Finite Group Databasebeta

← #11903772

Subgroups — #11903772

Order 1152.

2276 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#634C211yesmaximal, characteristic, complemented
2C3×#5543C211yesmaximal, characteristic, complemented
3C3×C4×#237C211yesmaximal, characteristic
4#10595274C212yesmaximal, complemented
5Dic3×#237C212yesmaximal
6#10594988C212yesmaximal, complemented
7#10594915C212yesmaximal, complemented
8C2×#63844C212yesmaximal, complemented
9#10594808C212yesmaximal, complemented
10#10594477C212yesmaximal, complemented
11#10594322C212yesmaximal, complemented
12#10594156C214yesmaximal, complemented
13#10594029C214yesmaximal, complemented
14C4×D3×Dic6C211yesmaximal, characteristic, complemented
15#10593860C211yesmaximal, characteristic, complemented
16#10593859C211yesmaximal, characteristic, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#86923—31nomaximal
19#41×Dic6—31nomaximal
20C22×#634C2212yes—
21C2×C3×#237C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic
23C32×C4×D4C2211yescharacteristic
24D4×C3⋊Dic3C2212yes—
25#64133C2212yes—
26#64097C2212yes—
27#64087C2214yes—
28#64078C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic
31C3×D4×Dic3C2212yes—
32C3×C4×#67C2212yes—
33C2×C3×C4⋊Dic3C2212yes—
34C3×#924C2212yes—
35C2×C3×C4×Dic3C2212yes—
36C3×#892C2211yescharacteristic
37C3×#890C2212yes—
38C3×#887C2211yescharacteristic
39C3×#67⋊C4C2212yes—
40C3×#878C2214yes—
41C3×#877C2212yes—
42C3×C42×D3C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63982C2214yes—
47#67⋊Dic3C2214yes—
48Dic3×#67C2214yes—
49C2×#3724C2214yes—
50#63964C2214yes—
51#63964C2214yes—
52#63955C2214yes—
53C2×Dic32C2214yes—
54#63919C2212yes—
55#63918C2212yes—
56C4×#627C2212yes—
57#63899C2214yes—
58#63896C2214yes—
59D3×C4⋊Dic3C2211yescharacteristic
60D3×Dic3⋊C4C2212yes—
61C4×D3×Dic3C2212yes—
62#63869C2212yes—
63#63869C2212yes—
64#63867C2214yes—
65#63866C2212yes—
66#63857C2212yes—
67#63856C2212yes—
68#63846C2214yes—
69#63845C2214yes—
70#63844C2211yescharacteristic
71#63844C2214yes—
72#63844C2212yes—
73#63844C2212yes—
74#63844C2212yes—
75#63844C2214yes—
76#63843C2212yes—
77Dic3×Dic6C2212yes—
78Dic3×Dic6C2212yes—
79Dic3×Dic6C2211yescharacteristic
80#63841C2212yes—
81#63840C2214yes—
82#63839C2214yes—
83#63837C2212yes—
84#63837C2214yes—
85C3×#554—31no—
86C3×C4×#41—31no—
87Dic3×#41—32no—
88#5728—31no—
89#5722—31no—
90#5688—32no—
91#5685—32no—
92#5636—34no—
93#5632—32no—
94#5622—32no—
95#5622—34no—
96C4×D3×Q8—31no—
97#5570—31no—
98#5569—32no—
99#5567—31no—
100Q8×Dic6—31no—
101#5543—32no—
102#5543D311yescharacteristic, complemented
103#5539—32no—
104#5539—32no—
105#5539—34no—
106D4×Dic6—31no—
107D4×Dic6—31no—
108D4×Dic6—32no—
109D4×Dic6—61no—
110C4×#237—32no—
