Finite Group Databasebeta

← #11775585

Subgroups — #11775585

Order 1152.

781 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 781 conjugacy classes of subgroups — too many to draw. Only its 100 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
1#10595081C211yesmaximal, characteristic
2C3⋊D3×C22⋊C8C211yesmaximal, characteristic, complemented
3#10591355C211yesmaximal, characteristic, complemented
4C3×#4470C212yesmaximal, complemented
5#10589149C212yesmaximal, complemented
6#68307—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3811—21no—
9C2×#3802C411yescharacteristic, complemented
10C2×C8×C3⋊D3—21no—
11C3×#930C2212yes—
12#63980—21no—
13C2×#3724—21no—
14C2×#3722—21no—
15#63921—21no—
16#63916C412yescomplemented
17#63912—21no—
18#63900C411yescharacteristic, complemented
19C32×C22⋊C8C2211yescharacteristic, complemented
20#63657C2211yescharacteristic, complemented
21#63647—21no—
22C3×C3⋊#95C2212yescomplemented
23D3×#121—32no—
24D3×C22⋊C8—32no—
25D3×C22⋊C8—61no—
26#4667—32no—
27C3×#327—32no—
28#4537—32no—
29#4470D312yescomplemented
30#4451—32no—
31C23×C3⋊D3D411yescharacteristic
32C22×D32—21no—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C2×C4×C3⋊D3—42no—
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C3×#67—22no—
41C22×C3×Dic3—22no—
42C2×C3×D12C2×C412yes—
43#3811—42no—
44#3811—42no—
45C2×#626—22no—
46C2×#625—21no—
47C2×#624—21no—
48#3802—42no—
49C2×C32×C8—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C8×C3⋊D3—42no—
52C3×(C2×D3)⋊C4—22no—
53C3×C4⋊Dic3C2×C412yes—
54#3724—21no—
55#3724—42no—
56#3722—42no—
57(C2×D3)⋊Dic3—22no—
58#1519—91noSylow
59C2×D3×D4—32no—
60C2×D3×D4—62no—
61C22×C4×D3—32no—
62C22×C4×D3—61no—
63C3×#121—32no—
64#939—62no—
65#938—32no—
66#930C2×D312yes—
67C2×(C2×D3)⋊C4—62no—
68C2×Dic3⋊C4—62no—
69C2×D3×C8—62no—
70C2×D3×C8—62no—
71#895—32no—
72D3×C4⋊C4—32no—
73#884—62no—
74D3×C22⋊C4—62no—
75C3×C22⋊C8—21no—
76C3×C22⋊C8C2×D312yescomplemented
77C3×#95—32no—
78C3⋊#95C2×D312yescomplemented
79#830—32no—
80#830—61no—
81(C2×D3)⋊C8—62no—
82(C2×D3)⋊C8—62no—
83C23×C32C2×D411yescharacteristic
84C22×C3⋊D3—41no—
85C22×C3⋊D3—41no—
86C22×C3⋊D3C22⋊C411yescharacteristic
87C22×C3⋊D3C22⋊C411yescharacteristic
88C22×C3⋊D3D812yes—
89C22×C3⋊D3SD1612yes—
90C22×C3×D3—22no—
91C2×D32—42no—
92C2×D32—42no—
93C2×D32—42no—
94C2×C32×C4—41no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3C22⋊C411yescharacteristic
99C2×C3⋊Dic3C22⋊C411yescharacteristic
100C4×C3⋊D3—22no—
101C4×C3⋊D3—22no—
102C4×C3⋊D3—41no—
103C4×C3⋊D3—41no—
104C3×#67—42no—
105C3×#67—42no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—42no—
108C2×C3×Dic3—42no—
109C2×C3×Dic3—42no—
110C3×D12—42no—
111#626—44no—
112#625—42no—
113#624—42no—
114C32×C8—41no—
115C3⋊(C3⋊C8)—41no—
116C2×#121—91no—
117C2×C22⋊C8—91no—
118#380—91no—
119#327—32no—
120#327—92no—
121C23×D3—32no—
122C23×D3—61no—
123C23×D3—62no—
124C2×C3×D4—32no—
125C2×C3×D4—62no—
126C22×C3×C4—21no—
127C22×C3×C4—62no—
