Finite Group Databasebeta

← D3×Q8×#67 #11902660

Subgroups — D3×Q8×#67 #11902660

Order 1152.

3276 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C2×D32×Q8C211yesmaximal, characteristic, complemented
3Q8×#638C211yesmaximal, characteristic, complemented
4C3×Q8×#67C211yesmaximal, characteristic, complemented
5D3×#946C213yesmaximal, complemented
6Q8×#626C211yesmaximal, characteristic, complemented
7Q8×#625C211yesmaximal, characteristic, complemented
8#10595403C213yesmaximal, complemented
9#10595400C213yesmaximal, complemented
10D3×Q8×Dic3C211yesmaximal, characteristic, complemented
11D3×#944C213yesmaximal, complemented
12C4×D3×#67C213yesmaximal
13Dic6×#67C213yesmaximal, complemented
14D3×#924C213yesmaximal, complemented
15#10594803C213yesmaximal, complemented
16C2×Q8×#67—31nomaximal
17D3×D4×Q8—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C2×C3×D3×Q8—28no—
21C2×C3×D3×Q8C2213yes—
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×D3×Q8C2213yescomplemented
24C2×C3×D3×Q8C2211yescharacteristic, complemented
25C2×C3×D3×Q8C2211yescharacteristic, complemented
26C22×C3×C4×D3C2213yes—
27C22×C3×Dic6C2213yescomplemented
28C2×D3×#67C2211yescharacteristic
29D32×Q8—28no—
30C2×C4×D32C2213yes—
31C2×#3797C2213yescomplemented
32C2×D3×Dic6C2213yes—
33C2×D3×Dic6C2213yescomplemented
34#64155C2213yescomplemented
35Q8×C3⋊Dic3C2211yescharacteristic, complemented
36#64153C2213yescomplemented
37C4×#638C2213yes—
38#64133C2213yescomplemented
39C3×#946C2213yescomplemented
40C3×Q8×Dic3C2211yescharacteristic, complemented
41C3×#944C2213yescomplemented
42C3×C4×#67C2213yes—
43C3×#924C2213yescomplemented
44Dic3×#67C2213yes—
45D3×#217C2213yes—
46#63964C2216yescomplemented
47#63952C2213yes—
48D3×(C2×D3)⋊C4C2213yes—
49#63904C2213yes—
50C4×#626C2213yes—
51C4×#625C2213yes—
52D3×C4⋊Dic3C2213yes—
53#63888C2216yescomplemented
54#63887C2216yescomplemented
55#63879C2213yes—
56D3×Dic3⋊C4C2213yes—
57D3×Dic3⋊C4C2216yes—
58C4×D3×Dic3C2213yes—
59#63873C2213yescomplemented
60#63871C2213yescomplemented
61#63866C2213yescomplemented
62#63857C2213yescomplemented
63#63856C2213yescomplemented
64#63856C2213yescomplemented
65#63851C2216yescomplemented
66#63843C2213yescomplemented
67Dic3×Dic6C2213yescomplemented
68#63839C2216yescomplemented
69#63839C2216yescomplemented
70C23×C3×Q8—31no—
71C22×D3×Q8—31no—
72C22×D3×Q8—31no—
73C22×D3×Q8D311yescharacteristic, complemented
74C3×D4×Q8—31no—
75Q8×#67—31no—
76Q8×#67—31no—
77Q8×#67—31no—
78Q8×#67—31no—
79Q8×#67—33no—
80Q8×#67—31no—
81Q8×#67—33no—
82Q8×#67—33no—
83Q8×#67—33no—
84Q8×#67—61no—
85Q8×#67D311yescharacteristic, direct product factor
86C2×#946—33no—
87C2×Q8×Dic3—31no—
88C2×#944—33no—
