Finite Group Databasebeta

← D3×#5567 #11903683

Subgroups — D3×#5567 #11903683

Order 1152.

2196 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596038C211yesmaximal, characteristic, complemented
2C3×C4×D3×Q8C211yesmaximal, characteristic
3C3×#5567C211yesmaximal, characteristic, complemented
4#10595420C212yesmaximal, complemented
5D3×#944C212yesmaximal
6#10594596C214yesmaximal, complemented
7#10594595C212yesmaximal, complemented
8D3×#889C214yesmaximal
9D3×#887C212yesmaximal
10D3×#870C212yesmaximal
11D3×#869C211yesmaximal, characteristic
12C4×D3×Dic6C212yesmaximal
13C4×D3×Dic6C211yesmaximal, characteristic
14#10593864C211yesmaximal, characteristic, complemented
15#10593860C211yesmaximal, characteristic, complemented
16#10593852C212yesmaximal, complemented
17#10593851C212yesmaximal, complemented
18D3×#557—31nomaximal
19C2×#5567—31nomaximal
20C2×C3×D3×Q8C2211yescharacteristic
21C2×D3×Dic6C2212yes—
22C2×D3×Dic6C2211yescharacteristic
23C32×C4×Q8C2211yescharacteristic
24#64153C2212yes—
25#64098C2214yes—
26#64096C2212yes—
27#64079C2212yes—
28#64078C2211yescharacteristic
29C4×#634C2212yes—
30C4×#634C2211yescharacteristic
31C3×Q8×Dic3C2211yescharacteristic
32C3×#944C2212yes—
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×D3×C4⋊C4C2212yes—
35C3×#889C2214yes—
36C3×#887C2211yescharacteristic
37C3×#887C2212yes—
38C3×#887C2212yes—
39C3×C42×D3C2211yescharacteristic
40C3×C42×D3C2212yes—
41C3×#870C2212yes—
42C3×#869C2211yescharacteristic
43C3×C4×Dic6C2212yes—
44C3×C4×Dic6C2212yes—
45C3×C4×Dic6C2211yescharacteristic
46C3×C4×Dic6C2211yescharacteristic
47#63918C2212yes—
48#63918C2212yes—
49C4×#627C2214yes—
50C4×#627C2212yes—
51D3×C4⋊Dic3C2212yes—
52D3×C4⋊Dic3C2212yes—
53D3×C4⋊Dic3C2211yescharacteristic
54D3×Dic3⋊C4C2214yes—
55D3×Dic3⋊C4C2214yes—
56D3×Dic3⋊C4C2214yes—
57D3×Dic3⋊C4C2212yes—
58C4×D3×Dic3C2212yes—
59C4×D3×Dic3C2214yes—
60#63873C2212yes—
61#63870C2214yes—
62#63869C2212yes—
63#63869C2212yes—
64#63867C2214yes—
65#63867C2214yes—
66#63867C2214yes—
67#63866C2212yes—
68#63866C2212yes—
69#63847C2214yes—
70#63847C2214yes—
71#63846C2214yes—
72#63845C2214yes—
73#63844C2212yes—
74#63844C2211yescharacteristic
75#63844C2212yes—
76#63843C2212yes—
77Dic3×Dic6C2211yescharacteristic
78Dic3×Dic6C2212yes—
79#63839C2214yes—
80#63839C2214yes—
81#63838C2214yes—
82#63837C2212yes—
83#63837C2214yes—
84#63837C2214yes—
85C3×#557—31no—
86C2×C3×C4×Q8—31no—
87C2×#944—32no—
88D3×C4⋊Q8—32no—
89D3×C4⋊Q8—31no—
90#5721—32no—
91#5721—31no—
92D3×#125—34no—
93D3×#125—32no—
94#5685—34no—
95#5685—32no—
96C4×D3×Q8—32no—
97C4×D3×Q8—32no—
98C4×D3×Q8—31no—
99C4×D3×Q8D311yescharacteristic
100#5570—31no—
