Finite Group Databasebeta

← #11808886

Subgroups — #11808886

Order 1152.

1296 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×C22⋊C4C211yesmaximal, characteristic
2C4×#3757C211yesmaximal, characteristic
3C4×#3757C211yesmaximal, characteristic
4#10592652C211yesmaximal, characteristic
5#10592651C211yesmaximal, characteristic
6#10592651C211yesmaximal, characteristic
7#10592647C211yesmaximal, characteristic
8C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
9#10592631C211yesmaximal, characteristic, complemented
10C4×#3750C211yesmaximal, characteristic, complemented
11C4×#3750C211yesmaximal, characteristic, complemented
12#10592361C211yesmaximal, characteristic, complemented
13#10592359C211yesmaximal, characteristic, complemented
14#10592358C211yesmaximal, characteristic, complemented
15#10592357C211yesmaximal, characteristic, complemented
16#73482—34nomaximal
17C23×C32×C4C2211yescharacteristic
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×C32×C42C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35C2×C4×C3⋊Dic3C2211yescharacteristic
36C32×#95C2211yescharacteristic
37C32×#95C2211yescharacteristic
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—
53C4×#217—34no—
54C4×#217—34no—
55#4953—34no—
56#4952—34no—
57#4952—34no—
58#4948—34no—
59C4×C4⋊Dic3—34no—
60#4932—34no—
61C4×Dic3⋊C4—34no—
62C4×Dic3⋊C4—34no—
63C3⋊#401—34no—
64#4660—34no—
65#4659—34no—
66#4658—34no—
67C24×C32C2311yescharacteristic
68C22×C32×C4—22no—
69C22×C32×C4—22no—
70C22×C32×C4—22no—
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2311yescharacteristic
85C32×C22⋊C4—22no—
86C32×C22⋊C4—22no—
87C32×C42—22no—
88C32×C42—22no—
89#3757—22no—
90#3757—22no—
91#3757—22no—
92#3757—22no—
93C4⋊(C3⋊Dic3)—22no—
94C4⋊(C3⋊Dic3)—22no—
95#3750—22no—
96#3750—22no—
97#3750—22no—
98#3750—22no—
99C4×C3⋊Dic3—22no—
100C4×C3⋊Dic3—22no—
101C4×C3⋊Dic3—22no—
102C4×C3⋊Dic3—22no—
103#2401—91noSylow
104C23×C3×C4C2×D314yes—
105C2×C3×C22⋊C4C2×D314yes—
106C2×C3×C22⋊C4C2×D314yes—
107C2×C3×C42C2×D314yes—
108C2×C3×C42C2×D314yes—
109C2×#217—34no—
110C2×#217—34no—
111C2×#217—34no—
112C2×#217—34no—
113C2×C4⋊Dic3—34no—
114C2×C4⋊Dic3—34no—
115C2×Dic3⋊C4—34no—
116C2×Dic3⋊C4—34no—
117C2×Dic3⋊C4—34no—
118C2×Dic3⋊C4—34no—
119C2×C4×Dic3—34no—
120C2×C4×Dic3—34no—
121C2×C4×Dic3—34no—
122C2×C4×Dic3—34no—
123C3×#95C2×D314yes—
124C3×#95C2×D314yes—
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—21no—
144C23×C32—21no—
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—44no—
162C2×C32×C4#4112yes—
163C2×C32×C4#4112yes—
164C2×C32×C4#4112yes—
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#4112yes—
189C2×C3⋊Dic3#4112yes—
190#401—91no—
191#400—91no—
192#400—91no—
193#400—91no—
194#397—91no—
195#397—91no—
196#397—91no—
197#396—91no—
198C4×C4⋊C4—91no—
199C4×C4⋊C4—91no—
200C4×C4⋊C4—91no—
201C4×C22⋊C4—91no—
202C4×C22⋊C4—91no—
203C4×C22⋊C4C3⋊D311yescharacteristic
204#376—91no—
205C24×C3C22×D314yes—
