Finite Group Databasebeta

← #11868913

Subgroups — #11868913

Order 1152.

1194 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596200C211yesmaximal, characteristic, complemented
2#10596016C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic, complemented
4#10592783C211yesmaximal, characteristic, complemented
5#10592708C211yesmaximal, characteristic, complemented
6#10592590C211yesmaximal, characteristic, complemented
7#10592589C211yesmaximal, characteristic, complemented
8#10592580C211yesmaximal, characteristic, complemented
9#10592579C211yesmaximal, characteristic, complemented
10#10592546C211yesmaximal, characteristic, complemented
11#10592538C211yesmaximal, characteristic, complemented
12#10592469C211yesmaximal, characteristic
13C3⋊D3×#102C211yesmaximal, characteristic
14#10592465C211yesmaximal, characteristic, complemented
15#10592460C211yesmaximal, characteristic, complemented
16#80967—34nomaximal
17C2×D4×C3⋊D3C2211yescharacteristic
18C32×C4⋊Q8C2211yescharacteristic, complemented
19C32×C4×D4C2211yescharacteristic
20#64155—21no—
21#64153—21no—
22D4×C3⋊Dic3C2211yescharacteristic
23C4×#638—21no—
24C2×#3752—21no—
25C2×#3743C2211yescharacteristic
26C2×C8×C3⋊D3C2211yescharacteristic
27#64105—21no—
28#64102C2211yescharacteristic
29#64101C2211yescharacteristic
30#64101C2211yescharacteristic
31C4⋊C4×C3⋊D3C2211yescharacteristic
32#64099C2211yescharacteristic, complemented
33#64098—21no—
34#64097C2211yescharacteristic, complemented
35#64090—21no—
36C22⋊C4×C3⋊D3—21no—
37C4×C4⋊(C3⋊D3)C2211yescharacteristic
38#64081C2211yescharacteristic
39#64079C2211yescharacteristic, complemented
40C32×#107C2211yescharacteristic, complemented
41C32×#107C2211yescharacteristic, complemented
42C32×C4⋊C8C2211yescharacteristic, complemented
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic
47#63648C2211yescharacteristic
48#63648C2211yescharacteristic
49#63645C2211yescharacteristic, complemented
50#63644C2211yescharacteristic, complemented
51#63641C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54#63636C2211yescharacteristic
55#63635C2211yescharacteristic, complemented
56#63635C2211yescharacteristic, complemented
57#63635C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
60#5729—34no—
61#5545—34no—
62C3×#474D314yescomplemented
63#5084—34no—
64#5009—34no—
65#4891—34no—
66#4890—34no—
67#4881—34no—
68#4880—34no—
69#4847—34no—
70#4839—34no—
71#4770—34no—
72D3×#102—34no—
73#4766—34no—
74#4761—34no—
75C23×C3⋊D3—21no—
76C2×C32×Q8—21no—
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C2×#638—21no—
80C22×C3⋊Dic3—21no—
81D4×C3⋊D3—22no—
82D4×C3⋊D3Q814yescomplemented
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3C2311yescharacteristic
88C2×#634—21no—
89C2×C32×C8C2311yescharacteristic
90C2×C32×C8C2311yescharacteristic
91C32×C4⋊C4—21no—
92C32×C4⋊C4C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C4⋊C4C2311yescharacteristic
95C32×C22⋊C4—21no—
96C32×C42C2311yescharacteristic
97#3757—21no—
98#3752—21no—
99#3752—21no—
100#3752—21no—
