Finite Group Databasebeta

← #11775277

Subgroups — #11775277

Order 1152.

524 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594949C211yesmaximal, characteristic
2C3×#4719C211yesmaximal, characteristic, complemented
3#10591242C211yesmaximal, characteristic, complemented
4#10589333C211yesmaximal, characteristic, complemented
5C3×#4470C211yesmaximal, characteristic
6#10589154C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic
8#70833—31nomaximal
9#68279—31nomaximal
10#64133C2211yescharacteristic
11C3×#930C2211yescharacteristic
12C2×C3×C4×Dic3C2211yescharacteristic
13Dic3×#67—21no—
14C2×Dic3⋊Dic3—21no—
15#63961—21no—
16C2×Dic32—21no—
17Dic3×D12C411yescharacteristic, complemented
18#63877—21no—
19#63869C411yescharacteristic, complemented
20#63860C411yescharacteristic, complemented
21#63859—21no—
22#63844C411yescharacteristic, complemented
23C32×C22⋊C8C2211yescharacteristic
24#63658C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#815—21no—
28C3×Dic3⋊C8—21no—
29#5600—31no—
30#5479—31no—
31C3×#432—31no—
32C4×C4⋊Dic3—31no—
33#4719D311yescharacteristic, complemented
34#4649—31no—
35C3×#327—31no—
36#4537—31no—
37#4470—31no—
38#4470D311yescharacteristic
39#4467—31no—
40#4467—31no—
41#4467—31no—
42#4467—61no—
43#4452—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×#634C2×C411yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12C2×C411yescharacteristic
52C2×D3×Dic3—21no—
53C2×C32×C8—21no—
54#3757—21no—
55C4⋊(C3⋊Dic3)C2×C411yescharacteristic
56#3750—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3C2×C411yescharacteristic
59C3×C4×Dic3C2×C411yescharacteristic
60C3×C4×Dic3C2×C411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65#3724—21no—
66Dic3⋊Dic3—24no—
67Dic3⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72Dic32—42no—
73#1509—91noSylow
74C3×#121—31no—
75C2×C3×C42—31no—
76#936—31no—
77#935—61no—
78D4×Dic3—31no—
79D4×Dic3—61no—
80#930C2×D311yescharacteristic
81#929—61no—
82C4×#67—61no—
83C2×C4⋊Dic3—61no—
84#924—31no—
85#924—31no—
86#924—61no—
87C2×Dic3⋊C4—61no—
88C2×C4×Dic3—61no—
89C2×C4×Dic3—61no—
90C2×C4×Dic3C2×D311yescharacteristic
91#890—31no—
92#887—31no—
93#879—61no—
94#877—61no—
95#876—61no—
96#875—31no—
97C4×D12—31no—
98#872—61no—
99#870—31no—
100C4×Dic6—31no—
101C3×C4⋊C8—61no—
102C3×C22⋊C8—21no—
103C3×C22⋊C8—31no—
104C3×C22⋊C8C2×D311yescharacteristic
105C3×C22⋊C8C2×D311yescharacteristic
106C3×#97—61no—
107C3×#95—31no—
108C3⋊#95—31no—
109C3⋊#95—31no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830C2×D311yescharacteristic
113#815—21no—
114Dic3⋊C8—21no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C2×C32×C4—41no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125#634—41no—
126C3×#67—41no—
127C3×#67—41no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3C22⋊C411yescharacteristic
138C2×C3×Dic3C22⋊C411yescharacteristic
139C3×D12—41no—
140D3×Dic3—42no—
141C32×C8—41no—
142C3×C3⋊C8—41no—
143#529—91no—
144#432—31no—
145C4×C4⋊C4—91no—
146#328—91no—
147#328—91no—
148#327—31no—
149#327—91no—
150C2×C3×D4—31no—
151C2×C3×D4—61no—
152C22×C3×C4—21no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C2×#67—21no—
