Finite Group Databasebeta

← #11872569

Subgroups — #11872569

Order 1152.

1110 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#10596005C211yesmaximal, characteristic
2#10595987C211yesmaximal, characteristic, complemented
3C32×#433C211yesmaximal, characteristic, complemented
4#10592550C211yesmaximal, characteristic, complemented
5#10592549C211yesmaximal, characteristic, complemented
6#10592544C211yesmaximal, characteristic, complemented
7#10592544C211yesmaximal, characteristic, complemented
8#10592438C211yesmaximal, characteristic, complemented
9#10592437C211yesmaximal, characteristic
10#10592436C211yesmaximal, characteristic
11#10592422C211yesmaximal, characteristic, complemented
12#10592415C211yesmaximal, characteristic, complemented
13#10592409C211yesmaximal, characteristic, complemented
14C4×#3746C211yesmaximal, characteristic, complemented
15C4×#3744C211yesmaximal, characteristic, complemented
16#79394—34nomaximal
17C22×#634C2211yescharacteristic
18C32×#117C2211yescharacteristic
19#64139C2211yescharacteristic
20#64135C2211yescharacteristic
21#64133C2211yescharacteristic
22C2×#3746C2211yescharacteristic
23C2×#3746C2211yescharacteristic
24C2×#3744C2211yescharacteristic
25C2×#3744C2211yescharacteristic
26#64107—21no—
27#64105—21no—
28#64096—21no—
29#64096—21no—
30#64094—21no—
31#64092—21no—
32#64086—21no—
33#64086—21no—
34#64084C2211yescharacteristic
35C4×C4⋊(C3⋊D3)C2211yescharacteristic
36#64078C2211yescharacteristic
37C4×#634C2211yescharacteristic
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#5534—34no—
61#5516—34no—
62C3×#433D314yescomplemented
63#4851—34no—
64#4850—34no—
65#4845—34no—
66#4845—34no—
67#4739—34no—
68#4738—34no—
69#4737—34no—
70#4723—34no—
71#4716—34no—
72#4710—34no—
73C4×Dic12—34no—
74C4×#204—34no—
75C22×C32×C4C2311yescharacteristic
76C2×#638—21no—
77C22×C3⋊Dic3—21no—
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4×C3⋊D3—21no—
80C2×#634—21no—
81C2×#634—22no—
82C2×#634—22no—
83C2×#634—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—
101#3752—21no—
102#3752—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—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3—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#3121—91noSylow
125C22×Dic6—34no—
126C3×#117C2×D314yes—
127#930—34no—
128#926—34no—
129#924—34no—
130C2×Dic12—34no—
131C2×Dic12—34no—
132C2×#204—34no—
133C2×#204—34no—
134#898—64no—
135#896—64no—
136#887—64no—
137#887—64no—
138#885—64no—
139#883—64no—
140#877—64no—
141#877—64no—
142#875—34no—
143C4×D12—34no—
144#869—34no—
145C4×Dic6—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—81no—
179C2×C3⋊Dic3—24no—
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—21no—
187C4⋊(C3⋊D3)—21no—
188C4⋊(C3⋊D3)—21no—
189C4×C3⋊D3—81no—
190#634—24no—
191#634—21no—
192#634—21no—
193#634—21no—
194#634—21no—
195#634—81no—
196#634#4112yes—
197#634#4112yes—
198C32×C8—21no—
199C32×C8—21no—
200C32×C8—21no—
201C32×C8—21no—
202#542—91no—
203#519—91no—
204#485—91no—
205#482—91no—
206#477—91no—
207#475—91no—
208#464—91no—
209#464—91no—
210#451—91no—
211#448—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—
220C2×D12—34no—
221C2×C4×D3—64no—
222C2×Dic6—34no—
223C2×Dic6—34no—
224C2×Dic6—34no—
225C2×Dic6—68no—
226C2×Dic6—68no—
227C2×Dic6—64no—
228C2×Dic6—64no—
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—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245C4⋊Dic3—34no—
246C4⋊Dic3—34no—
247C4⋊Dic3—34no—
248C4⋊Dic3—34no—
