Finite Group Databasebeta

← #11889786

Subgroups — #11889786

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596295C211yesmaximal, characteristic
2#10596113C211yesmaximal, characteristic, complemented
3C32×#452C211yesmaximal, characteristic, complemented
4#10592931C211yesmaximal, characteristic, complemented
5#10592887C211yesmaximal, characteristic, complemented
6#10592881C211yesmaximal, characteristic, complemented
7#10592872C211yesmaximal, characteristic, complemented
8#10592863C211yesmaximal, characteristic, complemented
9#10592751C211yesmaximal, characteristic, complemented
10#10592513C211yesmaximal, characteristic, complemented
11#10592496C211yesmaximal, characteristic, complemented
12#10592471C211yesmaximal, characteristic, complemented
13#10592465C211yesmaximal, characteristic, complemented
14#10592427C211yesmaximal, characteristic, complemented
15#10592421C211yesmaximal, characteristic, complemented
16#80254—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×#3830C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22#64155C2211yescharacteristic
23#64155C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic
25#64153C2211yescharacteristic
26C2×#3756C2211yescharacteristic
27#64148—21no—
28#64144—21no—
29D4×C3⋊Dic3C2211yescharacteristic
30#64138—21no—
31C4×#638C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33#64133C2211yescharacteristic
34C2×#3750—21no—
35C2×#3748C2211yescharacteristic
36C2×C8×C3⋊D3C2211yescharacteristic
37#64107—21no—
38#64101C2211yescharacteristic
39#64099—21no—
40#64099C2211yescharacteristic
41#64095—21no—
42#64086—21no—
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63662C2211yescharacteristic
49#63659C2211yescharacteristic
50#63659C2211yescharacteristic
51#63647C2211yescharacteristic
52#63645C2211yescharacteristic
53#63645C2211yescharacteristic
54#63643C2211yescharacteristic
55#63643C2211yescharacteristic
56#63642C2211yescharacteristic
57#63641C2211yescharacteristic
58#63637C2211yescharacteristic
59#63635C2211yescharacteristic
60#5824—34no—
61#5642—34no—
62C3×#452D314yescomplemented
63#5232—34no—
64#5188—34no—
65#5182—34no—
66#5173—34no—
67#5164—34no—
68#5052—34no—
69#4814—34no—
70#4797—34no—
71#4772—34no—
72#4766—34no—
73#4728—34no—
74#4722—34no—
75C32×#41—22no—
76C32×#41—41no—
77C2×C32×Q8C2311yescharacteristic
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4—21no—
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×#638—21no—
84C2×#638D411yescharacteristic
85C22×C3⋊Dic3—21no—
86C22×C3⋊Dic3—21no—
87C22×C3⋊Dic3—21no—
88#3830—22no—
89#3830—41no—
90C2×C4×C3⋊D3C2311yescharacteristic
91C2×#634C2311yescharacteristic
92C32×Q16—41no—
93C32×SD16—22no—
94C2×C32×C8C2311yescharacteristic
95C2×C32×C8C2311yescharacteristic
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2311yescharacteristic
98C32×C22⋊C4—21no—
99#3757—21no—
100#3757—21no—
101#3757D411yescharacteristic
102#3756—41no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106#3752D411yescharacteristic
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750D411yescharacteristic
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123#3748—41no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C8×C3⋊D3—41no—
127#3315—91noSylow
128C2×C3×#41C2×D314yes—
129C2×#237—34no—
130C2×C3×Q16C2×D314yes—
131C2×C3×SD16C2×D314yes—
132C3×C22⋊Q8C2×D314yes—
133#946—34no—
134#946—34no—
135Q8×Dic3—34no—
136#944—34no—
137C2×#216—34no—
138#939—64no—
139#935—64no—
140D4×Dic3—34no—
141#929—64no—
142C4×#67—34no—
143C2×C4⋊Dic3—34no—
144#924—34no—
145C2×Dic3⋊C4—64no—
146C2×#208—34no—
147C2×D3×C8—34no—
148#898—64no—
149#892—34no—
