Finite Group Databasebeta

← #11872415

Subgroups — #11872415

Order 1152.

1116 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595994C211yesmaximal, characteristic
2#10595989C211yesmaximal, characteristic, complemented
3C32×#433C211yesmaximal, characteristic, complemented
4#10592548C211yesmaximal, characteristic, complemented
5#10592546C211yesmaximal, characteristic, complemented
6#10592540C211yesmaximal, characteristic, complemented
7#10592528C211yesmaximal, characteristic, complemented
8#10592432C211yesmaximal, characteristic
9#10592432C211yesmaximal, characteristic
10#10592421C211yesmaximal, characteristic, complemented
11#10592420C211yesmaximal, characteristic, complemented
12#10592415C211yesmaximal, characteristic, complemented
13#10592409C211yesmaximal, characteristic, complemented
14C4×#3746C211yesmaximal, characteristic, complemented
15C4×#3744C211yesmaximal, characteristic, complemented
16#79385—34nomaximal
17C2×#3828C2211yescharacteristic
18C32×#117C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20#64133C2211yescharacteristic
21#64133C2211yescharacteristic
22C2×#3746C2211yescharacteristic
23C2×#3746C2211yescharacteristic
24C2×#3744C2211yescharacteristic
25C2×#3744C2211yescharacteristic
26#64101—21no—
27C4⋊C4×C3⋊D3—21no—
28#64098—21no—
29#64098—21no—
30#64090—21no—
31#64090—21no—
32#64088—21no—
33#64088—21no—
34C4×C4⋊(C3⋊D3)C2211yescharacteristic
35C4×C4⋊(C3⋊D3)C2211yescharacteristic
36#64079C2211yescharacteristic
37#64078C2211yescharacteristic
38C4×#634C2211yescharacteristic
39C4×#634C2211yescharacteristic
40C4×#634C2211yescharacteristic
41C4×#634C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C32×#97C2211yescharacteristic
47C32×C4×C8C2211yescharacteristic
48#63648C2211yescharacteristic
49#63648C2211yescharacteristic
50#63645C2211yescharacteristic
51#63645C2211yescharacteristic
52#63644C2211yescharacteristic
53#63644C2211yescharacteristic
54#63643C2211yescharacteristic
55#63643C2211yescharacteristic
56#63643C2211yescharacteristic
57#63643C2211yescharacteristic
58#63643C2211yescharacteristic
59#63643C2211yescharacteristic
60#5523—34no—
61#5518—34no—
62C3×#433D314yescomplemented
63#4849—34no—
64#4847—34no—
65#4841—34no—
66#4829—34no—
67#4733—34no—
68#4733—34no—
69#4722—34no—
70#4721—34no—
71#4716—34no—
72#4710—34no—
73C4×Dic12—34no—
74C4×#204—34no—
75C22×C32×C4C2311yescharacteristic
76C2×#638—21no—
77C22×C3⋊Dic3—21no—
78#3828—22no—
79#3828—22no—
80C2×C4⋊(C3⋊D3)C2311yescharacteristic
81C2×C4×C3⋊D3—21no—
82C2×C4×C3⋊D3—21no—
83C2×C4×C3⋊D3—21no—
84C2×#634C2311yescharacteristic
85C2×#634C2311yescharacteristic
86C2×#634C2311yescharacteristic
87C2×C32×C8C2311yescharacteristic
88C2×C32×C8C2311yescharacteristic
89C2×C32×C8C2311yescharacteristic
90C2×C32×C8C2311yescharacteristic
91C32×C4⋊C4D411yescharacteristic
92C32×C4⋊C4D411yescharacteristic
93C32×C22⋊C4D411yescharacteristic
94C32×C22⋊C4D411yescharacteristic
95C32×C42C2311yescharacteristic
96C32×C42C2311yescharacteristic
97#3757—21no—
98#3757—21no—
99#3752—21no—
100#3752—21no—
101C4⋊(C3⋊Dic3)—21no—
102C4⋊(C3⋊Dic3)—21no—
103C4⋊(C3⋊Dic3)—21no—
104C4⋊(C3⋊Dic3)C2311yescharacteristic
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109#3750—21no—
110#3750—21no—
111#3750—21no—
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120#3746—22no—
121#3746—22no—
122#3744—22no—
123#3744—22no—
124#3120—91noSylow
125C2×#235—34no—
126C3×#117C2×D314yes—
127C2×C4⋊Dic3—34no—
128#924—34no—
129#924—34no—
130C2×Dic12—34no—
131C2×Dic12—34no—
132C2×#204—34no—
133C2×#204—34no—
134#892—64no—
135D3×C4⋊C4—64no—
136#889—64no—
137#889—64no—
138#67⋊C4—64no—
139#67⋊C4—64no—
140#879—64no—
141#879—64no—
142C4×D12—34no—
