Finite Group Databasebeta

← #11774718

Subgroups — #11774718

Order 1152.

653 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C3×#4926C211yesmaximal, characteristic
3C3×C4×#208C211yesmaximal, characteristic
4#10589085C214yesmaximal, complemented
5#70802—31nomaximal
6#69857—31nomaximal
7C22×#634C411yescharacteristic
8C2×C32×C42C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C411yescharacteristic
10C2×#3750—21no—
11C2×C4×C3⋊Dic3—21no—
12C4×#634—21no—
13C4×#634—21no—
14C4×#634C412yes—
15C4×#634C2212yes—
16C2×C3×#208—21no—
17C3×#830—21no—
18C3×C4⋊(C3⋊C8)C2212yes—
19C3×#803—21no—
20C3×#803—21no—
21C3×C4×C3⋊C8C2212yes—
22C2×C4×Dic6—31no—
23C2×C4×Dic6—31no—
24C2×C4×Dic6—61no—
25C3×#432—31no—
26C3×C4×M16—31no—
27#4926D311yescharacteristic
28C4×#208D311yescharacteristic
29#4484—34no—
30#4456—34no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—21no—
36C2×#634—21no—
37C2×#634—24no—
38C2×#634C2×C412yes—
39C32×C42C2×C411yescharacteristic
40C32×C42D411yescharacteristic
41C32×C42D411yescharacteristic
42C32×C42C2311yescharacteristic
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)C2×C412yes—
45#3750—22no—
46#3750—22no—
47C4×C3⋊Dic3—22no—
48C4×C3⋊Dic3—22no—
49C3×#208—24no—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52#1491—91noSylow
53C22×Dic6—31no—
54C22×Dic6—31no—
55C22×Dic6—61no—
56C2×C3×M16—61no—
57C2×C3×C42—21no—
58C2×C3×C42C2×D311yescharacteristic
59C2×C3×C42C2×D311yescharacteristic
60C2×C4⋊Dic3—31no—
61C2×C4⋊Dic3—31no—
62C2×C4⋊Dic3—61no—
63C2×Dic3⋊C4—62no—
64C2×Dic3⋊C4—61no—
65C2×Dic3⋊C4—61no—
66C2×C4×Dic3—62no—
67C2×C4×Dic3—61no—
68C2×C4×Dic3—61no—
69C2×#208—21no—
70C4×Dic6—32no—
71C4×Dic6—32no—
72C4×Dic6—32no—
73C4×Dic6—32no—
74C4×Dic6—62no—
75C4×Dic6—62no—
76C4×Dic6—62no—
77C4×Dic6—62no—
78C4×Dic6—61no—
79C4×Dic6—61no—
80C4×Dic6—61no—
81C4×Dic6—61no—
82C3×C4⋊C8—32no—
83C3×C22⋊C8—61no—
84C3×#97—61no—
85C3×#97—61no—
86C3×C4×C8—32no—
87#830—21no—
88C4⋊(C3⋊C8)C2×D312yes—
89#803—21no—
90#803—21no—
91C4×C3⋊C8C2×D312yes—
92C23×C32C22⋊C411yescharacteristic
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C3⋊Dic3—24no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—42no—
106#634—24no—
107#634—22no—
108#634M1614yescomplemented
109C3×C3⋊C8—24no—
110C3×C3⋊C8—42no—
111C2×C4×Q8—91no—
112#432—31no—
113C4×M16—31no—
114Q8⋊C8—94no—
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4C4×D311yescharacteristic
119C22×C3×C4C4×D311yescharacteristic
120C22×C3×C4D1211yescharacteristic
121C22×C3×C4D1211yescharacteristic
122C22×C3×C4#6711yescharacteristic
123C22×C3×C4#6711yescharacteristic
124C22×Dic3—62no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—62no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C2×Dic6—32no—
131C2×Dic6—32no—
132C2×Dic6—62no—
133C2×Dic6—64no—
134C2×Dic6—64no—
135C2×Dic6—62no—
136C2×Dic6—68no—
137C2×Dic6—61no—
138C2×Dic6—61no—
139C3×M16—64no—
140C2×C3×C8—62no—
141C2×C3×C8—62no—
142C3×C42—21no—
143C3×C42—21no—
144C3×C42—21no—
145C3×C42—21no—
146C3×C42C4×D311yescharacteristic
147C3×C42C4×D311yescharacteristic
148C3×C42D1211yescharacteristic
149C3×C42D1211yescharacteristic
150C3×C42#6711yescharacteristic
151C3×C42#6711yescharacteristic
152C3×C42C22×D311yescharacteristic
153C3×C42C22×D311yescharacteristic
154C4⋊Dic3—32no—
155C4⋊Dic3—32no—
156C4⋊Dic3—62no—
157C4⋊Dic3—62no—
158C4⋊Dic3—61no—
159C4⋊Dic3—61no—
160Dic3⋊C4—64no—
161Dic3⋊C4—64no—
162Dic3⋊C4—62no—
163Dic3⋊C4—62no—
164Dic3⋊C4—62no—
165Dic3⋊C4—62no—
166C4×Dic3—64no—
167C4×Dic3—64no—
168C4×Dic3—62no—
169C4×Dic3—62no—
170C4×Dic3—62no—
171C4×Dic3—62no—
172#208—24no—
173C2×C3⋊C8—22no—
174C2×C3⋊C8—22no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32#10412yes—
178C22×C32C2×C22⋊C411yescharacteristic
179C32×C4—21no—
180C32×C4—21no—
181C32×C4—21no—
182C32×C4—21no—
183C32×C4C2×M1612yes—
