Finite Group Databasebeta

← #11868267

Subgroups — #11868267

Order 1152.

838 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 838 conjugacy classes of subgroups — too many to draw. Only its 129 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#10593909C211yesmaximal, characteristic, complemented
3#10593726C211yesmaximal, characteristic, complemented
4#10593396C212yesmaximal, complemented
5#10593367C214yesmaximal, complemented
6#10593365C212yesmaximal
7#10593347C214yesmaximal, complemented
8C2×#3802C2211yescharacteristic
9C2×C4×D32—21no—
10C2×#3797—21no—
11C2×#3787C2212yes—
12C42×C3⋊D3C2211yescharacteristic
13C3×C4×D12—21no—
14C3×#869—21no—
15#63921—21no—
16#63919—21no—
17#63919C2212yescomplemented
18#63902C2212yes—
19C4×#625C2212yes—
20#63900—21no—
21#63900C2212yes—
22#63900C2211yescharacteristic
23#63898—21no—
24#63873C2212yescomplemented
25#63779C2212yescomplemented
26C4⋊#622C2212yescomplemented
27#63743C2218yescomplemented
28#63739C2218yes—
29D3×C4⋊Q8—61no—
30C4×D3×D4—61no—
31C22×D32—21no—
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3C2311yescharacteristic
35C2×C3×D12—21no—
36C2×C3×C4×D3—22no—
37C2×C3×Dic6—22no—
38C2×#627—22no—
39C2×#625C2312yes—
40C2×#624—22no—
41C2×#624—21no—
42C2×D3×Dic3—22no—
43#3802—22no—
44#3802Q814yescomplemented
45C4×D32—44no—
46#3797—44no—
47C2×#622C2314yes—
48#3787—24no—
49C32×C42D411yescharacteristic
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3C2311yescharacteristic
52C4×C3⋊Dic3C2311yescharacteristic
53C3×(C2×D3)⋊C4—22no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—22no—
56C3×C4⋊Dic3—22no—
57#3724—22no—
58#3724C2314yes—
59#3724C2312yes—
60(C2×D3)⋊Dic3—22no—
61C2×#474—91nomaximal, Sylow
62C2×D3×Q8—62no—
63C2×D3×D4—61no—
64C22×C4×D3—62no—
65C3×C4⋊Q8—61no—
66C3×C4×D4—61no—
67#944—62no—
68D4×Dic3—61no—
69C4×#67—62no—
70#893—61no—
71D3×C4⋊C4—62no—
72D3×C4⋊C4—61no—
73D3×C4⋊C4—62no—
74#888—62no—
75#888—62no—
76#67⋊C4—62no—
77D3×C22⋊C4—62no—
78C4×D12—21no—
79C42×D3—61no—
80C42×D3—61no—
81#869—21no—
82C22×C3⋊D3C2×D411yescharacteristic
83C22×C3×D3—22no—
84C2×D32—24no—
85C2×D32—42no—
86C2×D32—42no—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C3⋊Dic3C2×D411yescharacteristic
91C2×C3⋊Dic3C2×D411yescharacteristic
92C2×C3⋊Dic3C2411yescharacteristic
93C4×C3⋊D3—22no—
94C4×C3⋊D3D814yes—
95C4×C3⋊D3C2×Q812yes—
96C4×C3⋊D3#4112yes—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—24no—
99C3×D12—24no—
100C3×C4×D3—44no—
101C3×Dic6—44no—
102#627—44no—
103#625—22no—
104#625C2×Q814yescomplemented
105#624—44no—
106#624—42no—
107D3×Dic3—44no—
108#622—24no—
109C2×C4⋊Q8—91no—
110C2×C4×D4—91no—
111#474—94no—
112#474—94no—
113C2×#107—92no—
114C2×C4⋊C8—91no—
115C2×#102—92no—
116C23×D3—62no—
117C2×C3×Q8—62no—
118C2×C3×D4—61no—
119C22×C3×C4—62no—
120C2×#67—62no—
121C22×Dic3—62no—
122D3×Q8—128no—
123D3×D4—64no—
124D3×D4—64no—
125C2×D12—21no—
126C2×C4×D3—22no—
127C2×C4×D3—61no—
128C2×C4×D3—61no—
129C2×C4×D3—61no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×C4×D3—61no—
133C2×C4×D3—62no—
134C2×C4×D3—64no—
135C2×C4×D3—62no—
136C2×C4×D3—128no—
137C2×Dic6—22no—
138C2×Dic6—64no—
139C3×C4⋊C4—62no—
140C3×C4⋊C4—62no—
141C3×C4⋊C4—61no—
142C3×C22⋊C4—62no—
143C3×C42—21no—
144C3×C42—21no—
145#217—62no—
146(C2×D3)⋊C4—22no—
147(C2×D3)⋊C4—62no—
148C4⋊Dic3—22no—
149C4⋊Dic3—22no—
150C4⋊Dic3—21no—
151Dic3⋊C4—62no—
152Dic3⋊C4—64no—
153Dic3⋊C4—64no—
154C4×Dic3—61no—
155C4×Dic3—61no—
156C4×Dic3—61no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C22×C32C22×D411yescharacteristic
161C2×C3⋊D3C22⋊Q812yes—
162C2×C3⋊D3C2×D812yes—
163C2×C3⋊D3#13712yes—
164C2×C3×D3—24no—
165C2×C3×D3—42no—
166C2×C3×D3—42no—
167D32—48no—
168C32×C4—21no—
169C32×C4C22⋊Q812yes—
170C32×C4C2×D812yes—
171C3⋊Dic3—21no—
172C3⋊Dic3C2×D812yes—
173C3⋊Dic3C22×Q811yescharacteristic
