Finite Group Databasebeta

← #11774715

Subgroups — #11774715

Order 1152.

539 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×Q8C211yesmaximal, characteristic
2C4×#3711C211yesmaximal, characteristic
3#10590263C211yesmaximal, characteristic
4#10589401C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71623—31nomaximal
9#68239—31nomaximal
10C2×C3×D3×Q8C411yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12C3×Q8×Dic3C411yescharacteristic
13C3×D3×C4⋊C4—21no—
14C3×D3×C4⋊C4C411yescharacteristic
15C3×#887—21no—
16C3×#887C411yescharacteristic
17C3×C42×D3—21no—
18C3×C42×D3C2211yescharacteristic
19C3×C4×Dic6—21no—
20C3×C4×Dic6C2211yescharacteristic
21C2×#3711—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26(C2×D3)⋊(C3⋊C8)—21no—
27#63554—21no—
28#63554—21no—
29C2×C3×C4×Q8—31no—
30C4×D3×Q8D311yescharacteristic
31#4926—31no—
32C4×#208—31no—
33#4835—31no—
34C4×ΓL(1,𝔽25)—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
45C3×D3×Q8—22no—
46C3×D3×Q8—22no—
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3C2×C411yescharacteristic
50C2×C3×C4×D3D411yescharacteristic
51C2×C3×C4×D3D411yescharacteristic
52C2×C3×Dic6—21no—
53C2×C3×Dic6C2×C411yescharacteristic
54C32×C4⋊C4—21no—
55C32×C4⋊C4C2×C411yescharacteristic
56C32×C42—21no—
57C32×C42C2311yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3C2×C411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3711—24no—
74#1491—91noSylow
75C22×C3×Q8—31no—
76C2×D3×Q8Dic311yescharacteristic
77C3×C4×Q8—21no—
78C3×C4×Q8—31no—
79C3×C4×Q8—31no—
80C3×C4×Q8—31no—
81C3×C4×Q8—61no—
82C3×C4×Q8—61no—
83C3×C4×Q8C2×D311yescharacteristic
84C3×C4×Q8C2×D311yescharacteristic
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—61no—
87C2×C3×C42—31no—
88C2×C3×C42—61no—
89Q8×Dic3Dic311yescharacteristic
90C2×#208—61no—
91C2×ΓL(1,𝔽25)—61no—
92D3×C4⋊C4—21no—
93D3×C4⋊C4Dic311yescharacteristic
94#887—21no—
95#887Dic311yescharacteristic
96C42×D3—21no—
97C42×D3C2×D311yescharacteristic
98C4×Dic6—21no—
99C4×Dic6C2×D311yescharacteristic
100C3×C4⋊C8—31no—
101C3×C4×C8—31no—
102#830—61no—
103(C2×D3)⋊C8—61no—
104#815—61no—
105#815—61no—
106C4⋊(C3⋊C8)—31no—
107C4⋊(C3⋊C8)—31no—
108C4⋊(C3⋊C8)—61no—
109C4⋊(C3⋊C8)C2×D311yescharacteristic
110#803—61no—
111#803—61no—
112C4×C3⋊C8—31no—
113C4×C3⋊C8—31no—
114C4×C3⋊C8—61no—
115C4×C3⋊C8C2×D311yescharacteristic
116C22×C3×D3C22⋊C411yescharacteristic
117C32×Q8—21no—
118C32×Q8M1612yescomplemented
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C2×C3×Dic3C22⋊C411yescharacteristic
129C3×C4×D3—24no—
130C3×C4×D3—22no—
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×C4×D3—21no—
135C3×C4×D3—42no—
136C3×Dic6—24no—
137C3×Dic6—21no—
138C3×Dic6M1612yescomplemented
139C3⋊(C3⋊C8)—22no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—22no—
142C3×C3⋊C8—41no—
143C2×C4×Q8—31no—
144#432—91no—
145C4×M16—91no—
146Q8⋊C8—31no—
147Q8⋊C8—91no—
148Q8⋊C8—91no—
149Q8⋊C8—91no—
150C2×C3×Q8—21no—
151C2×C3×Q8—31no—
152C2×C3×Q8—61no—
153C2×C3×Q8—62no—
154C2×C3×Q8—62no—
155C2×C3×Q8C4×D311yescharacteristic
