Finite Group Databasebeta

← C2×#10593860 #11903699

Subgroups — C2×#10593860 #11903699

Order 1152.

2241 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×#64078C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic
4C2×#63869C212yesmaximal
5C2×#63866C212yesmaximal
6C2×#63845C214yesmaximal
7C2×#63844C212yesmaximal
8C2×Dic3×Dic6C212yesmaximal
9#10593860C2116yesmaximal, direct product factor
10C2×#5567—31nomaximal
11C2×#5570—31nomaximal
12C22×#634C2212yes—
13C22×C3×Dic6C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2212yes—
17C2×C4⋊(C3⋊Dic3)C2212yes—
18#64078C2218yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×C4×Dic3C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C3×C4×Dic6C2218yes—
26C3×C4×Dic6C2218yes—
27C2×#3724C2214yes—
28C2×Dic3⋊Dic3C2214yes—
29C2×Dic3⋊Dic3C2214yes—
30C2×Dic32C2214yes—
31#63869C22116yes—
32#63866C22116yes—
33#63845C22132yes—
34#63844C22116yes—
35Dic3×Dic6C22116yes—
36C2×C3×C4×Q8—31no—
37C2×C3×C4×Q8—31no—
38C2×Q8×Dic3—32no—
39C2×#944—32no—
40#5570—316no—
41#5567—316no—
42C2×#890—34no—
43C2×#890—32no—
44C2×#889—34no—
45C2×#887—32no—
46C2×#870—32no—
47C2×#869—32no—
48C2×#869—31no—
49C2×#869—31no—
50C2×#869—61no—
51C2×C4×Dic6—32no—
52C2×C4×Dic6—32no—
53C2×C4×Dic6D311yescharacteristic
54C2×C4×Dic6D311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2314yes—
59C2×#634—28no—
60C2×#634C2318yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C2×C3×Dic6—24no—
66C2×C3×Dic6Q818yescomplemented
67C2×C3×Dic6C2314yes—
68C2×C3×Dic6C2314yes—
69C32×C42C2314yes—
70C4⋊(C3⋊Dic3)C2318yes—
71C4⋊(C3⋊Dic3)C2318yes—
72C3×C4⋊Dic3C2314yes—
73C3×C4⋊Dic3C2314yes—
74C3×Dic3⋊C4C2318yes—
75C3×Dic3⋊C4C2318yes—
76C3×C4×Dic3C2318yes—
77C3×C4×Dic3C2318yes—
78#3724C23116yes—
79Dic3⋊Dic3C23116yes—
80Dic3⋊Dic3C23116yes—
81Dic32C23116yes—
82C2×#557—91noSylow
83C22×C3×Q8—31no—
84C22×C3×Q8—31no—
85C22×Dic6—32no—
86C22×Dic6—32no—
87C22×Dic6—62no—
88C22×Dic6C2×D311yescharacteristic
89C22×Dic6C2×D311yescharacteristic
90C3×C4×Q8—38no—
91C3×C4×Q8—38no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C4⋊C4—32no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C42—21no—
97C2×C3×C42—32no—
98C2×C3×C42—32no—
99C2×C3×C42C2×D311yescharacteristic
100C2×C3×C42C2×D311yescharacteristic
101Q8×Dic3—316no—
102#944—316no—
103C2×C4⋊Dic3—32no—
104C2×C4⋊Dic3—32no—
105C2×C4⋊Dic3—32no—
106C2×C4⋊Dic3—32no—
107C2×C4⋊Dic3—34no—
108C2×C4⋊Dic3—34no—
109C2×C4⋊Dic3—62no—
110C2×C4⋊Dic3—62no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4⋊Dic3C2×D311yescharacteristic
113C2×Dic3⋊C4—34no—
114C2×Dic3⋊C4—34no—
115C2×Dic3⋊C4—34no—
116C2×Dic3⋊C4—34no—
117C2×Dic3⋊C4C2×D312yes—
118C2×Dic3⋊C4C2×D312yes—
119C2×C4×Dic3—34no—
120C2×C4×Dic3—34no—
121C2×C4×Dic3C2×D312yes—
122C2×C4×Dic3C2×D312yes—
123#890—332no—
124#890—316no—
125#889—332no—
126#887—316no—
127#870—316no—
128#869—316no—
129#869—38no—
130#869—38no—
131#869—68no—
132C4×Dic6—316no—
133C4×Dic6—316no—
134C4×Dic6C2×D318yes—
135C4×Dic6C2×D318yes—
136C23×C32C2411yescharacteristic
137C2×C32×C4—22no—
138C2×C32×C4C2×Q814yes—
139C2×C32×C4#4114yes—
140C2×C32×C4C2412yes—
141C2×C32×C4C2412yes—
