Finite Group Databasebeta

← #11796861

Subgroups — #11796861

Order 1152.

581 conjugacy classes of subgroups.

The subgroup lattice has 409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic
2C3×#5106C211yesmaximal, characteristic, complemented
3C2×C3×#812C211yesmaximal, characteristic, complemented
4#10589125C214yesmaximal, complemented
5#71450—31nomaximal
6#70656—31nomaximal
7C2×#3828—21no—
8C22×C32×C8C2211yescharacteristic
9C2×#3746C411yescharacteristic, complemented
10#64113—21no—
11#64113—21no—
12#64113C412yescomplemented
13#64113C2212yes—
14C2×#3745C411yescharacteristic, complemented
15C2×#3744—21no—
16C3×#926—21no—
17C3×#818—21no—
18C3×#817C2212yescomplemented
19C3×#812—21no—
20C3×#812C2212yescomplemented
21C2×C3×C3⋊C16—21no—
22C2×#904—31no—
23C2×#904—31no—
24C2×#904—61no—
25C2×C3×M32—31no—
26C3×#427—31no—
27#5106D311yescharacteristic, complemented
28C2×#812D311yescharacteristic, complemented
29#4518—34no—
30#4488—34no—
31C22×C32×C4D411yescharacteristic
32C2×#638—41no—
33#3828—22no—
34#3828—22no—
35#3828—41no—
36#3828—41no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4×C3⋊D3—41no—
39C2×#634—21no—
40C2×C32×C8C2×C411yescharacteristic
41C2×C32×C8C2×C411yescharacteristic
42C2×C32×C8D411yescharacteristic
43C2×C32×C8D411yescharacteristic
44C2×C32×C8D411yescharacteristic
45C2×C32×C8C2311yescharacteristic
46#3746—21no—
47#3746C2×C412yes—
48#3745—21no—
49#3745C2×C412yes—
50#3744—22no—
51#3744—22no—
52C3×#217—41no—
53C3×C4⋊Dic3—22no—
54C3×C4×Dic3—41no—
55C3×C3⋊C16—22no—
56#2145—91noSylow
57C2×#235—62no—
58C2×#235—61no—
59C2×#235—61no—
60C22×C3×C8—21no—
61C22×C3×C8C2×D311yescharacteristic
62C22×C3×C8C2×D311yescharacteristic
63C3×#117—61no—
64#926—21no—
65C2×Dic12—31no—
66C2×Dic12—31no—
67C2×Dic12—61no—
68#904—32no—
69#904—32no—
70#904—32no—
71#904—32no—
72#904—62no—
73#904—62no—
74#904—62no—
75#904—62no—
76#904—61no—
77#904—61no—
78#904—61no—
79#904—61no—
80C2×D24—31no—
81C2×D24—31no—
82C2×D24—61no—
83C2×#204—62no—
84C2×#204—61no—
85C2×#204—61no—
86C3×M32—32no—
87C3×M32—61no—
88C2×C3×C16—61no—
89C3×#107—61no—
90C3×#106—32no—
91#818—21no—
92#817C2×D312yescomplemented
93#812—21no—
94#812C2×D312yescomplemented
95C2×C3⋊C16—21no—
96C23×C32D811yescharacteristic
97C22×C3⋊D3—41no—
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C22⋊C411yescharacteristic
100C2×C32×C4D811yescharacteristic
101C2×C32×C4SD1611yescharacteristic
102C2×C32×C4SD1611yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104#638—42no—
105#638—42no—
106C2×C3⋊Dic3—41no—
107C4⋊(C3⋊D3)—22no—
108C4⋊(C3⋊D3)—41no—
109C4×C3⋊D3—42no—
110C4×C3⋊D3—42no—
111#634—22no—
112#634—41no—
113C2×C3×Dic3—42no—
114C32×C8C22⋊C411yescharacteristic
115C32×C8C22⋊C411yescharacteristic
116C32×C8C22×C411yescharacteristic
117C32×C8C2×D411yescharacteristic
118C2×#135—91no—
119C2×M32—31no—
120#427—31no—
121#360—94no—
122C22×C3×C4—21no—
123C22×C3×C4D1211yescharacteristic
124C22×C3×C4#6711yescharacteristic
125C2×#67—122no—
126C2×#67—121no—
127C2×#67—121no—
128#235—64no—
129#235—64no—
130#235—62no—
131#235—62no—
132#235—62no—
133#235—62no—
134#235—122no—
135#235—122no—
136#235—121no—
137#235—121no—
138#235—121no—
139#235—121no—
