Finite Group Databasebeta

← #11775879

Subgroups — #11775879

Order 1152.

547 conjugacy classes of subgroups.

The subgroup lattice has 473 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5668C211yesmaximal, characteristic
2D3×#803C211yesmaximal, characteristic, complemented
3#10590262C211yesmaximal, characteristic, complemented
4#10589406C211yesmaximal, characteristic, complemented
5C3×#4540C211yesmaximal, characteristic, complemented
6#10589086C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71798—31nomaximal
9#68345—31nomaximal
10C2×C3×#239C411yescharacteristic
11C2×C3×#237C411yescharacteristic
12C32×#124C2211yescharacteristic
13C3×#944C411yescharacteristic
14C3×#940C411yescharacteristic
15C3×#884—21no—
16C3×#884—21no—
17C3×#67⋊C4—21no—
18C3×#67⋊C4—21no—
19C3×#875C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C2×D3×C3⋊C8—21no—
22#63630C2211yescharacteristic
23#63630C2211yescharacteristic
24C3×#803C2211yescharacteristic
25C3×#803C2211yescharacteristic
26Dic3⋊(C3⋊C8)—21no—
27(C2×D3)⋊(C3⋊C8)—21no—
28#63554—21no—
29C3×#532—31no—
30#5668D311yescharacteristic
31#4926—31no—
32C2×#803—31no—
33#4705—31no—
34D3×#97—31no—
35C3×#329—31no—
36#4540—31no—
37#4540—31no—
38#4540—31no—
39#4540—31no—
40#4540—61no—
41#4540D311yescharacteristic, complemented
42#4464—31no—
43#4464—31no—
44C2×C32×Q8C2×C411yescharacteristic
45C2×C32×D4C2×C411yescharacteristic
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C3×#239—42no—
51C3×#237—42no—
52C2×C3×D12—21no—
53C2×C3×D12C2×C411yescharacteristic
54C2×C3×C4×D3—21no—
55C2×C3×C4×D3C2×C411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×C3×C4×D3D411yescharacteristic
58C2×C3×Dic6C2×C411yescharacteristic
59C32×C22⋊C4—21no—
60C32×C22⋊C4—21no—
61C32×C42C2311yescharacteristic
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73D3×C3⋊C8—24no—
74#1530—91noSylow
75C2×C3×#41—31no—
76C2×C3×#41—31no—
77C2×#239Dic311yescharacteristic
78C2×#237Dic311yescharacteristic
79C3×C4⋊Q8—31no—
80C3×#127—31no—
81C3×#124—21no—
82C3×#124—31no—
83C3×#124C2×D311yescharacteristic
84C3×#124C2×D311yescharacteristic
85C3×#121—61no—
86C3×#121—61no—
87C3×C4×D4—61no—
88C3×C4×D4—61no—
89C2×C3×C42—31no—
90#944Dic311yescharacteristic
91#940Dic311yescharacteristic
92C22×C3⋊C8—61no—
93C2×D3×C8—61no—
94#884—21no—
95#884—21no—
96#67⋊C4—21no—
97#67⋊C4—21no—
98#875C2×D311yescharacteristic
99C42×D3C2×D311yescharacteristic
100C3×#97—31no—
101C3×#97—31no—
102#830—61no—
103(C2×D3)⋊C8—61no—
104#815—61no—
105Dic3⋊C8—61no—
106C4⋊(C3⋊C8)—61no—
107#803—31no—
108#803—31no—
109#803—31no—
110#803—31no—
111#803—61no—
112#803—61no—
113#803—61no—
114#803C2×D311yescharacteristic
115#803C2×D311yescharacteristic
116C23×C32—21no—
117C22×C3×D3—21no—
118C22×C3×D3C22⋊C411yescharacteristic
119C32×Q8—41no—
120C32×D4—41no—
121C2×C32×C4—21no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C3×#67—42no—
126C3×#67—42no—
127C3×#67—42no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—42no—
130C2×C3×Dic3C22⋊C411yescharacteristic
131C2×C3×Dic3C22⋊C411yescharacteristic
132C2×C3×Dic3C22⋊C411yescharacteristic
133C3×D12—41no—
134C3×D12—42no—
135C3×C4×D3—22no—
136C3×C4×D3—22no—
137C3×C4×D3—41no—
138C3×C4×D3—42no—
139C3×Dic6—41no—
140C3⋊(C3⋊C8)—22no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—22no—
