Finite Group Databasebeta

← #11775062

Subgroups — #11775062

Order 1152.

723 conjugacy classes of subgroups.

The subgroup lattice has 431 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic
2C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#4925C211yesmaximal, characteristic, complemented
4#10589151C214yesmaximal, complemented
5#70789—31nomaximal
6#69469—31nomaximal
7C2×#3828—21no—
8C2×C32×C42C2211yescharacteristic
9#64139—21no—
10#64139C2212yes—
11#64084—21no—
12#64083C411yescharacteristic, complemented
13C4×C4⋊(C3⋊D3)—21no—
14C4×C4⋊(C3⋊D3)C412yescomplemented
15#64078C411yescharacteristic, complemented
16C2×C3×C4⋊Dic3—21no—
17C2×C3×C4×Dic3—21no—
18C3×C3⋊#95C2212yes—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×C4×C3⋊C8—21no—
22#5477—31no—
23#5477—31no—
24#5477—61no—
25C3×#431—31no—
26C3×C4×C4⋊C4—31no—
27C4×C4⋊Dic3D311yescharacteristic, complemented
28#4925D311yescharacteristic, complemented
29#4470—34no—
30#4451—34no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C2×#638—22no—
35#3828—42no—
36#3828—42no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)C2×C412yes—
40C2×C4×C3⋊D3—22no—
41C2×#634—21no—
42C22×C3×Dic3—22no—
43C32×C42C2×C411yescharacteristic
44C32×C42C2×C411yescharacteristic
45C32×C42D411yescharacteristic
46C32×C42D411yescharacteristic
47#3752—22no—
48#3752—22no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)C2×C412yes—
51C3×C4⋊Dic3—24no—
52C3×C4×Dic3—42no—
53C2×C3×C3⋊C8—22no—
54#1502—91noSylow
55C2×#235—62no—
56C2×#235—61no—
57C2×#235—61no—
58C2×C3×C4⋊C4—61no—
59C2×C3×C42—21no—
60C2×C3×C42—61no—
61C2×C3×C42C2×D311yescharacteristic
62C2×C3×C42C2×D311yescharacteristic
63#930—32no—
64#930—32no—
65#930—62no—
66#930—62no—
67#930—61no—
68#930—61no—
69C2×C4⋊Dic3—21no—
70C2×C4×Dic3—21no—
71#875—62no—
72#875—61no—
73#875—61no—
74#874—31no—
75#874—31no—
76#874—61no—
77C4×D12—32no—
78C4×D12—32no—
79C4×D12—62no—
80C4×D12—62no—
81C4×D12—61no—
82C4×D12—61no—
83#869—31no—
84#869—31no—
85#869—61no—
86C3×C4⋊C8—61no—
87C3×C22⋊C8—32no—
88C3×C4×C8—61no—
89C3×#95—32no—
90C3⋊#95C2×D312yes—
91#830C2×D312yes—
92C4⋊(C3⋊C8)—21no—
93C4×C3⋊C8—21no—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—22no—
96C2×C32×C4—22no—
97C2×C32×C4—41no—
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C22⋊C411yescharacteristic
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C22⋊C411yescharacteristic
102C2×C32×C4D812yes—
103C2×C32×C4SD1612yes—
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106#638—42no—
107#638—42no—
108C2×C3⋊Dic3—22no—
109C4⋊(C3⋊D3)—42no—
110C4⋊(C3⋊D3)—42no—
111C4⋊(C3⋊D3)—42no—
112C4×C3⋊D3—44no—
113#634—42no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—42no—
117C3×C3⋊C8—42no—
118#532—91no—
119#431—31no—
120C4×C4⋊C4—31no—
121#327—94no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—21no—
125C22×C3×C4—62no—
126C22×C3×C4D1211yescharacteristic
127C22×C3×C4D1211yescharacteristic
128C22×C3×C4#6711yescharacteristic
129C22×C3×C4#6711yescharacteristic
130C22×C3×C4C22×D311yescharacteristic
131C22×C3×C4C22×D311yescharacteristic
132C2×#67—64no—
133C2×#67—62no—
134C2×#67—62no—
135C22×Dic3—22no—
136#235—124no—
137#235—124no—
