Finite Group Databasebeta

← #11898375

Subgroups — #11898375

Order 1152.

826 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596013C211yesmaximal, characteristic, complemented
2#10593863C211yesmaximal, characteristic, complemented
3C3×#5019C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic
5#10591474C212yesmaximal
6#10591443C212yesmaximal, complemented
7#10590538C212yesmaximal, complemented
8#10590482C212yesmaximal, complemented
9#10590386C211yesmaximal, characteristic, complemented
10#10590365C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#80421—31nomaximal
13#79579—31nomaximal
14C32×C4×D4C2211yescharacteristic
15#64145C2212yes—
16#64135—21no—
17#64133—21no—
18#64096C2212yes—
19#64088—22no—
20#64078C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#214C2212yes—
23C2×C3×#213C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26#63863C2212yes—
27#63858—22no—
28#63857—21no—
29#63843C2212yes—
30#63841—21no—
31C2×#3719C2212yes—
32C2×#3719C2212yes—
33C2×#3716C2212yes—
34C3×#832C2211yescharacteristic
35C3×#810C2212yes—
36C3×#809C2211yescharacteristic
37C3×#807C2211yescharacteristic
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39C3×C4×C3⋊C8C2211yescharacteristic
40#63572C2212yes—
41#63567C2212yes—
42#63553C2212yes—
43#5732—31no—
44#5542—31no—
45#5542—31no—
46#5542—31no—
47#5542—61no—
48C3×#461—31no—
49C3×C4×D8—31no—
50#5168—32no—
51#5166—32no—
52#5155—32no—
53#5092—31no—
54#5019—31no—
55#5019D311yescharacteristic, complemented
56C4×#213D311yescharacteristic
57#4873—32no—
58#4841—31no—
59#4830—31no—
60#4798—32no—
61#4790—32no—
62#4767—32no—
63#4767—32no—
64#4699—31no—
65C8×Dic6—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634D411yescharacteristic
69C2×#634C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6C2312yes—
73C32×C4⋊C4C2311yescharacteristic
74C32×C22⋊C4—21no—
75C32×C42C2311yescharacteristic
76#3757—22no—
77#3757—22no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81#3750—22no—
82#3750D412yes—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3C2312yes—
85C3×#214—42no—
86C3×#213—22no—
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94Dic3⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3719—24no—
99#3719—42no—
100#3716—42no—
101#3393—91noSylow
102C2×C3×SD16—32no—
103C2×C3×D8—31no—
104C3×C4⋊Q8—31no—
105C3×C4×D4—21no—
106C3×C4×D4—31no—
107C3×C4×D4C2×D311yescharacteristic
108C3×C4×D4C2×D311yescharacteristic
109#947—32no—
110Q8×Dic3—32no—
111C2×#216—32no—
112C2×#216—32no—
113#936—32no—
114#936—32no—
115#936—32no—
116#936—62no—
117C2×#214—32no—
118C2×#214C2×D312yes—
119C2×#213C2×D311yescharacteristic
120#926—61no—
121#926—61no—
122#926—61no—
123#926—62no—
124#924—61no—
125#924—61no—
126#924—61no—
127#924—62no—
128C2×Dic12—32no—
129C2×Dic12—32no—
130C2×#204—32no—
131#898—62no—
132#897—61no—
133#892—61no—
134#887—32no—
135#887—32no—
136#887—32no—
137#887—62no—
138#879—62no—
139#879—62no—
140#879—62no—
141#879—64no—
142C4×D12C2×D311yescharacteristic
143#869—31no—
144#869—31no—
145#869—61no—
146#869C2×D311yescharacteristic
147C4×Dic6—31no—
148C4×Dic6—31no—
149C4×Dic6—61no—
150C3×#107—31no—
151C3×C4⋊C8—31no—
152C3×#103—32no—
153C3×#102—31no—
154C3×#102—31no—
155C3×C4×C8—31no—
156#832C2×D311yescharacteristic
157#816—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—32no—
160C8×Dic3—32no—
161C8×Dic3—32no—
162#810—32no—
163#810C2×D312yes—
164#809C2×D311yescharacteristic
165#807C2×D311yescharacteristic
166C4⋊(C3⋊C8)C2×D311yescharacteristic
167C4×C3⋊C8C2×D311yescharacteristic
168C23×C32—21no—
169C22×C3×D3—21no—
170C32×D4—21no—
