Finite Group Databasebeta

← #11896077

Subgroups — #11896077

Order 1152.

737 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593865C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3C4×#3744C211yesmaximal, characteristic
4C3×#4681C211yesmaximal, characteristic, complemented
5C3×#4679C211yesmaximal, characteristic, complemented
6#10590893C212yesmaximal
7#10590813C212yesmaximal
8#10590803C212yesmaximal, complemented
9#10590794C212yesmaximal, complemented
10#10590388C211yesmaximal, characteristic, complemented
11#10590300C211yesmaximal, characteristic
12#81626—31nomaximal
13#79981—31nomaximal
14C2×#3744C2211yescharacteristic
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63919—21no—
21#63918C2212yes—
22#63871—21no—
23#63864C2212yes—
24#63849—21no—
25#63848—22no—
26#63844C2212yes—
27#63843—21no—
28Dic3×Dic6C2212yes—
29#63839—22no—
30C2×#3719C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2211yescharacteristic
33#63644C2211yescharacteristic
34#63643C2211yescharacteristic
35C3×#816C2212yes—
36C3×#816C2212yes—
37C3×#815C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63566C2212yes—
42#63564C2212yes—
43#5732—31no—
44#5722—31no—
45#5584—31no—
46Q8×Dic6—31no—
47C3×#487—31no—
48C3×#446—31no—
49#5090—31no—
50#5084—31no—
51#4851—32no—
52#4849—31no—
53#4845—32no—
54#4842—31no—
55#4798—32no—
56#4794—32no—
57#4791—32no—
58#4789—32no—
59#4716—32no—
60#4714—32no—
61C4×#204—31no—
62C4×#204—31no—
63C4×#204—61no—
64#4681D311yescharacteristic, complemented
65#4679D311yescharacteristic, 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×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75C32×C42C2311yescharacteristic
76#3752—21no—
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—21no—
80C4×C3⋊Dic3—21no—
81#3744—22no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2312yes—
87C3×Dic3⋊C4D412yes—
88C3×C4×Dic3C2312yes—
89C2×C3×C3⋊C8C2312yes—
90#3724—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93#3722—22no—
94#3722—22no—
95Dic32—22no—
96Dic32—22no—
97#3719—24no—
98#3369—91noSylow
99C3×C4⋊Q8—31no—
100C3×C4⋊Q8—31no—
101C3×C4×Q8—31no—
102#947—32no—
103#946—61no—
104Q8×Dic3—32no—
105Q8×Dic3—61no—
106#944—62no—
107C2×#216—32no—
108C2×Dic12—32no—
109C2×#204—31no—
110C2×#204—31no—
111C2×#204—61no—
112#898—62no—
113#898—62no—
114#897—61no—
115#892—61no—
116#892—61no—
117#888—32no—
118#888—61no—
119#888—62no—
120#888—61no—
121#887—32no—
122#887—61no—
123#875—32no—
124C4×D12—31no—
125C4×D12—31no—
126C4×D12—61no—
127#869—32no—
128#869C2×D311yescharacteristic
129#869C2×D311yescharacteristic
130C4×Dic6—32no—
131C4×Dic6—31no—
132C4×Dic6—31no—
133C4×Dic6—32no—
134C4×Dic6—61no—
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—32no—
137C3×C4⋊C8—31no—
138C3×#103—32no—
139C3×#103—32no—
140C3×#97—32no—
141C3×C4×C8—21no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#835—32no—
145#821—31no—
146#821—31no—
147#821—32no—
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—61no—
157#816C2×D312yes—
158#816C2×D312yes—
159#815C2×D312yes—
160Dic3⋊C8C2×D312yes—
161#809—32no—
162#808—32no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C22×C3⋊D3—21no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C4⋊(C3⋊D3)—21no—
172C4⋊(C3⋊D3)—21no—
