Finite Group Databasebeta

← #11868702

Subgroups — #11868702

Order 1152.

764 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 115 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#10593882C211yesmaximal, characteristic, complemented
3#10593728C211yesmaximal, characteristic, complemented
4#10593394C212yesmaximal, complemented
5#10593364C214yesmaximal, complemented
6#10593363C212yesmaximal
7#10593359C212yesmaximal, complemented
8#10593347C212yesmaximal, complemented
9C2×#3802C2211yescharacteristic
10C2×C4×D32—21no—
11C2×#3788C2212yes—
12C42×C3⋊D3C2211yescharacteristic
13C3×C4×D12—21no—
14C3×C4×Dic6—21no—
15#63921—21no—
16#63919C2211yescharacteristic, complemented
17C4×#627—21no—
18#63902C2212yes—
19C4×#625C2212yes—
20#63900C2211yescharacteristic
21#63898—21no—
22#63874C2212yes—
23#63873C2211yescharacteristic, complemented
24#63871—21no—
25#63870C2212yescomplemented
26#63865—21no—
27C4⋊#622C2212yescomplemented
28C4⋊#622C2212yescomplemented
29#63743C2214yescomplemented
30#63742C2214yescomplemented
31#63739C2214yes—
32#63739C2214yes—
33#5578—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×C3×Dic6—21no—
42C2×#627—21no—
43C2×#625C2312yes—
44C2×#624—21no—
45C2×D3×Dic3—22no—
46#3802—22no—
47#3802Q814yescomplemented
48C4×D32—44no—
49C2×#622C2314yes—
50#3788—24no—
51C32×C42D411yescharacteristic
52C4×C3⋊Dic3D411yescharacteristic
53C4×C3⋊Dic3C2311yescharacteristic
54C4×C3⋊Dic3C2311yescharacteristic
55C3×(C2×D3)⋊C4—22no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×Dic3⋊C4—22no—
59C3×C4×Dic3—22no—
60#3724—21no—
61#3724C2312yes—
62#3724C2312yes—
63#3724C2312yes—
64Dic3⋊Dic3—22no—
65#3722—22no—
66(C2×D3)⋊Dic3—22no—
67#3077—91nomaximal, Sylow
68C2×D3×D4—61no—
69C22×C4×D3—62no—
70C3×C4×Q8—61no—
71C3×C4×D4—61no—
72#946—61no—
73#944—61no—
74D4×Dic3—61no—
75C4×#67—62no—
76#897—61no—
77#896—62no—
78#893—61no—
79D3×C4⋊C4—61no—
80#889—62no—
81#888—61no—
82#67⋊C4—62no—
83D3×C22⋊C4—62no—
84C4×D12—21no—
85#872—62no—
86C42×D3—61no—
87C42×D3—61no—
88C4×Dic6—21no—
89C4×Dic6—62no—
90C22×C3⋊D3C2×D411yescharacteristic
91C22×C3×D3—22no—
92C2×D32—24no—
93C2×D32—42no—
94C2×D32—42no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C3⋊Dic3C2×D411yescharacteristic
99C2×C3⋊Dic3C2×D411yescharacteristic
100C2×C3⋊Dic3C2411yescharacteristic
101C4×C3⋊D3—22no—
102C4×C3⋊D3—41no—
103C4×C3⋊D3C2×Q812yes—
104C4×C3⋊D3#4112yes—
105C2×C3×Dic3—22no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—22no—
108C3×D12—24no—
109C3×C4×D3—44no—
110C3×Dic6—42no—
111#627—42no—
112#625—22no—
113#625C2×Q814yes—
114#624—42no—
115D3×Dic3—44no—
116#622—24no—
117#533—91no—
118C2×C4×D4—91no—
