Finite Group Databasebeta

← #11824519

Subgroups — #11824519

Order 1152.

1034 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×D32⋊Q8C214yesmaximal, complemented
2C4×#3802C211yesmaximal, characteristic
3#10593909C211yesmaximal, characteristic, complemented
4C4×C4⋊#157C211yesmaximal, characteristic, complemented
5#10593413C212yesmaximal, complemented
6#10593408C214yesmaximal, complemented
7#10593407C212yesmaximal
8C2×#3802C2211yescharacteristic
9C2×C4×D32C2212yes—
10C2×#3797C2212yes—
11C2×C4⋊#157C2212yes—
12C2×C4×#157C2212yes—
13C2×#3773C2218yes—
14C2×D32⋊C4C2218yes—
15D32⋊Q8—216no—
16C42×C3⋊D3C2211yescharacteristic
17C3×C4×D12—21no—
18C3×#869—21no—
19#63921C2212yes—
20#63919—21no—
21#63919—21no—
22#63902—21no—
23C4×#625—21no—
24#63900C2212yes—
25#63900C2212yes—
26#63900C2211yescharacteristic
27#63898—21no—
28#63873—21no—
29#63781C2212yes—
30D3×C4⋊Q8—61no—
31C4×D3×D4—61no—
32C22×D32C2312yes—
33C22×#157C2314yes—
34C2×C4×C3⋊D3C2311yescharacteristic
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×C3×D12—21no—
38C2×C3×C4×D3—22no—
39C2×C3×Dic6—22no—
40C2×#627—22no—
41C2×#625—21no—
42C2×#624C2314yes—
43C2×#624C2312yes—
44C2×D3×Dic3—22no—
45#3802—22no—
46#3802Q814yescomplemented
47C4×D32—28no—
48#3797—28no—
49C4⋊#157D418yescomplemented
50C4×#157—24no—
51#3773—216no—
52D32⋊C4—216no—
53C32×C42D411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C3×(C2×D3)⋊C4—22no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—22no—
60C3×C4⋊Dic3—22no—
61#3724—22no—
62#3724—22no—
63#3724—21no—
64(C2×D3)⋊Dic3—22no—
65#2542—91nomaximal, Sylow
66C2×D3×Q8—62no—
67C2×D3×D4—61no—
68C22×C4×D3—62no—
69C3×C4⋊Q8—61no—
70C3×C4×D4—61no—
71#944—62no—
72D4×Dic3—61no—
73C4×#67—62no—
74#893—61no—
75D3×C4⋊C4—62no—
76D3×C4⋊C4—62no—
77D3×C4⋊C4—61no—
78#888—62no—
79#888—62no—
80#67⋊C4—62no—
81D3×C22⋊C4—62no—
82C4×D12—21no—
83C42×D3—61no—
84C42×D3—61no—
85#869—21no—
86C22×C3⋊D3C2411yescharacteristic
87C22×C3×D3—22no—
88C2×D32—22no—
89C2×D32—24no—
90C2×D32—24no—
91C2×D32C2×Q814yes—
92C2×#157—24no—
93C2×#157—24no—
94C2×#157C2×D418yes—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C3⋊Dic3C2×D411yescharacteristic
99C2×C3⋊Dic3C2×D411yescharacteristic
100C2×C3⋊Dic3C2×D411yescharacteristic
101C4×C3⋊D3—22no—
102C4×C3⋊D3C2×D414yes—
103C4×C3⋊D3C2×Q812yes—
104C4×C3⋊D3#4112yes—
105C2×C3×Dic3—22no—
106C2×C3×Dic3—24no—
107C3×D12—24no—
108C3×C4×D3—44no—
109C3×Dic6—44no—
110#627—44no—
111#625—24no—
112#624—28no—
113#624—24no—
114D3×Dic3—44no—
115C2×C4⋊Q8—91no—
116C2×C22⋊Q8—94no—
117C2×C4×D4—91no—
118#399—94no—
