Finite Group Databasebeta

← C2×#10589613 #11903217

Subgroups — C2×#10589613 #11903217

Order 1152.

1800 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C4×#611C211yesmaximal, characteristic
3C2×C4×#611C212yesmaximal
4C2×#63486C211yesmaximal, characteristic, complemented
5C2×#63486C212yesmaximal, complemented
6#10589613C2116yesmaximal, direct product factor
7C2×#63459C211yesmaximal, characteristic, complemented
8C2×#63458C212yesmaximal, complemented
9C2×C4⋊C4×D9C211yesmaximal, characteristic, complemented
10C2×#63451C212yesmaximal, complemented
11C2×#63450C211yesmaximal, characteristic, complemented
12C2×#63449C211yesmaximal, characteristic, complemented
13C2×#5511—31nomaximal
14C23×C4×C9C2211yescharacteristic
15C23×C4×C9C2212yes—
16C22×#611C2211yescharacteristic
17C22×C4×D9C2211yescharacteristic
18C22×C4×D9C2212yes—
19C22×Dic18C2211yescharacteristic
20C22×Dic18C2212yes—
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×C9×C4⋊C4C2211yescharacteristic
23C2×C9×C4⋊C4C2212yes—
24C2×C9×C4⋊C4C2218yescomplemented
25C2×#3676C2211yescharacteristic
26C2×#3676C2212yes—
27C4×#611C2218yes—
28C4×#611C22116yes—
29C2×(C2×D9)⋊C4C2211yescharacteristic
30C2×(C2×D9)⋊C4C2212yes—
31C2×C4⋊Dic9C2211yescharacteristic
32C2×C4⋊Dic9C2212yes—
33#63486C22116yescomplemented
34#63486C2218yescomplemented
35C2×Dic9⋊C4C2212yes—
36C2×Dic9⋊C4C2212yes—
37C2×Dic9⋊C4C2211yescharacteristic
38C2×Dic9⋊C4C2212yes—
39C2×Dic9⋊C4C2212yes—
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2212yes—
42#63459C2218yescomplemented
43#63458C22116yescomplemented
44C4⋊C4×D9C2218yescomplemented
45#63451C22116yescomplemented
46#63450C2218yescomplemented
47#63449C2218yescomplemented
48C22×C3×C4⋊C4D311yescharacteristic
49C2×C4×#67—31no—
50C2×C4×#67—32no—
51C2×#924—32no—
52C2×#924—31no—
53#5511—316no—
54C2×#897—31no—
55C2×#896—32no—
56C2×D3×C4⋊C4—31no—
57C2×#889—32no—
58C2×#888—31no—
59C2×#887—31no—
60C24×C9C2311yescharacteristic
61C23×D9C2311yescharacteristic
62C22×C4×C9—24no—
63C22×C4×C9—44no—
64C22×C4×C9C2312yes—
65C22×C4×C9C2311yescharacteristic
66C22×C4×C9C2314yes—
67C22×C4×C9C2312yes—
68C22×C4×C9C2318yes—
69C22×C4×C9C2311yescharacteristic
70C2×#611Q818yescomplemented
71C2×#611C2314yes—
72C22×Dic9C2311yescharacteristic
73C22×Dic9C2312yes—
74C22×Dic9C2312yes—
75C22×Dic9C2311yescharacteristic
76C22×Dic9C2311yescharacteristic
77C2×C4×D9—24no—
78C2×C4×D9—44no—
79C2×C4×D9C2314yes—
80C2×C4×D9C2318yes—
81C2×Dic18—24no—
82C2×Dic18—44no—
83C2×Dic18C2314yes—
84C2×Dic18C2318yes—
85C9×C4⋊C4C2314yes—
86C9×C4⋊C4C2314yes—
87C9×C4⋊C4C2318yes—
88#3676C2318yes—
89#3676C2314yes—
90(C2×D9)⋊C4C2314yes—
91(C2×D9)⋊C4C2318yes—
92C4⋊Dic9C2314yes—
93C4⋊Dic9C2318yes—