101#5569—32no—
102#5567—31no—
103#5567—31no—
104#5567—32no—
105#5567—34no—
106#5567—32no—
107#5567—32no—
108#5567—32no—
109#5567—31no—
110#5567—32no—
111#5567—31no—
112#5567—61no—
113#5567D311yescharacteristic, direct product factor
114C2×#889—34no—
115C2×#887—32no—
116C2×#870—32no—
117C2×#869—31no—
118C2×C4×Dic6—32no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2311yescharacteristic
121C2×#634C2312yes—
122C2×#634C2311yescharacteristic
123C3×D3×Q8—24no—
124C2×C3×C4×D3C2312yes—
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2312yes—
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×Dic6C2312yes—
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2311yescharacteristic
132C2×C3×Dic6C2311yescharacteristic
133C2×#627C2314yes—
134C2×#627C2312yes—
135C2×D3×Dic3C2314yes—
136C2×D3×Dic3C2312yes—
137C2×D3×Dic3C2312yes—
138D3×Dic6—28no—
139D3×Dic6Q818yescomplemented
140C32×C4⋊C4C2311yescharacteristic
141C32×C4⋊C4C2312yes—
142C32×C42C2311yescharacteristic
143C32×C42C2312yes—
144C4⋊(C3⋊Dic3)C2312yes—
145C4⋊(C3⋊Dic3)C2311yescharacteristic
146C4⋊(C3⋊Dic3)C2312yes—
147#3750C2314yes—
148#3750C2312yes—
149#3750C2314yes—
150#3750C2314yes—
151C4×C3⋊Dic3C2314yes—
152C4×C3⋊Dic3C2312yes—
153C3×C4⋊Dic3C2312yes—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×C4⋊Dic3C2312yes—
156C3×C4⋊Dic3C2311yescharacteristic
157C3×C4⋊Dic3C2312yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2312yes—
160C3×Dic3⋊C4C2312yes—
161C3×Dic3⋊C4C2312yes—
162C3×Dic3⋊C4C2312yes—
163C3×Dic3⋊C4C2314yes—
164C3×Dic3⋊C4C2314yes—
165C3×C4×Dic3C2311yescharacteristic
166C3×C4×Dic3C2312yes—
167C3×C4×Dic3C2314yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2311yescharacteristic
173#3724C2314yes—
174#3724C2314yes—
175#3724C2314yes—
176#3724C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2312yes—
183Dic3⋊Dic3C2314yes—
184Dic32C2312yes—
185Dic32C2314yes—
186Dic32C2312yes—
187Dic32C2314yes—
188C2×#557—91noSylow
189C22×C3×Q8—31no—
190C2×D3×Q8—31no—
191C2×D3×Q8—32no—
192C2×D3×Q8C2×D311yescharacteristic
193C22×Dic6—31no—
194C22×Dic6—32no—
195C3×C4⋊Q8—32no—
196C3×C4⋊Q8—31no—
197C3×#125—34no—
198C3×#125—32no—
199C3×C4×Q8—21no—
200C3×C4×Q8—31no—
201C3×C4×Q8—32no—
202C3×C4×Q8—31no—
203C3×C4×Q8—32no—
204C3×C4×Q8—32no—
205C3×C4×Q8—31no—
206C3×C4×Q8—32no—
207C3×C4×Q8—31no—
208C3×C4×Q8C2×D311yescharacteristic
209C3×C4×Q8C2×D311yescharacteristic
210C2×C3×C4⋊C4—31no—
211C2×C3×C4⋊C4—32no—
212C2×C3×C42—31no—
213C2×C3×C42—32no—
214Q8×Dic3—32no—
215Q8×Dic3—31no—
216Q8×Dic3—32no—
217Q8×Dic3C2×D311yescharacteristic
218#944—32no—
219#944—32no—
220#944—32no—
221#944—32no—
222#944—34no—
223#944—34no—
