Finite Group Databasebeta

← #11789677

Subgroups — #11789677

Order 1152.

509 conjugacy classes of subgroups.

The subgroup lattice has 445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5131C211yesmaximal, characteristic
2#10591139C211yesmaximal, characteristic, complemented
3C2×#63562C211yesmaximal, characteristic
4C2×#63558C211yesmaximal, characteristic
5#10591057C211yesmaximal, characteristic, complemented
6#10589424C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#70318—31nomaximal
9#68983—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#821—21no—
18C3×#821—21no—
19#63576—21no—
20#63574—21no—
21#63562—21no—
22#63562—21no—
23#63558C414yescomplemented
24#63554—21no—
25Dic3×C3⋊C8—21no—
26C3×#418—31no—
27C2×#833—31no—
28C2×#832—31no—
29#5131D311yescharacteristic
30C2×#823—31no—
31#5122—31no—
32#4997—31no—
33#4995—31no—
34C2×#809—31no—
35#4964—31no—
36C3×#343—31no—
37#4558—31no—
38#4558—31no—
39#4558—61no—
40#4554D311yescharacteristic, complemented
41C23×C3×D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12C2×C412yes—
50C32×M16—21no—
51C32×M16—21no—
52C2×C32×C8—21no—
53#3748—21no—
54#3748C2×C412yes—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)D411yescharacteristic
59C2×C3⋊(C3⋊C8)D411yescharacteristic
60C3×#217—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×C4⋊Dic3D411yescharacteristic
65C3×C4×Dic3—21no—
66C3×#208—21no—
67C3×#208C2×C412yes—
68C2×C3×C3⋊C8—21no—
69#1931—91noSylow
70C22×C3×D4—31no—
71C22×D12C2×D311yescharacteristic
72C2×C3×M16—21no—
73C2×C3×M16—31no—
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C2×D311yescharacteristic
76C3×#117—31no—
77C2×C3×C4⋊C4—31no—
78#926C2×D311yescharacteristic
79C2×C4⋊Dic3C2×D311yescharacteristic
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208C2×D311yescharacteristic
84C22×C3⋊C8—31no—
85C22×C3⋊C8—31no—
86C22×C3⋊C8—61no—
87C3×#102—61no—
88C3×#102—61no—
89#833—34no—
90#832—61no—
91#832—61no—
92#823—34no—
93#821—21no—
94#821—21no—
95#815—61no—
96C8×Dic3—61no—
97#809—61no—
98#809—61no—
99#808—61no—
100#808—61no—
101#807—61no—
102#807—61no—
103#803—61no—
104C4×C3⋊C8—61no—
105C23×C32#4111yescharacteristic
106C22×C3×D3—22no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C22×C3×D3—81no—
110C22×C3×D3—81no—
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—41no—
120C2×C3×Dic3—81no—
121C3×D12—22no—
122C3×D12—22no—
123C3×D12—41no—
124C3×D12—41no—
125C32×C8—41no—
126C3⋊(C3⋊C8)—22no—
127C3⋊(C3⋊C8)—21no—
128C3⋊(C3⋊C8)—21no—
129C3×C3⋊C8—22no—
130#428—91no—
131#418—31no—
132C2×#102—91no—
133C2×#100—91no—
134#405—91no—
135#343—31no—
136#341—91no—
137C24×C3—61no—
138C23×D3—21no—
139C2×C3×D4—32no—
140C2×C3×D4—61no—
141C2×C3×D4—61no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C22×C3×C4—21no—
146C22×C3×C4—61no—
147C22×C3×C4C22×D311yescharacteristic
148C22×C3×C4C22×D311yescharacteristic
149C22×Dic3—21no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12C4×D312yes—
156C3×M16—22no—
157C3×M16—21no—
158C3×M16—21no—
159C3×M16—21no—
160C3×M16—21no—
161C3×M16—32no—
162C3×M16—41no—
163C3×M16—61no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—41no—
167C2×C3×C8—61no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C42—61no—
174#217—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3#6711yescharacteristic
178C4⋊Dic3#6711yescharacteristic
179C4×Dic3—21no—
180#208—21no—
181#208—32no—
182#208—32no—
183#208—62no—
184#208—61no—
185#208—61no—
186#208—121no—
187#208C4×D312yes—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—31no—
190C2×C3⋊C8—31no—
191C2×C3⋊C8—31no—
192C2×C3⋊C8—31no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—121no—
202C2×C3⋊C8—121no—
203C2×C3⋊C8—121no—
204C22×C32—21no—
205C22×C32—21no—
206C22×C32#11711yescharacteristic
207C22×C32#12111yescharacteristic
208C22×C32#12611yescharacteristic
209C2×C3×D3—42no—
210C2×C3×D3—82no—
211C2×C3×D3—81no—
212C2×C3×D3—81no—
213C2×C3×D3—82no—
214C32×C4C4×D411yescharacteristic
215C32×C4C4×D411yescharacteristic
216C32×C4#12311yescharacteristic
217C32×C4#12411yescharacteristic
218C3×Dic3—41no—
219C3×Dic3—41no—
220C3×Dic3—81no—
221C22×D4—31no—
222C2×M16—31no—
223C2×M16—91no—
224C2×M16D3211yescharacteristic
225C22×C8—91no—
226#117—31no—
227C2×C4⋊C4—31no—
228#107—181no—
229#106—181no—
230#102—61no—
231#102—61no—
232#102—181no—
233#102—181no—
234#100—94no—
235#97—181no—
236C4×C8—181no—
237C23×C3—21no—
238C23×C3—62no—