89C2×C4×#67—33no—
90C2×#924—33no—
91#5727—33no—
92D3×C4⋊Q8—33no—
93#5632—33no—
94#5632—33no—
95D3×C22⋊Q8—33no—
96D3×C22⋊Q8—33no—
97Q8×D12—31no—
98C4×D3×Q8—31no—
99C4×D3×D4—33no—
100D4×Dic6—33no—
101C23×C3×D3C2311yescharacteristic
102C22×D32C2311yescharacteristic
103C2×C32×Q8—24no—
104C2×C32×Q8C2313yes—
105C2×C32×Q8C2311yescharacteristic
106C22×C32×C4C2313yes—
107C2×#638C2311yescharacteristic
108Q8×C3⋊D3—24no—
109C2×C4×C3⋊D3C2313yes—
110C2×#634C2313yes—
111C2×C3×#67C2311yescharacteristic
112C22×C3×Dic3C2313yes—
113C3×D3×Q8—24no—
114C3×D3×Q8—24no—
115C3×D3×Q8—212no—
116C3×D3×Q8—212no—
117C3×D3×Q8D418yescomplemented
118C2×C3×C4×D3—212no—
119C2×C3×C4×D3C2313yes—
120C2×C3×C4×D3C2313yes—
121C2×C3×C4×D3C2313yes—
122C2×C3×C4×D3C2313yes—
123C2×C3×C4×D3C2313yes—
124C2×C3×Dic6—212no—
125C2×C3×Dic6C2313yes—
126C2×C3×Dic6C2316yes—
127C2×C3×Dic6C2313yes—
128C2×C3×Dic6C2313yes—
129D3×#67Q818yesdirect product factor
130C2×#627C2316yes—
131C2×#626C2311yescharacteristic
132C2×#625C2311yescharacteristic
133C2×#624C2313yes—
134C2×D3×Dic3C2313yes—
135C2×D3×Dic3C2313yes—
136C2×D3×Dic3C2313yes—
137C2×D3×Dic3C2311yescharacteristic
138C4×D32—212no—
139#3797—212no—
140D3×Dic6—212no—
141D3×Dic6—212no—
142#3757C2313yes—
143#3752C2313yes—
144C4⋊(C3⋊Dic3)C2313yes—
145#3750C2313yes—
146#3750C2316yes—
147C4×C3⋊Dic3C2313yes—
148C3×#217C2313yes—
149C3×(C2×D3)⋊C4C2313yes—
150C3×C4⋊Dic3C2313yes—
151C3×Dic3⋊C4C2316yes—
152C3×Dic3⋊C4C2313yes—
153C3×C4×Dic3C2313yes—
154#3724C2313yes—
155#3724C2316yes—
156Dic3⋊Dic3C2313yes—
157Dic3⋊Dic3C2316yes—
158Dic3⋊Dic3C2316yes—
159#3722C2313yes—
160(C2×D3)⋊Dic3C2313yes—
161(C2×D3)⋊Dic3C2313yes—
162(C2×D3)⋊Dic3C2313yes—
163Dic32C2313yes—
164Dic32C2313yes—
165C2×D4×Q8—91noSylow
166C22×C3×Q8—21no—
167C22×C3×Q8—31no—
168C22×C3×Q8—31no—
169C22×C3×Q8—33no—
170C22×C3×Q8—33no—
171C22×C3×Q8—31no—
172C22×C3×Q8—33no—
173C22×C3×Q8—68no—
174C22×C3×Q8C2×D311yescharacteristic, complemented
175C22×C3×Q8C2×D311yescharacteristic, complemented
176C23×C3×C4—33no—
177C22×#67—31no—
178C2×D3×Q8—28no—
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×D3×Q8—33no—
182C2×D3×Q8—33no—
183C2×D3×Q8—33no—
184C2×D3×Q8—33no—
185C2×D3×Q8—61no—
186C2×D3×Q8—68no—
187C2×D3×Q8—68no—
188C2×D3×Q8C2×D313yes—
189C2×D3×Q8C2×D311yescharacteristic
190C2×D3×Q8C2×D313yescomplemented
191C2×D3×Q8C2×D311yescharacteristic, complemented
192C2×D3×Q8C2×D311yescharacteristic, complemented
193C2×D3×D4—31no—
194C22×C4×D3—33no—
195C22×C4×D3—33no—
196C22×C4×D3C2×D313yes—
197C22×Dic6—33no—
198C22×Dic6—33no—
199C22×Dic6C2×D313yescomplemented
200C3×C4⋊Q8—33no—
201C3×C22⋊Q8—33no—
202C3×C22⋊Q8—33no—
203C3×C4×Q8—31no—
204C3×C4×D4—33no—
