Finite Group Databasebeta

← #11903766

Subgroups — #11903766

Order 1152.

2250 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596201C211yesmaximal, characteristic, complemented
2C3×#5728C211yesmaximal, characteristic, complemented
3C3×#5722C211yesmaximal, characteristic, complemented
4#10595374C214yesmaximal, complemented
5#10595372C214yesmaximal, complemented
6#10594470C212yesmaximal, complemented
7#10594445C212yesmaximal, complemented
8#10594397C212yesmaximal, complemented
9#10594393C212yesmaximal, complemented
10#10594383C212yesmaximal, complemented
11#10594363C212yesmaximal, complemented
12#10594362C212yesmaximal
13#10594321C212yesmaximal, complemented
14C4×#3799C211yesmaximal, characteristic
15#10593903C211yesmaximal, characteristic, complemented
16C4×D3×Dic6C211yesmaximal, characteristic, complemented
17#10593861C211yesmaximal, characteristic, complemented
18Q8×#239—31nomaximal
19#86277—31nomaximal
20C2×#3799C2211yescharacteristic
21C2×#3797C2212yes—
22C2×D3×Dic6C2211yescharacteristic
23C32×C4⋊Q8C2211yescharacteristic
24#64155C2214yes—
25#64106C2212yes—
26#64102C2212yes—
27C4⋊C4×C3⋊D3C2212yes—
28#64099C2212yes—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C3×#946C2212yes—
32C3×Q8×Dic3C2212yes—
33C3×#944C2214yes—
34C3×#897C2212yes—
35C3×#892C2212yes—
36C3×#890C2212yes—
37C3×#888C2212yes—
38C3×#888C2212yes—
39C3×#887C2212yes—
40C3×#887C2212yes—
41C3×#887C2212yes—
42C3×C42×D3C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63918C2214yes—
47#63918C2212yes—
48C4×#627C2212yes—
49#63904C2212yes—
50C4×#626C2212yes—
51#63895C2214yes—
52#63895C2214yes—
53#63894C2212yes—
54#63894C2211yescharacteristic
55#63893C2214yes—
56D3×C4⋊Dic3C2211yescharacteristic
57#63888C2214yes—
58#63887C2214yes—
59#63883C2214yes—
60C4×#624C2214yes—
61C4×#624C2212yes—
62#63881C2214yes—
63#63880C2214yes—
64D3×Dic3⋊C4C2212yes—
65C4×D3×Dic3C2212yes—
66#63872C2212yes—
67#63871C2214yes—
68#63871C2212yes—
69#63866C2212yes—
70#63846C2214yes—
71#63846C2214yes—
72#63845C2214yes—
73#63844C2211yescharacteristic
74#63843C2212yes—
75Dic3×Dic6C2211yescharacteristic
76Dic3×Dic6C2214yes—
77Dic3×Dic6C2211yescharacteristic
78Dic3×Dic6C2212yes—
79#63841C2211yescharacteristic
80#63837C2214yes—
81#63837C2212yes—
82#63837C2214yes—
83#63836C2212yes—
84#63836C2214yes—
85C3×Q82—31no—
86C3×#533—31no—
87#5730—31no—
88#5730—31no—
89#5730—34no—
90#5730—32no—
91#5730—32no—
92#5730—61no—
93#5728—34no—
94#5728—32no—
95#5728—32no—
96#5728D311yescharacteristic, complemented
97#5727—31no—
98#5722D311yescharacteristic, complemented
99#5721—31no—
100#5690—32no—
101#5685—32no—
102#5636—34no—
103#5635—32no—
104#5632—32no—
105#5578—34no—
106#5578—32no—
107Q8×D12—32no—
