Finite Group Databasebeta

← #11794355

Subgroups — #11794355

Order 1152.

513 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592698C211yesmaximal, characteristic, complemented
2C3×#5001C211yesmaximal, characteristic
3C3×#4995C211yesmaximal, characteristic, complemented
4C2×#63578C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic
6C2×#63558C211yesmaximal, characteristic
7#10589167C211yesmaximal, characteristic, complemented
8#70676—31nomaximal
9#70317—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C4⋊(C3⋊(C3⋊C8))—22no—
18C3×#809—21no—
19C3×#809—21no—
20C3×#808—21no—
21C3×#807—21no—
22#63578—22no—
23#63562—22no—
24#63558—22no—
25C3×#428—31no—
26C3×#418—31no—
27C2×#833—31no—
28C2×#832—31no—
29C2×#823—31no—
30C2×#822—31no—
31C2×#822—31no—
32#5001D311yescharacteristic
33#4999—31no—
34#4999—31no—
35#4999—61no—
36#4995D311yescharacteristic, complemented
37C2×#809—31no—
38#4554—31no—
39#4530—31no—
40C23×C3×D3—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3×Dic3—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12Q812yes—
49C32×C4⋊C4D411yescharacteristic
50C32×C4⋊C4D411yescharacteristic
51C32×C22⋊C4—21no—
52C32×C42—21no—
53#3748—21no—
54#3748—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)D412yes—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208—21no—
64C3×#208D412yes—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#2063—91noSylow
68C22×C3×D4—31no—
69C22×D12C2×D311yescharacteristic
70C2×C3×M16—31no—
71C2×C3×M16—31no—
72C3×#117—21no—
73C3×#117C2×D311yescharacteristic
74C3×#117C2×D311yescharacteristic
75C2×C3×C4⋊C4—31no—
76C2×C4⋊Dic3C2×D311yescharacteristic
77C2×#208—31no—
78C2×#208—31no—
79C2×#208—61no—
80C2×#208C2×D311yescharacteristic
81C2×#208C2×D311yescharacteristic
82C22×C3⋊C8—31no—
83C22×C3⋊C8—31no—
84C22×C3⋊C8—61no—
85C3×#107—61no—
86C3×#106—61no—
87C3×#102—61no—
88C3×#102—61no—
89#833—62no—
90#832—62no—
91#823—62no—
92#822—62no—
93#822—62no—
94#809—21no—
95#809—21no—
96#809—62no—
97#808—21no—
98#807—21no—
99C4⋊(C3⋊C8)—62no—
100C4⋊(C3⋊C8)—62no—
101C4⋊(C3⋊C8)—64no—
102C23×C32#4111yescharacteristic
103C22×C3×D3—22no—
104C22×C3×D3—41no—
105C22×C3×D3—41no—
106C22×C3×D3—81no—
107C22×C3×D3—81no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×Q811yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C3×Dic3—41no—
117C2×C3×Dic3—81no—
118C3×D12—22no—
119C3×D12—22no—
120C3×D12—41no—
121C3×D12—41no—
122C3⋊(C3⋊C8)—22no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—41no—
126C2×#108—91no—
127#428—31no—
128#424—91no—
129#418—31no—
130C2×#102—91no—
131C2×#100—91no—
132#343—91no—
133C24×C3—61no—
134C23×D3—21no—
135C2×C3×D4—32no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C22×C3×C4—21no—
142C22×C3×C4—61no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C22×Dic3—21no—
146C2×D12—21no—
147C2×D12—21no—
148C2×D12—21no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12Dic612yes—
152C3×M16—32no—
153C3×M16—61no—
154C3×M16—61no—
155C3×M16—61no—
156C2×C3×C8—61no—
157C2×C3×C8—61no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4#6711yescharacteristic
163C3×C4⋊C4#6711yescharacteristic
164C3×C4⋊C4#6711yescharacteristic
165C3×C4⋊C4#6711yescharacteristic
166C3×C22⋊C4—22no—
167C3×C22⋊C4—21no—
168C3×C22⋊C4—21no—
169C3×C42—22no—
170C3×C42—21no—
171C3×C42—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174#208—21no—
175#208—21no—
176#208—21no—
177#208—61no—
178#208—61no—
179#208—61no—
180#208—61no—
181#208—121no—
182#208—121no—
183#208D1212yes—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—32no—
187C2×C3⋊C8—32no—
188C2×C3⋊C8—62no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—62no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—121no—
197C2×C3⋊C8—121no—
198C22×C32—21no—
199C22×C32—21no—
200C22×C32#12111yescharacteristic
201C22×C32C22⋊Q811yescharacteristic
202C22×C32#12611yescharacteristic
203C2×C3×D3—42no—
204C2×C3×D3—82no—
205C2×C3×D3—81no—
206C2×C3×D3—81no—
207C2×C3×D3—82no—
208C32×C4—41no—
209C32×C4—41no—
210C32×C4#12111yescharacteristic
211C32×C4#12111yescharacteristic
212C32×C4C22⋊Q811yescharacteristic
213C32×C4C22⋊Q811yescharacteristic
214C3×Dic3—81no—
215C22×D4—31no—
216C2×M16—31no—
217C2×M16—31no—
218C2×M16—91no—
219C22×C8—91no—
220#117D3211yescharacteristic
221C2×C4⋊C4—31no—
222#108—182no—
223#107—61no—
224#106—61no—
225C4⋊C8—182no—