128C22×C3×C4C22×D312yes—
129C2×#67—22no—
130C2×#67—62no—
131C2×#67—62no—
132C22×Dic3—22no—
133C22×Dic3—32no—
134C22×Dic3—61no—
135D3×D4—124no—
136D3×D4—124no—
137D3×D4—124no—
138C2×D12—62no—
139C2×D12C4×D312yes—
140C2×C4×D3—32no—
141C2×C4×D3—32no—
142C2×C4×D3—32no—
143C2×C4×D3—32no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—62no—
149C2×C4×D3—124no—
150C2×C4×D3—124no—
151C2×C3×C8—22no—
152C2×C3×C8—22no—
153C3×C4⋊C4—32no—
154C3×C22⋊C4—62no—
155#217—62no—
156(C2×D3)⋊C4—22no—
157(C2×D3)⋊C4—62no—
158(C2×D3)⋊C4—124no—
159C4⋊Dic3C4×D312yes—
160Dic3⋊C4—62no—
161Dic3⋊C4—124no—
162C2×C3⋊C8—62no—
163C2×C3⋊C8—62no—
164D3×C8—124no—
165D3×C8—124no—
166C22×C32—21no—
167C22×C32—21no—
168C22×C32C2×C22⋊C411yescharacteristic
169C22×C32C2×D811yescharacteristic
170C22×C32C2×SD1611yescharacteristic
171C2×C3⋊D3—21no—
172C2×C3⋊D3—21no—
173C2×C3⋊D3—21no—
174C2×C3⋊D3—21no—
175C2×C3⋊D3—42no—
176C2×C3⋊D3—42no—
177C2×C3⋊D3#10212yes—
178C2×C3⋊D3#10212yes—
179C2×C3×D3—42no—
180C2×C3×D3—42no—
181C2×C3×D3—42no—
182D32—84no—
183C32×C4—21no—
184C32×C4—21no—
185C3⋊Dic3—21no—
186C3⋊Dic3#9912yes—
187C3×Dic3—42no—
188C3×Dic3—82no—
189C22×D4—91no—
190C22×D4—181no—
191C23×C4—91no—
192C22×C8—181no—
193#121—32no—
194#121—92no—
195#121—181no—
196#121—181no—
197C2×C4⋊C4—91no—
198C2×C4⋊C4—181no—
199C2×C22⋊C4—181no—
200C2×C22⋊C4—181no—
201C22⋊C8—91no—
202C22⋊C8—181no—
203C22⋊C8D3211yescharacteristic, complemented
204#95—32no—
205C23×C3—21no—
206C23×C3—62no—
207C23×C3D3×D412yes—
208C22×D3—22no—
209C22×D3—32no—
210C22×D3—32no—
211C22×D3—34no—
212C22×D3—34no—
213C22×D3—61no—
214C22×D3—61no—
215C22×D3—62no—
216C22×D3—62no—
217C22×D3—124no—
218C22×D3—124no—
219C22×D3—124no—
220C22×D3—122no—
221C22×D3—122no—
222C22×D3—122no—
223C22×D3—122no—
224C3×D4—122no—
225C3×D4—122no—
226C3×D4—122no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—42no—
230C2×C3×C4—42no—
231C2×C3×C4—62no—
232C2×C3×C4—122no—
233C2×C3×C4—122no—
234C2×C3×C4—122no—
235C2×C3×C4C2×C4×D312yes—
236C2×C3×C4D3×D412yes—
237#67—42no—
238#67—42no—
239#67—124no—
240#67—124no—
241C2×Dic3—22no—
242C2×Dic3—32no—
243C2×Dic3—32no—
244C2×Dic3—42no—
245C2×Dic3—42no—
246C2×Dic3—42no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—64no—
250C2×Dic3—122no—
251D12—42no—
252D12—124no—
253C4×D3—64no—
254C4×D3—64no—
255C4×D3—64no—
256C4×D3—122no—
257C4×D3—124no—
258C4×D3—122no—
259C4×D3—122no—
260C4×D3—122no—
261C4×D3—122no—
262C3×C8—42no—
263C3×C8—42no—
264C3⋊C8—122no—
265C3⋊C8—122no—
266C2×C32—21no—
267C2×C32—21no—
268C2×C32C2×#9911yescharacteristic
269C2×C32C2×#10211yescharacteristic
270C2×C32#42111yescharacteristic
271C3⋊D3—22no—
272C3⋊D3—22no—
273C3×D3—82no—
274C24—91no—
275C24—181no—
276C2×D4—32no—
277C2×D4—62no—
278C2×D4—182no—
279C2×D4—181no—
280C2×D4—362no—
281C2×D4—362no—
282C2×D4—362no—
283C22×C4—62no—
284C22×C4—91no—
285C22×C4—91no—
286C22×C4—91no—
287C22×C4—91no—
288C22×C4—91no—
289C22×C4—181no—
290C22×C4—362no—
291C22×C4C2×D3211yescharacteristic
