Finite Group Databasebeta

← #11921862

Subgroups — #11921862

Order 1152.

586 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596575C211yesmaximal, characteristic
2C2×A4×C3⋊C8C211yesmaximal, characteristic, complemented
3C3×#5409C211yesmaximal, characteristic, complemented
4#10593176C212yesmaximal, complemented
5(C3⋊S4)⋊C8C212yesmaximal, complemented
6#85437—31nomaximal
7#78626—31nomaximal
8C2×C3×C4×A4C2211yescharacteristic
9#64269C412yes—
10C4⋊(C3⋊S4)C411yescharacteristic
11C4×C3⋊S4C2212yes—
12#64259C411yescharacteristic
13#63817—41nomaximal
14A4×C3⋊C8C2211yescharacteristic
15A4×C3⋊C8C2211yescharacteristic
16C3×A4⋊C8C2212yes—
17#5912—31no—
18#5912—61no—
19#5791—31no—
20C23×C3⋊C8D311yescharacteristic, complemented
21C2×#907—31no—
22C2×C8×A4—31no—
23#5409D311yescharacteristic, complemented
24#5400—32no—
25C8×S4—32no—
26C3×#407—31no—
27#5129—31no—
28#5122—31no—
29#5119—31no—
30#4730—32no—
31#4730—32no—
32#67⋊C8—32no—
33#67⋊C8—32no—
34C22×C3×A4C2×C411yescharacteristic
35C2×C3⋊S4C2×C412yes—
36#3828—41no—
37C3×C4×A4C2×C411yescharacteristic
38C3×C4×A4C2311yescharacteristic
39C3⋊SL(2,ℤ/4)C2×C412yes—
40C3×#208—41no—
41C2×C3×C3⋊C8—41no—
42#3712—42no—
43#3710—42no—
44#2929—91noSylow
45C23×C3×C4C2×D311yescharacteristic
46C2×#235—31no—
47C2×C4×A4—21no—
48C2×C4×A4C2×D311yescharacteristic
49GL(2,ℤ/4)—32no—
50GL(2,ℤ/4)—62no—
51C4⋊S4—31no—
52C4⋊S4—61no—
53C4×S4—32no—
54C4×S4—62no—
55A4⋊Q8—31no—
56A4⋊Q8—61no—
57C2×C3×M16—31no—
58C2×C3×M16—31no—
59#953—32no—
60#930—31no—
61#930—31no—
62#929—32no—
63C4×#67—32no—
64C4×#67—32no—
65#926—31no—
66#924—31no—
67#924—31no—
68C22×C3⋊C8—31no—
69C22×C3⋊C8—31no—
70C22×C3⋊C8—31no—
71C22×C3⋊C8—31no—
72C22×C3⋊C8C2×D311yescharacteristic
73C22×C3⋊C8C2×D311yescharacteristic
74#907—61no—
75#907—61no—
76#907—61no—
77#907—61no—
78#901—121no—
79C2×ΓL(1,𝔽25)—32no—
80C2×D3×C8—32no—
81C8×A4—31no—
82C8×A4—31no—
83A4⋊C8C2×D312yes—
84C3×C22⋊C8—32no—
85C3×C22⋊C8—32no—
86(C2×D3)⋊C8—32no—
87(C2×D3)⋊C8—32no—
88#815—32no—
89Dic3⋊C8—32no—
90Dic3⋊C8—32no—
91C8×Dic3—32no—
92C2×C3×A4—21no—
93C2×C3×A4C22×C411yescharacteristic
94C3⋊S4—22no—
95C2×C32×C4—41no—
96#638—42no—
97C4⋊(C3⋊D3)—41no—
98C4×C3⋊D3—42no—
99#634—41no—
100C3×C3⋊C8—42no—
101C3×C3⋊C8—41no—
102C3×C3⋊C8—41no—
103C2×#131—91no—
104C23×C8—31no—
105#525—91no—
106#435—92no—
107#435—92no—
108C8×D4—92no—
109C8×D4—92no—
110#424—91no—
111#408—91no—
112#407—31no—
113#405—91no—
114C24×C3C4×D311yescharacteristic
115C22×A4—21no—
116C22×A4C4×D311yescharacteristic
117C2×S4—32no—
118C2×S4—62no—
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4C4×D311yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C2×#67—32no—
126C2×#67—32no—
127C2×#67—32no—
128#235—61no—
129#235—61no—
130#235—61no—
131#235—61no—
132#235—121no—
133#235—241no—
134C2×D12—31no—
135C2×C4×D3—32no—
136C2×Dic6—31no—
137C4×A4—21no—
138C4×A4—21no—