108Q8×D12—31no—
109C4×#239—32no—
110C4×#239—31no—
111C4×D3×Q8—32no—
112C4×D3×Q8—32no—
113C4×D3×Q8—31no—
114#5570—32no—
115#5570—31no—
116#5522—32no—
117#5517—32no—
118C4×#235—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2312yes—
121C2×C4⋊(C3⋊D3)C2311yescharacteristic
122C2×C4×C3⋊D3C2312yes—
123C2×C4×C3⋊D3C2314yes—
124C2×#634C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×Dic6C2312yes—
129C2×C3×Dic6C2314yes—
130C2×C3×Dic6C2311yescharacteristic
131C2×C3×Dic6C2311yescharacteristic
132C2×#627C2312yes—
133C2×#627C2314yes—
134C2×#626C2312yes—
135C2×#624C2314yes—
136C2×#624C2312yes—
137C2×#624C2312yes—
138C2×D3×Dic3C2312yes—
139C2×D3×Dic3C2312yes—
140#3799Q818yescomplemented
141#3797—28no—
142D3×Dic6—24no—
143C32×C4⋊C4C2312yes—
144C32×C4⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146#3752C2312yes—
147#3752C2314yes—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150C4⋊(C3⋊Dic3)C2314yes—
151#3750C2312yes—
152#3750C2314yes—
153C4×C3⋊Dic3C2312yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4⋊Dic3C2311yescharacteristic
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2314yes—
159C3×C4⋊Dic3C2312yes—
160C3×Dic3⋊C4C2314yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2312yes—
165C3×C4×Dic3C2314yes—
166C3×C4×Dic3C2311yescharacteristic
167C3×C4×Dic3C2312yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2314yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2311yescharacteristic
172#3724C2312yes—
173Dic3⋊Dic3C2312yes—
174Dic3⋊Dic3C2314yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180#3722C2314yes—
181#3722C2312yes—
182(C2×D3)⋊Dic3C2312yes—
183Dic32C2312yes—
184Dic32C2312yes—
185Dic32C2312yes—
186Dic32C2312yes—
187Dic32C2314yes—
188Q8×#41—91noSylow
189C2×#239—31no—
190C2×D3×Q8—31no—
191C2×D3×Q8—32no—
192C2×D3×Q8—32no—
193C2×#235—31no—
194C22×Dic6—31no—
195C3×C4⋊Q8—21no—
196C3×C4⋊Q8—34no—
197C3×C4⋊Q8—32no—
198C3×C4⋊Q8—32no—
199C3×C4⋊Q8—31no—
200C3×C4⋊Q8C2×D311yescharacteristic
201C3×C4⋊Q8C2×D311yescharacteristic
202C3×#125—32no—
203C3×C22⋊Q8—32no—
204C3×C22⋊Q8—32no—
205C3×C4×Q8—32no—
206C3×C4×Q8—32no—
207C3×C4×Q8—32no—
208C3×C4×Q8—32no—
209C3×C4×Q8—31no—
210C3×C4×Q8—31no—
211C3×#117—32no—
212C2×C3×C42—31no—
213#946—34no—
214#946—34no—
215#946—34no—
216#946—32no—
217#946—34no—
218#946—34no—
219#946—64no—
220#946C2×D312yes—
221Q8×Dic3—32no—
222Q8×Dic3—32no—
223Q8×Dic3—34no—
224Q8×Dic3—31no—
225Q8×Dic3—31no—
226Q8×Dic3C2×D312yes—
227#944—32no—
228#944C2×D314yes—
229C4×#67—32no—
230C4×#67—32no—
231#926—31no—
232C2×C4⋊Dic3—31no—
233C2×Dic3⋊C4—32no—
234C2×C4×Dic3—32no—
235#897—34no—
236#897—32no—
237#897—32no—
238#897—32no—
239#897—34no—
240#897—34no—
241#897—34no—
