Finite Group Databasebeta

← D3×#5173 #11863770

Subgroups — D3×#5173 #11863770

Order 1152.

1596 conjugacy classes of subgroups.

The subgroup lattice has 997 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic
2C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
3D3×#946C211yesmaximal, characteristic, complemented
4C2×D3×#216C211yesmaximal, characteristic, complemented
5#10592872C211yesmaximal, characteristic, complemented
6C3×#5173C211yesmaximal, characteristic, complemented
7#10591656C211yesmaximal, characteristic, complemented
8#10591655C211yesmaximal, characteristic, complemented
9#10591466C211yesmaximal, characteristic, complemented
10#10591461C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic, complemented
12#10590961C211yesmaximal, characteristic, complemented
13#10590960C211yesmaximal, characteristic, complemented
14D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16C2×#5173—31nomaximal
17D3×#452—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×D3×#67—21no—
23C2×#3805—21no—
24C2×#3804—21no—
25C22×D3×Dic3—21no—
26D3×#237—24no—
27D3×#237—24no—
28C2×C4×D32C2211yescharacteristic
29C2×#3796C2211yescharacteristic
30C2×#3795C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C2×C32×SD16C2211yescharacteristic, complemented
33#64155C2211yescharacteristic, complemented
34C2×#3756C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C2×C3×#214C2211yescharacteristic, complemented
39C3×D3×SD16—24no—
40C2×C3×#204C2211yescharacteristic, complemented
41C2×C3×D3×C8C2211yescharacteristic
42D3×#216—24no—
43D3×(C2×D3)⋊C4—21no—
44D3×C4⋊Dic3C2211yescharacteristic
45#63888—21no—
46#63887—21no—
47D3×Dic3⋊C4—21no—
48#63871C2211yescharacteristic, complemented
49#63856C2211yescharacteristic, complemented
50C2×#3719C2211yescharacteristic, complemented
51C2×#3718C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic
53#63659C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#237—31no—
67C22×C3×SD16—31no—
68C2×#946—31no—
69C22×#216—31no—
70C2×D3×Q16—31no—
71C2×D3×SD16D311yescharacteristic, complemented
72D3×C22⋊Q8—31no—
73C3×#452—31no—
74#5239—31no—
75C2×#832—31no—
76#5187—31no—
77#5173—31no—
78#5173—31no—
79#5173—31no—
80#5173—31no—
81#5173—31no—
82#5173—31no—
83#5173—31no—
84#5173—31no—
85#5173—61no—
86#5173D311yescharacteristic, direct product factor
87C2×(C2×D3)⋊C8—31no—
88C2×#816—31no—
89#5047—31no—
90#4808—31no—
91D3×#103—31no—
92#4783—31no—
93D3×#102—31no—
94#4733—31no—
95D3×C22⋊C8—31no—
96C23×C3×D3—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101C22×C3⋊Dic3—21no—
102#3830—22no—
103#3830—22no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C3×D3×Q8—22no—
110C3×D3×Q8—22no—
111C3×#237—22no—
112C3×#237—22no—
113C3×D3×D4—22no—
114C3×D3×D4D414yes—
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×Dic6—21no—
