Finite Group Databasebeta

← #11868735

Subgroups — #11868735

Order 1152.

863 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 863 conjugacy classes of subgroups — too many to draw. Only its 176 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#10596199C211yesmaximal, characteristic
2C4×#3797C211yesmaximal, characteristic
3C3×#5091C212yesmaximal, complemented
4#10590602C212yesmaximal
5#10590582C212yesmaximal
6#10590494C214yesmaximal, complemented
7#10590340C211yesmaximal, characteristic
8#10590301C212yesmaximal, complemented
9#81108—32nomaximal
10C2×#3797C2211yescharacteristic
11C32×C4⋊Q8C2211yescharacteristic
12#64155—21no—
13Q8×C3⋊Dic3—21no—
14#64106—21no—
15#64101C2212yes—
16#64099C2212yes—
17#64096—21no—
18C42×C3⋊D3C2211yescharacteristic
19#64078C2211yescharacteristic
20C3×C4×Dic6C2212yes—
21C4×#627—21no—
22#63900C2211yescharacteristic
23#63883—21no—
24C4×#624—21no—
25#63843C2212yes—
26#63838—21no—
27C2×#3712C2212yes—
28C3×#810C2214yes—
29C3×#807C2214yes—
30C3×C4⋊(C3⋊C8)C2212yes—
31#63573C2214yes—
32#63572C2212yes—
33#63566C2214yes—
34#5728—32no—
35#5728—61no—
36C4×D3×Q8—32no—
37C3×#477—32no—
38#5091D312yescomplemented
39#5020—32no—
40#4881—34no—
41#4877—34no—
42#4851—32no—
43#4837—32no—
44#4802—34no—
45#4799—34no—
46C2×C32×Q8—21no—
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3C2311yescharacteristic
50C2×#634—21no—
51C2×C3×Dic6C2312yes—
52C2×#627—21no—
53C2×#624—21no—
54C2×#624—21no—
55#3797—22no—
56#3797Q814yescomplemented
57C32×C4⋊C4—21no—
58C32×C4⋊C4C2312yes—
59C32×C42C2311yescharacteristic
60#3752—22no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—22no—
63C4⋊(C3⋊Dic3)C2312yes—
64#3750—22no—
65C4×C3⋊Dic3—22no—
66C4×C3⋊Dic3D411yescharacteristic
67C4×C3⋊Dic3D411yescharacteristic
68C4×C3⋊Dic3C2311yescharacteristic
69C3×C4⋊Dic3C2312yes—
70C3×Dic3⋊C4—22no—
71C3×C4×Dic3—22no—
72C2×C3×C3⋊C8C2314yes—
73#3724—21no—
74Dic3⋊Dic3—22no—
75Dic32—22no—
76#3712—24no—
77#3078—91noSylow
78C2×D3×Q8—32no—
79C3×C4⋊Q8—21no—
80C3×C4⋊Q8C2×D312yes—
81C3×C4×Q8—32no—
82#946—62no—
83#946—62no—
84Q8×Dic3—32no—
85Q8×Dic3—62no—
86Q8×Dic3—62no—
87C2×ΓL(1,𝔽25)—34no—
88#897—62no—
89#897—62no—
90#892—34no—
91#892—62no—
92D3×C4⋊C4—32no—
93D3×C4⋊C4—62no—
94#890—34no—
95#890—62no—
96#887—32no—
97#887—62no—
98#887—62no—
99#887—62no—
100C42×D3—32no—
101C42×D3—61no—
102C42×D3—62no—
103#869—32no—
104#869—61no—
105C4×Dic6—62no—
106C4×Dic6C2×D312yes—
107C3×#107—34no—
108C3×C4⋊C8—32no—
109C3×#103—34no—
110#835—34no—
111#817—34no—
112#816—34no—
113Dic3⋊C8—34no—
114#810C2×D314yes—
115#808—34no—
116#807C2×D314yes—
117C4⋊(C3⋊C8)C2×D312yes—
118C22×C3⋊D3C2×D411yescharacteristic
119C32×Q8—42no—
120C2×C32×C4—22no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2411yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3C2×D411yescharacteristic
