Finite Group Databasebeta

← #11906190

Subgroups — #11906190

Order 1152.

2314 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596050C211yesmaximal, characteristic, complemented
2C3×#5578C211yesmaximal, characteristic, complemented
3C3×Q8×D12C211yesmaximal, characteristic, complemented
4D3×#946C212yesmaximal, complemented
5#10595403C212yesmaximal, complemented
6#10594635C214yesmaximal, complemented
7#10594631C212yesmaximal, complemented
8#10594395C214yesmaximal, complemented
9#10594393C212yesmaximal, complemented
10#10593994C212yesmaximal
11C4×D3×D12C211yesmaximal, characteristic
12#10593960C211yesmaximal, characteristic, complemented
13#10593958C212yesmaximal, complemented
14#10593954C212yesmaximal, complemented
15#10593929C212yesmaximal, complemented
16#10593903C211yesmaximal, characteristic, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#86761—31nomaximal
19#86280—31nomaximal
20C2×C3×D3×Q8C2212yescomplemented
21C2×D3×D12C2211yescharacteristic
22C2×C4×D32C2212yes—
23C2×#3797C2212yescomplemented
24C32×C4×Q8C2211yescharacteristic, complemented
25#64155C2212yescomplemented
26#64105C2214yescomplemented
27C4⋊C4×C3⋊D3C2212yescomplemented
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2212yes—
30#64079C2212yescomplemented
31#64078C2211yescharacteristic, complemented
32C3×#946C2211yescharacteristic
33C3×#944C2211yescharacteristic, complemented
34C3×#897C2211yescharacteristic
35C3×#897C2212yescomplemented
36C3×#897C2214yescomplemented
37C3×#896C2212yes—
38C3×#889C2212yescomplemented
39C3×#888C2211yescharacteristic, complemented
40C3×C4×D12C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×#872C2212yes—
43C3×C42×D3C2211yescharacteristic
44C3×#869C2211yescharacteristic, complemented
45C3×#869C2212yescomplemented
46C3×C4×Dic6C2211yescharacteristic, complemented
47C3×C4×Dic6C2212yescomplemented
48#63921C2214yes—
49D3×(C2×D3)⋊C4C2212yes—
50D3×(C2×D3)⋊C4C2214yes—
51#63918C2212yescomplemented
52#63904C2214yes—
53C4×#626C2212yes—
54#63900C2214yescomplemented
55#63899C2214yes—
56#63899C2214yescomplemented
57#63896C2214yescomplemented
58#63895C2214yescomplemented
59#63894C2212yes—
60#63894C2211yescharacteristic
61Dic3×D12C2211yescharacteristic
62Dic3×D12C2212yes—
63D3×C4⋊Dic3C2211yescharacteristic
64D3×C4⋊Dic3C2212yescomplemented
65#63888C2214yescomplemented
66#63888C2214yescomplemented
67#63887C2214yes—
68#63887C2214yescomplemented
69#63881C2214yes—
70#63880C2212yes—
71D3×Dic3⋊C4C2214yescomplemented
72#63871C2214yescomplemented
73#63871C2212yescomplemented
74#63869C2212yescomplemented
75#63869C2212yescomplemented
76#63857C2212yes—
77#63856C2212yes—
78#63856C2212yescomplemented
79#63851C2214yescomplemented