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122D3×#67—28no—
123C2×#627—21no—
124C2×#626—21no—
125C2×#625—21no—
126C2×#624D411yescharacteristic
127#3805—28no—
128#3804—28no—
129C2×D3×Dic3—28no—
130C2×D3×Dic3—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3—21no—
133C2×D3×Dic3—21no—
134C2×D3×Dic3D411yescharacteristic
135C2×D3×Dic3D411yescharacteristic
136C4×D32—22no—
137C4×D32—22no—
138#3796—22no—
139#3796—22no—
140#3795—22no—
141#3795—22no—
142D3×Dic6—22no—
143D3×Dic6D414yes—
144C32×SD16—22no—
145C2×C32×C8C2311yescharacteristic
146#3756—22no—
147#3752—21no—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149#3750—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C3×#216—22no—
152C3×#215—22no—
153C3×#214—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×Dic3⋊C4—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×#204—22no—
160C3×D3×C8—22no—
161#3724—21no—
162Dic3⋊Dic3—21no—
163Dic3⋊Dic3—21no—
164#3722—21no—
165(C2×D3)⋊Dic3—21no—
166#3719—22no—
167#3718—22no—
168D3×C3⋊C8—22no—
169C2×#452—91noSylow
170C2×C3×#41—31no—
171C22×C3×Q8—31no—
172C22×C3×D4—31no—
173C22×#67—61no—
174C23×Dic3—61no—
175D3×#41—64no—
176D3×#41—64no—
177C2×#239—31no—
178C2×D3×Q8—31no—
179C2×D3×Q8C2×D311yescharacteristic
180C2×#237—31no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—61no—
185C2×#237—64no—
186C2×#237—61no—
187C2×#237—61no—
188C2×#237—64no—
189C2×#237—61no—
190C2×#237C2×D311yescharacteristic
191C2×D3×D4—61no—
192C2×D3×D4C2×D311yescharacteristic
193C2×#235—31no—
194C2×#235—61no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×SD16—21no—
201C2×C3×SD16—31no—
202C2×C3×SD16—31no—
203C2×C3×SD16—31no—
204C2×C3×SD16—64no—
205C2×C3×SD16C2×D311yescharacteristic, complemented
206C2×C3×SD16C2×D311yescharacteristic, complemented
207C22×C3×C8—31no—
208C3×C22⋊Q8—31no—
209#946—31no—
210#946—31no—
211#946—31no—
212#946—31no—
213#946—61no—
214#946—61no—
215#946—61no—
216#946C2×D311yescharacteristic, complemented
217C2×#216—31no—
218C2×#216—31no—
219C2×#216—31no—
220C2×#216—31no—
221C2×#216—31no—
222C2×#216—61no—
223C2×#216—64no—
224C2×#216C2×D311yescharacteristic, complemented
225C2×#215C2×D311yescharacteristic, complemented
226C2×#214C2×D311yescharacteristic, complemented
227C2×(C2×D3)⋊C4—61no—
228C2×C4⋊Dic3—31no—
229#924—31no—
230C2×Dic3⋊C4—61no—
231C22×C3⋊C8—31no—
232D3×Q16—64no—
233D3×SD16—24no—
234C2×Dic12—31no—
235C2×#204C2×D311yescharacteristic, complemented
236C2×D3×C8—31no—
237C2×D3×C8C2×D311yescharacteristic
238#897—31no—
239#896—61no—
240D3×C4⋊C4—31no—
241D3×C4⋊C4—61no—
242D3×C22⋊C4—61no—
243#878—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#832—31no—
249#832—31no—
250#832—31no—
251#832—31no—
252#832—61no—
253#832C2×D311yescharacteristic, complemented
254#830—31no—
255#821—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—61no—