119#390—92no—
120#384—92no—
121C4×C4⋊C4—91no—
122C23×D3—62no—
123C2×C3×Q8—62no—
124C2×C3×D4—61no—
125C22×C3×C4—62no—
126C2×#67—62no—
127C22×Dic3—62no—
128D3×Q8—128no—
129D3×D4—64no—
130D3×D4—64no—
131C2×D12—21no—
132C2×C4×D3—22no—
133C2×C4×D3—61no—
134C2×C4×D3—61no—
135C2×C4×D3—61no—
136C2×C4×D3—61no—
137C2×C4×D3—61no—
138C2×C4×D3—62no—
139C2×C4×D3—64no—
140C2×C4×D3—61no—
141C2×C4×D3—62no—
142C2×C4×D3—128no—
143C2×Dic6—22no—
144C2×Dic6—64no—
145C3×C4⋊C4—62no—
146C3×C4⋊C4—62no—
147C3×C4⋊C4—61no—
148C3×C22⋊C4—62no—
149C3×C42—21no—
150C3×C42—21no—
151#217—62no—
152(C2×D3)⋊C4—22no—
153(C2×D3)⋊C4—62no—
154C4⋊Dic3—22no—
155C4⋊Dic3—22no—
156C4⋊Dic3—21no—
157Dic3⋊C4—62no—
158Dic3⋊C4—64no—
159Dic3⋊C4—64no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C22×C32C22×D411yescharacteristic
167C2×C3⋊D3C22×D412yes—
168C2×C3⋊D3C22×Q811yescharacteristic
169C2×C3⋊D3C2×#4111yescharacteristic
170C2×C3⋊D32−1+412yes—
171C2×C3×D3—24no—
172C2×C3×D3—42no—
173C2×C3×D3—42no—
174D32—28no—
175D32—44no—
176#157—28no—
177C32×C4—21no—
178C32×C4C22⋊Q812yescomplemented
179C32×C4#12712yes—
180C3⋊Dic3—21no—
181C3⋊Dic3C22⋊Q812yescomplemented
182C3⋊Dic3#12712yes—
183C3×Dic3—42no—
184C3×Dic3—44no—
185C22×Q8—92no—
186C22×D4—91no—
187C23×C4—92no—
188C4⋊Q8—61no—
189C4⋊Q8—181no—
190C4⋊Q8—181no—
191C4⋊Q8—181no—
192C22⋊Q8—1816no—
193C4×D4—61no—
194C4×D4—181no—
195C4×D4—181no—
196C4×D4—181no—
197C2×C4⋊C4—91no—
198C2×C4⋊C4—92no—
199C2×C4⋊C4—92no—
200C2×C4⋊C4—92no—
201C2×C4⋊C4—98no—
202C2×C22⋊C4—92no—
203C2×C22⋊C4—98no—
204C2×C42—91no—
205C2×C42—92no—
206#95—92no—
207C23×C3—62no—
208C22×D3—22no—
209C22×D3—64no—
210C22×D3—61no—
211C22×D3—61no—
212C22×D3—64no—
213C22×D3—124no—
214C22×D3—124no—
215C3×Q8—124no—
216C3×D4—64no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—64no—
224C2×C3×C4—62no—
225C2×C3×C4—124no—
226#67—68no—
227C2×Dic3—24no—
228C2×Dic3—22no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—61no—
234C2×Dic3—61no—
235C2×Dic3—124no—
236D12—24no—
237C4×D3—44no—
238C4×D3—64no—
239C4×D3—64no—
240C4×D3—62no—
241C4×D3—62no—
242C4×D3—62no—
243C4×D3—62no—
244C4×D3—64no—
245C4×D3—124no—
246C4×D3—128no—
247C4×D3—122no—
248C4×D3—124no—
249Dic6—44no—
250Dic6—128no—
251C2×C32C2×C22⋊Q811yescharacteristic
252C2×C32C2×#12711yescharacteristic
253C2×C32#53611yescharacteristic
254C3⋊D3#54712yes—
255C3⋊D3D4×Q812yes—
256C3×D3—44no—
257C24—92no—
258C2×Q8—62no—
259C2×Q8—182no—
260C2×Q8—188no—
261C2×D4—61no—
262C2×D4—94no—
263C2×D4—182no—
264C2×D4—181no—
265C22×C4—62no—
266C22×C4—94no—
267C22×C4—92no—
268C22×C4—91no—
269C22×C4—91no—
