Finite Group Databasebeta

← #11895268

Subgroups — #11895268

Order 1152.

754 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
1#10593960C211yesmaximal, characteristic, complemented
2#10593865C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic, complemented
4C3×#4841C211yesmaximal, characteristic, complemented
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590872C212yesmaximal, complemented
7#10590815C212yesmaximal, complemented
8Dic3×#204C212yesmaximal, complemented
9#10590754C212yesmaximal
10C4×#3714C211yesmaximal, characteristic
11#10590287C211yesmaximal, characteristic, complemented
12#80415—31nomaximal
13#79926—31nomaximal
14C4×C4⋊(C3⋊D3)C2211yescharacteristic
15#64078C2211yescharacteristic
16C2×C3×#204C2212yes—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63896—22no—
21Dic3×D12C2212yes—
22D3×C4⋊Dic3—21no—
23#63871—21no—
24#63869C2212yes—
25#63864C2212yes—
26#63856—21no—
27#63849—21no—
28#63848—22no—
29Dic3×Dic6C2212yes—
30C2×#3714C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63648C2212yes—
33#63644C2212yes—
34C3×#816C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×C8×Dic3C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2211yescharacteristic
39#63566C2212yes—
40#63566C2212yes—
41#63564C2211yescharacteristic
42#63563C2211yescharacteristic
43#5732—31no—
44#5584—31no—
45#5579—31no—
46#5543—31no—
47C3×#461—31no—
48C3×C8×Q8—31no—
49#5165—32no—
50Dic3×SD16—32no—
51#5079—31no—
52C4×#213—31no—
53#4844—32no—
54#4842—31no—
55#4842—31no—
56#4842—61no—
57#4841D311yescharacteristic, complemented
58#4830D311yescharacteristic, complemented
59#4829—32no—
60#4800—32no—
61#4799—32no—
62#4697—32no—
63C4×D24—31no—
64C4×#204—32no—
65#4681—31no—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634—21no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2312yes—
73C2×D3×Dic3—22no—
74C2×C32×C8C2312yes—
75C32×C42C2311yescharacteristic
76#3752—21no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80C3×(C2×D3)⋊C4—21no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3D411yescharacteristic
84C3×C4⋊Dic3C2311yescharacteristic
85C3×Dic3⋊C4D412yes—
86C3×C4×Dic3C2312yes—
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×#204—24no—
90#3724—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93#3722—22no—
94#3722—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97#3714—22no—
98#3360—91noSylow
99C2×C3×SD16—32no—
100C3×C4⋊Q8—31no—
101C3×C4×Q8—31no—
102C3×C4×D4—31no—
103#947—32no—
104#946—61no—
105#946—61no—
106Q8×Dic3—32no—
107D4×Dic3—32no—
108C2×#213—31no—
109C2×C4⋊Dic3—61no—
110#924—61no—
111C2×D24—31no—
112C2×#204C2×D312yes—
113#898—62no—
114#898—62no—
115#897—61no—
116#896—62no—
117#892—61no—
118#892—61no—
119D3×C4⋊C4—61no—
120#890—32no—
121#878—62no—
122#875—32no—
123C4×D12—32no—
124C4×D12—31no—
125C4×D12—31no—
126C4×D12—61no—
127C4×D12C2×D311yescharacteristic
128#870—32no—
129#869—31no—
130#869—31no—
131#869—61no—
132#869C2×D311yescharacteristic
133C4×Dic6—32no—
134C4×Dic6C2×D311yescharacteristic
135C3×C4⋊C8—21no—
136C3×C4⋊C8—32no—
137C3×C4⋊C8C2×D311yescharacteristic
138C3×C4⋊C8C2×D311yescharacteristic
139C3×#103—32no—
140C3×C4×C8—32no—
141C3×C4×C8—31no—
142#835—32no—
143#835—32no—
144#832—31no—
145#821—31no—
146#821—32no—
147#821—32no—
148#821—31no—
149#821—62no—
150#818—31no—
151#817—32no—
152#817—32no—
153#817—62no—
154#816—32no—
155#816—32no—
156#816C2×D312yes—
157Dic3⋊C8C2×D312yes—
158C8×Dic3C2×D312yes—
159#809—31no—
