Finite Group Databasebeta

← #11819121

Subgroups — #11819121

Order 1152.

1320 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×C22⋊C4C211yesmaximal, characteristic
2#10592909C211yesmaximal, characteristic
3C2×#63658C211yesmaximal, characteristic
4#10592645C211yesmaximal, characteristic
5#10592642C211yesmaximal, characteristic
6#10592642C211yesmaximal, characteristic
7#10592641C211yesmaximal, characteristic
8#10592636C211yesmaximal, characteristic, complemented
9#10592632C211yesmaximal, characteristic, complemented
10#10592632C211yesmaximal, characteristic, complemented
11#10592632C211yesmaximal, characteristic, complemented
12#10592361C211yesmaximal, characteristic, complemented
13#10592357C211yesmaximal, characteristic, complemented
14#10592357C211yesmaximal, characteristic, complemented
15#10592357C211yesmaximal, characteristic, complemented
16#73509—34nomaximal
17C23×C32×C4C2211yescharacteristic
18C23×C3⋊Dic3C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C42C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C32×#95C2211yescharacteristic
33C32×#95C2211yescharacteristic
34#63658C2211yescharacteristic
35#63658C2211yescharacteristic
36#63658C2211yescharacteristic
37#63658C2211yescharacteristic
38#63658C2211yescharacteristic
39#63658C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C4×C22⋊C4D314yes—
53#5210—34no—
54C2×C3⋊#95—34no—
55#4946—34no—
56#4943—34no—
57#4943—34no—
58#4942—34no—
59#4937—34no—
60#4933—34no—
61#4933—34no—
62#4933—34no—
63C3⋊#401—34no—
64#4658—34no—
65#4658—34no—
66#4658—34no—
67C24×C32C2311yescharacteristic
68C22×C32×C4—22no—
69C22×C32×C4—22no—
70C22×C32×C4—41no—
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3—22no—
78C22×C3⋊Dic3—22no—
79C22×C3⋊Dic3—22no—
80C22×C3⋊Dic3—22no—
81C22×C3⋊Dic3—22no—
82C22×C3⋊Dic3—41no—
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C32×C22⋊C4—22no—
92C32×C22⋊C4—22no—
93C32×C42—22no—
94C32×C42—41no—
95#3757—22no—
96#3757—22no—
97#3750—22no—
98#3750—22no—
99#3750—22no—
100#3750—41no—
101#3750—41no—
102#3750—41no—
103#2493—91noSylow
104C23×C3×C4C2×D314yes—
105C23×Dic3—34no—
106C23×Dic3—34no—
107C2×C3×C22⋊C4C2×D314yes—
108C2×C3×C22⋊C4C2×D314yes—
109C2×C3×C42C2×D314yes—
110C2×C3×C42C2×D314yes—
111C2×#217—34no—
112C2×#217—34no—
113C2×Dic3⋊C4—34no—
114C2×Dic3⋊C4—34no—
115C2×Dic3⋊C4—34no—
116C2×Dic3⋊C4—34no—
117C2×Dic3⋊C4—34no—
118C2×Dic3⋊C4—34no—
119C3×#95C2×D314yes—
120C3×#95C2×D314yes—
121C3⋊#95—34no—
122C3⋊#95—34no—
123C3⋊#95—34no—
124C3⋊#95—34no—
125C3⋊#95—34no—
126C3⋊#95—34no—
127C3⋊#95—34no—
128C3⋊#95—34no—
129C3⋊#95—34no—
130C3⋊#95—34no—
131C3⋊#95—34no—
132C3⋊#95—34no—
133C3⋊#95—34no—
134C3⋊#95—34no—
135C3⋊#95—34no—
136C3⋊#95—34no—
137C3⋊#95—34no—
138C3⋊#95—34no—
139C23×C32—21no—
140C23×C32—21no—
141C23×C32—21no—
142C23×C32—21no—
143C23×C32#4112yes—
144C23×C32#4112yes—
145C23×C32#4112yes—
146C23×C32C2411yescharacteristic
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—44no—
165C2×C32×C4#4112yes—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—44no—
190C2×C3⋊Dic3—44no—
191C2×C3⋊Dic3#4112yes—
192#401—91no—
193#400—91no—
194#400—91no—
195#400—91no—
196#387—91no—
197#387—91no—
198#387—91no—
199#385—91no—
200#385—91no—
201#383—91no—
202#381—91no—
203#381—91no—
