Finite Group Databasebeta

← #11789682

Subgroups — #11789682

Order 1152.

559 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592700C211yesmaximal, characteristic
2C3×#4997C211yesmaximal, characteristic, complemented
3C3×#4995C211yesmaximal, characteristic, complemented
4C2×#63564C211yesmaximal, characteristic
5C2×#63559C211yesmaximal, characteristic
6#10589167C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70673—31nomaximal
9#69892—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63636—21no—
18#63636—21no—
19C3×#808—21no—
20C3×#807—21no—
21C3×#803—21no—
22C3×C4×C3⋊C8—21no—
23#63564—21no—
24#63564—21no—
25#63559C414yescomplemented
26C3×#428—31no—
27C3×#405—31no—
28C2×#823—31no—
29C2×#823—31no—
30C2×#821—31no—
31#5001—31no—
32#5001—31no—
33#5001—61no—
34#4997D311yescharacteristic, complemented
35#4995D311yescharacteristic, complemented
36C2×#809—31no—
37#4558—31no—
38#4554—31no—
39#4552—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×C4⋊C4D411yescharacteristic
51C32×C4⋊C4D411yescharacteristic
52C32×C22⋊C4—21no—
53C32×C42—21no—
54#3748—21no—
55#3748—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208C2×C412yes—
62C3×#208C2×C412yes—
63C2×C3×C3⋊C8—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—31no—
74C2×C3×M16—31no—
75C22×C3×C8—31no—
76C3×#117—21no—
77C3×#117C2×D311yescharacteristic
78C3×#117C2×D311yescharacteristic
79C2×C3×C4⋊C4—31no—
80C2×C4⋊Dic3C2×D311yescharacteristic
81C2×#208—31no—
82C2×#208—31no—
83C2×#208—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8C2×D311yescharacteristic
87C3×#107—61no—
88C3×#106—61no—
89C3×#97—61no—
90C3×C4×C8—61no—
91#823—34no—
92#823—34no—
93#821—61no—
94#821—61no—
95#809—62no—
96#809—62no—
97#809—61no—
98#809—61no—
99#809—61no—
100#809—61no—
101#809—61no—
102#809—61no—
103#808—21no—
104#807—21no—
105#803—21no—
106C4×C3⋊C8—21no—
107C23×C32#4111yescharacteristic
108C22×C3⋊D3—22no—
109C22×C3⋊D3—41no—
110C22×C3⋊D3—41no—
111C22×C3⋊D3—81no—
112C22×C3⋊D3—81no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C4⋊(C3⋊D3)—22no—
122C4⋊(C3⋊D3)—22no—
123C4⋊(C3⋊D3)—41no—
124C4⋊(C3⋊D3)—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—81no—
127C3⋊(C3⋊C8)—41no—
128C3×C3⋊C8—22no—
129C3×C3⋊C8—22no—
130C3×C3⋊C8—21no—
131C3×C3⋊C8—21no—
132#428—31no—
133#418—91no—
134C2×#102—91no—
135C2×#100—91no—
136#405—31no—
137#343—91no—
138#341—91no—
139C23×D3—61no—
140C23×D3—61no—
141C23×D3—121no—
142C22×C3×C4—21no—
143C22×C3×C4—61no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C22×Dic3—21no—
147C2×D12—32no—
148C2×D12—32no—
149C2×D12—62no—
150C2×D12—62no—
151C2×D12—62no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—61no—
158C2×D12—61no—
159C2×D12—61no—
160C2×D12—61no—
161C2×D12—61no—
162C2×D12—121no—
163C2×D12—121no—
164C2×D12—121no—
165C3×M16—32no—
166C3×M16—32no—
167C3×M16—61no—
168C3×M16—61no—
169C2×C3×C8—31no—
170C2×C3×C8—31no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4D1211yescharacteristic
180C3×C4⋊C4D1211yescharacteristic
181C3×C4⋊C4#6711yescharacteristic
182C3×C4⋊C4#6711yescharacteristic
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—41no—
186C3×C42—21no—
187C3×C42—21no—
188C3×C42—41no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191#208—21no—
192#208—21no—
193#208—61no—
194#208—61no—
195#208—61no—
196#208—61no—
197#208—121no—
198#208—121no—
199#208C4×D312yes—
200#208C4×D312yes—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—62no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8#6711yescharacteristic
209C2×C3⋊C8#6711yescharacteristic
210C22×C32—21no—
211C22×C32—21no—
212C22×C32#11711yescharacteristic
213C22×C32#12111yescharacteristic
214C22×C32#12611yescharacteristic
215C2×C3⋊D3—42no—
216C2×C3⋊D3—82no—
217C2×C3⋊D3—81no—
218C2×C3⋊D3—81no—
219C2×C3⋊D3—82no—
220C32×C4—41no—
221C32×C4—41no—
222C32×C4C4×D411yescharacteristic
223C32×C4C4×D411yescharacteristic
224C32×C4#12311yescharacteristic
225C32×C4#12411yescharacteristic
226C3×Dic3—81no—
227C22×D4—91no—
228C2×M16—31no—
229C2×M16—31no—
230C2×M16—91no—
231C22×C8—31no—
232#117D3211yescharacteristic
233C2×C4⋊C4—31no—
234#107—61no—
235#106—61no—
236#102—181no—
237#102—181no—
238#102—181no—
239#102—181no—
240#100—94no—
241#97—61no—
242C4×C8—61no—
243C23×C3—21no—
244C23×C3#23511yescharacteristic
245C23×C3#23711yescharacteristic
246C22×D3—62no—
247C22×D3—62no—
248C22×D3—122no—
249C22×D3—122no—
250C22×D3—122no—
251C22×D3—121no—
252C22×D3—121no—
253C22×D3—121no—
254C22×D3—121no—
255C22×D3—242no—