126C2×C3⋊Dic3C2×D411yescharacteristic
127C2×C3⋊Dic3C2×D411yescharacteristic
128C4×C3⋊D3—22no—
129C4×C3⋊D3—41no—
130C4×C3⋊D3C2×Q812yes—
131C4×C3⋊D3#4112yes—
132#634—42no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C3×Dic6—22no—
136C3×Dic6C2×Q814yes—
137#627—24no—
138#624—24no—
139#624—42no—
140C3×C3⋊C8—24no—
141#533—91no—
142C2×C4×Q8—91no—
143#479—94no—
144#477—32no—
145#475—92no—
146#428—92no—
147#423—91no—
148#419—92no—
149C2×C3×Q8—22no—
150C2×C3×Q8—22no—
151C2×C3×Q8—32no—
152D3×Q8—38no—
153D3×Q8—64no—
154C2×C4×D3—32no—
155C2×C4×D3—32no—
156C2×C4×D3—32no—
157C2×C4×D3—61no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3—62no—
161C2×C4×D3—62no—
162C2×Dic6—62no—
163C2×Dic6—62no—
164C2×Dic6—62no—
165C2×Dic6C22×D312yes—
166C2×C3×C8—34no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—22no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—32no—
171C3×C4⋊C4—62no—
172C3×C4⋊C4C22×D314yes—
173C3×C42—21no—
174C3×C42—62no—
175C3×C42C22×D312yes—
176(C2×D3)⋊C4—64no—
177(C2×D3)⋊C4—64no—
178C4⋊Dic3—34no—
179C4⋊Dic3—62no—
180C4⋊Dic3—62no—
181C4⋊Dic3—64no—
182C4⋊Dic3—62no—
183C4⋊Dic3—64no—
184C4⋊Dic3—62no—
185C4⋊Dic3C22×D312yes—
186Dic3⋊C4—22no—
187Dic3⋊C4—62no—
188Dic3⋊C4—62no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191C4×Dic3—22no—
192C4×Dic3—32no—
193C4×Dic3—32no—
194C4×Dic3—32no—
195C4×Dic3—61no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3—62no—
199C4×Dic3—62no—
200C4×Dic3—64no—
201C4×Dic3—64no—
202C2×C3⋊C8C22×D314yes—
203ΓL(1,𝔽25)—68no—
204C22×C32C22×D411yescharacteristic
205C2×C3⋊D3—21no—
206C2×C3⋊D3—21no—
207C2×C3⋊D3C22⋊Q812yes—
208C32×C4—21no—
209C32×C4—42no—
210C32×C4#13712yes—
211C32×C4C22×Q811yescharacteristic
212C32×C4C2×#4111yescharacteristic
213C3⋊Dic3—21no—
214C3⋊Dic3—21no—
215C3⋊Dic3—42no—
216C3⋊Dic3C22⋊Q812yes—
217C3×Dic3—24no—
218C3×Dic3—42no—
219C22×Q8—91no—
220C2×M16—92no—
221C4⋊Q8—91no—
222C4⋊Q8D3211yescharacteristic
223#125—92no—
224C22⋊Q8—181no—
225C22⋊Q8—181no—
226C4×Q8—32no—
227C4×Q8—92no—
228C4×Q8—181no—
229C4×Q8—181no—
230C4×Q8—181no—
231C4×Q8—181no—
232#117—92no—
233C2×C4⋊C4—91no—
234C2×C4⋊C4—181no—
235C2×C42—91no—
236C2×C42—181no—
237#107—34no—
238#106—94no—
239C4⋊C8—32no—
240C4⋊C8—92no—
241#103—34no—
242#103—94no—
243C22×D3—32no—
244C22×D3—61no—
245C3×Q8—34no—
246C3×Q8—44no—
247C3×Q8—44no—
248C3×Q8—62no—
249C2×C3×C4—24no—
250C2×C3×C4—24no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—62no—
255C2×C3×C4—62no—
256C2×C3×C4D3×D412yes—
257C2×C3×C4D3×D412yes—
258C2×C3×C4C23×D312yes—
259C2×Dic3—22no—
260C2×Dic3—22no—
261C2×Dic3—32no—
262C2×Dic3—32no—
263C2×Dic3—32no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—61no—
267C2×Dic3—64no—
268C2×Dic3—64no—
269C4×D3—34no—
