Finite Group Databasebeta

← #11870803

Subgroups — #11870803

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 611 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic
3C3×#5031C211yesmaximal, characteristic, complemented
4C3×#5021C211yesmaximal, characteristic, complemented
5#10591603C212yesmaximal
6#10591581C212yesmaximal, complemented
7#10590528C212yesmaximal
8#10590482C212yesmaximal, complemented
9#10590388C211yesmaximal, characteristic, complemented
10#10590284C211yesmaximal, characteristic, complemented
11#10590256C211yesmaximal, characteristic
12#81092—31nomaximal
13#80456—31nomaximal
14C2×Q8×C3⋊D3C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16Q8×C3⋊Dic3C2211yescharacteristic
17C4⋊C4×C3⋊D3—21no—
18C4⋊C4×C3⋊D3C2211yescharacteristic
19#64096—21no—
20#64096C2211yescharacteristic
21C42×C3⋊D3—21no—
22C42×C3⋊D3C2211yescharacteristic
23C4×#634—21no—
24C4×#634C2211yescharacteristic
25C2×C3×#216C2212yes—
26C3×#869C2211yescharacteristic
27C3×#869C2211yescharacteristic
28#63872—21no—
29#63871—21no—
30#63871C2212yes—
31#63849—21no—
32#63843—21no—
33#63843C2212yes—
34C2×#3719C2212yes—
35C3×#835C2212yes—
36C3×#810C2212yes—
37C3×#807C2212yes—
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63567C2212yes—
42#63566C2212yes—
43#63557C2212yes—
44#63553C2212yes—
45#5728—31no—
46#5728—31no—
47C4×D3×Q8—31no—
48C4×D3×Q8—31no—
49C4×D3×Q8—61no—
50C3×#477—31no—
51C3×#462—31no—
52#5186—32no—
53Dic3×Q16—32no—
54#5091—31no—
55#5090—31no—
56#5031D311yescharacteristic, complemented
57#5021D311yescharacteristic, complemented
58#4884—32no—
59#4873—32no—
60#4850—31no—
61#4849—31no—
62#4833—31no—
63#4833—31no—
64#4811—32no—
65#4809—32no—
66#4790—32no—
67#4790—32no—
68C2×C32×Q8C2311yescharacteristic
69Q8×C3⋊D3—22no—
70Q8×C3⋊D3—22no—
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—21no—
73C2×C4×C3⋊D3D411yescharacteristic
74C2×C4×C3⋊D3D411yescharacteristic
75C2×C4×C3⋊D3C2311yescharacteristic
76C2×#634—21no—
77C2×#634C2311yescharacteristic
78C2×C3×Dic6—21no—
79C2×C3×Dic6C2312yes—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2311yescharacteristic
82C32×C42—21no—
83C32×C42C2311yescharacteristic
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87#3750—21no—
88#3750—21no—
89C4×C3⋊Dic3—21no—
90C4×C3⋊Dic3—21no—
91C4×C3⋊Dic3—21no—
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95C3×#216—24no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3C2312yes—
100C2×C3×C3⋊C8C2312yes—
101C2×C3×C3⋊C8C2312yes—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—22no—
104#3722—22no—
105Dic32—22no—
106#3719—24no—
107#3104—91noSylow
108C2×D3×Q8—31no—
109C2×D3×Q8—31no—
110C2×D3×Q8—61no—
111C2×C3×Q16—32no—
112C3×C4⋊Q8—31no—
113C3×C4⋊Q8—31no—
114C3×C4×Q8—21no—
115C3×C4×Q8C2×D311yescharacteristic
116C3×C4×Q8C2×D311yescharacteristic
117#946—32no—
118#946—61no—
119Q8×Dic3—31no—
120Q8×Dic3—31no—
121Q8×Dic3—32no—
122Q8×Dic3—61no—
123Q8×Dic3—61no—
124C2×#216—32no—
125C2×#216C2×D312yes—
126C2×Dic12—32no—
