Finite Group Databasebeta

← #10594167

Subgroups — #10594167

Order 576.

483 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64093C211yesmaximal, characteristic
2C3×#879C211yesmaximal, characteristic, complemented
3C3×#878C211yesmaximal, characteristic, complemented
4#63975C211yesmaximal, characteristic, complemented
5#63975C211yesmaximal, characteristic, complemented
6#63966C211yesmaximal, characteristic, complemented
7#63952C211yesmaximal, characteristic, complemented
8#63897C211yesmaximal, characteristic, complemented
9#63894C211yesmaximal, characteristic, complemented
10#63888C211yesmaximal, characteristic, complemented
11#63883C211yesmaximal, characteristic, complemented
12#63871C211yesmaximal, characteristic, complemented
13#63867C211yesmaximal, characteristic, complemented
14#63848C211yesmaximal, characteristic, complemented
15#63846C211yesmaximal, characteristic, complemented
16#5707—31nomaximal
17#5638—31nomaximal
18C2×#638C2211yescharacteristic
19C2×#638C2211yescharacteristic
20C2×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C4×C3⋊D3C2211yescharacteristic
22C22×C3×Dic3C2211yescharacteristic
23C2×C3×Dic6C2211yescharacteristic
24C2×#624C2211yescharacteristic
25C2×#624C2211yescharacteristic
26C2×#624C2211yescharacteristic
27C32×C22⋊C4C2211yescharacteristic
28#3752C2211yescharacteristic
29#3750C2211yescharacteristic
30C3×#217C2211yescharacteristic
31C3×#217C2211yescharacteristic
32C3×#217C2211yescharacteristic
33C3×C4⋊Dic3C2211yescharacteristic
34C3×C4⋊Dic3C2211yescharacteristic
35C3×Dic3⋊C4C2211yescharacteristic
36C3×Dic3⋊C4C2211yescharacteristic
37C3×Dic3⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39C3×C4×Dic3C2211yescharacteristic
40#3724C2211yescharacteristic
41Dic3⋊Dic3C2211yescharacteristic
42Dic3⋊Dic3C2211yescharacteristic
43Dic3⋊Dic3C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45Dic3⋊Dic3C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47#3722C2211yescharacteristic
48#3722C2211yescharacteristic
49#3722C2211yescharacteristic
50#3722C2211yescharacteristic
51#3722C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×#126—31no—
54C3×C22⋊Q8—31no—
55#946—31no—
56#946—31no—
57#929—31no—
58C4×#67—31no—
59#898—31no—
60#898—31no—
61#897—31no—
62#896—31no—
63#894—31no—
64#894—31no—
65#893—31no—
66D3×C4⋊C4—31no—
67D3×C4⋊C4—31no—
68#890—31no—
69#889—31no—
70#889—31no—
71#886—31no—
72#884—31no—
73#884—31no—
74#884—61no—
75#883—31no—
76#883—31no—
77#883—31no—
78#883—31no—
79#67⋊C4—31no—
80#879D311yescharacteristic, complemented
81#878D311yescharacteristic, complemented
82C4×D12—31no—
83#870—31no—
84C23×C32C2311yescharacteristic
85C22×C3⋊D3C2311yescharacteristic
86C22×C3⋊D3C2311yescharacteristic
87C2×C32×C4C2311yescharacteristic
88C2×C32×C4C2311yescharacteristic
89#638—22no—
90#638—41no—
91C2×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93C4⋊(C3⋊D3)—22no—
94C4×C3⋊D3—41no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C3×Dic6—41no—
105#624—22no—
106#624—41no—
107#624—41no—
108#539—91noSylow
109C2×C3×Q8—31no—
110C22×C3×C4—31no—
111C2×#67—31no—
112C2×#67—31no—
113C2×#67—31no—
114C2×#67—31no—
115C2×#67—61no—
116C2×#67—61no—
117C22×Dic3C2×D311yescharacteristic
118C2×D12—31no—
119C2×D12—31no—
120C2×D12—61no—
121C2×C4×D3—31no—
122C2×C4×D3—31no—
123C2×C4×D3—31no—
124C2×C4×D3—31no—
125C2×C4×D3—31no—
126C2×C4×D3—31no—
127C2×C4×D3—31no—
128C2×C4×D3—31no—
