Finite Group Databasebeta

← D3×#5239 #11863776

Subgroups — D3×#5239 #11863776

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×C3×D3×#41C211yesmaximal, characteristic
2C2×D3×#216C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4D3×#924C211yesmaximal, characteristic, complemented
5#10592938C211yesmaximal, characteristic, complemented
6C3×#5239C211yesmaximal, characteristic, complemented
7#10591599C211yesmaximal, characteristic, complemented
8#10591597C211yesmaximal, characteristic, complemented
9D3×#835C211yesmaximal, characteristic, complemented
10#10591463C211yesmaximal, characteristic, complemented
11#10591461C211yesmaximal, characteristic, complemented
12D3×#832C211yesmaximal, characteristic, complemented
13#10591173C211yesmaximal, characteristic, complemented
14#10591170C211yesmaximal, characteristic, complemented
15D3×#830C211yesmaximal, characteristic, complemented
16C2×#5239—31nomaximal
17D3×#452—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C3×D3×#41—24no—
20C3×D3×#41—24no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×#237—21no—
24C2×C3×#237C2211yescharacteristic
25C2×C3×D3×D4—21no—
26C2×C3×D3×D4C2211yescharacteristic
27C2×C3×#235—21no—
28C2×C3×#235C2211yescharacteristic
29C22×C3×C4×D3—21no—
30C22×C3×C4×D3C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C2×#3756C2211yescharacteristic, complemented
33C2×#3754C2211yescharacteristic, complemented
34#64133C2211yescharacteristic, complemented
35C2×C3×#216C2211yescharacteristic, complemented
36C2×C3×#214C2211yescharacteristic, complemented
37C3×#924C2211yescharacteristic, complemented
38D3×#217—21no—
39#63964—21no—
40D3×#216—24no—
41D3×#214—24no—
42D3×C4⋊Dic3C2211yescharacteristic
43D3×Dic3⋊C4—21no—
44#63857C2211yescharacteristic, complemented
45#63856C2211yescharacteristic, complemented
46#63851—21no—
47C2×#3719C2211yescharacteristic, complemented
48C2×#3718C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52C2×D3×C3⋊C8C2211yescharacteristic
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63657C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C22×C3×#41—31no—
66C2×D3×#41D311yescharacteristic
67C22×#216—31no—
68C22×#214—31no—
69C2×#924—31no—
70C2×D3×Q16—31no—
71C2×D3×SD16—31no—
72D3×C22⋊Q8—31no—
73C3×#452—31no—
74#5239—31no—
75#5239—31no—
76#5239—31no—
77#5239—31no—
78#5239—31no—
79#5239—31no—
80#5239—31no—
81#5239—31no—
82#5239—61no—
83#5239D311yescharacteristic, direct product factor
84C2×#835—31no—
85C2×#832—31no—
86C2×#830—31no—
87#5187—31no—
88#5173—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—
97C23×C3×D3D411yescharacteristic
98C32×#41—22no—
99C32×#41—22no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4—21no—
102C2×C32×D4C2311yescharacteristic
103C22×C32×C4—21no—
104C22×C32×C4C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3D411yescharacteristic
111C3×#239—22no—
112C3×#239—22no—
113C3×D3×Q8—22no—
114C3×D3×Q8D414yes—
115C3×#237—28no—
116C3×#237—22no—
117C3×#237—22no—
118C3×D3×D4—28no—
119C3×D3×D4—22no—
120C3×D3×D4D414yes—
121C3×#235—28no—
122C3×#235—22no—
123C3×#235—22no—
124C2×C3×D12—21no—
125C2×C3×D12C2311yescharacteristic
126C2×C3×C4×D3—28no—
127C2×C3×C4×D3—21no—
128C2×C3×C4×D3—21no—
129C2×C3×C4×D3—21no—
130C2×C3×C4×D3—22no—
