Finite Group Databasebeta

← #11878897

Subgroups — #11878897

Order 1152.

829 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#869C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic
3#10592398C211yesmaximal, characteristic, complemented
4C3×#4685C211yesmaximal, characteristic
5C3×#4681C211yesmaximal, characteristic, complemented
6#10590952C214yesmaximal
7#10590808C214yesmaximal, complemented
8#10590386C211yesmaximal, characteristic, complemented
9#10590288C211yesmaximal, characteristic, complemented
10#81604—31nomaximal
11#79313—31nomaximal
12C2×D3×Dic6C2212yes—
13C2×#3746C2214yes—
14#64078C2211yescharacteristic
15#64078C2211yescharacteristic
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#63857C2212yes—
26#63856—21no—
27#63844C2212yes—
28Dic3×Dic6—21no—
29#63841—21no—
30C2×#3719C2214yes—
31C32×C4×C8C2211yescharacteristic
32C3×(C2×D3)⋊C8C2212yes—
33C3×#816C2214yes—
34C3×Dic3⋊C8C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63567C2214yes—
37#5728—31no—
38D3×C4⋊Q8—31no—
39#5470—31no—
40C2×#869—31no—
41C3×#487—31no—
42C3×#431—31no—
43#5093—31no—
44#5092—31no—
45#4849—34no—
46#4809—34no—
47#4795—34no—
48#4739—34no—
49#4699—31no—
50#4699—31no—
51#4699—31no—
52#4699—61no—
53#4685D311yescharacteristic
54#4681—31no—
55#4681D311yescharacteristic, complemented
56C2×#634C2312yes—
57C2×#634C2312yes—
58C2×C3×C4×D3D411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C2×C3×C4×D3C2311yescharacteristic
61C2×C3×Dic6—21no—
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)—21no—
72#3746—44no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3C2312yes—
77C3×C4×Dic3D411yescharacteristic
78C3×C4×Dic3D411yescharacteristic
79C3×C4×Dic3C2311yescharacteristic
80C2×C3×C3⋊C8C2312yes—
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—
91C3×C4⋊Q8—31no—
92C3×C4⋊Q8—31no—
93C2×C3×C42—31no—
94#946—61no—
95Q8×Dic3—61no—
96#944—32no—
97C2×#216—34no—
98#926—61no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3—61no—
101#924—32no—
102#924—61no—
103C2×Dic12—34no—
104C2×Dic12—34no—
105C2×Dic12—34no—
106C2×Dic12—64no—
107#897—32no—
108#892—61no—
109D3×C4⋊C4—61no—
110D3×C4⋊C4—61no—
111#890—61no—
112#888—61no—
113#888—61no—
114#887—32no—
115C42×D3C2×D311yescharacteristic
116#870—61no—
117#869—32no—
118#869—31no—
119#869—31no—
120#869—31no—
121#869—31no—
122#869—61no—
123#869—61no—
124#869—61no—
125#869—61no—
126#869C2×D311yescharacteristic
127#869C2×D311yescharacteristic
128C4×Dic6—32no—
129C4×Dic6—61no—
130C3×C4⋊C8—32no—
131C3×#103—34no—
132C3×C22⋊C8—32no—
133C3×C4×C8—21no—
134C3×C4×C8—31no—
135C3×C4×C8C2×D311yescharacteristic
136C3×C4×C8C2×D311yescharacteristic
137(C2×D3)⋊C8C2×D312yes—
138#816—34no—
139#816C2×D314yes—
140Dic3⋊C8C2×D312yes—
141#810—34no—
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—24no—
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—42no—
161#627—44no—
162D3×Dic3—44no—
