Finite Group Databasebeta

← #11895168

Subgroups — #11895168

Order 1152.

801 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593903C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3C4×#3744C211yesmaximal, characteristic
4C3×#4681C211yesmaximal, characteristic, complemented
5C3×C8×Dic6C211yesmaximal, characteristic, complemented
6#10590890C212yesmaximal, complemented
7#10590803C212yesmaximal, complemented
8#10590792C212yesmaximal
9#10590760C212yesmaximal
10#10590379C211yesmaximal, characteristic
11#10590307C211yesmaximal, characteristic, complemented
12#81620—31nomaximal
13#79925—31nomaximal
14C2×#3797—21no—
15C2×#3744C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63918C2212yes—
22#63895—22no—
23#63894C2212yes—
24#63872—21no—
25#63871—21no—
26#63866C2212yes—
27#63846—22no—
28#63843—21no—
29Dic3×Dic6C2212yes—
30C2×#3717C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2211yescharacteristic
33#63644C2211yescharacteristic
34#63643C2211yescharacteristic
35C3×#816C2212yes—
36C3×#816C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×C8×Dic3C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63567C2212yes—
42#63566C2212yes—
43#5727—31no—
44#5721—31no—
45Q8×D12—31no—
46#5570—31no—
47C3×#487—31no—
48C3×C8×Q8—31no—
49#5094—31no—
50#5083—31no—
51#4851—31no—
52#4851—32no—
53#4841—31no—
54#4841—32no—
55#4818—32no—
56#4792—32no—
57#4791—32no—
58#4788—32no—
59C4×#204—31no—
60C4×#204—31no—
61C4×#204—32no—
62C4×#204—61no—
63#4681—32no—
64#4681D311yescharacteristic, complemented
65C8×Dic6D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2311yescharacteristic
69C2×C3×Dic6—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2312yes—
72C2×#627—22no—
73C2×#624—22no—
74#3797—44no—
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C42C2311yescharacteristic
78#3752—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82C4×C3⋊Dic3—21no—
83#3744—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2312yes—
92Dic3⋊Dic3—22no—
93Dic3⋊Dic3—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97Dic32—22no—
98#3717—24no—
99#3359—91noSylow
100C2×D3×Q8—61no—
101C2×D3×Q8—61no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8—31no—
104C3×C4×Q8—31no—
105#946—61no—
106Q8×Dic3—32no—
107Q8×Dic3—61no—
108#944—32no—
109C2×#215—32no—
110C2×#204—32no—
111C2×#204—31no—
112C2×#204—31no—
113C2×#204—61no—
114#897—62no—
115#897—61no—
116#896—62no—
117#893—32no—
118#890—62no—
119#890—61no—
120#890—61no—
121#889—62no—
122#888—32no—
123#887—61no—
124C4×D12—31no—
125C4×D12—31no—
126C4×D12—32no—
127C4×D12—61no—
128#869—32no—
129#869—32no—
130#869C2×D311yescharacteristic
131#869C2×D311yescharacteristic
132C4×Dic6—32no—
133C4×Dic6—31no—
134C4×Dic6—31no—
135C4×Dic6—61no—
136C4×Dic6C2×D311yescharacteristic
137C3×C4⋊C8—32no—
138C3×C4⋊C8—31no—
139C3×#103—32no—
140C3×#103—32no—
141C3×C4×C8—21no—
142C3×C4×C8—32no—
143C3×C4×C8C2×D311yescharacteristic
144C3×C4×C8C2×D311yescharacteristic
145#835—32no—
146#821—31no—
147#821—31no—
148#821—61no—
149#817—31no—
150#817—31no—
151#817—32no—
152#817—61no—
153#816—32no—
154#816—31no—
155#816—31no—
156#816—32no—
157#816—61no—
158#816C2×D312yes—
159#816C2×D312yes—
160Dic3⋊C8C2×D312yes—
161C8×Dic3C2×D312yes—
162#810—32no—
163#808—32no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C4⋊(C3⋊D3)—21no—