127#897—32no—
128#897—61no—
129#892—61no—
130#892—61no—
131D3×C4⋊C4—31no—
132D3×C4⋊C4—31no—
133D3×C4⋊C4—61no—
134D3×C4⋊C4—61no—
135D3×C4⋊C4—61no—
136D3×C4⋊C4—62no—
137#890—61no—
138#890—61no—
139#887—32no—
140#887—31no—
141#887—31no—
142#887—61no—
143#887—61no—
144#887—61no—
145#887—61no—
146#887—62no—
147C42×D3—31no—
148C42×D3—31no—
149C42×D3—61no—
150C42×D3—61no—
151C42×D3—61no—
152C42×D3—62no—
153#869C2×D311yescharacteristic
154#869C2×D311yescharacteristic
155C4×Dic6—31no—
156C4×Dic6—31no—
157C4×Dic6—61no—
158C4×Dic6—61no—
159C4×Dic6—61no—
160C4×Dic6—62no—
161C3×#107—32no—
162C3×C4⋊C8—31no—
163C3×C4⋊C8—31no—
164C3×#103—32no—
165C3×#103—32no—
166#835—32no—
167#835C2×D312yes—
168(C2×D3)⋊C8—32no—
169(C2×D3)⋊C8—32no—
170#818—32no—
171#816—32no—
172#816—32no—
173C8×Dic3—32no—
174C8×Dic3—32no—
175#810—32no—
176#810C2×D312yes—
177#807—32no—
178#807C2×D312yes—
179C4⋊(C3⋊C8)C2×D311yescharacteristic
180C4⋊(C3⋊C8)C2×D311yescharacteristic
181C22×C3⋊D3C2×D411yescharacteristic
182C32×Q8—21no—
183C32×Q8#4112yes—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C2×C3⋊Dic3C2×D411yescharacteristic
194C4×C3⋊D3—24no—
195C4×C3⋊D3—21no—
196C4×C3⋊D3—21no—
197C4×C3⋊D3—41no—
198C4×C3⋊D3—42no—
199C4×C3⋊D3Q1614yescomplemented
200#634—24no—
201#634—21no—
202#634#4112yes—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C3×Dic6—22no—
206C3×Dic6—22no—
207C3×Dic6—42no—
208C3×C3⋊C8—22no—
209C3×C3⋊C8—22no—
210#533—91no—
211C2×C4×Q8—91no—
212#484—92no—
213#477—31no—
214#477—91no—
215#462—31no—
216#462—91no—
217#451—92no—
218C4×Q16—92no—
219C4×Q16—92no—
220#431—91no—
221C2×C3×Q8—21no—
222C2×C3×Q8—32no—
223C2×C3×Q8—61no—
224C2×C3×Q8C22×D311yescharacteristic
225C2×C3×Q8C22×D311yescharacteristic
226D3×Q8—62no—
227D3×Q8—62no—
228D3×Q8—64no—
229D3×Q8—64no—
230D3×Q8—62no—
231D3×Q8—62no—
232C2×C4×D3—31no—
233C2×C4×D3—31no—
234C2×C4×D3—31no—
235C2×C4×D3—31no—
236C2×C4×D3—31no—
237C2×C4×D3—31no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—61no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×C4×D3—62no—
244C2×C4×D3—61no—
245C2×C4×D3—61no—
246C2×C4×D3—62no—
247C2×Dic6—21no—
248C2×Dic6—31no—
249C2×Dic6—31no—
250C2×Dic6—61no—
251C2×Dic6—61no—
252C2×Dic6—61no—
253C2×Dic6—62no—
254C2×Dic6C22×D312yes—
255C3×Q16—64no—
256C2×C3×C8—32no—
257C2×C3×C8—32no—
258C3×C4⋊C4—22no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—32no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4C22×D311yescharacteristic
267C3×C4⋊C4C22×D311yescharacteristic
268C3×C42—22no—
269C3×C42—21no—
270C3×C42—21no—
271C3×C42—21no—
272C3×C42C22×D311yescharacteristic
273C3×C42C22×D311yescharacteristic
274#216—24no—
275#216—64no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—62no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281C4⋊Dic3—31no—
282C4⋊Dic3—31no—
283C4⋊Dic3—61no—
284C4⋊Dic3—62no—
285C4⋊Dic3—62no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C4⋊Dic3—62no—
289C4⋊Dic3C22×D312yes—
290Dic3⋊C4—62no—
291Dic3⋊C4—62no—