111C4×#237D311yescharacteristic
112#5517—32no—
113#5517—34no—
114#5511—32no—
115C2×#887—32no—
116#5470—32no—
117#5470—31no—
118C2×C4×Dic6—32no—
119C2×C4×Dic6—31no—
120C2×C32×D4C2311yescharacteristic
121C22×C32×C4C2312yes—
122C22×C3⋊Dic3C2314yes—
123C2×#634—28no—
124C2×#634C2312yes—
125C2×#634C2314yes—
126C2×#634C2311yescharacteristic
127C2×C3×#67C2312yes—
128C22×C3×Dic3C2314yes—
129C22×C3×Dic3C2312yes—
130C22×C3×Dic3C2312yes—
131C3×#237Q818yescomplemented
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×Dic6C2311yescharacteristic
136C2×C3×Dic6C2312yes—
137C2×C3×Dic6C2311yescharacteristic
138C2×#627C2312yes—
139C2×#627C2314yes—
140C2×D3×Dic3C2312yes—
141C2×D3×Dic3C2312yes—
142D3×Dic6—24no—
143C32×C4⋊C4C2311yescharacteristic
144C32×C22⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146#3757C2314yes—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2312yes—
149C4⋊(C3⋊Dic3)C2312yes—
150#3750C2312yes—
151#3750C2314yes—
152C4×C3⋊Dic3C2312yes—
153C3×#217C2312yes—
154C3×#217C2314yes—
155C3×(C2×D3)⋊C4C2312yes—
156C3×C4⋊Dic3C2314yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×C4⋊Dic3C2312yes—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×Dic3⋊C4C2312yes—
162C3×Dic3⋊C4C2312yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2314yes—
165C3×C4×Dic3C2311yescharacteristic
166C3×C4×Dic3C2312yes—
167C3×C4×Dic3C2312yes—
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2312yes—
172#3724C2314yes—
173#3724C2312yes—
174#3724C2314yes—
175#3724C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2314yes—
183Dic32C2312yes—
184Dic32C2314yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2314yes—
188Q8×#41—91noSylow
189C2×C3×#41—31no—
190C2×D3×Q8—31no—
191C2×#237C2×D311yescharacteristic
192C22×Dic6—32no—
193C22×Dic6—32no—
194C22×Dic6—31no—
195C22×Dic6—62no—
196C3×C4⋊Q8—31no—
197C3×#125—32no—
198C3×C22⋊Q8—32no—
199C3×C22⋊Q8—34no—
200C3×C4×Q8—31no—
201C3×C4×Q8—31no—
202C3×C4×Q8—31no—
203C3×C4×D4—21no—
204C3×C4×D4—32no—
205C3×C4×D4—31no—
206C3×C4×D4—32no—
207C3×C4×D4—32no—
208C3×C4×D4C2×D311yescharacteristic
209C3×C4×D4C2×D311yescharacteristic
210C3×#117—31no—
211C3×#117—32no—
212C2×C3×C4⋊C4—32no—
213C2×C3×C42—32no—
214C2×C3×C42—31no—
215#946—32no—
216Q8×Dic3—32no—
217Q8×Dic3—32no—
218Q8×Dic3—32no—
219Q8×Dic3—31no—
220#944—34no—
221#944—32no—
222D4×Dic3—32no—
223D4×Dic3—32no—
224D4×Dic3—34no—
225D4×Dic3—34no—
226D4×Dic3—62no—
227D4×Dic3C2×D311yescharacteristic
228D4×Dic3C2×D312yes—
229C4×#67—34no—
230C4×#67C2×D312yes—
231#926—34no—
232#926—32no—
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3C2×D312yes—
235#924—32no—
236#924—32no—
237#924—32no—
238#924—34no—
239#924—34no—
240#924—32no—
241#924—62no—
242#924C2×D312yes—
243C2×Dic3⋊C4—34no—