205C2×#217—33no—
206#946—33no—
207#946—33no—
208#946—33no—
209#946—33no—
210#946—36no—
211#946—33no—
212#946—36no—
213#946—63no—
214#946C2×D313yescomplemented
215Q8×Dic3—31no—
216Q8×Dic3—31no—
217Q8×Dic3—33no—
218Q8×Dic3—33no—
219Q8×Dic3—61no—
220Q8×Dic3C2×D311yescharacteristic, complemented
221#944—33no—
222#944—33no—
223#944—33no—
224#944—33no—
225#944—36no—
226#944—36no—
227#944—33no—
228#944—63no—
229#944C2×D313yescomplemented
230D4×Dic3—33no—
231C4×#67—33no—
232C4×#67—33no—
233C4×#67—33no—
234C4×#67—33no—
235C4×#67—33no—
236C4×#67—33no—
237C4×#67—33no—
238C4×#67—33no—
239C4×#67—33no—
240C4×#67—63no—
241C4×#67C2×D313yes—
242C2×(C2×D3)⋊C4—33no—
243C2×C4⋊Dic3—33no—
244#924—33no—
245#924—33no—
246#924—33no—
247#924—33no—
248#924—36no—
249#924—33no—
250#924—36no—
251#924—63no—
252#924C2×D313yescomplemented
253C2×Dic3⋊C4—36no—
254C2×Dic3⋊C4—33no—
255C2×C4×Dic3—33no—
256#897—33no—
257#897—33no—
258#896—36no—
259#896—36no—
260#893—33no—
261D3×C4⋊C4—33no—
262D3×C4⋊C4—36no—
263D3×C4⋊C4—33no—
264#888—36no—
265#888—36no—
266#887—33no—
267#67⋊C4—33no—
268#67⋊C4—33no—
269D3×C22⋊C4—33no—
270D3×C22⋊C4—33no—
271#878—36no—
272#878—36no—
273C4×D12—33no—
274C42×D3—33no—
275#869—33no—
276C4×Dic6—33no—
277C23×C32C2411yescharacteristic
278C22×C3⋊D3C2411yescharacteristic
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3C2×Q814yescomplemented
282C22×C3×D3C2411yescharacteristic
283C22×C3×D3C2411yescharacteristic
284C22×C3×D3C2411yescharacteristic
285C2×D32—22no—
286C2×D32—22no—
287C2×D32C2×Q814yescomplemented
288C32×Q8—26no—
289C32×Q8C2×D414yescomplemented
290C2×C32×C4—26no—
291C2×C32×C4C2413yes—
292C2×C32×C4C2413yes—
293#638C2×Q814yescomplemented
294C2×C3⋊Dic3C2413yes—
295C2×C3⋊Dic3C2413yes—
296C2×C3⋊Dic3C2411yescharacteristic
297C4×C3⋊D3—26no—
298#634—26no—
299C3×#67C2×Q814yescomplemented
300C2×C3×Dic3—26no—
301C2×C3×Dic3C2413yes—
302C2×C3×Dic3C2413yes—
303C2×C3×Dic3C2413yes—
304C2×C3×Dic3C2413yes—
305C2×C3×Dic3C2411yescharacteristic
306C3×C4×D3—26no—
307C3×C4×D3—26no—
308C3×C4×D3—26no—
309C3×C4×D3—26no—
310C3×C4×D3C2×D4112yes—
311C3×Dic6—26no—
312C3×Dic6—26no—
313C3×Dic6—212no—
314C3×Dic6C2×D4112yescomplemented
315#627—212no—
316#626C2×Q814yescomplemented
317#625C2×Q814yescomplemented
318#624—26no—
319D3×Dic3—26no—
320D3×Dic3—26no—
321D3×Dic3—26no—
322D3×Dic3C2×Q814yescomplemented
323C23×Q8—31no—
324C23×Q8—91no—
325D4×Q8—31no—
326D4×Q8—93no—
327D4×Q8—91no—
328D4×Q8—93no—
329D4×Q8—93no—
330D4×Q8—93no—
331D4×Q8—91no—
332D4×Q8—91no—
333C2×C4⋊Q8—93no—
334C2×C22⋊Q8—93no—
335C2×C22⋊Q8—93no—
336C2×C4×Q8—91no—
337C2×C4×D4—93no—
338C24×C3—31no—
339C23×D3—31no—
340C23×D3—31no—
341C23×D3C22×D311yescharacteristic