206C22×C3×C4—28no—
207C22×C3×C4—28no—
208C22×C3×C4—28no—
209C22×C3×C4C22×D314yes—
210C22×C3×C4C22×D314yes—
211C22×C3×C4C22×D314yes—
212C22×C3×C4C22×D314yes—
213C22×C3×C4C22×D314yes—
214C22×C3×C4C22×D314yes—
215C22×Dic3—34no—
216C22×Dic3—34no—
217C22×Dic3—34no—
218C22×Dic3—34no—
219C22×Dic3—34no—
220C22×Dic3—34no—
221C22×Dic3—34no—
222C22×Dic3—34no—
223C3×C22⋊C4—28no—
224C3×C22⋊C4—28no—
225C3×C42—28no—
226C3×C42—28no—
227#217—68no—
228#217—68no—
229#217—68no—
230#217—68no—
231C4⋊Dic3—68no—
232C4⋊Dic3—68no—
233Dic3⋊C4—68no—
234Dic3⋊C4—68no—
235Dic3⋊C4—68no—
236Dic3⋊C4—68no—
237C4×Dic3—68no—
238C4×Dic3—68no—
239C4×Dic3—68no—
240C4×Dic3—68no—
241C22×C32—22no—
242C22×C32—22no—
243C22×C32—22no—
244C22×C32—41no—
245C22×C32—41no—
246C22×C32—41no—
247C22×C32—41no—
248C22×C32C2×#4111yescharacteristic
249C22×C32C2×#4111yescharacteristic
250C22×C32C2×#4111yescharacteristic
251C22×C32C2×#4111yescharacteristic
252C22×C32C2×#4111yescharacteristic
253C22×C32C2×#4111yescharacteristic
254C22×C32C2×#4111yescharacteristic
255C32×C4—22no—
256C32×C4—41no—
257C32×C4—41no—
258C32×C4—41no—
259C32×C4—41no—
260C32×C4#12614yes—
261C3⋊Dic3—22no—
262C3⋊Dic3—22no—
263C3⋊Dic3—41no—
264C3⋊Dic3—41no—
265C3⋊Dic3—41no—
266C3⋊Dic3—41no—
267C3⋊Dic3—41no—
268C3⋊Dic3—41no—
269C23×C4C2×C3⋊D311yescharacteristic
270C2×C4⋊C4—91no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4—91no—
276C2×C22⋊C4—91no—
277C2×C22⋊C4—91no—
278C2×C22⋊C4—91no—
279C2×C22⋊C4—91no—
280C2×C22⋊C4C2×C3⋊D311yescharacteristic
281C2×C22⋊C4C2×C3⋊D311yescharacteristic
282C2×C42—91no—
283C2×C42—91no—
284C2×C42—91no—
285C2×C42—91no—
286C2×C42C2×C3⋊D311yescharacteristic
287C2×C42C2×C3⋊D311yescharacteristic
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#95C2×C3⋊D311yescharacteristic
303#95C2×C3⋊D311yescharacteristic
304C23×C3—24no—
305C23×C3—24no—
306C23×C3—24no—
307C23×C3—24no—
308C23×C3—24no—
309C23×C3—24no—
310C23×C3#23518yes—
311C23×C3C23×D314yes—
312C2×C3×C4—24no—
313C2×C3×C4—24no—
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—416no—
327C2×C3×C4#23518yes—
328C2×C3×C4#23518yes—
329C2×C3×C4#23718yes—
330C2×C3×C4#23718yes—
331C2×Dic3—38no—
332C2×Dic3—38no—
333C2×Dic3—64no—
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×C32—42no—
356C2×C32C2×#12611yescharacteristic
357C2×C32#52911yescharacteristic
358C2×C32#52911yescharacteristic
359C2×C32#52911yescharacteristic
360C2×C32#52911yescharacteristic
361C2×C32#52911yescharacteristic
362C2×C32#52911yescharacteristic
363C24C22×C3⋊D311yescharacteristic
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—91no—
368C22×C4—91no—
369C22×C4—91no—
370C22×C4—91no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4C22×C3⋊D311yescharacteristic
376C22×C4C22×C3⋊D311yescharacteristic
377C22×C4C22×C3⋊D311yescharacteristic
378C22×C4C22×C3⋊D311yescharacteristic
379C22×C4C22×C3⋊D311yescharacteristic
380C22×C4C22×C3⋊D311yescharacteristic
381C4⋊C4—182no—
382C4⋊C4—182no—
383C4⋊C4—182no—
