Finite Group Databasebeta

← #11795402

Subgroups — #11795402

Order 1152.

649 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63659C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591224C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63574C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70181—31nomaximal
9#69654—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×#217—22no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18#63659—22no—
19C3×#832—22no—
20#63579—22no—
21#63575—22no—
22#63574—22no—
23C2×C3×#102—31no—
24C3×#390—31no—
25#5221D311yescharacteristic
26C2×#832—31no—
27C2×#832—31no—
28C2×#832—61no—
29C2×#832D311yescharacteristic
30C2×#818—31no—
31#4977—31no—
32C2×#808—31no—
33C2×#808—31no—
34C2×#807—31no—
35#4936—31no—
36#4550—31no—
37#4524—31no—
38C24×C32—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4Q812yes—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D412yes—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)D412yes—
55C3×#217—44no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
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—21no—
67C22×C3×D4C2×D311yescharacteristic
68C22×C3×D4C2×D311yescharacteristic
69C22×C3×C8—31no—
70C2×C3×C4⋊C4—31no—
71C2×C3×C4⋊C4—31no—
72C2×C3×C22⋊C4—62no—
73C2×C3×C42—31no—
74C2×#217—22no—
75C2×C4⋊Dic3—31no—
76C2×C4⋊Dic3—31no—
77C2×C4⋊Dic3—61no—
78C2×C4⋊Dic3C2×D311yescharacteristic
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×#102—62no—
86#832—22no—
87#832—62no—
88#832—62no—
89#832—64no—
90C3⋊#95—62no—
91C3⋊#95—62no—
92#818—62no—
93#808—62no—
94#808—62no—
95#807—62no—
96C23×C32—22no—
97C23×C32—41no—
98C23×C32—41no—
99C23×C32—42no—
100C23×C32—42no—
101C23×C32C2×D411yescharacteristic
102C32×D4—22no—
103C32×D4—22no—
104C32×D4—41no—
105C32×D4—41no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×Q811yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C3⋊Dic3—41no—
113C2×C3⋊Dic3—42no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C3⋊(C3⋊C8)—22no—
122C3×C3⋊C8—22no—
123C2×#107—91no—
124C2×#106—91no—
125C2×#102—31no—
126C2×#102—91no—
127#390—31no—
128#382—91no—
129#336—91no—
130C24×C3—21no—
131C24×C3—21no—
132C24×C3—41no—
133C2×C3×D4—22no—
134C2×C3×D4—22no—
135C2×C3×D4—21no—
136C2×C3×D4—21no—
137C2×C3×D4—21no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—22no—
146C2×C3×D4—41no—
147C2×C3×D4—41no—
148C2×C3×D4—41no—
149C2×C3×D4Dic612yes—
150C2×C3×D4Dic612yes—
151C22×C3×C4—21no—
152C22×C3×C4—32no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×Dic3—21no—
158C22×Dic3—21no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161C22×Dic3—121no—
162C22×Dic3#6712yes—
163C2×C3×C8—32no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C22⋊C4—124no—
171C3×C42—61no—
172C3×C42—61no—
173#217—44no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—62no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—121no—
184C4×Dic3—21no—
185C4×Dic3—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—32no—
190C2×C3⋊C8—62no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—121no—
196C2×C3⋊C8—121no—
197C2×C3⋊C8#6712yes—
198C22×C32—42no—
199C22×C32—44no—
200C22×C32—82no—
201C22×C32—81no—
202C22×C32—81no—
203C22×C32C22⋊Q811yescharacteristic
204C22×C32#12311yescharacteristic
205C22×C32#12711yescharacteristic
206C22×C32#13512yes—
207C22×C32AGL(1,ℤ/8)12yes—
208C32×C4C22⋊Q811yescharacteristic
209C32×C4C22⋊Q811yescharacteristic
210C32×C4#12311yescharacteristic
211C32×C4#12311yescharacteristic
212C3⋊Dic3—81no—
213C3×Dic3—42no—
214C3×Dic3—81no—
215C3×Dic3—81no—
216C22×D4D3211yescharacteristic
217C22×C8—31no—
218C22×C8—91no—
219C2×C4⋊C4—31no—
220C2×C4⋊C4—31no—
221C2×C4⋊C4—91no—
222C2×C22⋊C4—62no—
223C2×C42—31no—
224#107—182no—
225#106—182no—
226#102—62no—
227#102—182no—
228#95—182no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—21no—
232C23×C3—42no—
233C23×C3—42no—
234C23×C3—42no—
235C23×C3—41no—
236C23×C3—42no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3—41no—
240C23×C3—41no—
241C23×C3—41no—
242C23×C3—42no—
243C23×C3—82no—
244C23×C3—82no—
245C23×C3D3×D411yescharacteristic
246C23×C3C2×#6711yescharacteristic
247C3×D4—24no—
248C3×D4—22no—
249C3×D4—22no—
250C3×D4—22no—
251C3×D4—22no—
252C3×D4—42no—
253C3×D4—42no—
254C3×D4—42no—
255C3×D4—41no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4—122no—
269C2×C3×C4—121no—
