Finite Group Databasebeta

← #11789675

Subgroups — #11789675

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×#63660C211yesmaximal, characteristic
2C3×#5215C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591139C211yesmaximal, characteristic, complemented
5#10591055C211yesmaximal, characteristic, complemented
6#10589167C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70318—31nomaximal
9#70195—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3748C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63660C414yescomplemented
18C3×#832—21no—
19C3×#832—21no—
20C3×#832—21no—
21C3×#832—21no—
22#63576—21no—
23#63574—21no—
24#63554—21no—
25Dic3×C3⋊C8—21no—
26C3×#418—31no—
27C2×C3×#102—31no—
28C2×#833—31no—
29C2×#833—31no—
30C2×#833—61no—
31#5215D311yescharacteristic
32C2×#832D311yescharacteristic
33#5101—31no—
34#4997—31no—
35#4995—31no—
36#4964—31no—
37#4558—31no—
38#4554—31no—
39#4552—31no—
40#4530—31no—
41C24×C32—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4C2×C412yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3×Dic3—21no—
50#3748—21no—
51#3748—21no—
52#3748C2×C412yes—
53#3748C2×C412yes—
54C2×C3⋊(C3⋊C8)—21no—
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×C3×D4—21no—
71C22×C3×D4C2×D311yescharacteristic
72C22×C3×D4C2×D311yescharacteristic
73C2×C3×M16—31no—
74C22×C3×C8—31no—
75C3×#117—31no—
76C2×C3×C4⋊C4—31no—
77#926C2×D311yescharacteristic
78C2×C4⋊Dic3C2×D311yescharacteristic
79C2×#208—31no—
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—31no—
83C2×#208—61no—
84C2×#208—61no—
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8C2×D311yescharacteristic
87C3×#102—61no—
88C3×#102—61no—
89C3×#102—61no—
90C3×#102—61no—
91#833—34no—
92#833—34no—
93#833—64no—
94#832—21no—
95#832—21no—
96#832—21no—
97#832—21no—
98#815—61no—
99C8×Dic3—61no—
100#808—61no—
101#808—61no—
102#807—61no—
103#807—61no—
104#803—61no—
105C4×C3⋊C8—61no—
106C23×C32—22no—
107C23×C32—41no—
108C23×C32—41no—
109C23×C32—81no—
110C23×C32—81no—
111C23×C32#4111yescharacteristic
112C32×D4—22no—
113C32×D4—22no—
114C32×D4—41no—
115C32×D4—41no—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—81no—
126C3⋊(C3⋊C8)—22no—
127C3⋊(C3⋊C8)—22no—
128C3×C3⋊C8—21no—
129C3×C3⋊C8—21no—
130C3×C3⋊C8—41no—
131#428—91no—
132#418—31no—
133C2×#102—31no—
134C2×#100—91no—
135#405—91no—
136#343—91no—
137#341—91no—
138C24×C3—22no—
139C24×C3—21no—
140C24×C3—21no—
141C2×C3×D4—22no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—22no—
153C2×C3×D4—41no—
154C2×C3×D4—41no—
155C2×C3×D4—41no—
156C2×C3×D4—41no—
157C2×C3×D4C4×D312yes—
158C2×C3×D4C4×D312yes—
159C22×C3×C4—21no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—21no—
164C3×M16—61no—
165C3×M16—61no—
166C2×C3×C8—31no—
167C2×C3×C8—31no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C22⋊C4—61no—
176C3×C42—61no—
177#217—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3#6711yescharacteristic
181C4⋊Dic3#6711yescharacteristic
182C4×Dic3—21no—
183#208—21no—
184#208—21no—
185#208—32no—
186#208—32no—
187#208—32no—
188#208—32no—
189#208—62no—
190#208—62no—
191#208—61no—
192#208—61no—
193#208—61no—
194#208—61no—
195#208—121no—
196#208—121no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—121no—
205C2×C3⋊C8—121no—
206C2×C3⋊C8#6711yescharacteristic
207C2×C3⋊C8#6711yescharacteristic
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—42no—
211C22×C32—82no—
212C22×C32—82no—
213C22×C32—81no—
214C22×C32—81no—
215C22×C32#11711yescharacteristic
216C22×C32#12111yescharacteristic
217C22×C32#12611yescharacteristic
218C32×C4C4×D411yescharacteristic
219C32×C4C4×D411yescharacteristic
220C32×C4#12311yescharacteristic
221C32×C4#12411yescharacteristic
222C3×Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3—81no—
225C22×D4D3211yescharacteristic
226C2×M16—31no—
227C2×M16—91no—
228C2×M16—91no—
229C22×C8—31no—
230#117—31no—
231C2×C4⋊C4—31no—
232#107—181no—
233#106—181no—
234#102—61no—
235#102—61no—
236#102—61no—
237#102—61no—
238#100—94no—
239#97—181no—
240C4×C8—181no—
241C23×C3—24no—
242C23×C3—22no—
243C23×C3—22no—
244C23×C3—21no—
245C23×C3—42no—
246C23×C3—42no—
247C23×C3—41no—
248C23×C3—41no—
249C23×C3—41no—
250C23×C3—41no—
251C23×C3—81no—
252C23×C3—81no—
253C23×C3—81no—
254C23×C3—81no—
255C23×C3—82no—
256C23×C3—82no—