119#478—94no—
120#476—92no—
121#474—92no—
122#428—92no—
123#423—91no—
124#418—92no—
125C23×D3—62no—
126C2×C3×Q8—61no—
127C2×C3×D4—61no—
128C22×C3×C4—62no—
129C2×#67—62no—
130C22×Dic3—62no—
131D3×D4—64no—
132D3×D4—64no—
133C2×D12—21no—
134C2×C4×D3—22no—
135C2×C4×D3—61no—
136C2×C4×D3—61no—
137C2×C4×D3—61no—
138C2×C4×D3—61no—
139C2×C4×D3—61no—
140C2×C4×D3—61no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C4×D3—128no—
144C2×Dic6—21no—
145C2×Dic6—62no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—62no—
148C3×C4⋊C4—61no—
149C3×C22⋊C4—62no—
150C3×C42—21no—
151C3×C42—21no—
152C3×C42—62no—
153#217—62no—
154(C2×D3)⋊C4—22no—
155(C2×D3)⋊C4—62no—
156(C2×D3)⋊C4—62no—
157(C2×D3)⋊C4—62no—
158C4⋊Dic3—21no—
159C4⋊Dic3—21no—
160C4⋊Dic3—62no—
161Dic3⋊C4—22no—
162Dic3⋊C4—62no—
163Dic3⋊C4—62no—
164Dic3⋊C4—62no—
165Dic3⋊C4—62no—
166Dic3⋊C4—62no—
167C4×Dic3—22no—
168C4×Dic3—61no—
169C4×Dic3—61no—
170C4×Dic3—61no—
171C4×Dic3—61no—
172C4×Dic3—61no—
173C4×Dic3—61no—
174C22×C32C22×D411yescharacteristic
175C2×C3⋊D3—21no—
176C2×C3⋊D3—21no—
177C2×C3⋊D3C22⋊Q812yes—
178C2×C3×D3—24no—
179C2×C3×D3—42no—
180C2×C3×D3—42no—
181D32—48no—
182C32×C4—21no—
183C32×C4C22⋊Q812yes—
184C32×C4AGL(1,ℤ/8)12yes—
185C3⋊Dic3—21no—
186C3⋊Dic3—21no—
187C3⋊Dic3C22×Q811yescharacteristic
188C3⋊Dic3C2×#4111yescharacteristic
189C3×Dic3—42no—
190C3×Dic3—42no—
191C3×Dic3—42no—
192C22×D4—91no—
193C23×C4—181no—
194C2×M16—92no—
195C4⋊Q8—91no—
196C4⋊Q8—91no—
197#125—92no—
198C22⋊Q8—181no—
199C22⋊Q8—181no—
200C4×Q8—61no—
201C4×Q8—181no—
202C4×D4—61no—
203C4×D4—92no—
204C4×D4—92no—
205C4×D4—181no—
206#117—92no—
207C2×C4⋊C4—91no—
208C2×C22⋊C4—181no—
209C2×C42—91no—
210#107—94no—
211#106—94no—
212C4⋊C8—92no—
213C4⋊C8—92no—
214#102—94no—
215#102—94no—
216C23×C3—62no—
217C22×D3—22no—
218C22×D3—61no—
219C22×D3—61no—
220C22×D3—68no—
221C22×D3—124no—
222C22×D3—124no—
223C3×Q8—122no—
224C3×D4—64no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—62no—
232C2×C3×C4—62no—
233C2×C3×C4—62no—
234C2×C3×C4—124no—
235#67—64no—
236#67—64no—
237C2×Dic3—22no—
238C2×Dic3—22no—
239C2×Dic3—22no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—124no—
247D12—24no—
248C4×D3—44no—
249C4×D3—62no—
250C4×D3—62no—
251C4×D3—62no—
252C4×D3—62no—
253C4×D3—64no—
254C4×D3—122no—
255C4×D3—124no—
256C4×D3—122no—
257C4×D3—124no—
258C4×D3—122no—
259Dic6—42no—
260Dic6—124no—
261C2×C32C2×C22⋊Q811yescharacteristic
262C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
263C2×C32#57511yescharacteristic
264C3⋊D3—22no—
265C3×D3—44no—
266C24—181no—
267C2×Q8—61no—
268C2×Q8—181no—
269C2×D4—61no—
270C2×D4—94no—
271C2×D4—92no—
272C2×D4—182no—