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816—31no—
264#816—31no—
265#816—31no—
266#816—31no—
267#816—61no—
268#816C2×D311yescharacteristic, complemented
269#810—31no—
270#809—31no—
271C23×C32—21no—
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—24no—
275C22×C3×D3—42no—
276C22×C3×D3—42no—
277C22×C3×D3C2×D411yescharacteristic
278C22×C3×D3C2×D411yescharacteristic
279C2×D32—22no—
280C2×D32—22no—
281C2×D32—22no—
282C32×Q8—21no—
283C32×Q8—21no—
284C32×D4—21no—
285C32×D4C2×D412yes—
286C2×C32×C4—21no—
287C2×C32×C4C2411yescharacteristic
288#638—24no—
289C2×C3⋊Dic3—24no—
290C2×C3⋊Dic3—21no—
291C2×C3⋊Dic3—21no—
292C2×C3⋊Dic3C2×D411yescharacteristic
293C4×C3⋊D3—21no—
294C4×C3⋊D3—21no—
295#634—21no—
296#634C2×D412yes—
297C3×#67—24no—
298C3×#67—24no—
299C2×C3×Dic3—24no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C2×D411yescharacteristic
304C2×C3×Dic3C2×D411yescharacteristic
305C3×D12—21no—
306C3×D12C2×D412yes—
307C3×C4×D3—21no—
308C3×C4×D3—21no—
309C3×C4×D3—42no—
310C3×C4×D3C2×D412yes—
311C3×C4×D3C2×D412yes—
312C3×Dic6—21no—
313C3×Dic6—21no—
314C3×Dic6—21no—
315C3×Dic6—42no—
316C3×Dic6C2×D412yes—
317#627—24no—
318#626—24no—
319#625—24no—
320#624—22no—
321D3×Dic3—24no—
322D3×Dic3—24no—
323D3×Dic3—24no—
324D3×Dic3—22no—
325D3×Dic3—22no—
326D3×Dic3—42no—
327C32×C8—21no—
328C3⋊(C3⋊C8)—21no—
329C3×C3⋊C8—21no—
330C3×C3⋊C8—21no—
331C22×#41—91no—
332C22×Q16—91no—
333C22×SD16—31no—
334C2×C22⋊Q8—91no—
335#452—31no—
336#452—91no—
337#452—91no—
338#452—91no—
339#452—91no—
340#452—91no—
341#452—91no—
342#452—91no—
343C2×#103—91no—
344C2×#102—91no—
345C2×C22⋊C8—91no—
346C24×C3—61no—
347C23×D3—21no—
348C23×D3—31no—
349C23×D3—31no—
350C3×#41—62no—
351C3×#41—62no—
352C2×C3×Q8—21no—
353C2×C3×Q8—31no—
354C2×C3×Q8—31no—
355C2×C3×Q8—61no—
356C2×C3×Q8—62no—
357C2×C3×Q8—62no—
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×D4—21no—
361C2×C3×D4—34no—
362C2×C3×D4—31no—
363C2×C3×D4—62no—
364C2×C3×D4—61no—
365C2×C3×D4—61no—
366C2×C3×D4C22×D311yescharacteristic
367C2×C3×D4C22×D311yescharacteristic
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—61no—
371C22×C3×C4—61no—
372C2×#67—21no—
373C2×#67—21no—
374C2×#67—61no—
375C2×#67—68no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—121no—
381C22×Dic3—21no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—68no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—61no—
391C22×Dic3—121no—
392#239—62no—
393#239—62no—
394D3×Q8—22no—
395D3×Q8—22no—
396D3×Q8—34no—
397D3×Q8—62no—
398#237—22no—
399#237—22no—
400#237—62no—
401#237—62no—
402#237—62no—
403#237—62no—
404#237—62no—
405#237—68no—
406#237—68no—
407#237—68no—
408#237—62no—
409#237—62no—
410#237—62no—
411#237—122no—
412#237—122no—
413D3×D4—22no—
414D3×D4—68no—
415D3×D4#6714yes—
416#235—62no—
417#235—68no—
418#235—62no—
419C2×D12—61no—
420C2×D12C22×D311yescharacteristic
