Finite Group Databasebeta

← #11795401

Subgroups — #11795401

Order 1152.

677 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
1#10592920C211yesmaximal, characteristic
2C2×C3×#832C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591230C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63573C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#70182—31nomaximal
9#70181—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3757—22no—
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C3×#832—22no—
19C3×#832—22no—
20#63579—22no—
21#63575—22no—
22#63573—22no—
23C2×C3×#102—31no—
24C2×C3×#102—31no—
25#5221—31no—
26#5221—31no—
27#5221—61no—
28C2×#832D311yescharacteristic
29C2×#832D311yescharacteristic
30C2×#818—31no—
31C2×#817—31no—
32#4977—31no—
33#4977—31no—
34C2×#808—31no—
35C2×#807—31no—
36#4550—31no—
37#4550—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⋊Dic3D412yes—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50#3757—44no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8D412yes—
64C2×C3×C3⋊C8D412yes—
65#2092—91noSylow
66C22×C3×D4—21no—
67C22×C3×D4C2×D311yescharacteristic
68C22×C3×D4C2×D311yescharacteristic
69C22×C3×C8—31no—
70C22×C3×C8—31no—
71C2×C3×C4⋊C4—31no—
72C2×C3×C4⋊C4—31no—
73C2×#217—62no—
74C2×#217—62no—
75C2×#217—64no—
76C2×C4⋊Dic3—31no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—61no—
79C2×C4⋊Dic3C2×D311yescharacteristic
80C2×C4⋊Dic3C2×D311yescharacteristic
81C2×C4×Dic3—31no—
82C2×C4×Dic3—31no—
83C2×C4×Dic3—61no—
84C22×C3⋊C8C2×D311yescharacteristic
85C22×C3⋊C8C2×D311yescharacteristic
86C3×#102—62no—
87C3×#102—62no—
88#832—22no—
89#832—22no—
90C3⋊#95—62no—
91C3⋊#95—62no—
92#818—62no—
93#817—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—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—41no—
116C2×C3⋊Dic3—42no—
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—31no—
127#390—91no—
128#382—91no—
129#336—91no—
130C24×C3—22no—
131C24×C3—21no—
132C24×C3—21no—
133C2×C3×D4—22no—
134C2×C3×D4—21no—
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—22no—
145C2×C3×D4—41no—
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—61no—
153C22×C3×C4—61no—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×Dic3—21no—
157C22×Dic3—21no—
158C22×Dic3—32no—
159C22×Dic3—32no—
160C22×Dic3—62no—
161C22×Dic3—62no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C2×C3×C8—32no—
165C2×C3×C8—32no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174#217—128no—
175#217—124no—
176#217—124no—
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—121no—
186C4⋊Dic3—121no—
187C4×Dic3—61no—
188C4×Dic3—61no—
189C4×Dic3—61no—
190C4×Dic3—61no—
191C4×Dic3—121no—
192C4×Dic3—121no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8#6712yes—
198C2×C3⋊C8#6712yes—
199C22×C32—42no—
200C22×C32—44no—
201C22×C32—82no—
202C22×C32—81no—
203C22×C32—81no—
204C22×C32C22⋊Q811yescharacteristic
205C22×C32#12311yescharacteristic
206C22×C32#12711yescharacteristic
207C22×C32#13512yes—
208C22×C32AGL(1,ℤ/8)12yes—
209C32×C4C22⋊Q811yescharacteristic
210C32×C4C22⋊Q811yescharacteristic
211C32×C4#12311yescharacteristic
212C32×C4#12311yescharacteristic
213C3⋊Dic3—42no—
214C3⋊Dic3—81no—
215C3×Dic3—81no—
216C3×Dic3—81no—
217C22×D4D3211yescharacteristic
218C22×C8—31no—
219C22×C8—31no—
220C2×C4⋊C4—31no—
221C2×C4⋊C4—31no—
222C2×C4⋊C4—91no—
223C2×C22⋊C4—182no—
224C2×C42—91no—
225#107—182no—
226#106—182no—
227#102—62no—
228#102—62no—
229#95—182no—
230C23×C3—24no—
231C23×C3—22no—
232C23×C3—22no—
233C23×C3—21no—
234C23×C3—44no—
235C23×C3—42no—
236C23×C3—42no—
237C23×C3—44no—
238C23×C3—41no—
239C23×C3—41no—
240C23×C3—42no—
241C23×C3—42no—
242C23×C3—42no—
243C23×C3—42no—
244C23×C3—41no—
245C23×C3—41no—
246C23×C3D3×D411yescharacteristic
247C23×C3D3×D411yescharacteristic
248C3×D4—22no—
249C3×D4—22no—
250C3×D4—22no—
251C3×D4—22no—
252C3×D4—42no—
253C3×D4—42no—
254C3×D4—42no—
255C3×D4—42no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—122no—
267C2×C3×C4—122no—
268C2×C3×C4—121no—
269C2×C3×C4—121no—
270C2×C3×C4C2×Dic611yescharacteristic
271C2×C3×C4C2×Dic611yescharacteristic
272C2×C3×C4#23511yescharacteristic