143C3×C3⋊C8—41no—
144#532—31no—
145#432—91no—
146C2×#97—91no—
147#329—31no—
148#329—91no—
149#329—91no—
150#329—91no—
151C3×#41—122no—
152C3×#41—122no—
153C2×C3×Q8—21no—
154C2×C3×Q8—31no—
155C2×C3×Q8C4×D311yescharacteristic
156C2×C3×Q8C2×Dic311yescharacteristic
157C2×C3×D4—21no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4C4×D311yescharacteristic
164C2×C3×D4C2×Dic311yescharacteristic
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—61no—
169C22×C3×C4—61no—
170C2×#67—21no—
171C2×#67—21no—
172C2×#67—21no—
173C22×Dic3—21no—
174#239—42no—
175#237—42no—
176C2×D12—21no—
177C2×D12C2×Dic311yescharacteristic
178C2×C4×D3—21no—
179C2×C4×D3C2×Dic311yescharacteristic
180C2×C4×D3#6711yescharacteristic
181C2×C4×D3#6711yescharacteristic
182C2×Dic6C2×Dic311yescharacteristic
183C2×C3×C8—61no—
184C2×C3×C8—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—21no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—41no—
192C3×C22⋊C4—41no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C42—21no—
196C3×C42—31no—
197C3×C42—31no—
198C3×C42—31no—
199C3×C42C22×D311yescharacteristic
200C3×C42C22×D311yescharacteristic
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205C4×Dic3C2×Dic311yescharacteristic
206C4×Dic3#6711yescharacteristic
207C4×Dic3#6711yescharacteristic
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—64no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—121no—
216C2×C3⋊C8—121no—
217D3×C8—64no—
218C22×C32—41no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32C2×C22⋊C411yescharacteristic
222C2×C3×D3—21no—
223C2×C3×D3—21no—
224C2×C3×D3—41no—
225C2×C3×D3—41no—
226C2×C3×D3—41no—
227C2×C3×D3#10012yes—
228C32×C4—21no—
229C32×C4—21no—
230C32×C4—21no—
231C32×C4—41no—
232C3×Dic3—21no—
233C3×Dic3—21no—
234C3×Dic3—41no—
235C3×Dic3#10412yes—
236C2×#41—31no—
237C2×#41—31no—
238C22×C8—181no—
239C4⋊Q8—31no—
240#127—31no—
241#124—31no—
242#124D3211yescharacteristic
243#121—61no—
244#121—61no—
245C4×D4—61no—
246C4×D4—61no—
247C2×C42—31no—
248C4⋊C8—181no—
249C22⋊C8—181no—
250#97—31no—
251#97—31no—
252#97—91no—
253#97—91no—
254#97—181no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—31no—
258C23×C3—41no—
259C23×C3—61no—
260C22×D3—21no—
261C22×D3#21711yescharacteristic
262C3×Q8—41no—
263C3×Q8—41no—
264C3×Q8—81no—
265C3×Q8—121no—
266C3×D4—41no—
267C3×D4—41no—
268C3×D4—81no—
269C3×D4—121no—
270C3×D4—122no—
271C3×D4—122no—
272C3×D4—122no—
273C3×D4—122no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—31no—
280C2×C3×C4—31no—
281C2×C3×C4—31no—
282C2×C3×C4—41no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4—61no—
286C2×C3×C4—121no—
287C2×C3×C4—122no—
288C2×C3×C4—122no—
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4C22×Dic311yescharacteristic
293C2×C3×C4C2×#6711yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295#67—42no—
296#67—42no—
297#67—42no—
298C2×Dic3—21no—
299C2×Dic3—42no—
300C2×Dic3#21711yescharacteristic
301C2×Dic3#21711yescharacteristic
302C2×Dic3#21711yescharacteristic
303D12—41no—
304D12—42no—
305C4×D3—22no—
306C4×D3—22no—
307C4×D3—41no—
308C4×D3—42no—
309Dic6—41no—
310C3×C8—62no—
311C3×C8—121no—
312C3⋊C8—22no—
313C3⋊C8—41no—
314C3⋊C8—62no—
315C3⋊C8—62no—
316C3⋊C8—122no—
317C3⋊C8—121no—
318C3⋊C8—121no—
319C3⋊C8—122no—
320C2×C32—81no—
