Finite Group Databasebeta

← #11878899

Subgroups — #11878899

Order 1152.

817 conjugacy classes of subgroups.

The subgroup lattice has 463 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#869C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic
3#10592380C211yesmaximal, characteristic, complemented
4C3×#4699C211yesmaximal, characteristic, complemented
5C3×#4685C211yesmaximal, characteristic
6#10590949C214yesmaximal
7#10590800C214yesmaximal, complemented
8#10590386C211yesmaximal, characteristic, complemented
9#10590287C211yesmaximal, characteristic, complemented
10#81802—31nomaximal
11#79313—31nomaximal
12C2×D3×Dic6C2212yes—
13#64078C2211yescharacteristic
14#64078C2211yescharacteristic
15C2×C3×Dic12C2214yes—
16C3×C42×D3C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19#63918—21no—
20#63918—21no—
21D3×C4⋊Dic3—21no—
22D3×C4⋊Dic3—21no—
23#63869—21no—
24#63866C2212yes—
25#63857—21no—
26#63856C2212yes—
27#63844—21no—
28Dic3×Dic6C2212yes—
29#63841—21no—
30C2×#3719C2214yes—
31C32×C4×C8C2211yescharacteristic
32#63643C2214yes—
33C3×(C2×D3)⋊C8C2212yes—
34C3×Dic3⋊C8C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63566C2214yes—
37#5728—31no—
38D3×C4⋊Q8—31no—
39#5470—31no—
40C2×#869—31no—
41C3×#494—31no—
42C3×#431—31no—
43#5186—34no—
44#5182—34no—
45#5092—31no—
46#5079—31no—
47#4849—34no—
48#4739—34no—
49#4699—31no—
50#4699D311yescharacteristic, complemented
51#4685D311yescharacteristic
52#4681—31no—
53#4681—31no—
54#4681—31no—
55#4681—61no—
56C2×#634—21no—
57C2×#634C2312yes—
58C2×C3×C4×D3D411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C2×C3×C4×D3C2311yescharacteristic
61C2×C3×Dic6C2312yes—
62C2×C3×Dic6C2312yes—
63C2×#627—22no—
64C2×D3×Dic3—22no—
65D3×Dic6—44no—
66C2×C32×C8C2312yes—
67C32×C42C2311yescharacteristic
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)C2312yes—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4×Dic3D411yescharacteristic
77C3×C4×Dic3D411yescharacteristic
78C3×C4×Dic3C2311yescharacteristic
79C2×C3×C3⋊C8C2312yes—
80C3×Dic12—44no—
81#3724—22no—
82Dic3⋊Dic3—22no—
83Dic3⋊Dic3—22no—
84Dic3⋊Dic3—22no—
85(C2×D3)⋊Dic3—22no—
86Dic32—22no—
87#3719—44no—
88#3209—91noSylow
89C2×D3×Q8—32no—
90C22×Dic6—32no—
91C2×C3×Q16—34no—
92C3×C4⋊Q8—31no—
93C3×C4⋊Q8—31no—
94C2×C3×C42—31no—
95#946—32no—
96Q8×Dic3—32no—
97#944—32no—
98C2×#216—34no—
99#926—61no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3—61no—
102#924—32no—
103#924—61no—
104C2×Dic12—34no—
105C2×Dic12C2×D314yes—
106#897—61no—
107#892—61no—
108D3×C4⋊C4—61no—
109D3×C4⋊C4—61no—
110#890—61no—
111#888—61no—
112#888—61no—
113#887—61no—
114C42×D3C2×D311yescharacteristic
115#870—61no—
116#869—31no—
117#869—31no—
118#869—32no—
119#869—31no—
120#869—31no—
121#869—61no—
122#869—61no—
123#869—61no—
124#869—61no—
125#869C2×D311yescharacteristic
126#869C2×D311yescharacteristic
127C4×Dic6—32no—
128C4×Dic6—61no—
129C3×C4⋊C8—32no—
130C3×C22⋊C8—32no—
131C3×C4×C8—21no—
132C3×C4×C8—31no—
133C3×C4×C8C2×D311yescharacteristic
134C3×C4×C8C2×D311yescharacteristic
135#835—34no—
136(C2×D3)⋊C8C2×D312yes—
137#816—34no—
138#816—34no—
139#816—34no—
140#816—64no—
141Dic3⋊C8C2×D312yes—
142C4×C3⋊C8C2×D311yescharacteristic