173C4×C3⋊D3—42no—
174#634—21no—
175#634#4112yes—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×Dic6—22no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—81no—
184#627—82no—
185C32×C8—21no—
186C32×C8—21no—
187C3×C3⋊C8—22no—
188Q82—91no—
189#556—91no—
190#489—92no—
191#487—31no—
192#476—91no—
193#475—92no—
194#464—92no—
195#462—91no—
196#446—31no—
197#441—92no—
198C4×SD16—91no—
199C2×C3×Q8—31no—
200C2×C3×Q8—32no—
201C2×C3×Q8—61no—
202C2×D12—31no—
203C2×D12—31no—
204C2×D12—61no—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×C4×D3—121no—
208C2×Dic6—21no—
209C2×Dic6—31no—
210C2×Dic6—31no—
211C2×Dic6—61no—
212C2×Dic6—62no—
213C2×Dic6—62no—
214C2×Dic6D1211yescharacteristic
215C2×Dic6C22×D312yes—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—32no—
219C2×C3×C8C22×D311yescharacteristic
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C22×D311yescharacteristic
222C2×C3×C8C22×D311yescharacteristic
223C3×C4⋊C4—31no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C42—21no—
230C3×C42—32no—
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233#216—64no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—61no—
237(C2×D3)⋊C4—61no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—121no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3—21no—
244C4⋊Dic3—31no—
245C4⋊Dic3—31no—
246C4⋊Dic3—31no—
247C4⋊Dic3—31no—
248C4⋊Dic3—61no—
249C4⋊Dic3—61no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252C4⋊Dic3D1211yescharacteristic
253C4⋊Dic3C22×D312yes—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—61no—
257Dic3⋊C4—61no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—121no—
261Dic3⋊C4D1212yes—
262C4×Dic3—62no—
263C4×Dic3—62no—
264C4×Dic3—61no—
265C4×Dic3—61no—
266C4×Dic3—62no—
267C4×Dic3—62no—
268C4×Dic3—121no—
269C4×Dic3C22×D312yes—
270C2×C3⋊C8C22×D312yes—
271Dic12—64no—
272#204—62no—
273#204—62no—
274#204—64no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C32×C4—21no—
280C32×C4#13712yes—
281C32×C4C2×#4111yescharacteristic
282C32×C42−1+411yescharacteristic
283C3⋊Dic3—22no—
284C3⋊Dic3—41no—
285C3⋊Dic3—41no—
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—42no—
289C3×Dic3—42no—
290C2×Q16—92no—
291C2×SD16—91no—
292C4⋊Q8—31no—
293C4⋊Q8—31no—
294C4⋊Q8—92no—
295C4⋊Q8—181no—
296C4⋊Q8—182no—
297#126—182no—
298#124—92no—
299C22⋊Q8—181no—
300C4×Q8—31no—
301C4×Q8—92no—
302C4×Q8—92no—
303C4×Q8—91no—
304C4×Q8—181no—
305C4×D4—91no—
306#117—181no—
307#106—92no—
308#106—91no—
309C4⋊C8—32no—
310C4⋊C8—31no—
311#103—32no—
312#103—32no—
313#103—92no—
314#103—91no—
315#102—92no—
316#102—91no—
317#97—32no—
318C4×C8D3211yescharacteristic
319C22×D3—61no—
320C22×D3—61no—
321C22×D3—121no—
322C3×Q8—62no—
323C3×Q8—62no—
324C3×Q8—62no—
325C3×Q8—241no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—32no—
330C2×C3×C4—32no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3C2×D1212yes—
351C2×Dic3C2×D1212yes—
352D12—62no—
353D12—61no—
354D12—61no—
355D12—61no—
356D12—61no—
357D12—121no—
358C4×D3—122no—
359C4×D3—122no—
360C4×D3—242no—
361Dic6—22no—
362Dic6—22no—
363Dic6—22no—
364Dic6—32no—
365Dic6—32no—
366Dic6—62no—
367Dic6—61no—
368Dic6—61no—
369Dic6—81no—
370Dic6—121no—
371Dic6—242no—
372Dic6—242no—
373C3×C8—22no—
374C3×C8—21no—
375C3×C8—21no—