342C2×C3×Q8—24no—
343C2×C3×Q8—24no—
344C2×C3×Q8—21no—
345C2×C3×Q8—23no—
346C2×C3×Q8—38no—
347C2×C3×Q8—33no—
348C2×C3×Q8—36no—
349C2×C3×Q8—33no—
350C2×C3×Q8—33no—
351C2×C3×Q8—44no—
352C2×C3×Q8—612no—
353C2×C3×Q8—612no—
354C2×C3×Q8—612no—
355C2×C3×Q8—64no—
356C2×C3×Q8—64no—
357C2×C3×Q8C22×D313yes—
358C2×C3×Q8C22×D313yes—
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×Q8C22×D311yescharacteristic
361C2×C3×D4—31no—
362C22×C3×C4—23no—
363C22×C3×C4—33no—
364C22×C3×C4—33no—
365C22×C3×C4—33no—
366C22×C3×C4—33no—
367C22×C3×C4—33no—
368C22×C3×C4—33no—
369C22×C3×C4—612no—
370C22×C3×C4C22×D313yes—
371C22×C3×C4C22×D313yes—
372C2×#67—31no—
373C2×#67—31no—
374C2×#67—31no—
375C2×#67—31no—
376C2×#67—38no—
377C2×#67—31no—
378C2×#67—61no—
379C2×#67C22×D311yescharacteristic
380C22×Dic3—31no—
381C22×Dic3—33no—
382C22×Dic3—33no—
383C22×Dic3—33no—
384C22×Dic3C22×D313yes—
385D3×Q8—24no—
386D3×Q8—24no—
387D3×Q8—212no—
388D3×Q8—212no—
389D3×Q8—612no—
390D3×Q8—612no—
391D3×Q8—64no—
392D3×Q8—64no—
393D3×Q8—612no—
394D3×Q8—612no—
395D3×Q8—124no—
396D3×Q8#6718yesdirect product factor
397D3×D4—38no—
398C2×D12—31no—
399C2×C4×D3—212no—
400C2×C4×D3—31no—
401C2×C4×D3—33no—
402C2×C4×D3—33no—
403C2×C4×D3—33no—
404C2×C4×D3—33no—
405C2×C4×D3—33no—
406C2×C4×D3—33no—
407C2×C4×D3—33no—
408C2×C4×D3—63no—
409C2×C4×D3—612no—
410C2×C4×D3—612no—
411C2×C4×D3C22×D313yes—
412C2×C4×D3C22×D313yes—
413C2×C4×D3C22×D313yes—
414C2×C4×D3C22×D313yes—
415C2×C4×D3C22×D313yes—
416C2×Dic6—212no—
417C2×Dic6—33no—
418C2×Dic6—33no—
419C2×Dic6—36no—
420C2×Dic6—36no—
421C2×Dic6—63no—
422C2×Dic6—612no—
423C2×Dic6—612no—
424C2×Dic6C22×D313yes—
425C2×Dic6C22×D316yes—
426C2×Dic6C22×D313yes—
427C2×Dic6C22×D313yes—
428C3×C4⋊C4—33no—
429C3×C4⋊C4—33no—
430C3×C4⋊C4—36no—
431C3×C22⋊C4—33no—
432C3×C22⋊C4—33no—
433C3×C42—33no—
434#217—33no—
435#217—33no—
436#217—33no—
437#217—33no—
438#217—33no—
439#217—63no—
440#217C22×D313yes—
441(C2×D3)⋊C4—33no—
442(C2×D3)⋊C4—33no—
443(C2×D3)⋊C4—33no—
444(C2×D3)⋊C4—33no—
445(C2×D3)⋊C4—33no—
446(C2×D3)⋊C4—33no—
447(C2×D3)⋊C4—33no—
448(C2×D3)⋊C4—63no—
449(C2×D3)⋊C4C22×D313yes—
450C4⋊Dic3—33no—
451C4⋊Dic3—33no—
452C4⋊Dic3—33no—
453C4⋊Dic3—36no—
454C4⋊Dic3—36no—
455C4⋊Dic3—63no—
456C4⋊Dic3C22×D313yes—
457Dic3⋊C4—36no—
458Dic3⋊C4—33no—
459Dic3⋊C4—36no—
460Dic3⋊C4—33no—
461Dic3⋊C4—36no—
462Dic3⋊C4—36no—
463Dic3⋊C4—33no—
464Dic3⋊C4—36no—
465Dic3⋊C4—33no—
466Dic3⋊C4—36no—
467Dic3⋊C4—33no—
468Dic3⋊C4—66no—
469Dic3⋊C4—63no—
470Dic3⋊C4C22×D316yes—
471Dic3⋊C4C22×D313yes—
472C4×Dic3—33no—
473C4×Dic3—33no—
474C4×Dic3—33no—
475C4×Dic3—33no—
476C4×Dic3—33no—
477C4×Dic3—33no—
478C4×Dic3—63no—
