Finite Group Databasebeta

← C2×#10591031 #11899564

Subgroups — C2×#10591031 #11899564

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D8C211yesmaximal, characteristic, complemented
2C2×#63807C211yesmaximal, characteristic, complemented
3C2×#63654C211yesmaximal, characteristic, complemented
4C2×C3×#826C211yesmaximal, characteristic, complemented
5#10591031C218yesmaximal, direct product factor
6C2×#63548C211yesmaximal, characteristic, complemented
7C2×#63545C211yesmaximal, characteristic, complemented
8C2×#63543C211yesmaximal, characteristic, complemented
9C2×#5147—31nomaximal
10C2×#4911—31nomaximal
11C2×C3×D3×D4—21no—
12C2×#3795—21no—
13C2×C32×D8C2211yescharacteristic
14C2×#3746C2211yescharacteristic, complemented
15C2×C3×#213—21no—
16C3×D3×D8—22no—
17C3×D3×D8C2214yescomplemented
18C2×C3×D24C2211yescharacteristic
19C2×C3×D24C2211yescharacteristic, complemented
20C2×C3×D3×C8C2211yescharacteristic
21C2×#3716—21no—
22#63807—22no—
23#63807C2214yescomplemented
24#63654C2214yescomplemented
25C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
26C3×#826C2214yescomplemented
27C2×C3×C3⋊C16C2211yescharacteristic, complemented
28#63548C2214yescomplemented
29#63545C2214yescomplemented
30#63543C2214yescomplemented
31C22×C3×D8—31no—
32C2×#912—31no—
33C2×D3×D8D311yescharacteristic, complemented
34C2×#904—31no—
35C2×C3×D16—31no—
36C2×#827—31no—
37C2×#827—31no—
38C2×#827—31no—
39C2×#827—61no—
40#5147—38no—
41C2×#826—31no—
42C2×#826—31no—
43C2×#826D311yescharacteristic, complemented
44C2×#812—31no—
45#4911—38no—
46C2×#800—31no—
47C2×#798—31no—
48C23×C3×D3—41no—
49C2×C32×D4—21no—
50C2×#634—21no—
51C2×C3×#67—41no—
52C3×D3×D4—24no—
53C3×D3×D4—42no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×C4×D3D411yescharacteristic
57C2×#625—41no—
58C2×D3×Dic3—41no—
59#3795—24no—
60#3795—42no—
61C32×D8—21no—
62C32×D8C2312yes—
63C2×C32×C8C2311yescharacteristic
64#3746—21no—
65#3746C2312yescomplemented
66C3×#213—24no—
67C2×C3×C3⋊C8D411yescharacteristic
68C3×D24—21no—
69C3×D24—21no—
70C3×D24C2312yes—
71C3×D24C2312yescomplemented
72C3×D3×C8D412yes—
73C3×D3×C8C2312yes—
74#3716—24no—
75C3⋊(C3⋊C16)C2312yescomplemented
76C3×C3⋊C16C2312yescomplemented
77C2×#509—91noSylow
78C22×C3×D4—61no—
79C2×#237—61no—
80C2×D3×D4—21no—
81C2×#235—61no—
82C2×C3×D8—21no—
83C2×C3×D8—34no—
84C2×C3×D8—31no—
85C2×C3×D8—31no—
86C2×C3×D8—62no—
87C2×C3×D8—61no—
88C2×C3×D8C2×D311yescharacteristic
89C2×C3×D8C2×D311yescharacteristic
90C22×C3×C8—31no—
91C2×#214—61no—
92C2×#213—21no—
93#912—34no—
94#912—62no—
95D3×D8—22no—
96D3×D8C2×D314yescomplemented
97C2×Dic12—31no—
98C2×Dic12—31no—
99C2×Dic12—61no—
100#904—34no—
101#904—62no—
102C2×D24C2×D311yescharacteristic
103C2×D24C2×D311yescharacteristic, complemented
104C2×#204—61no—
105C2×D3×C8C2×D311yescharacteristic
106C3×D16—34no—
107C2×C3×C16—31no—
108#827—34no—
109#827—34no—
110#827—34no—
111#827—64no—
112#826—34no—
113#826—34no—
114#826C2×D314yescomplemented
115#812—34no—
116C2×C3⋊C16—31no—
117C2×C3⋊C16—31no—
118C2×C3⋊C16—61no—
119C2×C3⋊C16C2×D311yescharacteristic, complemented
120#800—34no—
121#798—34no—
122C23×C32—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—44no—
126C22×C3×D3—84no—
127C22×C3×D3D811yescharacteristic
128C32×D4—22no—
129C32×D4—41no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C3⋊Dic3—41no—
132#634—22no—
133#634—41no—
134C3×#67—44no—
135C2×C3×Dic3D811yescharacteristic
136C3×D12—22no—
137C3×D12—22no—
138C3×D12—41no—
139C3×D12—41no—
140C3×C4×D3D812yes—
141C3×C4×D3C2×D412yes—