244C2×Dic3⋊C4—34no—
245C2×Dic3⋊C4—32no—
246C2×C4×Dic3—34no—
247C2×C4×Dic3—34no—
248C2×C4×Dic3—32no—
249C2×C4×Dic3C2×D312yes—
250#897—32no—
251#896—34no—
252#896—34no—
253#892—32no—
254#892C2×D311yescharacteristic
255D3×C4⋊C4—32no—
256D3×C4⋊C4—31no—
257#890—34no—
258#890—34no—
259#890—32no—
260#890—32no—
261#890C2×D312yes—
262#889—34no—
263#889—34no—
264#889—34no—
265#888—34no—
266#888—32no—
267#888—32no—
268#888—32no—
269#888—32no—
270#888—34no—
271#888—34no—
272#888—32no—
273#888—62no—
274#887—32no—
275#887—32no—
276#887—34no—
277#887—34no—
278#887—34no—
279#887—32no—
280#887—32no—
281#887—31no—
282#887—32no—
283#887C2×D311yescharacteristic
284#67⋊C4—34no—
285#67⋊C4C2×D312yes—
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—64no—
295#878C2×D314yes—
296#877—34no—
297#877C2×D312yes—
298C42×D3—32no—
299C42×D3C2×D311yescharacteristic
300#870—32no—
301#870—32no—
302#870—34no—
303#869—32no—
304#869—31no—
305#869—31no—
306#869—32no—
307#869—61no—
308#869C2×D311yescharacteristic
309C4×Dic6—32no—
310C4×Dic6—31no—
311C4×Dic6—32no—
312C4×Dic6—31no—
313C4×Dic6—31no—
314C4×Dic6—31no—
315C4×Dic6—32no—
316C4×Dic6—34no—
317C4×Dic6—32no—
318C4×Dic6—34no—
319C4×Dic6—32no—
320C4×Dic6—32no—
321C4×Dic6—34no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—61no—
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D311yescharacteristic
327C23×C32C2412yes—
328C22×C3×D3C2411yescharacteristic
329C32×D4C2×Q814yescomplemented
330C2×C32×C4—24no—
331C2×C32×C4C2412yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C3⋊Dic3—28no—
336C2×C3⋊Dic3C2414yes—
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2412yes—
339#634—24no—
340#634—28no—
341#634#4114yescomplemented
342C3×#67C2×Q818yescomplemented
343C2×C3×Dic3—44no—
344C2×C3×Dic3—42no—
345C2×C3×Dic3C2×Q818yescomplemented
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2414yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2411yescharacteristic
350C2×C3×Dic3C2411yescharacteristic
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2411yescharacteristic
353C2×C3×Dic3C2412yes—
354C3×C4×D3—22no—
355C3×C4×D3—41no—
356C3×C4×D3C2×Q814yescomplemented
357C3×Dic6—22no—
358C3×Dic6—42no—
359C3×Dic6C2×Q814yescomplemented
360#627—24no—
361#627—44no—
362D3×Dic3—24no—
363D3×Dic3—42no—
364Q82—91no—
365#557—91no—
366#557—92no—
367#554—31no—
368#554—92no—
369#554—92no—
370#554—94no—
371D4×Q8—92no—
372D4×Q8—91no—
373#533—92no—
374#533—91no—
375#533—94no—
376#533—92no—
377C4×#41—31no—
378C4×#41—92no—
379C2×C4×Q8—92no—
380C2×C4×Q8—91no—
381C3×#41—38no—
382C2×C3×Q8—31no—
383C2×C3×Q8—31no—
384C2×C3×Q8—32no—
385C2×C3×D4—21no—
386C2×C3×D4—32no—
387C2×C3×D4C22×D311yescharacteristic
388C2×C3×D4C22×D311yescharacteristic
389C22×C3×C4—22no—
