Finite Group Databasebeta

← #11895267

Subgroups — #11895267

Order 1152.

760 conjugacy classes of subgroups.

The subgroup lattice has 527 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593958C211yesmaximal, characteristic, complemented
2#10593879C211yesmaximal, characteristic, complemented
3#10592540C211yesmaximal, characteristic, complemented
4C3×#4842C211yesmaximal, characteristic, complemented
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590863C212yesmaximal, complemented
7#10590860C212yesmaximal
8#10590809C212yesmaximal, complemented
9#10590758C212yesmaximal, complemented
10C4×#3714C211yesmaximal, characteristic
11#10590288C211yesmaximal, characteristic, complemented
12#81087—31nomaximal
13#79926—31nomaximal
14C2×#3744C2212yes—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63900—21no—
21#63894C2212yes—
22#63888—22no—
23#63871—21no—
24#63869C2212yes—
25#63861—22no—
26#63860C2212yes—
27#63856—21no—
28#63844C2212yes—
29#63841—21no—
30C2×#3714C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63643C2212yes—
33C3×#821C2212yes—
34C3×#817C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×C8×Dic3C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2211yescharacteristic
39#63567C2212yes—
40#63567C2212yes—
41#63564C2211yescharacteristic
42#63563C2211yescharacteristic
43#5730—31no—
44#5584—31no—
45#5579—31no—
46#5542—31no—
47C3×#476—31no—
48C3×C8×Q8—31no—
49#5093—31no—
50C4×#213—31no—
51#4857—32no—
52#4852—32no—
53#4844—32no—
54#4842D311yescharacteristic, complemented
55#4841—31no—
56#4841—31no—
57#4841—61no—
58#4830D311yescharacteristic, complemented
59#4829—32no—
60#4787—32no—
61#4768—32no—
62#4697—32no—
63C4×D24—31no—
64C4×#204—32no—
65#4681—31no—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2312yes—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×#624—22no—
74C2×C32×C8C2312yes—
75C32×C42C2311yescharacteristic
76#3752—21no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3744—24no—
81C3×(C2×D3)⋊C4—21no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3D411yescharacteristic
84C3×C4⋊Dic3C2311yescharacteristic
85C3×C4⋊Dic3C2312yes—
86C3×Dic3⋊C4D412yes—
87C3×C4×Dic3C2312yes—
88C2×C3×C3⋊C8C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90#3724—22no—
91#3724—22no—
92Dic3⋊Dic3—22no—
93#3722—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97#3714—22no—
98#3360—91noSylow
99C3×C4⋊Q8—31no—
100C3×C4×Q8—31no—
101C3×C4×D4—31no—
102#946—61no—
103#946—61no—
104#946—62no—
105#936—32no—
106C2×#213—31no—
107#926—61no—
108#924—61no—
109C2×D24—31no—
110C2×#204—32no—
111C2×#204—32no—
112C2×#204—62no—
113#898—62no—
114#897—61no—
115#896—62no—
116#893—32no—
117#892—61no—
118D3×C4⋊C4—61no—
119D3×C4⋊C4—61no—
120#890—32no—
121#887—32no—
122#879—62no—
123#875—32no—
124C4×D12—31no—
125C4×D12—31no—
126C4×D12—32no—
127C4×D12—61no—
128C4×D12C2×D311yescharacteristic
129#870—32no—
130#869—31no—
131#869—31no—
132#869—61no—
133#869C2×D311yescharacteristic
134C4×Dic6—32no—
135C4×Dic6C2×D311yescharacteristic
136C3×#106—32no—
137C3×C4⋊C8—21no—
138C3×C4⋊C8—32no—
139C3×C4⋊C8C2×D311yescharacteristic
140C3×C4⋊C8C2×D311yescharacteristic
141C3×#102—32no—
142C3×C4×C8—32no—
143C3×C4×C8—31no—
144#832—31no—
145#821—31no—
146#821—31no—
147#821C2×D312yes—
148#818—31no—
149#817C2×D312yes—
150#816—32no—
151#816—32no—
152#816—32no—
153#816—32no—