292Dic3⋊C4—61no—
293Dic3⋊C4—61no—
294Dic3⋊C4—61no—
295Dic3⋊C4—61no—
296Dic3⋊C4—62no—
297Dic3⋊C4—62no—
298Dic3⋊C4—62no—
299Dic3⋊C4—61no—
300Dic3⋊C4—61no—
301C4×Dic3—31no—
302C4×Dic3—31no—
303C4×Dic3—31no—
304C4×Dic3—31no—
305C4×Dic3—31no—
306C4×Dic3—31no—
307C4×Dic3—61no—
308C4×Dic3—61no—
309C4×Dic3—61no—
310C4×Dic3—62no—
311C4×Dic3—62no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316C4×Dic3—62no—
317C4×Dic3—62no—
318C4×Dic3—62no—
319C4×Dic3—61no—
320C4×Dic3—61no—
321C2×C3⋊C8C22×D312yes—
322C2×C3⋊C8C22×D312yes—
323Dic12—64no—
324C22×C32C22×D411yescharacteristic
325C2×C3⋊D3—21no—
326C2×C3⋊D3—21no—
327C2×C3⋊D3C2×Q1612yes—
328C32×C4—22no—
329C32×C4—21no—
330C32×C4—41no—
331C32×C4C2×Q1612yes—
332C32×C4C2×#4111yescharacteristic
333C32×C4C2×#4111yescharacteristic
334C3⋊Dic3—21no—
335C3⋊Dic3—22no—
336C3⋊Dic3—21no—
337C3⋊Dic3—41no—
338C3⋊Dic3C2×Q1612yes—
339C3×Dic3—42no—
340C3×Dic3—42no—
341C22×Q8—91no—
342C2×Q16—32no—
343C2×Q16—92no—
344C4⋊Q8—31no—
345C4⋊Q8—31no—
346#125—181no—
347C22⋊Q8—92no—
348C22⋊Q8—181no—
349C4×Q8—92no—
350C4×Q8—91no—
351C4×Q8—91no—
352C4×Q8—91no—
353C4×Q8—181no—
354C4×Q8—181no—
355C4×Q8—181no—
356C4×Q8D3211yescharacteristic
357#117—181no—
358C2×C4⋊C4—91no—
359C2×C4⋊C4—181no—
360C2×C42—91no—
361C2×C42—181no—
362#107—32no—
363#107—92no—
364C4⋊C8—31no—
365C4⋊C8—31no—
366#103—32no—
367#103—32no—
368#103—92no—
369#103—92no—
370C22⋊C8—92no—
371C4×C8—92no—
372C22×D3—31no—
373C22×D3—31no—
374C22×D3—61no—
375C3×Q8—22no—
376C3×Q8—21no—
377C3×Q8—21no—
378C3×Q8—22no—
379C3×Q8—62no—
380C3×Q8—62no—
381C3×Q8—122no—
382C3×Q8#23712yes—
383C3×Q8#23912yes—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—31no—
404C2×Dic3—31no—
405C2×Dic3—31no—
406C2×Dic3—31no—
407C2×Dic3—31no—
408C2×Dic3—31no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—62no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—62no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C4×D3—34no—
419C4×D3—34no—
420C4×D3—64no—
421C4×D3—68no—
422C4×D3—64no—
423C4×D3—64no—
424C4×D3—62no—
425C4×D3—62no—
426C4×D3—61no—
427C4×D3—61no—
428C4×D3—61no—
429C4×D3—61no—
430C4×D3—121no—
431C4×D3—121no—
432C4×D3—122no—
433C4×D3—124no—
434C4×D3—122no—
435C4×D3—122no—
436Dic6—22no—
437Dic6—22no—
438Dic6—32no—
439Dic6—32no—
440Dic6—42no—
441Dic6—62no—
442Dic6—68no—
443Dic6—64no—
444Dic6—64no—
445Dic6—62no—
446Dic6—61no—
447Dic6—61no—
448C3×C8—62no—
449C3×C8—62no—
450C3⋊C8—22no—
451C3⋊C8—22no—
452C2×C32#52511yescharacteristic
453C2×C32C22×Q1611yescharacteristic
454C2×C32#57511yescharacteristic
455C3⋊D3—22no—
456C2×Q8—32no—
457C2×Q8—61no—
458C2×Q8—91no—
459C2×Q8—181no—
460C2×Q8—182no—
461C2×Q8—182no—
462C2×Q8C2×D3211yescharacteristic
463C22×C4—91no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—181no—
467C22×C4—181no—
468Q16—64no—
469Q16—184no—
470C2×C8—32no—
471C2×C8—32no—
472C4⋊C4—21no—
473C4⋊C4—32no—
474C4⋊C4—61no—
475C4⋊C4—61no—
476C4⋊C4—61no—
477C4⋊C4—91no—
478C4⋊C4—181no—
479C4⋊C4—181no—
480C4⋊C4—181no—
481C4⋊C4—182no—