479C4×Dic3C22×D313yes—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32C22×Q812yescomplemented
483C22×C32C2511yescharacteristic
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3C22×Q812yescomplemented
487C2×C3×D3—21no—
488C2×C3×D3—21no—
489C2×C3×D3—21no—
490C2×C3×D3—21no—
491C2×C3×D3—28no—
492C2×C3×D3C22×D412yes—
493C2×C3×D3C22×Q812yes—
494C2×C3×D3C22×Q812yescomplemented
495C2×C3×D3C22×Q812yescomplemented
496C2×C3×D32−1+412yes—
497D32—28no—
498C32×C4—23no—
499C32×C4C22×D416yes—
500C3⋊Dic3—23no—
501C3⋊Dic3—23no—
502C3⋊Dic3C22×Q812yescomplemented
503C3×Dic3—23no—
504C3×Dic3—23no—
505C3×Dic3—23no—
506C3×Dic3C22×D416yes—
507C3×Dic3C22×Q812yescomplemented
508C22×Q8—31no—
509C22×Q8—33no—
510C22×Q8—31no—
511C22×Q8—33no—
512C22×Q8—31no—
513C22×Q8—33no—
514C22×Q8—68no—
515C22×Q8—93no—
516C22×Q8—93no—
517C22×Q8—93no—
518C22×Q8—91no—
519C22×Q8—188no—
520C22×Q8D3211yescharacteristic, complemented
521C22×D4—91no—
522C23×C4—33no—
523C23×C4—93no—
524C4⋊Q8—33no—
525C4⋊Q8—93no—
526C4⋊Q8—96no—
527C4⋊Q8—96no—
528C4⋊Q8—93no—
529C4⋊Q8—93no—
530C22⋊Q8—33no—
531C22⋊Q8—33no—
532C22⋊Q8—96no—
533C22⋊Q8—96no—
534C22⋊Q8—96no—
535C22⋊Q8—93no—
536C22⋊Q8—96no—
537C22⋊Q8—93no—
538C22⋊Q8—93no—
539C22⋊Q8—93no—
540C22⋊Q8—93no—
541C22⋊Q8—93no—
542C4×Q8—31no—
543C4×Q8—93no—
544C4×Q8—93no—
545C4×Q8—91no—
546C4×D4—33no—
547C4×D4—93no—
548C4×D4—93no—
549C4×D4—93no—
550C4×D4—93no—
551C4×D4—93no—
552C4×D4—93no—
553C4×D4—93no—
554C2×C4⋊C4—93no—
555C2×C4⋊C4—93no—
556C2×C4⋊C4—96no—
557C2×C22⋊C4—93no—
558C2×C22⋊C4—93no—
559C2×C42—93no—
560C23×C3—21no—
561C23×C3—31no—
562C23×C3—34no—
563C23×C3—31no—
564C23×C3—31no—
565C23×C3—62no—
566C23×C3—62no—
567C23×C3C23×D311yescharacteristic
568C23×C3C23×D311yescharacteristic
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—31no—
572C22×D3—31no—
573C22×D3—34no—
574C22×D3—34no—
575C22×D3—61no—
576C22×D3—62no—
577C22×D3—62no—
578C22×D3—62no—
579C22×D3—62no—
580C22×D3D3×Q814yescomplemented
581C22×D3C23×D311yescharacteristic
582C22×D3C23×D311yescharacteristic
583C22×D3C23×D311yescharacteristic
584C3×Q8—26no—
585C3×Q8—26no—
586C3×Q8—24no—
587C3×Q8—312no—
588C3×Q8—46no—
589C3×Q8—612no—
590C3×Q8—66no—
591C3×Q8—66no—
592C3×Q8D3×D414yescomplemented
593C3×Q8C2×#6714yescomplemented
594C3×D4—34no—
595C2×C3×C4—26no—
596C2×C3×C4—26no—
597C2×C3×C4—23no—
598C2×C3×C4—23no—
599C2×C3×C4—31no—
600C2×C3×C4—33no—
601C2×C3×C4—312no—
602C2×C3×C4—33no—
603C2×C3×C4—33no—
604C2×C3×C4—33no—
605C2×C3×C4—46no—
606C2×C3×C4—66no—
607C2×C3×C4—66no—
608C2×C3×C4—66no—
609C2×C3×C4—66no—
610C2×C3×C4—66no—
611C2×C3×C4C23×D313yes—
612C2×C3×C4C23×D313yes—
613C2×C3×C4C23×D313yes—
614C2×C3×C4C23×D313yes—
615#67—34no—
616#67—34no—
617#67—34no—
618#67—34no—
