22×D312yes—
491C4⋊Dic3C22×D311yescharacteristic
492C4⋊Dic3C22×D312yes—
493Dic3⋊C4—32no—
494Dic3⋊C4—32no—
495Dic3⋊C4—32no—
496Dic3⋊C4—32no—
497Dic3⋊C4—32no—
498Dic3⋊C4—32no—
499Dic3⋊C4—32no—
500Dic3⋊C4—32no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—32no—
508Dic3⋊C4—32no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—62no—
513Dic3⋊C4—62no—
514Dic3⋊C4—62no—
515Dic3⋊C4—62no—
516Dic3⋊C4C22×D314yes—
517Dic3⋊C4C22×D314yes—
518Dic3⋊C4C22×D314yes—
519C4×Dic3—31no—
520C4×Dic3—31no—
521C4×Dic3—32no—
522C4×Dic3—31no—
523C4×Dic3—31no—
524C4×Dic3—32no—
525C4×Dic3—31no—
526C4×Dic3—31no—
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—32no—
530C4×Dic3—32no—
531C4×Dic3—34no—
532C4×Dic3—32no—
533C4×Dic3—32no—
534C4×Dic3—34no—
535C4×Dic3—61no—
536C4×Dic3—61no—
537C4×Dic3—62no—
538C4×Dic3—61no—
539C4×Dic3—61no—
540C4×Dic3C22×D314yes—
541C4×Dic3C22×D312yes—
542C22×C32—21no—
543C22×C32—21no—
544C22×C32C22×Q812yes—
545C22×C32C2511yescharacteristic
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3C22×Q814yes—
549C32×C4—22no—
550C32×C4—22no—
551C32×C4C22×Q812yes—
552C32×C4C22×Q812yes—
553C3⋊Dic3—22no—
554C3⋊Dic3—21no—
555C3⋊Dic3—22no—
556C3⋊Dic3—21no—
557C3⋊Dic3H(5,𝔽2)12yes—
558C3⋊Dic32−1+412yes—
559C3×Dic3—22no—
560C3×Dic3—24no—
561C3×Dic3—24no—
562C3×Dic3—22no—
563C3×Dic3C22×Q814yes—
564C2×#41—31no—
565C22×Q8—92no—
566C22×Q8—94no—
567C4⋊Q8—32no—
568C4⋊Q8—32no—
569C4⋊Q8—92no—
570C4⋊Q8—94no—
571C4⋊Q8—92no—
572C4⋊Q8—92no—
573C4⋊Q8—94no—
574C4⋊Q8—92no—
575C4⋊Q8—92no—
576C4⋊Q8—92no—
577C4⋊Q8—94no—
578C4⋊Q8—94no—
579C4⋊Q8—91no—
580C4⋊Q8—91no—
581#125—32no—
582#125—32no—
583#125—92no—
584#125—94no—
585#125—94no—
586#125—92no—
587#125—91no—
588#125—91no—
589C22⋊Q8—34no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—94no—
594C22⋊Q8—94no—
595C22⋊Q8—94no—
596C22⋊Q8—94no—
597C22⋊Q8—92no—
598C22⋊Q8—92no—
599C4×Q8—32no—
600C4×Q8—94no—
601C4×Q8—94no—
602C4×Q8—91no—
603C4×Q8—91no—
604C4×Q8—92no—
605C4×Q8—92no—
606C4×Q8—92no—
607C4×D4—34no—
608C4×D4—32no—
609C4×D4—92no—
610C4×D4—92no—
611C4×D4—91no—
612C4×D4—91no—
613C4×D4—92no—
614C4×D4—94no—
615#117—31no—
616#117—32no—
617#117—92no—
618#117—92no—
619#117—91no—
620#117D3211yescharacteristic
621C2×C4⋊C4—31no—
622C2×C4⋊C4—31no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—92no—
625C2×C4⋊C4—94no—
626C2×C4⋊C4—92no—
627C2×C42—92no—
628C2×C42—91no—
629C23×C3—21no—
630C23×C3—32no—
631C23×C3C23×D311yescharacteristic
632C23×C3C23×D311yescharacteristic
633C22×D3C23×D312yes—
634C3×Q8—34no—
635C3×Q8—124no—
636C3×D4—38no—
637C3×D4—34no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—24no—
643C2×C3×C4—32no—
644C2×C3×C4—38no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—34no—
648C2×C3×C4—34no—
649C2×C3×C4—124no—
650C2×C3×C4—122no—
651C2×C3×C4—122no—
652C2×C3×C4C2×Dic614yescomplemented
653C2×C3×C4D3×Q814yescomplemented
654C2×C3×C4C23×D312yes—
655C2×C3×C4C23×D312yes—
656C2×C3×C4C23×D312yes—
657C2×C3×C4C23×D312yes—
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662#67C2×Dic618yescomplemented