174C3⋊Dic3C2×#4111yescharacteristic
175C3×Dic3—42no—
176C3×Dic3—44no—
177C22×Q8—181no—
178C22×D4—91no—
179C23×C4—181no—
180C22×C8—92no—
181C4⋊Q8—61no—
182C4⋊Q8—92no—
183C4⋊Q8—92no—
184C4⋊Q8—181no—
185C4×D4—61no—
186C4×D4—92no—
187C4×D4—92no—
188C4×D4—181no—
189C2×C4⋊C4—91no—
190C2×C4⋊C4—92no—
191C2×C4⋊C4—181no—
192C2×C22⋊C4—181no—
193C2×C42—91no—
194#107—98no—
195C4⋊C8—92no—
196C4⋊C8—92no—
197#102—98no—
198C23×C3—62no—
199C22×D3—22no—
200C22×D3—61no—
201C22×D3—61no—
202C22×D3—68no—
203C22×D3—124no—
204C22×D3—124no—
205C3×Q8—124no—
206C3×D4—64no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—64no—
214C2×C3×C4—62no—
215C2×C3×C4—124no—
216#67—64no—
217#67—64no—
218C2×Dic3—24no—
219C2×Dic3—22no—
220C2×Dic3—61no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—61no—
226C2×Dic3—124no—
227D12—24no—
228C4×D3—44no—
229C4×D3—64no—
230C4×D3—64no—
231C4×D3—62no—
232C4×D3—62no—
233C4×D3—62no—
234C4×D3—62no—
235C4×D3—64no—
236C4×D3—122no—
237C4×D3—124no—
238C4×D3—128no—
239C4×D3—124no—
240Dic6—44no—
241Dic6—128no—
242C2×C32C2×C22⋊Q811yescharacteristic
243C2×C32C22×D811yescharacteristic
244C2×C32C2×#13711yescharacteristic
245C3⋊D3#47414yescomplemented
246C3×D3—44no—
247C24—181no—
248C2×Q8—62no—
249C2×Q8—182no—
250C2×Q8—364no—
251C2×D4—61no—
252C2×D4—94no—
253C2×D4—92no—
254C2×D4—182no—
255C22×C4—62no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—181no—
260C22×C4—182no—
261C22×C4—182no—
262C22×C4—364no—
263C2×C8—94no—
264C2×C8—184no—
265C4⋊C4—61no—
266C4⋊C4—62no—
267C4⋊C4—62no—
268C4⋊C4—94no—
269C4⋊C4—92no—
270C4⋊C4—182no—
271C22⋊C4—62no—
272C22⋊C4—182no—
273C42—91no—
274C42—91no—
275C42—91no—
276C42GO+(4,𝔽2)11yescharacteristic
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—64no—
280C22×C3—122no—
281C22×C3—122no—
282C2×D3—24no—
283C2×D3—42no—
284C2×D3—42no—
285C2×D3—62no—
286C2×D3—62no—
287C2×D3—62no—
288C2×D3—62no—
289C2×D3—62no—
290C2×D3—62no—
291C2×D3—1216no—
292C3×C4—22no—
293C3×C4—22no—
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—22no—
297C3×C4—41no—
298C3×C4—124no—
299C3×C4—122no—
300Dic3—44no—
301Dic3—42no—
302Dic3—62no—
303Dic3—62no—
304Dic3—61no—
305Dic3—61no—
306Dic3—61no—
307Dic3—61no—
308Dic3—62no—
309Dic3—121no—
310C32C2×#47411yescharacteristic, complemented, Sylow
311C23—62no—
312C23—91no—
313C23—184no—
314C23—362no—
315C23—362no—
316Q8—124no—
317Q8—364no—
318D4—64no—
319D4—94no—
320D4—182no—
321C2×C4—62no—
322C2×C4—64no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—92no—
326C2×C4—92no—
327C2×C4—94no—
328C2×C4—91no—
329C2×C4—124no—
330C2×C4—182no—
331C2×C4—364no—
332C2×C4—362no—
333C2×C4—364no—
334C2×C4C2×GO+(4,𝔽2)11yescharacteristic
335C2×C4C2×GO+(4,𝔽2)11yescharacteristic
336C2×C4C2×GO+(4,𝔽2)11yescharacteristic
337C8—184no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—124no—
345D3—44no—
346D3—64no—
347D3—64no—
348C22—64no—
349C22—92no—
350C22—92no—
351C22—92no—
352C22—122no—
353C22—122no—
354C22—368no—
355C22C22×GO+(4,𝔽2)11yescharacteristic
356C4—21no—
357C4—91no—
358C4—91no—
359C4—92no—
360C4—122no—
361C4—124no—
362C4—181no—
363C4D32⋊Q812yes—
364C4#6422512yes—
365C3—21no—
366C3—21no—
367C2—94no—
368C2—124no—
369C2C2×D32⋊Q811yescharacteristic
370C2C2×#6422511yescharacteristic
371C2#1059650511yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#474
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. #10593909C2semidirect
3. #10593726C2semidirect
4. #10593396C2semidirect
5. #10593367C2semidirect
7. #10593347C2semidirect
17. #63919C22semidirect
24. #63873C22semidirect
25. #63779C22semidirect
26. C4⋊#622C22semidirect
27. #63743C22semidirect
44. #3802Q8semidirect
104. #625C2×Q8semidirect
245. C3⋊D3#474semidirect
310. C32C2×#474semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105939092
#105937262
#105933962
#105933672
#105933652
#105933472
C2×#4749