143C4×D12—34no—
144#870—34no—
145#869—34no—
146C4×Dic6—34no—
147C4×Dic6—34no—
148C4×Dic6—34no—
149C4×Dic6—34no—
150C3×C4⋊C8C2×D314yes—
151C3×C4⋊C8C2×D314yes—
152C3×C22⋊C8C2×D314yes—
153C3×C22⋊C8C2×D314yes—
154C3×#97C2×D314yes—
155C3×C4×C8C2×D314yes—
156#821—34no—
157#821—34no—
158#818—34no—
159#818—34no—
160#817—34no—
161#817—34no—
162#816—34no—
163#816—34no—
164#816—34no—
165#816—34no—
166#816—34no—
167#816—34no—
168C23×C32C2×D411yescharacteristic
169C22×C3⋊D3—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178#638—24no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—81no—
187C4⋊(C3⋊D3)—21no—
188C4⋊(C3⋊D3)#4112yes—
189C4×C3⋊D3—24no—
190C4×C3⋊D3—81no—
191C4×C3⋊D3—81no—
192#634—21no—
193#634—21no—
194#634—21no—
195#634—21no—
196#634—21no—
197#634#4112yes—
198C32×C8—21no—
199C32×C8—21no—
200C32×C8—21no—
201C32×C8—21no—
202#541—91no—
203#520—91no—
204#484—91no—
205#483—91no—
206#479—91no—
207#478—91no—
208#462—91no—
209#461—91no—
210#452—91no—
211#452—91no—
212#441—91no—
213#440—91no—
214C4×Q16—91no—
215C4×SD16—91no—
216#433C3⋊D311yescharacteristic, complemented
217C22×C3×C4C22×D314yes—
218C2×#67—64no—
219C22×Dic3—64no—
220#235—68no—
221#235—68no—
222C2×D12—34no—
223C2×C4×D3—64no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×Dic6—34no—
227C2×Dic6—34no—
228C2×Dic6—34no—
229C2×C3×C8C22×D314yes—
230C2×C3×C8C22×D314yes—
231C2×C3×C8C22×D314yes—
232C2×C3×C8C22×D314yes—
233C3×C4⋊C4D1214yes—
234C3×C4⋊C4D1214yes—
235C3×C22⋊C4D1214yes—
236C3×C22⋊C4D1214yes—
237C3×C42C22×D314yes—
238C3×C42C22×D314yes—
239#217—64no—
240#217—64no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—64no—
243C4⋊Dic3—34no—
244C4⋊Dic3—34no—
245C4⋊Dic3—34no—
246C4⋊Dic3—34no—
247C4⋊Dic3—64no—
248C4⋊Dic3—64no—
249C4⋊Dic3—64no—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262Dic12—68no—
263Dic12—68no—
264#204—68no—
265#204—68no—
266C22×C32—21no—
267C22×C32—21no—
268C22×C32—21no—
269C22×C32C22×D411yescharacteristic
270C2×C3⋊D3—22no—
271C2×C3⋊D3—41no—
272C2×C3⋊D3—41no—
273C32×C4—21no—
274C32×C4—21no—
275C32×C4—21no—
276C32×C4—21no—
277C32×C4—21no—
278C32×C4C2×#4111yescharacteristic
279C32×C4C2×#4111yescharacteristic
280C3⋊Dic3—22no—
281C3⋊Dic3—41no—
282C3⋊Dic3—41no—
283C3⋊Dic3—41no—
284C3⋊Dic3—41no—
285C3⋊Dic3—41no—
286C3⋊Dic3—41no—
287C2×#41—91no—
288C2×Q16—91no—
289C2×Q16—91no—
290C2×SD16—91no—
291C2×SD16—91no—
292C4⋊Q8—91no—
293#126—181no—
294#126—181no—
295#125—91no—
296#125—181no—
297#125—181no—
298C22⋊Q8—91no—
299C22⋊Q8—91no—
300C4×Q8—91no—
301C4×Q8—91no—
302C4×Q8—91no—
303C4×Q8—91no—
304C4×D4—91no—
305C4×D4—91no—
306C4×D4—181no—
307C4×D4—181no—
308#117—181no—
309#117C2×C3⋊D311yescharacteristic
310C2×C4⋊C4—91no—
311C2×C4⋊C4—181no—
312#107—91no—
313#107—91no—
314#106—91no—
315#106—91no—
316C4⋊C8C2×C3⋊D311yescharacteristic
317C4⋊C8C2×C3⋊D311yescharacteristic
318#103—91no—
319#103—91no—
320#103—91no—
321#103—91no—
322#103—91no—
323#103—91no—
324#102—91no—
325#102—91no—
326C22⋊C8C2×C3⋊D311yescharacteristic
327C22⋊C8C2×C3⋊D311yescharacteristic
328#97C2×C3⋊D311yescharacteristic
329C4×C8C2×C3⋊D311yescharacteristic
330C23×C3C2×D1214yes—
331C22×D3—64no—
332C2×C3×C4—24no—
333C2×C3×C4—24no—
334C2×C3×C4C2×D1214yes—
335C2×C3×C4C2×D1214yes—
336C2×C3×C4C2×D1214yes—
337C2×C3×C4C2×D1214yes—
338C2×C3×C4C2×D1214yes—
339C2×C3×C4C23×D314yes—
340#67—616no—
341C2×Dic3—64no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—64no—
345C2×Dic3—64no—
346C2×Dic3—64no—
347C2×Dic3—64no—
348C2×Dic3—244no—
349D12—38no—
350D12—64no—
351C4×D3—616no—
352C4×D3—244no—
353C4×D3—244no—
354Dic6—38no—
355Dic6—64no—
356Dic6—64no—
357Dic6—64no—
358Dic6—64no—
359Dic6—64no—
360C3×C8—24no—
361C3×C8—24no—
362C3×C8—24no—
