Finite Group Databasebeta

← #11789667

Subgroups — #11789667

Order 1152.

523 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592663C211yesmaximal, characteristic, complemented
2C2×C3×#809C211yesmaximal, characteristic
3#10591086C211yesmaximal, characteristic
4C2×#63558C211yesmaximal, characteristic
5#10591059C211yesmaximal, characteristic, complemented
6C3×#4530C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70195—31nomaximal
9#68983—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63635—21no—
18#63634—21no—
19C3×#809—21no—
20C3×#809—21no—
21#63563—21no—
22#63563—21no—
23#63558C414yescomplemented
24#63555—21no—
25#63553—21no—
26C2×C3×#102—31no—
27C2×#833—31no—
28#5215—31no—
29#5131—31no—
30C2×#823—31no—
31#5122—31no—
32#5101—31no—
33C2×#809D311yescharacteristic
34#4964—31no—
35#4964—31no—
36#4964—61no—
37C3×#343—31no—
38#4558—31no—
39#4552—31no—
40#4530D311yescharacteristic, complemented
41C23×C3×D3—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
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×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52#3757—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54C4⋊(C3⋊Dic3)D411yescharacteristic
55C4×C3⋊Dic3—21no—
56#3748—21no—
57#3748C2×C412yes—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
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×C3×D4—31no—
71C22×D12C2×D311yescharacteristic
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C22×C3×C8—31no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C4⋊C4C2×D311yescharacteristic
78#926—31no—
79#926—31no—
80#926—61no—
81C2×#208—31no—
82C2×#208—31no—
83C2×#208—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8C2×D311yescharacteristic
87C3×#102—61no—
88C3×#102—61no—
89#833—34no—
90#832—61no—
91#832—61no—
92#823—34no—
93#821—61no—
94#821—61no—
95#815—61no—
96#815—61no—
97C8×Dic3—61no—
98C8×Dic3—61no—
99#809—21no—
100#809—21no—
101#808—61no—
102#808—61no—
103#808—62no—
104#807—61no—
105#807—61no—
106#807—62no—
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—41no—
114C2×C32×C4—81no—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C3×D12—22no—
124C3×D12—22no—
125C3×D12—41no—
126C3×D12—41no—
127C3⋊(C3⋊C8)—22no—
128C3×C3⋊C8—22no—
129C3×C3⋊C8—21no—
130C3×C3⋊C8—21no—
131C3×C3⋊C8—41no—
132#428—91no—
133#418—91no—
134C2×#102—31no—
135C2×#100—91no—
136#405—91no—
137#343—31no—
138#341—91no—
139C24×C3—61no—
140C23×D3—21no—
141C2×C3×D4—32no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—41no—
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12—21no—
158C2×D12C4×D312yes—
159C3×M16—32no—
160C3×M16—61no—
161C3×M16—61no—
162C3×M16—61no—
163C2×C3×C8—31no—
164C2×C3×C8—31no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—41no—
175#217—61no—
176#217—61no—
177#217—121no—
178C4⋊Dic3—31no—
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181C4⋊Dic3—31no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—121no—
187#208—21no—
188#208—21no—
189#208—21no—
190#208—32no—
191#208—32no—
192#208—62no—
193#208—62no—
194#208—61no—
195#208—61no—
196#208C4×D312yes—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—62no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8#6711yescharacteristic
205C2×C3⋊C8#6711yescharacteristic
206C22×C32—21no—
207C22×C32—21no—
208C22×C32#11711yescharacteristic
209C22×C32#12111yescharacteristic
210C22×C32#12611yescharacteristic
211C2×C3×D3—42no—
212C2×C3×D3—82no—
213C2×C3×D3—81no—
214C2×C3×D3—81no—
215C2×C3×D3—82no—
216C32×C4—81no—
217C32×C4C4×D411yescharacteristic
218C32×C4C4×D411yescharacteristic
219C32×C4#12311yescharacteristic
220C32×C4#12411yescharacteristic
221C3⋊Dic3—41no—
222C3⋊Dic3—41no—
223C22×D4—31no—
224C2×M16—31no—
225C2×M16—31no—
226C2×M16—91no—
227C22×C8—31no—
228#117—91no—
229C2×C4⋊C4D3211yescharacteristic
230#107—181no—
231#106—181no—
232#102—61no—
233#102—61no—
234#102—181no—
235#102—181no—
236#100—94no—
237#97—181no—
238C4×C8—181no—
239C23×C3—21no—
240C23×C3—62no—
241C23×C3—121no—
242C23×C3—121no—
243C23×C3—241no—
244C23×C3—241no—
245C23×C3#23511yescharacteristic
246C23×C3#23711yescharacteristic
247C22×D3—22no—
248C22×D3—41no—
249C22×D3—41no—
250C22×D3—81no—
251C22×D3—81no—
252C3×D4—62no—
253C3×D4—62no—