226#102—61no—
227#102—61no—
228#102—182no—
229#100—182no—
230C23×C3—21no—
231C23×C3—62no—
232C23×C3—121no—
233C23×C3—121no—
234C23×C3—241no—
235C23×C3—241no—
236C23×C3#23711yescharacteristic
237C23×C3#23711yescharacteristic
238C22×D3—22no—
239C22×D3—41no—
240C22×D3—41no—
241C22×D3—81no—
242C22×D3—81no—
243C3×D4—62no—
244C3×D4—62no—
245C3×D4—121no—
246C3×D4—121no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—121no—
260C2×C3×C4—241no—
261C2×C3×C4C2×Dic611yescharacteristic
262C2×C3×C4C2×D1211yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4#23711yescharacteristic
269C2×C3×C4D3×Q811yescharacteristic
270C2×C3×C4#23911yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×Dic3—41no—
274C2×Dic3—81no—
275D12—22no—
276D12—22no—
277D12—41no—
278D12—41no—
279C3×C8—62no—
280C3×C8—121no—
281C3⋊C8—22no—
282C3⋊C8—41no—
283C3⋊C8—62no—
284C3⋊C8—62no—
285C3⋊C8—122no—
286C3⋊C8—122no—
287C3⋊C8—121no—
288C3⋊C8—121no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32#39611yescharacteristic
292C2×C32#47111yescharacteristic
293C2×C32#47211yescharacteristic
294C3×D3—82no—
295C24—61no—
296C2×D4—32no—
297C2×D4—61no—
298C2×D4—61no—
299C2×D4—61no—
300C2×D4—61no—
301C2×D4—61no—
302C22×C4—61no—
303C22×C4C2×D3211yescharacteristic
304M16—32no—
305M16—61no—
306M16—61no—
307M16—61no—
308M16—181no—
309M16—181no—
310C2×C8—61no—
311C2×C8—61no—
312C2×C8—92no—
313C2×C8—181no—
314C2×C8—181no—
315C2×C8—181no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4#62511yescharacteristic
319C4⋊C4#62511yescharacteristic
320C22⋊C4—21no—
321C42—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—122no—
332C22×C3—242no—
333C22×C3—242no—
334C22×C3—241no—
335C22×C3—241no—
336C22×C3#87811yescharacteristic
337C22×C3#87911yescharacteristic
338C22×C3#89711yescharacteristic
339C22×C3#89811yescharacteristic
340C22×C3#93911yescharacteristic
341C22×C3#93911yescharacteristic
342C2×D3—42no—
343C2×D3—82no—
344C2×D3—81no—
345C2×D3—81no—
346C2×D3—82no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—42no—
352C3×C4—42no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—241no—
358C3×C4#87811yescharacteristic
359C3×C4#88411yescharacteristic
360C3×C4#89511yescharacteristic
361C3×C4#89611yescharacteristic
362C3×C4#92411yescharacteristic
363C3×C4#93011yescharacteristic
364C3×C4#93811yescharacteristic
365C3×C4#94611yescharacteristic
366Dic3—81no—
367C32#206311yescharacteristic, complemented, Sylow
368C23—62no—
369C23—121no—
370C23—121no—
371C23—241no—
372C23—241no—
373C23#380511yescharacteristic
374D4—62no—
375D4—62no—
376D4—121no—
377D4—121no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—121no—
381C2×C4—241no—
382C2×C4D3×Dic611yescharacteristic
383C2×C4#379511yescharacteristic
384C2×C4#379911yescharacteristic
385C2×C4D3×D1211yescharacteristic
386C2×C4C2×#62511yescharacteristic
387C2×C4#381111yescharacteristic
388C8—62no—
389C8—121no—
390C8—182no—
391C8—361no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—41no—
400C2×C3—41no—
401C2×C3—242no—
402C2×C3#494811yescharacteristic
403C2×C3#499411yescharacteristic
404C2×C3#519911yescharacteristic
405C2×C3#519911yescharacteristic
406C2×C3#520011yescharacteristic
407C2×C3#520311yescharacteristic
408D3—82no—
409C22—21no—
410C22—21no—
411C22—122no—
412C22—242no—
413C22—242no—
414C22—241no—
415C22—241no—
416C22#6386111yescharacteristic
417C22#6389311yescharacteristic
418C22#6398011yescharacteristic
419C4—41no—
420C4—41no—
421C4—241no—
422C4#6385611yescharacteristic
423C4#6389611yescharacteristic
424C4#6390811yescharacteristic
425C4#6391011yescharacteristic
426C3—21no—
427C3#7031711yescharacteristic, complemented
428C3#7067611yescharacteristic, complemented
429C2—21no—
430C2—21no—
431C2—242no—
432C2#1059131911yescharacteristic
433C2#1059167811yescharacteristic
434C2#1059168111yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#121
prime radicalC22×C3×D12C22
hypercenter#117D32
hypocenterC32#2063
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10592698C2semidirect
3. C3×#4995C2semidirect
4. C2×#63578C2semidirect
7. #10589167C2semidirect
36. #4995D3semidirect
367. C32#2063semidirect
427. C3#70317semidirect
428. C3#70676semidirect

Maximal subgroups

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

subgroupindex
#105926982
C3×#50012
C3×#49952
C2×#635782
C2×#635622
C2×#635582
#105891672
#706763
#703173