663C2×Dic3—31no—
664C2×Dic3—31no—
665C2×Dic3—31no—
666C2×Dic3—31no—
667C2×Dic3—32no—
668C2×Dic3—32no—
669C2×Dic3—31no—
670C2×Dic3—31no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—32no—
674C2×Dic3—32no—
675C2×Dic3—42no—
676C2×Dic3—42no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3—64no—
684C2×Dic3—64no—
685C2×Dic3—62no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—122no—
690C2×Dic3—122no—
691C2×Dic3—124no—
692C2×Dic3C23×D312yes—
693C2×Dic3C23×D312yes—
694C2×Dic3C23×D314yes—
695C2×Dic3C23×D314yes—
696C2×Dic3C23×D312yes—
697D12C2×Dic614yescomplemented
698C4×D3—44no—
699C4×D3—64no—
700C4×D3—64no—
701C4×D3—124no—
702C4×D3C2×Dic618yescomplemented
703Dic6—44no—
704Dic6—68no—
705Dic6—68no—
706Dic6—64no—
707Dic6—64no—
708Dic6—64no—
709Dic6—64no—
710Dic6—124no—
711Dic6—124no—
712Dic6—124no—
713Dic6—124no—
714Dic6—124no—
715Dic6—124no—
716Dic6C2×Dic614yescomplemented
717C2×C32—22no—
718C2×C32C23×Q811yescharacteristic
719C2×C32C2×H(5,𝔽2)11yescharacteristic
720C2×C32C2×2−1+411yescharacteristic
721C3×D3—24no—
722#41—38no—
723C2×Q8—31no—
724C2×Q8—34no—
725C2×Q8—94no—
726C2×Q8—94no—
727C2×Q8—94no—
728C2×Q8—92no—
729C2×Q8—92no—
730C2×Q8—364no—
731C2×Q8—368no—
732C2×D4—32no—
733C2×D4—31no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—32no—
737C22×C4—34no—
738C22×C4—92no—
739C22×C4—92no—
740C22×C4—94no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4C2×D3211yescharacteristic
744C4⋊C4—32no—
745C4⋊C4—32no—
746C4⋊C4—34no—
747C4⋊C4—32no—
748C4⋊C4—32no—
749C4⋊C4—34no—
750C4⋊C4—31no—
751C4⋊C4—31no—
752C4⋊C4—34no—
753C4⋊C4—34no—
754C4⋊C4—94no—
755C4⋊C4—94no—
756C4⋊C4—94no—
757C4⋊C4—94no—
758C4⋊C4—92no—
759C4⋊C4—92no—
760C4⋊C4—94no—
761C4⋊C4—94no—
762C4⋊C4—91no—
763C4⋊C4—92no—
764C4⋊C4—91no—
765C4⋊C4—92no—
766C4⋊C4—92no—
767C4⋊C4—92no—
768C4⋊C4—92no—
769C4⋊C4—92no—
770C4⋊C4C2×D3211yescharacteristic
771C4⋊C4C2×D3211yescharacteristic
772C22⋊C4—32no—
773C22⋊C4—34no—
774C22⋊C4—92no—
775C22⋊C4—92no—
776C22⋊C4—94no—
777C22⋊C4—92no—
778C22⋊C4C2×D3212yes—
779C42—32no—
780C42—34no—
781C42—92no—
782C42—92no—
783C42—94no—
784C42—91no—
785C42—91no—
786C42—91no—
787C42—91no—
788C42—92no—
789C42C2×D3212yes—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—22no—
795C22×C3—21no—
796C22×C3—34no—
797C22×C3—41no—
798C22×C3—41no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3C22×Dic612yes—
802C22×C3C2×D3×Q812yes—
803C22×C3C24×D311yescharacteristic
804C22×C3C24×D311yescharacteristic
805C2×D3—22no—
806C2×D3—22no—
807C2×D3C22×Dic614yes—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—22no—
811C3×C4—22no—
812C3×C4—22no—
813C3×C4—22no—
814C3×C4—34no—
815C3×C4—42no—
816C3×C4—42no—
817C3×C4—64no—
818C3×C4—64no—
819C3×C4—62no—
820C3×C4—62no—
821C3×C4C22×Dic612yes—
822C3×C4C22×Dic612yes—
823C3×C4C2×D3×Q812yes—
824C3×C4C2×D3×Q812yes—
825Dic3—22no—
826Dic3—24no—
827Dic3—24no—
828Dic3—22no—
829Dic3—32no—
830Dic3—32no—
831Dic3—32no—
832Dic3—32no—
833Dic3—62no—
834Dic3—62no—
835Dic3—62no—
836Dic3—62no—
837Dic3—61no—