139C4×A4C4×D311yescharacteristic
140C4×A4C22×D311yescharacteristic
141SL(2,ℤ/4)—32no—
142SL(2,ℤ/4)—62no—
143C3×M16—61no—
144C3×M16—61no—
145C3×M16—61no—
146C3×M16—61no—
147C2×C3×C8—32no—
148C2×C3×C8—32no—
149C2×C3×C8—121no—
150#217—32no—
151#217—32no—
152#217—32no—
153(C2×D3)⋊C4—32no—
154(C2×D3)⋊C4—32no—
155C4⋊Dic3—31no—
156C4⋊Dic3—31no—
157Dic3⋊C4—32no—
158Dic3⋊C4—32no—
159C4×Dic3—32no—
160#208—41no—
161C2×C3⋊C8—31no—
162C2×C3⋊C8—31no—
163C2×C3⋊C8—31no—
164C2×C3⋊C8—31no—
165C2×C3⋊C8—31no—
166C2×C3⋊C8—31no—
167C2×C3⋊C8—31no—
168C2×C3⋊C8—61no—
169C2×C3⋊C8S411yescharacteristic, complemented
170ΓL(1,𝔽25)—62no—
171ΓL(1,𝔽25)—62no—
172ΓL(1,𝔽25)—122no—
173D3×C8—62no—
174D3×C8—62no—
175D3×C8—122no—
176C22×C32—41no—
177C2×C3⋊D3—42no—
178C3×A4#13111yescharacteristic, complemented
179C32×C4—41no—
180C32×C4—41no—
181C3⋊Dic3—42no—
182C2×#41—91no—
183C23×C4D3211yescharacteristic
184#131—181no—
185#131—181no—
186#131—181no—
187#131—181no—
188C2×M16—31no—
189C2×M16—31no—
190C2×M16—92no—
191C22×C8—31no—
192C22×C8—31no—
193C22×C8—91no—
194C22×C8—92no—
195C22×C8—91no—
196C22×C8—91no—
197C22×C8—91no—
198#123—92no—
199C22⋊Q8—91no—
200C22⋊Q8—91no—
201#121—91no—
202#121—91no—
203#120—92no—
204C4×D4—92no—
205C4×D4—92no—
206#117—91no—
207C4⋊C8—92no—
208C4⋊C8—92no—
209C22⋊C8—32no—
210C22⋊C8—32no—
211C22⋊C8—92no—
212C22⋊C8—92no—
213#97—92no—
214C4×C8—92no—
215C23×C3—21no—
216C23×C3—31no—
217C23×C3—31no—
218C23×C3—61no—
219C23×C3C2×C4×D311yescharacteristic
220C22×D3—32no—
221C2×A4—21no—
222C2×A4—21no—
223C2×A4—41no—
224C2×A4C2×C4×D311yescharacteristic
225S4—62no—
226S4—122no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—31no—
230C2×C3×C4—31no—
231C2×C3×C4—31no—
232C2×C3×C4—31no—
233C2×C3×C4—31no—
234C2×C3×C4—41no—
235C2×C3×C4—61no—
236C2×C3×C4—81no—
237C2×C3×C4C2×S411yescharacteristic
238#67—62no—
239#67—62no—
240#67—64no—
241#67—62no—
242#67—62no—
243#67—122no—
244#67—242no—
245C2×Dic3—32no—
246C2×Dic3—32no—
247C2×Dic3—32no—
248D12—61no—
249D12—61no—
250D12—121no—
251D12—241no—
252C4×D3—62no—
253C4×D3—62no—
254C4×D3—122no—
255C4×D3—242no—
256Dic6—61no—
257Dic6—61no—
258Dic6—121no—
259Dic6—241no—
260C3×C8—62no—
261C3×C8—62no—
262C3×C8—121no—
263C3×C8—121no—
264C3⋊C8—31no—
265C3⋊C8—31no—
266C3⋊C8—42no—
267C3⋊C8C2×S411yescharacteristic
268C3⋊C8C2×S411yescharacteristic
269C2×C32—41no—
270C2×C32—81no—
271C3⋊D3—82no—
272C24#62411yescharacteristic
273#41—181no—
274#41—181no—
275#41—181no—
276#41—181no—
277C2×Q8—91no—
278C2×D4—91no—
279C2×D4—92no—
280C2×D4—92no—
281C2×D4—92no—
282C22×C4—31no—
283C22×C4—31no—
284C22×C4—31no—
285C22×C4—31no—
286C22×C4—92no—
287C22×C4#62411yescharacteristic
288C22×C4C2×D3211yescharacteristic
289M16—61no—
290M16—61no—
291M16—61no—
292M16—61no—
293M16—182no—
294M16—182no—
295C2×C8—31no—
296C2×C8—32no—
297C2×C8—32no—
298C2×C8—91no—
299C2×C8—91no—
