Finite Group Databasebeta

← #11878921

Subgroups — #11878921

Order 1152.

842 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63866C211yesmaximal, characteristic
2#10594808C211yesmaximal, characteristic
3#10592438C211yesmaximal, characteristic
4C3×#4739C211yesmaximal, characteristic
5C3×#4718C211yesmaximal, characteristic
6#10591190C211yesmaximal, characteristic
7#10591186C211yesmaximal, characteristic
8#10590896C212yesmaximal, complemented
9#10590890C212yesmaximal, complemented
10#10590808C212yesmaximal, complemented
11#10590800C212yesmaximal, complemented
12#80178—31nomaximal
13#79313—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16#64133C2211yescharacteristic
17C2×#3746C2212yes—
18C3×#924C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×Dic12C2212yes—
21C2×Dic3⋊Dic3—21no—
22C2×Dic3⋊Dic3—21no—
23#63964—21no—
24#63955—21no—
25#63918C2211yescharacteristic
26#63867—21no—
27#63866—21no—
28#63866—21no—
29#63866C2212yes—
30#63866C2212yes—
31#63866C2211yescharacteristic
32#63844C2211yescharacteristic
33Dic3×Dic6C2211yescharacteristic
34#63837—21no—
35C2×#3719C2212yes—
36C2×#3719C2212yes—
37C32×C22⋊C8C2211yescharacteristic
38#63643C2212yes—
39C3×#830C2211yescharacteristic
40C3×#816C2212yes—
41C3×Dic3⋊C8C2212yes—
42C3×C8×Dic3C2212yes—
43#63567C2212yes—
44#63566C2212yes—
45C2×#944—31no—
46#5622—31no—
47#5470—31no—
48C2×#869—31no—
49C3×#451—31no—
50C3×#431—31no—
51#5228—31no—
52#5183—32no—
53#5182—32no—
54#5050—31no—
55#4849—32no—
56#4849—32no—
57#4795—32no—
58#4792—32no—
59#4739—31no—
60#4739—31no—
61#4739—31no—
62#4739—31no—
63#4739—61no—
64#4739D311yescharacteristic
65#4718D311yescharacteristic
66#4699—32no—
67#4681—32no—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—21no—
70C2×#634—21no—
71C2×#634—42no—
72C2×#634C2312yes—
73C2×#634C2311yescharacteristic
74C22×C3×Dic3—21no—
75C22×C3×Dic3D411yescharacteristic
76C22×C3×Dic3D411yescharacteristic
77C2×C3×Dic6—21no—
78C2×C3×Dic6—42no—
79C2×C3×Dic6C2311yescharacteristic
80C2×C3×Dic6C2312yes—
81C2×#627—21no—
82C2×C32×C8C2312yes—
83#3757—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86#3746—42no—
87C3×#217—21no—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×C4×Dic3D411yescharacteristic
91C3×C4×Dic3D411yescharacteristic
92C3×C4×Dic3C2311yescharacteristic
93C3×C4×Dic3C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95C3×Dic12—42no—
96#3724—21no—
97Dic3⋊Dic3—21no—
98Dic3⋊Dic3—21no—
99Dic3⋊Dic3—22no—
100Dic3⋊Dic3—22no—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—21no—
104Dic3⋊Dic3—21no—
105Dic32—21no—
106Dic32—21no—
107#3719—42no—
108#3719—42no—
109#3209—91noSylow
110C22×C3×Q8—31no—
111C22×Dic6—31no—
112C22×Dic6—31no—
113C22×Dic6—61no—
114C22×Dic6C2×D311yescharacteristic
115C2×C3×Q16—32no—
116C3×C22⋊Q8—31no—
117C2×C3×C42—31no—
118Q8×Dic3—31no—
119#944—32no—
120#944—31no—
121#944—32no—
122#944—61no—
123#944—61no—
124C2×#216—32no—
125C2×#216—32no—
126#926—61no—
