Finite Group Databasebeta

← C2×#10591046 #11899524

Subgroups — C2×#10591046 #11899524

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic, complemented
2C2×#63807C211yesmaximal, characteristic, complemented
3C2×#63656C211yesmaximal, characteristic, complemented
4C2×C3×#828C211yesmaximal, characteristic, complemented
5#10591046C218yesmaximal, direct product factor
6C2×#63548C211yesmaximal, characteristic, complemented
7C2×#63545C211yesmaximal, characteristic, complemented
8C2×D3×C3⋊C16C211yesmaximal, characteristic, complemented
9C2×#5194—31nomaximal
10C2×#4916—31nomaximal
11C2×C3×#239—21no—
12C2×#3795—21no—
13C2×C32×Q16C2211yescharacteristic
14C2×#3746C2211yescharacteristic
15C2×C3×#215—21no—
16C3×#919—22no—
17C3×#919C2214yescomplemented
18C2×C3×D24C2211yescharacteristic
19C2×C3×D24C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21C2×#3716—21no—
22#63807—22no—
23#63807C2214yescomplemented
24#63656C2214yescomplemented
25C2×C3⋊(C3⋊C16)C2211yescharacteristic
26C3×#828C2214yescomplemented
27C2×C3×C3⋊C16C2211yescharacteristic
28#63548C2214yescomplemented
29#63545C2214yescomplemented
30D3×C3⋊C16C2214yescomplemented
31C2×C3×#135—31no—
32C2×#919D311yescharacteristic, complemented
33C2×#912—31no—
34C2×#904—31no—
35C2×C3×SD32—31no—
36#5194—38no—
37C2×#829—31no—
38C2×#829—31no—
39C2×#829—61no—
40C2×#828D311yescharacteristic, complemented
41C2×#827—31no—
42C2×#826—31no—
43C2×#826—31no—
44C22×C3⋊C16—31no—
45#4916—38no—
46C2×#800—31no—
47C2×D3×C16—31no—
48C2×C32×Q8—21no—
49C2×#634—21no—
50C3×#239—24no—
51C3×#239—42no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—41no—
55C2×C3×C4×D3—41no—
56C2×C3×C4×D3D411yescharacteristic
57C2×#625—41no—
58C2×D3×Dic3—41no—
59#3795—24no—
60#3795—42no—
61C32×Q16—21no—
62C32×Q16C2312yes—
63C2×C32×C8C2311yescharacteristic
64#3746—21no—
65#3746C2312yes—
66C3×#215—24no—
67C2×C3×C3⋊C8D411yescharacteristic
68C3×D24—21no—
69C3×D24—21no—
70C3×D24C2312yes—
71C3×D24C2312yes—
72C3×D3×C8D412yes—
73C3×D3×C8C2312yes—
74#3716—24no—
75C3⋊(C3⋊C16)C2312yes—
76C3×C3⋊C16C2312yes—
77C2×#508—91noSylow
78C2×C3×#41—61no—
79C2×#239—21no—
80C2×#237—61no—
81C2×#235—61no—
82C3×#135—34no—
83C3×#135—62no—
84C2×C3×Q16—21no—
85C2×C3×Q16C2×D311yescharacteristic
86C2×C3×Q16C2×D311yescharacteristic
87C2×C3×SD16—61no—
88C2×C3×D8—31no—
89C2×C3×D8—31no—
90C22×C3×C8—31no—
91C2×#215—21no—
92C2×#214—61no—
93#919—22no—
94#919C2×D314yescomplemented
95#912—34no—
96#912—62no—
97C2×Dic12—31no—
98C2×Dic12—31no—
99C2×Dic12—61no—
100#904—34no—
101#904—62no—
102C2×D24C2×D311yescharacteristic
103C2×D24C2×D311yescharacteristic
104C2×#204—61no—
105C2×D3×C8C2×D311yescharacteristic
106C3×SD32—34no—
107C2×C3×C16—31no—
108#829—34no—
109#829—34no—
110#829—64no—
111#828C2×D314yescomplemented
112#827—34no—
113#826—34no—
114#826—34no—
115C2×C3⋊C16—31no—
116C2×C3⋊C16—31no—
117C2×C3⋊C16—34no—
118C2×C3⋊C16—61no—
119C2×C3⋊C16C2×D311yescharacteristic
120#800—34no—
121D3×C16—34no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3D811yescharacteristic
125C32×Q8—22no—
126C32×Q8—41no—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C3⋊Dic3—41no—
130#634—22no—
131#634—41no—
132C2×C3×Dic3D811yescharacteristic
133C3×D12—22no—
134C3×D12—22no—
135C3×D12—44no—