321C2×C32C2×#10011yescharacteristic
322C2×C32C2×#10411yescharacteristic
323C2×C32#42111yescharacteristic
324C3×D3—22no—
325C3×D3—81no—
326#41—122no—
327#41—122no—
328C2×Q8—31no—
329C2×Q8D3×Dic311yescharacteristic
330C2×D4—31no—
331C2×D4—61no—
332C2×D4—61no—
333C2×D4—61no—
334C2×D4—61no—
335C2×D4D3×Dic311yescharacteristic
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—31no—
339C22×C4—61no—
340C22×C4—61no—
341C2×C8—61no—
342C2×C8—61no—
343C2×C8—184no—
344C2×C8—181no—
345C2×C8—181no—
346C4⋊C4—61no—
347C4⋊C4—61no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—61no—
351C22⋊C4—61no—
352C42—31no—
353C42—31no—
354C42—31no—
355C42C2×D3211yescharacteristic
356C22×C3—21no—
357C22×C3—32no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—81no—
367C22×C3—81no—
368C22×C3—81no—
369C22×C3—121no—
370C22×C3—121no—
371C22×C3—121no—
372C22×C3D3×C22⋊C411yescharacteristic
373C22×C3C2×#21711yescharacteristic
374C2×D3—21no—
375C2×D3—21no—
376C2×D3—41no—
377C2×D3—41no—
378C2×D3—41no—
379C2×D3#83312yes—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—32no—
387C3×C4—41no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—41no—
392C3×C4—61no—
393C3×C4—61no—
394C3×C4—81no—
395C3×C4—121no—
396Dic3—21no—
397Dic3—21no—
398Dic3—41no—
399Dic3#83712yes—
400C32#153011yescharacteristic, complemented, Sylow
401C23—21no—
402C23—31no—
403C23—61no—
404Q8—41no—
405Q8—121no—
406D4—41no—
407D4—121no—
408D4—122no—
409D4—122no—
410D4—122no—
411D4—122no—
412C2×C4—21no—
413C2×C4—31no—
414C2×C4—31no—
415C2×C4—31no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—61no—
419C2×C4—121no—
420C2×C4—122no—
421C2×C4—122no—
422C2×C4C2×D3×Dic311yescharacteristic
423C2×C4D3×#6711yescharacteristic
424C2×C4D3×#6711yescharacteristic
425C8—62no—
426C8—121no—
427C8—182no—
428C8—361no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—62no—
433C2×C3—81no—
434C2×C3—81no—
435C2×C3—161no—
436C2×C3—241no—
437C2×C3D3×#10011yescharacteristic
438C2×C3D3×#10411yescharacteristic
439C2×C3#482111yescharacteristic
440C2×C3C2×#83311yescharacteristic
441C2×C3C2×#83711yescharacteristic
442C2×C3#523611yescharacteristic
443D3—22no—
444D3—81no—
445C22—32no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—61no—
450C22—61no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22D3×#21711yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—32no—
459C4—41no—
460C4—61no—
461C4—61no—
462C4—121no—
463C3—21no—
464C3#6834511yescharacteristic, complemented
465C3#7179811yescharacteristic, complemented
466C2—62no—
467C2—81no—
468C2—241no—
469C2D3×#83311yescharacteristic
470C2D3×#83711yescharacteristic
471C2#1059167011yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#124C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5668C2
cosocleC32×C42C23
hypercenter#124D32
hypocenterC32#1530
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. D3×#803C2semidirect
3. #10590262C2semidirect
4. #10589406C2semidirect
5. C3×#4540C2semidirect
6. #10589086C2semidirect
7. #10589086C2semidirect
41. #4540D3semidirect
400. C32#1530semidirect
464. C3#68345semidirect
465. C3#71798semidirect

Maximal subgroups

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

subgroupindex
C3×#56682
D3×#8032
#105902622
#105894062
C3×#45402
#105890862
#717983
#683453