363C3×C8—24no—
364C2×C32—41no—
365C2×C32#52511yescharacteristic
366C2×C32#57711yescharacteristic
367C2×C32#57811yescharacteristic
368C3⋊D3—42no—
369#41—182no—
370#41—182no—
371C2×Q8—91no—
372C2×Q8—91no—
373C2×Q8—91no—
374C2×D4—91no—
375C2×D4—181no—
376C22×C4—181no—
377C22×C4—181no—
378C22×C4—181no—
379C22×C4—181no—
380C22×C4C22×C3⋊D311yescharacteristic
381Q16—182no—
382Q16—182no—
383SD16—182no—
384SD16—182no—
385C2×C8C22×C3⋊D311yescharacteristic
386C2×C8C22×C3⋊D311yescharacteristic
387C2×C8C22×C3⋊D311yescharacteristic
388C2×C8C22×C3⋊D311yescharacteristic
389C4⋊C4—91no—
390C4⋊C4—91no—
391C4⋊C4—91no—
392C4⋊C4—91no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C4⋊C4—181no—
402C4⋊C4—181no—
403C4⋊C4—181no—
404C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
405C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22⋊C4—181no—
409C22⋊C4—181no—
410C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
411C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
412C42—181no—
413C42—181no—
414C42—181no—
415C42—181no—
416C42C22×C3⋊D311yescharacteristic
417C42C22×C3⋊D311yescharacteristic
418C22×C3—24no—
419C22×C3—24no—
420C22×C3—24no—
421C22×C3C22×D1214yes—
422C2×D3—68no—
423C2×D3—124no—
424C2×D3—124no—
425C3×C4—24no—
426C3×C4—24no—
427C3×C4—24no—
428C3×C4—24no—
429C3×C4—24no—
430C3×C4D3×#4114yes—
431C3×C4D3×#4114yes—
432Dic3—68no—
433Dic3—124no—
434Dic3—124no—
435Dic3—124no—
436Dic3—124no—
437Dic3—124no—
438Dic3—124no—
439C32#312011yescharacteristic, complemented, Sylow
440C23—181no—
441C23C2×C4⋊(C3⋊D3)11yescharacteristic
442Q8—92no—
443Q8—181no—
444Q8—181no—
445Q8—181no—
446Q8—181no—
447Q8—181no—
448D4—92no—
449D4—184no—
450D4—181no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—184no—
454C2×C4—181no—
455C2×C4—181no—
456C2×C4—181no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4—721no—
462C2×C4—721no—
463C2×C4—721no—
464C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
465C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
466C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
467C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
468C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
469C2×C4C23×C3⋊D311yescharacteristic
470C8—21no—
471C8—21no—
472C8—21no—
473C8—21no—
474C2×C3—44no—
475C2×C3#552414yes—
476C2×C3#575114yes—
477C2×C3#575314yes—
478D3—128no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—182no—
483C22—361no—
484C22—361no—
485C22C22×C4⋊(C3⋊D3)11yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—182no—
492C4—361no—
493C4—361no—
494C4—361no—
495C4—361no—
496C4—361no—
497C4—361no—
498C4#41×C3⋊D311yescharacteristic
499C4#41×C3⋊D311yescharacteristic
500C3#7938514yescomplemented
501C2—41no—
502C2—362no—
503C2#1059599511yescharacteristic
504C2#1059622211yescharacteristic
505C2#1059622411yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#433C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
hypercenter#433C3⋊D3
hypocenterC32#3120
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #10595989C2semidirect
3. C32×#433C2semidirect
4. #10592548C2semidirect
5. #10592546C2semidirect
6. #10592540C2semidirect
7. #10592528C2semidirect
10. #10592421C2semidirect
11. #10592420C2semidirect
12. #10592415C2semidirect
13. #10592409C2semidirect
14. C4×#3746C2semidirect
15. C4×#3744C2semidirect
62. C3×#433D3semidirect
216. #433C3⋊D3semidirect
439. C32#3120semidirect
500. C3#79385semidirect

Maximal subgroups

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

subgroupindex
#105959942
#105959892
C32×#4332
#105925482
#105925462
#105925402
#105925282
#105924322
#105924212
#105924202
#105924152
#105924092
C4×#37462
C4×#37442
#793853