156C2×C3×Q8C2×Dic311yescharacteristic
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—31no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162D3×Q8—22no—
163D3×Q8—22no—
164C2×C4×D3—21no—
165C2×C4×D3—21no—
166C2×C4×D3C2×Dic311yescharacteristic
167C2×C4×D3#6711yescharacteristic
168C2×C4×D3#6711yescharacteristic
169C2×Dic6—21no—
170C2×Dic6C2×Dic311yescharacteristic
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—41no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4C4×D311yescharacteristic
183C3×C4⋊C4C2×Dic311yescharacteristic
184C3×C42—21no—
185C3×C42—21no—
186C3×C42—21no—
187C3×C42—31no—
188C3×C42—31no—
189C3×C42—31no—
190C3×C42—41no—
191C3×C42—61no—
192C3×C42—61no—
193C3×C42—61no—
194C3×C42C22×D311yescharacteristic
195C3×C42C22×D311yescharacteristic
196C4⋊Dic3—21no—
197C4⋊Dic3C2×Dic311yescharacteristic
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201C4×Dic3—21no—
202C4×Dic3—21no—
203C4×Dic3—21no—
204C4×Dic3C2×Dic311yescharacteristic
205C4×Dic3#6711yescharacteristic
206C4×Dic3#6711yescharacteristic
207#208—64no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—121no—
215C2×C3⋊C8—121no—
216ΓL(1,𝔽25)—64no—
217C22×C32C2×C22⋊C411yescharacteristic
218C2×C3×D3—21no—
219C2×C3×D3—21no—
220C2×C3×D3#10412yes—
221C32×C4—22no—
222C32×C4—21no—
223C32×C4—41no—
224C32×C4C2×M1611yescharacteristic
225C32×C4C2×M1611yescharacteristic
226C32×C4#13711yescharacteristic
227C32×C4#13711yescharacteristic
228C3×Dic3—21no—
229C3×Dic3—22no—
230C3×Dic3—21no—
231C3×Dic3—21no—
232C3×Dic3—41no—
233C22×Q8—31no—
234C2×M16—181no—
235C4×Q8—31no—
236C4×Q8—31no—
237C4×Q8—31no—
238C4×Q8—61no—
239C4×Q8—61no—
240C4×Q8D3211yescharacteristic
241C2×C4⋊C4—31no—
242C2×C4⋊C4—61no—
243C2×C42—31no—
244C2×C42—61no—
245C4⋊C8—31no—
246C4⋊C8—91no—
247C22⋊C8—181no—
248#97—181no—
249#97—181no—
250C4×C8—31no—
251C4×C8—91no—
252C23×C3—31no—
253C22×D3#21711yescharacteristic
254C3×Q8—21no—
255C3×Q8—21no—
256C3×Q8—22no—
257C3×Q8—32no—
258C3×Q8—41no—
259C3×Q8—64no—
260C3×Q8—61no—
261C3×Q8ΓL(1,𝔽25)12yescomplemented
262C3×Q8#20812yescomplemented
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—31no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—62no—
276C2×C3×C4—64no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—122no—
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4C22×Dic311yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289C2×C3×C4C2×#6711yescharacteristic
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3#21711yescharacteristic
293C2×Dic3#21711yescharacteristic
294C2×Dic3#21711yescharacteristic
295C4×D3—24no—
296C4×D3—22no—
297C4×D3—21no—
298C4×D3—21no—
299C4×D3—21no—
300C4×D3—21no—
301C4×D3—42no—
302Dic6—24no—
303Dic6—21no—
304Dic6#20812yescomplemented
305C3×C8—62no—
306C3×C8—121no—
307C3⋊C8—22no—
308C3⋊C8—41no—
309C3⋊C8—62no—
310C3⋊C8—62no—
311C3⋊C8—122no—
312C3⋊C8—121no—
313C3⋊C8—121no—
314C3⋊C8—241no—
315C2×C32#40711yescharacteristic
316C2×C32#41911yescharacteristic
317C2×C32C2×#10411yescharacteristic
318C3×D3—22no—
319C2×Q8—31no—