184C32×C4#13712yes—
185C3⋊Dic3—24no—
186C3⋊Dic3—42no—
187C22×Q8—91no—
188C2×M16—61no—
189C4×Q8—92no—
190C4×Q8—92no—
191C4×Q8—181no—
192C4×Q8—181no—
193C2×C4⋊C4—91no—
194C2×C4⋊C4—181no—
195C2×C42—181no—
196C2×C42D3211yescharacteristic
197C4⋊C8—32no—
198C22⋊C8—61no—
199#97—61no—
200#97—61no—
201C4×C8—32no—
202C23×C3—21no—
203C23×C3(C2×D3)⋊C411yescharacteristic
204C23×C3(C2×D3)⋊C411yescharacteristic
205C2×C3×C4—24no—
206C2×C3×C4—24no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—42no—
220C2×C3×C4(C2×D3)⋊C411yescharacteristic
221C2×C3×C4(C2×D3)⋊C411yescharacteristic
222C2×C3×C4(C2×D3)⋊C411yescharacteristic
223C2×C3×C4(C2×D3)⋊C411yescharacteristic
224C2×C3×C4(C2×D3)⋊C411yescharacteristic
225C2×C3×C4(C2×D3)⋊C411yescharacteristic
226C2×C3×C4C2×C4×D311yescharacteristic
227C2×C3×C4C2×C4×D311yescharacteristic
228C2×C3×C4C2×D1211yescharacteristic
229C2×C3×C4C2×D1211yescharacteristic
230C2×C3×C4C2×#6711yescharacteristic
231C2×C3×C4C2×#6711yescharacteristic
232C2×Dic3—64no—
233C2×Dic3—68no—
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—64no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—124no—
242C2×Dic3—122no—
243C2×Dic3—122no—
244Dic6—34no—
245Dic6—34no—
246Dic6—64no—
247Dic6—68no—
248Dic6—64no—
249Dic6—64no—
250Dic6—64no—
251Dic6—62no—
252Dic6—62no—
253C3×C8—64no—
254C3×C8—122no—
255C3⋊C8—24no—
256C3⋊C8—42no—
257C2×C32—22no—
258C2×C32#40711yescharacteristic
259C2×C32#41911yescharacteristic
260C2×C32C2×#10411yescharacteristic
261C2×Q8—92no—
262C2×Q8—184no—
263C2×Q8—181no—
264C22×C4—181no—
265C22×C4—181no—
266C22×C4#62411yescharacteristic
267C22×C4#62611yescharacteristic
268C22×C4#62611yescharacteristic
269M16—64no—
270C2×C8—62no—
271C2×C8—62no—
272C4⋊C4—92no—
273C4⋊C4—181no—
274C4⋊C4—182no—
275C4⋊C4—182no—
276C42—182no—
277C42—182no—
278C42#62411yescharacteristic
279C42#62611yescharacteristic
280C42#62611yescharacteristic
281C42C2×D3211yescharacteristic
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—22no—
289C22×C3—21no—
290C22×C3#80512yes—
291C22×C3#82512yes—
292C22×C3C2×(C2×D3)⋊C411yescharacteristic
293C22×C3C2×(C2×D3)⋊C411yescharacteristic
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—22no—
305C3×C4—22no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4D3×M1612yes—
309C3×C4D3×M1612yes—
310C3×C4#90912yes—
311C3×C4#95112yes—
312Dic3—68no—
313Dic3—64no—
314Dic3—64no—
315Dic3—124no—
316Dic3—122no—
317Dic3—122no—
318C32#149111yescharacteristic, complemented, Sylow
319C23#372211yescharacteristic
320Q8—94no—
321Q8—184no—
322Q8—182no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—184no—
327C2×C4—182no—
328C2×C4—182no—
329C2×C4—362no—
330C2×C4#372211yescharacteristic
331C2×C4#372211yescharacteristic
332C2×C4#372211yescharacteristic
333C2×C4C2×#62411yescharacteristic
334C2×C4C2×#62611yescharacteristic
335C2×C4C2×#62611yescharacteristic
336C8—64no—
337C8—122no—
338C2×C3—24no—
339C2×C3—22no—
340C2×C3—22no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3C2×#80511yescharacteristic
345C2×C3#500411yescharacteristic
346C2×C3#512011yescharacteristic
347C2×C3#512611yescharacteristic
348C2×C3#512611yescharacteristic
349C2×C3C2×#82511yescharacteristic
350C22—21no—
351C22—21no—
352C22#6357012yes—
353C22C2×#372211yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—184no—
359C4—362no—
360C4#6381812yes—
361C4#6383112yes—
362C3—21no—
363C3#6985711yescharacteristic, complemented
364C3#7080211yescharacteristic, complemented
365C2—22no—
366C2#1059107411yescharacteristic
367C2#1059110711yescharacteristic
368C2C2×#6357011yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10589085C2semidirect
108. #634M16semidirect
318. C32#1491semidirect
363. C3#69857semidirect
364. C3#70802semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C3×#49262
C3×C4×#2082
#105890852
#708023
#698573