Finite Group Databasebeta

← #11789684

Subgroups — #11789684

Order 1152.

557 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63650C211yesmaximal, characteristic
2C3×#5121C211yesmaximal, characteristic, complemented
3#10591096C211yesmaximal, characteristic
4C2×#63564C211yesmaximal, characteristic
5#10591055C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70673—31nomaximal
9#68931—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63650C414yescomplemented
18C3×#818—21no—
19C3×#817—21no—
20#63564—21no—
21#63564—21no—
22#63564—21no—
23#63564—21no—
24#63554—21no—
25Dic3×C3⋊C8—21no—
26C3×#428—31no—
27#5131—31no—
28C2×#823—31no—
29C2×#823—31no—
30C2×#823—61no—
31#5121D311yescharacteristic, complemented
32C2×#821—31no—
33#5101—31no—
34#5001—31no—
35#4997—31no—
36C2×#809—31no—
37C3×#341—31no—
38#4558D311yescharacteristic, complemented
39#4554—31no—
40#4530—31no—
41C23×C3⋊D3—21no—
42C22×C32×C4C2311yescharacteristic
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)C2×C412yes—
49C22×C3×Dic3—21no—
50C32×M16—21no—
51C32×M16C2×C412yes—
52C2×C32×C8—21no—
53#3748—21no—
54#3748C2×C412yes—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4×Dic3—21no—
62C3×#208—21no—
63C3×#208—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8D411yescharacteristic
68C2×C3×C3⋊C8D411yescharacteristic
69#1931—91noSylow
70C22×D12—31no—
71C22×D12—31no—
72C22×D12—61no—
73C2×C3×M16—21no—
74C2×C3×M16—31no—
75C2×C3×M16C2×D311yescharacteristic
76C2×C3×M16C2×D311yescharacteristic
77C22×C3×C8—31no—
78C3×#117—31no—
79C2×C3×C4⋊C4—31no—
80#926C2×D311yescharacteristic
81C2×C4⋊Dic3C2×D311yescharacteristic
82C2×#208—31no—
83C2×#208—31no—
84C2×#208—61no—
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8C2×D311yescharacteristic
87C3×#107—61no—
88C3×#106—61no—
89#823—34no—
90#823—34no—
91#823—64no—
92#821—61no—
93#821—61no—
94#821—61no—
95#821—61no—
96#818—21no—
97#817—21no—
98#815—61no—
99C8×Dic3—61no—
100#809—61no—
101#809—61no—
102#809—61no—
103#809—61no—
104#803—61no—
105C4×C3⋊C8—61no—
106C23×C32#4111yescharacteristic
107C22×C3⋊D3—22no—
108C22×C3⋊D3—41no—
109C22×C3⋊D3—41no—
110C22×C3⋊D3—81no—
111C22×C3⋊D3—81no—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C4⋊(C3⋊D3)—22no—
119C4⋊(C3⋊D3)—22no—
120C4⋊(C3⋊D3)—41no—
121C4⋊(C3⋊D3)—41no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—81no—
126C32×C8—22no—
127C3⋊(C3⋊C8)—22no—
128C3×C3⋊C8—21no—
129C3×C3⋊C8—21no—
130C3×C3⋊C8—41no—
131#428—31no—
132#418—91no—
133C2×#102—91no—
134C2×#100—91no—
135#405—91no—
136#343—91no—
137#341—31no—
138C23×D3—62no—
139C23×D3—61no—
140C23×D3—61no—
141C22×C3×C4—21no—
142C22×C3×C4—61no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C22×Dic3—21no—
146C2×D12—32no—
147C2×D12—32no—
148C2×D12—62no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—62no—
158C2×D12—61no—
159C2×D12—61no—
160C2×D12—121no—
161C2×D12—121no—
162C2×D12—121no—
163C2×D12—121no—
164C3×M16—21no—
165C3×M16—21no—
166C3×M16—22no—
167C3×M16—41no—
168C3×M16—61no—
169C3×M16—61no—