320C2×Q8—61no—
321C2×Q8—62no—
322C2×Q8—62no—
323C2×Q8D3×Dic311yescharacteristic
324C22×C4—31no—
325C22×C4—31no—
326C22×C4—31no—
327C22×C4—61no—
328C22×C4—61no—
329M16—184no—
330C2×C8—61no—
331C2×C8—61no—
332C2×C8—181no—
333C2×C8—181no—
334C4⋊C4—21no—
335C4⋊C4—31no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4—61no—
340C4⋊C4D3×Dic311yescharacteristic
341C42—21no—
342C42—31no—
343C42—31no—
344C42—31no—
345C42—61no—
346C42—61no—
347C42—61no—
348C42C2×D3211yescharacteristic
349C22×C3—21no—
350C22×C3—32no—
351C22×C3—61no—
352C22×C3—61no—
353C22×C3D3×C22⋊C411yescharacteristic
354C22×C3C2×#21711yescharacteristic
355C2×D3—21no—
356C2×D3—21no—
357C2×D3#83712yes—
358C3×C4—22no—
359C3×C4—21no—
360C3×C4—22no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—41no—
367C3×C4—42no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—61no—
371C3×C4—62no—
372C3×C4—61no—
373C3×C4—61no—
374C3×C4—81no—
375C3×C4—121no—
376C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
377C3×C4D3×M1611yescharacteristic
378C3×C4#91511yescharacteristic
379C3×C4#91811yescharacteristic
380C3×C4C2×#20811yescharacteristic
381C3×C4C2×#20811yescharacteristic
382C3×C4#94211yescharacteristic
383C3×C4#94211yescharacteristic
384Dic3—21no—
385Dic3—22no—
386Dic3—21no—
387Dic3—21no—
388Dic3—41no—
389C32#149111yescharacteristic, complemented, Sylow
390C23—31no—
391Q8—21no—
392Q8—32no—
393Q8—64no—
394Q8—61no—
395Q8#371112yescomplemented
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—31no—
399C2×C4—31no—
400C2×C4—31no—
401C2×C4—62no—
402C2×C4—64no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—122no—
410C2×C4C2×D3×Dic311yescharacteristic
411C2×C4D3×#6711yescharacteristic
412C2×C4D3×#6711yescharacteristic
413C8—62no—
414C8—121no—
415C8—182no—
416C8—361no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—62no—
421C2×C3#472611yescharacteristic
422C2×C3#480211yescharacteristic
423C2×C3D3×#10411yescharacteristic
424C2×C3#520711yescharacteristic
425C2×C3#522511yescharacteristic
426C2×C3C2×#83711yescharacteristic
427D3—22no—
428C22—32no—
429C22—61no—
430C22—61no—
431C22D3×#21711yescharacteristic
432C4—22no—
433C4—21no—
434C4—41no—
435C4—61no—
436C4—61no—
437C4—62no—
438C4—61no—
439C4—121no—
440C4D3×#20811yescharacteristic
441C4C2×#371111yescharacteristic
442C4#6394611yescharacteristic
443C4#6394811yescharacteristic
444C3—21no—
445C3#6823911yescharacteristic, complemented
446C3#7162311yescharacteristic, complemented
447C2—62no—
448C2#1059115411yescharacteristic
449C2#1059155711yescharacteristic
450C2D3×#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#1491
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
118. C32×Q8M16semidirect
138. C3×Dic6M16semidirect
261. C3×Q8ΓL(1,𝔽25)semidirect
262. C3×Q8#208semidirect
304. Dic6#208semidirect
389. C32#1491semidirect
395. Q8#3711semidirect
445. C3#68239semidirect
446. C3#71623semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×Q82
C4×#37112
#105902632
#105894012
C3×#45352
#105890842
#105890832
#716233
#682393