Finite Group Databasebeta

← #11795399

Subgroups — #11795399

Order 1152.

613 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63635C211yesmaximal, characteristic, complemented
2C3×#4988C211yesmaximal, characteristic
3C2×C3×#807C211yesmaximal, characteristic, complemented
4#10591224C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic
6C2×#63562C211yesmaximal, characteristic
7#10589155C211yesmaximal, characteristic, complemented
8#70640—31nomaximal
9#69654—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—22no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18#63635—22no—
19C3×#807—22no—
20#63579—22no—
21#63563—22no—
22#63562—22no—
23C2×C3×#107—31no—
24C3×#390—31no—
25C2×#832—31no—
26C2×#832—31no—
27C2×#821—31no—
28#4988D311yescharacteristic
29#4977—31no—
30C2×#809—31no—
31C2×#808—31no—
32C2×#808—31no—
33C2×#808—61no—
34C2×#807D311yescharacteristic, complemented
35#4936—31no—
36#4550—31no—
37#4524—31no—
38C23×C3×D3—21no—
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C22×C3×Dic3—21no—
43C22×C3×Dic3D412yes—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12Q812yes—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)D412yes—
57C3×(C2×D3)⋊C4—44no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8D412yes—
65#2092—91noSylow
66C22×C3×D4—31no—
67C22×D12C2×D311yescharacteristic
68C22×C3×C8—31no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—31no—
71C2×C3×C4⋊C4C2×D311yescharacteristic
72C2×C3×C4⋊C4C2×D311yescharacteristic
73C2×C3×C22⋊C4—62no—
74C2×C3×C42—31no—
75C2×(C2×D3)⋊C4—22no—
76C2×C4⋊Dic3—31no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—61no—
79C2×C4⋊Dic3C2×D311yescharacteristic
80C2×C4×Dic3C2×D311yescharacteristic
81C22×C3⋊C8—31no—
82C22×C3⋊C8—31no—
83C22×C3⋊C8—61no—
84C22×C3⋊C8C2×D311yescharacteristic
85C3×#107—62no—
86#832—62no—
87#832—62no—
88C3⋊#95—62no—
89C3⋊#95—62no—
90#821—62no—
91#809—62no—
92#808—62no—
93#808—62no—
94#808—64no—
95#807—22no—
96C23×C32C2×D411yescharacteristic
97C22×C3×D3—22no—
98C22×C3×D3—41no—
99C22×C3×D3—41no—
100C22×C3×D3—42no—
101C22×C3×D3—42no—
102C2×C32×C4—41no—
103C2×C32×C4—42no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×Q811yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C3⋊Dic3—41no—
111C2×C3⋊Dic3—42no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—42no—
117C3×D12—22no—
118C3×D12—22no—
119C3×D12—41no—
120C3×D12—41no—
121C3⋊(C3⋊C8)—22no—
122C3×C3⋊C8—22no—
123C2×#107—31no—
124C2×#106—91no—
125C2×#102—91no—
126C2×#102—91no—
127#390—31no—
128#382—91no—
129#336—91no—
130C24×C3—61no—
131C23×D3—21no—
132C2×C3×D4—32no—
133C2×C3×D4—61no—
134C2×C3×D4—61no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—32no—
142C22×C3×C4—41no—
143C22×C3×C4—61no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C22×Dic3—21no—
147C22×Dic3—61no—
148C22×Dic3—61no—
149C22×Dic3—121no—
150C22×Dic3#6712yes—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12Dic612yes—
157C2×C3×C8—32no—
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C3×C4⋊C4—22no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—41no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C22⋊C4—124no—
169C3×C42—61no—
170C3×C42—61no—
171(C2×D3)⋊C4—44no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—62no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—121no—
180C4×Dic3—21no—
181C4×Dic3—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—32no—
185C2×C3⋊C8—32no—
186C2×C3⋊C8—62no—
187C2×C3⋊C8—62no—
188C2×C3⋊C8—62no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8#6712yes—
194C22×C32C22⋊Q811yescharacteristic
195C22×C32#12311yescharacteristic
196C22×C32#12711yescharacteristic
197C22×C32#13512yes—
198C22×C32AGL(1,ℤ/8)12yes—
199C2×C3×D3—42no—
200C2×C3×D3—44no—
201C2×C3×D3—82no—
202C2×C3×D3—81no—
203C2×C3×D3—81no—
204C32×C4—81no—
205C32×C4C22⋊Q811yescharacteristic
206C32×C4C22⋊Q811yescharacteristic
207C32×C4#12311yescharacteristic
208C32×C4#12311yescharacteristic
209C3⋊Dic3—81no—
210C3×Dic3—42no—
211C3×Dic3—81no—
212C22×D4—31no—
213C22×C8—31no—
214C22×C8—91no—
215C2×C4⋊C4—31no—
216C2×C4⋊C4—91no—
217C2×C4⋊C4D3211yescharacteristic
218C2×C22⋊C4—62no—
219C2×C42—31no—
220#107—62no—
221#106—182no—
222#102—182no—
223#102—182no—
224#95—182no—
225C23×C3—21no—
226C23×C3—62no—
227C23×C3—121no—
228C23×C3—122no—
229C23×C3—122no—
230C23×C3—121no—
231C23×C3D3×D411yescharacteristic
232C23×C3C2×#6711yescharacteristic
233C22×D3—22no—
234C22×D3—42no—
235C22×D3—41no—
236C22×D3—41no—
237C22×D3—42no—
238C3×D4—62no—
239C3×D4—62no—
240C3×D4—121no—
