Finite Group Databasebeta

← #11878922

Subgroups — #11878922

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 583 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5578C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic
3#10592730C211yesmaximal, characteristic, complemented
4C3×#5031C211yesmaximal, characteristic, complemented
5#10591653C212yesmaximal
6#10591626C212yesmaximal, complemented
7#10590604C212yesmaximal
8#10590560C212yesmaximal, complemented
9#10590385C211yesmaximal, characteristic, complemented
10#10590384C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic
12#83370—31nomaximal
13#80480—31nomaximal
14C2×D3×Dic6C2212yes—
15C32×C4×Q8C2211yescharacteristic
16C2×#3756C2212yes—
17#64078C2211yescharacteristic
18C3×#946C2211yescharacteristic
19C3×#944C2211yescharacteristic
20C2×C3×#216C2212yes—
21C3×#897C2211yescharacteristic
22C3×#896—21no—
23C3×#889—21no—
24C3×#888C2211yescharacteristic
25C3×#872—21no—
26C3×C42×D3C2211yescharacteristic
27C3×#869C2211yescharacteristic
28C3×C4×Dic6—21no—
29C3×C4×Dic6C2211yescharacteristic
30#63918—21no—
31#63918—21no—
32D3×C4⋊Dic3—21no—
33D3×C4⋊Dic3—21no—
34#63866C2212yes—
35C2×#3719C2212yes—
36C2×#3718C2212yes—
37#63637C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C3×#810C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63567C2212yes—
42#63565C2212yes—
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yes—
45C3×#533—31no—
46D3×C4⋊Q8—31no—
47#5578D311yescharacteristic
48C2×#869—31no—
49C3×#462—31no—
50#5186—32no—
51#5183—32no—
52#5093—32no—
53#5092—32no—
54#5090—31no—
55#5050—32no—
56#5050—32no—
57#5031—31no—
58#5031—31no—
59#5031—31no—
60#5031—31no—
61#5031—61no—
62#5031D311yescharacteristic, complemented
63#4925—31no—
64#4849—31no—
65#4833—31no—
66#4809—32no—
67#4792—32no—
68C2×C32×Q8C2311yescharacteristic
69C2×#634C2312yes—
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3D411yescharacteristic
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6—21no—
74C2×C3×Dic6C2311yescharacteristic
75C2×C3×Dic6C2312yes—
76C2×#627—22no—
77C2×D3×Dic3—22no—
78D3×Dic6—42no—
79D3×Dic6—42no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2311yescharacteristic
82C32×C42—21no—
83C32×C42C2311yescharacteristic
84#3756—42no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)—21no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#216—42no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—21no—
99C3×Dic3⋊C4—21no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105Dic3⋊Dic3—22no—
106Dic3⋊Dic3—22no—
107#3719—42no—
108#3718—42no—
109#3209—91noSylow
110C2×D3×Q8—32no—
111C22×Dic6—32no—
112C2×C3×Q16—32no—
113C3×C4⋊Q8—31no—
114C3×C4⋊Q8—31no—
115C3×C4⋊Q8—31no—
116C3×#125—61no—
117C3×C22⋊Q8—31no—
118C3×C22⋊Q8—31no—
119C3×C22⋊Q8—61no—
120C3×C4×Q8—21no—
121C3×C4×Q8—31no—
122C3×C4×Q8—61no—
123C3×C4×Q8C2×D311yescharacteristic
124C3×C4×Q8C2×D311yescharacteristic
125C3×#117—61no—
126C2×C3×C42—31no—
127#946C2×D311yescharacteristic