390C22×C3×C4—32no—
391C22×C3×C4—31no—
392C22×C3×C4—34no—
393C22×C3×C4—32no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4C22×D312yes—
397C22×C3×C4C22×D312yes—
398C2×#67C22×D312yes—
399C22×Dic3—34no—
400C22×Dic3—34no—
401C22×Dic3—32no—
402C22×Dic3—32no—
403C22×Dic3—64no—
404C22×Dic3C22×D312yes—
405C22×Dic3C22×D314yes—
406C22×Dic3C22×D312yes—
407D3×Q8—64no—
408#237Dic618yescomplemented
409C2×C4×D3—32no—
410C2×C4×D3—32no—
411C2×C4×D3C22×D311yescharacteristic
412C2×C4×D3C22×D311yescharacteristic
413C2×C4×D3C22×D311yescharacteristic
414C2×Dic6—31no—
415C2×Dic6—31no—
416C2×Dic6—32no—
417C2×Dic6—34no—
418C2×Dic6—32no—
419C2×Dic6—34no—
420C2×Dic6—32no—
421C2×Dic6—32no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—61no—
425C2×Dic6—62no—
426C2×Dic6—64no—
427C2×Dic6—64no—
428C2×Dic6—68no—
429C2×Dic6—68no—
430C2×Dic6—128no—
431C2×Dic6C22×D311yescharacteristic
432C2×Dic6C22×D312yes—
433C2×Dic6C22×D311yescharacteristic
434C3×C4⋊C4—21no—
435C3×C4⋊C4—31no—
436C3×C4⋊C4—32no—
437C3×C4⋊C4—34no—
438C3×C4⋊C4—34no—
439C3×C4⋊C4—32no—
440C3×C4⋊C4—32no—
441C3×C4⋊C4—32no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4C22×D311yescharacteristic
445C3×C4⋊C4C22×D311yescharacteristic
446C3×C22⋊C4—22no—
447C3×C22⋊C4—34no—
448C3×C22⋊C4—32no—
449C3×C22⋊C4—32no—
450C3×C22⋊C4C22×D312yes—
451C3×C22⋊C4C22×D312yes—
452C3×C42—21no—
453C3×C42—31no—
454C3×C42—31no—
455C3×C42—32no—
456C3×C42—32no—
457C3×C42—32no—
458C3×C42—31no—
459C3×C42—32no—
460C3×C42C22×D311yescharacteristic
461C3×C42C22×D311yescharacteristic
462#217—34no—
463#217—34no—
464#217—34no—
465#217—64no—
466#217C22×D312yes—
467#217C22×D314yes—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4C22×D312yes—
470C4⋊Dic3—31no—
471C4⋊Dic3—32no—
472C4⋊Dic3—32no—
473C4⋊Dic3—31no—
474C4⋊Dic3—32no—
475C4⋊Dic3—32no—
476C4⋊Dic3—32no—
477C4⋊Dic3—34no—
478C4⋊Dic3—32no—
479C4⋊Dic3—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3—34no—
482C4⋊Dic3—61no—
483C4⋊Dic3—62no—
484C4⋊Dic3—62no—
485C4⋊Dic3C22×D311yescharacteristic
486C4⋊Dic3C22×D312yes—
487C4⋊Dic3C22×D314yes—
488C4⋊Dic3C22×D311yescharacteristic
489C4⋊Dic3C22×D312yes—
490Dic3⋊C4—32no—
491Dic3⋊C4—34no—
492Dic3⋊C4—32no—
493Dic3⋊C4—34no—
494Dic3⋊C4—32no—
495Dic3⋊C4—32no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—32no—
502Dic3⋊C4—32no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—62no—
509Dic3⋊C4—64no—
510Dic3⋊C4C22×D312yes—
511Dic3⋊C4C22×D314yes—
512Dic3⋊C4C22×D312yes—
513Dic3⋊C4C22×D312yes—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—34no—
518C4×Dic3—32no—
519C4×Dic3—34no—
520C4×Dic3—34no—
521C4×Dic3—34no—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—34no—
525C4×Dic3—34no—
526C4×Dic3—62no—
527C4×Dic3C22×D311yescharacteristic
