Finite Group Databasebeta

← C2×#10591073 #11857405

Subgroups — C2×#10591073 #11857405

Order 1152.

2029 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C22×C3×#208C211yesmaximal, characteristic, complemented
3C23×C3×C3⋊C8C211yesmaximal, characteristic, complemented
4#10591073C218yesmaximal, direct product factor
5C2×#63557C214yesmaximal, complemented
6C2×#5129—31nomaximal
7C2×#5110—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×#638C412yes—
10C2×#3828—24no—
11C2×#3828—24no—
12C2×#3828C414yes—
13C2×#3828C2214yes—
14C22×C4⋊(C3⋊D3)C411yescharacteristic
15C22×C4×C3⋊D3C2212yes—
16C22×#634C411yescharacteristic
17C2×C3×#208—24no—
18C2×C3×#208C2214yescomplemented
19C22×C3×C3⋊C8—24no—
20C22×C3×C3⋊C8C2212yes—
21C22×C3×C3⋊C8C2212yes—
22C22×C3×C3⋊C8C2214yescomplemented
23#63557C22116yescomplemented
24C22×#235—31no—
25C22×#235—31no—
26C22×#235—61no—
27C22×C3×M16—31no—
28C23×C3×C8—31no—
29C22×#208D311yescharacteristic, complemented
30C23×C3⋊C8D311yescharacteristic, complemented
31#5129—38no—
32#5110—38no—
33C2×(C2×D3)⋊C8—34no—
34C2×(C2×D3)⋊C8—34no—
35C24×C32C2×C411yescharacteristic
36C23×C3⋊D3C2×C412yes—
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4C2×C412yes—
39C22×C32×C4D414yes—
40C22×C32×C4D414yes—
41C22×C32×C4C2311yescharacteristic
42C22×C32×C4C2312yes—
43C2×#638—28no—
44C2×#638C2×C418yes—
45C22×C3⋊Dic3C2×C412yes—
46#3828—216no—
47#3828—28no—
48#3828—28no—
49C2×C4⋊(C3⋊D3)—24no—
50C2×C4⋊(C3⋊D3)C2×C414yes—
51C2×C4×C3⋊D3—24no—
52C2×C4×C3⋊D3—24no—
53C2×C4×C3⋊D3C2×C414yes—
54C2×C4×C3⋊D3C2314yes—
55C2×#634—24no—
56C2×#634C2×C414yes—
57C3×#208—28no—
58C2×C3×C3⋊C8—24no—
59C2×C3×C3⋊C8—28no—
60C2×C3×C3⋊C8—24no—
61C2×C3×C3⋊C8C2314yes—
62C2×C3×C3⋊C8C2314yes—
63C2×#408—91noSylow
64C23×C3×C4—21no—
65C23×C3×C4C2×D311yescharacteristic
66C23×C3×C4C2×D311yescharacteristic
67C22×#67—32no—
68C22×#67—32no—
69C22×#67—62no—
70C2×#235—34no—
71C2×#235—34no—
72C2×#235—34no—
73C2×#235—34no—
74C2×#235—64no—
75C2×#235—64no—
76C2×#235—68no—
77C2×#235—68no—
78C2×#235—64no—
79C2×#235—64no—
80C2×#235—64no—
81C2×#235—64no—
82C22×D12—31no—
83C22×D12—31no—
84C22×D12—61no—
85C22×C4×D3—32no—
86C22×C4×D3—32no—
87C22×C4×D3—62no—
88C22×Dic6—31no—
89C22×Dic6—31no—
90C22×Dic6—61no—
91C2×C3×M16—34no—
92C2×C3×M16—64no—
93C22×C3×C8—32no—
94C22×C3×C8—34no—
95C22×C3×C8—32no—
96C22×C3×C8—64no—
97C2×#208—24no—
98C2×#208C2×D314yescomplemented
99C22×C3⋊C8—24no—
100C22×C3⋊C8C2×D312yes—
101C22×C3⋊C8C2×D312yes—
102C22×C3⋊C8C2×D314yescomplemented
103(C2×D3)⋊C8—316no—
104(C2×D3)⋊C8—316no—
105C23×C32—24no—
106C23×C32C22⋊C414yes—
107C23×C32C22×C412yes—
108C23×C32C22×C411yescharacteristic
109C22×C3⋊D3—24no—