142#625—44no—
143D3×Dic3—44no—
144C32×C8C2×D411yescharacteristic
145C32×C8C2411yescharacteristic
146C3×C3⋊C8C2×D412yes—
147C2×#135—91no—
148C22×D8—31no—
149#509—98no—
150C2×SD32—91no—
151C2×SD32—91no—
152C2×D16—31no—
153C2×D16—91no—
154C2×M32—91no—
155C24×C3—121no—
156C23×D3—41no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—41no—
160C2×C3×D4—64no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—122no—
164C2×C3×D4—121no—
165C22×C3×C4—31no—
166C2×#67—41no—
167C2×#67—121no—
168C2×#67—121no—
169C22×Dic3—121no—
170#237—64no—
171#237—122no—
172D3×D4—24no—
173D3×D4—42no—
174#235—64no—
175#235—122no—
176C2×D12—21no—
177C2×D12—21no—
178C2×C4×D3—121no—
179C2×C4×D3#6711yescharacteristic
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—121no—
183C3×D8—21no—
184C3×D8—21no—
185C3×D8—22no—
186C3×D8—32no—
187C3×D8—32no—
188C3×D8—41no—
189C3×D8—64no—
190C3×D8—61no—
191C3×D8—61no—
192C3×D8C22×D312yes—
193C3×D8C22×D312yes—
194C2×C3×C8—21no—
195C2×C3×C8—31no—
196C2×C3×C8—32no—
197C2×C3×C8—32no—
198C2×C3×C8C22×D311yescharacteristic
199C2×C3×C8C22×D311yescharacteristic
200#214—64no—
201#213—24no—
202C2×C3⋊C8#6711yescharacteristic
203Dic12—32no—
204Dic12—32no—
205Dic12—62no—
206Dic12—61no—
207Dic12—61no—
208Dic12—121no—
209D24—21no—
210D24—21no—
211D24C22×D312yes—
212D24C22×D312yescomplemented
213#204—64no—
214D3×C8#6712yes—
215D3×C8C22×D312yes—
216C3×C16—32no—
217C3⋊C16—32no—
218C3⋊C16—32no—
219C3⋊C16—62no—
220C3⋊C16C22×D312yescomplemented
221C22×C32—42no—
222C22×C32—82no—
223C22×C32C2×D811yescharacteristic
224C2×C3×D3—22no—
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C2×C3×D3—88no—
228C2×C3×D3—82no—
229C2×C3×D3—82no—
230C2×C3×D3C2×D812yes—
231C32×C4C2×D811yescharacteristic
232C32×C4C22×D411yescharacteristic
233C3⋊Dic3—42no—
234C3×Dic3C2×D812yes—
235C2×#41—181no—
236C22×D4—61no—
237#135—94no—
238#135—182no—
239C2×Q16—91no—
240C2×SD16—181no—
241C2×D8—34no—
242C2×D8—31no—
243C2×D8—31no—
244C2×D8—62no—
245C2×D8—61no—
246C2×D8D3211yescharacteristic
247C22×C8—31no—
248SD32—94no—
249SD32—94no—
250D16—34no—
251D16—94no—
252M32—94no—
253C2×C16—31no—
254C2×C16—91no—
255C23×C3—31no—
256C23×C3—41no—
257C23×C3—41no—
258C23×C3—81no—
259C23×C3—124no—
260C23×C3—121no—
261C23×C3—121no—
262C23×C3—244no—
263C22×D3—41no—
264C22×D3—41no—
265C22×D3—44no—
266C22×D3—84no—
267C22×D3#21311yescharacteristic
268C3×D4—22no—
269C3×D4—22no—
270C3×D4—42no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—62no—
274C3×D4—62no—
275C3×D4—81no—
276C3×D4—124no—
277C3×D4—121no—
278C3×D4—121no—
279C2×C3×C4—21no—
280C2×C3×C4—31no—
281C2×C3×C4—32no—
282C2×C3×C4—32no—
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285#67—44no—
286#67—124no—
287#67—124no—
288C2×Dic3—121no—
289C2×Dic3—121no—
290C2×Dic3—124no—
291C2×Dic3—241no—
292C2×Dic3#21311yescharacteristic
293D12—22no—
294D12—22no—
295D12—41no—
296D12—41no—
297C4×D3—124no—
298C4×D3#21312yes—
299C4×D3C2×#6712yes—
300Dic6—62no—
301Dic6—62no—
302Dic6—122no—
303Dic6—121no—
304Dic6—121no—
305Dic6—241no—
306C3×C8—21no—
307C3×C8—21no—
308C3×C8—32no—
309C3×C8D3×D411yescharacteristic
310C3×C8C2×#6711yescharacteristic
311C3×C8C23×D311yescharacteristic
312C3×C8C23×D311yescharacteristic
313C3⋊C8C2×#6712yes—
314C2×C32—82no—
315C2×C32#50912yescomplemented
316C2×C32C22×D811yescharacteristic
317C3×D3—22no—
318C3×D3—82no—
319C3×D3—82no—
320C24—121no—
321#41—184no—
322#41—362no—
323C2×Q8—181no—
324C2×D4—21no—
325C2×D4—64no—
326C2×D4—61no—
327C2×D4—61no—
328C2×D4—122no—
329C2×D4—121no—
