Finite Group Databasebeta

← D3×#4783 #11863772

Subgroups — D3×#4783 #11863772

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×D3×#214C211yesmaximal, characteristic, complemented
3C2×D3×Dic12C211yesmaximal, characteristic, complemented
4D3×#897C211yesmaximal, characteristic, complemented
5#10592482C211yesmaximal, characteristic, complemented
6C3×#4783C211yesmaximal, characteristic, complemented
7C3×D3×#102C211yesmaximal, characteristic, complemented
8#10591466C211yesmaximal, characteristic, complemented
9#10591463C211yesmaximal, characteristic, complemented
10#10590969C211yesmaximal, characteristic, complemented
11#10590965C211yesmaximal, characteristic, complemented
12D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
13#10590618C211yesmaximal, characteristic, complemented
14#10590614C211yesmaximal, characteristic, complemented
15D3×#810C211yesmaximal, characteristic, complemented
16D3×#452—31nomaximal
17C2×#4783—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×#67—21no—
22C2×#3805—21no—
23C2×#3804—21no—
24C22×D3×Dic3—21no—
25D3×#237—24no—
26D3×#237—24no—
27C2×C4×D32C2211yescharacteristic
28C2×#3796C2211yescharacteristic
29C2×#3795C2211yescharacteristic
30C2×D3×Dic6C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C2×#3754C2211yescharacteristic, complemented
33C2×#3746C2211yescharacteristic, complemented
34#64106C2211yescharacteristic, complemented
35C2×C3×#214C2211yescharacteristic, complemented
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×D3×C8C2211yescharacteristic
38C3×#897C2211yescharacteristic, complemented
39C3×D3×C4⋊C4C2211yescharacteristic
40D3×#214—24no—
41D3×(C2×D3)⋊C4—21no—
42#63895—21no—
43#63893—21no—
44D3×C4⋊Dic3—21no—
45#63871C2211yescharacteristic, complemented
46#63857C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3719C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52D3×Dic12—24no—
53C32×#102C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#237—31no—
67C22×#214—31no—
68C2×D3×Q16—31no—
69C2×D3×SD16—31no—
70C22×Dic12—31no—
71D3×C22⋊Q8—31no—
72C2×#897—31no—
73C3×#452—31no—
74C2×C3×#102—31no—
75#5239—31no—
76#5187—31no—
77#5173—31no—
78C2×(C2×D3)⋊C8—31no—
79#5047—31no—
80C2×#810—31no—
81#4808—31no—
82D3×#103—31no—
83#4783—31no—
84#4783—31no—
85#4783—31no—
86#4783—31no—
87#4783—31no—
88#4783—31no—
89#4783—31no—
90#4783—31no—
91#4783—61no—
92#4783D311yescharacteristic, direct product factor
93D3×#102D311yescharacteristic, complemented
94#4733—31no—
95D3×C22⋊C8—31no—
96C23×C3×D3—21no—
97C22×D32D411yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C2×#638—21no—
100C22×C3⋊Dic3—21no—
101#3830—22no—
102#3830—22no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C3×#237—22no—
110C3×#237—22no—
111C3×D3×D4—22no—
112C3×D3×D4D414yes—
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119D3×#67—28no—
120C2×#627—21no—
121C2×#627—21no—
122C2×#626—21no—
123C2×#625—21no—
124C2×#624D411yescharacteristic
125#3805—28no—
126#3804—28no—
127C2×D3×Dic3—28no—
128C2×D3×Dic3—21no—
129C2×D3×Dic3—21no—
130C2×D3×Dic3—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3D411yescharacteristic
133C2×D3×Dic3D411yescharacteristic
134C4×D32—22no—
135C4×D32—22no—
136#3796—22no—
137#3796—22no—
138#3795—22no—
139#3795—22no—
140D3×Dic6—22no—
141D3×Dic6—22no—
142D3×Dic6—22no—
143D3×Dic6D414yes—
144C2×C32×C8C2311yescharacteristic
145C32×C4⋊C4C2311yescharacteristic
146#3754—22no—
147#3752—21no—
148C4⋊(C3⋊Dic3)—21no—
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150#3746—22no—
151C3×#214—22no—
152C3×(C2×D3)⋊C4—21no—
153C3×C4⋊Dic3—21no—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×Dic3⋊C4—21no—
156C2×C3×C3⋊C8C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158C3×Dic12—22no—
159C3×D3×C8—22no—