163C32×C8—22no—
164C3×C3⋊C8—22no—
165#533—91no—
166C2×C4⋊Q8—91no—
167#494—91no—
168#494—91no—
169#487—31no—
170#487—91no—
171#462—94no—
172#451—94no—
173#431—31no—
174C2×C3×Q8—32no—
175C2×C3×Q8—61no—
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—21no—
186C2×Dic6—32no—
187C2×Dic6—32no—
188C2×Dic6—32no—
189C2×Dic6—32no—
190C2×Dic6—62no—
191C2×Dic6—62no—
192C2×Dic6—62no—
193C2×Dic6—62no—
194C2×Dic6—124no—
195C2×Dic6C22×D312yes—
196C2×C3×C8—22no—
197C2×C3×C8—32no—
198C2×C3×C8C22×D312yes—
199C2×C3×C8C22×D312yes—
200C3×C4⋊C4—32no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C42—21no—
205C3×C42—31no—
206C3×C42—31no—
207C3×C42—31no—
208C3×C42C22×D311yescharacteristic
209C3×C42C22×D311yescharacteristic
210#217—62no—
211#216—124no—
212(C2×D3)⋊C4—62no—
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—62no—
217C4⋊Dic3—62no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226C4⋊Dic3—62no—
227C4⋊Dic3—121no—
228C4⋊Dic3—121no—
229C4⋊Dic3—121no—
230C4⋊Dic3—121no—
231C4⋊Dic3C22×D312yes—
232Dic3⋊C4—62no—
233Dic3⋊C4—62no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237C4×Dic3—62no—
238C4×Dic3—62no—
239C4×Dic3D1211yescharacteristic
240C4×Dic3D1211yescharacteristic
241C4×Dic3C22×D311yescharacteristic
242C2×C3⋊C8C22×D312yes—
243Dic12—124no—
244Dic12—124no—
245Dic12—128no—
246Dic12—124no—
247C22×C32C22×D411yescharacteristic
248C2×C3×D3—21no—
249C2×C3×D3—21no—
250C2×C3×D3C2×Q1612yes—
251C32×C4C2×Q1612yes—
252C32×C4#13712yes—
253C32×C4H(5,𝔽2)12yes—
254C3⋊Dic3—42no—
255C3⋊Dic3—42no—
256C3×Dic3—21no—
257C3×Dic3—21no—
258C3×Dic3—42no—
259C3×Dic3—42no—
260C3×Dic3C2×Q1612yes—
261C22×Q8—92no—
262C2×Q16—94no—
263C2×Q16—94no—
264C4⋊Q8—31no—
265C4⋊Q8—31no—
266C4⋊Q8—92no—
267C4⋊Q8—91no—
268C4⋊Q8—91no—
269C4⋊Q8—181no—
270C4⋊Q8—181no—
271#125—181no—
272C22⋊Q8—92no—
273C22⋊Q8—181no—
274C4×Q8—92no—
275C4×Q8—181no—
276#117—181no—
277C2×C4⋊C4—181no—
278C2×C4⋊C4—181no—
279C2×C42—31no—
280C4⋊C8—32no—
281#103—34no—
282#103—94no—
283C22⋊C8—32no—
284C4×C8—31no—
285C4×C8D3211yescharacteristic
286C23×C3—31no—
287C22×D3C2×D1211yescharacteristic
288C3×Q8—64no—
289C3×Q8—122no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—31no—
294C2×C3×C4—34no—
295C2×C3×C4—31no—
296C2×C3×C4—31no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4C2×D1211yescharacteristic
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306C2×C3×C4C23×D311yescharacteristic
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C2×Dic3—124no—
316C2×Dic3C2×D1211yescharacteristic
317C2×Dic3C2×D1211yescharacteristic
318C2×Dic3C2×D1211yescharacteristic
319C4×D3—22no—
320C4×D3—22no—
321C4×D3—124no—
322C4×D3Dic1214yescomplemented
323Dic6—24no—
324Dic6—42no—
325Dic6—64no—
326Dic6—64no—
327Dic6—64no—
328Dic6—64no—
329Dic6—124no—
330Dic6—124no—
331Dic6—124no—
332Dic6—124no—
333C3×C8—24no—
334C3×C8—22no—
335C3×C8—22no—
336C3×C8—62no—
337C3⋊C8—22no—
338C2×C32#53511yescharacteristic