127C2×C4⋊Dic3—61no—
128C2×C4⋊Dic3—61no—
129#924—31no—
130#924—31no—
131#924—61no—
132#924—61no—
133#924C2×D311yescharacteristic
134C2×Dic3⋊C4—61no—
135C2×Dic3⋊C4—61no—
136C2×C4×Dic3C2×D311yescharacteristic
137C2×Dic12—32no—
138C2×Dic12—32no—
139C2×Dic12—32no—
140C2×Dic12—32no—
141C2×Dic12—62no—
142C2×Dic12C2×D312yes—
143#889—61no—
144#888—31no—
145#887—31no—
146#887—61no—
147#878—61no—
148#877—61no—
149#870—61no—
150#869—31no—
151#869—32no—
152#869—31no—
153#869—32no—
154#869—61no—
155#869—61no—
156C4×Dic6—31no—
157C4×Dic6—31no—
158C4×Dic6—61no—
159C3×C4⋊C8—32no—
160C3×#103—32no—
161C3×C22⋊C8—21no—
162C3×C22⋊C8—31no—
163C3×C22⋊C8C2×D311yescharacteristic
164C3×C22⋊C8C2×D311yescharacteristic
165C3×C4×C8—32no—
166#835—32no—
167#830C2×D311yescharacteristic
168#816—32no—
169#816—32no—
170#816—32no—
171#816—32no—
172#816—62no—
173#816C2×D312yes—
174Dic3⋊C8C2×D312yes—
175C8×Dic3C2×D312yes—
176#810—32no—
177C23×C32C2×D411yescharacteristic
178C2×C32×C4—22no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—42no—
185#634—22no—
186#634—22no—
187#634—22no—
188#634—42no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3Q1614yescomplemented
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C3×Dic6—22no—
200C3×Dic6—22no—
201C3×Dic6—22no—
202C3×Dic6—42no—
203#627—42no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#533—91no—
207C2×C4⋊Q8—91no—
208#494—92no—
209#487—92no—
210#462—92no—
211#462—92no—
212#451—31no—
213#451—91no—
214#451—91no—
215#451—91no—
216#431—31no—
217C2×C3×Q8—32no—
218C2×C3×Q8—31no—
219C2×C3×Q8—61no—
220C2×C3×Q8—122no—
221C22×C3×C4—21no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—61no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×Dic3—21no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—121no—
231C22×Dic3D1211yescharacteristic
232C22×Dic3D1211yescharacteristic
233C2×Dic6—21no—
234C2×Dic6—32no—
235C2×Dic6—32no—
236C2×Dic6—31no—
237C2×Dic6—31no—
238C2×Dic6—42no—
239C2×Dic6—62no—
240C2×Dic6—61no—
241C2×Dic6—61no—
242C2×Dic6—61no—
243C2×Dic6—61no—
244C2×Dic6—61no—
245C2×Dic6—121no—
246C2×Dic6—122no—
247C2×Dic6—122no—
248C2×Dic6—124no—
249C2×Dic6C22×D312yes—
250C2×Dic6C22×D311yescharacteristic
251C3×Q16—122no—
252C2×C3×C8—22no—
253C2×C3×C8—32no—
254C2×C3×C8C22×D312yes—
255C2×C3×C8C22×D312yes—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—61no—
258C3×C22⋊C4—61no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42—31no—
263#217—21no—
264#217—61no—
265#217—61no—
266#217—121no—
267#216—122no—
268#216—122no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—61no—
272C4⋊Dic3—61no—
273C4⋊Dic3—62no—
274C4⋊Dic3—62no—
275C4⋊Dic3—62no—
276C4⋊Dic3—62no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—61no—
280C4⋊Dic3C22×D311yescharacteristic
281Dic3⋊C4—21no—
282Dic3⋊C4—61no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—61no—
288Dic3⋊C4—61no—
289Dic3⋊C4—61no—
290Dic3⋊C4—62no—