80#63846C2214yescomplemented
81#63844C2212yescomplemented
82Dic3×Dic6C2212yescomplemented
83#63841C2212yes—
84#63839C2214yescomplemented
85C3×D4×Q8—31no—
86C3×#533—31no—
87Q8×#67—32no—
88C2×#946—32no—
89#5730—32no—
90#5730—32no—
91#5729—32no—
92#5728—31no—
93#5727—32no—
94#5727—31no—
95#5690—34no—
96#5636—34no—
97#5635—32no—
98#5634—34no—
99#5634—34no—
100D3×C22⋊Q8—32no—
101D3×C22⋊Q8—32no—
102D3×C22⋊Q8—32no—
103#5579—31no—
104#5579—31no—
105#5579—32no—
106#5579—31no—
107#5579—32no—
108#5579—61no—
109#5578D311yescharacteristic, complemented
110Q8×D12—31no—
111Q8×D12D311yescharacteristic, complemented
112#5545—32no—
113C4×D3×D4—31no—
114#5543—31no—
115#5539—32no—
116#5521—32no—
117#5519—32no—
118C2×C4×D12—31no—
119#5470—31no—
120C22×D32C2312yes—
121C2×C32×Q8C2311yescharacteristic
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4×C3⋊D3C2312yes—
124C2×C4×C3⋊D3C2314yes—
125C2×#634C2312yes—
126C3×D3×Q8—44no—
127C2×C3×D12C2311yescharacteristic
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2312yes—
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2314yes—
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×Dic6C2311yescharacteristic
134C2×C3×Dic6C2312yes—
135C2×C3×Dic6C2312yes—
136C2×C3×Dic6C2314yes—
137C2×#627C2314yes—
138C2×#626C2312yes—
139C2×#624C2314yes—
140C2×#624C2312yes—
141C2×D3×Dic3C2312yes—
142C2×D3×Dic3C2312yes—
143C2×D3×Dic3C2314yes—
144D3×D12Q818yescomplemented
145C4×D32—44no—
146#3797—44no—
147C32×C4⋊C4C2311yescharacteristic
148C32×C4⋊C4C2312yes—
149C32×C42C2311yescharacteristic
150C32×C42C2312yes—
151#3752C2312yes—
152#3752C2314yes—
153C4⋊(C3⋊Dic3)C2312yes—
154C4⋊(C3⋊Dic3)C2312yes—
155C4⋊(C3⋊Dic3)C2311yescharacteristic
156#3750C2314yes—
157#3750C2314yes—
158C3×(C2×D3)⋊C4C2312yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×C4⋊Dic3C2311yescharacteristic
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2314yes—
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×Dic3⋊C4C2312yes—
169C3×Dic3⋊C4C2312yes—
170C3×Dic3⋊C4C2312yes—
171C3×Dic3⋊C4C2312yes—
172C3×Dic3⋊C4C2312yes—
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2311yescharacteristic
175C3×C4×Dic3C2311yescharacteristic
176C3×C4×Dic3C2312yes—
177#3724C2314yes—
178#3724C2314yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183#3722C2314yes—
184#3722C2312yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2312yes—
187(C2×D3)⋊Dic3C2314yes—
188Dic32C2314yes—
189#3501—91noSylow
190C22×C3×Q8—32no—
191C2×D3×Q8—32no—
192C2×D3×Q8—32no—
193C2×D3×Q8C2×D312yescomplemented
194C2×D3×D4—31no—
195C22×D12—31no—
196C22×C4×D3—32no—
197C22×C4×D3—32no—
198C3×C4⋊Q8—31no—
199C3×C4⋊Q8—31no—
200C3×C4⋊Q8—31no—
201C3×C4⋊Q8—32no—
202C3×#125—32no—
203C3×C22⋊Q8—31no—