257C23×C3#23711yescharacteristic
258C23×C3#23711yescharacteristic
259C3×D4—22no—
260C3×D4—22no—
261C3×D4—22no—
262C3×D4—22no—
263C3×D4—42no—
264C3×D4—42no—
265C3×D4—42no—
266C3×D4—42no—
267C3×D4—41no—
268C3×D4—41no—
269C3×D4—41no—
270C3×D4—41no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—121no—
280C2×C3×C4—241no—
281C2×C3×C4C2×C4×D311yescharacteristic
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4#23511yescharacteristic
284C2×C3×C4#23511yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4#23711yescharacteristic
288C2×C3×C4#23711yescharacteristic
289C2×C3×C4#23711yescharacteristic
290C2×C3×C4#23711yescharacteristic
291C2×C3×C4C2×#6711yescharacteristic
292C2×C3×C4C2×#6711yescharacteristic
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—41no—
296C2×Dic3—81no—
297C3×C8—61no—
298C3×C8—61no—
299C3×C8—121no—
300C3⋊C8—21no—
301C3⋊C8—21no—
302C3⋊C8—41no—
303C3⋊C8—62no—
304C3⋊C8—62no—
305C3⋊C8—62no—
306C3⋊C8—62no—
307C3⋊C8—122no—
308C3⋊C8—122no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32—82no—
312C2×C32#38811yescharacteristic
313C2×C32#47111yescharacteristic
314C2×C32#47211yescharacteristic
315C24—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4#62412yes—
322C22×C4—61no—
323C22×C4C2×D3211yescharacteristic
324M16—61no—
325M16—61no—
326M16—92no—
327M16—92no—
328M16—181no—
329M16—181no—
330C2×C8—31no—
331C2×C8—31no—
332C2×C8—61no—
333C2×C8—61no—
334C2×C8—61no—
335C2×C8—181no—
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—44no—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—82no—
356C22×C3—82no—
357C22×C3—82no—
358C22×C3—82no—
359C22×C3—82no—
360C22×C3—82no—
361C22×C3—84no—
362C22×C3—84no—
363C22×C3—81no—
364C22×C3—81no—
365C22×C3—81no—
366C22×C3—81no—
367C22×C3#87711yescharacteristic
368C22×C3#87711yescharacteristic
369C22×C3#87911yescharacteristic
370C22×C3#87911yescharacteristic
371C22×C3#93811yescharacteristic
372C22×C3#93911yescharacteristic
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—121no—
378C3×C4—121no—
379C3×C4—241no—
380C3×C4#67⋊C411yescharacteristic
381C3×C4#67⋊C411yescharacteristic
382C3×C4#88311yescharacteristic
383C3×C4#88511yescharacteristic
384C3×C4C4×#6711yescharacteristic
385C3×C4C4×#6711yescharacteristic
386C3×C4#93511yescharacteristic
387C3×C4#93611yescharacteristic
388Dic3—41no—
389Dic3—41no—
390Dic3—81no—
391C32#193111yescharacteristic, complemented, Sylow
392C23—22no—
393C23—41no—
394C23—41no—
395C23—81no—
396C23—81no—
397C23#380511yescharacteristic
398D4—22no—
399D4—22no—
400D4—41no—
401D4—41no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—121no—
405C2×C4—241no—
406C2×C4#380411yescharacteristic
407C2×C4#380411yescharacteristic
408C2×C4#380511yescharacteristic
409C2×C4C2×#62411yescharacteristic
410C2×C4D3×#6711yescharacteristic
411C2×C4D3×#6711yescharacteristic
412C8—61no—
413C8—61no—
414C8—121no—
415C8—182no—
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—84no—
427C2×C3—82no—
428C2×C3—82no—
429C2×C3#494411yescharacteristic
430C2×C3#494511yescharacteristic
431C2×C3#516011yescharacteristic
432C2×C3#517711yescharacteristic
433C2×C3#519911yescharacteristic
434C2×C3#520011yescharacteristic
435C22—21no—
436C22—21no—
437C22—42no—
438C22—82no—
439C22—82no—
440C22—81no—
441C22—81no—
442C22#6395611yescharacteristic
443C22#6395711yescharacteristic
444C22#6397011yescharacteristic
445C4—121no—
446C4—121no—
447C4—241no—
448C4#6395211yescharacteristic
449C4#6395211yescharacteristic
450C4#6395911yescharacteristic
451C4#6396911yescharacteristic
452C3—21no—
453C3#7019511yescharacteristic, complemented
454C3#7031811yescharacteristic, complemented
455C2—21no—
456C2—21no—
457C2—82no—
458C2#1059150511yescharacteristic
459C2#1059150611yescharacteristic
460C2#1059170311yescharacteristic
subgroupG/H
centerC22#63970
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#121
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1931
LCSG ▷ C2×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. #10591139C2semidirect
5. #10591055C2semidirect
6. #10589167C2semidirect
7. #10589166C2semidirect
17. #63660C4semidirect
391. C32#1931semidirect
453. C3#70195semidirect
454. C3#70318semidirect

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
#105911392
#105910552
#105891672
#105891662
#703183
#701953