242#897—62no—
243#897C2×D312yes—
244#896—34no—
245#896—34no—
246#896—34no—
247#893—32no—
248#893—32no—
249#893—32no—
250#893—34no—
251#893—32no—
252#893—31no—
253#893—62no—
254#892—31no—
255#892—34no—
256#892—32no—
257#892C2×D312yes—
258D3×C4⋊C4—32no—
259D3×C4⋊C4—31no—
260D3×C4⋊C4—32no—
261D3×C4⋊C4—32no—
262D3×C4⋊C4—34no—
263D3×C4⋊C4—34no—
264D3×C4⋊C4—62no—
265#890—32no—
266#890—32no—
267#890—32no—
268#890—34no—
269#890—34no—
270#890—32no—
271#890—34no—
272#890—62no—
273#890C2×D312yes—
274#889—34no—
275#889—34no—
276#889—34no—
277#888—34no—
278#888—32no—
279#888C2×D312yes—
280#888C2×D312yes—
281#887—32no—
282#887—34no—
283#887—34no—
284#887—32no—
285#887—31no—
286#887C2×D312yes—
287#887C2×D312yes—
288#887C2×D312yes—
289#67⋊C4—34no—
290#67⋊C4—34no—
291#878—34no—
292#878—34no—
293C4×D12—32no—
294C4×D12—31no—
295C4×D12—31no—
296C4×D12—34no—
297C4×D12—31no—
298C4×D12—32no—
299C4×D12—61no—
300#872—32no—
301#872—34no—
302C42×D3—32no—
303C42×D3—34no—
304C42×D3—32no—
305C42×D3—32no—
306C42×D3—34no—
307C42×D3C2×D311yescharacteristic
308#869—32no—
309#869—32no—
310#869—34no—
311#869C2×D311yescharacteristic
312C4×Dic6—31no—
313C4×Dic6—31no—
314C4×Dic6—32no—
315C4×Dic6—34no—
316C4×Dic6—31no—
317C4×Dic6—31no—
318C4×Dic6—31no—
319C4×Dic6—32no—
320C4×Dic6—34no—
321C4×Dic6—34no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—61no—
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D311yescharacteristic
327C22×C3⋊D3C2412yes—
328C22×C3×D3C2411yescharacteristic
329C32×Q8—42no—
330C2×C32×C4C2414yes—
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2412yes—
337C4⋊(C3⋊D3)C2×Q814yescomplemented
338C4×C3⋊D3—24no—
339C4×C3⋊D3—44no—
340#634—22no—
341C2×C3×Dic3C2411yescharacteristic
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2414yes—
345C2×C3×Dic3C2411yescharacteristic
346C2×C3×Dic3C2411yescharacteristic
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C3×C4×D3—22no—
350C3×C4×D3—41no—
351C3×C4×D3C2×Q814yescomplemented
352C3×Dic6—24no—
353C3×Dic6—44no—
354C3×Dic6C2×Q814yescomplemented
355C3×Dic6#4114yescomplemented
356#627—24no—
357#627—28no—
358#626C2×Q818yescomplemented
359#624—28no—
360#624—42no—
361#624C2×Q818yescomplemented
362D3×Dic3—24no—
363D3×Dic3—42no—
364Q82—31no—
365#557—92no—
366#557—91no—
367#554—92no—
368#554—94no—
369#554—92no—
370#554—91no—
371D4×Q8—92no—
372D4×Q8—91no—
373#533—31no—
374#533—92no—
375#533—94no—
376#533—92no—
377C4×#41—91no—
378C4×#41—92no—
379C2×C4×Q8—91no—
380C2×C4×Q8—92no—
381C2×C3×Q8—22no—
382C2×C3×Q8—31no—
383C2×C3×Q8—31no—
384C2×C3×Q8—32no—
385C2×C3×Q8—34no—
386C2×C3×Q8C22×D312yes—
387C2×C3×Q8C22×D312yes—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C2×#67—32no—
392C22×Dic3—32no—