421C2×C4×D3—21no—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—61no—
429C2×C4×D3—62no—
430C2×C4×D3—62no—
431C2×C4×D3—61no—
432C2×C4×D3—61no—
433C2×C4×D3—68no—
434C2×C4×D3—61no—
435C2×C4×D3—62no—
436C2×C4×D3—62no—
437C2×C4×D3—61no—
438C2×C4×D3C22×D311yescharacteristic
439C2×C4×D3C22×D311yescharacteristic
440C2×Dic6—21no—
441C2×Dic6—31no—
442C2×Dic6—31no—
443C2×Dic6—34no—
444C2×Dic6—61no—
445C2×Dic6—62no—
446C2×Dic6—61no—
447C2×Dic6—61no—
448C2×Dic6C22×D311yescharacteristic
449C2×Dic6C22×D311yescharacteristic
450C3×Q16—62no—
451C3×SD16—22no—
452C3×SD16—22no—
453C3×SD16—42no—
454C3×SD16—62no—
455C3×SD16—62no—
456C3×SD16—62no—
457C2×C3×C8—21no—
458C2×C3×C8—31no—
459C2×C3×C8—31no—
460C2×C3×C8—62no—
461C2×C3×C8C22×D311yescharacteristic
462C2×C3×C8C22×D311yescharacteristic
463C3×C4⋊C4—31no—
464C3×C4⋊C4—61no—
465C3×C22⋊C4—61no—
466#217—61no—
467#216—22no—
468#216—62no—
469#216—62no—
470#216—62no—
471#216—62no—
472#216—62no—
473#216—122no—
474#215—22no—
475#214—22no—
476(C2×D3)⋊C4—21no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—121no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—61no—
486C4⋊Dic3—61no—
487C4⋊Dic3—61no—
488C4⋊Dic3C22×D311yescharacteristic
489Dic3⋊C4—21no—
490Dic3⋊C4—61no—
491Dic3⋊C4—61no—
492Dic3⋊C4—61no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495Dic3⋊C4—61no—
496Dic3⋊C4—121no—
497C2×C3⋊C8—31no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—61no—
500C2×C3⋊C8—62no—
501C2×C3⋊C8C22×D311yescharacteristic
502C2×C3⋊C8C22×D311yescharacteristic
503Dic12—62no—
504#204—22no—
505D3×C8—22no—
506D3×C8—62no—
507C22×C32—22no—
508C22×C32—41no—
509C22×C32—41no—
510C22×C32C22×D411yescharacteristic
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3×D3—22no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—41no—
519C2×C3×D3—41no—
520C2×C3×D3—48no—
521C2×C3×D3#12012yes—
522C2×C3×D3#13512yes—
523C2×C3×D3#13712yes—
524D32—44no—
525C32×C4—41no—
526C32×C4C22×D411yescharacteristic
527C32×C4C22×D411yescharacteristic
528C3⋊Dic3—21no—
529C3⋊Dic3—22no—
530C3⋊Dic3—41no—
531C3×Dic3—21no—
532C3×Dic3—22no—
533C3×Dic3—41no—
534C3×Dic3—41no—
535C3×Dic3#12012yes—
536C2×#41—31no—
537C2×#41—91no—
538C2×#41—91no—
539C2×#41—91no—
540C2×#41—181no—
541C2×#41—181no—
542C2×#41—184no—
543C2×#41—184no—
544C22×Q8—31no—
545C22×Q8—91no—
546C22×D4—31no—
547C22×D4—181no—
548C23×C4—91no—
549C23×C4—181no—
550C2×Q16—31no—
551C2×Q16—91no—
552C2×Q16—91no—
553C2×Q16—91no—
554C2×Q16—184no—
555C2×SD16—31no—
556C2×SD16—31no—
557C2×SD16—31no—
558C2×SD16—64no—
559C2×SD16D3211yescharacteristic, complemented
560C22×C8—31no—
561C22×C8—91no—
562C22⋊Q8—31no—
563C22⋊Q8—91no—
564C22⋊Q8—91no—
565C22⋊Q8—91no—
566C22⋊Q8—181no—
567C22⋊Q8—181no—
568C2×C4⋊C4—91no—
569C2×C4⋊C4—181no—
570C2×C22⋊C4—181no—
571#103—31no—
572#103—91no—
573#103—91no—
574#103—91no—
575#102—31no—
576#102—91no—