241C3×D4—121no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—42no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—62no—
254C2×C3×C4—62no—
255C2×C3×C4—62no—
256C2×C3×C4—82no—
257C2×C3×C4—122no—
258C2×C3×C4—121no—
259C2×C3×C4C2×Dic611yescharacteristic
260C2×C3×C4#23511yescharacteristic
261C2×C3×C4#23511yescharacteristic
262C2×C3×C4#23511yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4#23711yescharacteristic
267C2×C3×C4#23711yescharacteristic
268C2×C3×C4D3×Q811yescharacteristic
269C2×C3×C4#23911yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×Dic3—22no—
272C2×Dic3—22no—
273C2×Dic3—22no—
274C2×Dic3—42no—
275C2×Dic3—41no—
276C2×Dic3—122no—
277C2×Dic3—122no—
278C2×Dic3—121no—
279C2×Dic3—121no—
280C2×Dic3—122no—
281C2×Dic3—242no—
282D12—22no—
283D12—22no—
284D12—41no—
285D12—41no—
286C3×C8—62no—
287C3⋊C8—22no—
288C3⋊C8—64no—
289C3⋊C8—62no—
290C3⋊C8—62no—
291C2×C32#39911yescharacteristic
292C2×C32#47812yes—
293C2×C32#48212yes—
294C2×C32#49511yescharacteristic
295C2×C32#49611yescharacteristic
296C3×D3—82no—
297C24—61no—
298C2×D4—32no—
299C2×D4—61no—
300C2×D4—61no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—61no—
304C22×C4—21no—
305C22×C4—32no—
306C22×C4—61no—
307C22×C4—181no—
308C22×C4C2×D3211yescharacteristic
309C2×C8—32no—
310C2×C8—61no—
311C2×C8—61no—
312C2×C8—92no—
313C2×C8—181no—
314C2×C8—181no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C22⋊C4—124no—
322C42—61no—
323C42—61no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—21no—
329C22×C3—124no—
330C22×C3—122no—
331C22×C3—242no—
332C22×C3—241no—
333C22×C3—241no—
334C22×C3#89411yescharacteristic
335C22×C3#89611yescharacteristic
336C22×C3#91112yes—
337C22×C3#91912yes—
338C22×C3#92411yescharacteristic
339C22×C3#93212yes—
340C22×C3#93511yescharacteristic
341C22×C3#94011yescharacteristic
342C22×C3#94011yescharacteristic
343C22×C3#95012yes—
344C2×D3—42no—
345C2×D3—44no—
346C2×D3—82no—
347C2×D3—81no—
348C2×D3—81no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—82no—
354C3×C4—81no—
355C3×C4—81no—
356C3×C4—122no—
357C3×C4—241no—
358C3×C4#87811yescharacteristic
359C3×C4#87811yescharacteristic
360C3×C4#88311yescharacteristic
361C3×C4#88311yescharacteristic
362C3×C4#89411yescharacteristic
363C3×C4#89611yescharacteristic
364C3×C4#92911yescharacteristic
365C3×C4#94611yescharacteristic
366Dic3—42no—
367Dic3—81no—
368Dic3—242no—
369Dic3—241no—
370Dic3—241no—
371C32#209211yescharacteristic, complemented, Sylow
372C23—62no—
373C23—121no—
374C23—122no—
375C23—122no—
376C23—121no—
377C23D3×#6711yescharacteristic
378D4—62no—
379D4—62no—
380D4—121no—
381D4—121no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—62no—
385C2×C4—62no—
386C2×C4—62no—
387C2×C4—122no—
388C2×C4—121no—
389C2×C4—362no—
390C2×C4—361no—
391C2×C4D3×Dic611yescharacteristic
392C2×C4#379511yescharacteristic
393C2×C4#379611yescharacteristic
394C2×C4#379811yescharacteristic
395C2×C4D3×#6711yescharacteristic
396C2×C4#381111yescharacteristic
397C8—62no—
398C8—182no—
399C2×C3—21no—
400C2×C3—22no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—22no—
404C2×C3—242no—
405C2×C3#488512yes—
406C2×C3#489112yes—
407C2×C3#494911yescharacteristic
408C2×C3#499311yescharacteristic
409C2×C3#500912yes—
410C2×C3#503512yes—
411C2×C3#505911yescharacteristic
412C2×C3#507411yescharacteristic
413C2×C3#515411yescharacteristic
414C2×C3#519111yescharacteristic
415D3—82no—
416C22—122no—
417C22—124no—
418C22—241no—
419C22—241no—
420C22—242no—
421C22#6385111yescharacteristic
422C22#6388411yescharacteristic
423C22#6393212yes—
424C22#6394912yes—
425C22#6397911yescharacteristic
426C4—81no—
427C4—122no—
428C4—241no—
429C4—721no—
430C4#6385311yescharacteristic
431C4#6388711yescharacteristic
432C4#6389611yescharacteristic
433C4#6390511yescharacteristic
434C3—21no—
435C3#6965411yescharacteristic, complemented
436C3#7064011yescharacteristic, complemented
437C2—242no—
438C2#1059044612yes—
439C2#1059054212yes—
440C2#1059130311yescharacteristic
441C2#1059146911yescharacteristic
442C2#1059160911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2092
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#63635C2semidirect
3. C2×C3×#807C2semidirect
4. #10591224C2semidirect
7. #10589155C2semidirect
34. C2×#807D3semidirect
371. C32#2092semidirect
435. C3#69654semidirect
436. C3#70640semidirect

Maximal subgroups

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

subgroupindex
C2×#636352
C3×#49882
C2×C3×#8072
#105912242
C2×#635632
C2×#635622
#105891552
#706403
#696543