Finite Group Databasebeta

← #11795439

Subgroups — #11795439

Order 1152.

681 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
1C2×#63659C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591349C211yesmaximal, characteristic, complemented
5C2×#63576C211yesmaximal, characteristic, complemented
6C2×#63575C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70183—31nomaximal
9#69655—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
18C2×Dic3⋊Dic3—22no—
19#63659—22no—
20C3×#832—22no—
21#63576—22no—
22#63575—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#4975—31no—
32C2×#807—31no—
33C2×#807—31no—
34C2×#807—31no—
35#4935—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—
65Dic3⋊Dic3—44no—
66#2093—91noSylow
67C22×C3×D4—21no—
68C22×C3×D4C2×D311yescharacteristic
69C22×C3×D4C2×D311yescharacteristic
70C22×C3×C8—31no—
71C2×C3×C4⋊C4—31no—
72C2×C3×C4⋊C4—31no—
73C2×C3×C22⋊C4—62no—
74C2×C3×C42—31no—
75C2×#217—22no—
76C2×C4⋊Dic3—31no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—61no—
79C2×C4⋊Dic3—62no—
80C2×C4⋊Dic3C2×D311yescharacteristic
81C2×C4⋊Dic3C2×D311yescharacteristic
82C2×Dic3⋊C4—62no—
83C2×C4×Dic3C2×D311yescharacteristic
84C22×C3⋊C8—31no—
85C22×C3⋊C8—31no—
86C22×C3⋊C8—61no—
87C22×C3⋊C8C2×D311yescharacteristic
88C3×#102—62no—
89#832—22no—
90#832—62no—
91#832—62no—
92#832—64no—
93#818—62no—
94#807—62no—
95#807—62no—
96#807—62no—
97C23×C32—22no—
98C23×C32—41no—
99C23×C32—41no—
100C23×C32—42no—
101C23×C32—42no—
102C23×C32C2×D411yescharacteristic
103C32×D4—22no—
104C32×D4—22no—
105C32×D4—41no—
106C32×D4—41no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×Q811yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C3⋊Dic3—41no—
114C2×C3⋊Dic3—42no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3D814yes—
122C3⋊(C3⋊C8)—22no—
123C3×C3⋊C8—22no—
124C2×#107—91no—
125C2×#107—91no—
126C2×#102—31no—
127C2×#102—91no—
128#390—31no—
129#384—91no—
130#336—91no—
131C24×C3—21no—
132C24×C3—21no—
133C24×C3—41no—
134C2×C3×D4—22no—
135C2×C3×D4—22no—
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—21no—
146C2×C3×D4—22no—
147C2×C3×D4—41no—
148C2×C3×D4—41no—
149C2×C3×D4—41no—
150C2×C3×D4Dic612yes—
151C2×C3×D4Dic612yes—
152C22×C3×C4—21no—
153C22×C3×C4—32no—
154C22×C3×C4—61no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×Dic3—21no—
159C22×Dic3—21no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—121no—
163C22×Dic3#6712yes—
164C2×C3×C8—32no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C22⋊C4—124no—
172C3×C42—61no—
173C3×C42—61no—
174#217—44no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—62no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—121no—
185C4⋊Dic3—124no—
186Dic3⋊C4—124no—
187C4×Dic3—21no—
188C4×Dic3—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—32no—
192C2×C3⋊C8—32no—
193C2×C3⋊C8—62no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—121no—
199C2×C3⋊C8—121no—
200C2×C3⋊C8#6712yes—
201C22×C32—42no—
202C22×C32—44no—
203C22×C32—82no—
204C22×C32—81no—
205C22×C32—81no—
206C22×C32C22⋊Q811yescharacteristic
207C22×C32#12311yescharacteristic
208C22×C32#12711yescharacteristic
209C22×C32C2×D812yes—
210C22×C32#13712yes—
211C32×C4C22⋊Q811yescharacteristic
212C32×C4C22⋊Q811yescharacteristic
213C32×C4#12311yescharacteristic
214C32×C4#12311yescharacteristic
215C3⋊Dic3—81no—
216C3×Dic3—24no—
217C3×Dic3—81no—
218C3×Dic3—81no—
219C22×D4D3211yescharacteristic
220C22×C8—31no—
221C22×C8—91no—
222C2×C4⋊C4—31no—
223C2×C4⋊C4—31no—
224C2×C4⋊C4—91no—
225C2×C4⋊C4—182no—
226C2×C22⋊C4—62no—
227C2×C42—31no—
228#107—182no—
229#107—182no—
230#102—62no—
231#102—182no—
232C23×C3—22no—
233C23×C3—22no—
234C23×C3—21no—
235C23×C3—42no—
236C23×C3—42no—
237C23×C3—42no—
238C23×C3—41no—
239C23×C3—42no—
240C23×C3—42no—
241C23×C3—42no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—41no—
245C23×C3—42no—
246C23×C3—82no—
247C23×C3—82no—
248C23×C3D3×D411yescharacteristic
249C23×C3C2×#6711yescharacteristic
250C3×D4—24no—
251C3×D4—22no—
252C3×D4—22no—
253C3×D4—22no—
254C3×D4—22no—
255C3×D4—42no—
256C3×D4—42no—
257C3×D4—42no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—34no—
269C2×C3×C4—62no—
270C2×C3×C4—62no—
271C2×C3×C4—122no—
272C2×C3×C4—122no—
273C2×C3×C4—121no—
274C2×C3×C4—121no—
275C2×C3×C4C2×Dic611yescharacteristic