393C22×Dic3—32no—
394#239—38no—
395D3×Q8—68no—
396D3×Q8—64no—
397D3×Q8—68no—
398#235—38no—
399C2×D12—32no—
400C2×D12—31no—
401C2×D12—31no—
402C2×D12—61no—
403C2×C4×D3—32no—
404C2×C4×D3—32no—
405C2×C4×D3—32no—
406C2×C4×D3—32no—
407C2×C4×D3—32no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—32no—
411C2×C4×D3—34no—
412C2×C4×D3—34no—
413C2×C4×D3—32no—
414C2×C4×D3—32no—
415C2×C4×D3—62no—
416C2×C4×D3—64no—
417C2×C4×D3C22×D311yescharacteristic
418C2×C4×D3C22×D311yescharacteristic
419C2×C4×D3C22×D311yescharacteristic
420C2×Dic6—31no—
421C2×Dic6—31no—
422C2×Dic6—32no—
423C2×Dic6—34no—
424C2×Dic6—32no—
425C2×Dic6—34no—
426C2×Dic6—61no—
427C2×Dic6—64no—
428C2×Dic6C22×D312yes—
429C2×Dic6C22×D314yes—
430C2×Dic6C22×D311yescharacteristic
431C2×Dic6C22×D311yescharacteristic
432C3×C4⋊C4—22no—
433C3×C4⋊C4—22no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4—34no—
436C3×C4⋊C4—32no—
437C3×C4⋊C4—34no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—34no—
440C3×C4⋊C4—32no—
441C3×C4⋊C4—32no—
442C3×C4⋊C4—34no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4C22×D312yes—
445C3×C4⋊C4C22×D312yes—
446C3×C4⋊C4C22×D312yes—
447C3×C4⋊C4C22×D312yes—
448C3×C22⋊C4—34no—
449C3×C42—21no—
450C3×C42—31no—
451C3×C42—31no—
452C3×C42—34no—
453C3×C42—31no—
454C3×C42—34no—
455C3×C42—32no—
456C3×C42—32no—
457C3×C42C22×D311yescharacteristic
458C3×C42C22×D311yescharacteristic
459#217—32no—
460(C2×D3)⋊C4—32no—
461(C2×D3)⋊C4—32no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—32no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—32no—
466(C2×D3)⋊C4—34no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4—62no—
470(C2×D3)⋊C4—64no—
471(C2×D3)⋊C4C22×D314yes—
472C4⋊Dic3—31no—
473C4⋊Dic3—31no—
474C4⋊Dic3—31no—
475C4⋊Dic3—34no—
476C4⋊Dic3—31no—
477C4⋊Dic3—34no—
478C4⋊Dic3—32no—
479C4⋊Dic3—32no—
480C4⋊Dic3—34no—
481C4⋊Dic3—34no—
482C4⋊Dic3—32no—
483C4⋊Dic3—34no—
484C4⋊Dic3—34no—
485C4⋊Dic3—61no—
486C4⋊Dic3—61no—
487C4⋊Dic3—64no—
488C4⋊Dic3C22×D311yescharacteristic
489C4⋊Dic3C22×D311yescharacteristic
490C4⋊Dic3C22×D312yes—
491C4⋊Dic3C22×D314yes—
492C4⋊Dic3C22×D312yes—
493Dic3⋊C4—32no—
494Dic3⋊C4—34no—
495Dic3⋊C4—32no—
496Dic3⋊C4—34no—
497Dic3⋊C4—32no—
498Dic3⋊C4—32no—
499Dic3⋊C4—32no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—32no—
504Dic3⋊C4—32no—
505Dic3⋊C4—34no—
506Dic3⋊C4—62no—
507Dic3⋊C4—64no—
508Dic3⋊C4C22×D312yes—
509Dic3⋊C4C22×D314yes—
510Dic3⋊C4C22×D314yes—
511Dic3⋊C4C22×D312yes—
512Dic3⋊C4C22×D314yes—
513C4×Dic3—32no—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—34no—
519C4×Dic3—32no—
520C4×Dic3—32no—
521C4×Dic3—32no—
522C4×Dic3—34no—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—62no—