128#944—32no—
129#944C2×D311yescharacteristic
130C2×#216—32no—
131C2×#216—32no—
132C2×#216—32no—
133C2×#216—32no—
134C2×#216—32no—
135C2×#216—62no—
136C2×#216C2×D312yes—
137C2×C4⋊Dic3—61no—
138C2×C4⋊Dic3—61no—
139C2×Dic12—32no—
140#897C2×D311yescharacteristic
141#896—21no—
142D3×C4⋊C4—61no—
143D3×C4⋊C4—61no—
144#889—21no—
145#888—61no—
146#888—61no—
147#888C2×D311yescharacteristic
148#872—21no—
149C42×D3C2×D311yescharacteristic
150#869—32no—
151#869—31no—
152#869—31no—
153#869—61no—
154#869—61no—
155#869—61no—
156#869C2×D311yescharacteristic
157C4×Dic6—21no—
158C4×Dic6C2×D311yescharacteristic
159C3×C4⋊C8—31no—
160C3×#103—32no—
161#835—32no—
162#830—32no—
163(C2×D3)⋊C8—32no—
164#816—32no—
165C8×Dic3—32no—
166#810—32no—
167#810—32no—
168#810—32no—
169#810—32no—
170#810—62no—
171#810C2×D312yes—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—61no—
175C4⋊(C3⋊C8)C2×D311yescharacteristic
176C4×C3⋊C8—32no—
177C22×C3×D3C2×D411yescharacteristic
178C32×Q8—21no—
179C32×Q8—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—22no—
186#634—22no—
187#634—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3C2×D411yescharacteristic
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C3×C4×D3—21no—
195C3×C4×D3—21no—
196C3×C4×D3—22no—
197C3×C4×D3Q1614yescomplemented
198C3×Dic6—21no—
199C3×Dic6—22no—
200C3×Dic6—21no—
201C3×Dic6—22no—
202C3×Dic6—42no—
203#627—44no—
204D3×Dic3—44no—
205C3⋊(C3⋊C8)—22no—
206C3×C3⋊C8—22no—
207#533—31no—
208C2×C4⋊Q8—91no—
209#494—92no—
210#487—92no—
211#462—31no—
212#462—91no—
213#462—91no—
214#462—91no—
215#451—92no—
216#451—92no—
217#431—91no—
218C2×C3×Q8—21no—
219C2×C3×Q8—32no—
220C2×C3×Q8—31no—
221C2×C3×Q8—61no—
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×Q8C22×D311yescharacteristic
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×Dic3—62no—
228D3×Q8—122no—
229D3×Q8—122no—
230C2×C4×D3—62no—
231C2×C4×D3#6711yescharacteristic
232C2×C4×D3#6711yescharacteristic
233C2×C4×D3C22×D311yescharacteristic
234C2×Dic6—21no—
235C2×Dic6—32no—
236C2×Dic6—32no—
237C2×Dic6—62no—
238C2×Dic6—62no—
239C2×Dic6—62no—
240C2×Dic6—122no—
241C2×Dic6—122no—
242C2×Dic6C22×D312yes—
243C2×Dic6C22×D311yescharacteristic
244C3×Q16—122no—
245C2×C3×C8—32no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—31no—
250C3×C4⋊C4—41no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4C22×D311yescharacteristic
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C22⋊C4—61no—
262C3×C22⋊C4—61no—
263C3×C42—21no—
264C3×C42—21no—
265C3×C42—21no—
266C3×C42—31no—
267C3×C42—31no—
268C3×C42—31no—
269C3×C42—41no—
270C3×C42—61no—
271C3×C42C22×D311yescharacteristic
272C3×C42C22×D311yescharacteristic
273#216—42no—
274#216—122no—
275#216—122no—
276#216—122no—
277#216—122no—
278#216—122no—
279#216—124no—
280(C2×D3)⋊C4—21no—
281(C2×D3)⋊C4—21no—
282C4⋊Dic3—21no—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—62no—
286C4⋊Dic3—62no—
287C4⋊Dic3—61no—
288C4⋊Dic3—61no—
289C4⋊Dic3—61no—
