Finite Group Databasebeta

← #11774688

Subgroups — #11774688

Order 1152.

845 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 845 conjugacy classes of subgroups — too many to draw. Only its 112 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×D4×C3⋊D3C211yesmaximal, characteristic
2C4×#3712C211yesmaximal, characteristic, complemented
3#10590260C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
5#10589082C212yesmaximal, complemented
6#68175—32nomaximal
7C2×D4×C3⋊D3C411yescharacteristic
8C22×C4×C3⋊D3—21no—
9C32×C4×D4C2211yescharacteristic
10D4×C3⋊Dic3C411yescharacteristic
11C4×#638—21no—
12#64102C411yescharacteristic
13C4⋊C4×C3⋊D3C411yescharacteristic
14#64090—21no—
15C22⋊C4×C3⋊D3—21no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C42×C3⋊D3C2211yescharacteristic
18C2×#3712—21no—
19C3×C4⋊(C3⋊C8)C2212yescomplemented
20C3×C4×C3⋊C8C2212yescomplemented
21#63557—21no—
22#63555—21no—
23#63555—21no—
24C4×D3×D4—32no—
25C4×D3×D4—61no—
26#4835—32no—
27C4×ΓL(1,𝔽25)—32no—
28C3×D4⋊C8—32no—
29D4⋊(C3⋊C8)D312yescomplemented
30#4483—32no—
31#4459—32no—
32C23×C3⋊D3—21no—
33C2×C32×D4C2×C411yescharacteristic
34C22×C32×C4—21no—
35C2×#638—21no—
36C22×C3⋊Dic3—21no—
37D4×C3⋊D3—22no—
38D4×C3⋊D3—22no—
39C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
40C2×C4×C3⋊D3—21no—
41C2×C4×C3⋊D3—21no—
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3—44no—
44C2×C4×C3⋊D3C2×C411yescharacteristic
45C2×C4×C3⋊D3D411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C32×C4⋊C4C2×C411yescharacteristic
48C32×C22⋊C4—21no—
49C32×C42C2311yescharacteristic
50#3757—21no—
51#3752—21no—
52#3752—21no—
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54#3750—21no—
55C4×C3⋊Dic3C2×C411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C2×C3×C3⋊C8—22no—
59C2×C3×C3⋊C8—22no—
60#3712—24no—
61#1490—91noSylow
62C2×D3×D4—32no—
63C2×D3×D4—61no—
64C22×C4×D3—62no—
65C22×C4×D3—62no—
66C3×C4×D4—21no—
67C3×C4×D4C2×D312yes—
68D4×Dic3—32no—
69D4×Dic3—61no—
70C4×#67—62no—
71C4×#67—62no—
72C2×ΓL(1,𝔽25)—62no—
73#893—32no—
74#893—61no—
75D3×C4⋊C4—32no—
76D3×C4⋊C4—61no—
77#67⋊C4—62no—
78#67⋊C4—62no—
79D3×C22⋊C4—62no—
80D3×C22⋊C4—62no—
81C4×D12—32no—
82C4×D12—61no—
83C42×D3—32no—
84C42×D3—61no—
85C3×C4⋊C8—32no—
86C3×C4×C8—32no—
87(C2×D3)⋊C8—62no—
88#815—62no—
89#815—62no—
90C4⋊(C3⋊C8)C2×D312yescomplemented
91C4×C3⋊C8C2×D312yescomplemented
92C23×C32—21no—
93C22×C3⋊D3—24no—
94C22×C3⋊D3—21no—
95C22×C3⋊D3—42no—
96C22×C3⋊D3—42no—
97C22×C3⋊D3C22⋊C411yescharacteristic
98C32×D4—21no—
99C32×D4M1612yescomplemented
100C2×C32×C4—21no—
101C2×C32×C4—42no—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105#638—24no—
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—42no—
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C2×C3⋊Dic3C22⋊C411yescharacteristic
110C2×C3⋊Dic3C22⋊C411yescharacteristic
111C4⋊(C3⋊D3)—21no—
112C4⋊(C3⋊D3)M1612yescomplemented
113C4×C3⋊D3—21no—
114C4×C3⋊D3—21no—
115C4×C3⋊D3—22no—
116C4×C3⋊D3—22no—
117C4×C3⋊D3—42no—
118C4×C3⋊D3—42no—
119C4×C3⋊D3—42no—
120C3×C3⋊C8—24no—
121C3×C3⋊C8—42no—