173C4⋊(C3⋊D3)#4112yes—
174C4×C3⋊D3—42no—
175#634—21no—
176#634—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—42no—
184C3×Dic6SD1614yescomplemented
185#627—44no—
186#624—44no—
187C32×C8—21no—
188C32×C8—21no—
189C3×C3⋊C8—22no—
190#557—91no—
191D4×Q8—91no—
192#487—31no—
193#487—92no—
194#475—92no—
195#475—91no—
196#461—92no—
197#461—91no—
198C8×Q8—31no—
199C4×SD16—92no—
200C4×SD16—91no—
201C2×C3×Q8—31no—
202C2×C3×Q8—32no—
203C2×C3×Q8—61no—
204D3×Q8—124no—
205D3×Q8—124no—
206C2×D12—31no—
207C2×D12—31no—
208C2×D12—61no—
209C2×C4×D3—62no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3—62no—
213C2×C4×D3—121no—
214C2×Dic6—21no—
215C2×Dic6—31no—
216C2×Dic6—31no—
217C2×Dic6—61no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6D1211yescharacteristic
221C2×Dic6C22×D312yes—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—32no—
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C3×C4⋊C4—32no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—61no—
235C3×C42—21no—
236C3×C42—32no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#215—64no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—61no—
242(C2×D3)⋊C4—61no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—121no—
245C4⋊Dic3—21no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4⋊Dic3—31no—
249C4⋊Dic3—31no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256C4⋊Dic3—62no—
257C4⋊Dic3—62no—
258C4⋊Dic3D1211yescharacteristic
259C4⋊Dic3C22×D312yes—
260Dic3⋊C4—62no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—121no—
267Dic3⋊C4D1212yes—
268C4×Dic3—62no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—62no—
272C4×Dic3—121no—
273C4×Dic3C22×D312yes—
274C2×C3⋊C8C22×D312yes—
275#204—62no—
276#204—62no—
277#204—64no—
278#204—64no—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—22no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C32×C4—21no—
284C32×C4C2×SD1612yes—
285C32×C4C2×#4111yescharacteristic
286C32×C42−1+411yescharacteristic
287C3⋊Dic3—41no—
288C3⋊Dic3—41no—
289C3⋊Dic3—41no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3—42no—
293C3×Dic3C2×SD1614yes—
294C22×Q8—181no—
295C2×SD16—92no—
296C2×SD16—91no—
297C4⋊Q8—31no—
298C4⋊Q8—31no—
299C4⋊Q8—92no—
300C4⋊Q8—92no—
301#125—182no—
302#125—181no—
303C22⋊Q8—182no—
304C22⋊Q8—181no—
305C4×Q8—31no—
306C4×Q8—92no—
307C4×Q8—91no—
308C4×Q8—181no—
309C4×D4—92no—
310C4×D4—91no—
311#106—92no—
312#106—91no—
313C4⋊C8—32no—
314C4⋊C8—31no—
315#103—32no—
316#103—32no—
317#103—92no—
318#103—92no—
319#103—91no—
320#102—91no—
321C4×C8—32no—
322C4×C8D3211yescharacteristic
323C22×D3—61no—
324C22×D3—61no—
325C22×D3—121no—
326C3×Q8—34no—
327C3×Q8—62no—
328C3×Q8—62no—
329C3×Q8—122no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3C2×D1212yes—
355C2×Dic3C2×D1212yes—
356D12—32no—
357D12—32no—
358D12—62no—
359D12—61no—
360D12—61no—
361D12—121no—
362C4×D3—124no—
363C4×D3—122no—
364C4×D3—122no—
365C4×D3—124no—
366C4×D3—242no—
367Dic6—22no—
368Dic6—22no—
369Dic6—42no—
370Dic6—62no—
371Dic6—61no—
372Dic6—61no—
373Dic6—61no—
374Dic6—61no—
375Dic6—121no—
376Dic6—124no—
377Dic6—124no—
378Dic6#20414yescomplemented
379C3×C8—22no—
380C3×C8—21no—
381C3×C8—21no—
382C3×C8—21no—
383C3×C8—21no—
384C3×C8—41no—
385C3×C8—62no—
386C3⋊C8—22no—