290C4⋊Dic3—61no—
291C4⋊Dic3—121no—
292C4⋊Dic3—121no—
293C4⋊Dic3C22×D311yescharacteristic
294Dic3⋊C4—21no—
295Dic3⋊C4—21no—
296Dic3⋊C4—21no—
297Dic3⋊C4—21no—
298Dic3⋊C4—21no—
299Dic3⋊C4—62no—
300Dic3⋊C4—62no—
301C4×Dic3—21no—
302C4×Dic3#6711yescharacteristic
303C4×Dic3#6711yescharacteristic
304C4×Dic3C22×D311yescharacteristic
305C2×C3⋊C8—32no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—62no—
308C2×C3⋊C8C22×D312yes—
309Dic12—122no—
310C22×C32C22×D411yescharacteristic
311C2×C3×D3—21no—
312C2×C3×D3—21no—
313C2×C3×D3C2×Q1612yes—
314C32×C4—21no—
315C32×C4—41no—
316C32×C4—41no—
317C32×C4C2×Q1612yes—
318C32×C4H(5,𝔽2)11yescharacteristic
319C32×C4H(5,𝔽2)11yescharacteristic
320C3⋊Dic3—42no—
321C3×Dic3—21no—
322C3×Dic3—42no—
323C3×Dic3—41no—
324C3×Dic3—41no—
325C3×Dic3C2×Q1612yes—
326C3×Dic3#13712yes—
327C22×Q8—92no—
328C2×Q16—32no—
329C2×Q16—92no—
330C2×Q16—92no—
331C2×Q16—92no—
332C4⋊Q8—31no—
333C4⋊Q8—31no—
334C4⋊Q8—31no—
335C4⋊Q8—92no—
336C4⋊Q8—91no—
337C4⋊Q8—181no—
338C4⋊Q8—181no—
339#125—61no—
340C22⋊Q8—31no—
341C22⋊Q8—31no—
342C22⋊Q8—61no—
343C4×Q8—31no—
344C4×Q8—61no—
345C4×Q8D3211yescharacteristic
346#117—61no—
347C2×C4⋊C4—181no—
348C2×C4⋊C4—181no—
349C2×C42—31no—
350C4⋊C8—31no—
351C4⋊C8—91no—
352#103—32no—
353#103—92no—
354#103—92no—
355#103—92no—
356C22⋊C8—92no—
357C4×C8—92no—
358C23×C3—31no—
359C22×D3C2×#6711yescharacteristic
360C3×Q8—22no—
361C3×Q8—21no—
362C3×Q8—21no—
363C3×Q8—21no—
364C3×Q8—21no—
365C3×Q8—41no—
366C3×Q8—61no—
367C3×Q8—61no—
368C3×Q8—62no—
369C3×Q8—62no—
370C3×Q8—122no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—31no—
379C2×C3×C4—31no—
380C2×C3×C4—34no—
381C2×C3×C4—31no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—62no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—61no—
388C2×C3×C4—61no—
389C2×C3×C4—62no—
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396C2×Dic3—22no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—122no—
402C2×Dic3—124no—
403C2×Dic3C2×#6711yescharacteristic
404C2×Dic3C2×#6711yescharacteristic
405C2×Dic3C2×#6711yescharacteristic
406C4×D3—21no—
407C4×D3—21no—
408C4×D3—22no—
409C4×D3—124no—
410C4×D3#21614yescomplemented
411Dic6—22no—
412Dic6—21no—
413Dic6—21no—
414Dic6—22no—
415Dic6—42no—
416Dic6—62no—
417Dic6—62no—
418Dic6—62no—
419Dic6—62no—
420Dic6—122no—
421Dic6—122no—
422Dic6—124no—
423Dic6—124no—
424C3×C8—62no—
425C3⋊C8—22no—
426C3⋊C8—62no—
427C3⋊C8—62no—
428C3⋊C8—122no—
429C2×C32#53511yescharacteristic
430C2×C32C22×Q1611yescharacteristic
431C2×C32C2×#13711yescharacteristic
432C3×D3—22no—
433C2×Q8—32no—
434C2×Q8—31no—
435C2×Q8—61no—
436C2×Q8—92no—
437C2×Q8—182no—
438C2×Q8—362no—
439C2×Q8—362no—
440C2×Q8C2×D3211yescharacteristic
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—182no—
445Q16—122no—
446Q16—362no—
447Q16—362no—
448Q16—362no—
449C2×C8—32no—
450C2×C8—92no—
451C4⋊C4—21no—
452C4⋊C4—31no—
453C4⋊C4—61no—
454C4⋊C4—61no—
455C4⋊C4—61no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4—61no—