276C2×C3×C4C2×Dic611yescharacteristic
277C2×C3×C4#23511yescharacteristic
278C2×C3×C4#23511yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4#23711yescharacteristic
283C2×C3×C4#23711yescharacteristic
284C2×C3×C4#23711yescharacteristic
285C2×C3×C4#23711yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287C2×Dic3—22no—
288C2×Dic3—22no—
289C2×Dic3—42no—
290C2×Dic3—42no—
291C2×Dic3—41no—
292C2×Dic3—41no—
293C2×Dic3—122no—
294C2×Dic3—122no—
295C2×Dic3—122no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298C2×Dic3—242no—
299C2×Dic3#21314yes—
300C3×C8—62no—
301C3⋊C8—22no—
302C3⋊C8—62no—
303C3⋊C8—62no—
304C3⋊C8—122no—
305C2×C32—82no—
306C2×C32#39911yescharacteristic
307C2×C32#47412yes—
308C2×C32#48012yes—
309C2×C32#49311yescharacteristic
310C2×C32#49711yescharacteristic
311C24—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4#62712yes—
318C22×C4—32no—
319C22×C4—61no—
320C22×C4—61no—
321C22×C4—181no—
322C22×C4C2×D3211yescharacteristic
323C2×C8—32no—
324C2×C8—61no—
325C2×C8—61no—
326C2×C8—92no—
327C2×C8—181no—
328C2×C8—181no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C4⋊C4—364no—
336C22⋊C4—124no—
337C42—61no—
338C42—61no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—44no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—44no—
348C22×C3—44no—
349C22×C3—84no—
350C22×C3—82no—
351C22×C3—84no—
352C22×C3—82no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3—82no—
356C22×C3—82no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3#87811yescharacteristic
360C22×C3#88311yescharacteristic
361C22×C3D3×D812yes—
362C22×C3#91512yes—
363C22×C3#92411yescharacteristic
364C22×C3C2×#21312yes—
365C22×C3#93511yescharacteristic
366C22×C3#94011yescharacteristic
367C22×C3#94011yescharacteristic
368C22×C3#95112yes—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—64no—
374C3×C4—241no—
375C3×C4—241no—
376C3×C4#87811yescharacteristic
377C3×C4#87811yescharacteristic
378C3×C4#87811yescharacteristic
379C3×C4#88311yescharacteristic
380C3×C4#88311yescharacteristic
381C3×C4#88311yescharacteristic
382C3×C4#92411yescharacteristic
383C3×C4#93511yescharacteristic
384Dic3—24no—
385Dic3—81no—
386Dic3—81no—
387Dic3—242no—
388Dic3—241no—
389Dic3—241no—
390C32#209311yescharacteristic, complemented, Sylow
391C23—22no—
392C23—42no—
393C23—42no—
394C23—41no—
395C23—41no—
396C23D3×#6711yescharacteristic
397D4—22no—
398D4—22no—
399D4—41no—
400D4—41no—
401C2×C4—34no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—122no—
405C2×C4—122no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—362no—
409C2×C4—361no—
410C2×C4#380411yescharacteristic
411C2×C4#380411yescharacteristic
412C2×C4#380511yescharacteristic
413C2×C4C2×#62711yescharacteristic
414C2×C4D3×#6711yescharacteristic
415C2×C4#381111yescharacteristic
416C8—62no—
417C8—182no—
418C2×C3—21no—
419C2×C3—22no—
420C2×C3—22no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—84no—
424C2×C3—82no—
425C2×C3—82no—
426C2×C3#475912yes—
427C2×C3#477412yes—
428C2×C3#494911yescharacteristic
429C2×C3#494911yescharacteristic
430C2×C3#500712yes—
431C2×C3#503312yes—
432C2×C3#506011yescharacteristic
433C2×C3#507311yescharacteristic
434C2×C3#515111yescharacteristic
435C2×C3#516711yescharacteristic
436C22—44no—
437C22—42no—
438C22—81no—
439C22—82no—
440C22—81no—
441C22D3×#21312yes—
442C22#6392912yes—
443C22#6396411yescharacteristic
444C22#6396911yescharacteristic
445C22#6397911yescharacteristic
446C4—64no—
447C4—241no—
448C4—241no—
449C4—721no—
450C4#6396411yescharacteristic
451C4#6396911yescharacteristic
452C4#6397511yescharacteristic
453C4#6398211yescharacteristic
454C3—21no—
455C3#6965511yescharacteristic, complemented
456C3#7018311yescharacteristic, complemented
457C2—82no—
458C2#1059141012yes—
459C2#1059141312yes—
460C2#1059148211yescharacteristic
461C2#1059149111yescharacteristic
462C2#1059171511yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32#2093
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. #10591349C2semidirect
5. C2×#63576C2semidirect
6. C2×#63575C2semidirect
7. #10589155C2semidirect
390. C32#2093semidirect
455. C3#69655semidirect
456. C3#70183semidirect

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
#105913492
C2×#635762
C2×#635752
#105891552
#701833
#696553