171C32×D4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—42no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3C2×D412yes—
179C2×C3⋊Dic3C2×D412yes—
180#634—22no—
181#634—22no—
182#634—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C3×D12—21no—
186C3×D12—21no—
187C3×C4×D3—42no—
188C3×Dic6—22no—
189C3×Dic6—22no—
190C3×C3⋊C8—22no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8#4112yes—
193#556—91no—
194#556—91no—
195#495—92no—
196#494—91no—
197#464—92no—
198#464—92no—
199#461—31no—
200#461—91no—
201C8×Q8—91no—
202C4×Q16—92no—
203C4×D8—31no—
204C2×C3×Q8—32no—
205C2×C3×D4—21no—
206C2×C3×D4—31no—
207C2×C3×D4C22×D311yescharacteristic
208C2×C3×D4C22×D311yescharacteristic
209C22×C3×C4—22no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—61no—
213C2×D12C22×D311yescharacteristic
214C2×C4×D3—21no—
215C2×Dic6—31no—
216C2×Dic6—31no—
217C2×Dic6—32no—
218C2×Dic6—32no—
219C2×Dic6—61no—
220C2×Dic6—62no—
221C2×Dic6C22×D312yes—
222C3×SD16—122no—
223C3×D8—62no—
224C2×C3×C8—31no—
225C2×C3×C8—32no—
226C2×C3×C8—31no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4C22×D311yescharacteristic
232C3×C4⋊C4C22×D311yescharacteristic
233C3×C22⋊C4—22no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—21no—
236C3×C22⋊C4—61no—
237C3×C42—21no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#217—62no—
241#217—62no—
242#217—62no—
243#217—62no—
244#217—62no—
245#217—62no—
246#217—64no—
247#217—64no—
248#216—64no—
249#216—122no—
250#214—42no—
251#214—122no—
252#213—22no—
253(C2×D3)⋊C4—21no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—61no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3—62no—
264C4⋊Dic3—61no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3C22×D311yescharacteristic
269Dic3⋊C4—32no—
270Dic3⋊C4—32no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—64no—
276C4×Dic3—32no—
277C4×Dic3—32no—
278C4×Dic3—62no—
279C4×Dic3—62no—
280C4×Dic3—62no—
281C4×Dic3—62no—
282C4×Dic3—62no—
283C4×Dic3—64no—
284C2×C3⋊C8C22×D311yescharacteristic
285C2×C3⋊C8C22×D312yes—
286C2×C3⋊C8C22×D311yescharacteristic
287Dic12—64no—
288Dic12—122no—
289#204—122no—
290C22×C32—41no—
291C22×C32—41no—
292C22×C32—41no—
293C22×C32C22×D411yescharacteristic
294C2×C3×D3—41no—
295C2×C3×D3—41no—
296C2×C3×D3—41no—
297C32×C4—21no—
298C32×C4—41no—
299C32×C4#13512yes—
300C32×C4C2×#4111yescharacteristic
301C32×C4H(5,𝔽2)11yescharacteristic
302C3⋊Dic3—22no—
303C3⋊Dic3—22no—
304C3⋊Dic3—42no—
305C3×Dic3—42no—
306C3×Dic3—41no—
307C2×Q16—92no—
308C2×Q16—92no—
309C2×SD16—32no—
310C2×SD16—92no—
311C2×D8—31no—
312C4⋊Q8—31no—
313C4⋊Q8—91no—
314#126—182no—
315#126—182no—
316#124—92no—
317#124—92no—
318C22⋊Q8—181no—
319C22⋊Q8—181no—
320C4×Q8—91no—
321C4×Q8—92no—
322C4×Q8—92no—
323C4×D4—31no—
324C4×D4D3211yescharacteristic
325#117—181no—
326#117—181no—
327#107—31no—
328C4⋊C8—31no—
329C4⋊C8—92no—
330#103—32no—
331#103—92no—
332#102—31no—
333#102—31no—
334C4×C8—31no—
335C4×C8—92no—
336C23×C3—22no—
337C23×C3—21no—
338C23×C3—21no—
339C23×C3—61no—
340C22×D3—21no—
341C3×Q8—62no—
342C3×Q8—62no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—21no—
346C3×D4—21no—
347C3×D4—41no—
348C3×D4—41no—
349C3×D4—61no—
350C3×D4—61no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—44no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—61no—
361C2×C3×C4—62no—
362C2×C3×C4—122no—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369C2×Dic3—21no—
370C2×Dic3—22no—
371C2×Dic3—32no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—32no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—64no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380D12—21no—
381D12—21no—
382C4×D3—42no—
383Dic6—22no—
384Dic6—22no—