204C3×C22⋊Q8—32no—
205C3×C22⋊Q8—34no—
206C3×C22⋊Q8—32no—
207C3×C22⋊Q8—31no—
208C3×C4×Q8—21no—
209C3×C4×Q8—31no—
210C3×C4×Q8—32no—
211C3×C4×Q8C2×D311yescharacteristic, complemented
212C3×C4×Q8C2×D311yescharacteristic, complemented
213C3×C4×D4—32no—
214C3×C4×D4—31no—
215C3×#117—32no—
216C2×C3×C42—31no—
217#946—32no—
218#946—32no—
219#946—32no—
220#946—32no—
221#946—34no—
222#946—34no—
223#946—34no—
224#946—32no—
225#946—34no—
226#946—34no—
227#946—62no—
228#946C2×D311yescharacteristic
229Q8×Dic3—32no—
230#944—34no—
231#944C2×D311yescharacteristic, complemented
232D4×Dic3—31no—
233D4×Dic3—32no—
234C4×#67—34no—
235C4×#67—32no—
236C2×(C2×D3)⋊C4—32no—
237C2×(C2×D3)⋊C4—34no—
238#926—32no—
239C2×C4⋊Dic3—32no—
240C2×C4⋊Dic3—31no—
241#924—32no—
242#924—32no—
243#924—32no—
244#924—34no—
245C2×Dic3⋊C4—34no—
246#897—32no—
247#897—34no—
248#897—32no—
249#897—34no—
250#897C2×D311yescharacteristic
251#897C2×D314yescomplemented
252#897C2×D312yescomplemented
253#896—34no—
254#896—34no—
255#896—34no—
256#896—34no—
257#896—34no—
258#896—34no—
259#896—34no—
260#896—34no—
261#896—34no—
262#896—64no—
263#896C2×D312yes—
264#893—34no—
265#893—34no—
266#893—32no—
267#893—31no—
268#892—32no—
269D3×C4⋊C4—34no—
270D3×C4⋊C4—31no—
271D3×C4⋊C4—32no—
272D3×C4⋊C4—32no—
273D3×C4⋊C4—32no—
274D3×C4⋊C4—34no—
275D3×C4⋊C4—34no—
276D3×C4⋊C4—62no—
277#890—34no—
278#890—32no—
279#890—32no—
280#889—34no—
281#889C2×D312yescomplemented
282#888—34no—
283#888—32no—
284#888C2×D311yescharacteristic, complemented
285#887—32no—
286#67⋊C4—34no—
287#67⋊C4—32no—
288D3×C22⋊C4—32no—
289D3×C22⋊C4—34no—
290D3×C22⋊C4—34no—
291D3×C22⋊C4—34no—
292#878—34no—
293#878—34no—
294#878—34no—
295#878—34no—
296#878—34no—
297C4×D12—31no—
298C4×D12—32no—
299C4×D12—32no—
300C4×D12—31no—
301C4×D12—31no—
302C4×D12—32no—
303C4×D12—32no—
304C4×D12—32no—
305C4×D12—31no—
306C4×D12—32no—
307C4×D12—61no—
308C4×D12—62no—
309C4×D12C2×D311yescharacteristic
310C4×D12C2×D312yes—
311#872C2×D312yes—
312C42×D3C2×D311yescharacteristic
313#870—32no—
314#870—32no—
315#870—32no—
316#870—32no—
317#870—62no—
318#869—31no—
319#869—31no—
320#869—32no—
321#869—61no—
322#869C2×D311yescharacteristic, complemented
323#869C2×D312yescomplemented
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6C2×D311yescharacteristic, complemented
327C4×Dic6C2×D312yescomplemented
328C22×C3⋊D3C2412yes—
329C22×C3×D3C2411yescharacteristic
330C22×C3×D3C2412yes—
331C2×D32—42no—
332C2×D32—42no—
333C2×D32C2×Q818yescomplemented
334C32×Q8—22no—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2412yes—
337C2×C32×C4C2412yes—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C3⋊Dic3C2414yes—
341C2×C3⋊Dic3C2412yes—
342C4⋊(C3⋊D3)C2×Q814yescomplemented