330C2×D4—361no—
331C22×C4—31no—
332C22×C4—361no—
333Q16—92no—
334Q16—181no—
335SD16—184no—
336D8—21no—
337D8—32no—
338D8—32no—
339D8—64no—
340D8—61no—
341D8—61no—
342D8C2×D3212yes—
343C2×C8—31no—
344C2×C8—32no—
345C2×C8—32no—
346C2×C8C2×D3211yescharacteristic
347C16—32no—
348C16—92no—
349C22×C3—21no—
350C22×C3—32no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3—62no—
354C22×C3—82no—
355C22×C3—82no—
356C22×C3—82no—
357C22×C3—122no—
358C22×C3—122no—
359C22×C3—162no—
360C22×C3—248no—
361C22×C3—242no—
362C22×C3—242no—
363C22×C3D3×D811yescharacteristic
364C22×C3C2×#21311yescharacteristic
365C2×D3—22no—
366C2×D3—42no—
367C2×D3—42no—
368C2×D3—88no—
369C2×D3—82no—
370C2×D3—82no—
371C2×D3C2×#21312yes—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—32no—
375C3×C4D3×D811yescharacteristic
376C3×C4C2×#21311yescharacteristic
377C3×C4C2×D3×D411yescharacteristic
378C3×C4C22×#6711yescharacteristic
379Dic3—122no—
380Dic3—122no—
381Dic3—242no—
382Dic3C2×#21312yes—
383C32C2×#50911yescharacteristic, complemented, Sylow
384C23—31no—
385C23—41no—
386C23—124no—
387C23—121no—
388C23—121no—
389C23—244no—
390Q8—182no—
391Q8—361no—
392D4—22no—
393D4—41no—
394D4—62no—
395D4—62no—
396D4—124no—
397D4—121no—
398D4—121no—
399D4—364no—
400C2×C4—31no—
401C2×C4—32no—
402C2×C4—32no—
403C2×C4—364no—
404C2×C4—361no—
405C2×C4D3×#6711yescharacteristic
406C8—32no—
407C8D3×#6711yescharacteristic
408C8C22×D3211yescharacteristic
409C2×C3—21no—
410C2×C3—22no—
411C2×C3—62no—
412C2×C3—82no—
413C2×C3—82no—
414C2×C3—162no—
415C2×C3—242no—
416C2×C3—242no—
417C2×C3#491112yescomplemented
418C2×C3#514712yescomplemented
419C2×C3C2×D3×D811yescharacteristic
420C2×C3C22×#21311yescharacteristic
421D3—22no—
422D3—82no—
423D3—82no—
424C22—32no—
425C22—42no—
426C22—62no—
427C22—82no—
428C22—122no—
429C22—122no—
430C22—248no—
431C22—242no—
432C22—242no—
433C22D3×#21311yescharacteristic
434C4—32no—
435C4—362no—
436C4D3×#21311yescharacteristic
437C4C2×D3×#6711yescharacteristic
438C3—21no—
439C3C2×#491111yescharacteristic, complemented
440C3C2×#514711yescharacteristic, complemented
441C2—62no—
442C2—82no—
443C2—242no—
444C2—242no—
445C2#1059103112yesdirect product factor
446C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×D8C22
socleC22×C32C2×D8
hypercenterC2×D8D32
hypocenterC32C2×#509
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×D8C2semidirect
2. C2×#63807C2semidirect
3. C2×#63654C2semidirect
4. C2×C3×#826C2semidirect
5. #10591031C2direct (N × H)
6. C2×#63548C2semidirect
7. C2×#63545C2semidirect
8. C2×#63543C2semidirect
14. C2×#3746C22semidirect
17. C3×D3×D8C22semidirect
19. C2×C3×D24C22semidirect
23. #63807C22semidirect
24. #63654C22semidirect
25. C2×C3⋊(C3⋊C16)C22semidirect
26. C3×#826C22semidirect
27. C2×C3×C3⋊C16C22semidirect
28. #63548C22semidirect
29. #63545C22semidirect
30. #63543C22semidirect
33. C2×D3×D8D3semidirect
43. C2×#826D3semidirect
65. #3746C23semidirect
71. C3×D24C23semidirect
75. C3⋊(C3⋊C16)C23semidirect
76. C3×C3⋊C16C23semidirect
96. D3×D8C2×D3semidirect
103. C2×D24C2×D3semidirect
114. #826C2×D3semidirect
119. C2×C3⋊C16C2×D3semidirect
212. D24C22×D3semidirect
220. C3⋊C16C22×D3semidirect
315. C2×C32#509semidirect
383. C32C2×#509semidirect
417. C2×C3#4911semidirect
418. C2×C3#5147semidirect
439. C3C2×#4911semidirect
440. C3C2×#5147semidirect
445. C2#10591031direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D3×D82
C2×#638072
C2×#636542
C2×C3×#8262
#105910312
C2×#635482
C2×#635452
C2×#635432
C2×#51473
C2×#49113