270C22×C4—94no—
271C22×C4—91no—
272C22×C4—182no—
273C22×C4—188no—
274C4⋊C4—61no—
275C4⋊C4—62no—
276C4⋊C4—62no—
277C4⋊C4—98no—
278C4⋊C4—181no—
279C4⋊C4—182no—
280C4⋊C4—182no—
281C4⋊C4—1816no—
282C22⋊C4—62no—
283C22⋊C4—182no—
284C22⋊C4—1816no—
285C42—91no—
286C42—91no—
287C42—91no—
288C42—184no—
289C42GO+(4,𝔽2)11yescharacteristic
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—64no—
293C22×C3—122no—
294C22×C3—122no—
295C2×D3—24no—
296C2×D3—42no—
297C2×D3—42no—
298C2×D3—62no—
299C2×D3—62no—
300C2×D3—61no—
301C2×D3—61no—
302C2×D3—61no—
303C2×D3—61no—
304C2×D3—62no—
305C2×D3—62no—
306C2×D3—128no—
307C2×D3—128no—
308C3×C4—22no—
309C3×C4—22no—
310C3×C4—22no—
311C3×C4—22no—
312C3×C4—22no—
313C3×C4—41no—
314C3×C4—124no—
315C3×C4—122no—
316Dic3—44no—
317Dic3—42no—
318Dic3—62no—
319Dic3—62no—
320Dic3—62no—
321Dic3—62no—
322Dic3—62no—
323Dic3—121no—
324C32#254211yescharacteristic, complemented, Sylow
325C23—62no—
326C23—94no—
327C23—91no—
328C23—182no—
329C23—184no—
330C23—184no—
331Q8—124no—
332Q8—364no—
333D4—64no—
334D4—184no—
335C2×C4—62no—
336C2×C4—64no—
337C2×C4—91no—
338C2×C4—91no—
339C2×C4—92no—
340C2×C4—92no—
341C2×C4—94no—
342C2×C4—98no—
343C2×C4—91no—
344C2×C4—124no—
345C2×C4—182no—
346C2×C4—188no—
347C2×C4—184no—
348C2×C4—184no—
349C2×C4—184no—
350C2×C4—364no—
351C2×C4C2×GO+(4,𝔽2)11yescharacteristic
352C2×C4C2×GO+(4,𝔽2)11yescharacteristic
353C2×C4C2×GO+(4,𝔽2)11yescharacteristic
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—124no—
361D3—44no—
362D3—62no—
363D3—62no—
364D3—62no—
365D3—62no—
366C22—64no—
367C22—91no—
368C22—91no—
369C22—92no—
370C22—92no—
371C22—122no—
372C22—122no—
373C22—188no—
374C22—364no—
375C22C22×GO+(4,𝔽2)11yescharacteristic
376C4—21no—
377C4—92no—
378C4—92no—
379C4—122no—
380C4—124no—
381C4—188no—
382C4—181no—
383C4D32⋊Q812yescomplemented
384C4#6423112yes—
385C3—21no—
386C3—21no—
387C2—92no—
388C2—92no—
389C2—124no—
390C2C2×D32⋊Q811yescharacteristic
391C2#1059649411yescharacteristic
392C2C2×#6423111yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊D3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2542
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×D32⋊Q8C2semidirect
3. #10593909C2semidirect
4. C4×C4⋊#157C2semidirect
5. #10593413C2semidirect
6. #10593408C2semidirect
46. #3802Q8semidirect
49. C4⋊#157D4semidirect
178. C32×C4C22⋊Q8semidirect
181. C3⋊Dic3C22⋊Q8semidirect
324. C32#2542semidirect
383. C4D32⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×D32⋊Q82
C4×#38022
#105939092
C4×C4⋊#1572
#105934132
#105934082
#105934072
#25429