154#816—62no—
155Dic3⋊C8C2×D312yes—
156C8×Dic3C2×D312yes—
157#810—32no—
158#810—32no—
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—22no—
168C2×C3⋊Dic3—21no—
169C4⋊(C3⋊D3)—21no—
170C4⋊(C3⋊D3)#4112yes—
171C4×C3⋊D3—42no—
172#634—22no—
173#634—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—21no—
179C3×D12—21no—
180C3×C4×D3—42no—
181C3×Dic6—22no—
182C3×Dic6—81no—
183#624—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—31no—
193#463—92no—
194#461—91no—
195C8×Q8—31no—
196C4×SD16—92no—
197C4×D8—91no—
198C2×C3×Q8—31no—
199C2×C3×Q8—61no—
200C2×C3×D4—31no—
201C22×C3×C4—61no—
202C2×D12—31no—
203C2×D12—31no—
204C2×D12—61no—
205C2×D12C22×D311yescharacteristic
206C2×C4×D3—21no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—121no—
212C2×Dic6—21no—
213C2×Dic6—32no—
214C2×Dic6—32no—
215C2×Dic6—62no—
216C2×Dic6D1211yescharacteristic
217C2×C3×C8—22no—
218C2×C3×C8—31no—
219C2×C3×C8—31no—
220C2×C3×C8C22×D312yes—
221C2×C3×C8C22×D312yes—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—61no—
227C3×C22⋊C4—61no—
228C3×C42—21no—
229C3×C42—32no—
230C3×C42C22×D311yescharacteristic
231C3×C42C22×D311yescharacteristic
232#217—62no—
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—121no—
243C4⋊Dic3—21no—
244C4⋊Dic3—31no—
245C4⋊Dic3—31no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3—61no—
249C4⋊Dic3—61no—
250C4⋊Dic3—61no—
251C4⋊Dic3—62no—
252C4⋊Dic3—121no—
253C4⋊Dic3—121no—
254C4⋊Dic3D1211yescharacteristic
255C4⋊Dic3C22×D312yes—
256C4⋊Dic3C22×D311yescharacteristic
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4D1212yes—
263C4×Dic3—62no—
264C4×Dic3—62no—
265C4×Dic3C22×D312yes—
266C2×C3⋊C8C22×D311yescharacteristic
267C2×C3⋊C8C22×D311yescharacteristic
268D24—62no—
269#204—64no—
270#204—64no—
271#204—124no—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—22no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C32×C4—21no—
280C32×C4#13512yes—
281C32×C4C2×#4111yescharacteristic
282C32×C42−1+411yescharacteristic
283C3⋊Dic3—42no—
284C3⋊Dic3—41no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—41no—
288C3×Dic3—42no—
289C2×SD16—92no—
290C2×D8—91no—
291C4⋊Q8—31no—
292C4⋊Q8—91no—
293#126—182no—
294#125—92no—
295#124—92no—
296C22⋊Q8—182no—
297C22⋊Q8—181no—
298C22⋊Q8—181no—
299C4×Q8—31no—
300C4×Q8—92no—
301C4×D4—31no—
302C4×D4—92no—
303C4×D4—91no—
304#117—181no—
305C2×C4⋊C4—181no—
306#107—91no—
307#106—32no—
308C4⋊C8—32no—
309C4⋊C8D3211yescharacteristic
310#103—92no—
311#103—92no—
312#103—92no—
313#102—32no—
314#102—91no—
315#102—91no—
316C4×C8—32no—
317C4×C8—31no—
318C23×C3—61no—
319C22×D3—21no—
320C22×D3—61no—
321C22×D3—61no—
322C22×D3—121no—
323C3×Q8—62no—
324C3×Q8—241no—
325C3×D4—61no—
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—61no—
333C2×C3×C4—62no—
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—21no—
342C2×Dic3—22no—
343C2×Dic3—62no—
344C2×Dic3—61no—
345C2×Dic3—62no—
346C2×Dic3—61no—
347C2×Dic3—121no—
348C2×Dic3—122no—
349C2×Dic3C2×D1212yes—
350C2×Dic3C2×D1212yes—
351D12—21no—
352D12—21no—
353D12—32no—
354D12—32no—
355D12—62no—
356D12—61no—
357D12—61no—
358D12—121no—
359C4×D3—42no—
360C4×D3—122no—
361C4×D3—122no—
362C4×D3—242no—
363C4×D3—242no—
364C4×D3—242no—
365Dic6—22no—
366Dic6—62no—
367Dic6—62no—
368Dic6—62no—
369Dic6—62no—
370Dic6—81no—
371Dic6—122no—
372Dic6—122no—
373C3×C8—22no—
374C3×C8—22no—
375C3×C8—42no—