343C4×C3⋊D3—24no—
344C4×C3⋊D3—44no—
345#634—42no—
346C2×C3×Dic3C2414yes—
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2411yescharacteristic
352C2×C3×Dic3C2411yescharacteristic
353C3×D12C2×Q814yescomplemented
354C3×C4×D3—22no—
355C3×C4×D3—24no—
356C3×C4×D3—41no—
357C3×C4×D3—44no—
358C3×C4×D3C2×Q814yescomplemented
359C3×Dic6—22no—
360C3×Dic6—24no—
361C3×Dic6—42no—
362C3×Dic6—44no—
363#627—44no—
364#626C2×Q818yescomplemented
365#624—44no—
366#624—42no—
367D3×Dic3—42no—
368D3×Dic3—42no—
369D3×Dic3—44no—
370#554—92no—
371#554—91no—
372#554—92no—
373#554—94no—
374#554—92no—
375#554—91no—
376D4×Q8—31no—
377D4×Q8—91no—
378D4×Q8—92no—
379#544—92no—
380#543—94no—
381#533—31no—
382#533—91no—
383C2×C22⋊Q8—92no—
384C2×C22⋊Q8—92no—
385#518—92no—
386C2×C4×D4—91no—
387C23×D3—32no—
388C23×D3—32no—
389C2×C3×Q8—21no—
390C2×C3×Q8—32no—
391C2×C3×Q8—31no—
392C2×C3×Q8—34no—
393C2×C3×Q8—32no—
394C2×C3×Q8—124no—
395C2×C3×Q8C22×D311yescharacteristic
396C2×C3×Q8C22×D311yescharacteristic
397C2×C3×D4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—32no—
401C22×C3×C4—34no—
402C22×C3×C4—31no—
403C2×#67—32no—
404C22×Dic3—32no—
405C22×Dic3—32no—
406C22×Dic3—34no—
407D3×Q8—44no—
408D3×Q8—124no—
409D3×Q8—124no—
410D3×D4—38no—
411C2×D12—32no—
412C2×D12—31no—
413C2×D12—31no—
414C2×D12—38no—
415C2×D12—61no—
416C2×D12C22×D311yescharacteristic
417C2×C4×D3—32no—
418C2×C4×D3—32no—
419C2×C4×D3—32no—
420C2×C4×D3—34no—
421C2×C4×D3—32no—
422C2×C4×D3—34no—
423C2×C4×D3—34no—
424C2×C4×D3—32no—
425C2×C4×D3—34no—
426C2×C4×D3—34no—
427C2×C4×D3—32no—
428C2×C4×D3—62no—
429C2×C4×D3—64no—
430C2×C4×D3—124no—
431C2×C4×D3—124no—
432C2×C4×D3C22×D311yescharacteristic
433C2×C4×D3C22×D312yes—
434C2×C4×D3C22×D311yescharacteristic
435C2×C4×D3C22×D314yes—
436C2×C4×D3C22×D311yescharacteristic
437C2×Dic6—32no—
438C2×Dic6—32no—
439C2×Dic6—34no—
440C2×Dic6—34no—
441C2×Dic6—62no—
442C2×Dic6C22×D312yes—
443C2×Dic6C22×D311yescharacteristic
444C2×Dic6C22×D312yes—
445C2×Dic6C22×D314yes—
446C3×C4⋊C4—21no—
447C3×C4⋊C4—22no—
448C3×C4⋊C4—32no—
449C3×C4⋊C4—32no—
450C3×C4⋊C4—32no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4—31no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4—32no—
455C3×C4⋊C4—32no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—32no—
458C3×C4⋊C4—32no—
459C3×C4⋊C4C22×D311yescharacteristic
460C3×C4⋊C4C22×D312yes—
461C3×C4⋊C4C22×D311yescharacteristic
462C3×C4⋊C4C22×D312yes—
463C3×C22⋊C4—32no—
464C3×C22⋊C4—32no—
465C3×C22⋊C4—34no—
466C3×C22⋊C4—32no—
467C3×C42—21no—
468C3×C42—22no—
469C3×C42—31no—
470C3×C42—31no—
471C3×C42—32no—
472C3×C42—31no—
473C3×C42C22×D311yescharacteristic
474C3×C42C22×D312yes—
475C3×C42C22×D311yescharacteristic
