Finite Group Databasebeta

← #11796952

Subgroups — #11796952

Order 1152.

573 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
2C2×C3×#819C211yesmaximal, characteristic, complemented
3C2×C3×#812C211yesmaximal, characteristic, complemented
4#10589131C212yesmaximal, complemented
5#10589128C212yesmaximal, complemented
6#71442—31nomaximal
7#70687—31nomaximal
8C2×#3828—21no—
9C22×C32×C8C2211yescharacteristic
10C2×#3746C2211yescharacteristic
11#64113—21no—
12#64113—21no—
13#64113C412yes—
14#64113C412yes—
15C2×#3745C2211yescharacteristic
16C2×#3744—21no—
17C2×C3×#208—21no—
18C3×#819—21no—
19C3×#819C2212yes—
20C3×#812—21no—
21C3×#812C2212yes—
22C2×C3×C3⋊C16—21no—
23C2×#904—31no—
24C2×#904—31no—
25C2×#904—61no—
26C2×C3×M32—31no—
27C2×C3×#108—31no—
28C2×#819D311yescharacteristic, complemented
29C2×#812D311yescharacteristic, complemented
30#4517—32no—
31#4516—32no—
32#4496—32no—
33#4495—32no—
34C22×C32×C4D411yescharacteristic
35C2×#638—41no—
36#3828—22no—
37#3828—22no—
38#3828—41no—
39#3828—41no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4×C3⋊D3—41no—
42C2×#634—21no—
43C2×C32×C8C2×C411yescharacteristic
44C2×C32×C8C2×C411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C2×C32×C8D411yescharacteristic
47C2×C32×C8D411yescharacteristic
48C2×C32×C8C2311yescharacteristic
49#3746—21no—
50#3746C2×C412yes—
51#3745—21no—
52#3745C2×C412yes—
53#3744—22no—
54#3744—22no—
55C3×#208—22no—
56C3×#208—41no—
57C2×C3×C3⋊C8—41no—
58C3×C3⋊C16—22no—
59#2148—91noSylow
60C2×#235—62no—
61C2×#235—61no—
62C2×#235—61no—
63C2×C3×M16—61no—
64C22×C3×C8—21no—
65C22×C3×C8C2×D311yescharacteristic
66C22×C3×C8C2×D311yescharacteristic
67C2×#208—21no—
68C2×Dic12—31no—
69C2×Dic12—31no—
70C2×Dic12—61no—
71#904—32no—
72#904—32no—
73#904—32no—
74#904—32no—
75#904—62no—
76#904—62no—
77#904—62no—
78#904—62no—
79#904—61no—
80#904—61no—
81#904—61no—
82#904—61no—
83C2×D24—31no—
84C2×D24—31no—
85C2×D24—61no—
86C2×#204—62no—
87C2×#204—61no—
88C2×#204—61no—
89C3×M32—32no—
90C3×M32—61no—
91C2×C3×C16—61no—
92C3×#108—32no—
93C3×#108—61no—
94#819—21no—
95#819C2×D312yes—
96#812—21no—
97#812C2×D312yes—
98C2×C3⋊C16—21no—
99C23×C32SD1611yescharacteristic
100C22×C3⋊D3—41no—
101C2×C32×C4C22⋊C411yescharacteristic
102C2×C32×C4C22⋊C411yescharacteristic
103C2×C32×C4D811yescharacteristic
104C2×C32×C4D811yescharacteristic
105C2×C32×C4SD1611yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107#638—42no—
108#638—42no—
109C2×C3⋊Dic3—41no—
110C4⋊(C3⋊D3)—22no—
111C4⋊(C3⋊D3)—41no—
112C4×C3⋊D3—42no—
113C4×C3⋊D3—42no—
114#634—22no—
115#634—41no—
116C32×C8C22⋊C411yescharacteristic
117C32×C8C22⋊C411yescharacteristic
118C32×C8C22×C411yescharacteristic
119C32×C8C2×D411yescharacteristic
120C3×C3⋊C8—42no—
121C2×#135—91no—
122C2×M32—31no—
123C2×#108—31no—
124#362—92no—
125#361—92no—
126C22×C3×C4—21no—
127C22×C3×C4D1211yescharacteristic
128C22×C3×C4#6711yescharacteristic
129C2×#67—122no—
130C2×#67—121no—
131C2×#67—121no—
132#235—64no—
133#235—64no—
134#235—62no—
135#235—62no—
136#235—62no—