224#944—32no—
225#944—32no—
226#944—62no—
227#944C2×D312yes—
228C2×C4⋊Dic3—32no—
229C2×C4⋊Dic3—31no—
230C2×C4⋊Dic3—32no—
231C2×Dic3⋊C4—32no—
232C2×Dic3⋊C4—34no—
233C2×Dic3⋊C4—34no—
234C2×Dic3⋊C4—34no—
235C2×C4×Dic3—34no—
236C2×C4×Dic3—32no—
237D3×C4⋊C4—34no—
238D3×C4⋊C4—32no—
239D3×C4⋊C4—34no—
240D3×C4⋊C4—32no—
241D3×C4⋊C4—31no—
242D3×C4⋊C4—34no—
243D3×C4⋊C4—32no—
244D3×C4⋊C4C2×D312yes—
245D3×C4⋊C4C2×D311yescharacteristic
246#890—34no—
247#890—34no—
248#890—32no—
249#890—32no—
250#889—34no—
251#889—34no—
252#889—34no—
253#889—34no—
254#889—34no—
255#889—34no—
256#889—34no—
257#889—34no—
258#889—34no—
259#889—34no—
260#889—34no—
261#889—34no—
262#889—34no—
263#889—64no—
264#889C2×D314yes—
265#888—34no—
266#888—34no—
267#888—32no—
268#888—32no—
269#887—32no—
270#887—32no—
271#887—32no—
272#887—34no—
273#887—34no—
274#887—32no—
275#887—31no—
276#887—34no—
277#887—32no—
278#887—34no—
279#887—32no—
280#887—62no—
281#887C2×D312yes—
282#887C2×D312yes—
283#887C2×D311yescharacteristic
284C42×D3—34no—
285C42×D3—32no—
286C42×D3C2×D312yes—
287C42×D3C2×D311yescharacteristic
288#870—32no—
289#870—32no—
290#870—32no—
291#870—32no—
292#870—34no—
293#870—34no—
294#870—34no—
295#870—62no—
296#870C2×D312yes—
297#869—32no—
298#869—32no—
299#869—31no—
300#869—31no—
301#869—32no—
302#869—32no—
303#869—61no—
304#869C2×D311yescharacteristic
305C4×Dic6—32no—
306C4×Dic6—31no—
307C4×Dic6—32no—
308C4×Dic6—31no—
309C4×Dic6—32no—
310C4×Dic6—31no—
311C4×Dic6—32no—
312C4×Dic6—32no—
313C4×Dic6—31no—
314C4×Dic6—34no—
315C4×Dic6—34no—
316C4×Dic6—32no—
317C4×Dic6—34no—
318C4×Dic6—32no—
319C4×Dic6—34no—
320C4×Dic6—32no—
321C4×Dic6—62no—
322C4×Dic6—61no—
323C4×Dic6C2×D312yes—
324C4×Dic6C2×D311yescharacteristic
325C4×Dic6C2×D312yes—
326C4×Dic6C2×D311yescharacteristic
327C22×C3×D3C2411yescharacteristic
328C32×Q8—22no—
329C2×C32×C4C2412yes—
330C2×C32×C4C2411yescharacteristic
331C2×C32×C4C2412yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2414yes—
336C2×C3⋊Dic3C2412yes—
337#634—24no—
338#634C2×Q814yescomplemented
339C2×C3×Dic3C2412yes—
340C2×C3×Dic3C2412yes—
341C2×C3×Dic3C2414yes—
342C2×C3×Dic3C2411yescharacteristic
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2411yescharacteristic
346C2×C3×Dic3C2411yescharacteristic
347C3×C4×D3—24no—
348C3×C4×D3—24no—
349C3×C4×D3—22no—
350C3×C4×D3C2×Q814yes—
351C3×C4×D3#4114yes—
352C3×Dic6—24no—
353C3×Dic6—22no—
354C3×Dic6—24no—
355C3×Dic6C2×Q814yescomplemented
356#627—28no—
357#627C2×Q818yescomplemented
358D3×Dic3—28no—
359D3×Dic3—24no—
360D3×Dic3C2×Q818yes—
361#557—31no—
362#557—92no—
363#557—92no—
364#557—91no—
365#557—94no—
366#557—92no—
367#557—92no—
