Finite Group Databasebeta

← #11774772

Subgroups — #11774772

Order 1152.

499 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5578C211yesmaximal, characteristic
2#10590336C211yesmaximal, characteristic
3C4×D3×C3⋊C8C211yesmaximal, characteristic
4#10589401C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71826—31nomaximal
9#68240—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C3×#946C411yescharacteristic
12C3×#944C411yescharacteristic
13C3×#897C411yescharacteristic
14C3×#896—21no—
15C3×#889—21no—
16C3×#888C411yescharacteristic
17C3×#872—21no—
18C3×C42×D3C2211yescharacteristic
19C3×C4×Dic6—21no—
20C3×C4×Dic6C2211yescharacteristic
21C2×#3711—21no—
22C2×D3×C3⋊C8—21no—
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C4×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27Dic3⋊(C3⋊C8)—21no—
28Dic3×C3⋊C8—21no—
29C3×#533—31no—
30#5578D311yescharacteristic
31#4924—31no—
32C2×C4×C3⋊C8—31no—
33#4837—31no—
34C4×D3×C8—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4535—31no—
38#4535—31no—
39#4535—31no—
40#4535—61no—
41#4535D311yescharacteristic, complemented
42#4484—31no—
43#4456—31no—
44C2×C32×Q8C2×C411yescharacteristic
45C2×C3×C4×D3C2×C411yescharacteristic
46C2×C3×C4×D3D411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×Dic6—21no—
49C2×C3×Dic6C2×C411yescharacteristic
50C32×C4⋊C4—21no—
51C32×C4⋊C4C2×C411yescharacteristic
52C32×C42—21no—
53C32×C42C2311yescharacteristic
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×(C2×D3)⋊C4—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3C2×C411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#3711—42no—
72D3×C3⋊C8—24no—
73#1493—91noSylow
74C3×C4⋊Q8—31no—
75C3×C4⋊Q8—31no—
76C3×#125—61no—
77C3×C22⋊Q8—31no—
78C3×C22⋊Q8—31no—
79C3×C22⋊Q8—61no—
80C3×C4×Q8—21no—
81C3×C4×Q8—31no—
82C3×C4×Q8—61no—
83C3×C4×Q8C2×D311yescharacteristic
84C3×C4×Q8C2×D311yescharacteristic
85C3×#117—61no—
86C2×C3×C42—31no—
87#946Dic311yescharacteristic
88#944Dic311yescharacteristic
89C2×#208—61no—
90C22×C3⋊C8—61no—
91C2×ΓL(1,𝔽25)—61no—
92C2×D3×C8—61no—
93#897Dic311yescharacteristic
94#896—21no—
95#889—21no—
96#888Dic311yescharacteristic
97#872—21no—
98C42×D3C2×D311yescharacteristic
99C4×Dic6—21no—
100C4×Dic6C2×D311yescharacteristic
101C3×C4⋊C8—31no—
102C3×C4×C8—31no—
103Dic3⋊C8—61no—
104C8×Dic3—61no—
105C4⋊(C3⋊C8)—31no—
106C4⋊(C3⋊C8)—31no—
107C4⋊(C3⋊C8)—61no—
108C4⋊(C3⋊C8)—61no—
109C4⋊(C3⋊C8)C2×D311yescharacteristic
110C4×C3⋊C8—31no—
111C4×C3⋊C8—31no—
112C4×C3⋊C8—61no—
113C4×C3⋊C8—61no—
114C4×C3⋊C8C2×D311yescharacteristic
115C22×C3×D3C22⋊C411yescharacteristic
116C32×Q8—21no—
117C32×Q8—21no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C3×C4×D3—21no—
129C3×C4×D3—21no—
130C3×C4×D3—22no—
131C3×C4×D3SD1612yes—
132C3×C4×D3Q1612yes—
133C3×Dic6—21no—
134C3×Dic6—21no—
135C3×Dic6—42no—
136C3⋊(C3⋊C8)—22no—
137C3⋊(C3⋊C8)—41no—
138C3×C3⋊C8—22no—
139C3×C3⋊C8—41no—
140#533—31no—
141#423—91no—
142C2×C4×C8—91no—
143Q8⋊C8—31no—
