Finite Group Databasebeta

← C2×#10594315 #11903707

Subgroups — C2×#10594315 #11903707

Order 1152.

2241 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64097C211yesmaximal, characteristic
2C2×C3×#889C212yesmaximal
3C2×#63847C212yesmaximal
4C2×#63845C212yesmaximal
5C2×#63844C212yesmaximal
6C2×#63840C212yesmaximal
7C2×#63838C211yesmaximal, characteristic
8C2×#63838C211yesmaximal, characteristic
9C2×#63837C212yesmaximal
10#10594315C2116yesmaximal, direct product factor
11C2×#5685—32nomaximal
12C22×#634C2212yes—
13C22×#627C2211yescharacteristic
14C22×#627C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19#64097C2218yes—
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C3×#889C22116yes—
27C2×#3724C2211yescharacteristic
28C2×#3724C2212yes—
29C2×#3724C2211yescharacteristic
30C2×Dic3⋊Dic3C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32C2×Dic32C2212yes—
33C2×Dic32C2212yes—
34C2×Dic32C2212yes—
35#63847C22116yes—
36#63845C22116yes—
37#63844C22116yes—
38#63840C22116yes—
39#63838C2218yes—
40#63838C2218yes—
41#63837C22116yes—
42C2×C3×#125—32no—
43#5685—332no—
44C2×#890—32no—
45C2×#889—32no—
46C2×#889—32no—
47C2×#889—32no—
48C2×#889D312yes—
49C2×#888—32no—
50C2×#888—32no—
51C2×#888—32no—
52C2×#888—61no—
53C2×#887—32no—
54C2×#887—32no—
55C2×#887—32no—
56C2×#887—32no—
57C2×C4×Dic6—32no—
58C2×C4×Dic6—32no—
59C22×C32×C4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3C2312yes—
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C2×#634—28no—
65C2×#634C2318yes—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C2×#627—24no—
71C2×#627Q818yescomplemented
72C2×#627C2314yes—
73C2×#627C2314yes—
74C32×C4⋊C4C2314yes—
75C4⋊(C3⋊Dic3)C2314yes—
76#3750C2318yes—
77C4×C3⋊Dic3C2314yes—
78C3×C4⋊Dic3C2318yes—
79C3×Dic3⋊C4C2318yes—
80C3×Dic3⋊C4C2318yes—
81C3×Dic3⋊C4C2318yes—
82C3×Dic3⋊C4C2318yes—
83C3×C4×Dic3C2318yes—
84#3724C2314yes—
85#3724C2314yes—
86#3724C2318yes—
87Dic3⋊Dic3C2318yes—
88Dic3⋊Dic3C2318yes—
89Dic32C2318yes—
90Dic32C2318yes—
91Dic32C2318yes—
92C2×#557—91noSylow
93C22×Dic6—32no—
94C22×Dic6—32no—
95C22×Dic6—32no—
96C22×Dic6—32no—
97C22×Dic6—62no—
98C3×#125—316no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—32no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4C2×D312yes—
106C2×C3×C42—32no—
107C2×C4⋊Dic3—32no—
108C2×C4⋊Dic3—32no—
109C2×C4⋊Dic3—32no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3C2×D312yes—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—62no—
121C2×Dic3⋊C4C2×D312yes—
122C2×Dic3⋊C4C2×D312yes—
123C2×Dic3⋊C4C2×D312yes—
124C2×Dic3⋊C4C2×D312yes—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—61no—
133C2×C4×Dic3C2×D312yes—
134#890—316no—
135#889—316no—
136#889—316no—
137#889—316no—
138#889C2×D3116yes—
139#888—316no—
140#888—316no—
141#888—316no—
142#888—68no—
143#887—316no—
144#887—316no—
145#887—316no—
146#887—316no—
147C4×Dic6—316no—
148C4×Dic6—316no—
149C23×C32C2411yescharacteristic
150C2×C32×C4—22no—
151C2×C32×C4—24no—
152C2×C32×C4C2414yes—
153C2×C32×C4C2412yes—
154C2×C3⋊Dic3—24no—