368#557—91no—
369#557—91no—
370C2×C4⋊Q8—91no—
371C2×C4⋊Q8—92no—
372C2×#125—92no—
373C2×#125—94no—
374C2×C4×Q8—31no—
375C2×C4×Q8—92no—
376C2×C4×Q8—91no—
377C2×C4×Q8—92no—
378C2×C3×Q8—21no—
379C2×C3×Q8—31no—
380C2×C3×Q8—32no—
381C2×C3×Q8—31no—
382C2×C3×Q8—32no—
383C2×C3×Q8—64no—
384C2×C3×Q8C22×D311yescharacteristic
385C2×C3×Q8C22×D311yescharacteristic
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—32no—
389C22×C3×C4—32no—
390C22×C3×C4—31no—
391C22×Dic3—32no—
392C22×Dic3—32no—
393C22×Dic3—34no—
394D3×Q8—24no—
395D3×Q8—38no—
396D3×Q8—68no—
397C2×C4×D3—32no—
398C2×C4×D3—32no—
399C2×C4×D3—34no—
400C2×C4×D3C22×D312yes—
401C2×C4×D3C22×D311yescharacteristic
402C2×C4×D3C22×D312yes—
403C2×C4×D3C22×D311yescharacteristic
404C2×C4×D3C22×D311yescharacteristic
405C2×Dic6—31no—
406C2×Dic6—31no—
407C2×Dic6—32no—
408C2×Dic6—32no—
409C2×Dic6—38no—
410C2×Dic6—32no—
411C2×Dic6—32no—
412C2×Dic6—34no—
413C2×Dic6—34no—
414C2×Dic6—61no—
415C2×Dic6—62no—
416C2×Dic6—68no—
417C2×Dic6C22×D311yescharacteristic
418C2×Dic6C22×D312yes—
419C2×Dic6C22×D312yes—
420C2×Dic6C22×D311yescharacteristic
421C3×C4⋊C4—21no—
422C3×C4⋊C4—22no—
423C3×C4⋊C4—32no—
424C3×C4⋊C4—31no—
425C3×C4⋊C4—34no—
426C3×C4⋊C4—32no—
427C3×C4⋊C4—34no—
428C3×C4⋊C4—32no—
429C3×C4⋊C4—31no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—32no—
432C3×C4⋊C4—32no—
433C3×C4⋊C4—32no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4C22×D311yescharacteristic
436C3×C4⋊C4C22×D311yescharacteristic
437C3×C4⋊C4C22×D312yes—
438C3×C4⋊C4C22×D312yes—
439C3×C42—21no—
440C3×C42—22no—
441C3×C42—31no—
442C3×C42—31no—
443C3×C42—31no—
444C3×C42—32no—
445C3×C42—32no—
446C3×C42—32no—
447C3×C42—32no—
448C3×C42—34no—
449C3×C42C22×D311yescharacteristic
450C3×C42C22×D311yescharacteristic
451C3×C42C22×D312yes—
452C3×C42C22×D312yes—
453C4⋊Dic3—32no—
454C4⋊Dic3—31no—
455C4⋊Dic3—32no—
456C4⋊Dic3—31no—
457C4⋊Dic3—32no—
458C4⋊Dic3—32no—
459C4⋊Dic3—34no—
460C4⋊Dic3—32no—
461C4⋊Dic3—34no—
462C4⋊Dic3—32no—
463C4⋊Dic3—34no—
464C4⋊Dic3—34no—
465C4⋊Dic3—34no—
466C4⋊Dic3—62no—
467C4⋊Dic3—61no—
468C4⋊Dic3—62no—
469C4⋊Dic3C22×D311yescharacteristic
470C4⋊Dic3C22×D312yes—
471C4⋊Dic3C22×D311yescharacteristic
472C4⋊Dic3C22×D312yes—
473C4⋊Dic3C22×D312yes—
474Dic3⋊C4—32no—
475Dic3⋊C4—34no—
476Dic3⋊C4—34no—
477Dic3⋊C4—34no—
478Dic3⋊C4—32no—
479Dic3⋊C4—34no—
480Dic3⋊C4—34no—
481Dic3⋊C4—34no—
482Dic3⋊C4—32no—
483Dic3⋊C4—32no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—32no—
489Dic3⋊C4—32no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—62no—
498Dic3⋊C4—64no—
499Dic3⋊C4—64no—
500Dic3⋊C4—64no—
501Dic3⋊C4C22×D312yes—
502Dic3⋊C4C22×D312yes—
503Dic3⋊C4C22×D314yes—