476C3×C42C22×D312yes—
477#217—34no—
478#217—34no—
479#217—32no—
480(C2×D3)⋊C4—32no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—32no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—62no—
492(C2×D3)⋊C4—64no—
493(C2×D3)⋊C4C22×D312yes—
494(C2×D3)⋊C4C22×D312yes—
495(C2×D3)⋊C4C22×D312yes—
496(C2×D3)⋊C4C22×D314yes—
497C4⋊Dic3—32no—
498C4⋊Dic3—31no—
499C4⋊Dic3—32no—
500C4⋊Dic3—32no—
501C4⋊Dic3—32no—
502C4⋊Dic3—31no—
503C4⋊Dic3—34no—
504C4⋊Dic3—32no—
505C4⋊Dic3—34no—
506C4⋊Dic3—34no—
507C4⋊Dic3—62no—
508C4⋊Dic3—62no—
509C4⋊Dic3—61no—
510C4⋊Dic3C22×D312yes—
511C4⋊Dic3C22×D312yes—
512C4⋊Dic3C22×D311yescharacteristic
513C4⋊Dic3C22×D312yes—
514C4⋊Dic3C22×D311yescharacteristic
515C4⋊Dic3C22×D314yes—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—32no—
528Dic3⋊C4—64no—
529Dic3⋊C4—64no—
530Dic3⋊C4C22×D312yes—
531Dic3⋊C4C22×D312yes—
532Dic3⋊C4C22×D312yes—
533Dic3⋊C4C22×D312yes—
534Dic3⋊C4C22×D312yes—
535C4×Dic3—34no—
536C4×Dic3—34no—
537C4×Dic3C22×D311yescharacteristic
538C4×Dic3C22×D312yes—
539C4×Dic3C22×D311yescharacteristic
540C4×Dic3C22×D311yescharacteristic
541C22×C32C2511yescharacteristic
542C2×C3⋊D3—22no—
543C2×C3⋊D3—22no—
544C2×C3⋊D3C22×Q814yes—
545C2×C3×D3—21no—
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3—21no—
549C2×C3×D3C22×Q814yes—
550C2×C3×D3C22×Q812yes—
551D32—48no—
552C32×C4—22no—
553C32×C4—22no—
554C32×C4—21no—
555C32×C4C22×Q812yes—
556C32×C4H(5,𝔽2)12yes—
557C3⋊Dic3—22no—
558C3⋊Dic3—24no—
559C3×Dic3—21no—
560C3×Dic3—22no—
561C3×Dic3—22no—
562C3×Dic3—24no—
563C3×Dic3—22no—
564C3×Dic3—21no—
565C3×Dic3C22×Q812yes—
566C22×Q8—32no—
567C22×Q8—92no—
568C22×D4—91no—
569C23×C4—92no—
570C4⋊Q8—31no—
571C4⋊Q8—31no—
572C4⋊Q8—31no—
573C4⋊Q8—32no—
574C4⋊Q8—92no—
575C4⋊Q8—94no—
576C4⋊Q8—91no—
577#125—32no—
578#125—92no—
579#125—92no—
580#125—94no—
581#125—92no—
582C22⋊Q8—31no—
583C22⋊Q8—31no—
584C22⋊Q8—32no—
585C22⋊Q8—32no—
586C22⋊Q8—34no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—92no—
594C22⋊Q8—94no—
595C22⋊Q8—92no—
596C22⋊Q8—94no—
597C22⋊Q8—94no—
598C22⋊Q8—94no—
599C22⋊Q8—92no—
600C22⋊Q8—92no—
601C22⋊Q8—92no—
602C22⋊Q8—94no—
603C4×Q8—31no—
604C4×Q8—32no—
605C4×Q8—92no—
606C4×Q8—92no—
607C4×Q8D3211yescharacteristic, complemented
608C4×D4—31no—
609C4×D4—32no—
610C4×D4—92no—
611C4×D4—91no—
612C4×D4—92no—
613C4×D4—92no—
614C4×D4—91no—
615C4×D4—92no—
616C4×D4—94no—
617C4×D4—94no—
618C4×D4—91no—
619C4×D4—92no—
620#117—32no—
621#117—92no—
622C2×C4⋊C4—94no—
623C2×C4⋊C4—91no—
624C2×C4⋊C4—94no—
625C2×C4⋊C4—92no—
626C2×C4⋊C4—92no—
627C2×C22⋊C4—94no—
628C2×C22⋊C4—92no—
629C2×C22⋊C4—94no—
630C2×C42—31no—
631C23×C3—31no—
632C23×C3—32no—
633C22×D3—32no—
634C22×D3—32no—
635C22×D3—38no—
636C22×D3—38no—
637C22×D3—62no—