291Dic3⋊C4—62no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294Dic3⋊C4—121no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3—61no—
299C4×Dic3D1211yescharacteristic
300C4×Dic3D1211yescharacteristic
301C4×Dic3C22×D311yescharacteristic
302C4×Dic3C22×D311yescharacteristic
303C2×C3⋊C8C22×D312yes—
304Dic12—42no—
305Dic12—122no—
306Dic12—122no—
307Dic12—124no—
308Dic12—122no—
309Dic12—122no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32C2×Q1612yes—
313C22×C32C22×D411yescharacteristic
314C32×C4—21no—
315C32×C4H(5,𝔽2)12yes—
316C3⋊Dic3—42no—
317C3⋊Dic3—41no—
318C3⋊Dic3—41no—
319C3×Dic3—21no—
320C3×Dic3—42no—
321C3×Dic3—41no—
322C3×Dic3—41no—
323C3×Dic3C2×Q1612yes—
324C3×Dic3C2×Q1612yes—
325C3×Dic3#13712yes—
326C22×Q8—31no—
327C22×Q8—91no—
328C2×Q16—32no—
329C2×Q16—92no—
330C2×Q16—92no—
331C2×Q16—92no—
332C4⋊Q8—91no—
333C4⋊Q8—92no—
334C4⋊Q8—92no—
335C4⋊Q8—91no—
336C4⋊Q8—181no—
337C4⋊Q8—181no—
338#125—181no—
339C22⋊Q8—31no—
340C22⋊Q8—91no—
341C22⋊Q8—181no—
342C4×Q8—91no—
343C4×Q8—91no—
344C4×Q8—181no—
345#117—181no—
346C2×C4⋊C4—181no—
347C2×C4⋊C4—181no—
348C2×C42—31no—
349C4⋊C8—32no—
350#103—32no—
351#103—92no—
352#103—92no—
353#103—92no—
354C22⋊C8—31no—
355C22⋊C8D3211yescharacteristic
356C4×C8—32no—
357C23×C3—21no—
358C23×C3C2×D1211yescharacteristic
359C23×C3D3×D411yescharacteristic
360C3×Q8—62no—
361C3×Q8—62no—
362C3×Q8—62no—
363C3×Q8—122no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—34no—
369C2×C3×C4—31no—
370C2×C3×C4—31no—
371C2×C3×C4—31no—
372C2×C3×C4—31no—
373C2×C3×C4—42no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—62no—
378C2×C3×C4—122no—
379C2×C3×C4C2×D1211yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382C2×C3×C4C23×D311yescharacteristic
383C2×Dic3—22no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—22no—
387C2×Dic3—42no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—62no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—62no—
394C2×Dic3—122no—
395C2×Dic3—121no—
396C2×Dic3—121no—
397C2×Dic3—122no—
398C2×Dic3—122no—
399C2×Dic3—124no—
400C2×Dic3Dic1214yescomplemented
401C2×Dic3C2×D1211yescharacteristic
402C2×Dic3C2×D1211yescharacteristic
403C2×Dic3C2×D1211yescharacteristic
404C2×Dic3C2×D1211yescharacteristic
405Dic6—22no—
406Dic6—22no—
407Dic6—22no—
408Dic6—42no—
409Dic6—64no—
410Dic6—62no—
411Dic6—62no—
412Dic6—62no—
413Dic6—62no—
414Dic6—62no—
415Dic6—62no—
416Dic6—122no—
417Dic6—122no—
418Dic6—122no—
419Dic6—122no—
420Dic6—122no—
421Dic6—124no—
422Dic6—122no—
423C3×C8—22no—
424C3×C8—22no—
425C3×C8—42no—
426C3×C8—62no—
427C3⋊C8—22no—
428C2×C32—22no—
429C2×C32#53511yescharacteristic
430C2×C32C22×Q1611yescharacteristic
431C2×C32C2×#13711yescharacteristic
432C2×Q8—32no—
433C2×Q8—31no—
434C2×Q8—61no—
435C2×Q8—92no—
436C2×Q8—91no—
437C2×Q8—122no—
438C2×Q8—181no—
439C2×Q8—181no—
440C2×Q8—362no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—61no—
444C22×C4—181no—
445C22×C4C2×D3211yescharacteristic
446Q16—122no—
