Finite Group Databasebeta

← #11795434

Subgroups — #11795434

Order 1152.

645 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63645C211yesmaximal, characteristic, complemented
2C2×C3×#821C211yesmaximal, characteristic
3#10591349C211yesmaximal, characteristic, complemented
4#10591318C211yesmaximal, characteristic
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7C3×#4550C211yesmaximal, characteristic, complemented
8#70183—31nomaximal
9#68681—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×Dic3⋊Dic3—22no—
18C2×(C2×D3)⋊Dic3—22no—
19#63645—22no—
20C3×#821—22no—
21#63575—22no—
22#63563—22no—
23C2×C3×#102—31no—
24#5221—31no—
25C2×#832—31no—
26C2×#821—31no—
27C2×#821D311yescharacteristic
28C2×#818—31no—
29C2×#818—31no—
30C2×#818—31no—
31C2×#818—61no—
32#4975—31no—
33C2×#807—31no—
34#4939—31no—
35#4935—31no—
36C3×#336—31no—
37#4550D311yescharacteristic, complemented
38C23×C3×D3—21no—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3—21no—
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—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8D412yes—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8D412yes—
64Dic3⋊Dic3—44no—
65(C2×D3)⋊Dic3—44no—
66#2093—91noSylow
67C22×C3×D4—31no—
68C22×D12C2×D311yescharacteristic
69C22×C3×C8—21no—
70C22×C3×C8—31no—
71C22×C3×C8C2×D311yescharacteristic
72C22×C3×C8C2×D311yescharacteristic
73C2×C3×C4⋊C4—31no—
74C2×C3×C42—31no—
75C2×#217—62no—
76C2×(C2×D3)⋊C4—62no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—31no—
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—61no—
82C2×C4⋊Dic3—61no—
83C2×C4⋊Dic3—62no—
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×Dic3⋊C4—62no—
86C2×C4×Dic3C2×D311yescharacteristic
87C22×C3⋊C8C2×D311yescharacteristic
88C3×#102—62no—
89#832—62no—
90#821—22no—
91#821—62no—
92#818—62no—
93#818—64no—
94#818—62no—
95#818—62no—
96#807—62no—
97C23×C32C2×D411yescharacteristic
98C22×C3×D3—22no—
99C22×C3×D3—41no—
100C22×C3×D3—41no—
101C22×C3×D3—42no—
102C22×C3×D3—42no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×Q811yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—41no—
111C2×C3⋊Dic3—42no—
112C2×C3⋊Dic3—42no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3D814yes—
118C3×D12—22no—
119C3×D12—22no—
120C3×D12—41no—
121C3×D12—41no—
122C32×C8—22no—
123C3×C3⋊C8—22no—
124C2×#107—91no—
125C2×#107—91no—
126C2×#102—31no—
127C2×#102—91no—
128#390—91no—
129#384—91no—
130#336—31no—
131C24×C3—61no—
132C23×D3—21no—
133C2×C3×D4—32no—
134C2×C3×D4—61no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C22×C3×C4—21no—
140C22×C3×C4—32no—
141C22×C3×C4—61no—
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C22×Dic3—21no—
145C22×Dic3—61no—
146C22×Dic3—61no—
147C22×Dic3—61no—
148C22×Dic3—61no—
149C22×Dic3—121no—
150C22×Dic3—121no—
151C22×Dic3D1212yes—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12Dic612yes—
158C2×C3×C8—22no—
159C2×C3×C8—22no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—22no—
165C2×C3×C8—32no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8D1212yes—
169C2×C3×C8#6712yes—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C42—61no—
173C3×C42—61no—
174#217—124no—
175(C2×D3)⋊C4—124no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—62no—
179C4⋊Dic3—62no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—121no—
189C4⋊Dic3—121no—
190C4⋊Dic3—124no—
191Dic3⋊C4—124no—
192C4×Dic3—21no—
193C4×Dic3—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8D1212yes—
197C22×C32C22⋊Q811yescharacteristic
198C22×C32#12311yescharacteristic
199C22×C32#12711yescharacteristic
200C22×C32C2×D812yes—
201C22×C32#13712yes—
202C2×C3×D3—42no—
203C2×C3×D3—44no—
204C2×C3×D3—82no—
205C2×C3×D3—81no—
206C2×C3×D3—81no—
207C32×C4C22⋊Q811yescharacteristic
208C32×C4C22⋊Q811yescharacteristic
209C32×C4#12311yescharacteristic
210C32×C4#12311yescharacteristic
211C3⋊Dic3—81no—
212C3⋊Dic3—81no—
213C3×Dic3—24no—
214C3×Dic3—81no—
215C22×D4—31no—
216C22×C8—31no—
217C22×C8D3211yescharacteristic
218C2×C4⋊C4—31no—
219C2×C4⋊C4—91no—
220C2×C4⋊C4—91no—
221C2×C4⋊C4—182no—
222C2×C22⋊C4—182no—
223C2×C42—31no—
224#107—182no—
225#107—182no—
226#102—62no—
227#102—182no—
228C23×C3—21no—
229C23×C3—62no—
230C23×C3—121no—
231C23×C3—121no—
232C23×C3—122no—
233C23×C3—122no—
234C23×C3C2×D1211yescharacteristic
235C23×C3D3×D411yescharacteristic
236C22×D3—22no—
237C22×D3—41no—
238C22×D3—42no—
239C22×D3—42no—
240C22×D3—41no—
241C3×D4—62no—
242C3×D4—62no—
243C3×D4—121no—
244C3×D4—121no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—34no—
