Finite Group Databasebeta

← #11774558

Subgroups — #11774558

Order 1152.

837 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 837 conjugacy classes of subgroups — too many to draw. Only its 118 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
2#10590340C211yesmaximal, characteristic, complemented
3#10590297C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
5#10589082C212yesmaximal, complemented
6#68172—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#63572—21no—
22#63572—21no—
23#63557—21no—
24C4×D3×D4—32no—
25C4×D3×D4—61no—
26#4837—32no—
27#4685—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—42no—
44C2×C4×C3⋊D3—42no—
45C2×C4×C3⋊D3C2×C411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C4×C3⋊D3D411yescharacteristic
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2311yescharacteristic
51#3757—21no—
52#3752—21no—
53#3752—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—21no—
56C4×C3⋊Dic3C2×C411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59C2×C3×C3⋊C8—22no—
60C2×C3×C3⋊C8—22no—
61#3712—42no—
62#1486—91noSylow
63C2×D3×D4—32no—
64C2×D3×D4—61no—
65C22×C4×D3—62no—
66C22×C4×D3—62no—
67C3×C4×D4—21no—
68C3×C4×D4C2×D312yes—
69D4×Dic3—32no—
70D4×Dic3—61no—
71C4×#67—62no—
72C4×#67—62no—
73C2×ΓL(1,𝔽25)—62no—
74#893—32no—
75#893—61no—
76D3×C4⋊C4—32no—
77D3×C4⋊C4—61no—
78#67⋊C4—62no—
79#67⋊C4—62no—
80D3×C22⋊C4—62no—
81D3×C22⋊C4—62no—
82C4×D12—32no—
83C4×D12—61no—
84C42×D3—32no—
85C42×D3—61no—
86C3×C4⋊C8—32no—
87C3×C4×C8—32no—
88(C2×D3)⋊C8—62no—
89Dic3⋊C8—62no—
90Dic3⋊C8—62no—
91C4⋊(C3⋊C8)C2×D312yescomplemented
92C4×C3⋊C8C2×D312yescomplemented
93C23×C32—21no—
94C22×C3⋊D3—24no—
95C22×C3⋊D3—21no—
96C22×C3⋊D3—42no—
97C22×C3⋊D3—42no—
98C22×C3⋊D3C22⋊C411yescharacteristic
99C32×D4—21no—
100C32×D4M1612yescomplemented
101C2×C32×C4—21no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107#638—24no—
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3—42no—
110C2×C3⋊Dic3C22⋊C411yescharacteristic
111C2×C3⋊Dic3C22⋊C411yescharacteristic
112C2×C3⋊Dic3C22⋊C411yescharacteristic
113C4⋊(C3⋊D3)—21no—
114C4⋊(C3⋊D3)M1612yescomplemented
115C4×C3⋊D3—21no—
116C4×C3⋊D3—21no—
117C4×C3⋊D3—41no—
118C4×C3⋊D3—42no—
119C4×C3⋊D3—41no—
120C4×C3⋊D3—41no—
121C4×C3⋊D3—42no—
122C4×C3⋊D3D812yes—
123C4×C3⋊D3SD1612yes—
124C3×C3⋊C8—42no—
125C3×C3⋊C8—42no—
126C2×C4×D4—91no—
127#431—91no—
128#423—91no—
129D4⋊C8—32no—
130D4⋊C8—92no—
131C23×D3—62no—
132C23×D3—62no—
133C2×C3×D4—21no—
134C2×C3×D4C4×D312yes—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C2×#67—62no—
138C2×#67—62no—
139C22×Dic3—62no—
140C22×Dic3—62no—
141D3×D4—64no—
142D3×D4—64no—
143D3×D4—64no—
144D3×D4—64no—
145C2×D12—32no—
146C2×D12—61no—
147C2×C4×D3—32no—
148C2×C4×D3—32no—
149C2×C4×D3—32no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—62no—
154C2×C4×D3—62no—
155C2×C4×D3—62no—
156C2×C4×D3—62no—
157C2×C4×D3—62no—