101#3752—21no—
102#3752D411yescharacteristic
103#3752D411yescharacteristic
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109#3750—21no—
110#3750—21no—
111#3750—21no—
112#3750—21no—
113#3750D411yescharacteristic
114#3750D411yescharacteristic
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3743—22no—
121C8×C3⋊D3—22no—
122#3081—91noSylow
123C2×D3×D4—34no—
124C3×C4⋊Q8C2×D314yescomplemented
125C3×C4×D4C2×D314yes—
126#946—64no—
127#944—64no—
128D4×Dic3—34no—
129C4×#67—64no—
130C2×(C2×D3)⋊C4—64no—
131C2×ΓL(1,𝔽25)—34no—
132C2×D3×C8—34no—
133#896—64no—
134#893—34no—
135#892—34no—
136#892—34no—
137D3×C4⋊C4—34no—
138#890—34no—
139#889—64no—
140#888—34no—
141#67⋊C4—64no—
142D3×C22⋊C4—64no—
143C4×D12—34no—
144#872—34no—
145#870—34no—
146C3×#107C2×D314yescomplemented
147C3×#107C2×D314yescomplemented
148C3×C4⋊C8C2×D314yescomplemented
149C3×#102C2×D314yes—
150C3×#102C2×D314yes—
151#832—34no—
152#832—34no—
153#821—34no—
154#821—34no—
155#818—34no—
156#817—34no—
157Dic3⋊C8—34no—
158Dic3⋊C8—34no—
159#809—34no—
160#809—34no—
161#808—34no—
162#808—34no—
163#808—34no—
164#807—34no—
165C4⋊(C3⋊C8)—34no—
166C23×C32—21no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3—24no—
169C22×C3⋊D3—81no—
170C22×C3⋊D3—81no—
171C22×C3⋊D3C2×D411yescharacteristic
172C32×Q8—81no—
173C32×D4—21no—
174C32×D4C2×Q812yes—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—81no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2411yescharacteristic
182#638—24no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—81no—
187C2×C3⋊Dic3C2×D411yescharacteristic
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C4⋊(C3⋊D3)—21no—
191C4⋊(C3⋊D3)C2×Q812yes—
192C4×C3⋊D3—81no—
193C4×C3⋊D3—81no—
194C4×C3⋊D3—81no—
195C4×C3⋊D3C2×Q812yes—
196C4×C3⋊D3#4112yes—
197#634—81no—
198C32×C8—21no—
199C32×C8—21no—
200C3⋊(C3⋊C8)—21no—
201C3⋊(C3⋊C8)—21no—
202#544—91no—
203#518—91no—
204#478—91no—
205#478—91no—
206#478—91no—
207#478—91no—
208#476—91no—
209#476—91no—
210#474—91no—
211#474C3⋊D311yescharacteristic, complemented
212#428—91no—
213#427—91no—
214#424—91no—
215#418—91no—
216C2×#102—91no—
217C23×D3—64no—
218C2×C3×Q8—24no—
219C2×C3×D4C22×D314yes—
220C22×C3×C4—24no—
221C2×#67—64no—
222C22×Dic3—64no—
223D3×D4—316no—
224D3×D4—68no—
225C2×D12—34no—
226C2×C4×D3—34no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×Dic6—64no—
231C2×C3×C8C22×D314yes—
232C2×C3×C8C22×D314yes—
233C3×C4⋊C4—24no—
234C3×C4⋊C4C22×D314yes—
235C3×C4⋊C4C22×D314yes—
236C3×C4⋊C4C22×D314yes—
237C3×C22⋊C4—24no—
238C3×C42C22×D314yes—
239#217—64no—
240(C2×D3)⋊C4—34no—
241(C2×D3)⋊C4—34no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246C4⋊Dic3—34no—
247C4⋊Dic3—34no—
248C4⋊Dic3—34no—
249C4⋊Dic3—64no—
250Dic3⋊C4—34no—
251Dic3⋊C4—34no—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257C4×Dic3—34no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C2×C3⋊C8—34no—
261C2×C3⋊C8—34no—
262ΓL(1,𝔽25)—68no—
263D3×C8—68no—
264C22×C32—22no—
265C22×C32—41no—
266C22×C32—41no—
267C22×C32C22×D411yescharacteristic
268C2×C3⋊D3—21no—