170C3×M16C4×D312yes—
171C3×M16C4×D312yes—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C2×C3×C8—31no—
175C2×C3×C8—31no—
176C2×C3×C8—41no—
177C2×C3×C8—61no—
178C2×C3×C8—61no—
179C2×C3×C8—61no—
180C3×C4⋊C4—31no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C22⋊C4—61no—
185C3×C42—61no—
186#217—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—21no—
189C4⋊Dic3#6711yescharacteristic
190C4⋊Dic3#6711yescharacteristic
191C4×Dic3—21no—
192#208—21no—
193#208—21no—
194#208—32no—
195#208—32no—
196#208—62no—
197#208—61no—
198#208—61no—
199#208—121no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—121no—
206C2×C3⋊C8D1211yescharacteristic
207C2×C3⋊C8D1211yescharacteristic
208C22×C32—21no—
209C22×C32—21no—
210C22×C32#11711yescharacteristic
211C22×C32#12111yescharacteristic
212C22×C32#12611yescharacteristic
213C2×C3⋊D3—42no—
214C2×C3⋊D3—82no—
215C2×C3⋊D3—81no—
216C2×C3⋊D3—81no—
217C2×C3⋊D3—82no—
218C32×C4C4×D411yescharacteristic
219C32×C4C4×D411yescharacteristic
220C32×C4#12311yescharacteristic
221C32×C4#12411yescharacteristic
222C3×Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3—81no—
225C22×D4—91no—
226C2×M16—31no—
227C2×M16—91no—
228C2×M16D3211yescharacteristic
229C22×C8—31no—
230#117—31no—
231C2×C4⋊C4—31no—
232#107—61no—
233#106—61no—
234#102—181no—
235#102—181no—
236#102—181no—
237#102—181no—
238#100—94no—
239#97—181no—
240C4×C8—181no—
241C23×C3—21no—
242C23×C3#23711yescharacteristic
243C23×C3#23911yescharacteristic
244C22×D3—64no—
245C22×D3—62no—
246C22×D3—62no—
247C22×D3—122no—
248C22×D3—122no—
249C22×D3—121no—
250C22×D3—121no—
251C22×D3—121no—
252C22×D3—121no—
253C22×D3—241no—
254C22×D3—241no—
255C22×D3—241no—
256C22×D3—241no—
257C22×D3—242no—
258C22×D3—242no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—121no—
268C2×C3×C4—241no—
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4#23511yescharacteristic
273C2×C3×C4#23511yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4#23711yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4#23911yescharacteristic
279C2×C3×C4#23911yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—41no—
284C2×Dic3—81no—
285D12—62no—
286D12—62no—
287D12—62no—
288D12—62no—
289D12—122no—
290D12—122no—
291D12—122no—
292D12—122no—
293D12—121no—
294D12—121no—
295D12—121no—
296D12—121no—
297C3×C8—22no—
298C3×C8—22no—
299C3×C8—42no—
300C3×C8—61no—
301C3×C8—61no—
302C3×C8—121no—
303C3⋊C8—21no—
304C3⋊C8—21no—
305C3⋊C8—41no—
306C3⋊C8—62no—
307C3⋊C8—62no—
308C3⋊C8—122no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32#38811yescharacteristic
312C2×C32#47111yescharacteristic
313C2×C32#47211yescharacteristic
314C3⋊D3—82no—
315C24—181no—
316C2×D4—92no—
317C2×D4—181no—
318C2×D4—181no—
319C2×D4—181no—
320C2×D4—181no—
321C2×D4—181no—
322C22×C4—61no—
323C22×C4C2×D3211yescharacteristic
324M16—21no—
325M16—61no—
326M16—61no—
327M16—92no—
328M16—181no—
329M16#62412yes—
330C2×C8—21no—
331C2×C8—31no—
332C2×C8—31no—
333C2×C8—61no—
334C2×C8—61no—
335C2×C8—61no—
336C2×C8—181no—