158C2×C4×D3—62no—
159C2×C4×D3—124no—
160C2×C4×D3—124no—
161C2×C4×D3—124no—
162C2×C4×D3—124no—
163C2×C3×C8—62no—
164C2×C3×C8—62no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4C4×D312yes—
167C3×C22⋊C4—22no—
168C3×C22⋊C4—22no—
169C3×C42—21no—
170C3×C42C22×D312yes—
171#217—62no—
172#217—62no—
173(C2×D3)⋊C4—62no—
174(C2×D3)⋊C4—62no—
175(C2×D3)⋊C4—62no—
176(C2×D3)⋊C4—62no—
177C4⋊Dic3—32no—
178C4⋊Dic3—61no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181C4×Dic3—32no—
182C4×Dic3—32no—
183C4×Dic3—32no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C2×C3⋊C8—22no—
188C2×C3⋊C8—22no—
189ΓL(1,𝔽25)—124no—
190C22×C32—22no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32C2×C22⋊C411yescharacteristic
194C2×C3⋊D3—21no—
195C2×C3⋊D3—21no—
196C2×C3⋊D3—22no—
197C2×C3⋊D3—48no—
198C2×C3⋊D3—41no—
199C2×C3⋊D3—41no—
200C2×C3⋊D3#10212yes—
201C32×C4—21no—
202C32×C4—41no—
203C32×C4C2×M1611yescharacteristic
204C32×C4C2×M1611yescharacteristic
205C32×C4C2×D811yescharacteristic
206C32×C4C2×SD1611yescharacteristic
207C3⋊Dic3—21no—
208C3⋊Dic3—21no—
209C3⋊Dic3—41no—
210C3⋊Dic3#10212yes—
211C22×D4—91no—
212C23×C4—181no—
213C2×M16—181no—
214C4×D4—91no—
215C4×D4—91no—
216C4×D4—91no—
217C4×D4—181no—
218C4×D4—181no—
219C4×D4D3211yescharacteristic
220C2×C4⋊C4—91no—
221C2×C22⋊C4—181no—
222C2×C42—91no—
223C4⋊C8—32no—
224C4⋊C8—181no—
225C4⋊C8—181no—
226C22⋊C8—181no—
227C4×C8—32no—
228C23×C3—22no—
229C23×C3—22no—
230C22×D3—32no—
231C22×D3—61no—
232C22×D3—62no—
233C22×D3—68no—
234C22×D3—68no—
235C22×D3—62no—
236C22×D3—124no—
237C22×D3—124no—
238C22×D3—124no—
239C22×D3—124no—
240C3×D4—22no—
241C3×D4—22no—
242C3×D4—22no—
243C3×D4ΓL(1,𝔽25)14yescomplemented
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—42no—
252C2×C3×C4—42no—
253C2×C3×C4C2×C4×D312yes—
254C2×C3×C4D3×D412yes—
255C2×C3×C4D3×D412yes—
256#67—68no—
257#67—68no—
258C2×Dic3—32no—
259C2×Dic3—32no—
260C2×Dic3—32no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—124no—
267C2×Dic3—124no—
268D12—34no—
269D12—62no—
270D12—62no—
271D12—62no—
272C4×D3—34no—
273C4×D3—34no—
274C4×D3—62no—
275C4×D3—62no—
276C4×D3—62no—
277C4×D3—62no—
278C4×D3—62no—
279C4×D3—62no—
280C4×D3—124no—
281C4×D3—122no—
282C4×D3—124no—
283C4×D3—122no—
284C4×D3—122no—
285C4×D3—124no—
286C4×D3—122no—
287C4×D3—124no—
288C4×D3—122no—
289C4×D3—122no—
290C3×C8—122no—
291C3×C8—122no—
292C3⋊C8—42no—
293C3⋊C8—42no—
294C2×C32—42no—
295C2×C32#40711yescharacteristic
296C2×C32C2×#10211yescharacteristic
297C2×C32#42111yescharacteristic
298C3⋊D3—22no—
299C3⋊D3—42no—
300C24—181no—
301C2×D4—91no—
302C2×D4—181no—
303C2×D4—182no—
304C2×D4—182no—
305C2×D4#62411yescharacteristic
306C22×C4—21no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—181no—
311C22×C4—181no—
312C22×C4—181no—
313C22×C4—181no—
314C22×C4—362no—
315C22×C4—362no—
316M16—362no—
317C2×C8—62no—
318C2×C8—62no—
319C4⋊C4—91no—