528C4×Dic3C22×D312yes—
529C4×Dic3C22×D312yes—
530C4×Dic3C22×D311yescharacteristic
531C4×Dic3C22×D311yescharacteristic
532C4×Dic3C22×D312yes—
533C4×Dic3C22×D312yes—
534C22×C32—22no—
535C22×C32—22no—
536C22×C32C22×Q814yes—
537C22×C32C2511yescharacteristic
538C2×C3×D3—21no—
539C2×C3×D3—21no—
540C2×C3×D3C22×Q812yes—
541C32×C4—22no—
542C32×C4—21no—
543C32×C4C22×Q812yes—
544C32×C4C2×#4112yes—
545C3⋊Dic3—24no—
546C3⋊Dic3—22no—
547C3⋊Dic3C2×#4114yes—
548C3×Dic3—22no—
549C3×Dic3—21no—
550C3×Dic3—22no—
551C3×Dic3—22no—
552C3×Dic3—24no—
553C3×Dic3—21no—
554C3×Dic3C22×Q814yes—
555C3×Dic3C22×Q812yes—
556C2×#41—31no—
557C22×Q8—91no—
558C22×Q8—92no—
559C4⋊Q8—31no—
560C4⋊Q8—92no—
561C4⋊Q8—92no—
562C4⋊Q8—94no—
563C4⋊Q8—92no—
564C4⋊Q8—94no—
565C4⋊Q8—92no—
566C4⋊Q8—91no—
567#125—32no—
568#125—94no—
569#125—92no—
570#125—92no—
571#125—94no—
572#125—94no—
573C22⋊Q8—32no—
574C22⋊Q8—34no—
575C22⋊Q8—94no—
576C22⋊Q8—94no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—94no—
580C22⋊Q8—92no—
581C22⋊Q8—92no—
582C22⋊Q8—92no—
583C22⋊Q8—94no—
584C4×Q8—31no—
585C4×Q8—31no—
586C4×Q8—31no—
587C4×Q8—92no—
588C4×Q8—91no—
589C4×Q8—92no—
590C4×Q8—94no—
591C4×Q8—92no—
592C4×Q8—92no—
593C4×Q8—94no—
594C4×Q8—92no—
595C4×Q8—94no—
596C4×Q8—91no—
597C4×Q8—92no—
598C4×Q8—92no—
599C4×Q8—92no—
600C4×Q8—91no—
601C4×D4—31no—
602C4×D4—32no—
603C4×D4—32no—
604C4×D4—32no—
605C4×D4—94no—
606C4×D4—94no—
607C4×D4—92no—
608C4×D4D3211yescharacteristic
609#117—31no—
610#117—32no—
611#117—94no—
612#117—92no—
613C2×C4⋊C4—32no—
614C2×C4⋊C4—92no—
615C2×C4⋊C4—91no—
616C2×C4⋊C4—94no—
617C2×C42—32no—
618C2×C42—31no—
619C2×C42—92no—
620C2×C42—94no—
621C23×C3—22no—
622C23×C3—31no—
623C23×C3C23×D312yes—
624C23×C3C23×D312yes—
625C22×D3C23×D311yescharacteristic
626C3×Q8—34no—
627C3×Q8—62no—
628C3×Q8—122no—
629C3×D4—24no—
630C3×D4—38no—
631C3×D4C2×Dic614yescomplemented
632C3×D4D3×Q814yescomplemented
633C2×C3×C4—24no—
634C2×C3×C4—24no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—22no—
639C2×C3×C4—38no—
640C2×C3×C4—31no—
641C2×C3×C4—32no—
642C2×C3×C4—34no—
643C2×C3×C4—32no—
644C2×C3×C4—34no—
645C2×C3×C4—32no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—32no—
649C2×C3×C4—44no—
650C2×C3×C4—62no—
651C2×C3×C4—121no—
652C2×C3×C4—124no—
653C2×C3×C4—122no—
654C2×C3×C4C23×D312yes—
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
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—32no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—34no—
667C2×Dic3—34no—
668C2×Dic3—32no—
669C2×Dic3—42no—
670C2×Dic3—44no—
671C2×Dic3—62no—
672C2×Dic3—62no—
673C2×Dic3—64no—
674C2×Dic3—64no—
675C2×Dic3—68no—
676C2×Dic3—68no—
677C2×Dic3—128no—
678C2×Dic3—122no—
679C2×Dic3C2×Dic618yescomplemented
680C2×Dic3C23×D312yes—
