Finite Group Databasebeta

← #11785556

Subgroups — #11785556

Order 1152.

645 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 645 conjugacy classes of subgroups — too many to draw. Only its 148 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
1C2×#64157C211yesmaximal, characteristic
2C3×#5236C212yesmaximal
3C2×#63578C211yesmaximal, characteristic, complemented
4#10591138C211yesmaximal, characteristic, complemented
5#10589169C212yesmaximal, complemented
6#70396—32nomaximal
7C2×C32×#41C2211yescharacteristic
8#64157—21no—
9#64157—21no—
10#64157C412yescomplemented
11#64157C412yescomplemented
12C2×#3748—21no—
13C2×#3748C2211yescharacteristic
14C22×C3⋊(C3⋊C8)—21no—
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#926C2212yes—
17C2×C3×#208C2212yes—
18C3×#837—24no—
19#63578—21no—
20#63578—21no—
21#63576—21no—
22#63574—21no—
23C2×#948—32no—
24C2×#948—61no—
25C3×#421—32no—
26#5236D312yes—
27C2×#822—32no—
28#4998—32no—
29#4556—32no—
30#4533—32no—
31C32×#41—21no—
32C32×#41—21no—
33C32×#41C2×C412yes—
34C32×#41D412yes—
35C2×C32×Q8Q811yescharacteristic
36C2×C32×D4—21no—
37C2×C32×D4Q811yescharacteristic
38C22×C32×C4—21no—
39C22×C32×C4C2311yescharacteristic
40#3748—21no—
41#3748—22no—
42#3748—22no—
43#3748C2×C412yes—
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)—22no—
46C2×C3⋊(C3⋊C8)—22no—
47C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
48C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C2×C3⋊(C3⋊C8)D411yescharacteristic
52C2×C3⋊(C3⋊C8)D411yescharacteristic
53C3×#217—22no—
54C3×C4⋊Dic3—22no—
55C3×C4×Dic3—22no—
56C3×#208—22no—
57C3×#208—22no—
58C2×C3×C3⋊C8—22no—
59#1814—91noSylow
60C2×C3×#41—21no—
61C2×C3×#41C2×D312yes—
62C2×C3×M16—32no—
63C3×#117—32no—
64#948—34no—
65#948—34no—
66#948—62no—
67#948—62no—
68#948—62no—
69#948—62no—
70#948—62no—
71#948—62no—
72#926C2×D312yes—
73C2×#208—32no—
74C2×#208—61no—
75C2×#208—62no—
76C2×#208—62no—
77C2×#208C2×D312yes—
78C22×C3⋊C8—32no—
79C22×C3⋊C8—61no—
80C22×C3⋊C8—62no—
81C22×C3⋊C8—62no—
82C3×#104—64no—
83#837—24no—
84#822—62no—
85#822—62no—
86#808—62no—
87#807—62no—
88C23×C32—21no—
89C23×C32#4111yescharacteristic
90C32×Q8—21no—
91C32×Q8C4⋊C412yes—
92C32×D4—22no—
93C32×D4—22no—
94C32×D4—21no—
95C32×D4C4⋊C412yes—
96C2×C32×C4—21no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×Q811yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3×Dic3—42no—
106C3⋊(C3⋊C8)—22no—
107C3⋊(C3⋊C8)C22⋊C411yescharacteristic
108C3⋊(C3⋊C8)C22⋊C411yescharacteristic
109C3⋊(C3⋊C8)C22⋊C411yescharacteristic
110C3⋊(C3⋊C8)C22⋊C411yescharacteristic
111C3×C3⋊C8—42no—
112C2×#131—91no—
113C2×#108—91no—
114#427—91no—
115#421—32no—
116#344—92no—
117C3×#41—22no—
118C3×#41—22no—
119C3×#41—22no—
120C3×#41—22no—
121C3×#41—22no—
122C3×#41—22no—
123C3×#41C4×D314yes—
124C3×#41#6714yes—
125C2×C3×Q8—21no—
126C2×C3×Q8Dic612yes—
127C2×C3×D4—22no—
128C2×C3×D4—22no—
129C2×C3×D4—21no—
130C2×C3×D4Dic612yes—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—21no—
134C22×C3×C4C22×D312yes—
135C3×M16—62no—
136C3×M16—62no—
137C2×C3×C8—62no—
138C3×C4⋊C4—62no—
139C3×C22⋊C4—62no—
140C3×C42—62no—
141#217—22no—
142C4⋊Dic3—22no—
143C4×Dic3—22no—
144#208—22no—
145#208—22no—
146#208—34no—
147#208—62no—
148#208—64no—
149#208—64no—
150#208—64no—
151#208—64no—
152#208—62no—
153#208—62no—
154C2×C3⋊C8—22no—
155C2×C3⋊C8—32no—
156C2×C3⋊C8—32no—
157C2×C3⋊C8—32no—
158C2×C3⋊C8—32no—
159C2×C3⋊C8—32no—
160C2×C3⋊C8—32no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—61no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8—64no—
168C2×C3⋊C8—64no—
169C2×C3⋊C8—62no—
170C2×C3⋊C8—64no—
171C2×C3⋊C8—64no—
172C2×C3⋊C8—62no—
173C22×C32—22no—
174C22×C32—41no—
175C22×C32—42no—
176C22×C32#11711yescharacteristic
177C22×C32#12111yescharacteristic