204#380—91no—
205C4×C22⋊C4C3⋊D311yescharacteristic
206C2×#95—91no—
207C24×C3C22×D314yes—
208C22×C3×C4—28no—
209C22×C3×C4—28no—
210C22×C3×C4—44no—
211C22×C3×C4C22×D314yes—
212C22×C3×C4C22×D314yes—
213C22×C3×C4C22×D314yes—
214C22×C3×C4C22×D314yes—
215C22×C3×C4C22×D314yes—
216C22×C3×C4C22×D314yes—
217C22×Dic3—34no—
218C22×Dic3—34no—
219C22×Dic3—34no—
220C22×Dic3—34no—
221C22×Dic3—34no—
222C22×Dic3—34no—
223C22×Dic3—34no—
224C22×Dic3—34no—
225C22×Dic3—68no—
226C22×Dic3—68no—
227C22×Dic3—68no—
228C22×Dic3—68no—
229C22×Dic3—68no—
230C22×Dic3—124no—
231C3×C22⋊C4—28no—
232C3×C22⋊C4—28no—
233C3×C42—28no—
234C3×C42—44no—
235#217—68no—
236#217—68no—
237Dic3⋊C4—68no—
238Dic3⋊C4—68no—
239Dic3⋊C4—68no—
240Dic3⋊C4—124no—
241Dic3⋊C4—124no—
242Dic3⋊C4—124no—
243C22×C32—22no—
244C22×C32—22no—
245C22×C32—22no—
246C22×C32—22no—
247C22×C32—22no—
248C22×C32—22no—
249C22×C32#12614yes—
250C22×C32C2×#4111yescharacteristic
251C22×C32C2×#4111yescharacteristic
252C22×C32C2×#4111yescharacteristic
253C22×C32C2×#4111yescharacteristic
254C22×C32C2×#4111yescharacteristic
255C22×C32H(5,𝔽2)11yescharacteristic
256C22×C322−1+411yescharacteristic
257C32×C4—22no—
258C32×C4—41no—
259C32×C4—41no—
260C32×C4—41no—
261C32×C4—41no—
262C32×C4—41no—
263C3⋊Dic3—22no—
264C3⋊Dic3—41no—
265C3⋊Dic3—41no—
266C3⋊Dic3—41no—
267C3⋊Dic3—41no—
268C3⋊Dic3—41no—
269C3⋊Dic3—41no—
270C3⋊Dic3—41no—
271C23×C4—91no—
272C23×C4—91no—
273C23×C4C2×C3⋊D311yescharacteristic
274C2×C4⋊C4—91no—
275C2×C4⋊C4—91no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—91no—
278C2×C4⋊C4—91no—
279C2×C4⋊C4—91no—
280C2×C22⋊C4—91no—
281C2×C22⋊C4—91no—
282C2×C22⋊C4C2×C3⋊D311yescharacteristic
283C2×C22⋊C4C2×C3⋊D311yescharacteristic
284C2×C42C2×C3⋊D311yescharacteristic
285C2×C42C2×C3⋊D311yescharacteristic
286#95—91no—
287#95—91no—
288#95—91no—
289#95—91no—
290#95—91no—
291#95—91no—
292#95—91no—
293#95—91no—
294#95—91no—
295#95—91no—
296#95—91no—
297#95—91no—
298#95—91no—
299#95—91no—
300#95—91no—
301#95—91no—
302#95—91no—
303#95—91no—
304#95C2×C3⋊D311yescharacteristic
305#95C2×C3⋊D311yescharacteristic
306C23×C3—24no—
307C23×C3—24no—
308C23×C3—24no—
309C23×C3—24no—
310C23×C3#23518yes—
311C23×C3#23518yes—
312C23×C3#23518yes—
313C23×C3C23×D314yes—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—24no—
317C2×C3×C4—24no—
318C2×C3×C4—24no—
319C2×C3×C4—24no—
320C2×C3×C4—24no—
321C2×C3×C4—24no—
322C2×C3×C4—24no—
323C2×C3×C4—24no—
324C2×C3×C4—24no—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—24no—
330C2×C3×C4—24no—
331C2×C3×C4—416no—
332C2×C3×C4#23718yes—
333C2×Dic3—38no—
334C2×Dic3—64no—
335C2×Dic3—64no—
336C2×Dic3—64no—
337C2×Dic3—64no—
338C2×Dic3—64no—
339C2×Dic3—64no—
340C2×Dic3—64no—
341C2×Dic3—64no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—64no—
345C2×Dic3—64no—
346C2×Dic3—64no—
347C2×Dic3—64no—
348C2×Dic3—64no—
349C2×Dic3—64no—
350C2×Dic3—64no—
351C2×Dic3—64no—
352C2×Dic3—64no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—1216no—
358C2×Dic3—1216no—
359C2×C32—24no—
360C2×C32C2×#12611yescharacteristic
361C2×C32#52911yescharacteristic
362C2×C32#53911yescharacteristic
363C2×C32#55111yescharacteristic
364C2×C32#55111yescharacteristic
365C2×C32#55211yescharacteristic
366C2×C32#55211yescharacteristic