94Dic9⋊C4C2318yes—
95Dic9⋊C4C2314yes—
96Dic9⋊C4C2318yes—
97Dic9⋊C4C2318yes—
98Dic9⋊C4C2318yes—
99C4×Dic9C2314yes—
100C4×Dic9C2318yes—
101C2×#554—91noSylow
102C23×C3×C4C2×D311yescharacteristic
103C23×C3×C4C2×D312yes—
104C22×#67—31no—
105C22×C4×D3—31no—
106C22×C4×D3—32no—
107C22×Dic6—31no—
108C22×Dic6—32no—
109C2×C3×C4⋊C4C2×D311yescharacteristic
110C2×C3×C4⋊C4C2×D311yescharacteristic
111C2×C3×C4⋊C4C2×D312yes—
112C2×C3×C4⋊C4C2×D318yes—
113C2×#217—32no—
114C2×#217—31no—
115C4×#67—38no—
116C4×#67—316no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—32no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—32no—
121#924—316no—
122#924—38no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—31no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—32no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—32no—
130#897—38no—
131#896—316no—
132D3×C4⋊C4—38no—
133#889—316no—
134#888—38no—
135#887—38no—
136C23×C9—22no—
137C23×C9—22no—
138C23×C9C2×Q814yes—
139C23×C9C2412yes—
140C23×C9C2411yescharacteristic
141C22×D9—22no—
142C22×D9—22no—
143C22×D9C2×Q814yes—
144C22×D9C2412yes—
145C2×C4×C9—22no—
146C2×C4×C9—24no—
147C2×C4×C9—24no—
148C2×C4×C9—28no—
149C2×C4×C9—48no—
150C2×C4×C9#4114yes—
151C2×C4×C9C2414yes—
152C2×C4×C9C2412yes—
153C2×C4×C9C2414yes—
154C2×C4×C9C2412yes—
155#611C2×Q8116yescomplemented
156C2×Dic9—24no—
157C2×Dic9—22no—
158C2×Dic9—22no—
159C2×Dic9—24no—
160C2×Dic9C2×Q814yes—
161C2×Dic9C2414yes—
162C2×Dic9C2412yes—
163C2×Dic9C2412yes—
164C2×Dic9C2414yes—
165C2×Dic9C2412yes—
166C4×D9—28no—
167C4×D9—48no—
168Dic18—28no—
169Dic18—48no—
170#554—916no—
171C2×C4⋊Q8—91no—
172C2×#125—92no—
173C2×C22⋊Q8—92no—
174C2×C22⋊Q8—91no—
175C2×C22⋊Q8—92no—
176C2×C22⋊Q8—91no—
177C2×C4×Q8—91no—
178C2×C4×D4—92no—
179C2×C4×D4—91no—
180C22×C4⋊C4—91no—
181C22×C4⋊C4D911yescharacteristic, complemented
182C24×C3C22×D311yescharacteristic
183C23×D3—31no—
184C22×C3×C4—24no—
185C22×C3×C4—44no—
186C22×C3×C4C22×D312yes—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D312yes—
189C22×C3×C4C22×D314yes—
190C22×C3×C4C22×D318yes—
191C22×C3×C4C22×D311yescharacteristic
192C2×#67—38no—
193C2×#67—34no—
194C22×Dic3—31no—
195C22×Dic3—32no—
196C22×Dic3—31no—
197C22×Dic3—31no—
198C22×Dic3—32no—
199C2×C4×D3—34no—
200C2×C4×D3—38no—
201C2×C4×D3—64no—
202C2×C4×D3—124no—
203C2×Dic6—34no—
204C2×Dic6—38no—
205C2×Dic6—64no—
206C2×Dic6—124no—
207C3×C4⋊C4C22×D314yes—
208C3×C4⋊C4C22×D314yes—
209C3×C4⋊C4C22×D318yes—
210#217—38no—
211#217—34no—
212(C2×D3)⋊C4—34no—
213(C2×D3)⋊C4—38no—
214C4⋊Dic3—34no—
215C4⋊Dic3—38no—
216Dic3⋊C4—38no—
217Dic3⋊C4—38no—
218Dic3⋊C4—34no—
219Dic3⋊C4—38no—
220Dic3⋊C4—38no—
221C4×Dic3—34no—
222C4×Dic3—38no—