681C2×Dic3C23×D314yes—
682C2×Dic3C23×D312yes—
683C2×Dic3C23×D311yescharacteristic
684C2×Dic3C23×D312yes—
685C2×Dic3C23×D311yescharacteristic
686C2×Dic3C23×D311yescharacteristic
687C2×Dic3C23×D312yes—
688C4×D3—22no—
689C4×D3—41no—
690C4×D3—64no—
691C4×D3—122no—
692C4×D3C2×Dic614yescomplemented
693Dic6—22no—
694Dic6—34no—
695Dic6—34no—
696Dic6—42no—
697Dic6—64no—
698Dic6—64no—
699Dic6—64no—
700Dic6—68no—
701Dic6—68no—
702Dic6—64no—
703Dic6—64no—
704Dic6—128no—
705Dic6—124no—
706Dic6—124no—
707Dic6—124no—
708Dic6C2×Dic614yescomplemented
709C2×C32—24no—
710C2×C32C23×Q811yescharacteristic
711C2×C32C22×#4111yescharacteristic
712C2×C32#58511yescharacteristic
713C3×D3—22no—
714#41—38no—
715C2×Q8—31no—
716C2×Q8—31no—
717C2×Q8—32no—
718C2×Q8—92no—
719C2×Q8—94no—
720C2×Q8—91no—
721C2×Q8—94no—
722C2×Q8—92no—
723C2×Q8—188no—
724C2×Q8—184no—
725C2×D4—32no—
726C2×D4C2×D3211yescharacteristic
727C22×C4—32no—
728C22×C4—31no—
729C22×C4—32no—
730C22×C4—34no—
731C22×C4—31no—
732C22×C4—31no—
733C22×C4—92no—
734C22×C4—92no—
735C22×C4—94no—
736C22×C4C2×D3212yes—
737C4⋊C4—31no—
738C4⋊C4—34no—
739C4⋊C4—32no—
740C4⋊C4—32no—
741C4⋊C4—32no—
742C4⋊C4—32no—
743C4⋊C4—31no—
744C4⋊C4—32no—
745C4⋊C4—34no—
746C4⋊C4—92no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—92no—
750C4⋊C4—92no—
751C4⋊C4—94no—
752C4⋊C4—94no—
753C4⋊C4—94no—
754C4⋊C4—94no—
755C4⋊C4—94no—
756C4⋊C4—92no—
757C4⋊C4—91no—
758C4⋊C4—92no—
759C4⋊C4—94no—
760C4⋊C4—92no—
761C4⋊C4C2×D3211yescharacteristic
762C22⋊C4—32no—
763C22⋊C4—34no—
764C22⋊C4—32no—
765C22⋊C4—94no—
766C22⋊C4—94no—
767C22⋊C4C2×D3212yes—
768C42—31no—
769C42—32no—
770C42—31no—
771C42—32no—
772C42—31no—
773C42—32no—
774C42—32no—
775C42—92no—
776C42—92no—
777C42—94no—
778C42—94no—
779C42—94no—
780C42—92no—
781C42C2×D3211yescharacteristic
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—24no—
787C22×C3—21no—
788C22×C3—32no—
789C22×C3—42no—
790C22×C3—42no—
791C22×C3—61no—
792C22×C3—61no—
793C22×C3C22×Dic614yes—
794C22×C3C2×D3×Q814yes—
795C22×C3C24×D311yescharacteristic
796C22×C3C24×D311yescharacteristic
797C2×D3—21no—
798C2×D3—21no—
799C2×D3C22×Dic612yes—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—32no—
807C3×C4—34no—
808C3×C4—42no—
809C3×C4—41no—
810C3×C4—61no—
811C3×C4—62no—
812C3×C4—64no—
813C3×C4—62no—
814C3×C4—62no—
815C3×C4—61no—
816C3×C4C22×Dic612yes—
817C3×C4C2×D3×Q812yes—
818C3×C4D3×#4112yes—
819C3×C4D3×#4112yes—
820Dic3—22no—
821Dic3—21no—
822Dic3—22no—
823Dic3—21no—
824Dic3—24no—
825Dic3—22no—
826Dic3—34no—
827Dic3—34no—
828Dic3—64no—
829Dic3—64no—
830Dic3—64no—
831Dic3—62no—
832Dic3—62no—
833Dic3—124no—
834Dic3—122no—
835Dic3C22×Dic614yes—
836Dic3C22×Dic612yes—
837C32Q8×#4111yescharacteristic, complemented, Sylow
838C23—31no—
839C23C22×D3212yes—