143C22×C3×D3C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—22no—
149#634—24no—
150#634—42no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3C2×D411yescharacteristic
154C2×C3×Dic3C2×D411yescharacteristic
155C2×C3×Dic3C2×D411yescharacteristic
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×C4×D3Q1614yescomplemented
159C3×Dic6—24no—
160C3×Dic6—24no—
161#627—44no—
162D3×Dic3—44no—
163C32×C8—22no—
164C3×C3⋊C8—22no—
165#533—91no—
166C2×C4⋊Q8—91no—
167#494—31no—
168#494—91no—
169#487—91no—
170#487—91no—
171#462—94no—
172#451—94no—
173#431—31no—
174C2×C3×Q8—32no—
175C2×C3×Q8—32no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×Dic3—62no—
180D3×Q8—124no—
181C2×C4×D3—62no—
182C2×C4×D3D1211yescharacteristic
183C2×C4×D3D1211yescharacteristic
184C2×C4×D3C22×D311yescharacteristic
185C2×Dic6—32no—
186C2×Dic6—32no—
187C2×Dic6—62no—
188C2×Dic6—62no—
189C2×Dic6—61no—
190C2×Dic6—61no—
191C2×Dic6—62no—
192C2×Dic6—121no—
193C2×Dic6—124no—
194C2×Dic6C22×D312yes—
195C2×Dic6C22×D312yes—
196C3×Q16—124no—
197C2×C3×C8—22no—
198C2×C3×C8—32no—
199C2×C3×C8C22×D312yes—
200C2×C3×C8C22×D312yes—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C42—21no—
206C3×C42—31no—
207C3×C42—31no—
208C3×C42—31no—
209C3×C42C22×D311yescharacteristic
210C3×C42C22×D311yescharacteristic
211#217—62no—
212#216—124no—
213(C2×D3)⋊C4—62no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—21no—
217C4⋊Dic3—21no—
218C4⋊Dic3—32no—
219C4⋊Dic3—32no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3—62no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226C4⋊Dic3—61no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3—62no—
230C4⋊Dic3—121no—
231C4⋊Dic3—121no—
232C4⋊Dic3—121no—
233Dic3⋊C4—62no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238C4×Dic3—62no—
239C4×Dic3—62no—
240C4×Dic3D1211yescharacteristic
241C4×Dic3D1211yescharacteristic
242C4×Dic3C22×D311yescharacteristic
243C2×C3⋊C8C22×D312yes—
244Dic12—44no—
245Dic12—124no—
246C22×C32C22×D411yescharacteristic
247C2×C3×D3—21no—
248C2×C3×D3—21no—
249C2×C3×D3C2×Q1612yes—
250C32×C4C2×Q1612yes—
251C32×C4#13712yes—
252C32×C4H(5,𝔽2)12yes—
253C3⋊Dic3—42no—
254C3⋊Dic3—42no—
255C3×Dic3—21no—
256C3×Dic3—21no—
257C3×Dic3—42no—
258C3×Dic3—42no—
259C3×Dic3C2×Q1612yes—
260C22×Q8—92no—
261C2×Q16—34no—
262C2×Q16—94no—
263C4⋊Q8—31no—
264C4⋊Q8—31no—
265C4⋊Q8—92no—
266C4⋊Q8—91no—
267C4⋊Q8—91no—
268C4⋊Q8—181no—
269C4⋊Q8—181no—
270#125—181no—
271C22⋊Q8—92no—
272C22⋊Q8—181no—
273C4×Q8—92no—
274C4×Q8—181no—
275#117—181no—
276C2×C4⋊C4—181no—
277C2×C4⋊C4—181no—
278C2×C42—31no—
279C4⋊C8—32no—
280#103—94no—
281#103—94no—
282C22⋊C8—32no—
283C4×C8—31no—
284C4×C8D3211yescharacteristic
285C23×C3—31no—
286C22×D3C2×D1211yescharacteristic
287C3×Q8—64no—
288C3×Q8—64no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—31no—
293C2×C3×C4—34no—
294C2×C3×C4—31no—
295C2×C3×C4—31no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4C2×D1211yescharacteristic
301C2×C3×C4C2×D1211yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4C23×D311yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—122no—
313C2×Dic3—122no—
314C2×Dic3—124no—
315C2×Dic3C2×D1211yescharacteristic
316C2×Dic3C2×D1211yescharacteristic
317C2×Dic3C2×D1211yescharacteristic
318C4×D3—22no—