504Dic3⋊C4C22×D312yes—
505Dic3⋊C4C22×D312yes—
506Dic3⋊C4C22×D314yes—
507Dic3⋊C4C22×D314yes—
508C4×Dic3—34no—
509C4×Dic3—32no—
510C4×Dic3—34no—
511C4×Dic3—32no—
512C4×Dic3—32no—
513C4×Dic3—34no—
514C4×Dic3—34no—
515C4×Dic3—34no—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—32no—
519C4×Dic3—34no—
520C4×Dic3—64no—
521C4×Dic3—62no—
522C4×Dic3C22×D312yes—
523C4×Dic3C22×D311yescharacteristic
524C4×Dic3C22×D314yes—
525C4×Dic3C22×D312yes—
526C4×Dic3C22×D311yescharacteristic
527C4×Dic3C22×D312yes—
528C4×Dic3C22×D311yescharacteristic
529C4×Dic3C22×D312yes—
530C22×C32C2511yescharacteristic
531C2×C3×D3C22×Q812yes—
532C2×C3×D3C2×#4112yes—
533C2×C3×D32−1+412yes—
534C32×C4—22no—
535C32×C4—22no—
536C32×C4—21no—
537C32×C4C22×Q812yes—
538C32×C4C2×#4112yes—
539C3⋊Dic3—24no—
540C3⋊Dic3—22no—
541C3⋊Dic3C22×Q814yes—
542C3×Dic3—24no—
543C3×Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—21no—
547C3×Dic3C22×Q814yes—
548C3×Dic3C22×Q812yes—
549C3×Dic3C2×#4112yes—
550C22×Q8—31no—
551C22×Q8—91no—
552C22×Q8—92no—
553C4⋊Q8—32no—
554C4⋊Q8—31no—
555C4⋊Q8—92no—
556C4⋊Q8—92no—
557C4⋊Q8—92no—
558C4⋊Q8—92no—
559C4⋊Q8—94no—
560C4⋊Q8—94no—
561C4⋊Q8—92no—
562C4⋊Q8—92no—
563C4⋊Q8—91no—
564#125—34no—
565#125—32no—
566#125—94no—
567#125—94no—
568#125—94no—
569#125—92no—
570#125—92no—
571#125—94no—
572#125—94no—
573#125—94no—
574#125—94no—
575#125—94no—
576#125—94no—
577#125—92no—
578C4×Q8—31no—
579C4×Q8—32no—
580C4×Q8—31no—
581C4×Q8—32no—
582C4×Q8—31no—
583C4×Q8—32no—
584C4×Q8—32no—
585C4×Q8—31no—
586C4×Q8—94no—
587C4×Q8—92no—
588C4×Q8—94no—
589C4×Q8—92no—
590C4×Q8—92no—
591C4×Q8—91no—
592C4×Q8—94no—
593C4×Q8—92no—
594C4×Q8—92no—
595C4×Q8—91no—
596C4×Q8—94no—
597C4×Q8—92no—
598C4×Q8—92no—
599C4×Q8—92no—
600C4×Q8—91no—
601C4×Q8D3211yescharacteristic
602C2×C4⋊C4—31no—
603C2×C4⋊C4—32no—
604C2×C4⋊C4—94no—
605C2×C4⋊C4—92no—
606C2×C4⋊C4—91no—
607C2×C4⋊C4—94no—
608C2×C4⋊C4—92no—
609C2×C4⋊C4—94no—
610C2×C4⋊C4—92no—
611C2×C42—32no—
612C2×C42—31no—
613C2×C42—94no—
614C2×C42—92no—
615C23×C3—31no—
616C22×D3C23×D311yescharacteristic
617C3×Q8—22no—
618C3×Q8—22no—
619C3×Q8—34no—
620C3×Q8—42no—
621C3×Q8—64no—
622C3×Q8—64no—
623C3×Q8—62no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—21no—
629C2×C3×C4—31no—
630C2×C3×C4—32no—
631C2×C3×C4—31no—
632C2×C3×C4—34no—
633C2×C3×C4—34no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—34no—
637C2×C3×C4—32no—
638C2×C3×C4—31no—
639C2×C3×C4—64no—
640C2×C3×C4—62no—
641C2×C3×C4—64no—
642C2×C3×C4C23×D312yes—
643C2×C3×C4C23×D312yes—
644C2×C3×C4C23×D312yes—
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D312yes—