256C22×D3—242no—
257C22×D3—241no—
258C22×D3—241no—
259C22×D3—241no—
260C22×D3—241no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—121no—
274C2×C3×C4—241no—
275C2×C3×C4C2×C4×D311yescharacteristic
276C2×C3×C4C2×C4×D311yescharacteristic
277C2×C3×C4C2×D1211yescharacteristic
278C2×C3×C4#23511yescharacteristic
279C2×C3×C4#23511yescharacteristic
280C2×C3×C4#23511yescharacteristic
281C2×C3×C4#23511yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4#23911yescharacteristic
284C2×C3×C4#23911yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287C2×Dic3—41no—
288C2×Dic3—81no—
289D12—64no—
290D12—62no—
291D12—62no—
292D12—62no—
293D12—62no—
294D12—122no—
295D12—122no—
296D12—122no—
297D12—121no—
298D12—121no—
299D12—121no—
300D12—121no—
301C3×C8—62no—
302C3×C8—62no—
303C3×C8—61no—
304C3×C8—61no—
305C3⋊C8—22no—
306C3⋊C8—22no—
307C3⋊C8—21no—
308C3⋊C8—21no—
309C3⋊C8—122no—
310C3⋊C8—121no—
311C3⋊C8—121no—
312C2×C32—21no—
313C2×C32—21no—
314C2×C32#38811yescharacteristic
315C2×C32#47111yescharacteristic
316C2×C32#47211yescharacteristic
317C3⋊D3—82no—
318C24—181no—
319C2×D4—92no—
320C2×D4—181no—
321C2×D4—181no—
322C2×D4—181no—
323C2×D4—181no—
324C2×D4—181no—
325C22×C4—61no—
326C22×C4C2×D3211yescharacteristic
327M16—32no—
328M16—32no—
329M16—61no—
330M16—61no—
331M16—181no—
332M16—181no—
333C2×C8—31no—
334C2×C8—31no—
335C2×C8—61no—
336C2×C8—61no—
337C2×C8—61no—
338C2×C8—61no—
339C2×C8—181no—
340C4⋊C4—61no—
341C4⋊C4—61no—
342C4⋊C4#62611yescharacteristic
343C4⋊C4#62611yescharacteristic
344C22⋊C4—21no—
345C42—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3#87211yescharacteristic
356C22×C3#87611yescharacteristic
357C22×C3#89211yescharacteristic
358C22×C3#89811yescharacteristic
359C22×C3#93011yescharacteristic
360C22×C3#93911yescharacteristic
361C2×D3—124no—
362C2×D3—122no—
363C2×D3—122no—
364C2×D3—242no—
365C2×D3—242no—
366C2×D3—242no—
367C2×D3—242no—
368C2×D3—244no—
369C2×D3—244no—
370C2×D3—241no—
371C2×D3—241no—
372C2×D3—241no—
373C2×D3—241no—
374C2×D3—242no—
375C2×D3—242no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—81no—
385C3×C4—81no—
386C3×C4—241no—
387C3×C4C4×D1211yescharacteristic
388C3×C4#87511yescharacteristic
389C3×C4#89311yescharacteristic
390C3×C4#89411yescharacteristic
391C3×C4C4×#6711yescharacteristic
392C3×C4C4×#6711yescharacteristic
393C3×C4#92911yescharacteristic
394C3×C4#94711yescharacteristic
395Dic3—81no—
396C32#193111yescharacteristic, complemented, Sylow
397C23—182no—
398C23—361no—
399C23—361no—
400C23—721no—
401C23—721no—
402C23#380411yescharacteristic
403D4—182no—
404D4—182no—
405D4—361no—
406D4—361no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—121no—
410C2×C4—241no—
411C2×C4#379811yescharacteristic
412C2×C4#379911yescharacteristic
413C2×C4#379911yescharacteristic
414C2×C4C4×D3211yescharacteristic
415C2×C4C2×#62611yescharacteristic
416C2×C4D3×#6711yescharacteristic
417C8—61no—
418C8—61no—
419C8—62no—
420C8—62no—
421C8—361no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—41no—
430C2×C3—41no—
431C2×C3#494011yescharacteristic
432C2×C3#499011yescharacteristic
433C2×C3#514111yescharacteristic
434C2×C3#514211yescharacteristic
435C2×C3#519911yescharacteristic
436C2×C3#520311yescharacteristic
437D3—244no—
438D3—242no—
439D3—242no—
440C22—21no—
441C22—21no—
442C22—362no—
443C22—722no—
444C22—722no—
445C22—721no—
446C22—721no—
447C22#6383611yescharacteristic
448C22#6386811yescharacteristic
449C22#6397811yescharacteristic
450C4—41no—
451C4—41no—
452C4—241no—
453C4#6385011yescharacteristic
454C4#6386411yescharacteristic
455C4C4×#62611yescharacteristic
456C4#6390411yescharacteristic
457C3—21no—
458C3#6989211yescharacteristic, complemented
459C3#7067311yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2—722no—
463C2#1059128911yescharacteristic
464C2#1059167711yescharacteristic
465C2#1059168011yescharacteristic
subgroupG/H
centerC22#63978
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#121
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1931
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#4997C2semidirect
3. C3×#4995C2semidirect
6. #10589167C2semidirect
7. #10589166C2semidirect
25. #63559C4semidirect
34. #4997D3semidirect
35. #4995D3semidirect
396. C32#1931semidirect
458. C3#69892semidirect
459. C3#70673semidirect

Maximal subgroups

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

subgroupindex
#105927002
C3×#49972
C3×#49952
C2×#635642
C2×#635592
#105891672
#105891662
#706733
#698923