319C4×D3—22no—
320C4×D3—124no—
321C4×D3Dic1214yescomplemented
322Dic6—24no—
323Dic6—24no—
324Dic6—64no—
325Dic6—64no—
326Dic6—124no—
327Dic6—124no—
328Dic6—124no—
329Dic6—122no—
330Dic6—122no—
331Dic6—242no—
332C3×C8—22no—
333C3×C8—22no—
334C3×C8—42no—
335C3×C8—62no—
336C3⋊C8—22no—
337C2×C32#53511yescharacteristic
338C2×C32C22×Q1611yescharacteristic
339C2×C32C2×#13711yescharacteristic
340C3×D3—22no—
341C2×Q8—32no—
342C2×Q8—32no—
343C2×Q8—92no—
344C2×Q8—182no—
345C2×Q8—181no—
346C2×Q8—364no—
347C22×C4—31no—
348C22×C4—31no—
349C22×C4—31no—
350C22×C4—182no—
351Q16—124no—
352Q16—364no—
353C2×C8—32no—
354C2×C8C2×D3212yes—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—92no—
360C4⋊C4—182no—
361C4⋊C4—182no—
362C4⋊C4—182no—
363C4⋊C4—182no—
364C4⋊C4—181no—
365C4⋊C4—181no—
366C4⋊C4—181no—
367C22⋊C4—182no—
368C42—31no—
369C42—31no—
370C42—31no—
371C42—182no—
372C42C2×D3211yescharacteristic
373C22×C3—21no—
374C22×C3—32no—
375C22×C3—61no—
376C22×C3—61no—
377C22×C3C22×D1211yescharacteristic
378C22×C3C2×D3×D411yescharacteristic
379C2×D3—21no—
380C2×D3—21no—
381C2×D3C2×Dic1212yes—
382C3×C4—22no—
383C3×C4—22no—
384C3×C4—22no—
385C3×C4—32no—
386C3×C4—61no—
387C3×C4—61no—
388C3×C4—122no—
389C3×C4—122no—
390C3×C4C2×Dic1212yes—
391C3×C4#90912yes—
392C3×C4D3×Q1612yes—
393C3×C4#91812yes—
394C3×C4#100412yes—
395C3×C4#100912yes—
396Dic3—21no—
397Dic3—21no—
398Dic3—42no—
399Dic3—42no—
400Dic3—122no—
401Dic3—122no—
402Dic3—122no—
403Dic3—122no—
404Dic3—242no—
405Dic3—242no—
406Dic3C2×Dic1212yes—
407C32#320911yescharacteristic, complemented, Sylow
408C23—31no—
409Q8—64no—
410Q8—64no—
411Q8—184no—
412Q8—364no—
413Q8—362no—
414C2×C4—31no—
415C2×C4—34no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—182no—
423C2×C4—182no—
424C2×C4—364no—
425C2×C4D3×D1211yescharacteristic
426C2×C4D3×D1211yescharacteristic
427C2×C4C22×D3211yescharacteristic
428C8—22no—
429C8—62no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—62no—
434C2×C3#552511yescharacteristic
435C2×C3#571511yescharacteristic
436C2×C3C22×Dic1211yescharacteristic
437C2×C3C2×#90911yescharacteristic
438C2×C3C2×D3×Q1611yescharacteristic
439C2×C3C2×#91811yescharacteristic
440D3—22no—
441C22—32no—
442C22—61no—
443C22—61no—
444C22C2×D3×D1211yescharacteristic
445C4—32no—
446C4—61no—
447C4—61no—
448C4—122no—
449C4—122no—
450C4—362no—
451C4—362no—
452C4D3×Dic1212yes—
453C4#6380112yes—
454C4#6430712yes—
455C3—21no—
456C3#7931311yescharacteristic, complemented
457C3#8180211yescharacteristic, complemented
458C2—62no—
459C2#1059400011yescharacteristic
460C2C2×D3×Dic1211yescharacteristic
461C2C2×#6380111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4×C8D32
hypocenterC32#3209
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
3. #10592380C2semidirect
4. C3×#4699C2semidirect
7. #10590800C2semidirect
8. #10590386C2semidirect
9. #10590287C2semidirect
50. #4699D3semidirect
158. C3×C4×D3Q16semidirect
321. C4×D3Dic12semidirect
407. C32#3209semidirect
456. C3#79313semidirect
457. C3#81802semidirect

Maximal subgroups

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

subgroupindex
D3×#8692
#105938592
#105923802
C3×#46992
C3×#46852
#105909492
#105908002
#105903862
#105902872
#818023
#793133