Finite Group Databasebeta

← #11796688

Subgroups — #11796688

Order 1152.

597 conjugacy classes of subgroups.

The subgroup lattice has 353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic
2C2×C3×#818C211yesmaximal, characteristic, complemented
3C2×C3×#812C211yesmaximal, characteristic, complemented
4#10589119C212yesmaximal, complemented
5#10589116C212yesmaximal, complemented
6#71439—31nomaximal
7#70598—31nomaximal
8C2×#3828—21no—
9C22×C32×C8C2211yescharacteristic
10C2×#3746C2211yescharacteristic
11#64113—22no—
12#64113C414yescomplemented
13C2×#3745C2211yescharacteristic
14C2×#3744—21no—
15C2×C3×C4⋊Dic3—21no—
16C3×#818—21no—
17C3×#818C2212yes—
18C3×#812—22no—
19C2×C3×C3⋊C16C2212yes—
20C2×#904—31no—
21C2×#904—31no—
22C2×#904—61no—
23C2×C3×M32—31no—
24C2×C3×#107—31no—
25C2×#818D311yescharacteristic, complemented
26C2×#812D311yescharacteristic, complemented
27#4509—32no—
28#4503—32no—
29#4492—32no—
30#4491—32no—
31C22×C32×C4D411yescharacteristic
32C2×#638—41no—
33#3828—24no—
34#3828—42no—
35C2×C4⋊(C3⋊D3)—21no—
36C2×C4×C3⋊D3—41no—
37C2×#634—21no—
38C22×C3×Dic3—41no—
39C2×C32×C8C2×C412yes—
40C2×C32×C8D411yescharacteristic
41C2×C32×C8D412yes—
42C2×C32×C8C2311yescharacteristic
43#3746—21no—
44#3746C2×C412yescomplemented
45#3745—21no—
46#3745C2×C412yescomplemented
47#3744—24no—
48C3×C4⋊Dic3—22no—
49C3×C4⋊Dic3—41no—
50C3×C3⋊C16—22no—
51#2139—91noSylow
52C2×#235—62no—
53C2×#235—61no—
54C2×#235—61no—
55C22×C3×C8—21no—
56C22×C3×C8C2×D311yescharacteristic
57C22×C3×C8C2×D311yescharacteristic
58C2×C3×C4⋊C4—61no—
59C2×C4⋊Dic3—21no—
60C2×Dic12—31no—
61C2×Dic12—31no—
62C2×Dic12—61no—
63#904—34no—
64#904—34no—
65#904—64no—
66#904—64no—
67#904—62no—
68#904—62no—
69C2×D24—31no—
70C2×D24—31no—
71C2×D24—61no—
72C2×#204—62no—
73C2×#204—61no—
74C2×#204—61no—
75C3×M32—62no—
76C2×C3×C16—32no—
77C3×#107—32no—
78C3×#107—61no—
79#818—21no—
80#818C2×D312yes—
81#812—22no—
82C2×C3⋊C16C2×D312yes—
83C23×C32D811yescharacteristic
84C22×C3⋊D3—41no—
85C2×C32×C4C22⋊C412yes—
86C2×C32×C4D811yescharacteristic
87C2×C32×C4SD1612yes—
88C2×C32×C4C2×D411yescharacteristic
89#638—44no—
90C2×C3⋊Dic3—41no—
91C4⋊(C3⋊D3)—22no—
92C4⋊(C3⋊D3)—41no—
93C4×C3⋊D3—44no—
94#634—22no—
95#634—41no—
96C2×C3×Dic3—42no—
97C2×C3×Dic3—82no—
98C32×C8C22⋊C412yes—
99C32×C8C22×C411yescharacteristic
100C32×C8C2×D411yescharacteristic
101C2×#135—91no—
102C2×M32—31no—
103C2×#107—31no—
104#358—92no—
105#357—92no—
106C22×C3×C4—21no—
107C22×C3×C4—121no—
108C22×C3×C4D1211yescharacteristic
109C22×C3×C4#6711yescharacteristic
110C2×#67—122no—
111C2×#67—121no—
112C2×#67—121no—
113C22×Dic3—41no—
114#235—68no—
115#235—64no—
116#235—64no—
117#235—124no—
118#235—122no—
119#235—122no—
120C2×D12—62no—