110C22×C3⋊D3—28no—
111C22×C3⋊D3C22×C414yes—
112C2×C32×C4C22⋊C414yes—
113C2×C32×C4C22⋊C418yes—
114C2×C32×C4C22×C412yes—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D412yes—
117C2×C32×C4C2×D412yes—
118C2×C32×C4C2×D414yes—
119C2×C32×C4C2×D414yes—
120C2×C32×C4C2411yescharacteristic
121#638—216no—
122C2×C3⋊Dic3—24no—
123C2×C3⋊Dic3C22×C414yes—
124C4⋊(C3⋊D3)—28no—
125C4×C3⋊D3—28no—
126C4×C3⋊D3—24no—
127C4×C3⋊D3—24no—
128#634—28no—
129C3×C3⋊C8—24no—
130C3×C3⋊C8—24no—
131C22×#41—91no—
132C22×M16—31no—
133C23×C8—31no—
134#408—98no—
135C2×C22⋊C8—94no—
136C24×C3—21no—
137C24×C3C4×D311yescharacteristic
138C24×C3C4×D311yescharacteristic
139C23×D3—32no—
140C23×D3—32no—
141C23×D3—62no—
142C22×C3×C4—21no—
143C22×C3×C4—22no—
144C22×C3×C4—24no—
145C22×C3×C4—24no—
146C22×C3×C4—22no—
147C22×C3×C4—21no—
148C22×C3×C4C4×D311yescharacteristic
149C22×C3×C4C4×D311yescharacteristic
150C22×C3×C4C4×D312yes—
151C22×C3×C4C4×D312yes—
152C22×C3×C4D1214yes—
153C22×C3×C4D1214yes—
154C22×C3×C4#6714yes—
155C22×C3×C4#6714yes—
156C22×C3×C4C22×D312yes—
157C22×C3×C4C22×D312yes—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C2×#67—38no—
161C2×#67—38no—
162C2×#67—68no—
163C2×#67—616no—
164C2×#67—68no—
165C2×#67—68no—
166C22×Dic3—32no—
167C22×Dic3—32no—
168C22×Dic3—62no—
169#235—632no—
170#235—616no—
171#235—616no—
172#235—616no—
173#235—616no—
174#235—68no—
175#235—68no—
176#235—68no—
177#235—68no—
178C2×D12—34no—
179C2×D12—34no—
180C2×D12—64no—
181C2×D12—68no—
182C2×D12—64no—
183C2×D12—64no—
184C2×C4×D3—34no—
185C2×C4×D3—34no—
186C2×C4×D3—34no—
187C2×C4×D3—34no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C4×D3—68no—
191C2×C4×D3—68no—
192C2×C4×D3—64no—
193C2×C4×D3—64no—
194C2×C4×D3—64no—
195C2×C4×D3—64no—
196C2×Dic6—34no—
197C2×Dic6—34no—
198C2×Dic6—64no—
199C2×Dic6—68no—
200C2×Dic6—64no—
201C2×Dic6—64no—
202C3×M16—68no—
203C2×C3×C8—34no—
204C2×C3×C8—34no—
205C2×C3×C8—64no—
206C2×C3×C8—68no—
207C2×C3×C8—64no—
208#208—28no—
209C2×C3⋊C8—24no—
210C2×C3⋊C8—28no—
211C2×C3⋊C8—24no—
212C2×C3⋊C8C22×D314yes—
213C2×C3⋊C8C22×D314yes—
214C22×C32—24no—
215C22×C32—28no—
216C22×C32C2×C22⋊C414yes—
217C22×C32C2×C22⋊C412yes—
218C22×C32#13114yes—
219C22×C32C23×C411yescharacteristic
220C2×C3⋊D3—24no—
221C2×C3⋊D3—28no—
222C2×C3⋊D3—48no—
223C32×C4C2×C22⋊C414yes—
224C32×C4C2×C22⋊C412yes—
225C32×C4C22×D411yescharacteristic
226C32×C4C22×D411yescharacteristic
227C3⋊Dic3—24no—
228C2×#41—94no—
229C2×#41—94no—
230C2×#41—184no—
231C2×#41—184no—
232C22×Q8—91no—
233C22×D4—92no—
234C22×D4—91no—
235C23×C4—92no—
236C23×C4D3211yescharacteristic
237C2×M16—34no—
238C2×M16—64no—
239C22×C8—34no—
240C22×C8—32no—