223C22×C9—28no—
224C22×C9—22no—
225C22×C9—22no—
226C22×C9C22×Q814yes—
227C22×C9C22×Q812yes—
228C22×C9C2×#4112yes—
229C22×C9H(5,𝔽2)12yes—
230C22×C9C2511yescharacteristic
231C2×D9—28no—
232C2×D9—22no—
233C2×D9—22no—
234C2×D9C22×Q814yes—
235C4×C9—22no—
236C4×C9—24no—
237C4×C9—24no—
238C4×C9C2×#4114yes—
239Dic9—24no—
240Dic9—22no—
241Dic9—22no—
242Dic9—24no—
243Dic9C22×Q814yes—
244C22×Q8—91no—
245C22×Q8—92no—
246C22×D4—91no—
247C23×C4—91no—
248C23×C4—92no—
249C23×C4C2×D911yescharacteristic
250C23×C4C2×D912yes—
251C4⋊Q8—98no—
252#125—916no—
253C22⋊Q8—916no—
254C22⋊Q8—98no—
255C22⋊Q8—916no—
256C22⋊Q8—98no—
257C4×Q8—98no—
258C4×D4—916no—
259C4×D4—98no—
260C2×C4⋊C4—92no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—91no—
263C2×C4⋊C4—92no—
264C2×C4⋊C4—92no—
265C2×C4⋊C4—92no—
266C2×C4⋊C4—92no—
267C2×C4⋊C4—98no—
268C2×C4⋊C4C2×D911yescharacteristic
269C2×C4⋊C4C2×D912yes—
270C2×C4⋊C4C2×D911yescharacteristic
271C2×C4⋊C4C2×D918yescomplemented
272C2×C22⋊C4—92no—
273C2×C22⋊C4—91no—
274C2×C22⋊C4—92no—
275C2×C22⋊C4—91no—
276C2×C42—92no—
277C2×C42—91no—
278C23×C3—22no—
279C23×C3—22no—
280C23×C3D3×Q814yes—
281C23×C3C23×D312yes—
282C23×C3C23×D311yescharacteristic
283C22×D3—34no—
284C22×D3—32no—
285C22×D3—62no—
286C22×D3—62no—
287C2×C3×C4—22no—
288C2×C3×C4—24no—
289C2×C3×C4—24no—
290C2×C3×C4—28no—
291C2×C3×C4—48no—
292C2×C3×C4#23514yes—
293C2×C3×C4C23×D314yes—
294C2×C3×C4C23×D312yes—
295C2×C3×C4C23×D314yes—
296C2×C3×C4C23×D312yes—
297#67—316no—
298C2×Dic3—34no—
299C2×Dic3—32no—
300C2×Dic3—34no—
301C2×Dic3—32no—
302C2×Dic3—32no—
303C2×Dic3—34no—
304C2×Dic3—64no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—64no—
308C4×D3—68no—
309C4×D3—128no—
310Dic6—68no—
311Dic6—128no—
312C2×C9—24no—
313C2×C9#55414yescomplemented
314C2×C9C23×Q811yescharacteristic
315C2×C9C22×#4111yescharacteristic
316C2×C9C2×H(5,𝔽2)11yescharacteristic
317D9—24no—
318C24—91no—
319C24C22×D911yescharacteristic
320C2×Q8—94no—
321C2×Q8—98no—
322C2×Q8—184no—
323C2×Q8—364no—
324C2×D4—98no—
325C2×D4—94no—
326C22×C4—24no—
327C22×C4—44no—
328C22×C4—91no—
329C22×C4—92no—
330C22×C4—91no—
331C22×C4—91no—
332C22×C4—92no—
333C22×C4—94no—
334C22×C4—98no—
335C22×C4—184no—
336C22×C4—364no—
337C22×C4C22×D914yes—
338C22×C4C22×D912yes—
339C22×C4C22×D911yescharacteristic
340C22×C4C22×D912yes—
341C22×C4C22×D918yes—
342C22×C4C22×D911yescharacteristic
343C4⋊C4—98no—
344C4⋊C4—94no—
345C4⋊C4—94no—
346C4⋊C4—98no—
347C4⋊C4—98no—
348C4⋊C4—98no—
349C4⋊C4—98no—
350C4⋊C4C22×D914yes—
351C4⋊C4C22×D918yes—
352C4⋊C4C22×D914yes—
353C22⋊C4—98no—
354C22⋊C4—94no—
355C22⋊C4—98no—
356C22⋊C4—94no—
357C42—98no—
358C42—94no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—28no—