136C3×D12—41no—
137C3×D12—41no—
138C3×C4×D3—44no—
139C3×C4×D3D812yes—
140C3×C4×D3C2×D412yes—
141#625—44no—
142D3×Dic3—44no—
143C32×C8C2×D411yescharacteristic
144C32×C8C2411yescharacteristic
145C3×C3⋊C8C2×D412yes—
146C2×#135—31no—
147C2×#135—91no—
148#508—98no—
149C2×Q32—91no—
150C2×SD32—31no—
151C2×SD32—91no—
152C2×D16—91no—
153C22×C16—91no—
154C3×#41—64no—
155C3×#41—122no—
156C2×C3×Q8—21no—
157C2×C3×Q8—21no—
158C2×C3×Q8—41no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—121no—
162C22×C3×C4—31no—
163C22×C3×C4—121no—
164C2×#67—121no—
165C2×#67—121no—
166C22×Dic3—121no—
167#239—24no—
168#239—42no—
169#237—64no—
170#237—122no—
171#235—64no—
172#235—122no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12—41no—
176C2×C4×D3—41no—
177C2×C4×D3—121no—
178C2×C4×D3#6711yescharacteristic
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6—121no—
182C3×Q16—21no—
183C3×Q16—21no—
184C3×Q16—22no—
185C3×Q16—41no—
186C3×Q16C22×D312yes—
187C3×Q16C22×D312yes—
188C3×SD16—64no—
189C3×D8—32no—
190C3×D8—32no—
191C3×D8—61no—
192C3×D8—61no—
193C2×C3×C8—21no—
194C2×C3×C8—31no—
195C2×C3×C8—32no—
196C2×C3×C8—32no—
197C2×C3×C8C22×D311yescharacteristic
198C2×C3×C8C22×D311yescharacteristic
199#215—24no—
200#214—64no—
201C2×C3⋊C8#6711yescharacteristic
202Dic12—32no—
203Dic12—32no—
204Dic12—62no—
205Dic12—61no—
206Dic12—61no—
207Dic12—121no—
208D24—21no—
209D24—21no—
210D24C22×D312yes—
211D24C22×D312yes—
212#204—64no—
213D3×C8#6712yes—
214D3×C8C22×D312yes—
215C3×C16—32no—
216C3⋊C16—32no—
217C3⋊C16—32no—
218C3⋊C16—62no—
219C3⋊C16C22×D312yes—
220C22×C32C2×D811yescharacteristic
221C2×C3×D3—22no—
222C2×C3×D3—42no—
223C2×C3×D3—42no—
224C2×C3×D3—82no—
225C2×C3×D3—82no—
226C2×C3×D3C2×D812yes—
227C32×C4—42no—
228C32×C4C2×D811yescharacteristic
229C32×C4C22×D411yescharacteristic
230C3⋊Dic3—42no—
231C3×Dic3C2×D812yes—
232C2×#41—61no—
233C2×#41—181no—
234#135—34no—
235#135—62no—
236#135—94no—
237#135—182no—
238C2×Q16—91no—
239C2×Q16D3211yescharacteristic
240C2×SD16—61no—
241C2×SD16—181no—
242C2×D8—31no—
243C2×D8—31no—
244C22×C8—31no—
245Q32—94no—
246SD32—34no—
247SD32—94no—
248D16—94no—
249C2×C16—31no—
250C2×C16—94no—
251C2×C16—91no—
252C23×C3—31no—
253C23×C3—121no—
254C23×C3—121no—
255C22×D3—41no—
256C22×D3—41no—
257C22×D3#21311yescharacteristic
258C3×Q8—22no—
259C3×Q8—22no—
260C3×Q8—42no—
261C3×Q8—41no—
262C3×Q8—41no—
263C3×Q8—81no—
264C3×D4—62no—
265C3×D4—62no—
266C3×D4—124no—
267C3×D4—121no—
268C3×D4—121no—
269C2×C3×C4—21no—
270C2×C3×C4—31no—
271C2×C3×C4—32no—
272C2×C3×C4—32no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—81no—
276C2×C3×C4—124no—
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279#67—124no—
280#67—124no—
281C2×Dic3—121no—
282C2×Dic3—121no—
283C2×Dic3—124no—
284C2×Dic3—241no—
285C2×Dic3#21311yescharacteristic
286D12—22no—
287D12—22no—
288D12—44no—
289D12—41no—
290D12—41no—
291C4×D3—44no—
292C4×D3—124no—
293C4×D3#21312yes—
294C4×D3C2×#6712yes—
295Dic6—62no—
296Dic6—62no—
297Dic6—122no—
298Dic6—121no—
299Dic6—121no—
300Dic6—241no—
301C3×C8—21no—
302C3×C8—21no—
303C3×C8—32no—
304C3×C8D3×D411yescharacteristic
305C3×C8C2×#6711yescharacteristic
306C3×C8C23×D311yescharacteristic
307C3×C8C23×D311yescharacteristic
308C3⋊C8C2×#6712yes—