131C2×C3×C4×D3—22no—
132C2×C3×C4×D3D411yescharacteristic
133C2×C3×C4×D3D411yescharacteristic
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×Dic6—21no—
137C2×C3×Dic6C2311yescharacteristic
138C2×C3×Dic6C2311yescharacteristic
139C2×#627—21no—
140C2×D3×Dic3—21no—
141C2×D3×Dic3—21no—
142D3×Dic6—22no—
143D3×Dic6—22no—
144#3757—21no—
145#3756—22no—
146#3754—22no—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148#3750—21no—
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C3×#217—21no—
152C3×#216—22no—
153C3×#214—22no—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×Dic3⋊C4—21no—
156C2×C3×C3⋊C8C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158#3724—21no—
159Dic3⋊Dic3—21no—
160Dic3⋊Dic3—21no—
161(C2×D3)⋊Dic3—21no—
162(C2×D3)⋊Dic3—21no—
163#3719—22no—
164#3718—22no—
165#3716—22no—
166#3715—22no—
167D3×C3⋊C8—22no—
168D3×C3⋊C8—22no—
169C2×#452—91noSylow
170C2×C3×#41—21no—
171C2×C3×#41—31no—
172C2×C3×#41—31no—
173C2×C3×#41—31no—
174C2×C3×#41—61no—
175C2×C3×#41—61no—
176C2×C3×#41—64no—
177C2×C3×#41—64no—
178C2×C3×#41C2×D311yescharacteristic
179C2×C3×#41C2×D311yescharacteristic
180C22×C3×Q8—31no—
181C22×C3×D4—31no—
182C22×C3×D4—61no—
183C23×C3×C4—31no—
184C23×C3×C4—61no—
185D3×#41—24no—
186D3×#41—24no—
187C2×#239C2×D311yescharacteristic
188C2×D3×Q8—31no—
189C2×D3×Q8C2×D311yescharacteristic
190C2×#237—21no—
191C2×#237C2×D311yescharacteristic
192C2×D3×D4—21no—
193C2×D3×D4C2×D311yescharacteristic
194C2×#235—21no—
195C2×#235C2×D311yescharacteristic
196C22×C4×D3—21no—
197C22×C4×D3C2×D311yescharacteristic
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C3×C22⋊Q8—31no—
202C2×#217—61no—
203#946—31no—
204C2×#216—31no—
205C2×#216—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#216—31no—
209C2×#216—61no—
210C2×#216—64no—
211C2×#216C2×D311yescharacteristic, complemented
212C2×#215—31no—
213C2×#214—31no—
214C2×#214—31no—
215C2×#214—31no—
216C2×#214—31no—
217C2×#214—61no—
218C2×#214—64no—
219C2×#214C2×D311yescharacteristic, complemented
220C2×C4⋊Dic3—31no—
221#924—31no—
222#924—31no—
223#924—31no—
224#924—31no—
225#924—61no—
226#924—61no—
227#924—61no—
228#924C2×D311yescharacteristic, complemented
229C2×Dic3⋊C4—61no—
230C22×C3⋊C8—31no—
231C22×C3⋊C8—31no—
232D3×Q16—64no—
233D3×SD16—64no—
234C2×Dic12—31no—
235C2×#204—31no—
236C2×D3×C8—31no—
237C2×D3×C8—31no—
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#835—31no—
249#835—31no—
250#835—31no—
251#835—61no—
252#835C2×D311yescharacteristic, complemented
253#832—31no—
254#832—31no—
255#832—31no—
256#832—31no—
257#832—61no—
258#832C2×D311yescharacteristic, complemented
259#830—31no—
260#830—31no—
261#830—31no—
262#830—31no—
263#830—61no—
264#830C2×D311yescharacteristic, complemented
265#821—31no—
266(C2×D3)⋊C8—31no—
267(C2×D3)⋊C8—31no—
268#816—31no—
269#810—31no—
270#809—31no—
271C23×C32—21no—
272C23×C32C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—24no—
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3—42no—
279C22×C3×D3—42no—
280C22×C3×D3C2×D411yescharacteristic
281C22×C3×D3C2×D411yescharacteristic
282C32×Q8—21no—
283C32×Q8C2×D412yes—
284C32×D4—24no—
285C32×D4—21no—
286C32×D4C2×D412yes—
287C2×C32×C4—24no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4C2×D411yescharacteristic