142C2×C32×C4C2412yes—
143C2×C3⋊Dic3—28no—
144C2×C3⋊Dic3C2418yes—
145#634—216no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—24no—
148C2×C3×Dic3—24no—
149C2×C3×Dic3C2×Q818yes—
150C2×C3×Dic3C2414yes—
151C2×C3×Dic3C2414yes—
152C2×C3×Dic3C2414yes—
153C2×C3×Dic3C2414yes—
154C3×Dic6—28no—
155C3×Dic6C2×Q8116yescomplemented
156#557—916no—
157C2×C4⋊Q8—92no—
158C2×C4⋊Q8—91no—
159C2×#125—92no—
160C2×#125—94no—
161C2×C4×Q8—31no—
162C2×C4×Q8—31no—
163C2×C4×Q8—92no—
164C2×C4×Q8—92no—
165C2×C3×Q8—38no—
166C2×C3×Q8—34no—
167C2×C3×Q8—34no—
168C2×C3×Q8—64no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C22×Dic3—34no—
183C22×Dic3—34no—
184C22×Dic3—64no—
185C22×Dic3C22×D312yes—
186C22×Dic3C22×D312yes—
187C22×Dic3C22×D312yes—
188C22×Dic3C22×D312yes—
189C2×Dic6—24no—
190C2×Dic6—38no—
191C2×Dic6—38no—
192C2×Dic6—68no—
193C2×Dic6—68no—
194C2×Dic6—68no—
195C2×Dic6—128no—
196C2×Dic6Dic618yescomplemented
197C2×Dic6C22×D314yes—
198C2×Dic6C22×D314yes—
199C3×C4⋊C4—34no—
200C3×C4⋊C4—38no—
201C3×C4⋊C4—38no—
202C3×C4⋊C4—34no—
203C3×C42—24no—
204C3×C42—38no—
205C3×C42—38no—
206C3×C42C22×D314yes—
207C3×C42C22×D314yes—
208C4⋊Dic3—38no—
209C4⋊Dic3—38no—
210C4⋊Dic3—38no—
211C4⋊Dic3—38no—
212C4⋊Dic3—316no—
213C4⋊Dic3—316no—
214C4⋊Dic3—68no—
215C4⋊Dic3—68no—
216C4⋊Dic3C22×D314yes—
217C4⋊Dic3C22×D314yes—
218Dic3⋊C4—316no—
219Dic3⋊C4—316no—
220Dic3⋊C4—316no—
221Dic3⋊C4—316no—
222Dic3⋊C4C22×D318yes—
223Dic3⋊C4C22×D318yes—
224C4×Dic3—316no—
225C4×Dic3—316no—
226C4×Dic3C22×D318yes—
227C4×Dic3C22×D318yes—
228C22×C32C22×Q812yes—
229C22×C32C2×#4112yes—
230C22×C322−1+412yes—
231C22×C32C2511yescharacteristic
232C32×C4—22no—
233C32×C4C22×Q814yes—
234C32×C4C2×#4114yes—
235C3⋊Dic3—28no—
236C3×Dic3—24no—
237C3×Dic3—24no—
238C3×Dic3—24no—
239C3×Dic3C22×Q818yes—
240C22×Q8—31no—
241C22×Q8—31no—
242C22×Q8—92no—
243C4⋊Q8—916no—
244C4⋊Q8—98no—
245#125—916no—
246#125—932no—
247C4×Q8—38no—
248C4×Q8—38no—
249C4×Q8—916no—
250C4×Q8—916no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—32no—
253C2×C4⋊C4—32no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—94no—
256C2×C4⋊C4—94no—
257C2×C4⋊C4—94no—
258C2×C4⋊C4—92no—
259C2×C4⋊C4—92no—
260C2×C42—32no—
261C2×C42—32no—
262C2×C42—94no—
263C2×C42D3211yescharacteristic
264C23×C3—21no—
265C23×C3C23×D311yescharacteristic
266C23×C3C23×D311yescharacteristic
267C3×Q8—316no—
268C3×Q8—68no—
269C2×C3×C4—24no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—24no—
276C2×C3×C4—24no—
277C2×C3×C4—38no—
278C2×C3×C4—34no—
279C2×C3×C4—34no—
280C2×C3×C4—34no—
281C2×C3×C4—34no—
282C2×C3×C4—64no—
283C2×C3×C4—64no—
284C2×C3×C4—64no—
285C2×C3×C4C2×Dic614yes—
286C2×C3×C4#23514yes—
287C2×C3×C4D3×Q814yes—
288C2×C3×C4#23914yes—
289C2×C3×C4C23×D312yes—
290C2×C3×C4C23×D312yes—
291C2×C3×C4C23×D312yes—
292C2×C3×C4C23×D312yes—
293C2×C3×C4C23×D312yes—
294C2×C3×C4C23×D312yes—
295C2×Dic3—24no—
296C2×Dic3—24no—
297C2×Dic3—24no—
298C2×Dic3—38no—
299C2×Dic3—38no—
300C2×Dic3—68no—
301C2×Dic3—68no—
302C2×Dic3—68no—
303C2×Dic3—128no—
304C2×Dic3C2×Dic618yes—
305C2×Dic3C23×D314yes—
306C2×Dic3C23×D314yes—
307C2×Dic3C23×D314yes—
308C2×Dic3C23×D314yes—