160Dic3⋊Dic3—21no—
161Dic3⋊Dic3—21no—
162#3722—21no—
163(C2×D3)⋊Dic3—21no—
164#3719—22no—
165#3719—22no—
166#3716—22no—
167#3715—22no—
168D3×C3⋊C8—22no—
169C2×#452—91noSylow
170C2×C3×#41—31no—
171C22×C3×D4—31no—
172C22×#67—61no—
173C23×Dic3—61no—
174D3×#41—64no—
175D3×#41—64no—
176C2×#239—31no—
177C2×D3×Q8—31no—
178C2×D3×Q8—31no—
179C2×#237—31no—
180C2×#237—31no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—61no—
184C2×#237—64no—
185C2×#237—61no—
186C2×#237—61no—
187C2×#237—64no—
188C2×#237—61no—
189C2×#237C2×D311yescharacteristic
190C2×D3×D4—61no—
191C2×D3×D4C2×D311yescharacteristic
192C2×#235—31no—
193C2×#235—61no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—61no—
197C22×Dic6—31no—
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C22×C3×C8—31no—
202C3×C22⋊Q8—31no—
203C2×C3×C4⋊C4—31no—
204#946—31no—
205C2×#216—31no—
206C2×#216—31no—
207C2×#215—31no—
208C2×#214—31no—
209C2×#214—31no—
210C2×#214—31no—
211C2×#214—31no—
212C2×#214—61no—
213C2×#214—64no—
214C2×#214C2×D311yescharacteristic, complemented
215C2×(C2×D3)⋊C4—61no—
216C2×C4⋊Dic3—61no—
217#924—31no—
218C22×C3⋊C8—31no—
219D3×Q16—64no—
220D3×SD16—64no—
221C2×Dic12—31no—
222C2×Dic12—31no—
223C2×Dic12—31no—
224C2×Dic12—31no—
225C2×Dic12—61no—
226C2×Dic12—64no—
227C2×Dic12C2×D311yescharacteristic, complemented
228C2×#204—31no—
229C2×D3×C8—31no—
230C2×D3×C8C2×D311yescharacteristic
231#897—31no—
232#897—31no—
233#897—31no—
234#897—31no—
235#897—61no—
236#897—61no—
237#897—61no—
238#897C2×D311yescharacteristic, complemented
239#896—61no—
240D3×C4⋊C4—61no—
241D3×C4⋊C4C2×D311yescharacteristic
242D3×C22⋊C4—61no—
243#878—61no—
244C3×#103—31no—
245C3×#102—21no—
246C3×#102—31no—
247C3×#102—31no—
248C3×#102—31no—
249C3×#102C2×D311yescharacteristic, complemented
250C3×#102C2×D311yescharacteristic, complemented
251C3×C22⋊C8—31no—
252#835—31no—
253#832C2×D311yescharacteristic, complemented
254#830—31no—
255#821C2×D311yescharacteristic, complemented
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#810—31no—
265#810—31no—
266#810—31no—
267#810—31no—
268#810—61no—
269#810C2×D311yescharacteristic, complemented
270#809C2×D311yescharacteristic, complemented
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×D4—21no—
283C32×D4C2×D412yes—
284C2×C32×C4—21no—
285C2×C32×C4C2411yescharacteristic
286#638—24no—
287C2×C3⋊Dic3—24no—
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3C2×D411yescharacteristic
291C4×C3⋊D3—21no—
292C4×C3⋊D3—21no—
293#634—21no—
294#634—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×Dic6C2×D412yes—
316#627—24no—
317#627—42no—
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—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—31no—
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—31no—
353C2×C3×Q8—31no—
354C2×C3×D4—21no—
355C2×C3×D4—34no—
356C2×C3×D4—31no—
357C2×C3×D4—62no—
358C2×C3×D4—61no—
359C2×C3×D4—61no—
360C2×C3×D4C22×D311yescharacteristic
361C2×C3×D4C22×D311yescharacteristic
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—61no—
365C22×C3×C4—61no—
366C2×#67—21no—
367C2×#67—21no—
368C2×#67—61no—
369C2×#67—68no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—121no—
375C22×Dic3—21no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—68no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—121no—
386#239—62no—
387#239—62no—
388D3×Q8—34no—
389D3×Q8—62no—
390D3×Q8—62no—
391D3×Q8—62no—
392#237—22no—
393#237—22no—
394#237—62no—
395#237—62no—
396#237—62no—
397#237—62no—
398#237—62no—
399#237—68no—
400#237—68no—
401#237—68no—
402#237—62no—
403#237—62no—
404#237—62no—
405#237—122no—
406#237—122no—
407D3×D4—22no—
408D3×D4—68no—
409D3×D4D1214yes—
410#235—62no—
411#235—68no—
412#235—62no—
413C2×D12—61no—
414C2×D12C22×D311yescharacteristic