292C2×C32×C4C2411yescharacteristic
293C2×C3⋊Dic3—21no—
294C2×C3⋊Dic3—21no—
295#634—21no—
296#634—21no—
297C3×#67—24no—
298C3×#67—24no—
299C3×#67—24no—
300C2×C3×Dic3—24no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3C2×D411yescharacteristic
306C2×C3×Dic3C2×D411yescharacteristic
307C3×D12—24no—
308C3×D12—21no—
309C3×D12C2×D412yes—
310C3×C4×D3—24no—
311C3×C4×D3—24no—
312C3×C4×D3—22no—
313C3×C4×D3—24no—
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×C4×D3—22no—
317C3×C4×D3C2×D412yes—
318C3×C4×D3C2×D412yes—
319C3×Dic6—21no—
320C3×Dic6—24no—
321C3×Dic6—21no—
322C3×Dic6—21no—
323C3×Dic6C2×D412yes—
324#627—42no—
325D3×Dic3—42no—
326D3×Dic3—42no—
327C3⋊(C3⋊C8)—21no—
328C3⋊(C3⋊C8)—21no—
329C3×C3⋊C8—21no—
330C3×C3⋊C8—21no—
331C22×#41—31no—
332C22×Q16—91no—
333C22×SD16—91no—
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—31no—
347C24×C3—61no—
348C23×D3—21no—
349C23×D3#6711yescharacteristic
350C3×#41—22no—
351C3×#41—22no—
352C3×#41—22no—
353C3×#41—22no—
354C3×#41—42no—
355C3×#41—42no—
356C3×#41—62no—
357C3×#41—62no—
358C3×#41—68no—
359C3×#41—62no—
360C3×#41—68no—
361C3×#41—62no—
362C3×#41—62no—
363C3×#41—62no—
364C2×C3×Q8—21no—
365C2×C3×Q8—34no—
366C2×C3×Q8—31no—
367C2×C3×Q8—31no—
368C2×C3×Q8—61no—
369C2×C3×Q8—62no—
370C2×C3×Q8C22×D311yescharacteristic
371C2×C3×Q8C22×D311yescharacteristic
372C2×C3×D4—21no—
373C2×C3×D4—21no—
374C2×C3×D4—21no—
375C2×C3×D4—34no—
376C2×C3×D4—31no—
377C2×C3×D4—41no—
378C2×C3×D4—61no—
379C2×C3×D4—62no—
380C2×C3×D4—61no—
381C2×C3×D4—68no—
382C2×C3×D4—61no—
383C2×C3×D4—61no—
384C2×C3×D4C22×D311yescharacteristic
385C2×C3×D4C22×D311yescharacteristic
386C22×C3×C4—21no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—41no—
395C22×C3×C4—62no—
396C22×C3×C4—62no—
397C22×C3×C4—61no—
398C22×C3×C4—61no—
399C22×C3×C4—68no—
400C22×C3×C4—61no—
401C22×C3×C4—61no—
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C22×D311yescharacteristic
404C2×#67—21no—
405C2×#67—21no—
406C2×#67—21no—
407C22×Dic3—21no—
408C22×Dic3—61no—
409C22×Dic3—61no—
410C22×Dic3#6711yescharacteristic
411#239—22no—
412#239—22no—
413D3×Q8—22no—
414D3×Q8—62no—
415D3×Q8—62no—
416D3×Q8#6714yes—
417#237—28no—
418#237—22no—
419#237—22no—
420D3×D4—28no—
421D3×D4—22no—
422D3×D4#6714yes—
423#235—28no—
424#235—22no—
425#235—22no—
426C2×D12—21no—
427C2×D12C22×D311yescharacteristic
428C2×C4×D3—28no—
429C2×C4×D3—21no—
430C2×C4×D3—21no—
431C2×C4×D3—21no—
432C2×C4×D3—22no—
433C2×C4×D3—22no—
434C2×C4×D3—61no—
435C2×C4×D3—61no—
436C2×C4×D3#6711yescharacteristic
437C2×C4×D3#6711yescharacteristic
438C2×C4×D3C22×D311yescharacteristic
439C2×C4×D3C22×D311yescharacteristic
440C2×Dic6—21no—
441C2×Dic6—31no—
442C2×Dic6—31no—
443C2×Dic6—61no—
444C2×Dic6—62no—
445C2×Dic6—62no—
446C2×Dic6—61no—
447C2×Dic6—61no—
448C2×Dic6C22×D311yescharacteristic
449C2×Dic6C22×D311yescharacteristic
450C3×Q16—62no—
451C3×SD16—62no—
452C2×C3×C8—31no—
453C2×C3×C8—31no—
454C3×C4⋊C4—31no—
455C3×C4⋊C4—61no—
456C3×C22⋊C4—61no—
457#217—21no—
458#217—61no—
459#217—61no—
460#217—61no—
461#217—61no—
462#217—121no—
463#216—22no—
464#216—62no—
465#216—62no—
466#216—62no—
467#216—62no—
468#216—62no—
469#216—122no—
470#215—62no—
471#214—22no—
472#214—62no—
473#214—62no—
474#214—62no—
475#214—62no—