309Dic6—28no—
310Dic6—616no—
311Dic6—616no—
312Dic6—1216no—
313Dic6C2×Dic6116yescomplemented
314C2×C32#55714yescomplemented
315C2×C32C23×Q811yescharacteristic
316C2×C32C22×#4111yescharacteristic
317C2×C32C2×2−1+411yescharacteristic
318C2×Q8—34no—
319C2×Q8—34no—
320C2×Q8—38no—
321C2×Q8—64no—
322C2×Q8—98no—
323C2×Q8—188no—
324C22×C4—32no—
325C22×C4—32no—
326C22×C4—32no—
327C22×C4—32no—
328C22×C4—94no—
329C22×C4C2×D3211yescharacteristic
330C22×C4C2×D3211yescharacteristic
331C22×C4C2×D3211yescharacteristic
332C4⋊C4—34no—
333C4⋊C4—38no—
334C4⋊C4—38no—
335C4⋊C4—34no—
336C4⋊C4—916no—
337C4⋊C4—916no—
338C4⋊C4—916no—
339C4⋊C4—98no—
340C4⋊C4—98no—
341C42—38no—
342C42—38no—
343C42—916no—
344C42C2×D3214yes—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—21no—
349C22×C3C22×Dic612yes—
350C22×C3C2×#23512yes—
351C22×C3C2×D3×Q812yes—
352C22×C3C2×#23912yes—
353C22×C3#101012yes—
354C22×C3#101012yes—
355C22×C3C24×D311yescharacteristic
356C22×C3C24×D311yescharacteristic
357C3×C4—24no—
358C3×C4—22no—
359C3×C4—22no—
360C3×C4—24no—
361C3×C4—24no—
362C3×C4—38no—
363C3×C4—64no—
364C3×C4—64no—
365C3×C4—64no—
366C3×C4C22×Dic614yes—
367C3×C4C2×#23514yes—
368C3×C4C2×D3×Q814yes—
369C3×C4C2×#23914yes—
370Dic3—24no—
371Dic3—24no—
372Dic3—24no—
373Dic3—68no—
374Dic3—68no—
375Dic3—128no—
376Dic3C22×Dic618yes—
377C32C2×#55711yescharacteristic, complemented, Sylow
378C23C22×D3211yescharacteristic
379Q8—316no—
380Q8—68no—
381Q8—1816no—
382C2×C4—22no—
383C2×C4—38no—
384C2×C4—34no—
385C2×C4—34no—
386C2×C4—34no—
387C2×C4—34no—
388C2×C4—64no—
389C2×C4—64no—
390C2×C4—64no—
391C2×C4—98no—
392C2×C4—188no—
393C2×C4D3×Dic614yes—
394C2×C4#379914yes—
395C2×C4C22×D3212yes—
396C2×C4C22×D3212yes—
397C2×C4C22×D3212yes—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—24no—
402C2×C3#556714yescomplemented
403C2×C3#557014yescomplemented
404C2×C3C23×Dic611yescharacteristic
405C2×C3C22×#23511yescharacteristic
406C2×C3C22×D3×Q811yescharacteristic
407C2×C3C22×#23911yescharacteristic
408C2×C3C2×#101011yescharacteristic
409C2×C3C2×#101011yescharacteristic
410C22C2×D3×Dic612yes—
411C22#6429812yes—
412C22C2×#379912yes—
413C22C23×D3211yescharacteristic
414C4—22no—
415C4—38no—
416C4—64no—
417C4—64no—
418C4—64no—
419C4—188no—
420C4C2×D3×Dic614yes—
421C4C2×#379914yes—
422C3—21no—
423C3C2×#557011yescharacteristic, complemented
424C3C2×#556711yescharacteristic, complemented
425C2#1059386014yesdirect product factor
426C2C22×D3×Dic611yescharacteristic
427C2C2×#6429811yescharacteristic
428C2C22×#379911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#557
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
9. #10593860C2direct (N × H)
66. C2×C3×Dic6Q8semidirect
155. C3×Dic6C2×Q8semidirect
196. C2×Dic6Dic6semidirect
313. Dic6C2×Dic6semidirect
314. C2×C32#557semidirect
377. C32C2×#557semidirect
402. C2×C3#5567semidirect
403. C2×C3#5570semidirect
423. C3C2×#5570semidirect
424. C3C2×#5567semidirect
425. C2#10593860direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640782
C2×C3×C4×Dic62
C2×#638692
C2×#638662
C2×#638452
C2×#638442
C2×Dic3×Dic62
#105938602
C2×#55673
C2×#55703