619#67—34no—
620#67—64no—
621#67D3×Q814yesdirect product factor
622C2×Dic3—26no—
623C2×Dic3—31no—
624C2×Dic3—31no—
625C2×Dic3—34no—
626C2×Dic3—33no—
627C2×Dic3—33no—
628C2×Dic3—33no—
629C2×Dic3—33no—
630C2×Dic3—61no—
631C2×Dic3—63no—
632C2×Dic3—63no—
633C2×Dic3—66no—
634C2×Dic3—66no—
635C2×Dic3—66no—
636C2×Dic3C23×D313yes—
637C2×Dic3C23×D313yes—
638C2×Dic3C23×D313yes—
639C2×Dic3C23×D311yescharacteristic
640C2×Dic3C23×D313yes—
641D12—34no—
642C4×D3—26no—
643C4×D3—26no—
644C4×D3—26no—
645C4×D3—26no—
646C4×D3—34no—
647C4×D3—66no—
648C4×D3—66no—
649C4×D3—66no—
650C4×D3—66no—
651C4×D3—66no—
652C4×D3—66no—
653C4×D3—66no—
654C4×D3—126no—
655C4×D3C2×#67112yes—
656Dic6—26no—
657Dic6—26no—
658Dic6—212no—
659Dic6—612no—
660Dic6—66no—
661Dic6—66no—
662Dic6—612no—
663Dic6—126no—
664Dic6C2×#67112yescomplemented
665C2×C32—22no—
666C2×C32C23×D411yescharacteristic
667C2×C32C23×Q811yescharacteristic
668C2×C32C2×2−1+411yescharacteristic
669C3⋊D3—22no—
670C3×D3—22no—
671C3×D3—22no—
672C3×D3D4×Q814yescomplemented
673C24—31no—
674C24—91no—
675C2×Q8—24no—
676C2×Q8—38no—
677C2×Q8—33no—
678C2×Q8—33no—
679C2×Q8—36no—
680C2×Q8—33no—
681C2×Q8—612no—
682C2×Q8—612no—
683C2×Q8—612no—
684C2×Q8—64no—
685C2×Q8—64no—
686C2×Q8—96no—
687C2×Q8—93no—
688C2×Q8—1812no—
689C2×Q8—1812no—
690C2×Q8—1812no—
691C2×Q8—184no—
692C2×Q8C2×D3213yes—
693C2×Q8C2×D3211yescharacteristic
694C2×D4—31no—
695C2×D4—91no—
696C2×D4—98no—
697C2×D4—91no—
698C2×D4—91no—
699C22×C4—33no—
700C22×C4—33no—
701C22×C4—33no—
702C22×C4—33no—
703C22×C4—33no—
704C22×C4—33no—
705C22×C4—612no—
706C22×C4—93no—
707C22×C4—91no—
708C22×C4—93no—
709C22×C4—93no—
710C22×C4—93no—
711C22×C4—93no—
712C22×C4—1812no—
713C22×C4C2×D3213yes—
714C4⋊C4—33no—
715C4⋊C4—33no—
716C4⋊C4—36no—
717C4⋊C4—93no—
718C4⋊C4—93no—
719C4⋊C4—96no—
720C4⋊C4—96no—
721C4⋊C4—96no—
722C4⋊C4—93no—
723C4⋊C4—93no—
724C4⋊C4—96no—
725C22⋊C4—33no—
726C22⋊C4—33no—
727C22⋊C4—93no—
728C22⋊C4—93no—
729C22⋊C4—93no—
730C22⋊C4—93no—
731C22⋊C4—93no—
732C22⋊C4—93no—
733C42—33no—
734C42—93no—
735C42—93no—
736C42—93no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—22no—
742C22×C3—21no—
743C22×C3—32no—
744C22×C3—32no—
745C22×C3—32no—
746C22×C3—32no—
747C22×C3—32no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—68no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—61no—
754C22×C3—61no—
755C22×C3C2×D3×Q812yescomplemented
756C22×C3C2×D3×Q812yescomplemented
757C22×C3C24×D311yescharacteristic
758C22×C3C24×D311yescharacteristic
759C2×D3—21no—
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—28no—
764C2×D3—32no—
765C2×D3—32no—
766C2×D3—62no—
767C2×D3—68no—
