Finite Group Databasebeta

← #11794343

Subgroups — #11794343

Order 1152.

549 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63660C211yesmaximal, characteristic
2C3×#5215C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C2×#63577C211yesmaximal, characteristic, complemented
5#10591139C211yesmaximal, characteristic, complemented
6#10591116C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70317—31nomaximal
9#70197—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3748C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63660—22no—
18C3×#832—21no—
19C3×#832—21no—
20C3×#832—22no—
21#63577—22no—
22#63576—21no—
23#63574—21no—
24Dic3⋊(C3⋊C8)—22no—
25C3×#418—31no—
26C2×C3×#102—31no—
27C2×#833—31no—
28C2×#833—31no—
29C2×#833—61no—
30#5215D311yescharacteristic
31C2×#832D311yescharacteristic
32C2×#822—31no—
33C2×#819—31no—
34#5102—31no—
35#4999—31no—
36#4995—31no—
37#4964—31no—
38#4554—31no—
39#4530—31no—
40C24×C32—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4Q812yes—
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—21no—
49#3748—21no—
50#3748—21no—
51#3748—21no—
52#3748D412yes—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×#217—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4×Dic3—21no—
61C3×#208—21no—
62C3×#208—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8D412yes—
67#2063—91noSylow
68C22×C3×D4—21no—
69C22×C3×D4C2×D311yescharacteristic
70C22×C3×D4C2×D311yescharacteristic
71C2×C3×M16—31no—
72C22×C3×C8—31no—
73C3×#117—31no—
74C2×C3×C4⋊C4—31no—
75#926C2×D311yescharacteristic
76C2×C4⋊Dic3C2×D311yescharacteristic
77C2×#208—31no—
78C2×#208—31no—
79C2×#208—31no—
80C2×#208—31no—
81C2×#208—61no—
82C2×#208—61no—
83C2×#208C2×D311yescharacteristic
84C22×C3⋊C8C2×D311yescharacteristic
85C3×#102—61no—
86C3×#102—61no—
87C3×#102—62no—
88#833—62no—
89#833—62no—
90#833—64no—
91#832—21no—
92#832—21no—
93#832—22no—
94#822—62no—
95#819—62no—
96Dic3⋊C8—62no—
97#808—61no—
98#808—61no—
99#807—61no—
100#807—61no—
101C4⋊(C3⋊C8)—62no—
102C23×C32—22no—
103C23×C32—41no—
104C23×C32—41no—
105C23×C32—81no—
106C23×C32—81no—
107C23×C32#4111yescharacteristic
108C32×D4—22no—
109C32×D4—22no—
110C32×D4—41no—
111C32×D4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×Q811yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—41no—
121C2×C3×Dic3—81no—
122C3⋊(C3⋊C8)—22no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—41no—
126C2×#108—91no—
127#428—91no—
128#424—91no—
129#418—31no—
130C2×#102—31no—
131C2×#100—91no—
132#343—91no—
133C24×C3—22no—
134C24×C3—21no—
135C24×C3—21no—
136C2×C3×D4—22no—
137C2×C3×D4—21no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—22no—
148C2×C3×D4—41no—
149C2×C3×D4—41no—
150C2×C3×D4—41no—
151C2×C3×D4—41no—
152C2×C3×D4Dic612yes—
153C2×C3×D4Dic612yes—
154C22×C3×C4—21no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×Dic3—21no—
159C3×M16—61no—
160C3×M16—61no—
161C2×C3×C8—32no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C22⋊C4—61no—
170C3×C42—61no—
171#217—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3#6711yescharacteristic
175C4⋊Dic3#6711yescharacteristic
176C4×Dic3—21no—
177#208—21no—
178#208—21no—
179#208—32no—
180#208—32no—
181#208—62no—
182#208—61no—
183#208—61no—
184#208—62no—
185#208—61no—
186#208—61no—
187#208—61no—
188#208—61no—
189#208—121no—
190#208—121no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—121no—
199C2×C3⋊C8—121no—
200C2×C3⋊C8#6712yes—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32—42no—
204C22×C32—82no—
205C22×C32—82no—
206C22×C32—81no—
207C22×C32—81no—
208C22×C32#12111yescharacteristic
209C22×C32C22⋊Q811yescharacteristic
210C22×C32#12611yescharacteristic
211C32×C4#12111yescharacteristic
212C32×C4#12111yescharacteristic
213C32×C4C22⋊Q811yescharacteristic
214C32×C4C22⋊Q811yescharacteristic
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3—81no—
218C22×D4D3211yescharacteristic
219C2×M16—31no—
220C2×M16—91no—
221C2×M16—91no—
222C22×C8—31no—
223#117—31no—
224C2×C4⋊C4—31no—
225#108—182no—
226#107—181no—
227#106—181no—
228C4⋊C8—182no—
229#102—61no—
230#102—61no—
231#102—62no—
232#100—182no—
233C23×C3—24no—
234C23×C3—22no—
235C23×C3—22no—
236C23×C3—21no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3—41no—
