Finite Group Databasebeta

← #11795394

Subgroups — #11795394

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×#63645C211yesmaximal, characteristic, complemented
2C2×C3×#821C211yesmaximal, characteristic
3#10591318C211yesmaximal, characteristic
4#10591224C211yesmaximal, characteristic, complemented
5C2×#63573C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7C3×#4550C211yesmaximal, characteristic, complemented
8#70181—31nomaximal
9#68680—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×(C2×D3)⋊Dic3—22no—
18#63645—22no—
19C3×#821—22no—
20#63579—22no—
21#63573—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—61no—
31C2×#817—31no—
32#4977—31no—
33C2×#808—31no—
34#4939—31no—
35#4936—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—
64(C2×D3)⋊Dic3—44no—
65#2092—91noSylow
66C22×C3×D4—31no—
67C22×D12C2×D311yescharacteristic
68C22×C3×C8—21no—
69C22×C3×C8—31no—
70C22×C3×C8C2×D311yescharacteristic
71C22×C3×C8C2×D311yescharacteristic
72C2×C3×C4⋊C4—31no—
73C2×C3×C42—31no—
74C2×#217—62no—
75C2×(C2×D3)⋊C4—62no—
76C2×C4⋊Dic3—31no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—31no—
80C2×C4⋊Dic3—61no—
81C2×C4⋊Dic3—61no—
82C2×C4⋊Dic3C2×D311yescharacteristic
83C2×C4×Dic3C2×D311yescharacteristic
84C22×C3⋊C8C2×D311yescharacteristic
85C3×#102—62no—
86#832—62no—
87C3⋊#95—62no—
88C3⋊#95—62no—
89#821—22no—
90#821—62no—
91#818—64no—
92#818—62no—
93#818—62no—
94#817—62no—
95#808—62no—
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×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×Q811yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—42no—
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—
121C32×C8—22no—
122C3×C3⋊C8—22no—
123C2×#107—91no—
124C2×#106—91no—
125C2×#102—31no—
126C2×#102—91no—
127#390—91no—
128#382—91no—
129#336—31no—
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—32no—
140C22×C3×C4—61no—
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C22×Dic3—21no—
144C22×Dic3—61no—
145C22×Dic3—61no—
146C22×Dic3—61no—
147C22×Dic3—61no—
148C22×Dic3—121no—
149C22×Dic3—121no—
150C22×Dic3D1212yes—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12Dic612yes—
157C2×C3×C8—22no—
158C2×C3×C8—22no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—22no—
164C2×C3×C8—32no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C2×C3×C8D1212yes—
168C2×C3×C8#6712yes—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C42—61no—
172C3×C42—61no—
173#217—124no—
174(C2×D3)⋊C4—124no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3—62no—
178C4⋊Dic3—62no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—121no—
188C4⋊Dic3—121no—
189C4×Dic3—21no—
190C4×Dic3—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8D1212yes—
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×C4C22⋊Q811yescharacteristic
205C32×C4C22⋊Q811yescharacteristic
206C32×C4#12311yescharacteristic
207C32×C4#12311yescharacteristic
208C3⋊Dic3—81no—
209C3⋊Dic3—81no—
210C3×Dic3—42no—
211C3×Dic3—81no—
212C22×D4—31no—
213C22×C8—31no—
214C22×C8D3211yescharacteristic
215C2×C4⋊C4—31no—
216C2×C4⋊C4—91no—
217C2×C4⋊C4—91no—
218C2×C22⋊C4—182no—
219C2×C42—31no—
220#107—182no—
221#106—182no—
222#102—62no—
223#102—182no—
224#95—182no—
225C23×C3—21no—
226C23×C3—62no—
227C23×C3—121no—
228C23×C3—121no—
229C23×C3—122no—
230C23×C3—122no—
231C23×C3C2×D1211yescharacteristic
232C23×C3D3×D411yescharacteristic
233C22×D3—22no—
234C22×D3—41no—
235C22×D3—42no—
236C22×D3—42no—
237C22×D3—41no—
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—62no—
249C2×C3×C4—62no—
250C2×C3×C4—62no—
251C2×C3×C4—121no—
252C2×C3×C4—122no—
253C2×C3×C4C2×Dic611yescharacteristic
254C2×C3×C4C2×D1211yescharacteristic
255C2×C3×C4C2×D1211yescharacteristic
256C2×C3×C4#23511yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4#23711yescharacteristic
259C2×C3×C4#23711yescharacteristic
260C2×C3×C4#23711yescharacteristic
261C2×C3×C4#23711yescharacteristic