292C2×C8—21no—
293C2×C8—181no—
294C2×C8—362no—
295C4⋊C4—32no—
296C4⋊C4—181no—
297C4⋊C4—362no—
298C22⋊C4—62no—
299C22⋊C4—182no—
300C22⋊C4—362no—
301C22×C3—22no—
302C22×C3—22no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3—122no—
309C22×C3—122no—
310C22×C3—122no—
311C22×C3D3×C22⋊C412yes—
312C22×C3D3×D812yes—
313C22×C3D3×SD1612yes—
314C2×D3—34no—
315C2×D3—34no—
316C2×D3—42no—
317C2×D3—42no—
318C2×D3—42no—
319C2×D3—62no—
320C2×D3—62no—
321C2×D3—62no—
322C2×D3—62no—
323C2×D3—62no—
324C2×D3—62no—
325C2×D3—62no—
326C2×D3—62no—
327C2×D3—121no—
328C2×D3—121no—
329C2×D3—124no—
330C2×D3—124no—
331C2×D3—124no—
332C2×D3—124no—
333C2×D3—248no—
334C3×C4—22no—
335C3×C4—22no—
336C3×C4—22no—
337C3×C4—41no—
338C3×C4—122no—
339C3×C4—242no—
340Dic3—34no—
341Dic3—42no—
342Dic3—62no—
343Dic3—62no—
344Dic3—82no—
345Dic3—121no—
346C32#151911yescharacteristic, complemented, Sylow
347C23—62no—
348C23—91no—
349C23—91no—
350C23—92no—
351C23—92no—
352C23—361no—
353C23—361no—
354C23—362no—
355C23—362no—
356C23—362no—
357C23#380211yescharacteristic
358D4—122no—
359D4—122no—
360D4—122no—
361D4—362no—
362D4—364no—
363C2×C4—41no—
364C2×C4—62no—
365C2×C4—91no—
366C2×C4—91no—
367C2×C4—122no—
368C2×C4—122no—
369C2×C4—122no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4—361no—
374C2×C4—361no—
375C2×C4—362no—
376C2×C4C4×D3211yescharacteristic
377C2×C4#381111yescharacteristic
378C8—41no—
379C8—361no—
380C2×C3—22no—
381C2×C3—22no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—41no—
386C2×C3—41no—
387C2×C3—242no—
388C2×C3D3×#9912yes—
389C2×C3D3×#10212yes—
390C2×C3#482112yes—
391D3—64no—
392D3—64no—
393D3—64no—
394D3—82no—
395D3—122no—
396C22—21no—
397C22—21no—
398C22—92no—
399C22—92no—
400C22—122no—
401C22—122no—
402C22—122no—
403C22—181no—
404C22—181no—
405C22—181no—
406C22—181no—
407C22—362no—
408C22—362no—
409C22—724no—
410C22#6379611yescharacteristic
411C22#6379711yescharacteristic
412C22#6392111yescharacteristic
413C4—21no—
414C4—21no—
415C4—92no—
416C4—122no—
417C4—181no—
418C4—242no—
419C3—21no—
420C3#6830712yescomplemented
421C2—21no—
422C2—21no—
423C2—182no—
424C2—182no—
425C2—242no—
426C2#1059040411yescharacteristic
427C2#1059094011yescharacteristic
428C2#1059100911yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10595081C2
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1519
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×C22⋊C8C2semidirect
3. #10591355C2semidirect
4. C3×#4470C2semidirect
5. #10589149C2semidirect
9. C2×#3802C4semidirect
16. #63916C4semidirect
18. #63900C4semidirect
19. C32×C22⋊C8C22semidirect
20. #63657C22semidirect
22. C3×C3⋊#95C22semidirect
29. #4470D3semidirect
76. C3×C22⋊C8C2×D3semidirect
78. C3⋊#95C2×D3semidirect
203. C22⋊C8D32semidirect
346. C32#1519semidirect
420. C3#68307semidirect

Maximal subgroups

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

subgroupindex
#105950812
C3⋊D3×C22⋊C82
#105913552
C3×#44702
#105891492
#683073