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D311yescharacteristic
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—38no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—34no—
658C2×Dic3—34no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—64no—
662C2×Dic3—68no—
663C2×Dic3—64no—
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D314yes—
667C2×Dic3C23×D311yescharacteristic
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D311yescharacteristic
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D311yescharacteristic
672C4×D3—24no—
673C4×D3—24no—
674C4×D3—22no—
675C4×D3—38no—
676C4×D3—68no—
677C4×D3—64no—
678C4×D3#23514yes—
679C4×D3D3×Q814yes—
680Dic6—22no—
681Dic6—24no—
682Dic6—24no—
683Dic6—34no—
684Dic6—34no—
685Dic6—38no—
686Dic6—38no—
687Dic6—64no—
688Dic6—68no—
689Dic6—64no—
690Dic6—64no—
691Dic6—68no—
692Dic6—124no—
693Dic6D3×Q814yescomplemented
694C2×C32C23×Q811yescharacteristic
695C2×C32C22×#4111yescharacteristic
696C2×C32C2×2−1+411yescharacteristic
697C3×D3#55714yescomplemented
698C2×Q8—31no—
699C2×Q8—32no—
700C2×Q8—31no—
701C2×Q8—32no—
702C2×Q8—64no—
703C2×Q8—92no—
704C2×Q8—94no—
705C2×Q8—98no—
706C2×Q8—91no—
707C2×Q8—92no—
708C2×Q8—188no—
709C2×Q8C2×D3211yescharacteristic
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—32no—
713C22×C4—31no—
714C22×C4—32no—
715C22×C4—92no—
716C22×C4—92no—
717C22×C4—94no—
718C4⋊C4—32no—
719C4⋊C4—31no—
720C4⋊C4—32no—
721C4⋊C4—32no—
722C4⋊C4—32no—
723C4⋊C4—32no—
724C4⋊C4—34no—
725C4⋊C4—31no—
726C4⋊C4—34no—
727C4⋊C4—32no—
728C4⋊C4—34no—
729C4⋊C4—32no—
730C4⋊C4—94no—
731C4⋊C4—92no—
732C4⋊C4—92no—
733C4⋊C4—92no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4—94no—
741C4⋊C4—92no—
742C4⋊C4—94no—
743C4⋊C4—91no—
744C4⋊C4—94no—
745C4⋊C4—92no—
746C4⋊C4—94no—
747C4⋊C4—92no—
748C4⋊C4C2×D3211yescharacteristic
749C4⋊C4C2×D3212yes—
750C42—32no—
751C42—32no—
752C42—32no—
753C42—31no—
754C42—31no—
755C42—31no—
756C42—34no—
757C42—32no—
758C42—94no—
759C42—94no—
760C42—92no—
761C42—92no—
762C42—94no—
763C42—92no—
764C42C2×D3212yes—
765C42C2×D3211yescharacteristic
766C22×C3—21no—
767C22×C3—32no—
768C22×C3—32no—
769C22×C3—32no—
770C22×C3C24×D311yescharacteristic
771C22×C3C24×D311yescharacteristic
772C2×D3C2×#23512yes—
773C2×D3C2×D3×Q812yes—
774C2×D3#101012yes—
775C3×C4—22no—
776C3×C4—22no—
777C3×C4—22no—
778C3×C4—21no—
779C3×C4—22no—
780C3×C4—21no—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—32no—
784C3×C4—34no—
785C3×C4—32no—
786C3×C4—42no—
787C3×C4—42no—
788C3×C4—41no—
789C3×C4—64no—
790C3×C4—62no—
791C3×C4—62no—
792C3×C4—62no—
793C3×C4—61no—
794C3×C4C2×#23512yes—
795C3×C4C2×D3×Q812yes—
796C3×C4C2×D3×Q812yes—
797C3×C4D3×#4112yes—