526C4×Dic3C22×D311yescharacteristic
527C4×Dic3C22×D312yes—
528C4×Dic3C22×D312yes—
529C4×Dic3C22×D311yescharacteristic
530C4×Dic3C22×D314yes—
531C4×Dic3C22×D314yes—
532C4×Dic3C22×D311yescharacteristic
533C22×C32C2511yescharacteristic
534C2×C3⋊D3—22no—
535C2×C3⋊D3—22no—
536C2×C3⋊D3C22×Q814yes—
537C2×C3×D3—21no—
538C2×C3×D3—21no—
539C2×C3×D3C22×Q812yes—
540C32×C4—24no—
541C32×C4—21no—
542C32×C4C22×Q812yes—
543C32×C4C2×#4112yes—
544C3⋊Dic3—22no—
545C3⋊Dic3—22no—
546C3⋊Dic3—22no—
547C3×Dic3—24no—
548C3×Dic3—21no—
549C3×Dic3—22no—
550C3×Dic3—21no—
551C3×Dic3—22no—
552C3×Dic3C22×Q812yes—
553C3×Dic3C22×Q814yes—
554C3×Dic3C2×#4114yes—
555C2×#41—91no—
556C22×Q8—91no—
557C22×Q8—92no—
558C4⋊Q8—34no—
559C4⋊Q8—32no—
560C4⋊Q8—32no—
561C4⋊Q8—31no—
562C4⋊Q8—92no—
563C4⋊Q8—94no—
564C4⋊Q8—92no—
565C4⋊Q8D3211yescharacteristic
566#125—32no—
567#125—94no—
568#125—94no—
569#125—94no—
570#125—92no—
571#125—92no—
572C22⋊Q8—32no—
573C22⋊Q8—32no—
574C22⋊Q8—94no—
575C22⋊Q8—94no—
576C22⋊Q8—94no—
577C22⋊Q8—94no—
578C22⋊Q8—92no—
579C22⋊Q8—94no—
580C22⋊Q8—94no—
581C22⋊Q8—94no—
582C22⋊Q8—92no—
583C4×Q8—32no—
584C4×Q8—32no—
585C4×Q8—32no—
586C4×Q8—32no—
587C4×Q8—31no—
588C4×Q8—31no—
589C4×Q8—92no—
590C4×Q8—91no—
591C4×Q8—92no—
592C4×Q8—94no—
593C4×Q8—94no—
594C4×Q8—91no—
595C4×Q8—92no—
596C4×Q8—91no—
597C4×Q8—94no—
598C4×Q8—92no—
599C4×Q8—91no—
600C4×D4—94no—
601C4×D4—92no—
602C4×D4—91no—
603C4×D4—92no—
604C4×D4—94no—
605C4×D4—92no—
606C4×D4—92no—
607C4×D4—91no—
608#117—32no—
609#117—92no—
610#117—94no—
611#117—91no—
612C2×C4⋊C4—94no—
613C2×C4⋊C4—92no—
614C2×C4⋊C4—91no—
615C2×C4⋊C4—92no—
616C2×C42—31no—
617C2×C42—92no—
618C2×C42—94no—
619C2×C42—92no—
620C23×C3—31no—
621C22×D3—32no—
622C22×D3—32no—
623C22×D3—62no—
624C22×D3C23×D311yescharacteristic
625C3×Q8—34no—
626C3×Q8—34no—
627C3×Q8—42no—
628C3×Q8—42no—
629C3×Q8—64no—
630C3×Q8—82no—
631C3×Q8—124no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—24no—
636C2×C3×C4—31no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—34no—
640C2×C3×C4—31no—
641C2×C3×C4—34no—
642C2×C3×C4—32no—
643C2×C3×C4—32no—
644C2×C3×C4—31no—
645C2×C3×C4—62no—
646C2×C3×C4—121no—
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D314yes—
649C2×C3×C4C23×D314yes—
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655#67—38no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—32no—
659C2×Dic3—32no—
660C2×Dic3—32no—
661C2×Dic3—32no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—64no—
666C2×Dic3—122no—
667C2×Dic3C23×D311yescharacteristic
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D314yes—
671C2×Dic3C23×D311yescharacteristic
672C2×Dic3C23×D311yescharacteristic
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D312yes—
