Finite Group Databasebeta

← #11870538

Subgroups — #11870538

Order 1152.

772 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C4×#3802C211yesmaximal, characteristic
2#10593854C211yesmaximal, characteristic, complemented
3#10593727C211yesmaximal, characteristic, complemented
4#10593437C212yesmaximal, complemented
5#10593433C214yesmaximal, complemented
6#10593386C212yesmaximal, complemented
7#10593359C212yesmaximal, complemented
8#10593354C212yesmaximal
9C2×#3802C2211yescharacteristic
10C2×C4×D32—21no—
11C2×#3775C2214yes—
12C42×C3⋊D3C2211yescharacteristic
13C3×C4×D12—21no—
14C3×#870—21no—
15#63921—21no—
16#63919C2211yescharacteristic, complemented
17#63919C2211yescharacteristic, complemented
18#63902C2212yes—
19C4×#625C2212yes—
20#63900C2211yescharacteristic
21#63898—21no—
22#63865—21no—
23#63865C2212yes—
24#63849—21no—
25#63838—21no—
26#63838C2212yescomplemented
27#63778C2212yes—
28C4⋊#622C2212yescomplemented
29C4×#622C2212yescomplemented
30#63742C2214yescomplemented
31#63740C2214yescomplemented
32#63739C2214yes—
33#5688—61no—
34C4×D3×D4—61no—
35C22×D32—21no—
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3C2311yescharacteristic
39C2×C3×D12—21no—
40C2×C3×C4×D3—22no—
41C2×#627—21no—
42C2×#627C2312yes—
43C2×#625C2312yes—
44C2×#624—21no—
45C2×D3×Dic3—22no—
46#3802—24no—
47C4×D32—44no—
48C2×#622C2314yes—
49#3775—28no—
50C32×C42D411yescharacteristic
51C4×C3⋊Dic3D411yescharacteristic
52C4×C3⋊Dic3C2311yescharacteristic
53C4×C3⋊Dic3C2311yescharacteristic
54C3×(C2×D3)⋊C4—22no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×Dic3⋊C4—22no—
59C3×Dic3⋊C4—22no—
60#3724—21no—
61#3724C2312yes—
62#3724C2312yes—
63#3722—22no—
64(C2×D3)⋊Dic3—22no—
65Dic32—22no—
66#3101—91nomaximal, Sylow
67C2×D3×D4—61no—
68C22×C4×D3—62no—
69C3×#125—61no—
70C3×C4×D4—61no—
71D4×Dic3—61no—
72C4×#67—62no—
73#896—62no—
74#896—62no—
75#893—61no—
76#892—61no—
77#892—61no—
78D3×C4⋊C4—61no—
79#888—61no—
80#888—61no—
81#887—62no—
82#887—62no—
83#67⋊C4—62no—
84D3×C22⋊C4—62no—
85C4×D12—21no—
86C42×D3—61no—
87C42×D3—61no—
88#870—21no—
89C22×C3⋊D3C2×D411yescharacteristic
90C22×C3×D3—22no—
91C2×D32—24no—
92C2×D32—42no—
93C2×D32—42no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C3⋊Dic3C2×D411yescharacteristic
98C2×C3⋊Dic3C2×D411yescharacteristic
99C2×C3⋊Dic3C2411yescharacteristic
100C4×C3⋊D3—22no—
101C4×C3⋊D3—41no—
102C4×C3⋊D3SD1614yescomplemented
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—22no—
106C3×D12—24no—
107C3×C4×D3—44no—
108#627—24no—
109#627—42no—
110#625—22no—
111#625#4114yes—
112#624—42no—
113D3×Dic3—44no—
114#622—24no—
115#533—91no—
116C2×C4×D4—91no—
117#483—92no—
118#476—92no—
119#461—92no—
120#450—92no—
121C4×SD16—94no—
122#431—91no—
123C23×D3—62no—
124C2×C3×D4—61no—
125C22×C3×C4—62no—
126C2×#67—62no—
127C22×Dic3—62no—
128D3×D4—68no—
129C2×D12—21no—
130C2×C4×D3—22no—
131C2×C4×D3—61no—
132C2×C4×D3—61no—
133C2×C4×D3—61no—
134C2×C4×D3—61no—
135C2×C4×D3—61no—
136C2×C4×D3—61no—
137C2×C4×D3—62no—
138C2×C4×D3—62no—
139C2×C4×D3—128no—
140C2×Dic6—62no—
141C2×Dic6—62no—
142C3×C4⋊C4—62no—
143C3×C4⋊C4—62no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—61no—
147C3×C22⋊C4—62no—
148C3×C42—21no—
149C3×C42—21no—
150#217—62no—
151(C2×D3)⋊C4—22no—
152(C2×D3)⋊C4—62no—
153(C2×D3)⋊C4—62no—
154(C2×D3)⋊C4—62no—
155C4⋊Dic3—21no—
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158Dic3⋊C4—22no—
159Dic3⋊C4—22no—
160Dic3⋊C4—62no—
161Dic3⋊C4—62no—
162Dic3⋊C4—62no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C4×Dic3—61no—
167C4×Dic3—61no—
168C4×Dic3—61no—
169C4×Dic3—62no—
170C4×Dic3—62no—
171C22×C32C22×D411yescharacteristic
172C2×C3⋊D3—21no—
173C2×C3⋊D3—21no—
174C2×C3⋊D3C2×SD1612yes—
175C2×C3×D3—24no—
176C2×C3×D3—42no—
177C2×C3×D3—42no—
