Finite Group Databasebeta

← #11789678

Subgroups — #11789678

Order 1152.

513 conjugacy classes of subgroups.

The subgroup lattice has 445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5131C211yesmaximal, characteristic
2#10591131C211yesmaximal, characteristic, complemented
3C2×#63563C211yesmaximal, characteristic
4C2×#63558C211yesmaximal, characteristic
5#10591055C211yesmaximal, characteristic, complemented
6#10589420C211yesmaximal, characteristic, complemented
7C3×#4558C211yesmaximal, characteristic, complemented
8#70318—31nomaximal
9#68931—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#821—21no—
18C3×#821—21no—
19#63575—21no—
20#63573—21no—
21#63563—21no—
22#63563—21no—
23#63558C414yescomplemented
24#63554—21no—
25Dic3×C3⋊C8—21no—
26C3×#418—31no—
27C2×#833—31no—
28C2×#832—31no—
29#5131D311yescharacteristic
30C2×#823—31no—
31#5121—31no—
32C2×#821—31no—
33#5101—31no—
34#4997—31no—
35#4995—31no—
36C3×#341—31no—
37#4558D311yescharacteristic, complemented
38#4554—31no—
39#4554—31no—
40#4554—61no—
41C23×C3×D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12C2×C412yes—
50C32×M16—21no—
51C32×M16—21no—
52C2×C32×C8—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55#3748—21no—
56#3748C2×C412yes—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4×Dic3—21no—
62C3×#208—21no—
63C3×#208C2×C412yes—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8D411yescharacteristic
68C2×C3×C3⋊C8D411yescharacteristic
69#1931—91noSylow
70C22×C3×D4—31no—
71C22×D12C2×D311yescharacteristic
72C2×C3×M16—21no—
73C2×C3×M16—31no—
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C2×D311yescharacteristic
76C22×C3×C8—31no—
77C3×#117—31no—
78#926C2×D311yescharacteristic
79C2×C4⋊Dic3—31no—
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—61no—
82C2×#208—31no—
83C2×#208—31no—
84C2×#208—61no—
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8C2×D311yescharacteristic
87C3×#102—61no—
88C3×#102—61no—
89#833—34no—
90#832—61no—
91#832—61no—
92#823—34no—
93#821—21no—
94#821—21no—
95#821—61no—
96#821—61no—
97#818—61no—
98#817—61no—
99#815—61no—
100C8×Dic3—61no—
101#808—61no—
102#807—61no—
103#803—61no—
104C4×C3⋊C8—61no—
105C23×C32#4111yescharacteristic
106C22×C3×D3—22no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C22×C3×D3—81no—
110C22×C3×D3—81no—
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C3⋊Dic3—41no—
118C2×C3⋊Dic3—81no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C3×D12—22no—
122C3×D12—22no—
123C3×D12—41no—
124C3×D12—41no—
125C32×C8—41no—
126C3⋊(C3⋊C8)—22no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—21no—
129C3×C3⋊C8—21no—
130#428—91no—
131#418—31no—
132C2×#102—91no—
133C2×#100—91no—
134#405—91no—
135#343—91no—
136#341—31no—
137C24×C3—61no—
138C23×D3—21no—
139C2×C3×D4—32no—
140C2×C3×D4—61no—
141C2×C3×D4—61no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C22×C3×C4—21no—
146C22×C3×C4C22×D311yescharacteristic
147C22×C3×C4C22×D311yescharacteristic
148C22×Dic3—62no—
149C22×Dic3—61no—
150C22×Dic3—61no—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12C4×D312yes—
157C3×M16—22no—
158C3×M16—21no—
159C3×M16—21no—
160C3×M16—21no—
161C3×M16—21no—
162C3×M16—32no—
163C3×M16—41no—
164C3×M16—61no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—31no—
168C2×C3×C8—31no—
169C2×C3×C8—41no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—31no—
175C3×C22⋊C4—61no—
176C3×C42—61no—
177#217—21no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—121no—
183C4⋊Dic3—121no—
184C4⋊Dic3#6711yescharacteristic
185C4⋊Dic3#6711yescharacteristic
186C4×Dic3—21no—
187#208—21no—
188#208—32no—
189#208—32no—
190#208—62no—
191#208—61no—
192#208—61no—
193#208—121no—
194#208C4×D312yes—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—121no—
201C2×C3⋊C8D1211yescharacteristic
202C2×C3⋊C8D1211yescharacteristic
203C22×C32—21no—
204C22×C32—21no—
205C22×C32#11711yescharacteristic
206C22×C32#12111yescharacteristic
207C22×C32#12611yescharacteristic
208C2×C3×D3—42no—
209C2×C3×D3—82no—
210C2×C3×D3—81no—
211C2×C3×D3—81no—
212C2×C3×D3—82no—
213C32×C4C4×D411yescharacteristic
214C32×C4C4×D411yescharacteristic
215C32×C4#12311yescharacteristic
216C32×C4#12411yescharacteristic
217C3⋊Dic3—81no—
218C3×Dic3—41no—
219C3×Dic3—41no—
220C22×D4—31no—
221C2×M16—31no—
222C2×M16—91no—
223C2×M16D3211yescharacteristic
224C22×C8—31no—
225#117—31no—
226C2×C4⋊C4—91no—
227#107—181no—
228#106—181no—
229#102—61no—
230#102—61no—
231#102—181no—
232#102—181no—
233#100—94no—