638C22×D3—122no—
639C22×D3—122no—
640C22×D3—122no—
641C22×D3—122no—
642C22×D3C23×D311yescharacteristic
643C22×D3C23×D312yes—
644C3×Q8—22no—
645C3×Q8—22no—
646C3×Q8—42no—
647C3×Q8—62no—
648C3×Q8—64no—
649C3×Q8—122no—
650C3×Q8—124no—
651C3×D4—34no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—21no—
657C2×C3×C4—31no—
658C2×C3×C4—34no—
659C2×C3×C4—34no—
660C2×C3×C4—31no—
661C2×C3×C4—31no—
662C2×C3×C4—32no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—62no—
666C2×C3×C4—64no—
667C2×C3×C4—121no—
668C2×C3×C4—124no—
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D312yes—
671C2×C3×C4C23×D312yes—
672C2×C3×C4C23×D312yes—
673C2×C3×C4C23×D312yes—
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678C2×C3×C4C23×D311yescharacteristic
679#67—38no—
680C2×Dic3—34no—
681C2×Dic3—34no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—62no—
685C2×Dic3—64no—
686C2×Dic3—122no—
687C2×Dic3—122no—
688C2×Dic3—124no—
689C2×Dic3C23×D314yes—
690C2×Dic3C23×D311yescharacteristic
691C2×Dic3C23×D311yescharacteristic
692C2×Dic3C23×D312yes—
693C2×Dic3C23×D312yes—
694C2×Dic3C23×D312yes—
695C2×Dic3C23×D311yescharacteristic
696D12—38no—
697D12—34no—
698D12—34no—
699D12—64no—
700D12D3×Q814yescomplemented
701C4×D3—24no—
702C4×D3—22no—
703C4×D3—41no—
704C4×D3—44no—
705C4×D3—64no—
706C4×D3—64no—
707C4×D3—124no—
708C4×D3—122no—
709C4×D3—122no—
710C4×D3—124no—
711C4×D3—124no—
712C4×D3—124no—
713C4×D3—124no—
714C4×D3—124no—
715C4×D3—122no—
716C4×D3—122no—
717C4×D3—244no—
718C4×D3D3×Q814yescomplemented
719Dic6—24no—
720Dic6—22no—
721Dic6—42no—
722Dic6—44no—
723Dic6—124no—
724Dic6—124no—
725Dic6—122no—
726Dic6—122no—
727Dic6—242no—
728C2×C32C23×Q811yescharacteristic
729C2×C32C2×H(5,𝔽2)11yescharacteristic
730C2×C32#58511yescharacteristic
731C3⋊D3—24no—
732C3×D3—22no—
733C3×D3—24no—
734C24—92no—
735C2×Q8—31no—
736C2×Q8—32no—
737C2×Q8—32no—
738C2×Q8—34no—
739C2×Q8—94no—
740C2×Q8—92no—
741C2×Q8—124no—
742C2×Q8—364no—
743C2×Q8C2×D3211yescharacteristic
744C2×D4—31no—
745C2×D4—98no—
746C2×D4—92no—
747C2×D4—91no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—32no—
751C22×C4—31no—
752C22×C4—34no—
753C22×C4—94no—
754C22×C4—92no—
755C22×C4—94no—
756C22×C4—92no—
757C22×C4—92no—
758C22×C4—92no—
759C22×C4—94no—
760C22×C4—364no—
761C4⋊C4—32no—
762C4⋊C4—32no—
763C4⋊C4—31no—
764C4⋊C4—31no—
765C4⋊C4—34no—
766C4⋊C4—32no—
767C4⋊C4—32no—
768C4⋊C4—32no—
769C4⋊C4—32no—
770C4⋊C4—32no—
771C4⋊C4—32no—
772C4⋊C4—94no—
773C4⋊C4—92no—
774C4⋊C4—94no—
775C4⋊C4—94no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—92no—
779C4⋊C4—91no—
780C4⋊C4—94no—
781C4⋊C4—94no—
782C4⋊C4—92no—
783C4⋊C4C2×D3211yescharacteristic
784C4⋊C4C2×D3212yes—
785C22⋊C4—32no—
786C22⋊C4—32no—