320C4⋊C4—181no—
321C4⋊C4#62411yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—181no—
324C22⋊C4—181no—
325C22⋊C4—181no—
326C42—91no—
327C42—91no—
328C42—91no—
329C42C2×D3211yescharacteristic
330C22×C3—24no—
331C22×C3—24no—
332C22×C3—21no—
333C22×C3—42no—
334C22×C3—42no—
335C22×C3—42no—
336C22×C3—42no—
337C22×C3D3×C22⋊C412yes—
338C2×D3—34no—
339C2×D3—62no—
340C2×D3—62no—
341C2×D3—62no—
342C2×D3—62no—
343C2×D3—62no—
344C2×D3—64no—
345C2×D3—64no—
346C2×D3—1216no—
347C2×D3—1216no—
348C2×D3—122no—
349C2×D3—122no—
350C2×D3—122no—
351C2×D3—122no—
352C3×C4—22no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—41no—
358C3×C4—42no—
359C3×C4—42no—
360C3×C4C2×ΓL(1,𝔽25)12yes—
361C3×C4D3×M1612yes—
362C3×C4D3×D812yes—
363C3×C4D3×SD1612yes—
364Dic3—34no—
365Dic3—62no—
366Dic3—62no—
367Dic3—62no—
368Dic3—62no—
369Dic3—121no—
370Dic3—122no—
371Dic3—122no—
372C32#148611yescharacteristic, complemented, Sylow
373C23—21no—
374C23—91no—
375C23—184no—
376C23—181no—
377C23—362no—
378C23—362no—
379D4—21no—
380D4—92no—
381D4—184no—
382D4—181no—
383D4#371212yescomplemented
384C2×C4—21no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—91no—
388C2×C4—92no—
389C2×C4—92no—
390C2×C4—91no—
391C2×C4—91no—
392C2×C4—181no—
393C2×C4—181no—
394C2×C4—181no—
395C2×C4—361no—
396C2×C4—362no—
397C2×C4—362no—
398C2×C4—362no—
399C2×C4—361no—
400C2×C4—361no—
401C2×C4C2×#62411yescharacteristic
402C2×C4#381111yescharacteristic
403C2×C4#381111yescharacteristic
404C8—122no—
405C8—122no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—44no—
410C2×C3—44no—
411C2×C3#472612yes—
412C2×C3D3×#10212yes—
413C2×C3#482112yes—
414D3—64no—
415D3—64no—
416D3—124no—
417D3—124no—
418C22—22no—
419C22—41no—
420C22—41no—
421C22—92no—
422C22—181no—
423C22—181no—
424C22—182no—
425C22—368no—
426C22—361no—
427C22—361no—
428C22#6397411yescharacteristic
429C4—21no—
430C4—41no—
431C4—92no—
432C4—181no—
433C4—181no—
434C4—361no—
435C4#6381811yescharacteristic
436C4C2×#371211yescharacteristic
437C4#6392611yescharacteristic
438C4#6393011yescharacteristic
439C3—21no—
440C3#6817212yescomplemented
441C2—42no—
442C2—182no—
443C2—362no—
444C2#1059115911yescharacteristic
445C2#1059141611yescharacteristic
446C2#1059167211yescharacteristic
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#1486
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. #10590340C2semidirect
3. #10590297C2semidirect
4. C3×D4⋊(C3⋊C8)C2semidirect
5. #10589082C2semidirect
19. C3×C4⋊(C3⋊C8)C22semidirect
20. C3×C4×C3⋊C8C22semidirect
29. D4⋊(C3⋊C8)D3semidirect
91. C4⋊(C3⋊C8)C2×D3semidirect
92. C4×C3⋊C8C2×D3semidirect
100. C32×D4M16semidirect
114. C4⋊(C3⋊D3)M16semidirect
243. C3×D4ΓL(1,𝔽25)semidirect
372. C32#1486semidirect
383. D4#3712semidirect
440. C3#68172semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
#105903402
#105902972
C3×D4⋊(C3⋊C8)2
#105890822
#681723