675D12—38no—
676D12—34no—
677D12—34no—
678D12—64no—
679C4×D3—22no—
680C4×D3—38no—
681C4×D3—38no—
682C4×D3—41no—
683C4×D3—68no—
684C4×D3—64no—
685C4×D3—64no—
686C4×D3—64no—
687C4×D3—68no—
688C4×D3—124no—
689C4×D3—122no—
690C4×D3—122no—
691C4×D3—124no—
692C4×D3—124no—
693C4×D3—122no—
694C4×D3—244no—
695C4×D3D3×Q814yescomplemented
696Dic6—24no—
697Dic6—44no—
698Dic6—68no—
699Dic6—64no—
700Dic6—62no—
701Dic6—62no—
702Dic6—64no—
703Dic6—68no—
704Dic6—122no—
705Dic6D3×Q814yescomplemented
706Dic6#23914yescomplemented
707C2×C32C23×Q811yescharacteristic
708C2×C32C22×#4111yescharacteristic
709C2×C32#58511yescharacteristic
710C3⋊D3—24no—
711C3×D3—22no—
712#41—98no—
713C2×Q8—31no—
714C2×Q8—31no—
715C2×Q8—32no—
716C2×Q8—34no—
717C2×Q8—92no—
718C2×Q8—94no—
719C2×Q8—91no—
720C2×Q8—184no—
721C2×Q8—188no—
722C2×Q8C2×D3212yes—
723C2×D4—92no—
724C2×D4—91no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—92no—
729C22×C4—94no—
730C22×C4—92no—
731C22×C4—92no—
732C22×C4—92no—
733C22×C4—92no—
734C22×C4—94no—
735C4⋊C4—34no—
736C4⋊C4—34no—
737C4⋊C4—32no—
738C4⋊C4—31no—
739C4⋊C4—32no—
740C4⋊C4—34no—
741C4⋊C4—32no—
742C4⋊C4—31no—
743C4⋊C4—34no—
744C4⋊C4—32no—
745C4⋊C4—92no—
746C4⋊C4—92no—
747C4⋊C4—92no—
748C4⋊C4—94no—
749C4⋊C4—92no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4—94no—
753C4⋊C4—91no—
754C4⋊C4—94no—
755C4⋊C4—92no—
756C4⋊C4—91no—
757C4⋊C4—94no—
758C4⋊C4C2×D3212yes—
759C4⋊C4C2×D3212yes—
760C22⋊C4—34no—
761C22⋊C4—92no—
762C22⋊C4—94no—
763C22⋊C4—92no—
764C22⋊C4—94no—
765C22⋊C4—92no—
766C42—31no—
767C42—31no—
768C42—31no—
769C42—34no—
770C42—34no—
771C42—32no—
772C42—32no—
773C42—92no—
774C42—92no—
775C42—92no—
776C42—92no—
777C42—94no—
778C42—92no—
779C42C2×D3211yescharacteristic
780C22×C3—21no—
781C22×C3—32no—
782C22×C3—61no—
783C22×C3—61no—
784C22×C3C24×D311yescharacteristic
785C22×C3C24×D311yescharacteristic
786C2×D3—21no—
787C2×D3—21no—
788C2×D3—34no—
789C2×D3—34no—
790C2×D3—64no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—122no—
796C2×D3—122no—
797C2×D3C2×D3×Q812yes—
798C3×C4—21no—
799C3×C4—24no—
800C3×C4—24no—
801C3×C4—21no—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—32no—
805C3×C4—34no—
806C3×C4—34no—
807C3×C4—44no—
808C3×C4—41no—
809C3×C4—61no—
810C3×C4—64no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—61no—
814C3×C4C2×D3×Q812yes—
815C3×C4C2×D3×Q812yes—
816C3×C4C2×#23912yes—
817C3×C4D3×#4112yes—
818Dic3—24no—
819Dic3—21no—
820Dic3—21no—
821Dic3—22no—
822Dic3—22no—
823Dic3—62no—
824Dic3—62no—
825Dic3—62no—
826Dic3—62no—
827Dic3—62no—
828Dic3—62no—
829Dic3—122no—
830Dic3—122no—
831Dic3—122no—
832Dic3C2×D3×Q814yes—
833Dic3C2×D3×Q812yes—
834Dic3C2×#23914yes—