270C2×C3×C4—121no—
271C2×C3×C4—122no—
272C2×C3×C4C2×Dic611yescharacteristic
273C2×C3×C4C2×Dic611yescharacteristic
274C2×C3×C4#23511yescharacteristic
275C2×C3×C4#23511yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4#23711yescharacteristic
280C2×C3×C4#23711yescharacteristic
281C2×C3×C4#23711yescharacteristic
282C2×C3×C4#23711yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284C2×Dic3—22no—
285C2×Dic3—22no—
286C2×Dic3—22no—
287C2×Dic3—42no—
288C2×Dic3—42no—
289C2×Dic3—41no—
290C2×Dic3—41no—
291C2×Dic3—122no—
292C2×Dic3—122no—
293C2×Dic3—122no—
294C2×Dic3—121no—
295C2×Dic3—121no—
296C2×Dic3—242no—
297C3×C8—62no—
298C3⋊C8—22no—
299C3⋊C8—62no—
300C3⋊C8—62no—
301C3⋊C8—122no—
302C2×C32—82no—
303C2×C32#39911yescharacteristic
304C2×C32#47812yes—
305C2×C32#48212yes—
306C2×C32#49511yescharacteristic
307C2×C32#49611yescharacteristic
308C24—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4#62712yes—
315C22×C4—32no—
316C22×C4—61no—
317C22×C4—61no—
318C22×C4—181no—
319C22×C4C2×D3211yescharacteristic
320C2×C8—32no—
321C2×C8—61no—
322C2×C8—61no—
323C2×C8—92no—
324C2×C8—181no—
325C2×C8—181no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C22⋊C4—124no—
333C42—61no—
334C42—61no—
335C22×C3—22no—
336C22×C3—22no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—44no—
341C22×C3—42no—
342C22×C3—42no—
343C22×C3—44no—
344C22×C3—44no—
345C22×C3—84no—
346C22×C3—84no—
347C22×C3—82no—
348C22×C3—82no—
349C22×C3—81no—
350C22×C3—81no—
351C22×C3—82no—
352C22×C3—82no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3#87811yescharacteristic
356C22×C3#88311yescharacteristic
357C22×C3#91212yes—
358C22×C3#91412yes—
359C22×C3#92411yescharacteristic
360C22×C3#93212yes—
361C22×C3#93511yescharacteristic
362C22×C3#94011yescharacteristic
363C22×C3#94011yescharacteristic
364C22×C3#95012yes—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—122no—
370C3×C4—241no—
371C3×C4—241no—
372C3×C4#87811yescharacteristic
373C3×C4#87811yescharacteristic
374C3×C4#87811yescharacteristic
375C3×C4#88311yescharacteristic
376C3×C4#88311yescharacteristic
377C3×C4#88311yescharacteristic
378C3×C4#92411yescharacteristic
379C3×C4#93511yescharacteristic
380Dic3—42no—
381Dic3—81no—
382Dic3—81no—
383Dic3—242no—
384Dic3—241no—
385Dic3—241no—
386C32#209211yescharacteristic, complemented, Sylow
387C23—22no—
388C23—42no—
389C23—42no—
390C23—41no—
391C23—41no—
392C23D3×#6711yescharacteristic
393D4—22no—
394D4—22no—
395D4—41no—
396D4—41no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—122no—
401C2×C4—122no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—362no—
405C2×C4—361no—
406C2×C4#380411yescharacteristic
407C2×C4#380411yescharacteristic
408C2×C4#380511yescharacteristic
409C2×C4C2×#62711yescharacteristic
410C2×C4D3×#6711yescharacteristic
411C2×C4#381111yescharacteristic
412C8—62no—
413C8—182no—
414C2×C3—22no—
415C2×C3—22no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—84no—
420C2×C3—82no—
421C2×C3—82no—
422C2×C3#476612yes—
423C2×C3#478412yes—
424C2×C3#494911yescharacteristic
425C2×C3#494911yescharacteristic
426C2×C3#500912yes—
427C2×C3#503512yes—
428C2×C3#505911yescharacteristic
429C2×C3#507411yescharacteristic
430C2×C3#515511yescharacteristic
431C2×C3#517611yescharacteristic
432C22—44no—
433C22—42no—
434C22—82no—
435C22—81no—
436C22—81no—
437C22#6393312yes—
438C22#6393412yes—
439C22#6396411yescharacteristic
440C22#6396911yescharacteristic
441C22#6397911yescharacteristic
442C4—122no—
443C4—241no—
444C4—241no—
445C4—721no—
446C4#6396411yescharacteristic
447C4#6396911yescharacteristic
448C4#6397511yescharacteristic
449C4#6398211yescharacteristic
450C3—21no—
451C3#6965411yescharacteristic, complemented
452C3#7018111yescharacteristic, complemented
453C2—82no—
454C2#1059141112yes—
455C2#1059142312yes—
456C2#1059147011yescharacteristic
457C2#1059147211yescharacteristic
458C2#1059171511yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32#2092
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591224C2semidirect
5. C2×#63575C2semidirect
6. C2×#63574C2semidirect
7. #10589155C2semidirect
386. C32#2092semidirect
451. C3#69654semidirect
452. C3#70181semidirect

Maximal subgroups

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

subgroupindex
C2×#636592
C3×#52212
C2×C3×#8322
#105912242
C2×#635752
C2×#635742
#105891552
#701813
#696543