415C2×C4×D3—21no—
416C2×C4×D3—31no—
417C2×C4×D3—31no—
418C2×C4×D3—31no—
419C2×C4×D3—31no—
420C2×C4×D3—31no—
421C2×C4×D3—31no—
422C2×C4×D3—61no—
423C2×C4×D3—62no—
424C2×C4×D3—62no—
425C2×C4×D3—61no—
426C2×C4×D3—61no—
427C2×C4×D3—68no—
428C2×C4×D3—61no—
429C2×C4×D3—62no—
430C2×C4×D3—62no—
431C2×C4×D3—61no—
432C2×C4×D3C22×D311yescharacteristic
433C2×C4×D3C22×D311yescharacteristic
434C2×Dic6—31no—
435C2×Dic6—31no—
436C2×Dic6—34no—
437C2×Dic6—31no—
438C2×Dic6—31no—
439C2×Dic6—61no—
440C2×Dic6—61no—
441C2×Dic6—62no—
442C2×Dic6—62no—
443C2×Dic6—62no—
444C2×Dic6—61no—
445C2×Dic6—61no—
446C2×Dic6—61no—
447C2×Dic6—61no—
448C2×Dic6C22×D311yescharacteristic
449C2×Dic6C22×D311yescharacteristic
450C3×Q16—62no—
451C3×SD16—62no—
452C2×C3×C8—21no—
453C2×C3×C8—31no—
454C2×C3×C8—31no—
455C2×C3×C8—62no—
456C2×C3×C8C22×D311yescharacteristic
457C2×C3×C8C22×D311yescharacteristic
458C3×C4⋊C4—21no—
459C3×C4⋊C4—31no—
460C3×C4⋊C4—61no—
461C3×C4⋊C4—61no—
462C3×C4⋊C4C22×D311yescharacteristic
463C3×C4⋊C4C22×D311yescharacteristic
464C3×C22⋊C4—61no—
465#217—61no—
466#216—62no—
467#216—62no—
468#215—62no—
469#214—22no—
470#214—62no—
471#214—62no—
472#214—62no—
473#214—62no—
474#214—122no—
475(C2×D3)⋊C4—21no—
476(C2×D3)⋊C4—61no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—121no—
482C4⋊Dic3—21no—
483C4⋊Dic3—61no—
484C4⋊Dic3—61no—
485C4⋊Dic3—61no—
486C4⋊Dic3—61no—
487C4⋊Dic3—121no—
488C4⋊Dic3C22×D311yescharacteristic
489Dic3⋊C4—21no—
490Dic3⋊C4—61no—
491Dic3⋊C4—61no—
492C2×C3⋊C8—31no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—61no—
495C2×C3⋊C8—62no—
496C2×C3⋊C8C22×D311yescharacteristic
497C2×C3⋊C8C22×D311yescharacteristic
498Dic12—22no—
499Dic12—62no—
500Dic12—62no—
501Dic12—62no—
502Dic12—62no—
503Dic12—122no—
504#204—62no—
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—91no—
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—91no—
557C2×SD16—91no—
558C2×SD16—91no—
559C2×SD16—184no—
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—31no—
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—31no—
577#102—31no—
578#102D3211yescharacteristic, complemented
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—32no—
608C3×Q8—61no—
609C3×Q8—61no—
610C3×Q8—61no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—22no—
614C3×D4—32no—
615C3×D4—41no—
616C3×D4—64no—
617C3×D4—64no—
618C3×D4—61no—
619C3×D4C2×D1212yes—
620C3×D4D3×D412yes—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—31no—
625C2×C3×C4—32no—
626C2×C3×C4—32no—
627C2×C3×C4—31no—
628C2×C3×C4—41no—
629C2×C3×C4—64no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—122no—
636C2×C3×C4C23×D311yescharacteristic
637C2×C3×C4C23×D311yescharacteristic
638#67—24no—
639#67—24no—
640#67—64no—
641#67—64no—
642#67—64no—
643#67—64no—
644#67—64no—
645#67—124no—
646C2×Dic3—24no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—31no—
651C2×Dic3—31no—
652C2×Dic3—61no—
653C2×Dic3—64no—
654C2×Dic3—62no—
655C2×Dic3—64no—
656C2×Dic3—64no—
657C2×Dic3—64no—
658C2×Dic3—64no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—62no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—121no—
665C2×Dic3—124no—
666C2×Dic3—121no—
667C2×Dic3—122no—
668C2×Dic3D3×D411yescharacteristic
669C2×Dic3D3×D411yescharacteristic
670D12—21no—
671D12—64no—
672D12C2×D1212yes—
673C4×D3—21no—
674C4×D3—21no—
675C4×D3—42no—
676C4×D3—62no—
677C4×D3—62no—
678C4×D3—64no—
679C4×D3—64no—
680C4×D3—62no—
681C4×D3—64no—
682C4×D3—61no—
683C4×D3—61no—
684C4×D3—61no—
685C4×D3—61no—
686C4×D3—62no—
687C4×D3—121no—
688C4×D3—121no—
689C4×D3—122no—
690C4×D3C2×D1212yes—
691C4×D3D3×D412yes—
692Dic6—21no—
693Dic6—21no—
694Dic6—21no—
695Dic6—32no—
696Dic6—32no—
697Dic6—62no—
698Dic6—64no—
699Dic6—61no—
700Dic6—61no—
701Dic6—64no—