234#97—181no—
235C4×C8—181no—
236C23×C3—21no—
237C23×C3—62no—
238C23×C3—121no—
239C23×C3—121no—
240C23×C3—241no—
241C23×C3—241no—
242C23×C3#23711yescharacteristic
243C23×C3#23911yescharacteristic
244C22×D3—22no—
245C22×D3—41no—
246C22×D3—41no—
247C22×D3—81no—
248C22×D3—81no—
249C3×D4—62no—
250C3×D4—62no—
251C3×D4—121no—
252C3×D4—121no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4C2×C4×D311yescharacteristic
262C2×C3×C4C2×C4×D311yescharacteristic
263C2×C3×C4C2×D1211yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4#23511yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4#23711yescharacteristic
269C2×C3×C4#23711yescharacteristic
270C2×C3×C4#23711yescharacteristic
271C2×C3×C4#23711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—122no—
276C2×Dic3—121no—
277C2×Dic3—121no—
278C2×Dic3—241no—
279C2×Dic3—241no—
280C2×Dic3—242no—
281D12—22no—
282D12—22no—
283D12—41no—
284D12—41no—
285C3×C8—42no—
286C3×C8—41no—
287C3×C8—41no—
288C3×C8—61no—
289C3×C8—61no—
290C3×C8—62no—
291C3⋊C8—22no—
292C3⋊C8—21no—
293C3⋊C8—21no—
294C3⋊C8—62no—
295C3⋊C8—62no—
296C3⋊C8—122no—
297C2×C32—21no—
298C2×C32—21no—
299C2×C32#38811yescharacteristic
300C2×C32#47111yescharacteristic
301C2×C32#47211yescharacteristic
302C3×D3—82no—
303C24—61no—
304C2×D4—32no—
305C2×D4—61no—
306C2×D4—61no—
307C2×D4—61no—
308C2×D4—61no—
309C2×D4—61no—
310C22×C4—181no—
311C22×C4C2×D3211yescharacteristic
312M16—21no—
313M16—21no—
314M16—32no—
315M16—61no—
316M16—92no—
317M16—181no—
318C2×C8—21no—
319C2×C8—31no—
320C2×C8—31no—
321C2×C8—61no—
322C2×C8—61no—
323C2×C8—61no—
324C2×C8—181no—
325C4⋊C4—31no—
326C4⋊C4—31no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C22⋊C4—61no—
330C42—61no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—122no—
341C22×C3—242no—
342C22×C3—242no—
343C22×C3—241no—
344C22×C3—241no—
345C22×C3#87711yescharacteristic
346C22×C3#87911yescharacteristic
347C22×C3#89211yescharacteristic
348C22×C3#89511yescharacteristic
349C22×C3#89811yescharacteristic
350C22×C3#93911yescharacteristic
351C2×D3—42no—
352C2×D3—82no—
353C2×D3—81no—
354C2×D3—81no—
355C2×D3—82no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—121no—
361C3×C4—121no—
362C3×C4C4×D1211yescharacteristic
363C3×C4#67⋊C411yescharacteristic
364C3×C4#67⋊C411yescharacteristic
365C3×C4#88311yescharacteristic
366C3×C4#88511yescharacteristic
367C3×C4#88611yescharacteristic
368C3×C4C4×#6711yescharacteristic
369C3×C4#93611yescharacteristic
370Dic3—41no—
371Dic3—41no—
372Dic3—242no—
373Dic3—241no—
374Dic3—241no—
375C32#193111yescharacteristic, complemented, Sylow
376C23—62no—
377C23—121no—
378C23—121no—
379C23—241no—
380C23—241no—
381C23#379611yescharacteristic
382D4—62no—
383D4—62no—
384D4—121no—
385D4—121no—
386C2×C4—61no—
387C2×C4—61no—
388C2×C4—361no—
389C2×C4—721no—
390C2×C4#379511yescharacteristic
391C2×C4C4×D3211yescharacteristic
392C2×C4D3×D1211yescharacteristic
393C2×C4#380411yescharacteristic
394C2×C4#380511yescharacteristic
395C2×C4D3×#6711yescharacteristic
396C8—41no—
397C8—62no—
398C8—61no—
399C8—61no—
400C8—182no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—41no—
409C2×C3—41no—
410C2×C3—242no—
411C2×C3#467011yescharacteristic
412C2×C3#489711yescharacteristic
413C2×C3#489811yescharacteristic
414C2×C3#494511yescharacteristic
415C2×C3#519911yescharacteristic
416C2×C3#520011yescharacteristic
417D3—82no—
418C22—21no—
419C22—21no—
420C22—122no—
421C22—242no—
422C22—242no—
423C22—241no—
424C22—241no—
425C22#6385811yescharacteristic
426C22#6387811yescharacteristic
427C22#6388611yescharacteristic
428C4—121no—
429C4—121no—
430C4—721no—
431C4#6387911yescharacteristic
432C4#6388011yescharacteristic
433C4#6389111yescharacteristic
434C4#6395911yescharacteristic
435C3—21no—
436C3#6893111yescharacteristic, complemented
437C3#7031811yescharacteristic, complemented
438C2—21no—
439C2—21no—
440C2—242no—
441C2#1059098411yescharacteristic
442C2#1059098611yescharacteristic
443C2#1059128411yescharacteristic
subgroupG/H
centerC22#63886
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1931
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10591131C2semidirect
5. #10591055C2semidirect
6. #10589420C2semidirect
7. C3×#4558C2semidirect
23. #63558C4semidirect
37. #4558D3semidirect
375. C32#1931semidirect
436. C3#68931semidirect
437. C3#70318semidirect

Maximal subgroups

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

subgroupindex
C3×#51312
#105911312
C2×#635632
C2×#635582
#105910552
#105894202
C3×#45582
#703183
#689313