482C4⋊C4—182no—
483C4⋊C4—181no—
484C4⋊C4C2×D3211yescharacteristic
485C22⋊C4—182no—
486C42—21no—
487C42—91no—
488C42—91no—
489C42—91no—
490C42—181no—
491C42—181no—
492C42—182no—
493C42—181no—
494C42C2×D3211yescharacteristic
495C22×C3—21no—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C2×D3×D411yescharacteristic
498C2×D3—32no—
499C2×D3—32no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—61no—
504C2×D3—61no—
505C2×D3—61no—
506C2×D3—61no—
507C3×C4—24no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—22no—
511C3×C4—22no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—22no—
515C3×C4—41no—
516C3×C4—42no—
517C3×C4—41no—
518C3×C4—41no—
519C3×C4—122no—
520C3×C4—122no—
521C3×C4D3×Q1612yes—
522C3×C4D3×Q1612yes—
523C3×C4C2×#23711yescharacteristic
524C3×C4C2×#23911yescharacteristic
525C3×C4D3×#4111yescharacteristic
526C3×C4D3×#4111yescharacteristic
527Dic3—32no—
528Dic3—32no—
529Dic3—42no—
530Dic3—42no—
531Dic3—62no—
532Dic3—62no—
533Dic3—64no—
534Dic3—61no—
535Dic3—61no—
536Dic3—62no—
537Dic3—61no—
538Dic3—62no—
539Dic3—61no—
540Dic3—121no—
541Dic3—122no—
542Dic3—121no—
543Dic3—121no—
544C32#310411yescharacteristic, complemented, Sylow
545C23—91no—
546Q8—21no—
547Q8—62no—
548Q8—62no—
549Q8—92no—
550Q8—122no—
551Q8—184no—
552Q8—181no—
553Q8#379612yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—91no—
559C2×C4—94no—
560C2×C4—91no—
561C2×C4—91no—
562C2×C4—184no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—361no—
568C2×C4—362no—
569C2×C4#381111yescharacteristic
570C2×C4#381111yescharacteristic
571C2×C4C22×D3211yescharacteristic
572C8—62no—
573C8—62no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3#560611yescharacteristic
578C2×C3#562711yescharacteristic
579C2×C3C2×D3×Q1611yescharacteristic
580C2×C3C2×D3×Q1611yescharacteristic
581C2×C3#577311yescharacteristic
582C2×C3#577711yescharacteristic
583D3—64no—
584D3—62no—
585D3—62no—
586C22—92no—
587C22—181no—
588C22—181no—
589C22C2×#381111yescharacteristic
590C4—22no—
591C4—21no—
592C4—41no—
593C4—92no—
594C4—122no—
595C4—122no—
596C4—181no—
597C4—182no—
598C4—181no—
599C4—361no—
600C4#6394412yes—
601C4C2×#379611yescharacteristic
602C4#6430611yescharacteristic
603C3—21no—
604C3#8045611yescharacteristic, complemented
605C3#8109211yescharacteristic, complemented
606C2—182no—
607C2#1059492211yescharacteristic
608C2C2×#6394411yescharacteristic
609C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4×Q8D32
hypocenterC32#3104
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5031C2semidirect
4. C3×#5021C2semidirect
6. #10591581C2semidirect
8. #10590482C2semidirect
9. #10590388C2semidirect
10. #10590284C2semidirect
56. #5031D3semidirect
57. #5021D3semidirect
199. C4×C3⋊D3Q16semidirect
544. C32#3104semidirect
604. C3#80456semidirect
605. C3#81092semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
#105938662
C3×#50312
C3×#50212
#105916032
#105915812
#105905282
#105904822
#105903882
#105902842
#105902562
#810923
#804563