155C2×C3⋊Dic3C2×Q814yes—
156C2×C3⋊Dic3#4114yes—
157C2×C3⋊Dic3C2414yes—
158C2×C3⋊Dic3C2412yes—
159C2×C3⋊Dic3C2412yes—
160#634—216no—
161C2×C3×Dic3—24no—
162C2×C3×Dic3—24no—
163C2×C3×Dic3—24no—
164C2×C3×Dic3C2×Q818yes—
165C2×C3×Dic3C2414yes—
166C2×C3×Dic3C2414yes—
167C2×C3×Dic3C2414yes—
168C2×C3×Dic3C2414yes—
169#627—28no—
170#627C2×Q8116yescomplemented
171#557—916no—
172C2×C4⋊Q8—92no—
173C2×C4⋊Q8—91no—
174C2×#125—32no—
175C2×#125—92no—
176C2×#125—92no—
177C2×C4×Q8—92no—
178C2×C4×Q8—92no—
179C2×C4×Q8—91no—
180C2×C4×Q8—91no—
181C22×C3×C4—21no—
182C22×C3×C4—22no—
183C22×C3×C4—32no—
184C22×C3×C4—32no—
185C22×C3×C4—32no—
186C22×C3×C4—32no—
187C22×C3×C4C22×D312yes—
188C22×C3×C4C22×D312yes—
189C22×C3×C4C22×D312yes—
190C22×Dic3—32no—
191C22×Dic3—32no—
192C22×Dic3—32no—
193C22×Dic3—32no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3—62no—
197C22×Dic3C22×D312yes—
198C22×Dic3C22×D312yes—
199C22×Dic3C22×D312yes—
200C22×Dic3C22×D312yes—
201C2×Dic6—316no—
202C2×Dic6—38no—
203C2×Dic6—38no—
204C2×Dic6—38no—
205C2×Dic6—38no—
206C2×Dic6—68no—
207C2×Dic6—68no—
208C2×Dic6—68no—
209C2×Dic6—68no—
210C2×Dic6—128no—
211C3×C4⋊C4—24no—
212C3×C4⋊C4—38no—
213C3×C4⋊C4—38no—
214C3×C4⋊C4—38no—
215C3×C4⋊C4—38no—
216C3×C4⋊C4—38no—
217C3×C4⋊C4C22×D318yes—
218C3×C42—38no—
219C4⋊Dic3—38no—
220C4⋊Dic3—38no—
221C4⋊Dic3—38no—
222C4⋊Dic3—64no—
223C4⋊Dic3C22×D318yes—
224Dic3⋊C4—38no—
225Dic3⋊C4—38no—
226Dic3⋊C4—38no—
227Dic3⋊C4—38no—
228Dic3⋊C4—38no—
229Dic3⋊C4—38no—
230Dic3⋊C4—38no—
231Dic3⋊C4—38no—
232Dic3⋊C4—68no—
233Dic3⋊C4C22×D318yes—
234Dic3⋊C4C22×D318yes—
235Dic3⋊C4C22×D318yes—
236Dic3⋊C4C22×D318yes—
237C4×Dic3—38no—
238C4×Dic3—38no—
239C4×Dic3—38no—
240C4×Dic3—38no—
241C4×Dic3—38no—
242C4×Dic3—38no—
243C4×Dic3—38no—
244C4×Dic3—64no—
245C4×Dic3C22×D318yes—
246C22×C32C22×Q812yes—
247C22×C32C2×#4112yes—
248C22×C322−1+412yes—
249C22×C32C2511yescharacteristic
250C32×C4—22no—
251C32×C4—24no—
252C3⋊Dic3—24no—
253C3⋊Dic3C22×Q814yes—
254C3⋊Dic3C2×#4114yes—
255C3×Dic3—24no—
256C3×Dic3—24no—
257C3×Dic3—24no—
258C3×Dic3C22×Q818yes—
259C22×Q8—91no—
260C22×Q8—91no—
261C22×Q8—92no—
262C4⋊Q8—916no—
263C4⋊Q8—98no—
264#125—316no—
265#125—916no—
266#125—916no—
267C4×Q8—916no—
268C4×Q8—916no—
269C4×Q8—98no—
270C4×Q8—98no—
271C2×C4⋊C4—32no—
272C2×C4⋊C4—32no—
273C2×C4⋊C4—32no—
274C2×C4⋊C4—32no—
275C2×C4⋊C4—32no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—92no—
278C2×C4⋊C4—91no—
279C2×C4⋊C4—92no—
280C2×C4⋊C4—92no—
281C2×C4⋊C4—92no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4D3211yescharacteristic
284C2×C42—32no—
285C2×C42—92no—
286C2×C42—92no—
287C2×C42—92no—
288C2×C42—91no—
289C23×C3—21no—
290C23×C3C23×D312yes—
291C2×C3×C4—24no—
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—24no—
295C2×C3×C4—22no—
296C2×C3×C4—24no—
297C2×C3×C4—38no—
298C2×C3×C4—34no—
299C2×C3×C4—34no—
300C2×C3×C4—34no—
301C2×C3×C4—34no—
302C2×C3×C4—44no—
303C2×C3×C4—64no—
304C2×C3×C4—64no—
305C2×C3×C4—64no—
306C2×C3×C4C23×D314yes—
307C2×C3×C4C23×D314yes—
308C2×C3×C4C23×D314yes—
309C2×Dic3—24no—
