Finite Group Databasebeta

← #11860091

Subgroups — #11860091

Order 1152.

906 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 906 conjugacy classes of subgroups — too many to draw. Only its 159 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×#64227C211yesmaximal, characteristic
2C4×#3802C211yesmaximal, characteristic
3C4×#3797C211yesmaximal, characteristic, complemented
4#10593723C211yesmaximal, characteristic, complemented
5#10593432C214yesmaximal, complemented
6#10593431C214yesmaximal, complemented
7#10593396C211yesmaximal, characteristic, complemented
8#10593375C211yesmaximal, characteristic, complemented
9#10593365C211yesmaximal, characteristic
10C2×#3802C2211yescharacteristic
11C2×C4×D32—21no—
12C2×#3797C2211yescharacteristic
13C2×#3787C2211yescharacteristic
14C2×#3787C2211yescharacteristic
15C2×#3775C2214yes—
16#64227C418yescomplemented
17C42×C3⋊D3C2211yescharacteristic
18C3×C4×D12—21no—
19C3×C4×Dic6—21no—
20#63921—21no—
21C4×#627C2212yescomplemented
22#63902C2212yes—
23C4×#625C2212yes—
24#63900C2211yescharacteristic
25#63900C2211yescharacteristic
26#63898—21no—
27#63883—21no—
28C4×#624—21no—
29#63843—21no—
30#63838C2212yescomplemented
31#63777C2212yescomplemented
32#63777C2212yescomplemented
33#63743C2214yescomplemented
34#63740C2214yescomplemented
35#63739C2214yes—
36C4×D3×Q8—61no—
37C4×D3×D4—61no—
38C22×D32—21no—
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3C2311yescharacteristic
42C2×C3×D12—21no—
43C2×C3×C4×D3—22no—
44C2×C3×Dic6—21no—
45C2×#627C2312yes—
46C2×#625C2312yes—
47C2×#624—21no—
48C2×#624—21no—
49C2×#624—21no—
50C2×D3×Dic3—22no—
51#3802—22no—
52#3802C2×C414yes—
53C4×D32—44no—
54#3797—22no—
55#3797C2×C414yescomplemented
56C2×#622C2312yes—
57C2×#622C2312yes—
58#3787—22no—
59#3787C2×C414yescomplemented
60#3775C2×C4116yescomplemented
61C32×C42D411yescharacteristic
62C4×C3⋊Dic3D411yescharacteristic
63C4×C3⋊Dic3C2311yescharacteristic
64C4×C3⋊Dic3C2311yescharacteristic
65C3×(C2×D3)⋊C4—22no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×Dic3⋊C4—22no—
69C3×C4×Dic3—22no—
70#3724C2312yes—
71#3724C2312yes—
72Dic3⋊Dic3—22no—
73(C2×D3)⋊Dic3—22no—
74Dic32—22no—
75C2×#440—91nomaximal, Sylow
76C2×D3×Q8—61no—
77C2×D3×D4—61no—
78C22×C4×D3—62no—
79C3×C4×Q8—61no—
80C3×C4×D4—61no—
81Q8×Dic3—61no—
82D4×Dic3—61no—
83C4×#67—62no—
84#893—61no—
85D3×C4⋊C4—61no—
86D3×C4⋊C4—61no—
87D3×C4⋊C4—62no—
88#887—62no—
89#887—61no—
90#67⋊C4—62no—
91D3×C22⋊C4—62no—
92C4×D12—21no—
93C42×D3—61no—
94C42×D3—61no—
95C42×D3—62no—
96C4×Dic6—21no—
97C4×Dic6—62no—
98C22×C3⋊D3C2×D411yescharacteristic
99C22×C3×D3—22no—
100C2×D32—24no—
101C2×D32—42no—
102C2×D32—42no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C3⋊Dic3C2×D411yescharacteristic
107C2×C3⋊Dic3C2×D411yescharacteristic
108C2×C3⋊Dic3C2411yescharacteristic
109C4×C3⋊D3—22no—
110C4×C3⋊D3—22no—
111C4×C3⋊D3C22×C412yes—
112C4×C3⋊D3#4112yes—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—22no—
116C3×D12—24no—