768C2×D3—61no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—68no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3C2×D3×Q812yes—
776C2×D3C2×D3×Q812yescomplemented
777C2×D3C2×D3×Q812yescomplemented
778C2×D3#100712yes—
779C2×D3C22×#6712yes—
780C3×C4—23no—
781C3×C4—23no—
782C3×C4—26no—
783C3×C4—36no—
784C3×C4—32no—
785C3×C4—43no—
786C3×C4—63no—
787C3×C4—63no—
788C3×C4—63no—
789C3×C4C2×D3×D416yes—
790C3×C4C22×#6716yes—
791Dic3—23no—
792Dic3—23no—
793Dic3—23no—
794Dic3—32no—
795Dic3—32no—
796Dic3—62no—
797Dic3—63no—
798Dic3—63no—
799Dic3—63no—
800Dic3—63no—
801Dic3—123no—
802Dic3—123no—
803Dic3C2×D3×Q812yescomplemented
804Dic3C22×#6716yes—
805C32C2×D4×Q811yescharacteristic, complemented, Sylow
806C23—31no—
807C23—34no—
808C23—31no—
809C23—31no—
810C23—62no—
811C23—62no—
812C23—94no—
813C23—91no—
814C23—182no—
815C23—182no—
816C23C22×D3211yescharacteristic
817Q8—26no—
818Q8—312no—
819Q8—612no—
820Q8—66no—
821Q8—66no—
822Q8—1812no—
823Q8—186no—
824Q8D3×#6714yesdirect product factor
825D4—34no—
826D4—94no—
827D4—94no—
828D4—94no—
829C2×C4—26no—
830C2×C4—31no—
831C2×C4—33no—
832C2×C4—312no—
833C2×C4—33no—
834C2×C4—33no—
835C2×C4—33no—
836C2×C4—66no—
837C2×C4—66no—
838C2×C4—66no—
839C2×C4—66no—
840C2×C4—66no—
841C2×C4—94no—
842C2×C4—91no—
843C2×C4—93no—
844C2×C4—93no—
845C2×C4—186no—
846C2×C4—186no—
847C2×C4—186no—
848C2×C4—186no—
849C2×C4—186no—
850C2×C4C22×D3213yes—
851C2×C4C22×D3213yes—
852C2×C3—22no—
853C2×C3—22no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—34no—
858C2×C3—42no—
859C2×C3—62no—
860C2×C3—62no—
861C2×C3C22×D3×D411yescharacteristic
862C2×C3C22×D3×Q811yescharacteristic
863C2×C3C22×D3×Q811yescharacteristic
864C2×C3C2×#100711yescharacteristic
865C2×C3D3×2−1+411yescharacteristic
866C2×C3C23×#6711yescharacteristic
867D3—22no—
868D3—22no—
869D3—62no—
870D3—62no—
871D3—122no—
872D3Q8×#6714yesdirect product factor
873C22—21no—
874C22—21no—
875C22—32no—
876C22—32no—
877C22—32no—
878C22—32no—
879C22—32no—
880C22—68no—
881C22—61no—
882C22—61no—
883C22—61no—
884C22—61no—
885C22—92no—
886C22—188no—
887C22—181no—
888C22—181no—
889C22D32×Q812yescomplemented
890C22C23×D3211yescharacteristic
891C4—23no—
892C4—32no—
893C4—36no—
894C4—63no—
895C4—63no—
896C4—63no—
897C4—92no—
898C4—183no—
899C4—183no—
900C4C2×D3×#6716yes—
901C3—21no—
902C3D3×D4×Q811yescharacteristic, complemented
903C3C2×Q8×#6711yescharacteristic, complemented
904C2—22no—
905C2—34no—
906C2—62no—
907C2—62no—
908C2—182no—
909C2C2×D32×Q811yescharacteristic
910C2D3×#100711yescharacteristic
911C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
prime radicalC2×D3×#67C22
hypercenterC22×Q8D32
hypocenterC32C2×D4×Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×Q8C2semidirect