838Dic3—61no—
839Dic3—62no—
840Dic3—62no—
841Dic3—61no—
842Dic3—61no—
843Dic3—122no—
844Dic3—122no—
845Dic3—121no—
846Dic3—121no—
847Dic3C22×Dic614yes—
848C32#350311yescharacteristic, complemented, Sylow
849C23—32no—
850C23C22×D3211yescharacteristic
851Q8—34no—
852Q8—124no—
853Q8—184no—
854Q8—184no—
855Q8—188no—
856Q8—364no—
857Q8—364no—
858D4—38no—
859D4—34no—
860C2×C4—32no—
861C2×C4—38no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—34no—
865C2×C4—34no—
866C2×C4—91no—
867C2×C4—91no—
868C2×C4—92no—
869C2×C4—91no—
870C2×C4—91no—
871C2×C4—92no—
872C2×C4—124no—
873C2×C4—122no—
874C2×C4—122no—
875C2×C4—184no—
876C2×C4—184no—
877C2×C4—182no—
878C2×C4—182no—
879C2×C4—364no—
880C2×C4D3×Dic614yescomplemented
881C2×C4C22×D3212yes—
882C2×C4C22×D3212yes—
883C2×C4C22×D3211yescharacteristic
884C2×C4C22×D3211yescharacteristic
885C2×C3—22no—
886C2×C3—22no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—42no—
891C2×C3—64no—
892C2×C3C23×Dic611yescharacteristic
893C2×C3C22×D3×Q811yescharacteristic
894C2×C3D3×H(5,𝔽2)11yescharacteristic
895C2×C3D3×H(5,𝔽2)11yescharacteristic
896C2×C3D3×2−1+411yescharacteristic
897C2×C3D3×2−1+411yescharacteristic
898D3—24no—
899C22—21no—
900C22—21no—
901C22—34no—
902C22—62no—
903C22—62no—
904C22C2×D3×Dic612yes—
905C22C23×D3211yescharacteristic
906C4—22no—
907C4—22no—
908C4—34no—
909C4—64no—
910C4—64no—
911C4—62no—
912C4—62no—
913C4—92no—
914C4—92no—
915C4—181no—
916C4—182no—
917C4—181no—
918C4—182no—
919C4C2×D3×Dic612yes—
920C4C2×D3×Dic612yes—
921C3—21no—
922C3#8588911yescharacteristic, complemented
923C3#8658611yescharacteristic, complemented
924C2—22no—
925C2—64no—
926C2C22×D3×Dic611yescharacteristic
927C2#1059669211yescharacteristic
928C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
prime radicalC2×C3×#235C22
hypercenter#117D32
hypocenterC32#3503
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595988C2semidirect
3. C3×#5519C2semidirect
4. #10595051C2semidirect
5. C2×#63919C2semidirect
8. #10594505C2semidirect
9. #10594477C2semidirect
10. D3×#888C2semidirect
11. #10594342C2semidirect
12. #10594156C2semidirect
13. #10594071C2semidirect
14. #10593941C2semidirect
15. #10593904C2semidirect
16. #10593856C2semidirect
17. #10593853C2semidirect
109. #5519D3semidirect
128. C3×#235Q8semidirect
332. C2×C32×C4C2×Q8semidirect
347. C3×#67C2×Q8semidirect
355. C3×D12C2×Q8semidirect
357. C3×C4×D3C2×Q8semidirect
359. C3×Dic6C2×Q8semidirect
408. #235Dic6semidirect
652. C2×C3×C4C2×Dic6semidirect
653. C2×C3×C4D3×Q8semidirect
662. #67C2×Dic6semidirect
697. D12C2×Dic6semidirect
702. C4×D3C2×Dic6semidirect
716. Dic6C2×Dic6semidirect
848. C32#3503semidirect
880. C2×C4D3×Dic6semidirect
922. C3#85889semidirect
923. C3#86586semidirect

Maximal subgroups

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

subgroupindex
#105959882
C3×#55232
C3×#55192
#105950512
C2×#639192
#105949862
#105949582
#105945052
#105944772
D3×#8882
#105943422
#105941562
#105940712
#105939412
#105939042
#105938562
#105938532
#865863
#858893