122C2×C4×D4—91no—
123#432—91no—
124C4×M16—91no—
125D4⋊C8—32no—
126D4⋊C8—92no—
127C23×D3—62no—
128C23×D3—62no—
129C2×C3×D4—21no—
130C2×C3×D4C4×D312yes—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C2×#67—62no—
134C2×#67—62no—
135C22×Dic3—62no—
136C22×Dic3—62no—
137D3×D4—64no—
138D3×D4—64no—
139D3×D4—64no—
140D3×D4—64no—
141C2×D12—32no—
142C2×D12—61no—
143C2×C4×D3—32no—
144C2×C4×D3—32no—
145C2×C4×D3—32no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—61no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—62no—
153C2×C4×D3—62no—
154C2×C4×D3—62no—
155C2×C4×D3—128no—
156C2×C4×D3—124no—
157C2×C4×D3—124no—
158C2×C3×C8—62no—
159C2×C3×C8—62no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4C4×D312yes—
162C3×C22⋊C4—22no—
163C3×C22⋊C4—22no—
164C3×C42—21no—
165C3×C42C22×D312yes—
166#217—62no—
167#217—62no—
168(C2×D3)⋊C4—62no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—62no—
171(C2×D3)⋊C4—62no—
172C4⋊Dic3—32no—
173C4⋊Dic3—61no—
174Dic3⋊C4—62no—
175Dic3⋊C4—62no—
176C4×Dic3—32no—
177C4×Dic3—32no—
178C4×Dic3—32no—
179C4×Dic3—61no—
180C4×Dic3—61no—
181C4×Dic3—61no—
182C2×C3⋊C8—22no—
183C2×C3⋊C8—22no—
184ΓL(1,𝔽25)—68no—
185C22×C32—22no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32C2×C22⋊C411yescharacteristic
189C2×C3⋊D3—21no—
190C2×C3⋊D3—21no—
191C2×C3⋊D3—22no—
192C2×C3⋊D3—48no—
193C2×C3⋊D3—41no—
194C2×C3⋊D3—41no—
195C2×C3⋊D3#10412yes—
196C32×C4—21no—
197C32×C4—41no—
198C32×C4C2×M1611yescharacteristic
199C32×C4C2×M1611yescharacteristic
200C32×C4AGL(1,ℤ/8)12yes—
201C3⋊Dic3—21no—
202C3⋊Dic3—21no—
203C3⋊Dic3—21no—
204C3⋊Dic3—41no—
205C22×D4—91no—
206C23×C4—181no—
207C2×M16—181no—
208C4×D4—91no—
209C4×D4—91no—
210C4×D4—91no—
211C4×D4—181no—
212C4×D4—181no—
213C4×D4D3211yescharacteristic
214C2×C4⋊C4—91no—
215C2×C22⋊C4—181no—
216C2×C42—91no—
217C4⋊C8—32no—
218C22⋊C8—181no—
219#97—181no—
220#97—181no—
221C4×C8—32no—
222C23×C3—22no—
223C23×C3—22no—
224C22×D3—32no—
225C22×D3—61no—
226C22×D3—62no—
227C22×D3—68no—
228C22×D3—68no—
229C22×D3—62no—
230C22×D3—124no—
231C22×D3—124no—
232C22×D3—124no—
233C22×D3—124no—
234C3×D4—22no—
235C3×D4—22no—
236C3×D4—22no—
237C3×D4ΓL(1,𝔽25)14yescomplemented
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—44no—
244C2×C3×C4—42no—
245C2×C3×C4—42no—
246C2×C3×C4C2×C4×D312yes—
247C2×C3×C4D3×D412yes—
248C2×C3×C4D3×D412yes—
249#67—68no—
250#67—68no—
251C2×Dic3—32no—
252C2×Dic3—32no—
253C2×Dic3—32no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259C2×Dic3—124no—
260C2×Dic3—124no—
261D12—34no—
262D12—62no—
263D12—62no—
264D12—62no—
265C4×D3—64no—
266C4×D3—64no—
267C4×D3—62no—
268C4×D3—62no—
269C4×D3—62no—
270C4×D3—62no—
271C4×D3—62no—
272C4×D3—62no—
273C4×D3—122no—
274C4×D3—124no—
275C4×D3—124no—
276C4×D3—124no—
277C4×D3—124no—
278C4×D3—124no—
279C4×D3—122no—
280C4×D3—122no—
281C3×C8—64no—
282C3×C8—122no—
283C3⋊C8—24no—
284C3⋊C8—42no—
285C2×C32—42no—
286C2×C32#40711yescharacteristic
287C2×C32#41811yescharacteristic
288C2×C32C2×#10411yescharacteristic
289C3⋊D3—22no—
290C3⋊D3—42no—
291C24—181no—
292C2×D4—91no—
293C2×D4—181no—