144Q8⋊C8—91no—
145Q8⋊C8—91no—
146Q8⋊C8—91no—
147C2×C3×Q8—21no—
148C2×C3×Q8—31no—
149C2×C3×Q8—61no—
150C2×C3×Q8C4×D311yescharacteristic
151C2×C3×Q8C2×Dic311yescharacteristic
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C2×C4×D3C2×Dic311yescharacteristic
156C2×C4×D3#6711yescharacteristic
157C2×C4×D3#6711yescharacteristic
158C2×Dic6—21no—
159C2×Dic6C2×Dic311yescharacteristic
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—41no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4C4×D311yescharacteristic
174C3×C4⋊C4C2×Dic311yescharacteristic
175C3×C22⋊C4—61no—
176C3×C22⋊C4—61no—
177C3×C42—21no—
178C3×C42—21no—
179C3×C42—21no—
180C3×C42—31no—
181C3×C42—31no—
182C3×C42—31no—
183C3×C42—41no—
184C3×C42—61no—
185C3×C42C22×D311yescharacteristic
186C3×C42C22×D311yescharacteristic
187(C2×D3)⋊C4—21no—
188(C2×D3)⋊C4—21no—
189C4⋊Dic3—21no—
190C4⋊Dic3C2×Dic311yescharacteristic
191Dic3⋊C4—21no—
192Dic3⋊C4—21no—
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196C4×Dic3—21no—
197C4×Dic3C2×Dic311yescharacteristic
198C4×Dic3#6711yescharacteristic
199C4×Dic3#6711yescharacteristic
200#208—122no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—64no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—121no—
209C2×C3⋊C8—121no—
210ΓL(1,𝔽25)—122no—
211D3×C8—64no—
212C22×C32C2×C22⋊C411yescharacteristic
213C2×C3×D3—21no—
214C2×C3×D3—21no—
215C2×C3×D3#10312yes—
216C32×C4—21no—
217C32×C4—41no—
218C32×C4—41no—
219C32×C4#13111yescharacteristic
220C32×C4#13111yescharacteristic
221C32×C4C2×SD1611yescharacteristic
222C32×C4C2×Q1611yescharacteristic
223C3×Dic3—21no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3#10312yes—
227C3×Dic3#10412yes—
228C2×M16—181no—
229C22×C8—181no—
230C4⋊Q8—31no—
231C4⋊Q8—31no—
232#125—61no—
233C22⋊Q8—31no—
234C22⋊Q8—31no—
235C22⋊Q8—61no—
236C4×Q8—31no—
237C4×Q8—61no—
238C4×Q8D3211yescharacteristic
239#117—61no—
240C2×C42—31no—
241C4⋊C8—31no—
242C4⋊C8—91no—
243C4⋊C8—181no—
244C4×C8—31no—
245C4×C8—91no—
246C4×C8—181no—
247C23×C3—31no—
248C22×D3#21711yescharacteristic
249C3×Q8—22no—
250C3×Q8—21no—
251C3×Q8—21no—
252C3×Q8—21no—
253C3×Q8—21no—
254C3×Q8—41no—
255C3×Q8—61no—
256C3×Q8—61no—
257C3×Q8—122no—
258C2×C3×C4—21no—
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—31no—
266C2×C3×C4—31no—
267C2×C3×C4—32no—
268C2×C3×C4—32no—
269C2×C3×C4—31no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—62no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4C22×Dic311yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3#21711yescharacteristic
286C2×Dic3#21711yescharacteristic
287C2×Dic3#21711yescharacteristic
288C4×D3—21no—
289C4×D3—21no—
290C4×D3—22no—
291C4×D3#21512yes—
292C4×D3#21612yes—
293Dic6—21no—
294Dic6—21no—
295Dic6—42no—
296C3×C8—62no—
297C3×C8—121no—
298C3⋊C8—22no—
299C3⋊C8—41no—
300C3⋊C8—62no—
301C3⋊C8—62no—
302C3⋊C8—122no—
303C3⋊C8—121no—
304C3⋊C8—121no—
305C3⋊C8—241no—
306C2×C32#40811yescharacteristic
307C2×C32C2×#10311yescharacteristic