273C22×C4—62no—
274C22×C4—91no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—181no—
278C22×C4—182no—
279C22×C4—364no—
280M16—184no—
281C2×C8—94no—
282C4⋊C4—61no—
283C4⋊C4—62no—
284C4⋊C4—61no—
285C4⋊C4—92no—
286C4⋊C4—92no—
287C4⋊C4—92no—
288C4⋊C4—182no—
289C4⋊C4—181no—
290C22⋊C4—62no—
291C22⋊C4—182no—
292C22⋊C4—182no—
293C42—62no—
294C42—91no—
295C42—91no—
296C42—91no—
297C42GO+(4,𝔽2)11yescharacteristic
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—64no—
301C22×C3—122no—
302C22×C3—122no—
303C2×D3—24no—
304C2×D3—42no—
305C2×D3—42no—
306C2×D3—62no—
307C2×D3—62no—
308C2×D3—62no—
309C2×D3—62no—
310C2×D3—121no—
311C2×D3—121no—
312C2×D3—1216no—
313C3×C4—22no—
314C3×C4—22no—
315C3×C4—22no—
316C3×C4—22no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—122no—
320C3×C4—122no—
321C3×C4—122no—
322Dic3—42no—
323Dic3—42no—
324Dic3—42no—
325Dic3—61no—
326Dic3—61no—
327Dic3—61no—
328Dic3—61no—
329Dic3—62no—
330Dic3—62no—
331Dic3—121no—
332Dic3—121no—
333C32#307711yescharacteristic, complemented, Sylow
334C23—62no—
335C23—91no—
336C23—184no—
337C23—362no—
338C23—362no—
339Q8—122no—
340Q8—362no—
341D4—64no—
342D4—94no—
343D4—182no—
344C2×C4—62no—
345C2×C4—62no—
346C2×C4—62no—
347C2×C4—91no—
348C2×C4—92no—
349C2×C4—92no—
350C2×C4—91no—
351C2×C4—91no—
352C2×C4—124no—
353C2×C4—182no—
354C2×C4—361no—
355C2×C4—362no—
356C2×C4—364no—
357C2×C4C2×GO+(4,𝔽2)11yescharacteristic
358C2×C4C2×GO+(4,𝔽2)11yescharacteristic
359C2×C4C2×GO+(4,𝔽2)11yescharacteristic
360C8—184no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—124no—
368D3—44no—
369D3—64no—
370D3—122no—
371C22—64no—
372C22—92no—
373C22—122no—
374C22—122no—
375C22—181no—
376C22—181no—
377C22—368no—
378C22C22×GO+(4,𝔽2)11yescharacteristic
379C4—21no—
380C4—91no—
381C4—91no—
382C4—122no—
383C4—122no—
384C4—122no—
385C4—181no—
386C4—181no—
387C4D32⋊Q812yes—
388C4#6422412yes—
389C3—21no—
390C3—21no—
391C2—124no—
392C2—182no—
393C2C2×D32⋊Q811yescharacteristic
394C2C2×#6422411yescharacteristic
395C2#1059650211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32#3077
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. #10593882C2semidirect
3. #10593728C2semidirect
4. #10593394C2semidirect
5. #10593364C2semidirect
7. #10593359C2semidirect
8. #10593347C2semidirect
16. #63919C22semidirect
23. #63873C22semidirect
25. #63870C22semidirect
27. C4⋊#622C22semidirect
28. C4⋊#622C22semidirect
29. #63743C22semidirect
30. #63742C22semidirect
47. #3802Q8semidirect
333. C32#3077semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105938822
#105937282
#105933942
#105933642
#105933632
#105933592
#105933472
#30779