Finite Group Databasebeta

← #11794352

Subgroups — #11794352

Order 1152.

515 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592663C211yesmaximal, characteristic, complemented
2C2×C3×#809C211yesmaximal, characteristic
3C2×#63577C211yesmaximal, characteristic, complemented
4#10591119C211yesmaximal, characteristic, complemented
5#10591086C211yesmaximal, characteristic
6C2×#63558C211yesmaximal, characteristic
7C3×#4530C211yesmaximal, characteristic, complemented
8#70197—31nomaximal
9#68996—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—22no—
20#63577—22no—
21#63572—22no—
22#63563—21no—
23#63563—21no—
24#63558—22no—
25C2×C3×#102—31no—
26C2×#833—31no—
27#5215—31no—
28#5131—31no—
29C2×#823—31no—
30C2×#822—31no—
31#5119—31no—
32C2×#819—31no—
33#5102—31no—
34C2×#809D311yescharacteristic
35#4964—31no—
36#4964—31no—
37#4964—61no—
38C3×#343—31no—
39#4530D311yescharacteristic, complemented
40C23×C3×D3—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
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⋊C4—21no—
50C32×C4⋊C4—21no—
51#3757—21no—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53C4⋊(C3⋊Dic3)D411yescharacteristic
54C4×C3⋊Dic3—21no—
55#3748—21no—
56#3748D412yes—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C2×C3×C3⋊C8—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—31no—
69C22×D12C2×D311yescharacteristic
70C2×C3×M16—31no—
71C2×C3×M16—31no—
72C22×C3×C8—31no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4C2×D311yescharacteristic
75C2×C3×C4⋊C4C2×D311yescharacteristic
76#926—31no—
77#926—31no—
78#926—61no—
79C2×#208—31no—
80C2×#208—31no—
81C2×#208—61no—
82C2×#208C2×D311yescharacteristic
83C2×#208C2×D311yescharacteristic
84C22×C3⋊C8C2×D311yescharacteristic
85C3×#102—62no—
86#833—62no—
87#832—61no—
88#832—61no—
89#823—62no—
90#822—62no—
91#821—61no—
92#821—61no—
93#819—62no—
94Dic3⋊C8—62no—
95Dic3⋊C8—62no—
96#809—22no—
97#808—61no—
98#808—61no—
99#808—62no—
100#807—61no—
101#807—61no—
102#807—62no—
103C23×C32#4111yescharacteristic
104C22×C3×D3—22no—
105C22×C3×D3—41no—
106C22×C3×D3—41no—
107C22×C3×D3—81no—
108C22×C3×D3—81no—
109C2×C32×C4—41no—
110C2×C32×C4—81no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×Q811yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C3×D12—22no—
120C3×D12—22no—
121C3×D12—41no—
122C3×D12—41no—
123C3⋊(C3⋊C8)—22no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—41no—
126C3×C3⋊C8—41no—
127C2×#108—91no—
128#428—91no—
129#424—91no—
130#418—91no—
131C2×#102—31no—
132C2×#100—91no—
133#343—31no—
134C24×C3—61no—
135C23×D3—21no—
136C2×C3×D4—32no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C2×C3×D4—61no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—41no—
146C22×C3×C4C22×D311yescharacteristic
147C22×C3×C4C22×D311yescharacteristic
148C2×D12—21no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12Dic612yes—
154C3×M16—61no—
155C3×M16—61no—
156C3×M16—61no—
157C3×M16—61no—
158C2×C3×C8—32no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—41no—
169#217—61no—
170#217—61no—
171#217—121no—
172C4⋊Dic3—31no—
173C4⋊Dic3—31no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180C4×Dic3—121no—
181#208—21no—
182#208—21no—
183#208—21no—
184#208—21no—
185#208—32no—
186#208—32no—
187#208—62no—
188#208—62no—
189#208—61no—
190#208—61no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—62no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8#6712yes—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32#12111yescharacteristic
202C22×C32C22⋊Q811yescharacteristic
203C22×C32#12611yescharacteristic
204C2×C3×D3—42no—
205C2×C3×D3—82no—
206C2×C3×D3—81no—
207C2×C3×D3—81no—
208C2×C3×D3—82no—
209C32×C4—81no—
210C32×C4#12111yescharacteristic
211C32×C4#12111yescharacteristic
212C32×C4C22⋊Q811yescharacteristic
213C32×C4C22⋊Q811yescharacteristic
214C3⋊Dic3—41no—
215C3⋊Dic3—41no—
216C22×D4—31no—
217C2×M16—31no—
218C2×M16—31no—
219C2×M16—91no—
220C22×C8—31no—
221#117—91no—
222C2×C4⋊C4D3211yescharacteristic
223#108—182no—
224#107—181no—
225#106—181no—
226C4⋊C8—182no—
227#102—62no—
228#102—181no—
229#102—181no—
230#100—182no—
231C23×C3—21no—
232C23×C3—62no—
233C23×C3—121no—
234C23×C3—121no—
235C23×C3—241no—