2. C2×D32×Q8C2semidirect
3. Q8×#638C2semidirect
4. C3×Q8×#67C2semidirect
5. D3×#946C2semidirect
6. Q8×#626C2semidirect
7. Q8×#625C2semidirect
8. #10595403C2semidirect
9. #10595400C2semidirect
10. D3×Q8×Dic3C2semidirect
11. D3×#944C2semidirect
13. Dic6×#67C2semidirect
14. D3×#924C2semidirect
15. #10594803C2semidirect
18. C22×C32×Q8C22semidirect
19. C2×Q8×C3⋊D3C22semidirect
23. C2×C3×D3×Q8C22semidirect
24. C2×C3×D3×Q8C22semidirect
25. C2×C3×D3×Q8C22semidirect
27. C22×C3×Dic6C22semidirect
31. C2×#3797C22semidirect
33. C2×D3×Dic6C22semidirect
34. #64155C22semidirect
35. Q8×C3⋊Dic3C22semidirect
36. #64153C22semidirect
38. #64133C22semidirect
39. C3×#946C22semidirect
40. C3×Q8×Dic3C22semidirect
41. C3×#944C22semidirect
43. C3×#924C22semidirect
46. #63964C22semidirect
53. #63888C22semidirect
54. #63887C22semidirect
59. #63873C22semidirect
60. #63871C22semidirect
61. #63866C22semidirect
62. #63857C22semidirect
63. #63856C22semidirect
64. #63856C22semidirect
65. #63851C22semidirect
66. #63843C22semidirect
67. Dic3×Dic6C22semidirect
68. #63839C22semidirect
69. #63839C22semidirect
73. C22×D3×Q8D3semidirect
85. Q8×#67D3direct (N × H)
117. C3×D3×Q8D4semidirect
129. D3×#67Q8direct (N × H)
174. C22×C3×Q8C2×D3semidirect
175. C22×C3×Q8C2×D3semidirect
190. C2×D3×Q8C2×D3semidirect
191. C2×D3×Q8C2×D3semidirect
192. C2×D3×Q8C2×D3semidirect
199. C22×Dic6C2×D3semidirect
214. #946C2×D3semidirect
220. Q8×Dic3C2×D3semidirect
229. #944C2×D3semidirect
252. #924C2×D3semidirect
281. C22×C3×D3C2×Q8semidirect
287. C2×D32C2×Q8semidirect
289. C32×Q8C2×D4semidirect
293. #638C2×Q8semidirect
299. C3×#67C2×Q8semidirect
314. C3×Dic6C2×D4semidirect
316. #626C2×Q8semidirect
317. #625C2×Q8semidirect
322. D3×Dic3C2×Q8semidirect
396. D3×Q8#67direct (N × H)
482. C22×C32C22×Q8semidirect
486. C2×C3⋊D3C22×Q8semidirect
494. C2×C3×D3C22×Q8semidirect
495. C2×C3×D3C22×Q8semidirect
502. C3⋊Dic3C22×Q8semidirect
507. C3×Dic3C22×Q8semidirect
520. C22×Q8D32semidirect
580. C22×D3D3×Q8semidirect
592. C3×Q8D3×D4semidirect
593. C3×Q8C2×#67semidirect
621. #67D3×Q8direct (N × H)
664. Dic6C2×#67semidirect
672. C3×D3D4×Q8semidirect
755. C22×C3C2×D3×Q8semidirect
756. C22×C3C2×D3×Q8semidirect
776. C2×D3C2×D3×Q8semidirect
777. C2×D3C2×D3×Q8semidirect
803. Dic3C2×D3×Q8semidirect
805. C32C2×D4×Q8semidirect
824. Q8D3×#67direct (N × H)
872. D3Q8×#67direct (N × H)
889. C22D32×Q8semidirect
902. C3D3×D4×Q8semidirect
903. C3C2×Q8×#67semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C2×D32×Q82
Q8×#6382
C3×Q8×#672
D3×#9462
Q8×#6262
Q8×#6252
#105954032
#105954002
D3×Q8×Dic32
D3×#9442
C4×D3×#672
Dic6×#672
D3×#9242
#105948032
C2×Q8×#673
D3×D4×Q83