337C4⋊C4—31no—
338C4⋊C4—31no—
339C4⋊C4—61no—
340C4⋊C4—61no—
341C22⋊C4—61no—
342C42—61no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3#89211yescharacteristic
353C22×C3#89211yescharacteristic
354C22×C3#89511yescharacteristic
355C22×C3#89811yescharacteristic
356C22×C3#89811yescharacteristic
357C22×C3#93911yescharacteristic
358C2×D3—124no—
359C2×D3—122no—
360C2×D3—122no—
361C2×D3—242no—
362C2×D3—242no—
363C2×D3—242no—
364C2×D3—242no—
365C2×D3—244no—
366C2×D3—241no—
367C2×D3—241no—
368C2×D3—241no—
369C2×D3—241no—
370C2×D3—242no—
371C2×D3—242no—
372C2×D3—244no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—121no—
378C3×C4—121no—
379C3×C4—241no—
380C3×C4C4×D1211yescharacteristic
381C3×C4#67⋊C411yescharacteristic
382C3×C4#88511yescharacteristic
383C3×C4#88611yescharacteristic
384C3×C4#89311yescharacteristic
385C3×C4#89411yescharacteristic
386C3×C4C4×#6711yescharacteristic
387C3×C4#94711yescharacteristic
388Dic3—41no—
389Dic3—41no—
390Dic3—81no—
391C32#193111yescharacteristic, complemented, Sylow
392C23—182no—
393C23—361no—
394C23—361no—
395C23—721no—
396C23—721no—
397C23#379611yescharacteristic
398D4—182no—
399D4—182no—
400D4—361no—
401D4—361no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—121no—
405C2×C4—241no—
406C2×C4#379611yescharacteristic
407C2×C4#379911yescharacteristic
408C2×C4D3×D1211yescharacteristic
409C2×C4#380411yescharacteristic
410C2×C4C2×#62411yescharacteristic
411C2×C4D3×#6711yescharacteristic
412C8—22no—
413C8—61no—
414C8—61no—
415C8—121no—
416C8—182no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—41no—
425C2×C3—41no—
426C2×C3#467011yescharacteristic
427C2×C3#489711yescharacteristic
428C2×C3#489811yescharacteristic
429C2×C3#499011yescharacteristic
430C2×C3#519911yescharacteristic
431C2×C3#520311yescharacteristic
432D3—244no—
433D3—242no—
434D3—242no—
435C22—21no—
436C22—21no—
437C22—362no—
438C22—722no—
439C22—722no—
440C22—721no—
441C22—721no—
442C22#6384811yescharacteristic
443C22#6384911yescharacteristic
444C22#6388611yescharacteristic
445C4—121no—
446C4—121no—
447C4—241no—
448C4#6389011yescharacteristic
449C4#6389411yescharacteristic
450C4#6390711yescharacteristic
451C4#6395211yescharacteristic
452C3—21no—
453C3#6893111yescharacteristic, complemented
454C3#7067311yescharacteristic, complemented
455C2—21no—
456C2—21no—
457C2—722no—
458C2#1059098411yescharacteristic
459C2#1059098511yescharacteristic
460C2#1059126611yescharacteristic
subgroupG/H
centerC22#63886
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1931
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C3×#5121C2semidirect
5. #10591055C2semidirect
6. C3×#4558C2semidirect
7. #10589167C2semidirect
17. #63650C4semidirect
31. #5121D3semidirect
38. #4558D3semidirect
391. C32#1931semidirect
453. C3#68931semidirect
454. C3#70673semidirect

Maximal subgroups

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

subgroupindex
C2×#636502
C3×#51212
#105910962
C2×#635642
#105910552
C3×#45582
#105891672
#706733
#689313