Finite Group Databasebeta

← #11787263

Subgroups — #11787263

Order 1152.

666 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C22×C4⋊#157C211yesmaximal, characteristic
2#10594925C211yesmaximal, characteristic
3C2×#63730C212yesmaximal, complemented
4#10591152C211yesmaximal, characteristic
5#10590049C212yesmaximal, complemented
6C23×#157—21no—
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3797C2211yescharacteristic
9C2×C4⋊#157—21no—
10C2×C4⋊#157—24no—
11C2×C4⋊#157C2212yes—
12C3×#924—21no—
13#63982C412yescomplemented
14#63974—21no—
15#63900C2211yescharacteristic
16#63883—21no—
17#63871—21no—
18#63865C412yescomplemented
19C2×#3710C2212yes—
20#63730—24no—
21C3×#830—21no—
22#63557—21no—
23D3×C22⋊Q8—61no—
24D3×C22⋊C8—61no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—24no—
27C22×#157—22no—
28C22×#157—42no—
29C22×#157—42no—
30C22×C32×C4D411yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3C2311yescharacteristic
38C2×C3×Dic6—21no—
39C2×#627C2×C412yescomplemented
40C2×#624—21no—
41C2×#624—21no—
42#3797—22no—
43#3797—22no—
44C4⋊#157—24no—
45C4⋊#157—22no—
46C4⋊#157D414yes—
47C3×#217—22no—
48C3×C4⋊Dic3—21no—
49C3×Dic3⋊C4—22no—
50C2×C3×C3⋊C8—22no—
51#3724C2×C412yescomplemented
52Dic3⋊Dic3—22no—
53#3722—22no—
54#3710—22no—
55#3710—22no—
56#1872—91nomaximal, Sylow
57C2×D3×Q8—61no—
58C22×C4×D3—61no—
59C22×C4×D3—61no—
60C3×C22⋊Q8—61no—
61#946—61no—
62#924—21no—
63C2×D3×C8—62no—
64#897—61no—
65#896—62no—
66D3×C4⋊C4—61no—
67D3×C4⋊C4—62no—
68D3×C22⋊C4—62no—
69#878—62no—
70C3×C22⋊C8—61no—
71#830—21no—
72(C2×D3)⋊C8—62no—
73C23×C32C22⋊C411yescharacteristic
74C22×C3⋊D3—21no—
75C22×C3⋊D3—21no—
76C22×C3⋊D3—21no—
77C22×C3⋊D3—21no—
78C22×C3⋊D3C22⋊C411yescharacteristic
79C22×C3⋊D3SD1612yes—
80C22×C3⋊D3Q1612yes—
81C22×C3⋊D3C2×D411yescharacteristic
82C2×#157—24no—
83C2×#157—48no—
84C2×#157—42no—
85C2×#157—42no—
86C2×C32×C4—22no—
87C2×C32×C4C22⋊C411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3C22⋊C411yescharacteristic
91C2×C3⋊Dic3C22×C411yescharacteristic
92C4×C3⋊D3—21no—
93C4×C3⋊D3—21no—
94C4×C3⋊D3—22no—
95C4×C3⋊D3—22no—
96C4×C3⋊D3C2×D412yes—
97C4×C3⋊D3#4112yes—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C3×Dic6—42no—
101#627—24no—
102#624—41no—
103#624—41no—
104#624—41no—
105#624—41no—
106C3×C3⋊C8—42no—
107C2×C22⋊Q8—91no—
108C22×C4⋊C4—91no—
109C2×#103—92no—
110C2×C22⋊C8—91no—
111#340—92no—
112C23×D3—61no—
113C23×D3—61no—
114C2×C3×Q8—61no—
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×Dic3—61no—
118C22×Dic3—61no—
119D3×Q8—122no—
120D3×Q8—122no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C4×D3—61no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×C4×D3—122no—
132C2×C4×D3—122no—