447Q16—362no—
448Q16—362no—
449Q16—362no—
450C2×C8—32no—
451C2×C8C2×D3212yes—
452C4⋊C4—31no—
453C4⋊C4—61no—
454C4⋊C4—91no—
455C4⋊C4—182no—
456C4⋊C4—182no—
457C4⋊C4—182no—
458C4⋊C4—182no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C4⋊C4—181no—
464C4⋊C4—181no—
465C22⋊C4—61no—
466C22⋊C4—181no—
467C42—31no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—181no—
472C42—181no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—22no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3C2×Dic1212yes—
482C22×C3D3×Q1612yes—
483C22×C3C22×D1211yescharacteristic
484C22×C3C2×D3×D411yescharacteristic
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—32no—
489C3×C4—32no—
490C3×C4—32no—
491C3×C4—41no—
492C3×C4—61no—
493C3×C4—121no—
494C3×C4—122no—
495C3×C4—121no—
496C3×C4#100412yes—
497C3×C4#100912yes—
498Dic3—21no—
499Dic3—41no—
500Dic3—42no—
501Dic3—41no—
502Dic3—124no—
503Dic3—121no—
504Dic3—121no—
505Dic3—122no—
506Dic3—121no—
507Dic3—122no—
508Dic3—121no—
509Dic3—241no—
510Dic3—241no—
511Dic3C2×Dic1212yes—
512Dic3C2×Dic1212yes—
513Dic3#90912yes—
514C32#320911yescharacteristic, complemented, Sylow
515C23D3×D1211yescharacteristic
516Q8—62no—
517Q8—62no—
518Q8—62no—
519Q8—122no—
520Q8—182no—
521Q8—182no—
522Q8—182no—
523Q8—362no—
524Q8—362no—
525C2×C4—22no—
526C2×C4—31no—
527C2×C4—31no—
528C2×C4—31no—
529C2×C4—34no—
530C2×C4—31no—
531C2×C4—62no—
532C2×C4—61no—
533C2×C4—61no—
534C2×C4—62no—
535C2×C4—122no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—182no—
539C2×C4—362no—
540C2×C4D3×D1211yescharacteristic
541C2×C4C22×D3211yescharacteristic
542C8—22no—
543C8—62no—
544C2×C3—22no—
545C2×C3—22no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—42no—
550C2×C3#552511yescharacteristic
551C2×C3#559211yescharacteristic
552C2×C3C22×Dic1211yescharacteristic
553C2×C3C2×#90911yescharacteristic
554C2×C3C2×D3×Q1611yescharacteristic
555C2×C3D3×#13711yescharacteristic
556C22—21no—
557C22—21no—
558C22D3×Dic1212yes—
559C22C2×D3×D1211yescharacteristic
560C4—21no—
561C4—32no—
562C4—32no—
563C4—32no—
564C4—61no—
565C4—122no—
566C4—121no—
567C4—121no—
568C4—362no—
569C4—361no—
570C4—361no—
571C4#6431412yes—
572C3—21no—
573C3#7931311yescharacteristic, complemented
574C3#8017811yescharacteristic, complemented
575C2—22no—
576C2#1059408011yescharacteristic
577C2C2×D3×Dic1211yescharacteristic
578C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22⋊C8D32
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
8. #10590896C2semidirect
9. #10590890C2semidirect
10. #10590808C2semidirect
11. #10590800C2semidirect
194. C2×C3×Dic3Q16semidirect
400. C2×Dic3Dic12semidirect
514. C32#3209semidirect
573. C3#79313semidirect
574. C3#80178semidirect

Maximal subgroups

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

subgroupindex
C2×#638662
#105948082
#105924382
C3×#47392
C3×#47182
#105911902
#105911862
#105908962
#105908902
#105908082
#105908002
#801783
#793133