150#890—34no—
151#890—64no—
152#886—64no—
153#877—64no—
154C3×#103C2×D314yes—
155C3×#102C2×D314yes—
156C3×C22⋊C8C2×D314yes—
157#835—34no—
158#835—34no—
159#835—34no—
160#832—34no—
161#832—34no—
162(C2×D3)⋊C8—34no—
163#818—34no—
164#818—34no—
165#816—34no—
166#816—34no—
167#815—34no—
168Dic3⋊C8—34no—
169#810—34no—
170#808—34no—
171C23×C32—21no—
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—21no—
177C32×Q8—21no—
178C32×D4—21no—
179C32×D4—42no—
180C32×D4#4112yes—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—42no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189#638—41no—
190#638—42no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—42no—
196C2×C3⋊Dic3—42no—
197C2×C3⋊Dic3—42no—
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C2×C3⋊Dic3C2×D411yescharacteristic
201C4×C3⋊D3—21no—
202C4×C3⋊D3—21no—
203#634—21no—
204#634—21no—
205C32×C8—21no—
206C32×C8—21no—
207C3⋊(C3⋊C8)—21no—
208C3⋊(C3⋊C8)—21no—
209#552—91no—
210#547—91no—
211#491—91no—
212#485—91no—
213#484—91no—
214#478—91no—
215#470—91no—
216#467—91no—
217#462—91no—
218#452—91no—
219#452C3⋊D311yescharacteristic, complemented
220#440—91no—
221#435—91no—
222#417—91no—
223#416—91no—
224C3×#41—28no—
225C3×#41—44no—
226C2×C3×Q8C22×D314yes—
227C2×C3×Q8C22×D314yes—
228C2×C3×D4—24no—
229C2×C3×D4C22×D314yes—
230C22×C3×C4—24no—
231C22×C3×C4C22×D314yes—
232C2×#67—34no—
233C2×#67—64no—
234C22×Dic3—64no—
235C22×Dic3—64no—
236C22×Dic3—64no—
237#237—68no—
238#237—124no—
239C2×C4×D3—34no—
240C2×Dic6—34no—
241C3×Q16—44no—
242C3×SD16—28no—
243C2×C3×C8C22×D314yes—
244C2×C3×C8C22×D314yes—
245C3×C4⋊C4—24no—
246C3×C4⋊C4C22×D314yes—
247C3×C22⋊C4—24no—
248#217—34no—
249#217—64no—
250#217—64no—
251#216—124no—
252(C2×D3)⋊C4—34no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256C4⋊Dic3—34no—
257C4⋊Dic3—34no—
258C4⋊Dic3—34no—
259C4⋊Dic3—64no—
260C4⋊Dic3—64no—
261C4⋊Dic3—64no—
262Dic3⋊C4—34no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269C4×Dic3—34no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272#208—124no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—34no—
275D3×C8—124no—
276C22×C32—22no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32—21no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—21no—
284C2×C3⋊D3—21no—
285C2×C3⋊D3—21no—
286C32×C4—21no—
287C32×C4—41no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4C2×#4111yescharacteristic
291C32×C4H(5,𝔽2)11yescharacteristic
292C3⋊Dic3—21no—
293C3⋊Dic3—21no—
294C3⋊Dic3—21no—
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C2×#41—91no—
300C2×#41C2×C3⋊D311yescharacteristic
301C2×Q16—91no—
302C2×Q16C2×C3⋊D311yescharacteristic
303C2×SD16C2×C3⋊D311yescharacteristic
304C2×M16—91no—
305C22×C8—91no—
306C4⋊Q8—91no—
307#126—181no—
308#125—91no—
309#125—181no—
310#123—181no—
311#123—181no—
312#123—181no—
313C22⋊Q8—91no—
314C22⋊Q8—91no—
315C22⋊Q8—91no—
316C22⋊Q8C2×C3⋊D311yescharacteristic
317#121—181no—
318C4×Q8—91no—
319C4×D4—91no—
320C4×D4—91no—
321#117—91no—
322#117—181no—
323C2×C4⋊C4—91no—
324C2×C4⋊C4—181no—
325#107—91no—
326#107—91no—
327#106—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103C2×C3⋊D311yescharacteristic
336#102—91no—
337#102—91no—
338#102C2×C3⋊D311yescharacteristic
339C22⋊C8—91no—
340C22⋊C8C2×C3⋊D311yescharacteristic
341#97—91no—
342C23×C3—24no—
343C23×C3D3×D414yes—
344C22×D3—34no—
345C3×Q8—24no—
346C3×Q8—24no—
347C3×Q8—24no—
348C3×Q8—24no—
349C3×D4—24no—
350C3×D4—48no—
351C3×D4#23718yes—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—48no—
358C2×C3×C4D3×D414yes—
359C2×C3×C4C23×D314yes—
360#67—124no—
361#67—128no—
362C2×Dic3—34no—
363C2×Dic3—34no—