133C2×C4×D3—122no—
134C2×C4×D3—122no—
135C2×Dic6—21no—
136C2×Dic6—62no—
137C2×C3×C8—62no—
138C3×C4⋊C4—62no—
139C3×C4⋊C4—61no—
140C3×C22⋊C4—62no—
141#217—22no—
142(C2×D3)⋊C4—62no—
143(C2×D3)⋊C4—62no—
144C4⋊Dic3—21no—
145C4⋊Dic3—62no—
146Dic3⋊C4—22no—
147Dic3⋊C4—62no—
148Dic3⋊C4—62no—
149C2×C3⋊C8—22no—
150D3×C8—122no—
151D3×C8—122no—
152C22×C32—21no—
153C22×C32—21no—
154C22×C32#10312yescomplemented
155C22×C32C2×C22⋊C411yescharacteristic
156C2×C3⋊D3—21no—
157C2×C3⋊D3—21no—
158C2×C3⋊D3—22no—
159C2×C3⋊D3—22no—
160C2×C3⋊D3—22no—
161C2×C3⋊D3—22no—
162C2×C3⋊D3#10312yescomplemented
163C2×C3⋊D3#12011yescharacteristic
164C2×C3⋊D3#12311yescharacteristic
165C2×C3⋊D3C2×SD1611yescharacteristic
166C2×C3⋊D3C2×Q1611yescharacteristic
167C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
168C2×C3⋊D3#13711yescharacteristic
169#157—44no—
170C32×C4—21no—
171C32×C4#12112yes—
172C3⋊Dic3—21no—
173C3⋊Dic3C4×D412yes—
174C3×Dic3—42no—
175C3×Dic3—42no—
176C22×Q8—91no—
177C23×C4—91no—
178C23×C4—181no—
179C22×C8—92no—
180C22⋊Q8—61no—
181C22⋊Q8—92no—
182C22⋊Q8—92no—
183C22⋊Q8—181no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—92no—
186C2×C4⋊C4—181no—
187C2×C4⋊C4—184no—
188C2×C4⋊C4—181no—
189C2×C22⋊C4—181no—
190#103—184no—
191C22⋊C8—61no—
192C22⋊C8—181no—
193C23×C3—21no—
194C23×C3—21no—
195C22×D3—61no—
196C22×D3—61no—
197C22×D3—61no—
198C22×D3—61no—
199C22×D3—62no—
200C22×D3—62no—
201C22×D3—62no—
202C22×D3—62no—
203C22×D3—121no—
204C22×D3—121no—
205C22×D3—121no—
206C22×D3—121no—
207C22×D3—121no—
208C22×D3—121no—
209C22×D3—121no—
210C22×D3—121no—
211C3×Q8—122no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—42no—
217C2×C3×C4—42no—
218C2×C3×C4—62no—
219C2×C3×C4—62no—
220C2×Dic3—22no—
221C2×Dic3—22no—
222C2×Dic3—61no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—61no—
226C2×Dic3—122no—
227C2×Dic3—122no—
228C4×D3—62no—
229C4×D3—62no—
230C4×D3—62no—
231C4×D3—62no—
232C4×D3—122no—
233C4×D3—122no—
234C4×D3—122no—
235C4×D3—122no—
236C4×D3—121no—
237C4×D3—121no—
238C4×D3—121no—
239C4×D3—121no—
240C4×D3—122no—
241C4×D3—122no—
242C4×D3—122no—
243C4×D3—122no—
244Dic6—42no—
245Dic6—124no—
246C3×C8—122no—
247C3⋊C8—42no—
248C2×C32—22no—
249C2×C32#38611yescharacteristic
250C2×C32C2×#10311yescharacteristic
251C2×C32#41711yescharacteristic
252C3⋊D3—22no—
253C3⋊D3#45011yescharacteristic
254C3⋊D3#45111yescharacteristic
255C3⋊D3#48311yescharacteristic
256C3⋊D3#48411yescharacteristic
257C24—91no—
258C2×Q8—61no—
259C2×Q8—92no—
260C2×Q8—182no—
261C2×Q8—182no—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—182no—
268C22×C4—182no—
269C22×C4—181no—
270C22×C4—181no—
271C22×C4—182no—
272C22×C4—184no—
273C22×C4—362no—
274C22×C4—362no—