476#214—122no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—61no—
479C4⋊Dic3—31no—
480C4⋊Dic3—31no—
481C4⋊Dic3—61no—
482C4⋊Dic3—61no—
483C4⋊Dic3—61no—
484C4⋊Dic3C22×D311yescharacteristic
485Dic3⋊C4—21no—
486Dic3⋊C4—61no—
487Dic3⋊C4—61no—
488Dic3⋊C4—61no—
489Dic3⋊C4—61no—
490Dic3⋊C4—61no—
491Dic3⋊C4—61no—
492Dic3⋊C4—121no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—31no—
497C2×C3⋊C8—61no—
498C2×C3⋊C8—61no—
499C2×C3⋊C8—62no—
500C2×C3⋊C8—62no—
501C2×C3⋊C8C22×D311yescharacteristic
502C2×C3⋊C8C22×D311yescharacteristic
503Dic12—62no—
504#204—62no—
505D3×C8—62no—
506D3×C8—62no—
507C22×C32—21no—
508C22×C32—22no—
509C22×C32—21no—
510C22×C32—21no—
511C22×C32—41no—
512C22×C32—41no—
513C22×C32C22×D411yescharacteristic
514C2×C3×D3—21no—
515C2×C3×D3—22no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—41no—
519C2×C3×D3—41no—
520C2×C3×D3—44no—
521C2×C3×D3—48no—
522C2×C3×D3#12012yes—
523C2×C3×D3#13512yes—
524C2×C3×D3#13712yes—
525C32×C4—22no—
526C32×C4—21no—
527C32×C4C22×D411yescharacteristic
528C32×C4C22×D411yescharacteristic
529C3⋊Dic3—41no—
530C3⋊Dic3—41no—
531C3×Dic3—22no—
532C3×Dic3—21no—
533C3×Dic3—41no—
534C3×Dic3—41no—
535C3×Dic3#12012yes—
536C2×#41—31no—
537C2×#41—31no—
538C2×#41—31no—
539C2×#41—61no—
540C2×#41—61no—
541C2×#41—64no—
542C2×#41—64no—
543C2×#41D3211yescharacteristic
544C22×Q8—31no—
545C22×Q8—91no—
546C22×D4—31no—
547C22×D4—61no—
548C23×C4—31no—
549C23×C4—61no—
550C2×Q16—31no—
551C2×Q16—91no—
552C2×Q16—91no—
553C2×Q16—91no—
554C2×Q16—184no—
555C2×SD16—31no—
556C2×SD16—91no—
557C2×SD16—91no—
558C2×SD16—91no—
559C2×SD16—184no—
560C22×C8—91no—
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—21no—
586C23×C3—31no—
587C23×C3—31no—
588C23×C3—41no—
589C23×C3—64no—
590C23×C3—62no—
591C23×C3—62no—
592C23×C3—62no—
593C23×C3—61no—
594C23×C3—122no—
595C23×C3—122no—
596C23×C3D3×D411yescharacteristic
597C23×C3C2×#6711yescharacteristic
598C22×D3—21no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—24no—
603C22×D3—42no—
604C22×D3—42no—
605C22×D3C2×#6711yescharacteristic
606C22×D3C2×#6711yescharacteristic
607C3×Q8—21no—
608C3×Q8—21no—
609C3×Q8—22no—
610C3×Q8—32no—
611C3×Q8—41no—
612C3×Q8—64no—
613C3×Q8—61no—
614C3×Q8—61no—
615C3×Q8—61no—
616C3×Q8D3×D412yes—
617C3×Q8C2×#6712yes—
618C3×D4—24no—
619C3×D4—24no—
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—22no—
623C3×D4—32no—
624C3×D4—41no—
625C3×D4—44no—
626C3×D4—64no—
627C3×D4—64no—
628C3×D4—64no—
629C3×D4—64no—
630C3×D4—61no—
631C3×D4D3×D412yes—
632C3×D4C2×#6712yes—
633C2×C3×C4—24no—
634C2×C3×C4—24no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—31no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—31no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—44no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4—64no—
654C2×C3×C4—64no—
655C2×C3×C4—64no—
656C2×C3×C4—62no—
657C2×C3×C4—64no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4D3×D411yescharacteristic
664C2×C3×C4C2×#6711yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667#67—24no—
668#67—24no—
669#67—24no—
670C2×Dic3—24no—
671C2×Dic3—21no—
672C2×Dic3—22no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—121no—
680C2×Dic3—121no—
681C2×Dic3—122no—
682C2×Dic3—122no—
683C2×Dic3C2×#6711yescharacteristic
684C2×Dic3C2×#6711yescharacteristic