339C2×C32C22×Q1611yescharacteristic
340C2×C32C2×#13711yescharacteristic
341C3×D3—22no—
342C2×Q8—32no—
343C2×Q8—61no—
344C2×Q8—92no—
345C2×Q8—92no—
346C2×Q8—182no—
347C2×Q8—364no—
348C22×C4—31no—
349C22×C4—31no—
350C22×C4—31no—
351C22×C4—182no—
352Q16—364no—
353Q16—364no—
354C2×C8—32no—
355C2×C8C2×D3212yes—
356C4⋊C4—32no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—182no—
361C4⋊C4—182no—
362C4⋊C4—182no—
363C4⋊C4—182no—
364C4⋊C4—181no—
365C4⋊C4—181no—
366C4⋊C4—181no—
367C4⋊C4—181no—
368C22⋊C4—182no—
369C42—31no—
370C42—31no—
371C42—31no—
372C42—182no—
373C42C2×D3211yescharacteristic
374C22×C3—21no—
375C22×C3—32no—
376C22×C3—61no—
377C22×C3—61no—
378C22×C3C22×D1211yescharacteristic
379C22×C3C2×D3×D411yescharacteristic
380C2×D3—21no—
381C2×D3—21no—
382C2×D3C2×Dic1212yes—
383C3×C4—22no—
384C3×C4—22no—
385C3×C4—22no—
386C3×C4—32no—
387C3×C4—61no—
388C3×C4—61no—
389C3×C4—122no—
390C3×C4—122no—
391C3×C4C2×Dic1212yes—
392C3×C4#90912yes—
393C3×C4#91512yes—
394C3×C4D3×Q1612yes—
395C3×C4#100912yes—
396C3×C4#100912yes—
397Dic3—21no—
398Dic3—21no—
399Dic3—42no—
400Dic3—42no—
401Dic3—122no—
402Dic3—122no—
403Dic3—122no—
404Dic3—122no—
405Dic3—242no—
406Dic3—242no—
407Dic3C2×Dic1212yes—
408C32#320911yescharacteristic, complemented, Sylow
409C23—31no—
410Q8—64no—
411Q8—122no—
412Q8—184no—
413Q8—184no—
414Q8—364no—
415C2×C4—31no—
416C2×C4—34no—
417C2×C4—31no—
418C2×C4—31no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—182no—
424C2×C4—182no—
425C2×C4—364no—
426C2×C4D3×D1211yescharacteristic
427C2×C4D3×D1211yescharacteristic
428C2×C4C22×D3211yescharacteristic
429C8—22no—
430C8—62no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—62no—
435C2×C3#552511yescharacteristic
436C2×C3#567411yescharacteristic
437C2×C3C22×Dic1211yescharacteristic
438C2×C3C2×#90911yescharacteristic
439C2×C3C2×#91511yescharacteristic
440C2×C3C2×D3×Q1611yescharacteristic
441D3—22no—
442C22—32no—
443C22—61no—
444C22—61no—
445C22C2×D3×D1211yescharacteristic
446C4—32no—
447C4—61no—
448C4—61no—
449C4—122no—
450C4—122no—
451C4—362no—
452C4—362no—
453C4D3×Dic1212yes—
454C4#6380012yes—
455C4#6430812yes—
456C3—21no—
457C3#7931311yescharacteristic, complemented
458C3#8160411yescharacteristic, complemented
459C2—62no—
460C2#1059400111yescharacteristic
461C2C2×D3×Dic1211yescharacteristic
462C2C2×#6380011yescharacteristic
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. #10592398C2semidirect
5. C3×#4681C2semidirect
7. #10590808C2semidirect
8. #10590386C2semidirect
9. #10590288C2semidirect
55. #4681D3semidirect
158. C3×C4×D3Q16semidirect
322. C4×D3Dic12semidirect
408. C32#3209semidirect
457. C3#79313semidirect
458. C3#81604semidirect

Maximal subgroups

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

subgroupindex
D3×#8692
#105938592
#105923982
C3×#46852
C3×#46812
#105909522
#105908082
#105903862
#105902882
#816043
#793133