269C2×C3⋊D3—21no—
270C2×C3⋊D3—22no—
271C2×C3⋊D3—41no—
272C2×C3⋊D3—41no—
273C2×C3⋊D3—84no—
274C2×C3⋊D3C22⋊Q812yes—
275C32×C4—21no—
276C32×C4—21no—
277C32×C4—41no—
278C32×C4—41no—
279C32×C4—41no—
280C32×C4C22×Q811yescharacteristic
281C32×C4C2×#4111yescharacteristic
282C3⋊Dic3—21no—
283C3⋊Dic3—21no—
284C3⋊Dic3—41no—
285C3⋊Dic3—41no—
286C3⋊Dic3—41no—
287C3⋊Dic3C22⋊Q812yes—
288C22×D4—91no—
289C2×M16—91no—
290C22×C8—91no—
291C4⋊Q8—91no—
292C4⋊Q8—181no—
293C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
294#125—91no—
295#125—91no—
296#125—181no—
297C22⋊Q8—181no—
298C22⋊Q8—181no—
299C4×D4—91no—
300C4×D4—91no—
301C4×D4—91no—
302C4×D4—181no—
303C4×D4—181no—
304C4×D4C2×C3⋊D311yescharacteristic
305#117—91no—
306#117—91no—
307#117—91no—
308C2×C4⋊C4—91no—
309C2×C22⋊C4—181no—
310C2×C22⋊C4—181no—
311#107—91no—
312#107—91no—
313#107C2×C3⋊D311yescharacteristic, complemented
314#107C2×C3⋊D311yescharacteristic, complemented
315#106—91no—
316#106—91no—
317#106—91no—
318#106—91no—
319C4⋊C8—91no—
320C4⋊C8—91no—
321C4⋊C8—91no—
322C4⋊C8C2×C3⋊D311yescharacteristic, complemented
323#102—91no—
324#102—91no—
325#102—91no—
326#102—91no—
327#102—91no—
328#102—91no—
329#102C2×C3⋊D311yescharacteristic
330#102C2×C3⋊D311yescharacteristic
331C23×C3—24no—
332C22×D3—34no—
333C22×D3—616no—
334C22×D3—64no—
335C22×D3—244no—
336C22×D3—244no—
337C3×Q8—84no—
338C3×D4—24no—
339C3×D4D3×Q818yes—
340C2×C3×C4—24no—
341C2×C3×C4—24no—
342C2×C3×C4—24no—
343C2×C3×C4—84no—
344C2×C3×C4D3×D414yes—
345C2×C3×C4D3×D414yes—
346C2×C3×C4C23×D314yes—
347#67—616no—
348C2×Dic3—34no—
349C2×Dic3—34no—
350C2×Dic3—34no—
351C2×Dic3—64no—
352C2×Dic3—64no—
353C2×Dic3—64no—
354C2×Dic3—244no—
355D12—38no—
356D12—64no—
357C4×D3—38no—
358C4×D3—38no—
359C4×D3—244no—
360C4×D3—244no—
361C4×D3—244no—
362Dic6—244no—
363C3×C8—24no—
364C3×C8—24no—
365C3⋊C8—64no—
366C3⋊C8—64no—
367C2×C32—42no—
368C2×C32C2×C22⋊Q811yescharacteristic
369C2×C32#57611yescharacteristic
370C2×C32#57711yescharacteristic
371C3⋊D3—22no—
372C3⋊D3—42no—
373C24—181no—
374C2×Q8—21no—
375C2×Q8—181no—
376C2×D4—94no—
377C2×D4—91no—
378C2×D4—182no—
379C2×D4—181no—
380C2×D4C22×C3⋊D311yescharacteristic
381C22×C4—21no—
382C22×C4—91no—
383C22×C4—181no—
384C22×C4—181no—
385C22×C4—181no—
386C22×C4—181no—
387M16—182no—
388C2×C8—91no—
389C2×C8—91no—
390C2×C8—182no—
391C2×C8C22×C3⋊D311yescharacteristic
392C2×C8C22×C3⋊D311yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—91no—
395C4⋊C4—91no—
396C4⋊C4—91no—
397C4⋊C4—91no—
398C4⋊C4—91no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C4⋊C4—181no—
402C4⋊C4—181no—
403C4⋊C4—181no—
404C4⋊C4—181no—
405C4⋊C4C22×C3⋊D311yescharacteristic
406C4⋊C4C22×C3⋊D311yescharacteristic
407C4⋊C4C22×C3⋊D311yescharacteristic
408C22⋊C4—21no—
409C22⋊C4—91no—
410C22⋊C4—91no—
411C22⋊C4—181no—
412C22⋊C4—181no—
413C22⋊C4—181no—
414C22⋊C4—181no—
415C22⋊C4—181no—
416C42—91no—
417C42—181no—
418C42—181no—
419C42C22×C3⋊D311yescharacteristic
420C22×C3—28no—
421C22×C3—44no—
422C22×C3—44no—
423C22×C3C2×D3×D414yes—
424C2×D3—38no—