685D12—24no—
686D12—21no—
687D12C2×#6712yes—
688C4×D3—24no—
689C4×D3—24no—
690C4×D3—22no—
691C4×D3—24no—
692C4×D3—21no—
693C4×D3—21no—
694C4×D3—22no—
695C4×D3—122no—
696C4×D3—122no—
697C4×D3C2×#6712yes—
698C4×D3C2×#6712yes—
699Dic6—21no—
700Dic6—24no—
701Dic6—21no—
702Dic6—21no—
703Dic6—61no—
704Dic6—61no—
705Dic6—61no—
706Dic6—61no—
707Dic6—121no—
708Dic6—121no—
709Dic6—122no—
710Dic6—122no—
711Dic6C2×#6712yes—
712C3×C8—61no—
713C3×C8—61no—
714C3⋊C8—21no—
715C3⋊C8—21no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—61no—
719C3⋊C8—61no—
720C3⋊C8—121no—
721C3⋊C8—121no—
722C2×C32—41no—
723C2×C32—42no—
724C2×C32C2×#12011yescharacteristic
725C2×C32C2×#13511yescharacteristic
726C2×C32C2×#13711yescharacteristic
727C3×D3—41no—
728C3×D3—42no—
729C3×D3#45214yescomplemented
730C24—31no—
731C24—61no—
732#41—22no—
733#41—22no—
734#41—62no—
735#41—62no—
736#41—68no—
737#41—62no—
738#41—68no—
739#41—62no—
740#41—62no—
741#41—62no—
742C2×Q8—34no—
743C2×Q8—31no—
744C2×Q8—31no—
745C2×Q8—61no—
746C2×Q8—62no—
747C2×Q8—91no—
748C2×Q8—181no—
749C2×Q8—182no—
750C2×Q8—182no—
751C2×Q8C2×D3211yescharacteristic
752C2×D4—21no—
753C2×D4—34no—
754C2×D4—31no—
755C2×D4—61no—
756C2×D4—62no—
757C2×D4—61no—
758C2×D4—68no—
759C2×D4—61no—
760C2×D4—61no—
761C2×D4C2×D3211yescharacteristic
762C22×C4—21no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—62no—
769C22×C4—62no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—68no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—181no—
776C22×C4—181no—
777C22×C4C2×D3211yescharacteristic
778Q16—62no—
779Q16—182no—
780Q16—182no—
781Q16—182no—
782SD16—62no—
783SD16—182no—
784SD16—182no—
785SD16—182no—
786C2×C8—31no—
787C2×C8—31no—
788C2×C8—91no—
789C2×C8—91no—
790C2×C8—182no—
791C2×C8—182no—
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—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—22no—
809C22×C3—21no—
810C22×C3—22no—
811C22×C3—21no—
812C22×C3—32no—
813C22×C3—32no—
814C22×C3—32no—
815C22×C3—42no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—62no—
826C22×C3—61no—
827C22×C3—81no—
828C22×C3—81no—
829C22×C3—124no—
830C22×C3—128no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3C2×D3×D411yescharacteristic
834C22×C3C22×#6711yescharacteristic
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—22no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—44no—
842C2×D3—48no—
843C2×D3#95012yes—
844C2×D3#95112yes—
845C2×D3#95312yes—
846C3×C4—22no—
847C3×C4—21no—
848C3×C4—21no—
849C3×C4—22no—
850C3×C4—21no—
851C3×C4—21no—
852C3×C4—32no—
853C3×C4—41no—
854C3×C4—42no—
855C3×C4—61no—
856C3×C4—62no—
857C3×C4—121no—
858C3×C4—121no—
859C3×C4C2×D3×D411yescharacteristic
860C3×C4C2×D3×D411yescharacteristic
861C3×C4C22×#6711yescharacteristic
862C3×C4C22×#6711yescharacteristic
863Dic3—22no—
864Dic3—21no—
865Dic3—41no—
866Dic3—41no—
867Dic3—121no—
868Dic3—121no—
869Dic3—121no—
870Dic3—121no—
871Dic3—241no—
872Dic3—241no—
873Dic3#95312yes—
874C32C2×#45211yescharacteristic, complemented, Sylow
875C23—21no—
876C23—31no—
877C23—31no—
878C23—64no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—61no—
883C23—122no—
884C23—122no—
885C23D3×#6711yescharacteristic
886Q8—21no—
887Q8—32no—
888Q8—64no—
889Q8—61no—
890Q8—61no—