252C2×C3×C4—62no—
253C2×C3×C4—62no—
254C2×C3×C4—121no—
255C2×C3×C4—122no—
256C2×C3×C4C2×Dic611yescharacteristic
257C2×C3×C4C2×D1211yescharacteristic
258C2×C3×C4C2×D1211yescharacteristic
259C2×C3×C4#23511yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4#23711yescharacteristic
262C2×C3×C4#23711yescharacteristic
263C2×C3×C4#23711yescharacteristic
264C2×C3×C4#23711yescharacteristic
265C2×C3×C4#23711yescharacteristic
266C2×C3×C4D3×Q811yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×Dic3—22no—
269C2×Dic3—22no—
270C2×Dic3—42no—
271C2×Dic3—41no—
272C2×Dic3—122no—
273C2×Dic3—122no—
274C2×Dic3—121no—
275C2×Dic3—121no—
276C2×Dic3—122no—
277C2×Dic3—122no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280C2×Dic3—121no—
281C2×Dic3—121no—
282C2×Dic3—242no—
283C2×Dic3—242no—
284C2×Dic3D2414yes—
285D12—22no—
286D12—22no—
287D12—41no—
288D12—41no—
289C3×C8—24no—
290C3×C8—22no—
291C3×C8—22no—
292C3×C8—62no—
293C3⋊C8—22no—
294C2×C32#39911yescharacteristic
295C2×C32#47412yes—
296C2×C32#48012yes—
297C2×C32#49311yescharacteristic
298C2×C32#49711yescharacteristic
299C3×D3—82no—
300C24—61no—
301C2×D4—32no—
302C2×D4—61no—
303C2×D4—61no—
304C2×D4—61no—
305C2×D4—61no—
306C2×D4—61no—
307C22×C4—32no—
308C22×C4—61no—
309C22×C4—181no—
310C22×C4—181no—
311C22×C4C2×D3211yescharacteristic
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—32no—
315C2×C8—61no—
316C2×C8—61no—
317C2×C8#62612yes—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C4⋊C4—364no—
325C22⋊C4—364no—
326C42—61no—
327C42—61no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—122no—
334C22×C3—124no—
335C22×C3—241no—
336C22×C3—241no—
337C22×C3—242no—
338C22×C3#87411yescharacteristic
339C22×C3#87811yescharacteristic
340C22×C3#88311yescharacteristic
341C22×C3#88611yescharacteristic
342C22×C3#89711yescharacteristic
343C22×C3C2×D2412yes—
344C22×C3#90912yes—
345C22×C3D3×D812yes—
346C22×C3#91512yes—
347C22×C3#94011yescharacteristic
348C2×D3—42no—
349C2×D3—44no—
350C2×D3—81no—
351C2×D3—81no—
352C2×D3—82no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—64no—
358C3×C4—241no—
359C3×C4#87811yescharacteristic
360C3×C4#88311yescharacteristic
361C3×C4#88611yescharacteristic
362C3×C4#88611yescharacteristic
363C3×C4#89711yescharacteristic
364C3×C4#89711yescharacteristic
365C3×C4#92411yescharacteristic
366C3×C4#93511yescharacteristic
367Dic3—24no—
368Dic3—81no—
369Dic3—242no—
370Dic3—242no—
371Dic3—241no—
372Dic3—241no—
373Dic3—241no—
374Dic3—241no—
375C32#209311yescharacteristic, complemented, Sylow
376C23—62no—
377C23—122no—
378C23—122no—
379C23—121no—
380C23—121no—
381C23D3×D1211yescharacteristic
382D4—62no—
383D4—62no—
384D4—121no—
385D4—121no—
386C2×C4—34no—
387C2×C4—62no—
388C2×C4—62no—
389C2×C4—122no—
390C2×C4—121no—
391C2×C4—362no—
392C2×C4—362no—
393C2×C4—361no—
394C2×C4—361no—
395C2×C4D3×Dic611yescharacteristic
396C2×C4#379511yescharacteristic
397C2×C4D3×D1211yescharacteristic
398C2×C4#380511yescharacteristic
399C2×C4#380511yescharacteristic
400C2×C4C2×#62611yescharacteristic
401C8—22no—
402C8—62no—
403C2×C3—22no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—22no—
408C2×C3—242no—
409C2×C3#467711yescharacteristic
410C2×C3#469511yescharacteristic
411C2×C3#471511yescharacteristic
412C2×C3#473612yes—
413C2×C3#475912yes—
414C2×C3#477412yes—
415C2×C3#484612yes—
416C2×C3#494911yescharacteristic
417C2×C3#515111yescharacteristic
418C2×C3#516711yescharacteristic
419D3—82no—
420C22—124no—
421C22—122no—
422C22—241no—
423C22—241no—
424C22—242no—
425C22D3×D2412yes—
426C22#6380012yes—
427C22#6389111yescharacteristic
428C22#6389311yescharacteristic
429C22#6391111yescharacteristic
430C4—64no—
431C4—241no—
432C4—721no—
433C4—721no—
434C4#6385711yescharacteristic
435C4#6389111yescharacteristic
436C4#6389311yescharacteristic
437C4#6396211yescharacteristic
438C3—21no—
439C3#6868111yescharacteristic, complemented
440C3#7018311yescharacteristic, complemented
441C2—242no—
442C2#1059068012yes—
443C2#1059076212yes—
444C2#1059088011yescharacteristic
445C2#1059089711yescharacteristic
446C2#1059131711yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32#2093
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63645C2semidirect
3. #10591349C2semidirect
5. C2×#63575C2semidirect
7. C3×#4550C2semidirect
37. #4550D3semidirect
375. C32#2093semidirect
439. C3#68681semidirect
440. C3#70183semidirect

Maximal subgroups

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

subgroupindex
C2×#636452
C2×C3×#8212
#105913492
#105913182
C2×#635752
C2×#635632
C3×#45502
#701833
#686813