241C22×C8—32no—
242C22×C8—64no—
243C22⋊C8—916no—
244C23×C3—24no—
245C23×C3—24no—
246C23×C3—24no—
247C23×C3—21no—
248C23×C3—22no—
249C23×C3—44no—
250C23×C3(C2×D3)⋊C414yes—
251C23×C3(C2×D3)⋊C414yes—
252C23×C3C2×C4×D312yes—
253C23×C3C2×C4×D312yes—
254C23×C3C2×C4×D311yescharacteristic
255C23×C3C2×C4×D311yescharacteristic
256C22×D3—34no—
257C22×D3—34no—
258C22×D3—64no—
259C22×D3—68no—
260C22×D3—68no—
261C22×D3—68no—
262C22×D3—64no—
263C22×D3—64no—
264C22×D3—128no—
265C2×C3×C4—21no—
266C2×C3×C4—24no—
267C2×C3×C4—28no—
268C2×C3×C4—22no—
269C2×C3×C4—21no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—24no—
273C2×C3×C4—24no—
274C2×C3×C4(C2×D3)⋊C414yes—
275C2×C3×C4(C2×D3)⋊C414yes—
276C2×C3×C4(C2×D3)⋊C418yes—
277C2×C3×C4(C2×D3)⋊C418yes—
278C2×C3×C4C2×C4×D312yes—
279C2×C3×C4C2×C4×D312yes—
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4C2×C4×D311yescharacteristic
282C2×C3×C4C2×D1212yes—
283C2×C3×C4C2×D1212yes—
284C2×C3×C4C2×D1214yes—
285C2×C3×C4C2×D1214yes—
286C2×C3×C4C2×#6712yes—
287C2×C3×C4C2×#6712yes—
288C2×C3×C4C2×#6714yes—
289C2×C3×C4C2×#6714yes—
290C2×C3×C4C23×D311yescharacteristic
291C2×C3×C4C23×D311yescharacteristic
292#67—632no—
293#67—616no—
294#67—616no—
295C2×Dic3—34no—
296C2×Dic3—34no—
297C2×Dic3—64no—
298C2×Dic3—68no—
299C2×Dic3—64no—
300C2×Dic3—64no—
301D12—616no—
302D12—68no—
303D12—68no—
304C4×D3—68no—
305C4×D3—68no—
306C4×D3—616no—
307C4×D3—68no—
308C4×D3—68no—
309C4×D3—64no—
310C4×D3—64no—
311C4×D3—64no—
312C4×D3—64no—
313Dic6—616no—
314Dic6—68no—
315Dic6—68no—
316C3×C8—64no—
317C3×C8—64no—
318C3⋊C8—24no—
319C3⋊C8—24no—
320C2×C32—24no—
321C2×C32#40814yescomplemented
322C2×C32C22×C22⋊C411yescharacteristic
323C2×C32C2×#13112yes—
324C3⋊D3—44no—
325C24—92no—
326C24#62411yescharacteristic
327#41—1816no—
328#41—188no—
329#41—188no—
330C2×Q8—94no—
331C2×Q8—184no—
332C2×D4—98no—
333C2×D4—94no—
334C2×D4—188no—
335C2×D4—184no—
336C22×C4—92no—
337C22×C4—94no—
338C22×C4—94no—
339C22×C4—184no—
340C22×C4—184no—
341C22×C4#62411yescharacteristic
342C22×C4#62412yes—
343C22×C4#62614yes—
344C22×C4#62614yes—
345C22×C4C2×D3212yes—
346C22×C4C2×D3211yescharacteristic
347M16—68no—
348C2×C8—34no—
349C2×C8—34no—
350C2×C8—64no—
351C2×C8—68no—
352C2×C8—64no—
353C22×C3—28no—
354C22×C3—24no—
355C22×C3—24no—
356C22×C3—28no—
357C22×C3—21no—
358C22×C3—24no—
359C22×C3—22no—
360C22×C3—24no—
361C22×C3—48no—
362C22×C3—44no—
363C22×C3#90114yes—
364C22×C3#90714yes—
365C22×C3C2×(C2×D3)⋊C414yes—
366C22×C3C2×(C2×D3)⋊C414yes—
367C22×C3C2×(C2×D3)⋊C412yes—
368C22×C3C2×(C2×D3)⋊C412yes—
369C22×C3C22×C4×D311yescharacteristic
370C22×C3C22×C4×D311yescharacteristic
371C2×D3—68no—