159C22×Dic3—21no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—121no—
164C22×Dic3D1211yescharacteristic
165C22×Dic3D1211yescharacteristic
166C2×D12C4×D311yescharacteristic
167C2×C4×D3—61no—
168C2×Dic6—31no—
169C2×Dic6—31no—
170C2×Dic6—61no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—41no—
174C2×C3×C8—61no—
175C3×C4⋊C4—31no—
176C3×C22⋊C4—61no—
177C3×C42—31no—
178C3×C42—31no—
179C3×C42—31no—
180C3×C42—31no—
181#217—61no—
182#217—61no—
183#217—61no—
184#217—61no—
185#217—61no—
186#217—121no—
187(C2×D3)⋊C4—21no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—61no—
190(C2×D3)⋊C4—61no—
191C4⋊Dic3—31no—
192C4⋊Dic3—31no—
193C4⋊Dic3—61no—
194C4⋊Dic3—64no—
195C4⋊Dic3—61no—
196C4⋊Dic3C4×D311yescharacteristic
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—64no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—121no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—122no—
209C4×Dic3—122no—
210C4×Dic3C4×D311yescharacteristic
211C4×Dic3C4×D311yescharacteristic
212C4×Dic3#6711yescharacteristic
213C4×Dic3#6711yescharacteristic
214C2×C3⋊C8—21no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32C2×C22⋊C411yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C22×C32#13711yescharacteristic
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C32×C4—21no—
224C32×C4—21no—
225C3⋊Dic3—42no—
226C3⋊Dic3—41no—
227C3⋊Dic3—41no—
228C3×Dic3—21no—
229C3×Dic3—21no—
230C3×Dic3—21no—
231C3×Dic3—42no—
232C3×Dic3—41no—
233C3×Dic3#10412yes—
234#126—181no—
235#125—91no—
236#124—91no—
237#123—181no—
238C22⋊Q8—91no—
239#121—31no—
240C4×Q8—91no—
241C4×D4—91no—
242C4×D4—181no—
243#117—181no—
244C2×C4⋊C4—181no—
245C2×C42—31no—
246C2×C42—181no—
247C4⋊C8—61no—
248C22⋊C8—31no—
249C22⋊C8D3211yescharacteristic
250#97—61no—
251#95—31no—
252#95—91no—
253C23×C3—21no—
254C23×C3—61no—
255C23×C3C2×D1211yescharacteristic
256C23×C3D3×D411yescharacteristic
257C22×D3—21no—
258C3×D4—121no—
259C3×D4—121no—
260C3×D4—121no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—31no—
264C2×C3×C4—31no—
265C2×C3×C4—31no—
266C2×C3×C4—31no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—62no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—62no—
273C2×C3×C4—61no—
274C2×C3×C4—81no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4C2×C4×D311yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281#67—41no—
282#67—41no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—22no—
286C2×Dic3—22no—
287C2×Dic3—21no—
288C2×Dic3—41no—
289C2×Dic3—41no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298C2×Dic3—122no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—121no—
303C2×Dic3—122no—
304C2×Dic3—241no—
305C2×Dic3—241no—
306C2×Dic3(C2×D3)⋊C411yescharacteristic
307C2×Dic3(C2×D3)⋊C411yescharacteristic
308C2×Dic3(C2×D3)⋊C411yescharacteristic
309C2×Dic3(C2×D3)⋊C411yescharacteristic
310D12—41no—
311C4×D3—122no—
312Dic6—121no—
313Dic6—121no—
314Dic6—241no—
315C3×C8—41no—
316C3×C8—41no—
317C3×C8—81no—
318C3×C8—121no—
319C3⋊C8—41no—
320C2×C32—21no—
321C2×C32—21no—
322C2×C32#41011yescharacteristic
323C2×C32#41711yescharacteristic
324C2×C32C2×#10411yescharacteristic
325C3×D3—81no—
326C2×Q8—91no—
327C2×D4—31no—
328C2×D4—61no—