577#102—91no—
578#102—91no—
579C22⋊C8—31no—
580C22⋊C8—91no—
581C22⋊C8—91no—
582C22⋊C8—91no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—31no—
586C23×C3—31no—
587C23×C3—41no—
588C23×C3—64no—
589C23×C3—61no—
590C23×C3—122no—
591C23×C3—122no—
592C22×D3—21no—
593C22×D3—24no—
594C22×D3—31no—
595C22×D3—31no—
596C22×D3—42no—
597C22×D3—42no—
598C22×D3—61no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3D3×D411yescharacteristic
606C22×D3D3×D411yescharacteristic
607C3×Q8—21no—
608C3×Q8—21no—
609C3×Q8—21no—
610C3×Q8—21no—
611C3×Q8—32no—
612C3×Q8—41no—
613C3×Q8—41no—
614C3×Q8—61no—
615C3×Q8—61no—
616C3×Q8—61no—
617C3×Q8—122no—
618C3×D4—21no—
619C3×D4—21no—
620C3×D4—22no—
621C3×D4—32no—
622C3×D4—41no—
623C3×D4—64no—
624C3×D4—64no—
625C3×D4—61no—
626C3×D4D3×D412yes—
627C3×D4C2×#6712yes—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—31no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—31no—
635C2×C3×C4—41no—
636C2×C3×C4—64no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—122no—
643C2×C3×C4C23×D311yescharacteristic
644C2×C3×C4C23×D311yescharacteristic
645#67—24no—
646#67—24no—
647#67—64no—
648#67—64no—
649#67—64no—
650#67—64no—
651#67—64no—
652#67—124no—
653C2×Dic3—24no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—61no—
660C2×Dic3—64no—
661C2×Dic3—62no—
662C2×Dic3—64no—
663C2×Dic3—64no—
664C2×Dic3—64no—
665C2×Dic3—64no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—62no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—121no—
672C2×Dic3—124no—
673C2×Dic3—121no—
674C2×Dic3—122no—
675C2×Dic3D3×D411yescharacteristic
676C2×Dic3D3×D411yescharacteristic
677D12—21no—
678D12—64no—
679D12C2×#6712yes—
680C4×D3—21no—
681C4×D3—21no—
682C4×D3—42no—
683C4×D3—62no—
684C4×D3—62no—
685C4×D3—64no—
686C4×D3—64no—
687C4×D3—62no—
688C4×D3—64no—
689C4×D3—61no—
690C4×D3—61no—
691C4×D3—61no—
692C4×D3—61no—
693C4×D3—62no—
694C4×D3—121no—
695C4×D3—121no—
696C4×D3—122no—
697C4×D3D3×D412yes—
698C4×D3C2×#6712yes—
699Dic6—21no—
700Dic6—21no—
701Dic6—21no—
702Dic6—32no—
703Dic6—32no—
704Dic6—42no—
705Dic6—62no—
706Dic6—64no—
707Dic6—61no—
708Dic6—61no—
709Dic6—64no—
710Dic6—121no—
711Dic6D3×D412yes—
712C3×C8—21no—
713C3×C8—21no—
714C3×C8—41no—
715C3×C8—61no—
716C3×C8—61no—
717C3⋊C8—21no—
718C3⋊C8—21no—
719C3⋊C8—61no—
720C3⋊C8—61no—
721C3⋊C8—121no—
722C2×C32—42no—
723C2×C32C2×#12011yescharacteristic
724C2×C32C2×#13511yescharacteristic
725C2×C32C2×#13711yescharacteristic
726C3⋊D3—41no—
727C3×D3—41no—
728C3×D3—42no—
729C3×D3#45214yescomplemented
730C24—61no—
731C24—91no—
732#41—62no—
733#41—62no—
734#41—182no—
735#41—182no—
736#41—188no—
737#41—182no—
738#41—182no—
739#41—188no—
740#41—182no—
741#41—182no—
742C2×Q8—31no—
743C2×Q8—31no—
744C2×Q8—61no—
745C2×Q8—62no—
746C2×Q8—62no—
747C2×Q8—94no—
748C2×Q8—91no—
749C2×Q8—181no—
750C2×Q8—182no—
751C2×Q8C2×D3211yescharacteristic