300C2×C8—91no—
301C2×C8—91no—
302C2×C8—91no—
303C2×C8—91no—
304C2×C8—91no—
305C2×C8—182no—
306C2×C8—182no—
307C2×C8—181no—
308C4⋊C4—91no—
309C4⋊C4—91no—
310C4⋊C4—92no—
311C4⋊C4—92no—
312C22⋊C4—92no—
313C22⋊C4—92no—
314C22⋊C4—92no—
315C22⋊C4—92no—
316C22⋊C4—92no—
317C42—92no—
318C22×C3—31no—
319C22×C3—31no—
320C22×C3—32no—
321C22×C3—31no—
322C22×C3—41no—
323C22×C3—61no—
324C22×C3—61no—
325C22×C3—61no—
326C22×C3—81no—
327C22×C3#90111yescharacteristic, complemented
328C22×C3C4×S411yescharacteristic
329C2×D3—62no—
330C2×D3—62no—
331C2×D3—62no—
332C2×D3—122no—
333C2×D3—242no—
334A4—21no—
335A4#90711yescharacteristic, complemented
336C3×C4—31no—
337C3×C4—31no—
338C3×C4—41no—
339C3×C4—41no—
340C3×C4—81no—
341C3×C4—81no—
342C3×C4C4×S411yescharacteristic
343C3×C4C22×S411yescharacteristic
344Dic3—62no—
345Dic3—62no—
346Dic3—62no—
347Dic3—122no—
348Dic3—242no—
349C32—41noSylow
350C23—21no—
351C23—31no—
352C23—31no—
353C23—61no—
354C23—92no—
355C23C2×#62411yescharacteristic
356Q8—181no—
357Q8—181no—
358D4—181no—
359D4—182no—
360D4—182no—
361D4—184no—
362D4—182no—
363D4—182no—
364D4—181no—
365C2×C4—31no—
366C2×C4—31no—
367C2×C4—31no—
368C2×C4—31no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—61no—
373C2×C4—92no—
374C2×C4—92no—
375C2×C4—92no—
376C2×C4—182no—
377C2×C4—182no—
378C2×C4D3×S411yescharacteristic
379C8—31no—
380C8—31no—
381C8—62no—
382C8—62no—
383C8—91no—
384C8—91no—
385C2×C3—21no—
386C2×C3—31no—
387C2×C3—31no—
388C2×C3—41no—
389C2×C3—61no—
390C2×C3—81no—
391C2×C3—81no—
392C2×C3—161no—
393C2×C3C2×C4×S411yescharacteristic
394D3—122no—
395D3—242no—
396D3—482no—
397C22—31no—
398C22—31no—
399C22—32no—
400C22—31no—
401C22—61no—
402C22—61no—
403C22—61no—
404C22—182no—
405C22—182no—
406C22—182no—
407C22#6381711yescharacteristic, complemented
408C22(C3⋊S4)⋊C411yescharacteristic
409C4—31no—
410C4—31no—
411C4—182no—
412C4—182no—
413C4—182no—
414C4(C3⋊S4)⋊C411yescharacteristic
415C4C2×D3×S411yescharacteristic
416C3—41no—
417C3—81no—
418C3#8543711yescharacteristic, complemented
419C2—21no—
420C2—31no—
421C2—31no—
422C2—61no—
423C2—362no—
424C2C2×(C3⋊S4)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC4C2×D3×S4
commutatorC2×C3×A4C22×C4
FittingC23×C3×C4C2×D3
socleC23×C3C2×C4×D3
prime radical#10596575C2
cosocleC3×C4×A4C23
hypercenterC2×C4D3×S4
hypocenterC3×A4#131
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×A4×C3⋊C8C2semidirect
3. C3×#5409C2semidirect
4. #10593176C2semidirect
5. (C3⋊S4)⋊C8C2semidirect
20. C23×C3⋊C8D3semidirect
23. #5409D3semidirect
169. C2×C3⋊C8S4semidirect
178. C3×A4#131semidirect
327. C22×C3#901semidirect
335. A4#907semidirect
407. C22#63817semidirect
418. C3#85437semidirect

Maximal subgroups

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

subgroupindex
#105965752
C2×A4×C3⋊C82
C3×#54092
#105931762
(C3⋊S4)⋊C82
#854373
#786263
#638174