178C22×C32C22⋊Q811yescharacteristic
179C32×C4—22no—
180C32×C4C2×C22⋊C411yescharacteristic
181C32×C4C2×C4⋊C411yescharacteristic
182C32×C4#12111yescharacteristic
183C32×C4C22⋊Q811yescharacteristic
184C3×Dic3—82no—
185C2×#41D3211yescharacteristic
186#131—92no—
187#131—92no—
188#131—181no—
189#131—181no—
190C2×M16—32no—
191C2×M16—91no—
192C2×M16—181no—
193C22×C8—91no—
194C22×C8—181no—
195#117—32no—
196#108—181no—
197#108—181no—
198#107—181no—
199#106—181no—
200#104—64no—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—21no—
204C23×C3#23712yes—
205C3×Q8—22no—
206C3×Q8—22no—
207C3×Q8—22no—
208C3×Q8Dic3⋊C414yes—
209C3×D4—24no—
210C3×D4—24no—
211C3×D4—22no—
212C3×D4—24no—
213C3×D4—24no—
214C3×D4—22no—
215C3×D4—22no—
216C3×D4Dic3⋊C414yes—
217C2×C3×C4—24no—
218C2×C3×C4—22no—
219C2×C3×C4—24no—
220C2×C3×C4—22no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—122no—
230C2×C3×C4C2×Dic612yes—
231C2×C3×C4C2×C4×D312yes—
232C2×C3×C4D3×D412yes—
233C2×C3×C4D3×D412yes—
234C2×C3×C4#23712yes—
235C2×C3×C4C2×#6712yes—
236C2×Dic3—42no—
237C3×C8—122no—
238C3⋊C8—32no—
239C3⋊C8—32no—
240C3⋊C8—32no—
241C3⋊C8—32no—
242C3⋊C8—42no—
243C3⋊C8—61no—
244C3⋊C8—61no—
245C3⋊C8—61no—
246C3⋊C8—61no—
247C3⋊C8—64no—
248C3⋊C8—64no—
249C2×C32—21no—
250C2×C32—21no—
251C2×C32—21no—
252C2×C32—42no—
253C2×C32#38011yescharacteristic
254#41—21no—
255#41—21no—
256#41#62412yes—
257#41#62512yes—
258C2×Q8#62711yescharacteristic
259C2×D4—21no—
260C2×D4#62711yescharacteristic
261C22×C4—21no—
262C22×C4C2×D3211yescharacteristic
263M16—62no—
264M16—62no—
265M16—92no—
266M16—182no—
267M16—182no—
268M16—181no—
269C2×C8—62no—
270C2×C8—91no—
271C2×C8—91no—
272C2×C8—91no—
273C2×C8—91no—
274C2×C8—91no—
275C2×C8—91no—
276C2×C8—182no—
277C2×C8—182no—
278C2×C8—181no—
279C4⋊C4—62no—
280C22⋊C4—62no—
281C42—62no—
282C22×C3—24no—
283C22×C3—24no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—42no—
288C22×C3—42no—
289C22×C3—44no—
290C22×C3—44no—
291C22×C3#87712yes—
292C22×C3#87812yes—
293C22×C3#93912yes—
294C3×C4—24no—
295C3×C4—24no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—242no—
301C3×C4#87812yes—
302C3×C4D3×C22⋊C412yes—
303C3×C4C2×Dic3⋊C412yes—
304C3×C4#93912yes—
305Dic3—82no—
306C32#181411yescharacteristic, complemented, Sylow
307C23—21no—
308C23#380511yescharacteristic
309Q8—21no—
310Q8#372412yes—
311D4—22no—
312D4—22no—
313D4—21no—
314D4#372412yes—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—122no—
319C2×C4#380511yescharacteristic
320C2×C4C2×#62411yescharacteristic
321C2×C4C2×#62511yescharacteristic
322C2×C4C2×#62711yescharacteristic
323C2×C4#381111yescharacteristic
324C2×C4#381111yescharacteristic
325C8—91no—
326C8—91no—
327C8—91no—
328C8—91no—
329C8—122no—
330C8—182no—
331C2×C3—22no—
332C2×C3—22no—
333C2×C3—22no—
334C2×C3—22no—
335C2×C3—21no—
336C2×C3—41no—
337C2×C3—41no—
338C2×C3—44no—
339C2×C3—44no—
340C2×C3#494212yes—
341C22—22no—
342C22—41no—
343C22—42no—
344C22#6395711yescharacteristic
345C22#6398011yescharacteristic
346C22#6398211yescharacteristic
347C4—22no—
348C4—242no—
349C4C2×#372411yescharacteristic
350C4#6397411yescharacteristic
351C4#6398011yescharacteristic
352C4#6398211yescharacteristic
353C3—21no—
354C3#7039612yescomplemented
355C2—21no—
356C2—21no—
357C2—21no—
358C2—42no—
359C2#1059172011yescharacteristic
subgroupG/H
centerC4#63980
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32#380
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1814
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. C2×#63578C2semidirect
4. #10591138C2semidirect
5. #10589169C2semidirect
10. #64157C4semidirect
11. #64157C4semidirect
306. C32#1814semidirect
354. C3#70396semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C3×#52362
C2×#635782
#105911382
#105891692
#703963