178D32—48no—
179C32×C4—21no—
180C32×C4—21no—
181C32×C4C2×SD1612yes—
182C3⋊Dic3—21no—
183C3⋊Dic3C2×SD1612yes—
184C3⋊Dic3C2×#4112yes—
185C3×Dic3—42no—
186C3×Dic3—42no—
187C3×Dic3—42no—
188C22×D4—91no—
189C23×C4—181no—
190C2×SD16—94no—
191C4⋊Q8—91no—
192C4⋊Q8—91no—
193#125—61no—
194C22⋊Q8—92no—
195C22⋊Q8—181no—
196C4×Q8—92no—
197C4×Q8—181no—
198C4×D4—61no—
199C4×D4—92no—
200C4×D4—92no—
201C4×D4—181no—
202#117—181no—
203C2×C4⋊C4—91no—
204C2×C22⋊C4—181no—
205C2×C42—91no—
206#106—94no—
207C4⋊C8—92no—
208#103—94no—
209#102—94no—
210C22⋊C8—92no—
211C4×C8—92no—
212C23×C3—62no—
213C22×D3—22no—
214C22×D3—61no—
215C22×D3—61no—
216C22×D3—68no—
217C22×D3—124no—
218C22×D3—124no—
219C3×D4—64no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—62no—
227C2×C3×C4—62no—
228C2×C3×C4—62no—
229C2×C3×C4—124no—
230#67—64no—
231#67—64no—
232C2×Dic3—22no—
233C2×Dic3—22no—
234C2×Dic3—22no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—124no—
242D12—24no—
243C4×D3—44no—
244C4×D3—64no—
245C4×D3—64no—
246C4×D3—64no—
247C4×D3—122no—
248C4×D3—124no—
249C4×D3—122no—
250C4×D3—124no—
251C4×D3—122no—
252Dic6—124no—
253Dic6—124no—
254C2×C32#52511yescharacteristic
255C2×C32C22×SD1611yescharacteristic
256C2×C32#57511yescharacteristic
257C3⋊D3—22no—
258C3×D3—44no—
259C24—181no—
260C2×Q8—92no—
261C2×Q8—181no—
262C2×D4—61no—
263C2×D4—92no—
264C2×D4—184no—
265C22×C4—62no—
266C22×C4—91no—
267C22×C4—91no—
268C22×C4—91no—
269C22×C4—181no—
270C22×C4—182no—
271C22×C4—364no—
272SD16—188no—
273C2×C8—94no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—62no—
278C4⋊C4—62no—
279C4⋊C4—92no—
280C4⋊C4—92no—
281C4⋊C4—181no—
282C22⋊C4—62no—
283C22⋊C4—182no—
284C22⋊C4—182no—
285C42—91no—
286C42—91no—
287C42—91no—
288C42—182no—
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—62no—
301C2×D3—62no—
302C2×D3—121no—
303C2×D3—121no—
304C2×D3—1216no—
305C3×C4—22no—
306C3×C4—22no—
307C3×C4—22no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—122no—
312C3×C4—122no—
313C3×C4—122no—
314Dic3—42no—
315Dic3—42no—
316Dic3—42no—
317Dic3—62no—
318Dic3—62no—
319Dic3—62no—
320Dic3—62no—
321Dic3—62no—
322Dic3—121no—
323C32#310111yescharacteristic, complemented, Sylow
324C23—62no—
325C23—91no—
326C23—184no—
327C23—362no—
328C23—362no—
329Q8—184no—
330Q8—362no—
331D4—64no—
332D4—94no—
333D4—182no—
334C2×C4—62no—
335C2×C4—62no—
336C2×C4—62no—
337C2×C4—91no—
338C2×C4—91no—
339C2×C4—94no—
340C2×C4—91no—
341C2×C4—124no—
342C2×C4—182no—
343C2×C4—361no—
344C2×C4—364no—
345C2×C4—362no—
346C2×C4C2×GO+(4,𝔽2)11yescharacteristic
347C2×C4C2×GO+(4,𝔽2)11yescharacteristic
348C2×C4C2×GO+(4,𝔽2)11yescharacteristic
349C8—184no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—124no—
357D3—44no—
358D3—64no—
359D3—122no—
360C22—64no—
361C22—92no—
362C22—122no—
363C22—122no—
364C22—181no—
365C22—181no—
366C22—368no—
367C22C22×GO+(4,𝔽2)11yescharacteristic
368C4—21no—
369C4—21no—
370C4—92no—
371C4—92no—
372C4—122no—
373C4—122no—
374C4—122no—
375C4—181no—
376C4#6422712yes—
377C3—21no—
378C3—21no—
379C2—124no—
380C2—182no—
381C2#1059650211yescharacteristic
382C2C2×#6422711yescharacteristic
383C2#1059651011yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32#3101
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593854C2semidirect
3. #10593727C2semidirect
4. #10593437C2semidirect
5. #10593433C2semidirect
6. #10593386C2semidirect
7. #10593359C2semidirect
16. #63919C22semidirect
17. #63919C22semidirect
26. #63838C22semidirect
28. C4⋊#622C22semidirect
29. C4×#622C22semidirect
30. #63742C22semidirect
31. #63740C22semidirect
102. C4×C3⋊D3SD16semidirect
323. C32#3101semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105938542
#105937272
#105934372
#105934332
#105933862
#105933592
#105933542
#31019