117C3×C4×D3—44no—
118C3×Dic6—24no—
119#627—22no—
120#627C22×C414yescomplemented
121#625—22no—
122#625C22×C414yes—
123#624—24no—
124#624—42no—
125#624—42no—
126D3×Dic3—44no—
127#622—22no—
128#622C22×C414yescomplemented
129C22×SD16—91no—
130C2×C4×Q8—91no—
131C2×C4×D4—91no—
132#440—94no—
133#440—94no—
134C2×#107—91no—
135C2×#103—91no—
136C2×#102—91no—
137C2×#97—91no—
138C23×D3—62no—
139C2×C3×Q8—61no—
140C2×C3×D4—61no—
141C22×C3×C4—62no—
142C2×#67—62no—
143C22×Dic3—62no—
144D3×Q8—64no—
145D3×Q8—64no—
146D3×D4—64no—
147D3×D4—64no—
148C2×D12—21no—
149C2×C4×D3—22no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×C4×D3—61no—
155C2×C4×D3—61no—
156C2×C4×D3—62no—
157C2×C4×D3—62no—
158C2×C4×D3—62no—
159C2×C4×D3—62no—
160C2×C4×D3—128no—
161C2×Dic6—21no—
162C2×Dic6—62no—
163C3×C4⋊C4—62no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C22⋊C4—62no—
167C3×C42—21no—
168C3×C42—21no—
169C3×C42—62no—
170#217—62no—
171(C2×D3)⋊C4—22no—
172(C2×D3)⋊C4—62no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3—62no—
176Dic3⋊C4—22no—
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179Dic3⋊C4—62no—
180C4×Dic3—22no—
181C4×Dic3—61no—
182C4×Dic3—61no—
183C4×Dic3—61no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—62no—
188C4×Dic3—62no—
189C22×C32C22×D411yescharacteristic
190C2×C3⋊D3C4×D412yes—
191C2×C3⋊D3AGL(1,ℤ/8)12yes—
192C2×C3⋊D3#13712yes—
193C2×C3×D3—24no—
194C2×C3×D3—42no—
195C2×C3×D3—42no—
196D32—48no—
197C32×C4—21no—
198C32×C4—21no—
199C32×C4C4×D412yes—
200C3⋊Dic3—21no—
201C3⋊Dic3—21no—
202C3⋊Dic3C23×C411yescharacteristic
203C3⋊Dic3C2×#4111yescharacteristic
204C3×Dic3—24no—
205C3×Dic3—42no—
206C3×Dic3—42no—
207C22×Q8—91no—
208C22×D4—91no—
209C23×C4—181no—
210C2×SD16—94no—
211C2×SD16—98no—
212C22×C8—91no—
213C22×C8—91no—
214C4×Q8—61no—
215C4×Q8—92no—
216C4×Q8—92no—
217C4×Q8—181no—
218C4×D4—61no—
219C4×D4—92no—
220C4×D4—92no—
221C4×D4—181no—
222C2×C4⋊C4—91no—
223C2×C4⋊C4—91no—
224C2×C4⋊C4—181no—
225C2×C22⋊C4—181no—
226C2×C42—91no—
227C2×C42—181no—
228#107—94no—
229#103—94no—
230#102—94no—
231#97—92no—
232#97—92no—
233C23×C3—62no—
234C22×D3—22no—
235C22×D3—61no—
236C22×D3—61no—
237C22×D3—68no—
238C22×D3—124no—
239C22×D3—124no—
240C3×Q8—64no—
241C3×D4—64no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4—62no—
251C2×C3×C4—124no—
252#67—64no—
253#67—64no—
254C2×Dic3—22no—
255C2×Dic3—22no—
256C2×Dic3—22no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—124no—
264D12—24no—
265C4×D3—44no—
266C4×D3—62no—
267C4×D3—62no—
268C4×D3—62no—
269C4×D3—62no—
270C4×D3—68no—
271C4×D3—64no—
272C4×D3—64no—
273C4×D3—122no—
274C4×D3—122no—
275C4×D3—124no—
276C4×D3—124no—
277C4×D3—124no—
278Dic6—24no—
279Dic6—64no—
280Dic6—64no—
281C2×C32C2×C4×D411yescharacteristic
282C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
283C2×C32C2×#13711yescharacteristic
284C3⋊D3#44014yescomplemented
285C3×D3—44no—
286C24—181no—
287C2×Q8—61no—
288C2×Q8—92no—
289C2×Q8—94no—
290C2×Q8—182no—
291C2×D4—61no—
292C2×D4—94no—