310C2×Dic3—24no—
311C2×Dic3—24no—
312C2×Dic3—38no—
313C2×Dic3—38no—
314C2×Dic3—34no—
315C2×Dic3—34no—
316C2×Dic3—34no—
317C2×Dic3—34no—
318C2×Dic3—64no—
319C2×Dic3—64no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—64no—
323C2×Dic3—64no—
324C2×Dic3—64no—
325C2×Dic3—124no—
326C2×Dic3D3×Q818yes—
327C2×Dic3C23×D314yes—
328C2×Dic3C23×D314yes—
329C2×Dic3C23×D314yes—
330C2×Dic3C23×D314yes—
331Dic6—332no—
332Dic6—616no—
333Dic6—616no—
334Dic6—616no—
335Dic6—1216no—
336C2×C32#55714yescomplemented
337C2×C32C23×Q811yescharacteristic
338C2×C32C22×#4111yescharacteristic
339C2×C32C2×2−1+411yescharacteristic
340C2×Q8—94no—
341C2×Q8—98no—
342C2×Q8—94no—
343C2×Q8—98no—
344C2×Q8—188no—
345C2×Q8—184no—
346C22×C4—32no—
347C22×C4—32no—
348C22×C4—32no—
349C22×C4—32no—
350C22×C4—91no—
351C22×C4—91no—
352C22×C4—92no—
353C22×C4C2×D3212yes—
354C22×C4C2×D3211yescharacteristic
355C4⋊C4—38no—
356C4⋊C4—38no—
357C4⋊C4—38no—
358C4⋊C4—38no—
359C4⋊C4—38no—
360C4⋊C4—94no—
361C4⋊C4—98no—
362C4⋊C4—94no—
363C4⋊C4—98no—
364C4⋊C4—98no—
365C4⋊C4—98no—
366C4⋊C4—94no—
367C4⋊C4C2×D3214yes—
368C42—38no—
369C42—98no—
370C42—98no—
371C42—98no—
372C42—94no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—21no—
377C22×C3C2×D3×Q814yes—
378C22×C3D3×#4114yes—
379C22×C3#101014yes—
380C22×C3C24×D312yes—
381C3×C4—24no—
382C3×C4—24no—
383C3×C4—24no—
384C3×C4—24no—
385C3×C4—38no—
386C3×C4—44no—
387C3×C4—64no—
388C3×C4—64no—
389C3×C4—64no—
390Dic3—24no—
391Dic3—24no—
392Dic3—24no—
393Dic3—38no—
394Dic3—38no—
395Dic3—64no—
396Dic3—64no—
397Dic3—64no—
398Dic3—64no—
399Dic3—124no—
400Dic3C2×D3×Q818yes—
401C32C2×#55711yescharacteristic, complemented, Sylow
402C23C22×D3211yescharacteristic
403Q8—916no—
404Q8—1816no—
405Q8—188no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—38no—
409C2×C4—34no—
410C2×C4—34no—
411C2×C4—34no—
412C2×C4—34no—
413C2×C4—64no—
414C2×C4—64no—
415C2×C4—64no—
416C2×C4—94no—
417C2×C4—94no—
418C2×C4—92no—
419C2×C4—92no—
420C2×C4—94no—
421C2×C4—184no—
422C2×C4C22×D3214yes—
423C2×C4C22×D3212yes—
424C2×C3—24no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3#568518yescomplemented
429C2×C3C22×D3×Q812yes—
430C2×C3C2×D3×#4112yes—
431C2×C3C2×#101012yes—
432C22#6429812yes—
433C22#6431212yes—
434C22D32×Q812yes—
435C22C23×D3211yescharacteristic
436C4—22no—
437C4—24no—
438C4—38no—
439C4—64no—
440C4—64no—
441C4—64no—
442C4—94no—
443C4—94no—
444C4—184no—
445C3—21no—
446C3C2×#568512yescomplemented
447C2#1059431514yesdirect product factor
448C2C2×#6429811yescharacteristic
449C2C2×#6431211yescharacteristic
450C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#557
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
10. #10594315C2direct (N × H)
71. C2×#627Q8semidirect
170. #627C2×Q8semidirect
336. C2×C32#557semidirect
401. C32C2×#557semidirect
428. C2×C3#5685semidirect
446. C3C2×#5685semidirect
447. C2#10594315direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640972
C2×C3×#8892
C2×#638472
C2×#638452
C2×#638442
C2×#638402
C2×#638382
C2×#638372
#105943152
C2×#56853