137#235—62no—
138#235—122no—
139#235—122no—
140#235—121no—
141#235—121no—
142#235—121no—
143#235—121no—
144C2×D12—62no—
145C2×D12—61no—
146C2×D12—61no—
147C2×C4×D3—122no—
148C2×C4×D3—121no—
149C2×C4×D3—121no—
150C2×Dic6—62no—
151C2×Dic6—61no—
152C2×Dic6—61no—
153C3×M16—62no—
154C3×M16—121no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—121no—
162C2×C3×C8C4×D311yescharacteristic
163C2×C3×C8C4×D311yescharacteristic
164C2×C3×C8C4×D311yescharacteristic
165C2×C3×C8C4×D311yescharacteristic
166C2×C3×C8D1211yescharacteristic
167C2×C3×C8D1211yescharacteristic
168C2×C3×C8D1211yescharacteristic
169C2×C3×C8#6711yescharacteristic
170C2×C3×C8#6711yescharacteristic
171C2×C3×C8#6711yescharacteristic
172C2×C3×C8C22×D311yescharacteristic
173C2×C3×C8C22×D311yescharacteristic
174#208—22no—
175#208—41no—
176C2×C3⋊C8—41no—
177Dic12—32no—
178Dic12—32no—
179Dic12—62no—
180Dic12—62no—
181Dic12—61no—
182Dic12—61no—
183D24—32no—
184D24—32no—
185D24—62no—
186D24—62no—
187D24—61no—
188D24—61no—
189#204—64no—
190#204—64no—
191#204—62no—
192#204—62no—
193#204—62no—
194#204—62no—
195C3×C16—62no—
196C3⋊C16—22no—
197C22×C32—41no—
198C22×C32#10211yescharacteristic
199C22×C32#10211yescharacteristic
200C22×C32C2×SD1611yescharacteristic
201C2×C3⋊D3—42no—
202C2×C3⋊D3—82no—
203C32×C4#10211yescharacteristic
204C32×C4#10211yescharacteristic
205C32×C4C2×C22⋊C411yescharacteristic
206C32×C4C2×D811yescharacteristic
207C3⋊Dic3—42no—
208C2×#41—181no—
209#135—92no—
210#135—92no—
211#135—181no—
212#135—181no—
213C2×Q16—91no—
214C2×SD16—181no—
215C2×D8—91no—
216C2×M16—61no—
217C22×C8D3211yescharacteristic
218M32—32no—
219M32—61no—
220C2×C16—61no—
221#108—32no—
222#108—61no—
223C23×C3—21no—
224C23×C3#20411yescharacteristic
225C23×C3#21511yescharacteristic
226C22×D3—122no—
227C22×D3—121no—
228C22×D3—121no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4#20411yescharacteristic
236C2×C3×C4D2411yescharacteristic
237C2×C3×C4D2411yescharacteristic
238C2×C3×C4(C2×D3)⋊C411yescharacteristic
239C2×C3×C4(C2×D3)⋊C411yescharacteristic
240C2×C3×C4(C2×D3)⋊C411yescharacteristic
241C2×C3×C4(C2×D3)⋊C411yescharacteristic
242C2×C3×C4#21311yescharacteristic
243C2×C3×C4#21311yescharacteristic
244C2×C3×C4#21511yescharacteristic
245C2×C3×C4C2×D1211yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247#67—124no—
248#67—124no—
249#67—122no—
250#67—122no—
251#67—122no—
252#67—122no—
253C2×Dic3—122no—
254C2×Dic3—121no—
255C2×Dic3—121no—
256D12—64no—
257D12—62no—
258D12—62no—
259D12—122no—
260D12—121no—
261D12—121no—
262C4×D3—124no—
263C4×D3—124no—
264C4×D3—122no—
265C4×D3—122no—
266C4×D3—122no—
267C4×D3—122no—
268Dic6—64no—
269Dic6—62no—
270Dic6—62no—
271Dic6—122no—
272Dic6—121no—
273Dic6—121no—
274C3×C8—21no—
275C3×C8—21no—
276C3×C8—21no—
277C3×C8—21no—
278C3×C8—122no—
279C3×C8(C2×D3)⋊C411yescharacteristic
280C3×C8(C2×D3)⋊C411yescharacteristic
281C3×C8(C2×D3)⋊C411yescharacteristic
282C3×C8(C2×D3)⋊C411yescharacteristic
283C3×C8C2×C4×D311yescharacteristic
284C3×C8C2×C4×D311yescharacteristic