129C2×C4×D3—61no—
130C2×Dic6C2×D311yescharacteristic
131C3×C4⋊C4—31no—
132C3×C4⋊C4—31no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4—31no—
135C3×C4⋊C4—31no—
136C3×C4⋊C4—31no—
137C3×C22⋊C4—21no—
138C3×C22⋊C4—31no—
139C3×C22⋊C4—31no—
140C3×C22⋊C4—31no—
141C3×C22⋊C4C2×D311yescharacteristic
142C3×C22⋊C4C2×D311yescharacteristic
143C3×C42—31no—
144#217C2×D311yescharacteristic
145#217C2×D311yescharacteristic
146#217C2×D311yescharacteristic
147(C2×D3)⋊C4—31no—
148(C2×D3)⋊C4—31no—
149(C2×D3)⋊C4—31no—
150(C2×D3)⋊C4—31no—
151(C2×D3)⋊C4—31no—
152(C2×D3)⋊C4—31no—
153(C2×D3)⋊C4—31no—
154(C2×D3)⋊C4—31no—
155(C2×D3)⋊C4—31no—
156(C2×D3)⋊C4—31no—
157(C2×D3)⋊C4—31no—
158(C2×D3)⋊C4—31no—
159(C2×D3)⋊C4—61no—
160C4⋊Dic3—31no—
161C4⋊Dic3—31no—
162C4⋊Dic3—31no—
163C4⋊Dic3—31no—
164C4⋊Dic3—31no—
165C4⋊Dic3—31no—
166C4⋊Dic3C2×D311yescharacteristic
167C4⋊Dic3C2×D311yescharacteristic
168Dic3⋊C4—31no—
169Dic3⋊C4—31no—
170Dic3⋊C4—31no—
171Dic3⋊C4—31no—
172Dic3⋊C4—31no—
173Dic3⋊C4—31no—
174Dic3⋊C4—31no—
175Dic3⋊C4—31no—
176Dic3⋊C4—31no—
177Dic3⋊C4—31no—
178Dic3⋊C4—61no—
179Dic3⋊C4C2×D311yescharacteristic
180Dic3⋊C4C2×D311yescharacteristic
181Dic3⋊C4C2×D311yescharacteristic
182Dic3⋊C4C2×D311yescharacteristic
183C4×Dic3—31no—
184C4×Dic3—31no—
185C4×Dic3C2×D311yescharacteristic
186C22×C32—21no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32C2411yescharacteristic
190C2×C3⋊D3—21no—
191C2×C3⋊D3—21no—
192C2×C3⋊D3—21no—
193C2×C3⋊D3—21no—
194C2×C3⋊D3—21no—
195C2×C3⋊D3#4112yes—
196C32×C4—21no—
197C32×C4—21no—
198C3⋊Dic3—21no—
199C3⋊Dic3—21no—
200C3×Dic3—21no—
201C3×Dic3—21no—
202C3×Dic3—21no—
203C3×Dic3—21no—
204C3×Dic3—21no—
205C3×Dic3—21no—
206C3×Dic3—21no—
207C3×Dic3—21no—
208#126—31no—
209#126—91no—
210#125—91no—
211#125—91no—
212#123—91no—
213#123—91no—
214#123—91no—
215#123—91no—
216C22⋊Q8—31no—
217C22⋊Q8—91no—
218C22⋊Q8—91no—
219#121—91no—
220C4×D4—91no—
221C4×D4—91no—
222C2×C4⋊C4—91no—
223C23×C3—21no—
224C23×C3C22×D311yescharacteristic
225C23×C3C22×D311yescharacteristic
226C22×D3—31no—
227C22×D3—31no—
228C22×D3—31no—
229C22×D3—31no—
230C22×D3—61no—
231C22×D3—61no—
232C3×Q8—121no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—31no—
236C2×C3×C4—31no—
237C2×C3×C4—31no—
238C2×C3×C4—31no—
239C2×C3×C4—31no—
240C2×C3×C4—31no—
241C2×C3×C4—31no—
242C2×C3×C4—31no—
243C2×C3×C4—121no—
244C2×C3×C4C22×D311yescharacteristic
245C2×C3×C4C22×D311yescharacteristic
246C2×C3×C4C22×D311yescharacteristic
247C2×C3×C4C22×D311yescharacteristic
248#67—62no—
249#67—62no—
250#67—122no—
251#67—121no—
252#67—121no—
253#67—122no—
254C2×Dic3—31no—
255C2×Dic3—31no—
256C2×Dic3—31no—
257C2×Dic3—31no—
258C2×Dic3—41no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3C22×D311yescharacteristic
262C2×Dic3C22×D311yescharacteristic
263C2×Dic3C22×D311yescharacteristic
264C2×Dic3C22×D311yescharacteristic
265C2×Dic3C22×D311yescharacteristic
266C2×Dic3C22×D311yescharacteristic
267C2×Dic3C22×D311yescharacteristic
268C2×Dic3C22×D311yescharacteristic
269D12—62no—
270D12—62no—
271D12—122no—
272C4×D3—62no—
273C4×D3—62no—
274C4×D3—121no—
275C4×D3—121no—
276C4×D3—121no—
277C4×D3—121no—
278C4×D3—121no—
279C4×D3—121no—
280C4×D3—122no—
281Dic6—41no—
282C2×C32—41no—
283C2×C32C2×#4111yescharacteristic
284C2×C32H(5,𝔽2)11yescharacteristic
285C2×C322−1+411yescharacteristic
286C3⋊D3—22no—
287C3⋊D3—41no—
288C2×Q8—31no—
289C2×D4—91no—
290C2×D4—91no—
291C2×D4—91no—
292C22×C4—31no—