387C2×C32#54811yescharacteristic
388C2×C32C22×SD1611yescharacteristic
389C2×C32#57811yescharacteristic
390C3⋊D3—42no—
391C2×Q8—31no—
392C2×Q8—32no—
393C2×Q8—61no—
394C2×Q8—91no—
395C2×Q8—182no—
396C2×Q8—364no—
397C2×D4—91no—
398C22×C4—182no—
399C22×C4—181no—
400SD16—182no—
401SD16—184no—
402C2×C8—32no—
403C2×C8C2×D3211yescharacteristic
404C2×C8C2×D3211yescharacteristic
405C4⋊C4—32no—
406C4⋊C4—31no—
407C4⋊C4—32no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C4⋊C4—91no—
412C4⋊C4—91no—
413C4⋊C4—182no—
414C4⋊C4—182no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C4⋊C4—181no—
418C22⋊C4—182no—
419C22⋊C4—181no—
420C42—32no—
421C42—182no—
422C42—181no—
423C42C2×D3211yescharacteristic
424C22×C3—21no—
425C22×C3C22×D1211yescharacteristic
426C22×C3C2×D3×D411yescharacteristic
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—122no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—241no—
435C2×D3—241no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—21no—
441C3×C4—34no—
442C3×C4—41no—
443C3×C4—62no—
444C3×C4—122no—
445C3×C4—122no—
446C3×C4C2×#20412yes—
447C3×C4D3×SD1612yes—
448C3×C4#100711yescharacteristic
449C3×C4D3×#4111yescharacteristic
450C3×C4D3×#4111yescharacteristic
451C3×C4#101011yescharacteristic
452Dic3—22no—
453Dic3—42no—
454Dic3—42no—
455Dic3—122no—
456Dic3—121no—
457Dic3—121no—
458Dic3—121no—
459Dic3—121no—
460Dic3—121no—
461Dic3—121no—
462Dic3—241no—
463Dic3—241no—
464Dic3C2×#20414yes—
465C32#335911yescharacteristic, complemented, Sylow
466C23—181no—
467Q8—34no—
468Q8—62no—
469Q8—62no—
470Q8—122no—
471Q8—181no—
472Q8—181no—
473Q8—364no—
474D4—92no—
475D4—181no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—364no—
484C2×C4—362no—
485C2×C4D3×D1211yescharacteristic
486C2×C4D3×D1211yescharacteristic
487C2×C4C22×D3211yescharacteristic
488C8—21no—
489C8—21no—
490C8—62no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3#557611yescharacteristic
495C2×C3#567711yescharacteristic
496C2×C3C22×#20411yescharacteristic
497C2×C3#575311yescharacteristic
498C2×C3C2×D3×SD1611yescharacteristic
499C2×C3#576611yescharacteristic
500D3—122no—
501D3—122no—
502D3—242no—
503C22—182no—
504C22—361no—
505C22—361no—
506C22C2×D3×D1211yescharacteristic
507C4—21no—
508C4—34no—
509C4—62no—
510C4—122no—
511C4—122no—
512C4—361no—
513C4—361no—
514C4—361no—
515C4D3×#20412yes—
516C4#6429711yescharacteristic
517C4#6430611yescharacteristic
518C3—21no—
519C3#7992511yescharacteristic, complemented
520C3#8162011yescharacteristic, complemented
521C2—362no—
522C2#1059390111yescharacteristic
523C2C2×D3×#20411yescharacteristic
524C2#1059469111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterC4×C8D32
hypocenterC32#3359
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
2. #10593861C2semidirect
4. C3×#4681C2semidirect
5. C3×C8×Dic6C2semidirect
6. #10590890C2semidirect
7. #10590803C2semidirect
11. #10590307C2semidirect
64. #4681D3semidirect
65. C8×Dic6D3semidirect
184. C3×Dic6SD16semidirect
378. Dic6#204semidirect
465. C32#3359semidirect
519. C3#79925semidirect
520. C3#81620semidirect

Maximal subgroups

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

subgroupindex
#105939032
#105938612
C4×#37442
C3×#46812
C3×C8×Dic62
#105908902
#105908032
#105907922
#105907602
#105903792
#105903072
#816203
#799253