138#235—122no—
139#235—122no—
140#235—122no—
141#235—122no—
142C2×D12—32no—
143C2×D12—32no—
144C2×D12—62no—
145C2×D12—62no—
146C2×D12—62no—
147C2×D12—61no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—61no—
151C2×C4×D3—64no—
152C2×C4×D3—62no—
153C2×C4×D3—62no—
154C2×Dic6—62no—
155C2×Dic6—61no—
156C2×Dic6—61no—
157C2×C3×C8—62no—
158C3×C4⋊C4—64no—
159C3×C42—21no—
160C3×C42—21no—
161C3×C42—21no—
162C3×C42—21no—
163C3×C42—122no—
164C3×C42C4×D311yescharacteristic
165C3×C42C4×D311yescharacteristic
166C3×C42C4×D311yescharacteristic
167C3×C42C4×D311yescharacteristic
168C3×C42D1211yescharacteristic
169C3×C42D1211yescharacteristic
170C3×C42#6711yescharacteristic
171C3×C42#6711yescharacteristic
172(C2×D3)⋊C4—64no—
173(C2×D3)⋊C4—64no—
174(C2×D3)⋊C4—62no—
175(C2×D3)⋊C4—62no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—62no—
178C4⋊Dic3—24no—
179C4⋊Dic3—32no—
180C4⋊Dic3—32no—
181C4⋊Dic3—62no—
182C4⋊Dic3—62no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4×Dic3—42no—
186C2×C3⋊C8—22no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32C2×C22⋊C411yescharacteristic
190C22×C32C2×D811yescharacteristic
191C22×C32C2×SD1611yescharacteristic
192C2×C3⋊D3—42no—
193C2×C3⋊D3—42no—
194C2×C3⋊D3—42no—
195C32×C4—21no—
196C32×C4—21no—
197C32×C4—21no—
198C32×C4#10212yes—
199C32×C4#10212yes—
200C32×C4#10412yes—
201C3⋊Dic3—42no—
202C3×Dic3—44no—
203C2×#41—181no—
204C4⋊Q8—91no—
205#127—91no—
206#124—181no—
207#121—92no—
208#121—181no—
209C4×D4—92no—
210C4×D4—181no—
211C2×C4⋊C4—61no—
212C2×C42—61no—
213C2×C42D3211yescharacteristic
214C4⋊C8—61no—
215C22⋊C8—32no—
216C4×C8—61no—
217#95—32no—
218C23×C3—21no—
219C23×C3C2×D1211yescharacteristic
220C23×C3C2×#6711yescharacteristic
221C22×D3—64no—
222C22×D3—62no—
223C22×D3—62no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—42no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—42no—
238C2×C3×C4—64no—
239C2×C3×C4—122no—
240C2×C3×C4—122no—
241C2×C3×C4#20412yes—
242C2×C3×C4D2412yes—
243C2×C3×C4(C2×D3)⋊C411yescharacteristic
244C2×C3×C4(C2×D3)⋊C411yescharacteristic
245C2×C3×C4(C2×D3)⋊C411yescharacteristic
246C2×C3×C4(C2×D3)⋊C411yescharacteristic
247C2×C3×C4(C2×D3)⋊C411yescharacteristic
248C2×C3×C4(C2×D3)⋊C411yescharacteristic
249C2×C3×C4(C2×D3)⋊C411yescharacteristic
250C2×C3×C4(C2×D3)⋊C411yescharacteristic
251C2×C3×C4#21312yes—
252C2×C3×C4#21512yes—
253C2×C3×C4C2×C4×D311yescharacteristic
254C2×C3×C4C2×C4×D311yescharacteristic
255C2×C3×C4C2×D1211yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257#67—124no—
258#67—124no—
259#67—122no—
260#67—122no—
261#67—122no—
262#67—122no—
263C2×Dic3—24no—
264C2×Dic3—42no—
265C2×Dic3—42no—
266C2×Dic3—64no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269D12—122no—
270D12—122no—
271D12—124no—
272D12—124no—
273D12—124no—
274D12—122no—
275D12—122no—
276D12—122no—
277D12—122no—
278C4×D3—128no—
279C4×D3—124no—
280C4×D3—124no—
281Dic6—124no—
282Dic6—122no—
283Dic6—122no—
284C3×C8—122no—
285C3⋊C8—42no—
286C2×C32—21no—
287C2×C32—21no—
288C2×C32#41011yescharacteristic
289C2×C32C2×#10211yescharacteristic
290C2×C32C2×#10411yescharacteristic
291C3⋊D3—82no—
292#41—362no—
293#41—362no—
294C2×Q8—181no—