275C22×C4GO+(4,𝔽2)11yescharacteristic
276C2×C8—62no—
277C2×C8—182no—
278C2×C8—182no—
279C4⋊C4—61no—
280C4⋊C4—62no—
281C4⋊C4—92no—
282C4⋊C4—94no—
283C4⋊C4—182no—
284C4⋊C4—182no—
285C4⋊C4—184no—
286C22⋊C4—62no—
287C22⋊C4—182no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C2×D3—61no—
297C2×D3—61no—
298C2×D3—61no—
299C2×D3—61no—
300C2×D3—61no—
301C2×D3—61no—
302C2×D3—61no—
303C2×D3—61no—
304C2×D3—61no—
305C2×D3—61no—
306C2×D3—61no—
307C2×D3—61no—
308C2×D3—62no—
309C2×D3—62no—
310C2×D3—122no—
311C2×D3—122no—
312C2×D3—122no—
313C2×D3—122no—
314C2×D3—122no—
315C2×D3—122no—
316C2×D3—122no—
317C2×D3—122no—
318C2×D3—121no—
319C2×D3—121no—
320C2×D3—121no—
321C2×D3—121no—
322C3×C4—22no—
323C3×C4—22no—
324C3×C4—41no—
325C3×C4—41no—
326C3×C4—122no—
327C3×C4—122no—
328Dic3—42no—
329Dic3—42no—
330Dic3—62no—
331Dic3—62no—
332Dic3—121no—
333Dic3—121no—
334C32#187211yescharacteristic, complemented, Sylow
335C23—91no—
336C23—91no—
337C23—92no—
338C23—92no—
339C23—181no—
340C23—181no—
341C23—181no—
342C23—181no—
343C23D32⋊C411yescharacteristic
344Q8—122no—
345Q8—184no—
346C2×C4—22no—
347C2×C4—62no—
348C2×C4—62no—
349C2×C4—91no—
350C2×C4—92no—
351C2×C4—92no—
352C2×C4—91no—
353C2×C4—182no—
354C2×C4—181no—
355C2×C4—181no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4—184no—
359C2×C4—361no—
360C2×C4—361no—
361C2×C4—361no—
362C2×C4—361no—
363C2×C4—362no—
364C2×C4—362no—
365C2×C4—368no—
366C2×C4D32⋊C411yescharacteristic
367C2×C4C2×GO+(4,𝔽2)11yescharacteristic
368C8—122no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—42no—
376C2×C3—42no—
377D3—61no—
378D3—61no—
379D3—61no—
380D3—61no—
381D3—61no—
382D3—61no—
383D3—61no—
384D3—61no—
385D3—122no—
386D3—122no—
387C22—21no—
388C22—21no—
389C22—91no—
390C22—91no—
391C22—91no—
392C22—91no—
393C22—91no—
394C22—91no—
395C22—92no—
396C22—182no—
397C22—182no—
398C22—182no—
399C22—182no—
400C22—181no—
401C22—181no—
402C22#6373012yescomplemented
403C22C2×D32⋊C411yescharacteristic
404C4—21no—
405C4—92no—
406C4—122no—
407C4—122no—
408C4—181no—
409C4—364no—
410C4#6424212yes—
411C3—21no—
412C3—21no—
413C2—22no—
414C2—91no—
415C2—91no—
416C2—91no—
417C2—91no—
418C2—182no—
419C2#1059331911yescharacteristic
420C2C2×#6373011yescharacteristic
421C2#1059351511yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1872
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63730C2semidirect
5. #10590049C2semidirect
13. #63982C4semidirect
18. #63865C4semidirect
39. C2×#627C2×C4semidirect
51. #3724C2×C4semidirect
154. C22×C32#103semidirect
162. C2×C3⋊D3#103semidirect
334. C32#1872semidirect
402. C22#63730semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
#105949252
C2×#637302
#105911522
#105900492
#18729