372C2×D3—68no—
373C2×D3—68no—
374C2×D3—64no—
375C2×D3—64no—
376C2×D3—128no—
377C2×D3—1216no—
378C2×D3—128no—
379C2×D3—128no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—24no—
383C3×C4—22no—
384C3×C4C2×(C2×D3)⋊C414yes—
385C3×C4C2×(C2×D3)⋊C414yes—
386C3×C4C2×(C2×D3)⋊C412yes—
387C3×C4C2×(C2×D3)⋊C412yes—
388C3×C4C22×D1211yescharacteristic
389C3×C4C22×D1211yescharacteristic
390C3×C4C22×#6711yescharacteristic
391C3×C4C22×#6711yescharacteristic
392Dic3—68no—
393Dic3—64no—
394Dic3—64no—
395C32C2×#40811yescharacteristic, complemented, Sylow
396C23—24no—
397C23—94no—
398C23—188no—
399C23—184no—
400C23#372214yes—
401C23C2×#62412yes—
402C23C2×#62411yescharacteristic
403Q8—188no—
404D4—1816no—
405D4—188no—
406C2×C4—94no—
407C2×C4—184no—
408C2×C4—184no—
409C2×C4—184no—
410C2×C4—188no—
411C2×C4#372214yes—
412C2×C4#372218yes—
413C2×C4C2×#62411yescharacteristic
414C2×C4C2×#62412yes—
415C2×C4C2×#62612yes—
416C2×C4C2×#62612yes—
417C2×C4C2×#62614yes—
418C2×C4C2×#62614yes—
419C2×C4C22×D3211yescharacteristic
420C8—64no—
421C8—64no—
422C2×C3—24no—
423C2×C3—24no—
424C2×C3—24no—
425C2×C3—21no—
426C2×C3—22no—
427C2×C3—44no—
428C2×C3#511014yescomplemented
429C2×C3#512914yescomplemented
430C2×C3C2×#90112yes—
431C2×C3C2×#90712yes—
432C2×C3C22×(C2×D3)⋊C411yescharacteristic
433C2×C3C22×(C2×D3)⋊C411yescharacteristic
434D3—128no—
435D3—124no—
436D3—124no—
437C22—28no—
438C22—24no—
439C22—184no—
440C22—188no—
441C22—368no—
442C22#6381714yes—
443C22C2×#372214yes—
444C22C2×#372212yes—
445C22C22×#62411yescharacteristic
446C4—184no—
447C4C2×#372212yes—
448C4C2×#372214yes—
449C4C22×#62611yescharacteristic
450C4C22×#62611yescharacteristic
451C3—21no—
452C3C2×#511011yescharacteristic, complemented
453C3C2×#512911yescharacteristic, complemented
454C2—24no—
455C2—364no—
456C2#1059107314yesdirect product factor
457C2C2×#6381712yes—
458C2C22×#372211yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC22×#3828C2
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#408
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#208C2semidirect
3. C23×C3×C3⋊C8C2semidirect
4. #10591073C2direct (N × H)
5. C2×#63557C2semidirect
18. C2×C3×#208C22semidirect
22. C22×C3×C3⋊C8C22semidirect
23. #63557C22semidirect
29. C22×#208D3semidirect
30. C23×C3⋊C8D3semidirect
98. C2×#208C2×D3semidirect
102. C22×C3⋊C8C2×D3semidirect
321. C2×C32#408semidirect
395. C32C2×#408semidirect
428. C2×C3#5110semidirect
429. C2×C3#5129semidirect
452. C3C2×#5110semidirect
453. C3C2×#5129semidirect
456. C2#10591073direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C22×C3×#2082
C23×C3×C3⋊C82
#105910732
C2×#635572
C2×#51293
C2×#51103