752C2×D4—34no—
753C2×D4—31no—
754C2×D4—62no—
755C2×D4—61no—
756C2×D4—61no—
757C2×D4—181no—
758C2×D4—188no—
759C2×D4—181no—
760C2×D4—181no—
761C2×D4C2×D3211yescharacteristic
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—91no—
767C22×C4—91no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—182no—
771C22×C4—182no—
772C22×C4—181no—
773C22×C4—181no—
774C22×C4—181no—
775C22×C4—188no—
776C22×C4—181no—
777C22×C4—181no—
778Q16—62no—
779Q16—182no—
780Q16—182no—
781Q16—182no—
782SD16—22no—
783SD16—62no—
784SD16—62no—
785SD16—62no—
786C2×C8—31no—
787C2×C8—31no—
788C2×C8—62no—
789C2×C8—91no—
790C2×C8—182no—
791C2×C8C2×D3211yescharacteristic
792C4⋊C4—31no—
793C4⋊C4—61no—
794C4⋊C4—91no—
795C4⋊C4—181no—
796C4⋊C4—181no—
797C4⋊C4—181no—
798C4⋊C4—181no—
799C22⋊C4—61no—
800C22⋊C4—181no—
801C22⋊C4—181no—
802C22⋊C4—181no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—21no—
806C22×C3—32no—
807C22×C3—32no—
808C22×C3—32no—
809C22×C3—42no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—62no—
818C22×C3—81no—
819C22×C3—81no—
820C22×C3—128no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3C2×D3×D411yescharacteristic
824C22×C3C2×D3×D411yescharacteristic
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—22no—
828C2×D3—21no—
829C2×D3—41no—
830C2×D3—41no—
831C2×D3—48no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—121no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—124no—
842C2×D3—124no—
843C2×D3#91512yes—
844C2×D3#91612yes—
845C2×D3#93712yes—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—32no—
849C3×C4—41no—
850C3×C4—41no—
851C3×C4—62no—
852C3×C4—61no—
853C3×C4—81no—
854C3×C4—121no—
855C3×C4—121no—
856C3×C4C2×D3×D411yescharacteristic
857C3×C4C2×D3×D411yescharacteristic
858C3×C4C2×D3×D411yescharacteristic
859C3×C4C22×#6711yescharacteristic
860Dic3—22no—
861Dic3—21no—
862Dic3—41no—
863Dic3—41no—
864Dic3—62no—
865Dic3—61no—
866Dic3—62no—
867Dic3—61no—
868Dic3—122no—
869Dic3—121no—
870Dic3—121no—
871Dic3—121no—
872Dic3—241no—
873Dic3#93712yes—
874C32C2×#45211yescharacteristic, complemented, Sylow
875C23—21no—
876C23—31no—
877C23—31no—
878C23—64no—
879C23—61no—
880C23—91no—
881C23—122no—
882C23—122no—
883C23—182no—
884C23—182no—
885C23—182no—
886Q8—21no—
887Q8—21no—
888Q8—32no—
889Q8—61no—
890Q8—61no—
891Q8—61no—
892Q8—92no—
893Q8—122no—
894Q8—184no—
895Q8—181no—
896D4—21no—
897D4—32no—
898D4—64no—
899D4—64no—
900D4—61no—
901D4—184no—
902D4—184no—
903D4—184no—
904D4D3×#6712yes—
905C2×C4—21no—
906C2×C4—31no—
907C2×C4—32no—
908C2×C4—32no—
909C2×C4—31no—
910C2×C4—64no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—91no—
917C2×C4—122no—
918C2×C4—182no—
919C2×C4—182no—
920C2×C4—182no—
921C2×C4—184no—
922C2×C4—184no—
923C2×C4—184no—
924C2×C4—184no—
925C2×C4—181no—
926C2×C4—181no—
927C2×C4—181no—
928C2×C4—181no—
929C2×C4—362no—