160#807—31no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3⋊D3—21no—
163C22×C3×D3—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—22no—
169C4⋊(C3⋊D3)—21no—
170C4⋊(C3⋊D3)—21no—
171C4×C3⋊D3—42no—
172#634—81no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12#4112yes—
179C3×C4×D3—42no—
180C3×Dic6—22no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183D3×Dic3—82no—
184C32×C8—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#556—91no—
188#554—91no—
189#488—92no—
190#487—91no—
191#479—92no—
192#476—91no—
193#463—92no—
194#461—31no—
195C8×Q8—31no—
196C4×SD16—92no—
197C4×D8—91no—
198C2×C3×Q8—31no—
199C2×C3×Q8—32no—
200C2×C3×D4—31no—
201C22×C3×C4—61no—
202C22×Dic3—62no—
203C2×D12—31no—
204C2×D12—31no—
205C2×D12—61no—
206C2×D12C22×D311yescharacteristic
207C2×C4×D3—21no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—62no—
211C2×C4×D3—121no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—121no—
215C2×Dic6D1211yescharacteristic
216C2×Dic6C22×D312yes—
217C3×SD16—64no—
218C2×C3×C8—22no—
219C2×C3×C8—31no—
220C2×C3×C8—31no—
221C2×C3×C8C22×D312yes—
222C2×C3×C8C22×D312yes—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C22⋊C4—61no—
229C3×C42—21no—
230C3×C42—32no—
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233#217—62no—
234#213—62no—
235(C2×D3)⋊C4—21no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—61no—
240(C2×D3)⋊C4—61no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—121no—
244C4⋊Dic3—21no—
245C4⋊Dic3—21no—
246C4⋊Dic3—31no—
247C4⋊Dic3—32no—
248C4⋊Dic3—31no—
249C4⋊Dic3—32no—
250C4⋊Dic3—61no—
251C4⋊Dic3—62no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256C4⋊Dic3—121no—
257C4⋊Dic3D1211yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4D1212yes—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C4×Dic3C22×D312yes—
267C2×C3⋊C8C22×D311yescharacteristic
268C2×C3⋊C8C22×D311yescharacteristic
269D24—62no—
270#204—24no—
271C22×C32C22×D411yescharacteristic
272C2×C3⋊D3—41no—
273C2×C3⋊D3—41no—
274C2×C3⋊D3—41no—
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4#13512yes—
280C32×C4C2×#4111yescharacteristic
281C32×C42−1+411yescharacteristic
282C3⋊Dic3—41no—
283C3⋊Dic3—42no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—41no—
288C2×SD16—32no—
289C2×D8—91no—
290C4⋊Q8—31no—
291C4⋊Q8—91no—
292#126—182no—
293#125—92no—
294#124—92no—
295C22⋊Q8—182no—
296C22⋊Q8—181no—
297C22⋊Q8—181no—
298C4×Q8—31no—
299C4×Q8—92no—
300C4×D4—31no—
301C4×D4—92no—
302C4×D4—91no—
303#117—181no—
304C2×C4⋊C4—181no—
305#107—91no—
306#106—92no—
307C4⋊C8—32no—
308C4⋊C8D3211yescharacteristic
309#103—32no—
310#103—92no—
311#103—92no—
312#102—91no—
313#102—91no—
314#102—92no—
315C4×C8—32no—
316C4×C8—31no—
317C23×C3—61no—
318C22×D3—21no—
319C22×D3—61no—
320C22×D3—61no—
321C22×D3—121no—
322C3×Q8—62no—
323C3×Q8—62no—
324C3×Q8—62no—
325C3×D4—32no—
326C3×D4—61no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—62no—
333C2×C3×C4—61no—
334C2×C3×C4—122no—
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×Dic3—22no—
342C2×Dic3—21no—
343C2×Dic3—61no—
344C2×Dic3—62no—
345C2×Dic3—61no—
346C2×Dic3—62no—
347C2×Dic3—122no—
348C2×Dic3—121no—
349C2×Dic3—242no—
350C2×Dic3C2×D1212yes—
351C2×Dic3C2×D1212yes—
352D12—21no—
353D12—62no—
354D12—61no—
355D12—61no—
356D12—61no—
357D12—61no—
358D12—121no—
359D12#23712yes—
360C4×D3—42no—
361C4×D3—122no—
362C4×D3—122no—
363C4×D3—242no—
364C4×D3—242no—
365Dic6—22no—
366Dic6—22no—
367Dic6—22no—
368Dic6—241no—
369Dic6—241no—