376C3×C8—61no—
377C3×C8—61no—
378C3⋊C8—21no—
379C3⋊C8—21no—
380C2×C32#54811yescharacteristic
381C2×C32C2×#13511yescharacteristic
382C2×C32#57711yescharacteristic
383C3⋊D3—42no—
384C3×D3—81no—
385C2×Q8—31no—
386C2×Q8—61no—
387C2×Q8—92no—
388C2×D4—31no—
389C2×D4—91no—
390C22×C4—61no—
391C22×C4—182no—
392C22×C4—181no—
393SD16—184no—
394D8—182no—
395C2×C8—31no—
396C2×C8—31no—
397C2×C8C2×D3212yes—
398C4⋊C4—31no—
399C4⋊C4—32no—
400C4⋊C4—32no—
401C4⋊C4—31no—
402C4⋊C4—61no—
403C4⋊C4—91no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C22⋊C4—61no—
410C22⋊C4—182no—
411C22⋊C4—182no—
412C22⋊C4—182no—
413C22⋊C4—181no—
414C42—32no—
415C42—182no—
416C42C2×D3211yescharacteristic
417C22×C3—21no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3C22×D1211yescharacteristic
422C22×C3C2×D3×D411yescharacteristic
423C2×D3—41no—
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—122no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—241no—
434C2×D3—241no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—41no—
441C3×C4—62no—
442C3×C4—62no—
443C3×C4—121no—
444C3×C4—122no—
445C3×C4#90412yes—
446C3×C4#91612yes—
447C3×C4#100711yescharacteristic
448C3×C4#100711yescharacteristic
449C3×C4D3×#4111yescharacteristic
450C3×C4D3×#4111yescharacteristic
451Dic3—22no—
452Dic3—22no—
453Dic3—41no—
454Dic3—42no—
455Dic3—122no—
456Dic3—121no—
457Dic3—121no—
458Dic3—122no—
459Dic3—242no—
460Dic3—241no—
461C32#336011yescharacteristic, complemented, Sylow
462C23—61no—
463C23—181no—
464Q8—62no—
465Q8—182no—
466Q8—182no—
467Q8—241no—
468D4—61no—
469D4—61no—
470D4—92no—
471D4—181no—
472C2×C4—32no—
473C2×C4—32no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—122no—
477C2×C4—182no—
478C2×C4—181no—
479C2×C4—362no—
480C2×C4—722no—
481C2×C4D3×D1211yescharacteristic
482C2×C4D3×D1211yescharacteristic
483C2×C4C22×D3211yescharacteristic
484C8—22no—
485C8—61no—
486C8—61no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—241no—
491C2×C3#557611yescharacteristic
492C2×C3#563311yescharacteristic
493C2×C3C2×#90411yescharacteristic
494C2×C3#575111yescharacteristic
495C2×C3C2×#91611yescharacteristic
496C2×C3#577511yescharacteristic
497D3—81no—
498D3—122no—
499D3—122no—
500D3—242no—
501C22—121no—
502C22—121no—
503C22—121no—
504C22—182no—
505C22—361no—
506C22—361no—
507C22C2×D3×D1211yescharacteristic
508C4—21no—
509C4—62no—
510C4—62no—
511C4—121no—
512C4—122no—
513C4—362no—
514C4—361no—
515C4#6380612yes—
516C4#6431211yescharacteristic
517C4#6431611yescharacteristic
518C3—21no—
519C3#7992611yescharacteristic, complemented
520C3#8108711yescharacteristic, complemented
521C2—241no—
522C2—362no—
523C2#1059432911yescharacteristic
524C2C2×#6380611yescharacteristic
525C2#1059471311yescharacteristic
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. #10593958C2semidirect
2. #10593879C2semidirect
3. #10592540C2semidirect
4. C3×#4842C2semidirect
5. C3×#4830C2semidirect
6. #10590863C2semidirect
8. #10590809C2semidirect
9. #10590758C2semidirect
11. #10590288C2semidirect
54. #4842D3semidirect
58. #4830D3semidirect
461. C32#3360semidirect
519. C3#79926semidirect
520. C3#81087semidirect

Maximal subgroups

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

subgroupindex
#105939582
#105938792
#105925402
C3×#48422
C3×#48302
#105908632
#105908602
#105908092
#105907582
C4×#37142
#105902882
#810873
#799263