798Dic3—22no—
799Dic3—24no—
800Dic3—22no—
801Dic3—21no—
802Dic3—22no—
803Dic3—34no—
804Dic3—34no—
805Dic3—64no—
806Dic3—64no—
807Dic3—64no—
808Dic3—62no—
809Dic3—62no—
810Dic3—124no—
811Dic3—122no—
812Dic3C2×#23512yes—
813Dic3C2×D3×Q812yes—
814Dic3C2×D3×Q814yes—
815C32C2×#55711yescharacteristic, complemented, Sylow
816C23—31no—
817Q8—22no—
818Q8—34no—
819Q8—64no—
820Q8—62no—
821Q8—64no—
822Q8—98no—
823Q8—94no—
824Q8—188no—
825Q8—184no—
826C2×C4—31no—
827C2×C4—32no—
828C2×C4—31no—
829C2×C4—34no—
830C2×C4—34no—
831C2×C4—32no—
832C2×C4—31no—
833C2×C4—32no—
834C2×C4—32no—
835C2×C4—34no—
836C2×C4—64no—
837C2×C4—64no—
838C2×C4—62no—
839C2×C4—98no—
840C2×C4—92no—
841C2×C4—92no—
842C2×C4—94no—
843C2×C4—188no—
844C2×C4—184no—
845C2×C4C22×D3212yes—
846C2×C4C22×D3211yescharacteristic
847C2×C4C22×D3212yes—
848C2×C4C22×D3211yescharacteristic
849C2×C4C22×D3211yescharacteristic
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—34no—
854C2×C3C22×#23511yescharacteristic
855C2×C3C22×D3×Q811yescharacteristic
856C2×C3C22×D3×Q811yescharacteristic
857C2×C3C2×D3×#4111yescharacteristic
858C2×C3C2×#101011yescharacteristic
859C2×C3D3×2−1+411yescharacteristic
860D3#556714yesdirect product factor
861C22—32no—
862C22—32no—
863C22—32no—
864C22C23×D3211yescharacteristic
865C4—22no—
866C4—22no—
867C4—21no—
868C4—32no—
869C4—32no—
870C4—34no—
871C4—62no—
872C4—64no—
873C4—62no—
874C4—61no—
875C4—62no—
876C4—94no—
877C4—184no—
878C4—182no—
879C4D3×#23512yes—
880C4D32×Q812yes—
881C3—21no—
882C3C2×#556711yescharacteristic, complemented
883C3D3×#55711yescharacteristic, complemented
884C2—34no—
885C2C2×D3×#23511yescharacteristic
886C2C2×D32×Q811yescharacteristic
887C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC22×C3×D3C24
hypercenterC4×Q8D32
hypocenterC32C2×#557
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596038C2semidirect
3. C3×#5567C2semidirect
4. #10595420C2semidirect
6. #10594596C2semidirect
7. #10594595C2semidirect
14. #10593864C2semidirect
15. #10593860C2semidirect
16. #10593852C2semidirect
17. #10593851C2semidirect
113. #5567D3direct (N × H)
139. D3×Dic6Q8semidirect
338. #634C2×Q8semidirect
355. C3×Dic6C2×Q8semidirect
357. #627C2×Q8semidirect
693. Dic6D3×Q8semidirect
697. C3×D3#557semidirect
815. C32C2×#557semidirect
860. D3#5567direct (N × H)
882. C3C2×#5567semidirect
883. C3D3×#557semidirect

Maximal subgroups

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

subgroupindex
#105960382
C3×C4×D3×Q82
C3×#55672
#105954202
D3×#9442
#105945962
#105945952
D3×#8892
D3×#8872
D3×#8702
D3×#8692
C4×D3×Dic62
#105938642
#105938602
#105938522
#105938512
D3×#5573
C2×#55673