295C2×D4—92no—
296C2×D4—182no—
297C2×D4—181no—
298C2×D4—181no—
299C22×C4—62no—
300C22×C4—182no—
301C22×C4#62611yescharacteristic
302C22×C4#62611yescharacteristic
303C22×C4C2×D3211yescharacteristic
304C2×C8—62no—
305C4⋊C4—64no—
306C4⋊C4—92no—
307C4⋊C4—181no—
308C22⋊C4—182no—
309C22⋊C4—182no—
310C42—122no—
311C42#62411yescharacteristic
312C42#62411yescharacteristic
313C42#62611yescharacteristic
314C42#62611yescharacteristic
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3C2×#20411yescharacteristic
325C22×C3C2×D2411yescharacteristic
326C22×C3C2×(C2×D3)⋊C411yescharacteristic
327C22×C3C2×(C2×D3)⋊C411yescharacteristic
328C22×C3C2×#21311yescharacteristic
329C22×C3C2×#21511yescharacteristic
330C2×D3—124no—
331C2×D3—124no—
332C2×D3—124no—
333C2×D3—122no—
334C2×D3—122no—
335C2×D3—122no—
336C2×D3—122no—
337C2×D3—122no—
338C2×D3—122no—
339C3×C4—22no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—22no—
347C3×C4—22no—
348C3×C4—22no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—124no—
352C3×C4#80512yes—
353C3×C4#80912yes—
354C3×C4#80912yes—
355C3×C4#82112yes—
356C3×C4#82112yes—
357C3×C4#82512yes—
358Dic3—44no—
359Dic3—124no—
360Dic3—122no—
361Dic3—122no—
362C32#150211yescharacteristic, complemented, Sylow
363C23—182no—
364C23C2×#62611yescharacteristic
365Q8—362no—
366D4—362no—
367D4—362no—
368D4—362no—
369D4—362no—
370D4—362no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—64no—
374C2×C4—122no—
375C2×C4—122no—
376C2×C4—182no—
377C2×C4—364no—
378C2×C4#371412yes—
379C2×C4#371712yes—
380C2×C4#372211yescharacteristic
381C2×C4#372211yescharacteristic
382C2×C4#372211yescharacteristic
383C2×C4#372211yescharacteristic
384C2×C4C2×#62411yescharacteristic
385C2×C4C2×#62611yescharacteristic
386C8—122no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—41no—
395C2×C3—41no—
396C2×C3C2×#80511yescharacteristic
397C2×C3C2×#80911yescharacteristic
398C2×C3#500611yescharacteristic
399C2×C3#500611yescharacteristic
400C2×C3C2×#82111yescharacteristic
401C2×C3C2×#82511yescharacteristic
402D3—244no—
403D3—242no—
404D3—242no—
405C22—21no—
406C22—21no—
407C22—362no—
408C22—362no—
409C22—362no—
410C22C2×#371411yescharacteristic
411C22C2×#371711yescharacteristic
412C22C2×#372211yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—124no—
417C4—362no—
418C4#6356412yes—
419C4#6356412yes—
420C4#6357012yes—
421C3—21no—
422C3#6946911yescharacteristic, complemented
423C3#7078911yescharacteristic, complemented
424C2—21no—
425C2—21no—
426C2—722no—
427C2C2×#6356411yescharacteristic
428C2C2×#6357011yescharacteristic
429C2#1059123211yescharacteristic
subgroupG/H
centerC2×C4#3722
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595948C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1502
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×C4⋊Dic3C2semidirect
3. C3×#4925C2semidirect
4. #10589151C2semidirect
12. #64083C4semidirect
14. C4×C4⋊(C3⋊D3)C4semidirect
15. #64078C4semidirect
27. C4×C4⋊Dic3D3semidirect
28. #4925D3semidirect
362. C32#1502semidirect
422. C3#69469semidirect
423. C3#70789semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×C4×C4⋊Dic32
C3×#49252
#105891512
#707893
#694693