891Q8—61no—
892Q8—181no—
893Q8—181no—
894Q8—362no—
895Q8D3×#6712yes—
896D4—24no—
897D4—21no—
898D4—32no—
899D4—64no—
900D4—64no—
901D4—64no—
902D4—64no—
903D4—61no—
904D4D3×#6712yes—
905C2×C4—24no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—31no—
910C2×C4—32no—
911C2×C4—32no—
912C2×C4—31no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—64no—
916C2×C4—64no—
917C2×C4—64no—
918C2×C4—62no—
919C2×C4—64no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—181no—
926C2×C4—181no—
927C2×C4—362no—
928C2×C4—362no—
929C2×C4D3×#6711yescharacteristic
930C2×C4C22×D3211yescharacteristic
931C8—61no—
932C8—61no—
933C8—181no—
934C8—181no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—34no—
939C2×C3—41no—
940C2×C3—42no—
941C2×C3—41no—
942C2×C3—42no—
943C2×C3—81no—
944C2×C3—82no—
945C2×C3—121no—
946C2×C3—122no—
947C2×C3D3×#12011yescharacteristic
948C2×C3D3×#13511yescharacteristic
949C2×C3D3×#13711yescharacteristic
950C2×C3C2×#95011yescharacteristic
951C2×C3C2×#95111yescharacteristic
952C2×C3C2×#95311yescharacteristic
953D3—41no—
954D3—42no—
955D3#523914yesdirect product factor
956C22—21no—
957C22—21no—
958C22—21no—
959C22—22no—
960C22—32no—
961C22—32no—
962C22—32no—
963C22—41no—
964C22—41no—
965C22—61no—
966C22—61no—
967C22—62no—
968C22—61no—
969C22—124no—
970C22—128no—
971C22—121no—
972C22—121no—
973C22C2×D3×#6711yescharacteristic
974C4—21no—
975C4—22no—
976C4—32no—
977C4—61no—
978C4—62no—
979C4—121no—
980C4—121no—
981C4—361no—
982C4—361no—
983C4C2×D3×#6711yescharacteristic
984C4C2×D3×#6711yescharacteristic
985C3—21no—
986C3D3×#45211yescharacteristic, complemented
987C3C2×#523911yescharacteristic, complemented
988C2—34no—
989C2—41no—
990C2—42no—
991C2—121no—
992C2—122no—
993C2D3×#95011yescharacteristic
994C2D3×#95111yescharacteristic
995C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×#41C2
hypercenterC2×#41D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×D3×#216C2semidirect
3. C2×D3×#214C2semidirect
4. D3×#924C2semidirect
5. #10592938C2semidirect
6. C3×#5239C2semidirect
7. #10591599C2semidirect
8. #10591597C2semidirect
9. D3×#835C2semidirect
10. #10591463C2semidirect
11. #10591461C2semidirect
12. D3×#832C2semidirect
13. #10591173C2semidirect
14. #10591170C2semidirect
15. D3×#830C2semidirect
32. C2×#3756C22semidirect
33. C2×#3754C22semidirect
34. #64133C22semidirect
35. C2×C3×#216C22semidirect
36. C2×C3×#214C22semidirect
37. C3×#924C22semidirect
44. #63857C22semidirect
45. #63856C22semidirect
47. C2×#3719C22semidirect
48. C2×#3718C22semidirect
49. C2×#3716C22semidirect
50. C2×#3715C22semidirect
53. #63662C22semidirect
54. #63659C22semidirect
55. #63657C22semidirect
56. C3×#835C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
83. #5239D3direct (N × H)
211. C2×#216C2×D3semidirect
219. C2×#214C2×D3semidirect
228. #924C2×D3semidirect
252. #835C2×D3semidirect
258. #832C2×D3semidirect
264. #830C2×D3semidirect
729. C3×D3#452semidirect
874. C32C2×#452semidirect
955. D3#5239direct (N × H)
986. C3D3×#452semidirect
987. C3C2×#5239semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×D3×#2162
C2×D3×#2142
D3×#9242
#105929382
C3×#52392
#105915992
#105915972
D3×#8352
#105914632
#105914612
D3×#8322
#105911732
#105911702
D3×#8302
C2×#52393
D3×#4523