121C2×D12—61no—
122C2×D12—61no—
123C2×C4×D3—122no—
124C2×C4×D3—121no—
125C2×C4×D3—121no—
126C2×Dic6—62no—
127C2×Dic6—61no—
128C2×Dic6—61no—
129C2×C3×C8—22no—
130C2×C3×C8—21no—
131C2×C3×C8—22no—
132C2×C3×C8—21no—
133C2×C3×C8C4×D312yes—
134C2×C3×C8C4×D312yes—
135C2×C3×C8D1211yescharacteristic
136C2×C3×C8D1212yes—
137C2×C3×C8#6711yescharacteristic
138C2×C3×C8#6712yes—
139C2×C3×C8C22×D311yescharacteristic
140C2×C3×C8C22×D311yescharacteristic
141C3×C4⋊C4—62no—
142C3×C4⋊C4—121no—
143C4⋊Dic3—22no—
144C4⋊Dic3—41no—
145Dic12—32no—
146Dic12—32no—
147Dic12—62no—
148Dic12—62no—
149Dic12—61no—
150Dic12—61no—
151D24—32no—
152D24—32no—
153D24—62no—
154D24—62no—
155D24—61no—
156D24—61no—
157#204—68no—
158#204—64no—
159#204—64no—
160C3×C16—62no—
161C3⋊C16—22no—
162C22×C32—21no—
163C22×C32—21no—
164C22×C32#10212yes—
165C22×C32C2×D811yescharacteristic
166C2×C3⋊D3—42no—
167C2×C3⋊D3—81no—
168C2×C3⋊D3—81no—
169C32×C4#10212yes—
170C32×C4C2×C22⋊C411yescharacteristic
171C32×C4C2×SD1611yescharacteristic
172C3⋊Dic3—42no—
173C3×Dic3—82no—
174C2×#41—181no—
175#135—94no—
176#135—182no—
177C2×Q16—91no—
178C2×SD16—181no—
179C2×D8—91no—
180C22×C8D3211yescharacteristic
181C2×C4⋊C4—61no—
182M32—62no—
183C2×C16—32no—
184#107—32no—
185#107—61no—
186C23×C3—21no—
187C23×C3D2411yescharacteristic
188C23×C3#21311yescharacteristic
189C22×D3—122no—
190C22×D3—121no—
191C22×D3—121no—
192C2×C3×C4—21no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—21no—
196C2×C3×C4—122no—
197C2×C3×C4—242no—
198C2×C3×C4#20412yes—
199C2×C3×C4D2411yescharacteristic
200C2×C3×C4(C2×D3)⋊C412yes—
201C2×C3×C4(C2×D3)⋊C412yes—
202C2×C3×C4#21311yescharacteristic
203C2×C3×C4#21512yes—
204C2×C3×C4C2×D1211yescharacteristic
205C2×C3×C4C2×#6711yescharacteristic
206#67—128no—
207#67—124no—
208#67—124no—
209C2×Dic3—42no—
210C2×Dic3—82no—
211C2×Dic3—122no—
212C2×Dic3—121no—
213C2×Dic3—121no—
214D12—64no—
215D12—62no—
216D12—62no—
217D12—122no—
218D12—121no—
219D12—121no—
220C4×D3—128no—
221C4×D3—124no—
222C4×D3—124no—
223Dic6—64no—
224Dic6—62no—
225Dic6—62no—
226Dic6—122no—
227Dic6—121no—
228Dic6—121no—
229C3×C8—22no—
230C3×C8—21no—
231C3×C8—21no—
232C3×C8(C2×D3)⋊C412yes—
233C3×C8(C2×D3)⋊C412yes—
234C3×C8C2×C4×D311yescharacteristic
235C3×C8C2×C4×D311yescharacteristic
236C3×C8C2×D1211yescharacteristic
237C3×C8C2×#6711yescharacteristic
238C2×C32—22no—
239C2×C32C2×#10211yescharacteristic
240C2×C32#50911yescharacteristic
241C2×C32#51011yescharacteristic
242C3⋊D3—82no—
243#41—184no—
244#41—362no—
245C2×Q8—181no—
246C2×D4—181no—
247C2×D4—361no—
248C22×C4—121no—
249C22×C4—361no—
250C22×C4#62611yescharacteristic
251Q16—92no—
252Q16—181no—
253SD16—184no—
254D8—92no—
255D8—181no—
256C2×C8#62412yes—