370Dic6—242no—
371C3×C8—22no—
372C3×C8—22no—
373C3×C8—42no—
374C3×C8—61no—
375C3×C8—61no—
376C3⋊C8—21no—
377C3⋊C8—21no—
378C2×C32#54811yescharacteristic
379C2×C32C2×#13511yescharacteristic
380C2×C32#57711yescharacteristic
381C3⋊D3—81no—
382C3×D3—42no—
383C2×Q8—31no—
384C2×Q8—32no—
385C2×Q8—181no—
386C2×D4—31no—
387C2×D4—91no—
388C22×C4—61no—
389C22×C4—182no—
390C22×C4—181no—
391SD16—64no—
392D8—182no—
393C2×C8—31no—
394C2×C8—31no—
395C2×C8C2×D3212yes—
396C4⋊C4—31no—
397C4⋊C4—32no—
398C4⋊C4—31no—
399C4⋊C4—61no—
400C4⋊C4—61no—
401C4⋊C4—92no—
402C4⋊C4—91no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—181no—
407C22⋊C4—61no—
408C22⋊C4—182no—
409C22⋊C4—182no—
410C22⋊C4—182no—
411C22⋊C4—181no—
412C42—32no—
413C42—182no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3—62no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3C22×D1211yescharacteristic
420C22×C3C2×D3×D411yescharacteristic
421C2×D3—22no—
422C2×D3—41no—
423C2×D3—41no—
424C2×D3—122no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—241no—
432C2×D3—241no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—22no—
438C3×C4—41no—
439C3×C4—62no—
440C3×C4—62no—
441C3×C4—121no—
442C3×C4—122no—
443C3×C4#90412yes—
444C3×C4#91612yes—
445C3×C4C2×#23711yescharacteristic
446C3×C4#100711yescharacteristic
447C3×C4D3×#4111yescharacteristic
448C3×C4#101011yescharacteristic
449Dic3—22no—
450Dic3—22no—
451Dic3—41no—
452Dic3—42no—
453Dic3—121no—
454Dic3—122no—
455Dic3—121no—
456Dic3—122no—
457Dic3—242no—
458Dic3—241no—
459C32#336011yescharacteristic, complemented, Sylow
460C23—61no—
461C23—181no—
462Q8—62no—
463Q8—62no—
464Q8—62no—
465Q8—721no—
466D4—32no—
467D4—61no—
468D4—181no—
469D4—181no—
470C2×C4—32no—
471C2×C4—32no—
472C2×C4—62no—
473C2×C4—61no—
474C2×C4—122no—
475C2×C4—181no—
476C2×C4—182no—
477C2×C4—362no—
478C2×C4—722no—
479C2×C4D3×D1211yescharacteristic
480C2×C4D3×D1211yescharacteristic
481C2×C4C22×D3211yescharacteristic
482C8—22no—
483C8—61no—
484C8—61no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—122no—
489C2×C3#557611yescharacteristic
490C2×C3#559811yescharacteristic
491C2×C3C2×#90411yescharacteristic
492C2×C3#575111yescharacteristic
493C2×C3C2×#91611yescharacteristic
494C2×C3#577811yescharacteristic
495D3—42no—
496D3—242no—
497D3—241no—
498D3—241no—
499C22—62no—
500C22—121no—
501C22—121no—
502C22—361no—
503C22—361no—
504C22—361no—
505C22C2×D3×D1211yescharacteristic
506C4—21no—
507C4—62no—
508C4—62no—
509C4—122no—
510C4—121no—
511C4—361no—
512C4—362no—
513C4#6380612yes—
514C4D3×#23711yescharacteristic
515C4#6431511yescharacteristic
516C3—21no—
517C3#7992611yescharacteristic, complemented
518C3#8041511yescharacteristic, complemented
519C2—122no—
520C2—721no—
521C2#1059438211yescharacteristic
522C2C2×#6380611yescharacteristic
523C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4⋊C8D32
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593960C2semidirect
2. #10593865C2semidirect
3. #10592541C2semidirect
4. C3×#4841C2semidirect
5. C3×#4830C2semidirect
6. #10590872C2semidirect
7. #10590815C2semidirect
8. Dic3×#204C2semidirect
11. #10590287C2semidirect
57. #4841D3semidirect
58. #4830D3semidirect
459. C32#3360semidirect
517. C3#79926semidirect
518. C3#80415semidirect

Maximal subgroups

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

subgroupindex
#105939602
#105938652
#105925412
C3×#48412
C3×#48302
#105908722
#105908152
Dic3×#2042
#105907542
C4×#37142
#105902872
#804153
#799263