249C4⋊Dic3—64no—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256C4×Dic3—64no—
257C4×Dic3—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—41no—
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—22no—
282C3⋊Dic3—41no—
283C3⋊Dic3—41no—
284C3⋊Dic3—41no—
285C3⋊Dic3—41no—
286C3⋊Dic3—41no—
287C22×Q8—91no—
288C2×Q16—91no—
289C2×Q16—91no—
290C2×SD16—91no—
291C2×SD16—91no—
292C4⋊Q8—91no—
293#126—181no—
294#124—91no—
295#124—181no—
296#123—181no—
297C22⋊Q8—91no—
298C22⋊Q8—181no—
299#121—91no—
300C4×Q8—91no—
301C4×Q8—91no—
302C4×Q8—91no—
303C4×Q8—91no—
304C4×Q8—91no—
305C4×Q8—181no—
306C4×Q8—181no—
307C4×D4—91no—
308#117—91no—
309#117—181no—
310#117—181no—
311#117C2×C3⋊D311yescharacteristic
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—244no—
341C2×Dic3—616no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—64no—
345C2×Dic3—64no—
346C2×Dic3—64no—
347C2×Dic3—64no—
348C2×Dic3—64no—
349D12—64no—
350D12—64no—
351C4×D3—244no—
352Dic6—38no—
353Dic6—38no—
354Dic6—616no—
355Dic6—64no—
356Dic6—64no—
357Dic6—64no—
358Dic6—64no—
359Dic6—244no—
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—81no—
369C2×Q8—91no—
370C2×Q8—91no—
371C2×Q8—91no—
372C2×Q8—182no—
373C2×Q8—182no—
374C2×Q8—181no—
375C2×Q8—181no—
376C2×D4—91no—
377C2×D4—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⋊C4C4⋊(C3⋊D3)11yescharacteristic
401C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
402C22⋊C4—181no—
403C22⋊C4—181no—
404C22⋊C4—181no—
405C22⋊C4—181no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
409C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
410C42—181no—
411C42—181no—
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—124no—
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—68no—
434Dic3—124no—
435Dic3—124no—
436Dic3—124no—
437Dic3—124no—
438Dic3—124no—
439C32#312111yescharacteristic, complemented, Sylow
440C23—181no—
441C23C2×C4⋊(C3⋊D3)11yescharacteristic
442Q8—92no—
443Q8—92no—
444Q8—184no—
445Q8—181no—
446Q8—181no—
447Q8—181no—
448Q8—181no—
449Q8—721no—
450D4—181no—
451D4—181no—
452D4—721no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—184no—
456C2×C4—181no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4—181no—
462C2×C4—181no—
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—244no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—361no—
483C22—361no—
484C22—361no—
485C22C22×C4⋊(C3⋊D3)11yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—182no—
492C4—182no—
493C4—361no—
494C4—361no—
495C4—361no—
496C4—361no—
497C4—361no—
498C4#41×C3⋊D311yescharacteristic
499C4#41×C3⋊D311yescharacteristic
500C3#7939414yescomplemented
501C2—41no—
502C2—721no—
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 radical#64139C22
hypercenter#433C3⋊D3
hypocenterC32#3121
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. #10595987C2semidirect
3. C32×#433C2semidirect
4. #10592550C2semidirect
5. #10592549C2semidirect
6. #10592544C2semidirect
7. #10592544C2semidirect
8. #10592438C2semidirect
11. #10592422C2semidirect
12. #10592415C2semidirect
13. #10592409C2semidirect
14. C4×#3746C2semidirect
15. C4×#3744C2semidirect
62. C3×#433D3semidirect
216. #433C3⋊D3semidirect
439. C32#3121semidirect
500. C3#79394semidirect

Maximal subgroups

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

subgroupindex
#105960052
#105959872
C32×#4332
#105925502
#105925492
#105925442
#105924382
#105924372
#105924362
#105924222
#105924152
#105924092
C4×#37462
C4×#37442
#793943