236C23×C3—241no—
237C23×C3#23511yescharacteristic
238C23×C3#23711yescharacteristic
239C22×D3—22no—
240C22×D3—41no—
241C22×D3—41no—
242C22×D3—81no—
243C22×D3—81no—
244C3×D4—62no—
245C3×D4—62no—
246C3×D4—121no—
247C3×D4—121no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—42no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—82no—
258C2×C3×C4—81no—
259C2×C3×C4—81no—
260C2×C3×C4C2×Dic611yescharacteristic
261C2×C3×C4#23511yescharacteristic
262C2×C3×C4#23511yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4#23711yescharacteristic
270C2×C3×C4D3×Q811yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—121no—
277C2×Dic3—121no—
278D12—22no—
279D12—22no—
280D12—41no—
281D12—41no—
282C3×C8—62no—
283C3×C8—121no—
284C3×C8—121no—
285C3⋊C8—22no—
286C3⋊C8—41no—
287C3⋊C8—41no—
288C3⋊C8—64no—
289C3⋊C8—62no—
290C3⋊C8—62no—
291C2×C32—21no—
292C2×C32—21no—
293C2×C32#39611yescharacteristic
294C2×C32#47111yescharacteristic
295C2×C32#47211yescharacteristic
296C3×D3—82no—
297C24—61no—
298C2×D4—32no—
299C2×D4—61no—
300C2×D4—61no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—61no—
304C22×C4—21no—
305C22×C4C2×D3211yescharacteristic
306M16—61no—
307M16—61no—
308M16—61no—
309M16—61no—
310M16—92no—
311M16—181no—
312C2×C8—32no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8—61no—
317C2×C8—181no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—91no—
321C4⋊C4—91no—
322C22⋊C4—181no—
323C42—181no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—122no—
334C22×C3—242no—
335C22×C3—242no—
336C22×C3—241no—
337C22×C3—241no—
338C22×C3#87611yescharacteristic
339C22×C3#87811yescharacteristic
340C22×C3#87911yescharacteristic
341C22×C3#88411yescharacteristic
342C22×C3#89611yescharacteristic
343C22×C3#93811yescharacteristic
344C2×D3—42no—
345C2×D3—82no—
346C2×D3—81no—
347C2×D3—81no—
348C2×D3—82no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—82no—
354C3×C4—81no—
355C3×C4—81no—
356C3×C4#87811yescharacteristic
357C3×C4#88411yescharacteristic
358C3×C4#88411yescharacteristic
359C3×C4#88411yescharacteristic
360C3×C4#89611yescharacteristic
361C3×C4#89611yescharacteristic
362C3×C4#92411yescharacteristic
363C3×C4#93911yescharacteristic
364Dic3—121no—
365Dic3—121no—
366Dic3—121no—
367Dic3—121no—
368Dic3—241no—
369Dic3—241no—
370C32#206311yescharacteristic, complemented, Sylow
371C23—62no—
372C23—121no—
373C23—121no—
374C23—241no—
375C23—241no—
376C23#380411yescharacteristic
377D4—62no—
378D4—62no—
379D4—121no—
380D4—121no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4—181no—
384C2×C4—181no—
385C2×C4D3×Dic611yescharacteristic
386C2×C4#379511yescharacteristic
387C2×C4#379811yescharacteristic
388C2×C4#380211yescharacteristic
389C2×C4D3×#6711yescharacteristic
390C2×C4#381111yescharacteristic
391C8—62no—
392C8—121no—
393C8—121no—
394C8—182no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—41no—
403C2×C3—41no—
404C2×C3—242no—
405C2×C3#467611yescharacteristic
406C2×C3#474911yescharacteristic
407C2×C3#475411yescharacteristic
408C2×C3#494811yescharacteristic
409C2×C3#516011yescharacteristic
410C2×C3#517711yescharacteristic
411D3—82no—
412C22—21no—
413C22—21no—
414C22—122no—
415C22—242no—
416C22—242no—
417C22—241no—
418C22—241no—
419C22#6385911yescharacteristic
420C22#6389911yescharacteristic
421C22#6395811yescharacteristic
422C4—81no—
423C4—361no—
424C4—361no—
425C4#6385111yescharacteristic
426C4#6388511yescharacteristic
427C4#6389611yescharacteristic
428C4#6391211yescharacteristic
429C3—21no—
430C3#6899611yescharacteristic, complemented
431C3#7019711yescharacteristic, complemented
432C2—21no—
433C2—21no—
434C2—242no—
435C2#1059130911yescharacteristic
436C2#1059140611yescharacteristic
437C2#1059154211yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2063
LCSG ▷ C22×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
3. C2×#63577C2semidirect
4. #10591119C2semidirect
7. C3×#4530C2semidirect
39. #4530D3semidirect
370. C32#2063semidirect
430. C3#68996semidirect
431. C3#70197semidirect

Maximal subgroups

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

subgroupindex
#105926632
C2×C3×#8092
C2×#635772
#105911192
#105910862
C2×#635582
C3×#45302
#701973
#689963