840Q8—34no—
841Q8—62no—
842Q8—94no—
843Q8—122no—
844Q8—188no—
845Q8—184no—
846Q8—184no—
847Q8—364no—
848D4—38no—
849D4D3×Dic614yescomplemented
850C2×C4—24no—
851C2×C4—38no—
852C2×C4—31no—
853C2×C4—32no—
854C2×C4—34no—
855C2×C4—31no—
856C2×C4—31no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—34no—
861C2×C4—62no—
862C2×C4—92no—
863C2×C4—94no—
864C2×C4—92no—
865C2×C4—121no—
866C2×C4—122no—
867C2×C4—124no—
868C2×C4—184no—
869C2×C4—188no—
870C2×C4—362no—
871C2×C4C22×D3212yes—
872C2×C4C22×D3211yescharacteristic
873C2×C4C22×D3211yescharacteristic
874C2×C4C22×D3211yescharacteristic
875C2×C3—24no—
876C2×C3—24no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—44no—
881C2×C3—62no—
882C2×C3C23×Dic611yescharacteristic
883C2×C3C22×D3×Q811yescharacteristic
884C2×C3C2×D3×#4111yescharacteristic
885C2×C3C2×D3×#4111yescharacteristic
886C2×C3#596411yescharacteristic
887C2×C3#596611yescharacteristic
888D3—22no—
889C22—22no—
890C22—22no—
891C22—32no—
892C22—61no—
893C22—61no—
894C22C2×D3×Dic614yes—
895C22C23×D3211yescharacteristic
896C4—22no—
897C4—21no—
898C4—32no—
899C4—34no—
900C4—61no—
901C4—62no—
902C4—61no—
903C4—62no—
904C4—64no—
905C4—62no—
906C4—94no—
907C4—184no—
908C4—182no—
909C4C2×D3×Dic612yes—
910C4#6431212yes—
911C3—21no—
912C3#41×Dic611yescharacteristic, complemented
913C3#8692311yescharacteristic, complemented
914C2—24no—
915C2—62no—
916C2C22×D3×Dic611yescharacteristic
917C2C2×#6431211yescharacteristic
918C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC2×C3×#237C22
hypercenterC4×D4D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×#634C2semidirect
2. C3×#5543C2semidirect
4. #10595274C2semidirect
6. #10594988C2semidirect
7. #10594915C2semidirect
8. C2×#63844C2semidirect
9. #10594808C2semidirect
10. #10594477C2semidirect
11. #10594322C2semidirect
12. #10594156C2semidirect
13. #10594029C2semidirect
14. C4×D3×Dic6C2semidirect
15. #10593860C2semidirect
16. #10593859C2semidirect
17. #10593856C2semidirect
102. #5543D3semidirect
131. C3×#237Q8semidirect
329. C32×D4C2×Q8semidirect
341. #634#41semidirect
342. C3×#67C2×Q8semidirect
345. C2×C3×Dic3C2×Q8semidirect
356. C3×C4×D3C2×Q8semidirect
359. C3×Dic6C2×Q8semidirect
408. #237Dic6semidirect
631. C3×D4C2×Dic6semidirect
632. C3×D4D3×Q8semidirect
662. #67C2×Dic6semidirect
679. C2×Dic3C2×Dic6semidirect
692. C4×D3C2×Dic6semidirect
708. Dic6C2×Dic6semidirect
837. C32Q8×#41semidirect
849. D4D3×Dic6semidirect
912. C3#41×Dic6semidirect
913. C3#86923semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
C3×#55432
C3×C4×#2372
#105952742
Dic3×#2372
#105949882
#105949152
C2×#638442
#105948082
#105944772
#105943222
#105941562
#105940292
C4×D3×Dic62
#105938602
#105938592
#105938562
#869233
#41×Dic63