293C2×D4—92no—
294C2×D4—182no—
295C22×C4—62no—
296C22×C4—91no—
297C22×C4—91no—
298C22×C4—91no—
299C22×C4—181no—
300C22×C4—181no—
301C22×C4—181no—
302C22×C4—182no—
303C22×C4—364no—
304SD16—916no—
305C2×C8—92no—
306C2×C8—94no—
307C2×C8—92no—
308C2×C8—182no—
309C4⋊C4—61no—
310C4⋊C4—61no—
311C4⋊C4—62no—
312C4⋊C4—92no—
313C4⋊C4—92no—
314C4⋊C4—182no—
315C22⋊C4—62no—
316C22⋊C4—182no—
317C42—62no—
318C42—91no—
319C42—91no—
320C42—91no—
321C42—182no—
322C42GO+(4,𝔽2)11yescharacteristic
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—64no—
326C22×C3—122no—
327C22×C3—122no—
328C2×D3—24no—
329C2×D3—42no—
330C2×D3—42no—
331C2×D3—62no—
332C2×D3—62no—
333C2×D3—62no—
334C2×D3—62no—
335C2×D3—62no—
336C2×D3—62no—
337C2×D3—1216no—
338C3×C4—22no—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—64no—
345C3×C4—122no—
346C3×C4—122no—
347Dic3—24no—
348Dic3—42no—
349Dic3—42no—
350Dic3—61no—
351Dic3—61no—
352Dic3—61no—
353Dic3—61no—
354Dic3—62no—
355Dic3—62no—
356Dic3—121no—
357Dic3—121no—
358C32C2×#44011yescharacteristic, complemented, Sylow
359C23—62no—
360C23—91no—
361C23—184no—
362C23—362no—
363C23—362no—
364Q8—64no—
365Q8—94no—
366Q8—182no—
367D4—64no—
368D4—94no—
369D4—182no—
370C2×C4—62no—
371C2×C4—62no—
372C2×C4—62no—
373C2×C4—91no—
374C2×C4—92no—
375C2×C4—92no—
376C2×C4—91no—
377C2×C4—91no—
378C2×C4—124no—
379C2×C4—182no—
380C2×C4—182no—
381C2×C4—184no—
382C2×C4—362no—
383C2×C4—362no—
384C2×C4—364no—
385C2×C4C2×GO+(4,𝔽2)11yescharacteristic
386C2×C4C2×GO+(4,𝔽2)11yescharacteristic
387C2×C4C2×GO+(4,𝔽2)11yescharacteristic
388C8—94no—
389C8—182no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—124no—
397D3—44no—
398D3—64no—
399D3—64no—
400C22—64no—
401C22—92no—
402C22—92no—
403C22—92no—
404C22—122no—
405C22—122no—
406C22—368no—
407C22C22×GO+(4,𝔽2)11yescharacteristic
408C4—21no—
409C4—21no—
410C4—64no—
411C4—91no—
412C4—91no—
413C4—122no—
414C4—122no—
415C4—181no—
416C4—181no—
417C4C4×GO+(4,𝔽2)12yes—
418C3—21no—
419C3—21no—
420C2—94no—
421C2—124no—
422C2#1059650111yescharacteristic
423C2#1059650511yescharacteristic
424C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#3802C22
cosocleC2×C3⋊Dic3C24
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#440
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
3. C4×#3797C2semidirect
4. #10593723C2semidirect
5. #10593432C2semidirect
6. #10593431C2semidirect
7. #10593396C2semidirect
8. #10593375C2semidirect
16. #64227C4semidirect
21. C4×#627C22semidirect
30. #63838C22semidirect
31. #63777C22semidirect
32. #63777C22semidirect
33. #63743C22semidirect
34. #63740C22semidirect
55. #3797C2×C4semidirect
59. #3787C2×C4semidirect
60. #3775C2×C4semidirect
120. #627C22×C4semidirect
128. #622C22×C4semidirect
284. C3⋊D3#440semidirect
358. C32C2×#440semidirect

Maximal subgroups

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

subgroupindex
C2×#642272
C4×#38022
C4×#37972
#105937232
#105934322
#105934312
#105933962
#105933752
#105933652
C2×#4409