930C2×C4C22×D3211yescharacteristic
931C8—21no—
932C8—61no—
933C8—61no—
934C8—181no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—34no—
939C2×C3—42no—
940C2×C3—42no—
941C2×C3—82no—
942C2×C3—122no—
943C2×C3—121no—
944C2×C3D3×#12011yescharacteristic
945C2×C3C2×#91511yescharacteristic
946C2×C3C2×#91611yescharacteristic
947C2×C3D3×#13511yescharacteristic
948C2×C3D3×#13711yescharacteristic
949C2×C3C2×#93711yescharacteristic
950D3—41no—
951D3—42no—
952D3—121no—
953D3—121no—
954D3—241no—
955D3#517314yesdirect product factor
956C22—22no—
957C22—32no—
958C22—32no—
959C22—32no—
960C22—41no—
961C22—41no—
962C22—61no—
963C22—61no—
964C22—61no—
965C22—62no—
966C22—128no—
967C22—121no—
968C22—121no—
969C22—181no—
970C22—181no—
971C22—181no—
972C22—364no—
973C22D32×D411yescharacteristic
974C4—32no—
975C4—41no—
976C4—61no—
977C4—62no—
978C4—121no—
979C4—121no—
980C4—181no—
981C4—182no—
982C4—361no—
983C4D32×D411yescharacteristic
984C4C2×D3×#6711yescharacteristic
985C3—21no—
986C3D3×#45211yescharacteristic, complemented
987C3C2×#517311yescharacteristic, complemented
988C2—34no—
989C2—42no—
990C2—121no—
991C2—122no—
992C2—361no—
993C2D3×#91511yescharacteristic
994C2D3×#91611yescharacteristic
995C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×D3×#237C2
hypercenterC2×SD16D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×SD16C2semidirect
3. D3×#946C2semidirect
4. C2×D3×#216C2semidirect
5. #10592872C2semidirect
6. C3×#5173C2semidirect
7. #10591656C2semidirect
8. #10591655C2semidirect
9. #10591466C2semidirect
10. #10591461C2semidirect
11. D3×#832C2semidirect
12. #10590961C2semidirect
13. #10590960C2semidirect
14. D3×(C2×D3)⋊C8C2semidirect
15. D3×#816C2semidirect
32. C2×C32×SD16C22semidirect
33. #64155C22semidirect
34. C2×#3756C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#214C22semidirect
40. C2×C3×#204C22semidirect
48. #63871C22semidirect
49. #63856C22semidirect
50. C2×#3719C22semidirect
51. C2×#3718C22semidirect
53. #63659C22semidirect
54. #63647C22semidirect
55. #63643C22semidirect
56. C3×#832C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
71. C2×D3×SD16D3semidirect
86. #5173D3direct (N × H)
205. C2×C3×SD16C2×D3semidirect
206. C2×C3×SD16C2×D3semidirect
216. #946C2×D3semidirect
224. C2×#216C2×D3semidirect
225. C2×#215C2×D3semidirect
226. C2×#214C2×D3semidirect
235. C2×#204C2×D3semidirect
253. #832C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
268. #816C2×D3semidirect
559. C2×SD16D32semidirect
729. C3×D3#452semidirect
874. C32C2×#452semidirect
955. D3#5173direct (N × H)
986. C3D3×#452semidirect
987. C3C2×#5173semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×C3×D3×SD162
D3×#9462
C2×D3×#2162
#105928722
C3×#51732
#105916562
#105916552
#105914662
#105914612
D3×#8322
#105909612
#105909602
D3×(C2×D3)⋊C82
D3×#8162
C2×#51733
D3×#4523