787C22⋊C4—34no—
788C22⋊C4—32no—
789C22⋊C4—92no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4—92no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4—92no—
796C42—31no—
797C42—31no—
798C42—31no—
799C42—32no—
800C42—94no—
801C42C2×D3211yescharacteristic
802C42C2×D3212yes—
803C22×C3—21no—
804C22×C3—34no—
805C22×C3—32no—
806C22×C3—61no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3—61no—
810C22×C3C24×D311yescharacteristic
811C22×C3C24×D311yescharacteristic
812C2×D3—22no—
813C2×D3—21no—
814C2×D3—21no—
815C2×D3—22no—
816C2×D3—34no—
817C2×D3—34no—
818C2×D3—64no—
819C2×D3—62no—
820C2×D3—62no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—122no—
824C2×D3—122no—
825C2×D3—128no—
826C2×D3—128no—
827C2×D3C2×D3×Q812yes—
828C2×D3C2×D3×Q814yes—
829C3×C4—22no—
830C3×C4—22no—
831C3×C4—22no—
832C3×C4—21no—
833C3×C4—21no—
834C3×C4—22no—
835C3×C4—22no—
836C3×C4—22no—
837C3×C4—32no—
838C3×C4—41no—
839C3×C4—42no—
840C3×C4—42no—
841C3×C4—62no—
842C3×C4—61no—
843C3×C4—64no—
844C3×C4—62no—
845C3×C4—62no—
846C3×C4—61no—
847C3×C4#100412yes—
848C3×C4C2×D3×Q812yes—
849C3×C4C2×D3×Q812yes—
850C3×C4#100912yes—
851Dic3—24no—
852Dic3—22no—
853Dic3—22no—
854Dic3—21no—
855Dic3—21no—
856Dic3—22no—
857Dic3—62no—
858Dic3—62no—
859Dic3—64no—
860Dic3—64no—
861Dic3—124no—
862Dic3—122no—
863Dic3C2×D3×Q812yes—
864C32#350111yescharacteristic, complemented, Sylow
865C23—31no—
866C23—32no—
867C23—98no—
868C23—92no—
869C23—362no—
870C23—362no—
871Q8—22no—
872Q8—64no—
873Q8—62no—
874Q8—124no—
875Q8—122no—
876Q8—362no—
877Q8—364no—
878D4—34no—
879D4—98no—
880D4—94no—
881C2×C4—31no—
882C2×C4—34no—
883C2×C4—31no—
884C2×C4—31no—
885C2×C4—32no—
886C2×C4—32no—
887C2×C4—34no—
888C2×C4—32no—
889C2×C4—62no—
890C2×C4—64no—
891C2×C4—94no—
892C2×C4—92no—
893C2×C4—124no—
894C2×C4—121no—
895C2×C4—184no—
896C2×C4—364no—
897C2×C4—362no—
898C2×C4—364no—
899C2×C4—362no—
900C2×C4—362no—
901C2×C4—364no—
902C2×C4C22×D3211yescharacteristic
903C2×C4C22×D3212yes—
904C2×C4C22×D3212yes—
905C2×C4C22×D3211yescharacteristic
906C2×C4C22×D3211yescharacteristic
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—64no—
911C2×C3—62no—
912C2×C3C2×#100411yescharacteristic
913C2×C3C22×D3×Q811yescharacteristic
914C2×C3C22×D3×Q811yescharacteristic
915C2×C3C2×#100911yescharacteristic
916C2×C3#596411yescharacteristic
917C2×C3#596811yescharacteristic
918D3—22no—
919D3—24no—
920D3—64no—
921D3—64no—
922D3—124no—
923C22—32no—
924C22—34no—
925C22—62no—
926C22—61no—
927C22—61no—
928C22—62no—
929C22—94no—
930C22—182no—
931C22—182no—
932C22—368no—
933C22C23×D3211yescharacteristic
934C4—22no—
935C4—21no—
936C4—22no—
937C4—32no—
938C4—61no—
939C4—62no—
940C4—64no—
941C4—62no—
942C4—61no—
943C4—62no—