376C3×C8—21no—
377C3×C8—21no—
378C3×C8—41no—
379C3×C8—62no—
380C3⋊C8—22no—
381C2×C32#54811yescharacteristic
382C2×C32C2×#13711yescharacteristic
383C2×C32#57711yescharacteristic
384C3⋊D3—81no—
385C2×Q8—31no—
386C2×Q8—32no—
387C2×Q8—61no—
388C2×Q8—91no—
389C2×Q8—182no—
390C2×D4—91no—
391C22×C4—181no—
392Q16—184no—
393SD16—182no—
394C2×C8—32no—
395C2×C8C2×D3211yescharacteristic
396C2×C8C2×D3211yescharacteristic
397C4⋊C4—31no—
398C4⋊C4—32no—
399C4⋊C4—32no—
400C4⋊C4—61no—
401C4⋊C4—61no—
402C4⋊C4—61no—
403C4⋊C4—91no—
404C4⋊C4—91no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C4⋊C4—181no—
409C22⋊C4—182no—
410C22⋊C4—182no—
411C22⋊C4—181no—
412C42—32no—
413C42—182no—
414C42—182no—
415C42—181no—
416C42C2×D3211yescharacteristic
417C22×C3—21no—
418C22×C3C22×D1211yescharacteristic
419C22×C3C2×D3×D411yescharacteristic
420C2×D3—122no—
421C2×D3—121no—
422C2×D3—121no—
423C2×D3—121no—
424C2×D3—121no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—241no—
428C2×D3—241no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—22no—
434C3×C4—41no—
435C3×C4—62no—
436C3×C4—62no—
437C3×C4—122no—
438C3×C4—122no—
439C3×C4#90912yes—
440C3×C4#91812yes—
441C3×C4#100711yescharacteristic
442C3×C4D3×#4111yescharacteristic
443C3×C4D3×#4111yescharacteristic
444C3×C4#101011yescharacteristic
445Dic3—22no—
446Dic3—22no—
447Dic3—42no—
448Dic3—42no—
449Dic3—62no—
450Dic3—62no—
451Dic3—122no—
452Dic3—121no—
453Dic3—121no—
454Dic3—121no—
455Dic3—121no—
456Dic3—241no—
457Dic3—241no—
458C32#336911yescharacteristic, complemented, Sylow
459C23—181no—
460Q8—62no—
461Q8—62no—
462Q8—62no—
463Q8—92no—
464Q8—181no—
465Q8—241no—
466Q8—722no—
467D4—181no—
468D4—181no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—362no—
477C2×C4D3×D1211yescharacteristic
478C2×C4D3×D1211yescharacteristic
479C2×C4C22×D3211yescharacteristic
480C8—21no—
481C8—21no—
482C8—62no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3#557611yescharacteristic
487C2×C3#567711yescharacteristic
488C2×C3C2×#90911yescharacteristic
489C2×C3#575111yescharacteristic
490C2×C3#576211yescharacteristic
491C2×C3C2×#91811yescharacteristic
492D3—242no—
493D3—241no—
494D3—241no—
495C22—361no—
496C22—361no—
497C22—361no—
498C22C2×D3×D1211yescharacteristic
499C4—21no—
500C4—62no—
501C4—62no—
502C4—122no—
503C4—122no—
504C4—182no—
505C4—361no—
506C4—361no—
507C4#6380112yes—
508C4#6429711yescharacteristic
509C4#6430611yescharacteristic
510C3—21no—
511C3#7998111yescharacteristic, complemented
512C3#8162611yescharacteristic, complemented
513C2—721no—
514C2#1059390111yescharacteristic
515C2#1059467711yescharacteristic
516C2C2×#6380111yescharacteristic
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#3369
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. #10593856C2semidirect
4. C3×#4681C2semidirect
5. C3×#4679C2semidirect
8. #10590803C2semidirect
9. #10590794C2semidirect
10. #10590388C2semidirect
64. #4681D3semidirect
65. #4679D3semidirect
458. C32#3369semidirect
511. C3#79981semidirect
512. C3#81626semidirect

Maximal subgroups

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

subgroupindex
#105938652
#105938562
C4×#37442
C3×#46812
C3×#46792
#105908932
#105908132
#105908032
#105907942
#105903882
#105903002
#816263
#799813