140C2×D12—62no—
141C2×D12—61no—
142C2×D12—61no—
143C2×C4×D3—122no—
144C2×C4×D3—121no—
145C2×C4×D3—121no—
146C2×Dic6—62no—
147C2×Dic6—61no—
148C2×Dic6—61no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8C4×D311yescharacteristic
156C2×C3×C8C4×D311yescharacteristic
157C2×C3×C8C4×D311yescharacteristic
158C2×C3×C8C4×D311yescharacteristic
159C2×C3×C8D1211yescharacteristic
160C2×C3×C8D1211yescharacteristic
161C2×C3×C8D1211yescharacteristic
162C2×C3×C8#6711yescharacteristic
163C2×C3×C8#6711yescharacteristic
164C2×C3×C8#6711yescharacteristic
165C2×C3×C8C22×D311yescharacteristic
166C2×C3×C8C22×D311yescharacteristic
167C3×C4⋊C4—62no—
168C3×C22⋊C4—121no—
169C3×C42—121no—
170#217—41no—
171C4⋊Dic3—22no—
172C4×Dic3—41no—
173Dic12—32no—
174Dic12—32no—
175Dic12—62no—
176Dic12—62no—
177Dic12—61no—
178Dic12—61no—
179D24—32no—
180D24—32no—
181D24—62no—
182D24—62no—
183D24—61no—
184D24—61no—
185#204—64no—
186#204—64no—
187#204—62no—
188#204—62no—
189#204—62no—
190#204—62no—
191C3×C16—62no—
192C3⋊C16—22no—
193C22×C32—41no—
194C22×C32#10211yescharacteristic
195C22×C32#10211yescharacteristic
196C22×C32C2×D811yescharacteristic
197C2×C3⋊D3—42no—
198C2×C3⋊D3—82no—
199C32×C4#10211yescharacteristic
200C32×C4#10211yescharacteristic
201C32×C4C2×C22⋊C411yescharacteristic
202C32×C4C2×SD1611yescharacteristic
203C3⋊Dic3—42no—
204C3×Dic3—82no—
205C2×#41—181no—
206#135—92no—
207#135—92no—
208#135—181no—
209#135—181no—
210C2×Q16—91no—
211C2×SD16—181no—
212C2×D8—91no—
213C22×C8D3211yescharacteristic
214#117—61no—
215M32—32no—
216M32—61no—
217C2×C16—61no—
218#107—61no—
219#106—32no—
220C23×C3—21no—
221C23×C3D2411yescharacteristic
222C23×C3#21311yescharacteristic
223C22×D3—122no—
224C22×D3—121no—
225C22×D3—121no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—122no—
233C2×C3×C4#20411yescharacteristic
234C2×C3×C4#20411yescharacteristic
235C2×C3×C4D2411yescharacteristic
236C2×C3×C4(C2×D3)⋊C411yescharacteristic
237C2×C3×C4(C2×D3)⋊C411yescharacteristic
238C2×C3×C4(C2×D3)⋊C411yescharacteristic
239C2×C3×C4(C2×D3)⋊C411yescharacteristic
240C2×C3×C4#21311yescharacteristic
241C2×C3×C4#21511yescharacteristic
242C2×C3×C4#21511yescharacteristic
243C2×C3×C4C2×D1211yescharacteristic
244C2×C3×C4C2×#6711yescharacteristic
245#67—124no—
246#67—124no—
247#67—122no—
248#67—122no—
249#67—122no—
250#67—122no—
251C2×Dic3—42no—
252C2×Dic3—122no—
253C2×Dic3—121no—
254C2×Dic3—121no—
255D12—64no—
256D12—62no—
257D12—62no—
258D12—122no—
259D12—121no—
260D12—121no—
261C4×D3—124no—
262C4×D3—124no—
263C4×D3—122no—
264C4×D3—122no—
265C4×D3—122no—
266C4×D3—122no—
267Dic6—64no—
268Dic6—62no—
269Dic6—62no—
270Dic6—122no—
271Dic6—121no—
272Dic6—121no—
273C3×C8—21no—
274C3×C8—21no—
275C3×C8—21no—
276C3×C8—21no—
277C3×C8(C2×D3)⋊C411yescharacteristic
278C3×C8(C2×D3)⋊C411yescharacteristic
279C3×C8(C2×D3)⋊C411yescharacteristic
280C3×C8(C2×D3)⋊C411yescharacteristic
281C3×C8C2×C4×D311yescharacteristic
282C3×C8C2×C4×D311yescharacteristic
283C3×C8C2×D1211yescharacteristic
284C3×C8C2×#6711yescharacteristic
285C2×C32—21no—
286C2×C32—21no—
287C2×C32—21no—
288C2×C32C2×#10211yescharacteristic
289C3⋊D3—82no—
290#41—182no—
291#41—182no—
292#41—361no—
293#41—361no—