385Dic6—62no—
386Dic6—62no—
387Dic6—62no—
388Dic6—62no—
389Dic6—62no—
390Dic6—62no—
391Dic6—122no—
392Dic6—122no—
393Dic6—122no—
394C3×C8—32no—
395C3×C8—61no—
396C3×C8—62no—
397C3⋊C8—22no—
398C3⋊C8—21no—
399C3⋊C8#23512yes—
400C2×C32—81no—
401C2×C32#55011yescharacteristic
402C2×C32C2×#13511yescharacteristic
403C2×C32#57811yescharacteristic
404C3×D3—81no—
405C2×Q8—32no—
406C2×Q8—91no—
407C2×Q8—92no—
408C2×D4—31no—
409C2×D4C2×D3211yescharacteristic
410C22×C4—21no—
411C22×C4—61no—
412Q16—184no—
413Q16—362no—
414SD16—122no—
415SD16—362no—
416D8—62no—
417C2×C8—31no—
418C2×C8—31no—
419C2×C8—32no—
420C4⋊C4—31no—
421C4⋊C4—61no—
422C4⋊C4—61no—
423C4⋊C4—91no—
424C4⋊C4—92no—
425C4⋊C4—182no—
426C4⋊C4—182no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4C2×D3211yescharacteristic
430C22⋊C4—21no—
431C22⋊C4—61no—
432C22⋊C4—182no—
433C22⋊C4—182no—
434C22⋊C4—182no—
435C22⋊C4—182no—
436C42—92no—
437C42—182no—
438C42—182no—
439C42C2×D3211yescharacteristic
440C22×C3—21no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—41no—
450C22×C3—121no—
451C22×C3—121no—
452C22×C3—121no—
453C22×C3C2×D3×D411yescharacteristic
454C22×C3C2×D3×D411yescharacteristic
455C2×D3—41no—
456C2×D3—41no—
457C2×D3—41no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—41no—
464C3×C4—42no—
465C3×C4—41no—
466C3×C4—41no—
467C3×C4—121no—
468C3×C4—122no—
469C3×C4#91212yes—
470C3×C4#91612yes—
471C3×C4C2×#23511yescharacteristic
472C3×C4#100411yescharacteristic
473C3×C4D3×#4111yescharacteristic
474C3×C4#100911yescharacteristic
475Dic3—41no—
476Dic3—42no—
477Dic3—62no—
478Dic3—62no—
479Dic3—62no—
480Dic3—62no—
481Dic3—122no—
482Dic3—122no—
483Dic3—124no—
484Dic3—122no—
485Dic3—122no—
486C32#339311yescharacteristic, complemented, Sylow
487C23—21no—
488C23—61no—
489Q8—62no—
490Q8—62no—
491Q8—182no—
492Q8—182no—
493Q8—182no—
494D4—21no—
495D4—21no—
496D4—61no—
497D4—61no—
498C2×C4—21no—
499C2×C4—42no—
500C2×C4—61no—
501C2×C4—62no—
502C2×C4—92no—
503C2×C4—92no—
504C2×C4—122no—
505C2×C4—182no—
506C2×C4#381111yescharacteristic
507C2×C4#381111yescharacteristic
508C2×C4C22×D3211yescharacteristic
509C8—32no—
510C8—62no—
511C8—61no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—82no—
516C2×C3—81no—
517C2×C3—81no—
518C2×C3—241no—
519C2×C3#555311yescharacteristic
520C2×C3#559911yescharacteristic
521C2×C3C2×#91211yescharacteristic
522C2×C3C2×#91611yescharacteristic
523C2×C3#577111yescharacteristic
524C2×C3#577911yescharacteristic
525D3—81no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—121no—
530C22—121no—
531C22—121no—
532C22C2×#381111yescharacteristic
533C4—21no—
534C4—41no—
535C4—121no—
536C4—122no—
537C4—182no—
538C4—182no—
539C4—362no—
540C4#6393612yes—
541C4D3×#23511yescharacteristic
542C4#6430711yescharacteristic
543C3—21no—
544C3#7957911yescharacteristic, complemented
545C3#8042111yescharacteristic, complemented
546C2—81no—
547C2—241no—
548C2#1059491911yescharacteristic
549C2C2×#6393611yescharacteristic
550C2#1059547211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC4×D4D32
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596013C2semidirect
2. #10593863C2semidirect
3. C3×#5019C2semidirect
6. #10591443C2semidirect
7. #10590538C2semidirect
8. #10590482C2semidirect
9. #10590386C2semidirect
10. #10590365C2semidirect
11. #10590254C2semidirect
55. #5019D3semidirect
486. C32#3393semidirect
544. C3#79579semidirect
545. C3#80421semidirect

Maximal subgroups

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

subgroupindex
#105960132
#105938632
C3×#50192
C3×C4×#2132
#105914742
#105914432
#105905382
#105904822
#105903862
#105903652
#105902542
#804213
#795793