262C2×C3×C4#23711yescharacteristic
263C2×C3×C4D3×Q811yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265C2×Dic3—22no—
266C2×Dic3—22no—
267C2×Dic3—22no—
268C2×Dic3—42no—
269C2×Dic3—41no—
270C2×Dic3—122no—
271C2×Dic3—122no—
272C2×Dic3—121no—
273C2×Dic3—121no—
274C2×Dic3—122no—
275C2×Dic3—122no—
276C2×Dic3—122no—
277C2×Dic3—122no—
278C2×Dic3—121no—
279C2×Dic3—121no—
280C2×Dic3—242no—
281C2×Dic3—242no—
282D12—22no—
283D12—22no—
284D12—41no—
285D12—41no—
286C3×C8—24no—
287C3×C8—22no—
288C3×C8—22no—
289C3×C8—62no—
290C3⋊C8—22no—
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—32no—
305C22×C4—61no—
306C22×C4—181no—
307C22×C4—181no—
308C22×C4C2×D3211yescharacteristic
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—32no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8#62612yes—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C22⋊C4—364no—
322C42—61no—
323C42—61no—
324C22×C3—22no—
325C22×C3—22no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—122no—
330C22×C3—124no—
331C22×C3—241no—
332C22×C3—241no—
333C22×C3—242no—
334C22×C3#87411yescharacteristic
335C22×C3#87811yescharacteristic
336C22×C3#88311yescharacteristic
337C22×C3#88611yescharacteristic
338C22×C3#89711yescharacteristic
339C22×C3#90412yes—
340C22×C3#90812yes—
341C22×C3#91212yes—
342C22×C3#91412yes—
343C22×C3#94011yescharacteristic
344C2×D3—42no—
345C2×D3—44no—
346C2×D3—81no—
347C2×D3—81no—
348C2×D3—82no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—122no—
354C3×C4—241no—
355C3×C4#87811yescharacteristic
356C3×C4#88311yescharacteristic
357C3×C4#88611yescharacteristic
358C3×C4#88611yescharacteristic
359C3×C4#89711yescharacteristic
360C3×C4#89711yescharacteristic
361C3×C4#92411yescharacteristic
362C3×C4#93511yescharacteristic
363Dic3—42no—
364Dic3—81no—
365Dic3—242no—
366Dic3—242no—
367Dic3—241no—
368Dic3—241no—
369Dic3—241no—
370Dic3—241no—
371C32#209211yescharacteristic, complemented, Sylow
372C23—62no—
373C23—122no—
374C23—122no—
375C23—121no—
376C23—121no—
377C23D3×D1211yescharacteristic
378D4—62no—
379D4—62no—
380D4—121no—
381D4—121no—
382C2×C4—62no—
383C2×C4—62no—
384C2×C4—62no—
385C2×C4—122no—
386C2×C4—121no—
387C2×C4—362no—
388C2×C4—362no—
389C2×C4—361no—
390C2×C4—361no—
391C2×C4D3×Dic611yescharacteristic
392C2×C4#379511yescharacteristic
393C2×C4D3×D1211yescharacteristic
394C2×C4#380511yescharacteristic
395C2×C4#380511yescharacteristic
396C2×C4C2×#62611yescharacteristic
397C8—22no—
398C8—62no—
399C2×C3—22no—
400C2×C3—21no—
401C2×C3—22no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—242no—
405C2×C3#467711yescharacteristic
406C2×C3#469611yescharacteristic
407C2×C3#471211yescharacteristic
408C2×C3#473712yes—
409C2×C3#476612yes—
410C2×C3#478412yes—
411C2×C3#484712yes—
412C2×C3#494911yescharacteristic
413C2×C3#515511yescharacteristic
414C2×C3#517611yescharacteristic
415D3—82no—
416C22—124no—
417C22—122no—
418C22—242no—
419C22—241no—
420C22—241no—
421C22#6379412yes—
422C22#6380712yes—
423C22#6389111yescharacteristic
424C22#6389311yescharacteristic
425C22#6391111yescharacteristic
426C4—122no—
427C4—241no—
428C4—721no—
429C4—721no—
430C4#6385711yescharacteristic
431C4#6389111yescharacteristic
432C4#6389311yescharacteristic
433C4#6396211yescharacteristic
434C3—21no—
435C3#6868011yescharacteristic, complemented
436C3#7018111yescharacteristic, complemented
437C2—242no—
438C2#1059076712yes—
439C2#1059083412yes—
440C2#1059086411yescharacteristic
441C2#1059088111yescharacteristic
442C2#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#2092
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
4. #10591224C2semidirect
5. C2×#63573C2semidirect
7. C3×#4550C2semidirect
37. #4550D3semidirect
371. C32#2092semidirect
435. C3#68680semidirect
436. C3#70181semidirect

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
#105913182
#105912242
C2×#635732
C2×#635632
C3×#45502
#701813
#686803