362C22×C3C2×#23512yes—
363C22×C3#100412yes—
364C22×C3C2×D3×Q814yes—
365C22×C3C2×D3×Q812yes—
366C22×C3C24×D311yescharacteristic
367C2×D3—34no—
368C2×D3—62no—
369C2×D3—62no—
370C2×D3—68no—
371C3×C4—22no—
372C3×C4—24no—
373C3×C4—24no—
374C3×C4C2×#23514yes—
375Dic3—34no—
376Dic3—64no—
377Dic3—62no—
378Dic3—62no—
379Dic3—64no—
380C9C2×#55411yescharacteristic, complemented, Sylow
381C23—22no—
382C23—22no—
383C23—92no—
384C23—94no—
385C23—182no—
386C23—182no—
387C23Q8×D914yes—
388C23C23×D912yes—
389C23C23×D911yescharacteristic
390Q8—188no—
391Q8—368no—
392D4—916no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—28no—
397C2×C4—48no—
398C2×C4—92no—
399C2×C4—94no—
400C2×C4—94no—
401C2×C4—92no—
402C2×C4—92no—
403C2×C4—94no—
404C2×C4—182no—
405C2×C4—184no—
406C2×C4—184no—
407C2×C4—182no—
408C2×C4—188no—
409C2×C4—368no—
410C2×C4#369714yes—
411C2×C4C23×D914yes—
412C2×C4C23×D912yes—
413C2×C4C23×D914yes—
414C2×C4C23×D912yes—
415C2×C3—24no—
416C2×C3#551114yes—
417C2×C3C22×#23511yescharacteristic
418C2×C3C2×#100411yescharacteristic
419C2×C3C22×D3×Q811yescharacteristic
420D3—64no—
421C22—22no—
422C22—22no—
423C22—28no—
424C22—94no—
425C22—182no—
426C22—182no—
427C22—188no—
428C22C2×#369712yes—
429C22#6371012yes—
430C22C2×Q8×D914yes—
431C22C2×Q8×D912yes—
432C22C24×D911yescharacteristic
433C4—22no—
434C4—24no—
435C4—24no—
436C4—94no—
437C4—182no—
438C4—184no—
439C4—184no—
440C4—182no—
441C4C2×#369714yes—
442C3C2×#551111yescharacteristic
443C2—24no—
444C2—184no—
445C2#1058961314yesdirect product factor
446C2C22×#369711yescharacteristic
447C2C2×#6371011yescharacteristic
448C2C22×Q8×D911yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC22×C9×C4⋊C4C2
socleC23×C3C23×D3
prime radicalC22×#611C22
hypercenterC22×C4⋊C4D9
hypocenterC9C2×#554
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C9×C4⋊C4C2semidirect
4. C2×#63486C2semidirect
5. C2×#63486C2semidirect
6. #10589613C2direct (N × H)
7. C2×#63459C2semidirect
8. C2×#63458C2semidirect
9. C2×C4⋊C4×D9C2semidirect
10. C2×#63451C2semidirect
11. C2×#63450C2semidirect
12. C2×#63449C2semidirect
24. C2×C9×C4⋊C4C22semidirect
33. #63486C22semidirect
34. #63486C22semidirect
42. #63459C22semidirect
43. #63458C22semidirect
44. C4⋊C4×D9C22semidirect
45. #63451C22semidirect
46. #63450C22semidirect
47. #63449C22semidirect
70. C2×#611Q8semidirect
155. #611C2×Q8semidirect
181. C22×C4⋊C4D9semidirect
271. C2×C4⋊C4C2×D9semidirect
313. C2×C9#554semidirect
380. C9C2×#554semidirect
445. C2#10589613direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C9×C4⋊C42
C2×C4×#6112
C2×#634862
#105896132
C2×#634592
C2×#634582
C2×C4⋊C4×D92
C2×#634512
C2×#634502
C2×#634492
C2×#55113