384C4⋊C4—182no—
385C4⋊C4—182no—
386C4⋊C4—182no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—182no—
390C22⋊C4—182no—
391C22⋊C4—182no—
392C22⋊C4—182no—
393C42—22no—
394C42—22no—
395C42—182no—
396C42—182no—
397C42—182no—
398C42—182no—
399C22×C3—28no—
400C22×C3—28no—
401C22×C3—28no—
402C22×C3—44no—
403C22×C3—44no—
404C22×C3—44no—
405C22×C3—44no—
406C22×C3C2×#23514yes—
407C22×C3C2×#23514yes—
408C22×C3C2×#23514yes—
409C22×C3C2×#23714yes—
410C22×C3C2×#23714yes—
411C22×C3D3×#4114yes—
412C22×C3D3×#4114yes—
413C3×C4—28no—
414C3×C4—44no—
415C3×C4—44no—
416C3×C4—44no—
417C3×C4—44no—
418C3×C4#879116yes—
419Dic3—68no—
420Dic3—68no—
421Dic3—124no—
422Dic3—124no—
423Dic3—124no—
424Dic3—124no—
425Dic3—124no—
426Dic3—124no—
427C32#240111yescharacteristic, complemented, Sylow
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23#382812yes—
435C23C23×C3⋊D311yescharacteristic
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
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—44no—
451C2×C4—92no—
452C2×C4—92no—
453C2×C4—181no—
454C2×C4—181no—
455C2×C4—181no—
456C2×C4—181no—
457C2×C4—181no—
458C2×C4—181no—
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#382812yes—
476C2×C4#382812yes—
477C2×C4#383012yes—
478C2×C4#383012yes—
479C2×C3—48no—
480C2×C3#547914yes—
481C2×C3C2×#87914yes—
482C2×C3#552814yes—
483C2×C3#553814yes—
484C2×C3#553814yes—
485C2×C3#553814yes—
486C2×C3#555714yes—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22C2×#382811yescharacteristic
495C22C2×#382811yescharacteristic
496C22C2×#382811yescharacteristic
497C22C2×#383011yescharacteristic
498C22C2×#383011yescharacteristic
499C22#41×C3⋊D311yescharacteristic
500C22#41×C3⋊D311yescharacteristic
501C4—22no—
502C4—41no—
503C4—41no—
504C4—41no—
505C4—41no—
506C4—182no—
507C4—182no—
508C4—361no—
509C4—361no—
510C4—361no—
511C4—361no—
512C4—361no—
513C4—361no—
514C4#6408814yes—
515C3#7348214yescomplemented
516C2—42no—
517C2#1059595011yescharacteristic
518C2C2×#6408811yescharacteristic
519C2#1059599911yescharacteristic
520C2#1059600911yescharacteristic
521C2#1059600911yescharacteristic
522C2#1059600911yescharacteristic
523C2#1059602811yescharacteristic
subgroupG/H
centerC22×C4C22×C3⋊D3
commutator, socle, cosocleC23×C32C24
FrattiniC23C23×C3⋊D3
FittingC32×C4×C22⋊C4C2
prime radicalC24×C32C23
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32#2401
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C4×C4⋊(C3⋊Dic3)C2semidirect
9. #10592631C2semidirect
10. C4×#3750C2semidirect
11. C4×#3750C2semidirect
12. #10592361C2semidirect
13. #10592359C2semidirect
14. #10592358C2semidirect
15. #10592357C2semidirect
427. C32#2401semidirect
515. C3#73482semidirect

Maximal subgroups

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

subgroupindex
C32×C4×C22⋊C42
C4×#37572
#105926522
#105926512
#105926472
C4×C4⋊(C3⋊Dic3)2
#105926312
C4×#37502
#105923612
#105923592
#105923582
#105923572
#734823