270C4×D3—34no—
271C4×D3—62no—
272C4×D3—62no—
273C4×D3—68no—
274C4×D3—64no—
275C4×D3—122no—
276C4×D3—124no—
277C4×D3—122no—
278C4×D3—122no—
279Dic6—22no—
280Dic6—68no—
281Dic6—124no—
282Dic6—124no—
283Dic6D3×Q814yes—
284C3×C8—64no—
285C3⋊C8—24no—
286C2×C32C2×C22⋊Q811yescharacteristic
287C2×C32C2×#13711yescharacteristic
288C2×C32#57511yescharacteristic
289C3⋊D3—22no—
290C2×Q8—21no—
291C2×Q8—32no—
292C2×Q8—94no—
293C2×Q8—181no—
294C2×Q8—182no—
295C2×Q8—181no—
296C22×C4—91no—
297C22×C4—91no—
298C22×C4—91no—
299C22×C4—181no—
300C22×C4—181no—
301M16—184no—
302C2×C8—34no—
303C4⋊C4—21no—
304C4⋊C4—32no—
305C4⋊C4—62no—
306C4⋊C4—92no—
307C4⋊C4—182no—
308C4⋊C4—182no—
309C4⋊C4—181no—
310C4⋊C4—182no—
311C4⋊C4—181no—
312C4⋊C4C2×D3212yes—
313C22⋊C4—182no—
314C42—62no—
315C42—91no—
316C42—91no—
317C42—91no—
318C42—182no—
319C42—182no—
320C42C2×D3211yescharacteristic
321C22×C3—21no—
322C22×C3C2×D3×D412yes—
323C2×D3—34no—
324C2×D3—62no—
325C2×D3—62no—
326C2×D3—62no—
327C2×D3—121no—
328C2×D3—121no—
329C3×C4—22no—
330C3×C4—22no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—22no—
334C3×C4—44no—
335C3×C4—44no—
336C3×C4—64no—
337C3×C4—122no—
338C3×C4#91814yes—
339C3×C4C2×D3×Q812yes—
340C3×C4D3×#4112yes—
341Dic3—24no—
342Dic3—34no—
343Dic3—42no—
344Dic3—62no—
345Dic3—62no—
346Dic3—62no—
347Dic3—121no—
348Dic3—121no—
349Dic3—124no—
350Dic3—124no—
351C32#307811yescharacteristic, complemented, Sylow
352C23—91no—
353Q8—34no—
354Q8—42no—
355Q8—62no—
356Q8—184no—
357Q8—362no—
358C2×C4—22no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—91no—
362C2×C4—92no—
363C2×C4—92no—
364C2×C4—91no—
365C2×C4—91no—
366C2×C4—184no—
367C2×C4—182no—
368C2×C4—182no—
369C2×C4—361no—
370C2×C4—362no—
371C2×C4#381111yescharacteristic
372C2×C4#381111yescharacteristic
373C2×C4C22×D3211yescharacteristic
374C8—64no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3D3×C22⋊Q812yes—
379C2×C3C2×#91812yes—
380C2×C3#577312yes—
381D3—64no—
382D3—122no—
383C22—92no—
384C22—181no—
385C22—181no—
386C22C2×#381111yescharacteristic
387C4—21no—
388C4—42no—
389C4—64no—
390C4—92no—
391C4—122no—
392C4—181no—
393C4—181no—
394C4—362no—
395C4#6394512yes—
396C4D32×Q811yescharacteristic
397C4#6431911yescharacteristic
398C3—21no—
399C3#8110812yescomplemented
400C2—182no—
401C2#1059510111yescharacteristic
402C2C2×#6394511yescharacteristic
403C2#1059542911yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5091C2semidirect
6. #10590494C2semidirect
8. #10590301C2semidirect
38. #5091D3semidirect
56. #3797Q8semidirect
351. C32#3078semidirect
399. C3#81108semidirect

Maximal subgroups

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

subgroupindex
#105961992
C4×#37972
C3×#50912
#105906022
#105905822
#105904942
#105903402
#105903012
#811083