239C23×C3—121no—
240C23×C3—121no—
241C23×C3—241no—
242C23×C3—241no—
243C23×C3#23511yescharacteristic
244C23×C3#23711yescharacteristic
245C22×D3—22no—
246C22×D3—41no—
247C22×D3—41no—
248C22×D3—81no—
249C22×D3—81no—
250C3×D4—62no—
251C3×D4—62no—
252C3×D4—121no—
253C3×D4—121no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—121no—
263C2×C3×C4—241no—
264C2×C3×C4C2×C4×D311yescharacteristic
265C2×C3×C4C2×C4×D311yescharacteristic
266C2×C3×C4#23511yescharacteristic
267C2×C3×C4#23511yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4#23711yescharacteristic
272C2×C3×C4#23711yescharacteristic
273C2×C3×C4#23711yescharacteristic
274C2×C3×C4#23911yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—41no—
279C2×Dic3—81no—
280D12—22no—
281D12—22no—
282D12—41no—
283D12—41no—
284C3×C8—42no—
285C3×C8—41no—
286C3×C8—41no—
287C3×C8—62no—
288C3⋊C8—22no—
289C3⋊C8—61no—
290C3⋊C8—61no—
291C3⋊C8—62no—
292C3⋊C8—61no—
293C3⋊C8—61no—
294C3⋊C8—62no—
295C3⋊C8—121no—
296C3⋊C8—121no—
297C3⋊C8—122no—
298C2×C32—21no—
299C2×C32—21no—
300C2×C32#38811yescharacteristic
301C2×C32#47111yescharacteristic
302C2×C32#47211yescharacteristic
303C3×D3—82no—
304C24—61no—
305C2×D4—32no—
306C2×D4—61no—
307C2×D4—61no—
308C2×D4—61no—
309C2×D4—61no—
310C2×D4—61no—
311C22×C4—61no—
312C22×C4C2×D3211yescharacteristic
313M16—21no—
314M16—21no—
315M16—32no—
316M16—61no—
317M16—92no—
318M16—181no—
319C2×C8—21no—
320C2×C8—61no—
321C2×C8—91no—
322C2×C8—91no—
323C2×C8—181no—
324C2×C8—181no—
325C2×C8—181no—
326C4⋊C4—31no—
327C4⋊C4—31no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C22⋊C4—61no—
331C42—61no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—122no—
342C22×C3—242no—
343C22×C3—242no—
344C22×C3—241no—
345C22×C3—241no—
346C22×C3#87211yescharacteristic
347C22×C3#87711yescharacteristic
348C22×C3#87911yescharacteristic
349C22×C3#88411yescharacteristic
350C22×C3#89811yescharacteristic
351C22×C3#93911yescharacteristic
352C2×D3—42no—
353C2×D3—82no—
354C2×D3—81no—
355C2×D3—81no—
356C2×D3—82no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—121no—
362C3×C4—121no—
363C3×C4—241no—
364C3×C4#67⋊C411yescharacteristic
365C3×C4#67⋊C411yescharacteristic
366C3×C4#88311yescharacteristic
367C3×C4#88511yescharacteristic
368C3×C4#89311yescharacteristic
369C3×C4#89411yescharacteristic
370C3×C4C4×#6711yescharacteristic
371C3×C4#93611yescharacteristic
372Dic3—41no—
373Dic3—41no—
374Dic3—81no—
375C32#193111yescharacteristic, complemented, Sylow
376C23—62no—
377C23—121no—
378C23—121no—
379C23—241no—
380C23—241no—
381C23#379511yescharacteristic
382D4—62no—
383D4—62no—
384D4—121no—
385D4—121no—
386C2×C4—61no—
387C2×C4—61no—
388C2×C4—121no—
389C2×C4—241no—
390C2×C4#379911yescharacteristic
391C2×C4C4×D3211yescharacteristic
392C2×C4#380211yescharacteristic
393C2×C4#380411yescharacteristic
394C2×C4#380511yescharacteristic
395C2×C4D3×#6711yescharacteristic
396C8—41no—
397C8—62no—
398C8—181no—
399C8—181no—
400C8—182no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—41no—
409C2×C3—41no—
410C2×C3—242no—
411C2×C3#466911yescharacteristic
412C2×C3#474911yescharacteristic
413C2×C3#475411yescharacteristic
414C2×C3#494511yescharacteristic
415C2×C3#519911yescharacteristic
416C2×C3#520011yescharacteristic
417D3—82no—
418C22—21no—
419C22—21no—
420C22—122no—
421C22—242no—
422C22—242no—
423C22—241no—
424C22—241no—
425C22#6386111yescharacteristic
426C22#6387711yescharacteristic
427C22#6388511yescharacteristic
428C4—121no—
429C4—121no—
430C4—241no—
431C4#6385411yescharacteristic
432C4#6390211yescharacteristic
433C4#6390411yescharacteristic
434C4#6395911yescharacteristic
435C3—21no—
436C3#6898311yescharacteristic, complemented
437C3#7031811yescharacteristic, complemented
438C2—21no—
439C2—21no—
440C2—242no—
441C2#1059098011yescharacteristic
442C2#1059098211yescharacteristic
443C2#1059128211yescharacteristic
subgroupG/H
centerC22#63885
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC22×C3×D12C22
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. #10591139C2semidirect
5. #10591057C2semidirect
6. #10589424C2semidirect
7. C3×#4554C2semidirect
23. #63558C4semidirect
40. #4554D3semidirect
375. C32#1931semidirect
436. C3#68983semidirect
437. C3#70318semidirect

Maximal subgroups

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

subgroupindex
C3×#51312
#105911392
C2×#635622
C2×#635582
#105910572
#105894242
C3×#45542
#703183
#689833