308C2×C32C2×#10411yescharacteristic
309C3×D3—22no—
310C2×Q8—31no—
311C2×Q8—61no—
312C2×Q8D3×Dic311yescharacteristic
313C22×C4—31no—
314C22×C4—31no—
315C22×C4—31no—
316M16—362no—
317C2×C8—61no—
318C2×C8—61no—
319C2×C8—184no—
320C2×C8—181no—
321C2×C8—181no—
322C4⋊C4—21no—
323C4⋊C4—31no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4D3×Dic311yescharacteristic
331C22⋊C4—61no—
332C22⋊C4—61no—
333C42—21no—
334C42—31no—
335C42—31no—
336C42—31no—
337C42—61no—
338C42C2×D3211yescharacteristic
339C22×C3—21no—
340C22×C3—32no—
341C22×C3—61no—
342C22×C3—61no—
343C22×C3D3×C22⋊C411yescharacteristic
344C22×C3C2×#21711yescharacteristic
345C2×D3—21no—
346C2×D3—21no—
347C2×D3#83512yes—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—32no—
355C3×C4—32no—
356C3×C4—41no—
357C3×C4—42no—
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—61no—
363C3×C4—81no—
364C3×C4—121no—
365C3×C4—121no—
366C3×C4#90111yescharacteristic
367C3×C4#90711yescharacteristic
368C3×C4D3×SD1611yescharacteristic
369C3×C4D3×Q1611yescharacteristic
370C3×C4C2×#21511yescharacteristic
371C3×C4C2×#21611yescharacteristic
372C3×C4#94811yescharacteristic
373C3×C4#94811yescharacteristic
374Dic3—21no—
375Dic3—41no—
376Dic3—41no—
377Dic3#83512yes—
378Dic3#83712yes—
379C32#149311yescharacteristic, complemented, Sylow
380C23—31no—
381Q8—21no—
382Q8—21no—
383Q8—61no—
384Q8—61no—
385Q8—122no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—32no—
391C2×C4—32no—
392C2×C4—31no—
393C2×C4—62no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4C2×D3×Dic311yescharacteristic
399C2×C4D3×#6711yescharacteristic
400C2×C4D3×#6711yescharacteristic
401C8—62no—
402C8—121no—
403C8—182no—
404C8—361no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—62no—
409C2×C3#472711yescharacteristic
410C2×C3D3×#10311yescharacteristic
411C2×C3D3×#10411yescharacteristic
412C2×C3C2×#83511yescharacteristic
413C2×C3#523411yescharacteristic
414C2×C3C2×#83711yescharacteristic
415D3—22no—
416C22—32no—
417C22—61no—
418C22—61no—
419C22D3×#21711yescharacteristic
420C4—21no—
421C4—32no—
422C4—32no—
423C4—41no—
424C4—41no—
425C4—61no—
426C4—121no—
427C4—121no—
428C4#6381411yescharacteristic
429C4#6381511yescharacteristic
430C4D3×#21511yescharacteristic
431C4D3×#21611yescharacteristic
432C3—21no—
433C3#6824011yescharacteristic, complemented
434C3#7182611yescharacteristic, complemented
435C2—62no—
436C2#1059114511yescharacteristic
437C2D3×#83511yescharacteristic
438C2D3×#83711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1493
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
4. #10589401C2semidirect
5. C3×#4535C2semidirect
6. #10589084C2semidirect
7. #10589083C2semidirect
41. #4535D3semidirect
379. C32#1493semidirect
433. C3#68240semidirect
434. C3#71826semidirect

Maximal subgroups

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

subgroupindex
C3×#55782
#105903362
C4×D3×C3⋊C82
#105894012
C3×#45352
#105890842
#105890832
#718263
#682403