329C22×C4—31no—
330C22×C4—31no—
331C22×C4—61no—
332C22×C4—181no—
333C22×C4—181no—
334C22×C4C2×D3211yescharacteristic
335C2×C8—21no—
336C2×C8—61no—
337C4⋊C4—31no—
338C4⋊C4—91no—
339C4⋊C4—181no—
340C4⋊C4—181no—
341C4⋊C4—181no—
342C4⋊C4—184no—
343C4⋊C4—181no—
344C22⋊C4—61no—
345C22⋊C4—181no—
346C22⋊C4—181no—
347C22⋊C4—181no—
348C22⋊C4—181no—
349C42—31no—
350C42—31no—
351C42—31no—
352C42—31no—
353C42—181no—
354C42—362no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—121no—
365C22×C3—121no—
366C22×C3—121no—
367C22×C3D3×C22⋊C411yescharacteristic
368C22×C3#90811yescharacteristic
369C22×C3#90911yescharacteristic
370C22×C3#91111yescharacteristic
371C22×C3#91511yescharacteristic
372C22×C3C2×(C2×D3)⋊C411yescharacteristic
373C2×D3—41no—
374C2×D3—41no—
375C2×D3—41no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—32no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—61no—
384C3×C4—61no—
385C3×C4—61no—
386C3×C4—122no—
387C3×C4—121no—
388Dic3—21no—
389Dic3—21no—
390Dic3—21no—
391Dic3—42no—
392Dic3—41no—
393Dic3—122no—
394Dic3—122no—
395Dic3—121no—
396Dic3—121no—
397Dic3—121no—
398Dic3—121no—
399Dic3—241no—
400Dic3—241no—
401Dic3—242no—
402Dic3#82512yes—
403C32#150911yescharacteristic, complemented, Sylow
404C23—61no—
405C23D3×D1211yescharacteristic
406Q8—361no—
407D4—121no—
408D4—121no—
409D4—121no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—41no—
415C2×C4—62no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—62no—
419C2×C4—61no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—182no—
423C2×C4—181no—
424C2×C4—181no—
425C2×C4—362no—
426C2×C4—361no—
427C2×C4—361no—
428C2×C4C4×D3211yescharacteristic
429C2×C4D3×#6711yescharacteristic
430C8—41no—
431C8—121no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—241no—
442C2×C3#474011yescharacteristic
443C2×C3#477111yescharacteristic
444C2×C3D3×#10411yescharacteristic
445C2×C3#500611yescharacteristic
446C2×C3#513311yescharacteristic
447C2×C3C2×#82511yescharacteristic
448D3—81no—
449C22—21no—
450C22—21no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22#6379511yescharacteristic
455C22#6380011yescharacteristic
456C22D3×(C2×D3)⋊C411yescharacteristic
457C4—21no—
458C4—21no—
459C4—32no—
460C4—61no—
461C4—61no—
462C4—61no—
463C4—122no—
464C4—121no—
465C4—362no—
466C4—361no—
467C4—361no—
468C3—21no—
469C3#6827911yescharacteristic, complemented
470C3#7083311yescharacteristic, complemented
471C2—21no—
472C2—21no—
473C2—241no—
474C2#1059040511yescharacteristic
475C2#1059067011yescharacteristic
476C2D3×#82511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C22
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1509
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4719C2semidirect
3. #10591242C2semidirect
4. #10589333C2semidirect
6. #10589154C2semidirect
17. Dic3×D12C4semidirect
19. #63869C4semidirect
20. #63860C4semidirect
22. #63844C4semidirect
33. #4719D3semidirect
403. C32#1509semidirect
469. C3#68279semidirect
470. C3#70833semidirect

Maximal subgroups

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

subgroupindex
#105949492
C3×#47192
#105912422
#105893332
C3×#44702
#105891542
#105891502
#708333
#682793