285C3×C8C2×D1211yescharacteristic
286C3×C8C2×#6711yescharacteristic
287C3⋊C8—42no—
288C2×C32—21no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32C2×#10211yescharacteristic
292C3⋊D3—82no—
293#41—182no—
294#41—182no—
295#41—361no—
296#41—361no—
297C2×Q8—181no—
298C2×D4—181no—
299C2×D4—361no—
300C22×C4—361no—
301C22×C4#62611yescharacteristic
302Q16—92no—
303Q16—181no—
304SD16—182no—
305SD16—182no—
306D8—92no—
307D8—181no—
308M16—62no—
309M16—121no—
310C2×C8—121no—
311C2×C8#62411yescharacteristic
312C2×C8#62411yescharacteristic
313C2×C8#62611yescharacteristic
314C2×C8#62611yescharacteristic
315C2×C8#62611yescharacteristic
316C2×C8C2×D3211yescharacteristic
317C16—62no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—42no—
324C22×C3#80911yescharacteristic
325C22×C3#80911yescharacteristic
326C22×C3#82111yescharacteristic
327C22×C3#82111yescharacteristic
328C22×C3C2×#20411yescharacteristic
329C22×C3C2×#21511yescharacteristic
330C2×D3—124no—
331C2×D3—122no—
332C2×D3—122no—
333C2×D3—244no—
334C2×D3—242no—
335C2×D3—242no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4#80911yescharacteristic
341C3×C4#80911yescharacteristic
342C3×C4#82111yescharacteristic
343C3×C4#82111yescharacteristic
344C3×C4C2×D2411yescharacteristic
345C3×C4C2×(C2×D3)⋊C411yescharacteristic
346C3×C4C2×(C2×D3)⋊C411yescharacteristic
347C3×C4C2×#21311yescharacteristic
348Dic3—124no—
349Dic3—122no—
350Dic3—122no—
351C32#214811yescharacteristic, complemented, Sylow
352C23—361no—
353C23#371711yescharacteristic
354Q8—182no—
355Q8—361no—
356D4—182no—
357D4—362no—
358D4—362no—
359D4—361no—
360C2×C4—361no—
361C2×C4—362no—
362C2×C4—362no—
363C2×C4#371411yescharacteristic
364C2×C4#371411yescharacteristic
365C2×C4#371711yescharacteristic
366C2×C4#372211yescharacteristic
367C2×C4#372211yescharacteristic
368C2×C4C2×#62611yescharacteristic
369C8—122no—
370C8#372211yescharacteristic
371C8#372211yescharacteristic
372C8C2×#62411yescharacteristic
373C8C2×#62611yescharacteristic
374C2×C3—22no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—41no—
383C2×C3—41no—
384C2×C3C2×#80911yescharacteristic
385C2×C3C2×#82111yescharacteristic
386D3—244no—
387D3—242no—
388D3—242no—
389C22—41no—
390C22—362no—
391C22—722no—
392C22#6356411yescharacteristic
393C22#6356411yescharacteristic
394C22C2×#371711yescharacteristic
395C4—362no—
396C4#6356411yescharacteristic
397C4#6356411yescharacteristic
398C4C2×#371411yescharacteristic
399C4C2×#372211yescharacteristic
400C3—21no—
401C3#7068711yescharacteristic, complemented
402C3#7144211yescharacteristic, 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#2148
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. C2×C3×#819C2semidirect
3. C2×C3×#812C2semidirect
4. #10589131C2semidirect
5. #10589128C2semidirect
28. C2×#819D3semidirect
29. C2×#812D3semidirect
351. C32#2148semidirect
401. C3#70687semidirect
402. C3#71442semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
C2×C3×#8192
C2×C3×#8122
#105891312
#105891282
#714423
#706873