240C23×C3—41no—
241C23×C3—41no—
242C23×C3—41no—
243C23×C3—81no—
244C23×C3—81no—
245C23×C3—81no—
246C23×C3—81no—
247C23×C3—82no—
248C23×C3—82no—
249C23×C3#23711yescharacteristic
250C23×C3#23711yescharacteristic
251C3×D4—22no—
252C3×D4—22no—
253C3×D4—22no—
254C3×D4—22no—
255C3×D4—42no—
256C3×D4—42no—
257C3×D4—42no—
258C3×D4—42no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—41no—
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—61no—
270C2×C3×C4—61no—
271C2×C3×C4—121no—
272C2×C3×C4—241no—
273C2×C3×C4C2×Dic611yescharacteristic
274C2×C3×C4C2×Dic611yescharacteristic
275C2×C3×C4#23511yescharacteristic
276C2×C3×C4#23511yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4#23711yescharacteristic
282C2×C3×C4#23711yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—41no—
288C2×Dic3—81no—
289C3×C8—62no—
290C3×C8—121no—
291C3⋊C8—22no—
292C3⋊C8—41no—
293C3⋊C8—62no—
294C3⋊C8—62no—
295C3⋊C8—122no—
296C3⋊C8—122no—
297C3⋊C8—121no—
298C3⋊C8—121no—
299C2×C32—21no—
300C2×C32—21no—
301C2×C32—82no—
302C2×C32#39611yescharacteristic
303C2×C32#47111yescharacteristic
304C2×C32#47211yescharacteristic
305C24—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4#62712yes—
312C22×C4—61no—
313C22×C4C2×D3211yescharacteristic
314M16—61no—
315M16—61no—
316M16—92no—
317M16—181no—
318M16—181no—
319M16—181no—
320C2×C8—32no—
321C2×C8—61no—
322C2×C8—61no—
323C2×C8—61no—
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—44no—
342C22×C3—42no—
343C22×C3—42no—
344C22×C3—82no—
345C22×C3—82no—
346C22×C3—82no—
347C22×C3—82no—
348C22×C3—82no—
349C22×C3—82no—
350C22×C3—84no—
351C22×C3—84no—
352C22×C3—81no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3—81no—
356C22×C3#87811yescharacteristic
357C22×C3#87811yescharacteristic
358C22×C3#87911yescharacteristic
359C22×C3#87911yescharacteristic
360C22×C3#93811yescharacteristic
361C22×C3#93911yescharacteristic
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—121no—
367C3×C4—121no—
368C3×C4—241no—
369C3×C4#87811yescharacteristic
370C3×C4#87811yescharacteristic
371C3×C4#88411yescharacteristic
372C3×C4#88411yescharacteristic
373C3×C4#92411yescharacteristic
374C3×C4#92411yescharacteristic
375C3×C4#93811yescharacteristic
376C3×C4#93911yescharacteristic
377Dic3—41no—
378Dic3—41no—
379Dic3—81no—
380C32#206311yescharacteristic, complemented, Sylow
381C23—22no—
382C23—41no—
383C23—41no—
384C23—81no—
385C23—81no—
386C23#380511yescharacteristic
387D4—22no—
388D4—22no—
389D4—41no—
390D4—41no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—121no—
394C2×C4—241no—
395C2×C4#380411yescharacteristic
396C2×C4#380411yescharacteristic
397C2×C4C2×#62711yescharacteristic
398C2×C4D3×#6711yescharacteristic
399C2×C4D3×#6711yescharacteristic
400C2×C4#381111yescharacteristic
401C8—62no—
402C8—121no—
403C8—182no—
404C8—361no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—41no—
413C2×C3—41no—
414C2×C3—84no—
415C2×C3—82no—
416C2×C3—82no—
417C2×C3#494811yescharacteristic
418C2×C3#494811yescharacteristic
419C2×C3#516011yescharacteristic
420C2×C3#517711yescharacteristic
421C2×C3#519911yescharacteristic
422C2×C3#520011yescharacteristic
423C22—21no—
424C22—21no—
425C22—42no—
426C22—82no—
427C22—82no—
428C22—81no—
429C22—81no—
430C22#6395611yescharacteristic
431C22#6397011yescharacteristic
432C22#6398211yescharacteristic
433C4—121no—
434C4—121no—
435C4—241no—
436C4#6395811yescharacteristic
437C4#6396411yescharacteristic
438C4#6396411yescharacteristic
439C4#6397111yescharacteristic
440C3—21no—
441C3#7019711yescharacteristic, complemented
442C3#7031711yescharacteristic, complemented
443C2—21no—
444C2—21no—
445C2—82no—
446C2#1059150511yescharacteristic
447C2#1059150611yescharacteristic
448C2#1059169111yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#121
hypercenterC22×D4D32
hypocenterC32#2063
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. C2×#63577C2semidirect
5. #10591139C2semidirect
6. #10591116C2semidirect
7. #10589167C2semidirect
380. C32#2063semidirect
441. C3#70197semidirect
442. C3#70317semidirect

Maximal subgroups

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

subgroupindex
C2×#636602
C3×#52152
C2×C3×#8322
C2×#635772
#105911392
#105911162
#105891672
#703173
#701973