364C2×Dic3—34no—
365C2×Dic3—64no—
366C2×Dic3—64no—
367C2×Dic3—64no—
368C2×Dic3—64no—
369C2×Dic3—128no—
370C2×Dic3—128no—
371C2×Dic3—128no—
372C4×D3—64no—
373C4×D3—64no—
374Dic6—64no—
375Dic6—64no—
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32—41no—
381C2×C32—42no—
382C2×C32#54611yescharacteristic
383C2×C32#57511yescharacteristic
384C2×C32#57811yescharacteristic
385C3⋊D3—41no—
386#41—22no—
387#41—41no—
388#41—182no—
389#41—361no—
390C2×Q8—91no—
391C2×Q8C22×C3⋊D311yescharacteristic
392C2×Q8C22×C3⋊D311yescharacteristic
393C2×D4—21no—
394C2×D4—91no—
395C2×D4—181no—
396C2×D4C22×C3⋊D311yescharacteristic
397C22×C4—21no—
398C22×C4—91no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—41no—
404Q16—361no—
405SD16—22no—
406M16—361no—
407C2×C8—91no—
408C2×C8—91no—
409C2×C8—361no—
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—91no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C4⋊C4C22×C3⋊D311yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—91no—
429C22⋊C4—91no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C22⋊C4—181no—
435C42—91no—
436C42—181no—
437C42—181no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—28no—
441C22×C3—24no—
442C22×C3—44no—
443C22×C3—44no—
444C22×C3C2×D3×D414yes—
445C2×D3—64no—
446C2×D3—64no—
447C2×D3—64no—
448C3×C4—24no—
449C3×C4—44no—
450C3×C4—44no—
451C3×C4—44no—
452C3×C4C2×#23714yes—
453C3×C4#100414yes—
454Dic3—64no—
455Dic3—64no—
456Dic3—64no—
457Dic3—124no—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461C32#331511yescharacteristic, complemented, Sylow
462C23—21no—
463C23—91no—
464C23D4×C3⋊D311yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—21no—
468Q8—21no—
469Q8—181no—
470Q8—181no—
471D4—21no—
472D4—42no—
473D4—361no—
474D4—362no—
475D4#383012yes—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—42no—
482C2×C4—91no—
483C2×C4—91no—
484C2×C4—91no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—362no—
492C2×C4—362no—
493C2×C4—362no—
494C2×C4D4×C3⋊D311yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—21no—
497C8—21no—
498C8—181no—
499C8—181no—
500C2×C3—44no—
501C2×C3—48no—
502C2×C3#559114yes—
503C2×C3#577114yes—
504C2×C3#577714yes—
505D3—124no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—22no—
510C22—41no—
511C22—41no—
512C22—181no—
513C22—181no—
514C22—181no—
515C22C2×D4×C3⋊D311yescharacteristic
516C4—21no—
517C4—41no—
518C4—41no—
519C4—41no—
520C4—181no—
521C4—181no—
522C4—181no—
523C4—361no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4C2×#383011yescharacteristic
528C4#6436111yescharacteristic
529C3#8025414yescomplemented
530C2—41no—
531C2—42no—
532C2—361no—
533C2#1059606211yescharacteristic
534C2#1059624211yescharacteristic
535C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#452C2
socleC22×C32C22×D4
prime radical#10596295C2
hypercenter#452C3⋊D3
hypocenterC32#3315
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #10596113C2semidirect
3. C32×#452C2semidirect
4. #10592931C2semidirect
5. #10592887C2semidirect
6. #10592881C2semidirect
7. #10592872C2semidirect
8. #10592863C2semidirect
9. #10592751C2semidirect
10. #10592513C2semidirect
11. #10592496C2semidirect
12. #10592471C2semidirect
13. #10592465C2semidirect
14. #10592427C2semidirect
15. #10592421C2semidirect
62. C3×#452D3semidirect
219. #452C3⋊D3semidirect
461. C32#3315semidirect
529. C3#80254semidirect

Maximal subgroups

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

subgroupindex
#105962952
#105961132
C32×#4522
#105929312
#105928872
#105928812
#105928722
#105928632
#105927512
#105925132
#105924962
#105924712
#105924652
#105924272
#105924212
#802543