254C3×D4—121no—
255C3×D4—121no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—42no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—82no—
266C2×C3×C4—81no—
267C2×C3×C4—81no—
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4#23511yescharacteristic
271C2×C3×C4#23511yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4#23711yescharacteristic
276C2×C3×C4#23711yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4#23911yescharacteristic
279C2×C3×C4C2×#6711yescharacteristic
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—121no—
285C2×Dic3—121no—
286D12—22no—
287D12—22no—
288D12—41no—
289D12—41no—
290C3×C8—61no—
291C3×C8—61no—
292C3×C8—62no—
293C3×C8—121no—
294C3⋊C8—22no—
295C3⋊C8—21no—
296C3⋊C8—21no—
297C3⋊C8—41no—
298C3⋊C8—64no—
299C3⋊C8—62no—
300C3⋊C8—62no—
301C2×C32—21no—
302C2×C32—21no—
303C2×C32#38811yescharacteristic
304C2×C32#47111yescharacteristic
305C2×C32#47211yescharacteristic
306C3×D3—82no—
307C24—61no—
308C2×D4—32no—
309C2×D4—61no—
310C2×D4—61no—
311C2×D4—61no—
312C2×D4—61no—
313C2×D4—61no—
314C22×C4—21no—
315C22×C4C2×D3211yescharacteristic
316M16—32no—
317M16—61no—
318M16—61no—
319M16—61no—
320M16—92no—
321M16—181no—
322C2×C8—31no—
323C2×C8—31no—
324C2×C8—61no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—181no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—91no—
332C4⋊C4—91no—
333C22⋊C4—181no—
334C42—181no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—122no—
345C22×C3—242no—
346C22×C3—242no—
347C22×C3—241no—
348C22×C3—241no—
349C22×C3#87211yescharacteristic
350C22×C3#87711yescharacteristic
351C22×C3#87911yescharacteristic
352C22×C3#88411yescharacteristic
353C22×C3#89811yescharacteristic
354C22×C3#93811yescharacteristic
355C2×D3—42no—
356C2×D3—82no—
357C2×D3—81no—
358C2×D3—81no—
359C2×D3—82no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—82no—
365C3×C4—81no—
366C3×C4—81no—
367C3×C4#67⋊C411yescharacteristic
368C3×C4#67⋊C411yescharacteristic
369C3×C4#88511yescharacteristic
370C3×C4#88511yescharacteristic
371C3×C4#89311yescharacteristic
372C3×C4#89411yescharacteristic
373C3×C4C4×#6711yescharacteristic
374C3×C4#93511yescharacteristic
375Dic3—121no—
376Dic3—121no—
377Dic3—121no—
378Dic3—121no—
379Dic3—241no—
380Dic3—241no—
381C32#193111yescharacteristic, complemented, Sylow
382C23—62no—
383C23—121no—
384C23—121no—
385C23—241no—
386C23—241no—
387C23#380411yescharacteristic
388D4—62no—
389D4—62no—
390D4—121no—
391D4—121no—
392C2×C4—41no—
393C2×C4—81no—
394C2×C4—181no—
395C2×C4—181no—
396C2×C4#379511yescharacteristic
397C2×C4#379511yescharacteristic
398C2×C4#379611yescharacteristic
399C2×C4C4×D3211yescharacteristic
400C2×C4D3×#6711yescharacteristic
401C2×C4#381111yescharacteristic
402C8—62no—
403C8—61no—
404C8—61no—
405C8—121no—
406C8—182no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—41no—
415C2×C3—41no—
416C2×C3—242no—
417C2×C3#466911yescharacteristic
418C2×C3#474911yescharacteristic
419C2×C3#475411yescharacteristic
420C2×C3#494411yescharacteristic
421C2×C3#516011yescharacteristic
422C2×C3#517711yescharacteristic
423D3—82no—
424C22—21no—
425C22—21no—
426C22—122no—
427C22—242no—
428C22—242no—
429C22—241no—
430C22—241no—
431C22#6385811yescharacteristic
432C22#6387711yescharacteristic
433C22#6395811yescharacteristic
434C4—81no—
435C4—361no—
436C4—361no—
437C4#6387911yescharacteristic
438C4#6388111yescharacteristic
439C4#6388411yescharacteristic
440C4#6391311yescharacteristic
441C3—21no—
442C3#6898311yescharacteristic, complemented
443C3#7019511yescharacteristic, complemented
444C2—21no—
445C2—21no—
446C2—242no—
447C2#1059128111yescharacteristic
448C2#1059140611yescharacteristic
449C2#1059154211yescharacteristic
subgroupG/H
centerC22#63958
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1931
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10592663C2semidirect
5. #10591059C2semidirect
6. C3×#4530C2semidirect
7. #10589166C2semidirect
23. #63558C4semidirect
40. #4530D3semidirect
381. C32#1931semidirect
442. C3#68983semidirect
443. C3#70195semidirect

Maximal subgroups

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

subgroupindex
#105926632
C2×C3×#8092
#105910862
C2×#635582
#105910592
C3×#45302
#105891662
#701953
#689833