425C2×D3—64no—
426C2×D3—64no—
427C2×D3—68no—
428C2×D3—124no—
429C2×D3—124no—
430C2×D3—2416no—
431C3×C4—24no—
432C3×C4—24no—
433C3×C4—44no—
434C3×C4—44no—
435C3×C4—44no—
436C3×C4C2×D3×Q814yes—
437C3×C4D3×#4114yes—
438Dic3—38no—
439Dic3—64no—
440Dic3—64no—
441Dic3—124no—
442Dic3—124no—
443Dic3—124no—
444C32#308111yescharacteristic, complemented, Sylow
445C23—21no—
446C23—91no—
447C23—184no—
448C23—181no—
449C23—721no—
450C23—721no—
451Q8—81no—
452Q8—721no—
453D4—21no—
454D4—92no—
455D4—184no—
456D4—181no—
457D4Q8×C3⋊D312yes—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—81no—
462C2×C4—91no—
463C2×C4—92no—
464C2×C4—92no—
465C2×C4—91no—
466C2×C4—91no—
467C2×C4—181no—
468C2×C4—181no—
469C2×C4—181no—
470C2×C4—721no—
471C2×C4—721no—
472C2×C4—721no—
473C2×C4—721no—
474C2×C4D4×C3⋊D311yescharacteristic
475C2×C4D4×C3⋊D311yescharacteristic
476C2×C4C23×C3⋊D311yescharacteristic
477C8—21no—
478C8—21no—
479C8—181no—
480C8—181no—
481C2×C3—48no—
482C2×C3D3×C22⋊Q814yes—
483C2×C3#575714yes—
484C2×C3#577814yes—
485D3—68no—
486D3—128no—
487C22—22no—
488C22—41no—
489C22—41no—
490C22—92no—
491C22—181no—
492C22—181no—
493C22—182no—
494C22—361no—
495C22—361no—
496C22—724no—
497C22C2×D4×C3⋊D311yescharacteristic
498C4—21no—
499C4—21no—
500C4—41no—
501C4—41no—
502C4—41no—
503C4—92no—
504C4—181no—
505C4—181no—
506C4—361no—
507C4—361no—
508C4—361no—
509C4C2×Q8×C3⋊D311yescharacteristic
510C4#41×C3⋊D311yescharacteristic
511C3#8096714yescomplemented
512C2—42no—
513C2—182no—
514C2—362no—
515C2C3⋊D3×C22⋊Q811yescharacteristic
516C2#1059622811yescharacteristic
517C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#474C3⋊D3
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10596200C2semidirect
3. C32×#474C2semidirect
4. #10592783C2semidirect
5. #10592708C2semidirect
6. #10592590C2semidirect
7. #10592589C2semidirect
8. #10592580C2semidirect
9. #10592579C2semidirect
10. #10592546C2semidirect
11. #10592538C2semidirect
14. #10592465C2semidirect
15. #10592460C2semidirect
18. C32×C4⋊Q8C22semidirect
32. #64099C22semidirect
34. #64097C22semidirect
39. #64079C22semidirect
40. C32×#107C22semidirect
41. C32×#107C22semidirect
42. C32×C4⋊C8C22semidirect
49. #63645C22semidirect
50. #63644C22semidirect
51. #63641C22semidirect
52. #63641C22semidirect
55. #63635C22semidirect
56. #63635C22semidirect
57. #63635C22semidirect
58. #63634C22semidirect
59. C4⋊(C3⋊(C3⋊C8))C22semidirect
62. C3×#474D3semidirect
82. D4×C3⋊D3Q8semidirect
124. C3×C4⋊Q8C2×D3semidirect
146. C3×#107C2×D3semidirect
147. C3×#107C2×D3semidirect
148. C3×C4⋊C8C2×D3semidirect
211. #474C3⋊D3semidirect
293. C4⋊Q8C2×C3⋊D3semidirect
313. #107C2×C3⋊D3semidirect
314. #107C2×C3⋊D3semidirect
322. C4⋊C8C2×C3⋊D3semidirect
444. C32#3081semidirect
511. C3#80967semidirect

Maximal subgroups

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

subgroupindex
#105962002
#105960162
C32×#4742
#105927832
#105927082
#105925902
#105925892
#105925802
#105925792
#105925462
#105925382
#105924692
C3⋊D3×#1022
#105924652
#105924602
#809673