944C4—182no—
945C4—184no—
946C4#6430712yes—
947C4D32×Q812yes—
948C3—21no—
949C3#8628011yescharacteristic, complemented
950C3#8676111yescharacteristic, complemented
951C2—62no—
952C2—64no—
953C2—184no—
954C2C2×#6430711yescharacteristic
955C2C2×D32×Q811yescharacteristic
956C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×D3×D12C22
hypercenterC4×Q8D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596050C2semidirect
2. C3×#5578C2semidirect
3. C3×Q8×D12C2semidirect
4. D3×#946C2semidirect
5. #10595403C2semidirect
6. #10594635C2semidirect
7. #10594631C2semidirect
8. #10594395C2semidirect
9. #10594393C2semidirect
12. #10593960C2semidirect
13. #10593958C2semidirect
14. #10593954C2semidirect
15. #10593929C2semidirect
16. #10593903C2semidirect
17. #10593859C2semidirect
20. C2×C3×D3×Q8C22semidirect
23. C2×#3797C22semidirect
24. C32×C4×Q8C22semidirect
25. #64155C22semidirect
26. #64105C22semidirect
27. C4⋊C4×C3⋊D3C22semidirect
30. #64079C22semidirect
31. #64078C22semidirect
33. C3×#944C22semidirect
35. C3×#897C22semidirect
36. C3×#897C22semidirect
38. C3×#889C22semidirect
39. C3×#888C22semidirect
44. C3×#869C22semidirect
45. C3×#869C22semidirect
46. C3×C4×Dic6C22semidirect
47. C3×C4×Dic6C22semidirect
51. #63918C22semidirect
54. #63900C22semidirect
56. #63899C22semidirect
57. #63896C22semidirect
58. #63895C22semidirect
64. D3×C4⋊Dic3C22semidirect
65. #63888C22semidirect
66. #63888C22semidirect
68. #63887C22semidirect
71. D3×Dic3⋊C4C22semidirect
72. #63871C22semidirect
73. #63871C22semidirect
74. #63869C22semidirect
75. #63869C22semidirect
78. #63856C22semidirect
79. #63851C22semidirect
80. #63846C22semidirect
81. #63844C22semidirect
82. Dic3×Dic6C22semidirect
84. #63839C22semidirect
109. #5578D3semidirect
111. Q8×D12D3semidirect
144. D3×D12Q8semidirect
193. C2×D3×Q8C2×D3semidirect
211. C3×C4×Q8C2×D3semidirect
212. C3×C4×Q8C2×D3semidirect
231. #944C2×D3semidirect
251. #897C2×D3semidirect
252. #897C2×D3semidirect
281. #889C2×D3semidirect
284. #888C2×D3semidirect
322. #869C2×D3semidirect
323. #869C2×D3semidirect
326. C4×Dic6C2×D3semidirect
327. C4×Dic6C2×D3semidirect
333. C2×D32C2×Q8semidirect
342. C4⋊(C3⋊D3)C2×Q8semidirect
353. C3×D12C2×Q8semidirect
358. C3×C4×D3C2×Q8semidirect
364. #626C2×Q8semidirect
607. C4×Q8D32semidirect
700. D12D3×Q8semidirect
718. C4×D3D3×Q8semidirect
864. C32#3501semidirect
949. C3#86280semidirect
950. C3#86761semidirect

Maximal subgroups

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

subgroupindex
#105960502
C3×#55782
C3×Q8×D122
D3×#9462
#105954032
#105946352
#105946312
#105943952
#105943932
#105939942
C4×D3×D122
#105939602
#105939582
#105939542
#105939292
#105939032
#105938592
#867613
#862803