702Dic6—61no—
703Dic6—61no—
704Dic6—61no—
705Dic6—61no—
706Dic6—121no—
707Dic6—121no—
708Dic6—121no—
709Dic6—122no—
710Dic6—122no—
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—94no—
745C2×Q8—91no—
746C2×Q8—91no—
747C2×Q8—181no—
748C2×Q8—181no—
749C2×Q8—182no—
750C2×Q8—182no—
751C2×Q8—182no—
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—62no—
783SD16—182no—
784SD16—182no—
785SD16—182no—
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—61no—
795C4⋊C4—181no—
796C4⋊C4—181no—
797C4⋊C4—181no—
798C4⋊C4C2×D3211yescharacteristic
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—22no—
826C2×D3—21no—
827C2×D3—21no—
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#88212yes—
844C2×D3#91212yes—
845C2×D3#91512yes—
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×C4C22×D1211yescharacteristic
857C3×C4C2×D3×D411yescharacteristic
858C3×C4C2×D3×D411yescharacteristic
859C3×C4C2×D3×D411yescharacteristic
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#88212yes—
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—32no—
887Q8—61no—
888Q8—61no—
889Q8—61no—
890Q8—92no—
891Q8—184no—
892Q8—181no—
893Q8—181no—
894Q8—181no—
895Q8—362no—
896D4—21no—
897D4—32no—
898D4—64no—
899D4—64no—
900D4—61no—
901D4—184no—
902D4—184no—
903D4—184no—
904D4D3×D1212yes—
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×C3C2×#88211yescharacteristic
945C2×C3D3×#12011yescharacteristic
946C2×C3C2×#91211yescharacteristic
947C2×C3C2×#91511yescharacteristic
948C2×C3D3×#13511yescharacteristic
949C2×C3D3×#13711yescharacteristic
950D3—41no—
951D3—42no—
952D3—121no—
953D3—121no—
954D3—241no—
955D3#478314yesdirect 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—
983C4C2×D3×D1211yescharacteristic
984C4D32×D411yescharacteristic
985C3—21no—
986C3C2×#478311yescharacteristic, complemented
987C3D3×#45211yescharacteristic, complemented
988C2—34no—
989C2—42no—
990C2—121no—
991C2—122no—
992C2—361no—
993C2D3×#88211yescharacteristic
994C2D3×#91211yescharacteristic
995C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D3×#237C2
hypercenter#102D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×D3×#214C2semidirect
3. C2×D3×Dic12C2semidirect
4. D3×#897C2semidirect
5. #10592482C2semidirect
6. C3×#4783C2semidirect
7. C3×D3×#102C2semidirect
8. #10591466C2semidirect
9. #10591463C2semidirect
10. #10590969C2semidirect
11. #10590965C2semidirect
12. D3×(C2×D3)⋊C8C2semidirect
13. #10590618C2semidirect
14. #10590614C2semidirect
15. D3×#810C2semidirect
32. C2×#3754C22semidirect
33. C2×#3746C22semidirect
34. #64106C22semidirect
35. C2×C3×#214C22semidirect
36. C2×C3×Dic12C22semidirect
38. C3×#897C22semidirect
45. #63871C22semidirect
46. #63857C22semidirect
47. C2×#3719C22semidirect
48. C2×#3719C22semidirect
49. C2×#3716C22semidirect
50. C2×#3715C22semidirect
53. C32×#102C22semidirect
54. #63647C22semidirect
55. #63637C22semidirect
56. C3×#832C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63567C22semidirect
62. #63565C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
92. #4783D3direct (N × H)
93. D3×#102D3semidirect
214. C2×#214C2×D3semidirect
227. C2×Dic12C2×D3semidirect
238. #897C2×D3semidirect
249. C3×#102C2×D3semidirect
250. C3×#102C2×D3semidirect
253. #832C2×D3semidirect
255. #821C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
269. #810C2×D3semidirect
270. #809C2×D3semidirect
578. #102D32semidirect
729. C3×D3#452semidirect
874. C32C2×#452semidirect
955. D3#4783direct (N × H)
986. C3C2×#4783semidirect
987. C3D3×#452semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×D3×#2142
C2×D3×Dic122
D3×#8972
#105924822
C3×#47832
C3×D3×#1022
#105914662
#105914632
#105909692
#105909652
D3×(C2×D3)⋊C82
#105906182
#105906142
D3×#8102
D3×#4523
C2×#47833