Finite Group Databasebeta

← #11789726

Subgroups — #11789726

Order 1152.

477 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5005C211yesmaximal, characteristic
2#10591141C211yesmaximal, characteristic, complemented
3C2×#63569C211yesmaximal, characteristic
4#10591076C211yesmaximal, characteristic
5Dic3×#208C211yesmaximal, characteristic, complemented
6#10589399C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8#70401—31nomaximal
9#68750—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#805—22no—
18#63577—22no—
19#63569—21no—
20#63569—21no—
21#63560C412yescomplemented
22#63558C412yescomplemented
23#63554—21no—
24Dic3×C3⋊C8—21no—
25C3×#421—31no—
26#5237—31no—
27C2×#837—31no—
28#5132—31no—
29#5125—31no—
30#5124—31no—
31Dic3×M16—31no—
32#5005D311yescharacteristic
33C2×#805—31no—
34C4×#208—31no—
35C3×#339—31no—
36#4533—31no—
37#4533—31no—
38#4533—61no—
39#4532D311yescharacteristic, complemented
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67—21no—
42C22×C3×Dic3—21no—
43C3×#235—21no—
44C3×#235—21no—
45C3×#235—21no—
46C3×#235—21no—
47C2×C3×D12C2×C411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6C2×C411yescharacteristic
50C32×C4⋊C4—21no—
51C32×C22⋊C4—21no—
52C32×C42—21no—
53#3748—21no—
54#3748—21no—
55#3748—21no—
56#3748C2×C412yes—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×#208—21no—
63C3×#208—21no—
64C3×#208C2×C412yes—
65C3×#208D412yes—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1932—91noSylow
69C2×C3×#41—31no—
70C2×#235C2×D311yescharacteristic
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C3×#117—21no—
74C3×#117C2×D311yescharacteristic
75C3×#117C2×D311yescharacteristic
76C2×C3×C42—31no—
77C2×C4×Dic3C2×D311yescharacteristic
78C2×#208—31no—
79C2×#208—31no—
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C3×#104—62no—
87#837—61no—
88#837—61no—
89#836—32no—
90#833—32no—
91#824—32no—
92#823—32no—
93#822—62no—
94#819—62no—
95#815—61no—
96C8×Dic3—61no—
97#805—22no—
98#805—61no—
99#805—61no—
100#803—61no—
101C4×C3⋊C8—61no—
102C23×C32#4111yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4—41no—
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C3×#67—41no—
112C3×#67—41no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—42no—
117C3×D12—21no—
118C3×D12—21no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—21no—
122C3×Dic6—21no—
123C3⋊(C3⋊C8)—22no—
124C3⋊(C3⋊C8)—41no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—22no—
127#430—91no—
128#421—31no—
129C2×#104—91no—
130#413—91no—
131C4×M16—91no—
132#344—91no—
133#339—31no—
134C3×#41—61no—
135C3×#41—61no—
136C3×#41—61no—
137C3×#41—61no—
138C2×C3×Q8—31no—
139C2×C3×D4—31no—
140C2×C3×D4—61no—
141C22×C3×C4—21no—
142C22×C3×C4—61no—
143C22×C3×C4—61no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C2×#67—21no—
147C22×Dic3—21no—
148#235—21no—
149#235—21no—
150#235—21no—
151#235—21no—
152C2×D12C4×D311yescharacteristic
153C2×C4×D3—21no—
154C2×Dic6C4×D311yescharacteristic
155C3×M16—32no—
156C3×M16—32no—
157C3×M16—61no—
158C3×M16—61no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—41no—
164C3×C22⋊C4—22no—
165C3×C22⋊C4—21no—
166C3×C22⋊C4—21no—
167C3×C42—21no—
168C3×C42—21no—
169C3×C42—31no—
170C3×C42—31no—
171C3×C42—41no—
172C3×C42—61no—
173C4×Dic3—21no—
174C4×Dic3D1211yescharacteristic
175C4×Dic3D1211yescharacteristic
176#208—21no—
177#208—21no—
178#208—32no—
179#208—32no—
180#208—62no—
181#208—61no—
182#208—61no—
183#208—61no—
184#208—61no—
185#208—61no—
186#208—61no—
187#208—121no—
188#208—121no—
189#208—121no—
190#208C4×D312yes—
191#208#6712yes—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—62no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—121no—
200C22×C32—41no—
201C22×C32#11711yescharacteristic
202C22×C32#12311yescharacteristic
203C22×C32#12411yescharacteristic
204C2×C3×D3—41no—
205C2×C3×D3—81no—
206C32×C4—81no—
207C32×C4C4×D411yescharacteristic
208C32×C4C4×D411yescharacteristic
209C32×C4#12111yescharacteristic
210C32×C4#12611yescharacteristic
211C3×Dic3—22no—
212C3×Dic3—41no—
213C3×Dic3—41no—
214C2×#41—31no—
215C2×M16—31no—
216C2×M16—31no—
217C2×M16—91no—
218C2×M16—91no—
219#117D3211yescharacteristic
220C2×C42—31no—
221#108—182no—
222#104—62no—
223#104—181no—
224#104—181no—
225#101—92no—
226#100—92no—
227#97—181no—