309C2×C32#50812yescomplemented
310C2×C32C22×D811yescharacteristic
311C3×D3—22no—
312C3×D3—82no—
313C3×D3—82no—
314#41—64no—
315#41—122no—
316#41—184no—
317#41—362no—
318C2×Q8—21no—
319C2×Q8—181no—
320C2×D4—61no—
321C2×D4—61no—
322C2×D4—121no—
323C2×D4—361no—
324C22×C4—31no—
325C22×C4—121no—
326C22×C4—361no—
327Q16—21no—
328Q16—92no—
329Q16—181no—
330Q16C2×D3212yes—
331SD16—64no—
332SD16—184no—
333D8—32no—
334D8—32no—
335D8—61no—
336D8—61no—
337C2×C8—31no—
338C2×C8—32no—
339C2×C8—32no—
340C2×C8C2×D3211yescharacteristic
341C16—32no—
342C16—92no—
343C22×C3—21no—
344C22×C3—32no—
345C22×C3—62no—
346C22×C3—122no—
347C22×C3—122no—
348C22×C3—242no—
349C22×C3—242no—
350C22×C3D3×D811yescharacteristic
351C22×C3C2×#21311yescharacteristic
352C2×D3—22no—
353C2×D3—42no—
354C2×D3—42no—
355C2×D3—82no—
356C2×D3—82no—
357C2×D3C2×#21312yes—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—32no—
361C3×C4—42no—
362C3×C4—42no—
363C3×C4—82no—
364C3×C4D3×D811yescharacteristic
365C3×C4C2×#21311yescharacteristic
366C3×C4C2×D3×D411yescharacteristic
367C3×C4C22×#6711yescharacteristic
368Dic3—122no—
369Dic3—122no—
370Dic3—242no—
371Dic3C2×#21312yes—
372C32C2×#50811yescharacteristic, complemented, Sylow
373C23—31no—
374C23—121no—
375C23—121no—
376Q8—22no—
377Q8—41no—
378Q8—182no—
379Q8—361no—
380D4—62no—
381D4—62no—
382D4—124no—
383D4—121no—
384D4—121no—
385D4—364no—
386C2×C4—31no—
387C2×C4—32no—
388C2×C4—32no—
389C2×C4—41no—
390C2×C4—124no—
391C2×C4—364no—
392C2×C4—361no—
393C2×C4D3×#6711yescharacteristic
394C8—32no—
395C8D3×#6711yescharacteristic
396C8C22×D3211yescharacteristic
397C2×C3—21no—
398C2×C3—22no—
399C2×C3—62no—
400C2×C3—242no—
401C2×C3—242no—
402C2×C3#491612yescomplemented
403C2×C3#519412yescomplemented
404C2×C3C2×D3×D811yescharacteristic
405C2×C3C22×#21311yescharacteristic
406D3—22no—
407D3—82no—
408D3—82no—
409C22—32no—
410C22—62no—
411C22—122no—
412C22—122no—
413C22—242no—
414C22—242no—
415C22D3×#21311yescharacteristic
416C4—32no—
417C4—42no—
418C4—362no—
419C4D3×#21311yescharacteristic
420C4C2×D3×#6711yescharacteristic
421C3—21no—
422C3C2×#491611yescharacteristic, complemented
423C3C2×#519411yescharacteristic, complemented
424C2—62no—
425C2—242no—
426C2—242no—
427C2#1059104612yesdirect product factor
428C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
hypercenterC2×Q16D32
hypocenterC32C2×#508
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#919C2semidirect
2. C2×#63807C2semidirect
3. C2×#63656C2semidirect
4. C2×C3×#828C2semidirect
5. #10591046C2direct (N × H)
6. C2×#63548C2semidirect
7. C2×#63545C2semidirect
8. C2×D3×C3⋊C16C2semidirect
17. C3×#919C22semidirect
23. #63807C22semidirect
24. #63656C22semidirect
26. C3×#828C22semidirect
28. #63548C22semidirect
29. #63545C22semidirect
30. D3×C3⋊C16C22semidirect
32. C2×#919D3semidirect
40. C2×#828D3semidirect
94. #919C2×D3semidirect
111. #828C2×D3semidirect
309. C2×C32#508semidirect
372. C32C2×#508semidirect
402. C2×C3#4916semidirect
403. C2×C3#5194semidirect
422. C3C2×#4916semidirect
423. C3C2×#5194semidirect
427. C2#10591046direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9192
C2×#638072
C2×#636562
C2×C3×#8282
#105910462
C2×#635482
C2×#635452
C2×D3×C3⋊C162
C2×#51943
C2×#49163