293C22×C4—91no—
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—91no—
297C4⋊C4—31no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—91no—
304C4⋊C4—91no—
305C4⋊C4—91no—
306C4⋊C4—91no—
307C4⋊C4—91no—
308C4⋊C4—91no—
309C4⋊C4—91no—
310C4⋊C4—91no—
311C22⋊C4—31no—
312C22⋊C4—31no—
313C22⋊C4—31no—
314C22⋊C4—91no—
315C22⋊C4—91no—
316C22⋊C4—91no—
317C22⋊C4—91no—
318C22⋊C4—91no—
319C22⋊C4—91no—
320C22⋊C4D3211yescharacteristic
321C42—31no—
322C42—91no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3C23×D311yescharacteristic
334C22×C3C23×D311yescharacteristic
335C2×D3—32no—
336C2×D3—32no—
337C2×D3—62no—
338C2×D3—61no—
339C2×D3—61no—
340C2×D3—61no—
341C2×D3—61no—
342C2×D3—61no—
343C2×D3—61no—
344C2×D3—61no—
345C2×D3—61no—
346C2×D3—61no—
347C2×D3—61no—
348C2×D3—121no—
349C2×D3—121no—
350C2×D3—121no—
351C2×D3—121no—
352C2×D3—121no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—61no—
360C3×C4—61no—
361C3×C4—61no—
362C3×C4—61no—
363C3×C4—61no—
364C3×C4—61no—
365C3×C4—61no—
366C3×C4—61no—
367Dic3—21no—
368Dic3—21no—
369Dic3—21no—
370Dic3—21no—
371Dic3—21no—
372Dic3—21no—
373Dic3—21no—
374Dic3—21no—
375Dic3—62no—
376Dic3—61no—
377Dic3—61no—
378Dic3—61no—
379Dic3—61no—
380Dic3—121no—
381C32#53911yescharacteristic, complemented, Sylow
382C23—91no—
383C23—91no—
384C23C2×D3211yescharacteristic
385Q8—121no—
386D4—182no—
387D4—182no—
388D4—361no—
389C2×C4—31no—
390C2×C4—31no—
391C2×C4—31no—
392C2×C4—31no—
393C2×C4—31no—
394C2×C4—31no—
395C2×C4—31no—
396C2×C4—31no—
397C2×C4—91no—
398C2×C4—91no—
399C2×C4—121no—
400C2×C4—182no—
401C2×C4—361no—
402C2×C4—361no—
403C2×C4—361no—
404C2×C4C2×D3211yescharacteristic
405C2×C4C2×D3211yescharacteristic
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—41no—
410C2×C3—41no—
411C2×C3—81no—
412C2×C3#100411yescharacteristic
413C2×C3#100711yescharacteristic
414C2×C3D3×#4111yescharacteristic
415C2×C3D3×#4111yescharacteristic
416C2×C3#100911yescharacteristic
417C2×C3#101011yescharacteristic
418D3—62no—
419D3—62no—
420D3—122no—
421D3—121no—
422D3—121no—
423D3—241no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—92no—
428C22—181no—
429C22—181no—
430C22—181no—
431C22—181no—
432C22—181no—
433C22C22×D3211yescharacteristic
434C4—21no—
435C4—21no—
436C4—61no—
437C4—61no—
438C4—61no—
439C4—61no—
440C4—61no—
441C4—61no—
442C4—61no—
443C4—61no—
444C4—181no—
445C4—181no—
446C3—21no—
447C3#563811yescharacteristic, complemented
448C3#570711yescharacteristic, complemented
449C2—41no—
450C2—182no—
451C2—361no—
452C2#6429711yescharacteristic
453C2#6431211yescharacteristic
454C2#6431411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
prime radical#64093C2
hypercenterC22⋊C4D32
hypocenterC32#539
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#879C2semidirect
3. C3×#878C2semidirect
4. #63975C2semidirect
5. #63975C2semidirect
6. #63966C2semidirect
7. #63952C2semidirect
8. #63897C2semidirect
9. #63894C2semidirect
10. #63888C2semidirect
11. #63883C2semidirect
12. #63871C2semidirect
13. #63867C2semidirect
14. #63848C2semidirect
15. #63846C2semidirect
80. #879D3semidirect
81. #878D3semidirect
381. C32#539semidirect
447. C3#5638semidirect
448. C3#5707semidirect

Maximal subgroups

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

subgroupindex
#640932
C3×#8792
C3×#8782
#639752
#639662
#639522
#638972
#638942
#638882
#638832
#638712
#638672
#638482
#638462
#57073
#56383