273C2×C3×C4#23511yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4#23711yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4#23711yescharacteristic
279C2×C3×C4#23711yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×Dic3—42no—
283C2×Dic3—42no—
284C2×Dic3—41no—
285C2×Dic3—41no—
286C2×Dic3—64no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—122no—
294C2×Dic3—122no—
295C2×Dic3—122no—
296C2×Dic3—124no—
297C2×Dic3—122no—
298C2×Dic3—122no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C3×C8—62no—
302C3×C8—62no—
303C3⋊C8—22no—
304C3⋊C8—22no—
305C2×C32—82no—
306C2×C32#39911yescharacteristic
307C2×C32#47812yes—
308C2×C32#48212yes—
309C2×C32#49511yescharacteristic
310C2×C32#49611yescharacteristic
311C24—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4#62712yes—
318C22×C4—61no—
319C22×C4—61no—
320C22×C4—92no—
321C22×C4—181no—
322C22×C4C2×D3211yescharacteristic
323C2×C8—32no—
324C2×C8—32no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C22⋊C4—364no—
336C42—181no—
337C42—181no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—44no—
344C22×C3—48no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—44no—
348C22×C3—44no—
349C22×C3—84no—
350C22×C3—82no—
351C22×C3—82no—
352C22×C3—81no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3—81no—
356C22×C3—82no—
357C22×C3—82no—
358C22×C3#87811yescharacteristic
359C22×C3#87811yescharacteristic
360C22×C3#88311yescharacteristic
361C22×C3#88311yescharacteristic
362C22×C3#91112yes—
363C22×C3#91212yes—
364C22×C3#91412yes—
365C22×C3#91612yes—
366C22×C3#94011yescharacteristic
367C22×C3#94011yescharacteristic
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—241no—
373C3×C4—241no—
374C3×C4#87811yescharacteristic
375C3×C4#87811yescharacteristic
376C3×C4#88311yescharacteristic
377C3×C4#88311yescharacteristic
378C3×C4#92411yescharacteristic
379C3×C4#92411yescharacteristic
380C3×C4#93511yescharacteristic
381C3×C4#93511yescharacteristic
382Dic3—81no—
383Dic3—81no—
384Dic3—124no—
385Dic3—122no—
386Dic3—122no—
387Dic3—242no—
388Dic3—241no—
389Dic3—241no—
390C32#209211yescharacteristic, complemented, Sylow
391C23—22no—
392C23—42no—
393C23—42no—
394C23—41no—
395C23—41no—
396C23#381111yescharacteristic
397D4—22no—
398D4—22no—
399D4—41no—
400D4—41no—
401C2×C4—122no—
402C2×C4—122no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—182no—
406C2×C4—182no—
407C2×C4—182no—
408C2×C4—362no—
409C2×C4—361no—
410C2×C4#380411yescharacteristic
411C2×C4#380411yescharacteristic
412C2×C4#380511yescharacteristic
413C2×C4C2×#62711yescharacteristic
414C2×C4D3×#6711yescharacteristic
415C2×C4D3×#6711yescharacteristic
416C8—62no—
417C8—62no—
418C2×C3—22no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—22no—
423C2×C3—84no—
424C2×C3—82no—
425C2×C3—82no—
426C2×C3#476312yes—
427C2×C3#476612yes—
428C2×C3#477912yes—
429C2×C3#478412yes—
430C2×C3#494911yescharacteristic
431C2×C3#494911yescharacteristic
432C2×C3#515411yescharacteristic
433C2×C3#515511yescharacteristic
434C2×C3#516811yescharacteristic
435C2×C3#517611yescharacteristic
436C22—42no—
437C22—44no—
438C22—82no—
439C22—81no—
440C22—81no—
441C22#6393612yes—
442C22#6393712yes—
443C22#6397511yescharacteristic
444C22#6397911yescharacteristic
445C22#6398211yescharacteristic
446C4—241no—
447C4—241no—
448C4—362no—
449C4—721no—
450C4#6396411yescharacteristic
451C4#6396411yescharacteristic
452C4#6396911yescharacteristic
453C4#6396911yescharacteristic
454C3—21no—
455C3#7018111yescharacteristic, complemented
456C3#7018211yescharacteristic, complemented
457C2—82no—
458C2#1059142512yes—
459C2#1059147411yescharacteristic
460C2#1059147511yescharacteristic
461C2#1059147912yes—
462C2#1059171511yescharacteristic
subgroupG/H
centerC23#3811
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. #10591230C2semidirect
5. C2×#63575C2semidirect
6. C2×#63573C2semidirect
7. #10589156C2semidirect
390. C32#2092semidirect
455. C3#70181semidirect
456. C3#70182semidirect

Maximal subgroups

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

subgroupindex
#105929202
C2×C3×#8322
#105912302
C2×#635752
C2×#635732
#105891562
#701823
#701813