367C24C22×C3⋊D311yescharacteristic
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—41no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—182no—
380C22×C4—182no—
381C22×C4—182no—
382C22×C4—182no—
383C22×C4—182no—
384C22×C4—361no—
385C22×C4C22×C3⋊D311yescharacteristic
386C22×C4C22×C3⋊D311yescharacteristic
387C22×C4C22×C3⋊D311yescharacteristic
388C22×C4C22×C3⋊D311yescharacteristic
389C22×C4C22×C3⋊D311yescharacteristic
390C22×C4C22×C3⋊D311yescharacteristic
391C4⋊C4—182no—
392C4⋊C4—182no—
393C4⋊C4—182no—
394C4⋊C4—361no—
395C4⋊C4—361no—
396C4⋊C4—361no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—182no—
400C22⋊C4—182no—
401C42—22no—
402C42—41no—
403C22×C3—28no—
404C22×C3—28no—
405C22×C3—28no—
406C22×C3—28no—
407C22×C3—28no—
408C22×C3—28no—
409C22×C3#876116yes—
410C22×C3C2×#23514yes—
411C22×C3C2×#23514yes—
412C22×C3C2×#23514yes—
413C22×C3C2×#23714yes—
414C22×C3#100414yes—
415C22×C3D3×#4114yes—
416C22×C3#101014yes—
417C3×C4—28no—
418C3×C4—44no—
419C3×C4—44no—
420C3×C4—44no—
421C3×C4—44no—
422C3×C4—44no—
423Dic3—68no—
424Dic3—124no—
425Dic3—124no—
426Dic3—124no—
427Dic3—124no—
428Dic3—124no—
429Dic3—124no—
430Dic3—124no—
431C32#249311yescharacteristic, complemented, Sylow
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23#382812yes—
437C23#382812yes—
438C23#382812yes—
439C23C23×C3⋊D311yescharacteristic
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—44no—
458C2×C4—92no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4—181no—
462C2×C4—181no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—181no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—364no—
483C2×C4—364no—
484C2×C4#383012yes—
485C2×C3—216no—
486C2×C3C2×#87614yes—
487C2×C3#549514yes—
488C2×C3#553114yes—
489C2×C3#553814yes—
490C2×C3#554114yes—
491C2×C3#555614yes—
492C2×C3#556414yes—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22#6408514yes—
500C22C2×#382811yescharacteristic
501C22C2×#382811yescharacteristic
502C22C2×#382811yescharacteristic
503C22C2×#383011yescharacteristic
504C22#6436111yescharacteristic
505C22#41×C3⋊D311yescharacteristic
506C22#6436711yescharacteristic
507C4—22no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—41no—
513C4—182no—
514C4—361no—
515C4—361no—
516C4—361no—
517C4—361no—
518C4—361no—
519C4—361no—
520C4—361no—
521C3#7350914yescomplemented
522C2—24no—
523C2C2×#6408511yescharacteristic
524C2#1059596611yescharacteristic
525C2#1059600211yescharacteristic
526C2#1059600911yescharacteristic
527C2#1059601211yescharacteristic
528C2#1059602711yescharacteristic
529C2#1059603511yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×C4×C22⋊C4C2
prime radicalC24×C32C23
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32#2493
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10592636C2semidirect
9. #10592632C2semidirect
10. #10592632C2semidirect
11. #10592632C2semidirect
12. #10592361C2semidirect
13. #10592357C2semidirect
14. #10592357C2semidirect
15. #10592357C2semidirect
431. C32#2493semidirect
521. C3#73509semidirect

Maximal subgroups

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

subgroupindex
C32×C4×C22⋊C42
#105929092
C2×#636582
#105926452
#105926422
#105926412
#105926362
#105926322
#105923612
#105923572
#735093