Finite Group Databasebeta

← #11788355

Subgroups — #11788355

Order 1152.

648 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 71 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#10594925C211yesmaximal, characteristic
2C22×#3712C211yesmaximal, characteristic
3#10593803C211yesmaximal, characteristic
4C2×#63728C212yesmaximal, complemented
5#10590052C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×#3797C2211yescharacteristic
8C2×#3788C2212yes—
9C3×#924—21no—
10C22×C3×C3⋊C8—21no—
11#63982—21no—
12#63974C412yes—
13#63900C2211yescharacteristic
14#63883C412yes—
15#63871—21no—
16#63865—21no—
17C2×#3712—21no—
18C2×#3712—24no—
19C2×#3712C2212yes—
20C22⋊#622—21no—
21#63778—21no—
22#63728—24no—
23C22×ΓL(1,𝔽25)—61no—
24D3×C22⋊Q8—61no—
25C23×C3⋊D3C2×C411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C2×C4×C3⋊D3—22no—
29C2×C4×C3⋊D3—22no—
30C2×C4×C3⋊D3C2×C411yescharacteristic
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3C2311yescharacteristic
34C2×C3×Dic6—21no—
35C2×#627—21no—
36C2×#624C2×C412yes—
37C2×#624C2×C412yes—
38#3797—22no—
39#3797—22no—
40C2×#622—22no—
41#3788—22no—
42#3788—22no—
43C3×#217—22no—
44C3×C4⋊Dic3—21no—
45C3×Dic3⋊C4—22no—
46C2×C3×C3⋊C8—24no—
47C2×C3×C3⋊C8—22no—
48#3724—21no—
49Dic3⋊Dic3—22no—
50#3722—22no—
51#3712—24no—
52#3712—22no—
53#3712D414yes—
54#1901—91nomaximal, Sylow
55C2×D3×Q8—61no—
56C22×C4×D3—61no—
57C22×C4×D3—61no—
58C22×C3×C8—61no—
59C3×C22⋊Q8—61no—
60#946—61no—
61#924—21no—
62C22×C3⋊C8—21no—
63C2×ΓL(1,𝔽25)—62no—
64C2×ΓL(1,𝔽25)—68no—
65C2×ΓL(1,𝔽25)—62no—
66#897—61no—
67#896—62no—
68D3×C4⋊C4—62no—
69D3×C4⋊C4—61no—
70D3×C22⋊C4—62no—
71#878—62no—
72C23×C32C22⋊C411yescharacteristic
73C22×C3⋊D3—22no—
74C22×C3⋊D3—22no—
75C22×C3⋊D3—41no—
76C22×C3⋊D3C22⋊C411yescharacteristic
77C22×C3⋊D3C22×C411yescharacteristic
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C4×C3⋊D3—22no—
86C4×C3⋊D3—21no—
87C4×C3⋊D3—21no—
88C4×C3⋊D3—22no—
89C4×C3⋊D3C2×D412yes—
90C4×C3⋊D3#4112yes—
91C2×C3×Dic3—22no—
92C2×C3×Dic3—22no—
93C3×Dic6—41no—
94C3×Dic6—41no—
95#627—42no—
96#624—24no—
97#624—42no—
98#622—42no—
99C3×C3⋊C8—24no—
100C22×M16—91no—
101C2×C22⋊Q8—91no—
102C2×#101—92no—
103#407—91no—
104#343—92no—
105C23×D3—61no—
106C23×D3—61no—
107C2×C3×Q8—61no—
108C22×C3×C4—21no—
109C22×C3×C4—21no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112D3×Q8—122no—
113D3×Q8—122no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—64no—
125C2×C4×D3—64no—
126C2×C4×D3—122no—
127C2×C4×D3—122no—
128C2×Dic6—21no—
129C2×Dic6—62no—
130C2×C3×C8—64no—
131C2×C3×C8—62no—
132C3×C4⋊C4—62no—
133C3×C4⋊C4—61no—
134C3×C22⋊C4—62no—
135#217—22no—
136(C2×D3)⋊C4—62no—
137(C2×D3)⋊C4—62no—
138C4⋊Dic3—21no—
139C4⋊Dic3—62no—
140Dic3⋊C4—22no—
141Dic3⋊C4—62no—
142Dic3⋊C4—62no—
143C2×C3⋊C8—24no—
144C2×C3⋊C8—22no—
145ΓL(1,𝔽25)—64no—
146ΓL(1,𝔽25)—64no—
147ΓL(1,𝔽25)—68no—
148C22×C32—21no—
149C22×C32—21no—
150C22×C32#10112yescomplemented
151C22×C32C2×C22⋊C411yescharacteristic
152C2×C3⋊D3—21no—
153C2×C3⋊D3—21no—
154C2×C3⋊D3—21no—
155C2×C3⋊D3—21no—
156C2×C3⋊D3—21no—
157C2×C3⋊D3—44no—
158C2×C3⋊D3C4×D412yes—
159C32×C4—21no—
160C32×C4#12011yescharacteristic
161C32×C4#12311yescharacteristic
162C3⋊Dic3—21no—
163C3⋊Dic3#12112yes—
164C3×Dic3—42no—
165C3×Dic3—42no—
166C22×Q8—91no—
167C23×C4—91no—
168C2×M16—92no—
169C2×M16—92no—
170C2×M16—184no—
171C2×M16—181no—
172C22×C8—61no—
173C22⋊Q8—61no—
174C22⋊Q8—181no—
175C22⋊Q8—181no—
176C22⋊Q8—181no—
177C2×C4⋊C4—91no—
178C2×C4⋊C4—92no—
179C2×C22⋊C4—92no—
180#101—184no—