460C4⋊C4—61no—
461C4⋊C4—182no—
462C4⋊C4—182no—
463C4⋊C4—181no—
464C4⋊C4—181no—
465C4⋊C4C2×D3211yescharacteristic
466C22⋊C4—61no—
467C22⋊C4—61no—
468C42—21no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—61no—
473C42C2×D3211yescharacteristic
474C22×C3—21no—
475C22×C3—32no—
476C22×C3—61no—
477C22×C3—61no—
478C22×C3C2×D3×D411yescharacteristic
479C22×C3C22×#6711yescharacteristic
480C2×D3—21no—
481C2×D3—21no—
482C2×D3C2×#21612yes—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—32no—
489C3×C4—32no—
490C3×C4—41no—
491C3×C4—42no—
492C3×C4—41no—
493C3×C4—41no—
494C3×C4—41no—
495C3×C4—41no—
496C3×C4—61no—
497C3×C4—81no—
498C3×C4—121no—
499C3×C4—122no—
500C3×C4—121no—
501C3×C4D3×Q1612yes—
502C3×C4C2×#21612yes—
503C3×C4#100411yescharacteristic
504C3×C4#100911yescharacteristic
505C3×C4#100911yescharacteristic
506C3×C4#100911yescharacteristic
507Dic3—21no—
508Dic3—41no—
509Dic3—41no—
510Dic3—42no—
511Dic3—122no—
512Dic3—122no—
513Dic3—242no—
514Dic3C2×#21612yes—
515Dic3#95112yes—
516C32#320911yescharacteristic, complemented, Sylow
517C23—31no—
518Q8—21no—
519Q8—21no—
520Q8—62no—
521Q8—61no—
522Q8—61no—
523Q8—62no—
524Q8—122no—
525Q8—182no—
526Q8—182no—
527Q8—364no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—31no—
531C2×C4—31no—
532C2×C4—34no—
533C2×C4—31no—
534C2×C4—62no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—61no—
539C2×C4—62no—
540C2×C4—182no—
541C2×C4—364no—
542C2×C4D3×#6711yescharacteristic
543C2×C4D3×#6711yescharacteristic
544C2×C4C22×D3211yescharacteristic
545C8—62no—
546C8—182no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—62no—
551C2×C3#560711yescharacteristic
552C2×C3C2×D3×Q1611yescharacteristic
553C2×C3D3×#13711yescharacteristic
554C2×C3C22×#21611yescharacteristic
555C2×C3C2×#95111yescharacteristic
556C2×C3#583011yescharacteristic
557D3—22no—
558C22—32no—
559C22—61no—
560C22—61no—
561C22C2×D3×#6711yescharacteristic
562C4—21no—
563C4—32no—
564C4—32no—
565C4—41no—
566C4—41no—
567C4—61no—
568C4—121no—
569C4—122no—
570C4—121no—
571C4—362no—
572C4D3×#21612yes—
573C4#6430711yescharacteristic
574C4#6430811yescharacteristic
575C3—21no—
576C3#8048011yescharacteristic, complemented
577C3#8337011yescharacteristic, complemented
578C2—62no—
579C2#1059506411yescharacteristic
580C2C2×D3×#21611yescharacteristic
581C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4×Q8D32
hypocenterC32#3209
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. #10592730C2semidirect
4. C3×#5031C2semidirect
6. #10591626C2semidirect
8. #10590560C2semidirect
9. #10590385C2semidirect
10. #10590384C2semidirect
62. #5031D3semidirect
197. C3×C4×D3Q16semidirect
410. C4×D3#216semidirect
516. C32#3209semidirect
576. C3#80480semidirect
577. C3#83370semidirect

Maximal subgroups

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

subgroupindex
C3×#55782
D3×#8692
#105927302
C3×#50312
#105916532
#105916262
#105906042
#105905602
#105903852
#105903842
#105902482
#833703
#804803