294C2×D4—182no—
295C2×D4—182no—
296C2×D4#62411yescharacteristic
297C22×C4—21no—
298C22×C4—91no—
299C22×C4—91no—
300C22×C4—91no—
301C22×C4—181no—
302C22×C4—181no—
303C22×C4—181no—
304C22×C4—181no—
305C22×C4—364no—
306M16—184no—
307C2×C8—62no—
308C2×C8—62no—
309C4⋊C4—91no—
310C4⋊C4—181no—
311C4⋊C4#62411yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—181no—
314C22⋊C4—181no—
315C22⋊C4—181no—
316C42—91no—
317C42—91no—
318C42—91no—
319C42C2×D3211yescharacteristic
320C22×C3—24no—
321C22×C3—24no—
322C22×C3—21no—
323C22×C3—42no—
324C22×C3—42no—
325C22×C3—42no—
326C22×C3—42no—
327C22×C3D3×C22⋊C412yes—
328C2×D3—34no—
329C2×D3—62no—
330C2×D3—62no—
331C2×D3—62no—
332C2×D3—62no—
333C2×D3—62no—
334C2×D3—64no—
335C2×D3—64no—
336C2×D3—1216no—
337C2×D3—1216no—
338C2×D3—122no—
339C2×D3—122no—
340C2×D3—122no—
341C2×D3—122no—
342C3×C4—22no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—22no—
346C3×C4—41no—
347C3×C4—42no—
348C3×C4—42no—
349C3×C4C2×ΓL(1,𝔽25)12yes—
350C3×C4D3×M1612yes—
351C3×C4#91112yes—
352C3×C4#91412yes—
353Dic3—62no—
354Dic3—62no—
355Dic3—62no—
356Dic3—62no—
357Dic3—62no—
358Dic3—121no—
359Dic3—122no—
360Dic3—122no—
361C32#149011yescharacteristic, complemented, Sylow
362C23—21no—
363C23—91no—
364C23—184no—
365C23—181no—
366C23—362no—
367C23—362no—
368D4—21no—
369D4—92no—
370D4—184no—
371D4—181no—
372D4#371212yescomplemented
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—91no—
376C2×C4—91no—
377C2×C4—91no—
378C2×C4—182no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—182no—
382C2×C4—181no—
383C2×C4—362no—
384C2×C4—362no—
385C2×C4—362no—
386C2×C4—362no—
387C2×C4C2×#62411yescharacteristic
388C2×C4#381111yescharacteristic
389C2×C4#381111yescharacteristic
390C8—64no—
391C8—122no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—44no—
396C2×C3—44no—
397C2×C3#472612yes—
398C2×C3#477012yes—
399C2×C3D3×#10412yes—
400D3—64no—
401D3—64no—
402D3—124no—
403D3—124no—
404C22—22no—
405C22—41no—
406C22—41no—
407C22—92no—
408C22—181no—
409C22—181no—
410C22—182no—
411C22—368no—
412C22—361no—
413C22—361no—
414C22#6397411yescharacteristic
415C4—21no—
416C4—41no—
417C4—181no—
418C4—181no—
419C4—181no—
420C4—361no—
421C4#6381811yescharacteristic
422C4C2×#371211yescharacteristic
423C4#6393712yes—
424C3—21no—
425C3#6817512yescomplemented
426C2—42no—
427C2—182no—
428C2—362no—
429C2#1059115911yescharacteristic
430C2#1059142611yescharacteristic
431C2#1059167111yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×D4×C3⋊D3C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×#3712C2semidirect
3. #10590260C2semidirect
4. C3×D4⋊(C3⋊C8)C2semidirect
5. #10589082C2semidirect
19. C3×C4⋊(C3⋊C8)C22semidirect
20. C3×C4×C3⋊C8C22semidirect
29. D4⋊(C3⋊C8)D3semidirect
90. C4⋊(C3⋊C8)C2×D3semidirect
91. C4×C3⋊C8C2×D3semidirect
99. C32×D4M16semidirect
112. C4⋊(C3⋊D3)M16semidirect
237. C3×D4ΓL(1,𝔽25)semidirect
361. C32#1490semidirect
372. D4#3712semidirect
425. C3#68175semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
C4×#37122
#105902602
C3×D4⋊(C3⋊C8)2
#105890822
#681753