181C22⋊C8—181no—
182C22⋊C8—181no—
183C23×C3—21no—
184C23×C3—21no—
185C22×D3—61no—
186C22×D3—61no—
187C22×D3—61no—
188C22×D3—61no—
189C22×D3—64no—
190C22×D3—64no—
191C22×D3—122no—
192C22×D3—122no—
193C22×D3—122no—
194C22×D3—122no—
195C3×Q8—121no—
196C3×Q8—121no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—41no—
204C2×C3×C4—41no—
205C2×C3×C4—62no—
206C2×C3×C4—62no—
207C2×Dic3—22no—
208C2×Dic3—22no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—64no—
214C2×Dic3—122no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—62no—
218C4×D3—62no—
219C4×D3—62no—
220C4×D3—64no—
221C4×D3—64no—
222C4×D3—62no—
223C4×D3—124no—
224C4×D3—122no—
225C4×D3—121no—
226C4×D3—121no—
227C4×D3—122no—
228C4×D3—124no—
229Dic6—41no—
230Dic6—41no—
231Dic6—124no—
232C3×C8—64no—
233C3⋊C8—24no—
234C2×C32—22no—
235C2×C32#38611yescharacteristic
236C2×C32C2×#10111yescharacteristic
237C2×C32#41311yescharacteristic
238C3⋊D3—22no—
239C3⋊D3—41no—
240C24—91no—
241C2×Q8—61no—
242C2×Q8—181no—
243C2×Q8—182no—
244C2×Q8—182no—
245C22×C4—92no—
246C22×C4—92no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—182no—
253C22×C4—182no—
254C22×C4GO+(4,𝔽2)11yescharacteristic
255M16—94no—
256M16—182no—
257M16—184no—
258M16—182no—
259M16—182no—
260C2×C8—64no—
261C2×C8—62no—
262C2×C8—182no—
263C4⋊C4—61no—
264C4⋊C4—62no—
265C4⋊C4—181no—
266C4⋊C4—182no—
267C22⋊C4—62no—
268C22⋊C4—182no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—22no—
274C22×C3—22no—
275C22×C3—41no—
276C22×C3—41no—
277C2×D3—62no—
278C2×D3—62no—
279C2×D3—62no—
280C2×D3—62no—
281C2×D3—62no—
282C2×D3—62no—
283C2×D3—121no—
284C2×D3—121no—
285C2×D3—121no—
286C2×D3—121no—
287C2×D3—121no—
288C2×D3—121no—
289C2×D3—128no—
290C2×D3—128no—
291C3×C4—22no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—41no—
297C3×C4—122no—
298C3×C4—122no—
299Dic3—42no—
300Dic3—42no—
301Dic3—62no—
302Dic3—62no—
303Dic3—62no—
304Dic3—121no—
305C32#190111yescharacteristic, complemented, Sylow
306C23—91no—
307C23—91no—
308C23—182no—
309C23—182no—
310C23—361no—
311C23D32⋊C411yescharacteristic
312Q8—121no—
313Q8—121no—
314Q8—362no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—62no—
318C2×C4—62no—
319C2×C4—91no—
320C2×C4—92no—
321C2×C4—92no—
322C2×C4—91no—
323C2×C4—182no—
324C2×C4—182no—
325C2×C4—182no—
326C2×C4—184no—
327C2×C4—181no—
328C2×C4—181no—
329C2×C4—362no—
330C2×C4D32⋊C411yescharacteristic
331C2×C4C2×GO+(4,𝔽2)11yescharacteristic
332C8—64no—
333C8—362no—
334C2×C3—24no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—42no—
342D3—64no—
343D3—122no—
344D3—122no—
345D3—122no—
346C22—21no—
347C22—21no—
348C22—92no—
349C22—181no—
350C22—181no—
351C22—181no—
352C22—181no—
353C22—181no—
354C22—364no—
355C22#6372812yescomplemented
356C22C2×D32⋊C411yescharacteristic
357C4—21no—
358C4—92no—
359C4—122no—
360C4—122no—
361C4—181no—
362C4#6423311yescharacteristic
363C4#6424111yescharacteristic
364C3—21no—
365C3—21no—
366C2—22no—
367C2—182no—
368C2—361no—
369C2#1059331111yescharacteristic
370C2C2×#6372811yescharacteristic
371C2#1059351411yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC22×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1901
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63728C2semidirect
5. #10590052C2semidirect
150. C22×C32#101semidirect
305. C32#1901semidirect
355. C22#63728semidirect

Maximal subgroups

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

subgroupindex
#105949252
C22×#37122
#105938032
C2×#637282
#105900522
#19019