228C4×C8—181no—
229C23×C3—21no—
230C23×C3—61no—
231C23×C3#23711yescharacteristic
232C23×C3#23711yescharacteristic
233C22×D3—21no—
234C3×Q8—61no—
235C3×Q8—61no—
236C3×D4—61no—
237C3×D4—61no—
238C3×D4—121no—
239C3×D4—121no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—42no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4—61no—
252C2×C3×C4—122no—
253C2×C3×C4—121no—
254C2×C3×C4—121no—
255C2×C3×C4C2×C4×D311yescharacteristic
256C2×C3×C4C2×C4×D311yescharacteristic
257C2×C3×C4C2×D1211yescharacteristic
258C2×C3×C4#23511yescharacteristic
259C2×C3×C4#23511yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4#23711yescharacteristic
263C2×C3×C4#23711yescharacteristic
264C2×C3×C4#23711yescharacteristic
265C2×C3×C4#23911yescharacteristic
266C2×C3×C4C2×#6711yescharacteristic
267#67—41no—
268#67—41no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—42no—
273D12—21no—
274D12—21no—
275C4×D3—41no—
276C4×D3—41no—
277Dic6—21no—
278Dic6—21no—
279C3×C8—62no—
280C3×C8—62no—
281C3⋊C8—22no—
282C3⋊C8—22no—
283C3⋊C8—62no—
284C3⋊C8—62no—
285C3⋊C8—122no—
286C3⋊C8—122no—
287C3⋊C8—121no—
288C3⋊C8—121no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32#38811yescharacteristic
293C3×D3—81no—
294#41—61no—
295#41—61no—
296#41—61no—
297#41—61no—
298C2×Q8—31no—
299C2×D4—31no—
300C2×D4—61no—
301C22×C4—61no—
302C22×C4—61no—
303C22×C4C2×D3211yescharacteristic
304M16—32no—
305M16—32no—
306M16—61no—
307M16—61no—
308M16—92no—
309M16—181no—
310M16—181no—
311M16—181no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—181no—
315C2×C8—181no—
316C4⋊C4—21no—
317C22⋊C4—21no—
318C42—21no—
319C42—31no—
320C42—31no—
321C42—61no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—81no—
328C22×C3—121no—
329C22×C3—241no—
330C22×C3#87711yescharacteristic
331C22×C3#88311yescharacteristic
332C22×C3#88511yescharacteristic
333C22×C3#88611yescharacteristic
334C22×C3#89211yescharacteristic
335C22×C3#93611yescharacteristic
336C2×D3—41no—
337C2×D3—81no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—62no—
343C3×C4—81no—
344C3×C4—81no—
345C3×C4—82no—
346C3×C4—121no—
347C3×C4—121no—
348C3×C4C4×D1211yescharacteristic
349C3×C4#87911yescharacteristic
350C3×C4#67⋊C411yescharacteristic
351C3×C4#67⋊C411yescharacteristic
352C3×C4#89511yescharacteristic
353C3×C4#89811yescharacteristic
354C3×C4C4×#6711yescharacteristic
355C3×C4#93911yescharacteristic
356Dic3—22no—
357Dic3—41no—
358Dic3—41no—
359C32#193211yescharacteristic, complemented, Sylow
360C23—61no—
361C23#380511yescharacteristic
362Q8—61no—
363Q8—61no—
364D4—61no—
365D4—61no—
366D4—121no—
367D4—121no—
368C2×C4—41no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—61no—
372C2×C4—122no—
373C2×C4—121no—
374C2×C4—121no—
375C2×C4#379511yescharacteristic
376C2×C4#379611yescharacteristic
377C2×C4C4×D3211yescharacteristic
378C2×C4D3×D1211yescharacteristic
379C2×C4#380411yescharacteristic
380C2×C4D3×#6711yescharacteristic
381C8—62no—
382C8—62no—
383C8—182no—
384C8—361no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—41no—
393C2×C3—41no—
394C2×C3—41no—
395C2×C3—241no—
396C2×C3#467011yescharacteristic
397C2×C3#494511yescharacteristic
398D3—81no—
399C22—41no—
400C22—121no—
401C22—241no—
402C22#6387811yescharacteristic
403C22#6389111yescharacteristic
404C22#6395911yescharacteristic
405C4—62no—
406C4—81no—
407C4—121no—
408C4—121no—
409C4#6385811yescharacteristic
410C4#6387911yescharacteristic
411C4#6388011yescharacteristic
412C4#6388611yescharacteristic
413C3—21no—
414C3#6875011yescharacteristic, complemented
415C3#7040111yescharacteristic, complemented
416C2—21no—
417C2—21no—
418C2—21no—
419C2—241no—
420C2#1059128411yescharacteristic
subgroupG/H
centerC4#63886
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#388
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1932
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10591141C2semidirect
5. Dic3×#208C2semidirect
6. #10589399C2semidirect
7. C3×#4532C2semidirect
21. #63560C4semidirect
22. #63558C4semidirect
39. #4532D3semidirect
359. C32#1932semidirect
414. C3#68750semidirect
415. C3#70401semidirect

Maximal subgroups

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

subgroupindex
C3×#50052
#105911412
C2×#635692
#105910762
Dic3×#2082
#105893992
C3×#45322
#704013
#687503