835C32Q8×#4111yescharacteristic, complemented, Sylow
836C23—31no—
837C23—92no—
838Q8—34no—
839Q8—34no—
840Q8—42no—
841Q8—64no—
842Q8—124no—
843Q8—184no—
844Q8—188no—
845Q8—182no—
846D4—98no—
847D4—94no—
848C2×C4—31no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—34no—
852C2×C4—31no—
853C2×C4—31no—
854C2×C4—34no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—62no—
858C2×C4—98no—
859C2×C4—92no—
860C2×C4—92no—
861C2×C4—92no—
862C2×C4—121no—
863C2×C4—188no—
864C2×C4—184no—
865C2×C4—184no—
866C2×C4—364no—
867C2×C4—362no—
868C2×C4—362no—
869C2×C4C22×D3214yes—
870C2×C4C22×D3211yescharacteristic
871C2×C4C22×D3211yescharacteristic
872C2×C4C22×D3211yescharacteristic
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—62no—
877C2×C3C22×D3×Q811yescharacteristic
878C2×C3C22×D3×Q811yescharacteristic
879C2×C3C22×#23911yescharacteristic
880C2×C3C2×D3×#4111yescharacteristic
881C2×C3#596411yescharacteristic
882C2×C3#596611yescharacteristic
883D3—22no—
884D3—64no—
885D3—64no—
886D3—124no—
887C22—32no—
888C22—61no—
889C22—61no—
890C22—94no—
891C22—182no—
892C22—182no—
893C22C23×D3211yescharacteristic
894C4—21no—
895C4—24no—
896C4—32no—
897C4—34no—
898C4—34no—
899C4—61no—
900C4—62no—
901C4—62no—
902C4—61no—
903C4—64no—
904C4—182no—
905C4—182no—
906C4—182no—
907C4D32×Q812yes—
908C4D3×#23912yes—
909C3—21no—
910C3#8627711yescharacteristic, complemented
911C3Q8×#23911yescharacteristic, complemented
912C2—62no—
913C2—184no—
914C2#1059667811yescharacteristic
915C2C2×D32×Q811yescharacteristic
916C2C2×D3×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC2×#3799C22
hypercenterC4⋊Q8D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
2. C3×#5728C2semidirect
3. C3×#5722C2semidirect
4. #10595374C2semidirect
5. #10595372C2semidirect
6. #10594470C2semidirect
7. #10594445C2semidirect
8. #10594397C2semidirect
9. #10594393C2semidirect
10. #10594383C2semidirect
11. #10594363C2semidirect
13. #10594321C2semidirect
15. #10593903C2semidirect
16. C4×D3×Dic6C2semidirect
17. #10593861C2semidirect
96. #5728D3semidirect
98. #5722D3semidirect
140. #3799Q8semidirect
337. C4⋊(C3⋊D3)C2×Q8semidirect
351. C3×C4×D3C2×Q8semidirect
354. C3×Dic6C2×Q8semidirect
355. C3×Dic6#41semidirect
358. #626C2×Q8semidirect
361. #624C2×Q8semidirect
695. C4×D3D3×Q8semidirect
705. Dic6D3×Q8semidirect
706. Dic6#239semidirect
835. C32Q8×#41semidirect
910. C3#86277semidirect
911. C3Q8×#239semidirect

Maximal subgroups

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

subgroupindex
#105962012
C3×#57282
C3×#57222
#105953742
#105953722
#105944702
#105944452
#105943972
#105943932
#105943832
#105943632
#105943622
#105943212
C4×#37992
#105939032
C4×D3×Dic62
#105938612
Q8×#2393
#862773