257C2×C8#62611yescharacteristic
258C2×C8#62612yes—
259C2×C8C2×D3211yescharacteristic
260C4⋊C4—62no—
261C4⋊C4—121no—
262C16—62no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—22no—
268C22×C3—21no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3#80912yes—
272C22×C3#82112yes—
273C22×C3C2×D2411yescharacteristic
274C22×C3C2×#21311yescharacteristic
275C2×D3—124no—
276C2×D3—122no—
277C2×D3—122no—
278C2×D3—242no—
279C2×D3—242no—
280C2×D3—241no—
281C2×D3—241no—
282C2×D3—241no—
283C2×D3—241no—
284C3×C4—22no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—242no—
288C3×C4#80912yes—
289C3×C4#82112yes—
290C3×C4C2×#20411yescharacteristic
291C3×C4C2×(C2×D3)⋊C411yescharacteristic
292C3×C4C2×(C2×D3)⋊C411yescharacteristic
293C3×C4C2×#21511yescharacteristic
294Dic3—82no—
295Dic3—124no—
296Dic3—122no—
297Dic3—122no—
298C32#213911yescharacteristic, complemented, Sylow
299C23—361no—
300C23#371411yescharacteristic
301Q8—182no—
302Q8—361no—
303D4—182no—
304D4—364no—
305D4—361no—
306C2×C4—122no—
307C2×C4—242no—
308C2×C4—361no—
309C2×C4—364no—
310C2×C4#371411yescharacteristic
311C2×C4#371712yes—
312C2×C4#372212yes—
313C2×C4C2×#62611yescharacteristic
314C8#372212yes—
315C8C2×#62411yescharacteristic
316C8C2×#62611yescharacteristic
317C2×C3—22no—
318C2×C3—22no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—42no—
323C2×C3#490811yescharacteristic
324C2×C3#490911yescharacteristic
325C2×C3C2×#80911yescharacteristic
326C2×C3C2×#82111yescharacteristic
327C2×C3#514711yescharacteristic
328C2×C3#517911yescharacteristic
329D3—244no—
330D3—242no—
331D3—242no—
332C22—21no—
333C22—21no—
334C22—362no—
335C22—721no—
336C22—721no—
337C22#6356412yes—
338C22C2×#371411yescharacteristic
339C4—242no—
340C4—362no—
341C4#6356412yes—
342C4C2×#371711yescharacteristic
343C4C2×#372211yescharacteristic
344C3—21no—
345C3#7059811yescharacteristic, complemented
346C3#7143911yescharacteristic, complemented
347C2—22no—
348C2—722no—
349C2#1059063311yescharacteristic
350C2#1059064211yescharacteristic
351C2C2×#6356411yescharacteristic
subgroupG/H
centerC22C2×#3714
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC22×C32×C8C22
socleC22×C32C2×D8
prime radicalC2×#64113C2
cosocleC2×C32×C8C23
hypercenterC22×C8D32
hypocenterC32#2139
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#818C2semidirect
3. C2×C3×#812C2semidirect
4. #10589119C2semidirect
5. #10589116C2semidirect
12. #64113C4semidirect
25. C2×#818D3semidirect
26. C2×#812D3semidirect
44. #3746C2×C4semidirect
46. #3745C2×C4semidirect
298. C32#2139semidirect
345. C3#70598semidirect
346. C3#71439semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
C2×C3×#8182
C2×C3×#8122
#105891192
#105891162
#714393
#705983