294C2×Q8—181no—
295C2×D4—181no—
296C2×D4—361no—
297C22×C4—361no—
298C22×C4#62611yescharacteristic
299Q16—92no—
300Q16—181no—
301SD16—182no—
302SD16—182no—
303D8—92no—
304D8—181no—
305C2×C8#62411yescharacteristic
306C2×C8#62411yescharacteristic
307C2×C8#62611yescharacteristic
308C2×C8#62611yescharacteristic
309C2×C8#62611yescharacteristic
310C2×C8C2×D3211yescharacteristic
311C4⋊C4—62no—
312C22⋊C4—121no—
313C42—121no—
314C16—62no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—42no—
321C22×C3#80911yescharacteristic
322C22×C3#80911yescharacteristic
323C22×C3#82111yescharacteristic
324C22×C3#82111yescharacteristic
325C22×C3C2×D2411yescharacteristic
326C22×C3C2×#21311yescharacteristic
327C2×D3—124no—
328C2×D3—122no—
329C2×D3—122no—
330C2×D3—244no—
331C2×D3—242no—
332C2×D3—242no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—242no—
338C3×C4#80911yescharacteristic
339C3×C4#80911yescharacteristic
340C3×C4#82111yescharacteristic
341C3×C4#82111yescharacteristic
342C3×C4C2×#20411yescharacteristic
343C3×C4C2×(C2×D3)⋊C411yescharacteristic
344C3×C4C2×(C2×D3)⋊C411yescharacteristic
345C3×C4C2×#21511yescharacteristic
346Dic3—82no—
347Dic3—124no—
348Dic3—122no—
349Dic3—122no—
350C32#214511yescharacteristic, complemented, Sylow
351C23—361no—
352C23#371411yescharacteristic
353Q8—182no—
354Q8—361no—
355D4—182no—
356D4—362no—
357D4—362no—
358D4—361no—
359C2×C4—122no—
360C2×C4—361no—
361C2×C4—362no—
362C2×C4—362no—
363C2×C4#371411yescharacteristic
364C2×C4#371711yescharacteristic
365C2×C4#371711yescharacteristic
366C2×C4#372211yescharacteristic
367C2×C4#372211yescharacteristic
368C2×C4C2×#62611yescharacteristic
369C8#372211yescharacteristic
370C8#372211yescharacteristic
371C8C2×#62411yescharacteristic
372C8C2×#62611yescharacteristic
373C2×C3—22no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—41no—
382C2×C3—41no—
383C2×C3C2×#80911yescharacteristic
384C2×C3C2×#82111yescharacteristic
385D3—244no—
386D3—242no—
387D3—242no—
388C22—41no—
389C22—362no—
390C22—722no—
391C22#6356411yescharacteristic
392C22#6356411yescharacteristic
393C22C2×#371411yescharacteristic
394C4—242no—
395C4—362no—
396C4#6356411yescharacteristic
397C4#6356411yescharacteristic
398C4C2×#371711yescharacteristic
399C4C2×#372211yescharacteristic
400C3—21no—
401C3#7065611yescharacteristic, complemented
402C3#7145011yescharacteristic, complemented
403C2—21no—
404C2—21no—
405C2—21no—
406C2—722no—
407C2C2×#6356411yescharacteristic
subgroupG/H
centerC4#63564
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC22×C32×C8C22
socleC2×C32C2×#102
prime radicalC2×#64113C2
cosocleC2×C32×C8C23
hypercenterC22×C8D32
hypocenterC32#2145
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C3×#5106C2semidirect
3. C2×C3×#812C2semidirect
4. #10589125C2semidirect
9. C2×#3746C4semidirect
12. #64113C4semidirect
14. C2×#3745C4semidirect
18. C3×#817C22semidirect
20. C3×#812C22semidirect
27. #5106D3semidirect
28. C2×#812D3semidirect
92. #817C2×D3semidirect
94. #812C2×D3semidirect
350. C32#2145semidirect
401. C3#70656semidirect
402. C3#71450semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
C3×#51062
C2×C3×#8122
#105891252
#714503
#706563