Finite Group Databasebeta

← C2×#10594866 #11901106

Subgroups — C2×#10594866 #11901106

Order 1152.

3469 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C23×C3×Dic6C211yesmaximal, characteristic, complemented
3C2×C3×#926C211yesmaximal, characteristic, complemented
4C2×#63966C214yesmaximal, complemented
5#10594866C2116yesmaximal, direct product factor
6C2×#63871C214yesmaximal, complemented
7C2×#63866C212yesmaximal, complemented
8C2×#63864C212yesmaximal, complemented
9C2×#5816—31nomaximal
10C2×#5526—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638C2212yes—
13C2×#3828—28no—
14C2×#3828C2218yes—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2212yes—
17C22×#634C2211yescharacteristic
18C23×C3×Dic3C2212yes—
19C22×C3×Dic6—28no—
20C22×C3×Dic6C2212yes—
21C22×C3×Dic6C2212yes—
22C22×C3×Dic6C2218yescomplemented
23C2×C3×#217C2212yes—
24C3×#926C2218yescomplemented
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4×Dic3C2212yes—
27#63966C22132yescomplemented
28C2×Dic3⋊Dic3C2218yes—
29C2×#3722C2218yes—
30#63871C22132yescomplemented
31#63866C22116yescomplemented
32#63864C22116yescomplemented
33C23×C3×Q8—31no—
34C22×#235—31no—
35C22×#235—31no—
36C22×#235—61no—
37C23×Dic6D311yescharacteristic, complemented
38C2×C3×#117—31no—
39#5816—316no—
40C2×#947—32no—
41C2×#946—34no—
42C2×#944—32no—
43C2×#929—34no—
44C2×#926D311yescharacteristic, complemented
45#5526—316no—
46C2×#897—34no—
47C2×#886—34no—
48C2×#875—32no—
49C2×#869—32no—
50C24×C32C2311yescharacteristic
51C23×C3⋊D3C2312yes—
52C22×C32×C4D418yes—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2314yes—
56C2×#638—28no—
57C2×#638C2318yes—
58C22×C3⋊Dic3C2312yes—
59#3828—232no—
60C2×C4⋊(C3⋊D3)—24no—
61C2×C4⋊(C3⋊D3)C2314yes—
62C2×C4×C3⋊D3—28no—
63C2×C4×C3⋊D3C2318yes—
64C2×#634—24no—
65C2×#634C2314yes—
66C22×C3×Dic3—28no—
67C22×C3×Dic3C2314yes—
68C22×C3×Dic3C2314yes—
69C22×C3×Dic3C2318yes—
70C2×C3×Dic6—28no—
71C2×C3×Dic6—28no—
72C2×C3×Dic6—232no—
73C2×C3×Dic6C2318yes—
74C2×C3×Dic6C2318yes—
75C3×#217C2318yes—
76C3×C4⋊Dic3C2318yes—
77C3×C4×Dic3C2318yes—
78Dic3⋊Dic3C23132yes—
79#3722C23132yes—
80C2×#536—91noSylow
81C22×C3×Q8—32no—
82C22×C3×Q8—32no—
83C22×C3×Q8—38no—
84C22×C3×Q8—68no—
85C23×C3×C4—21no—
86C23×C3×C4—32no—
87C23×C3×C4C2×D311yescharacteristic
88C23×C3×C4C2×D311yescharacteristic
89C22×#67—32no—
90C22×#67—32no—
91C22×#67—62no—
92C23×Dic3C2×D312yes—
93C2×#235—38no—
94C2×#235—38no—
95C2×#235—68no—
96C2×#235—616no—
97C2×#235—68no—
98C2×#235—68no—
99C22×D12—31no—
100C22×D12—31no—
101C22×D12—61no—
102C22×C4×D3—32no—
103C22×C4×D3—32no—
104C22×C4×D3—62no—
105C22×Dic6—28no—
106C22×Dic6—31no—
107C22×Dic6—31no—
108C22×Dic6—61no—
109C22×Dic6C2×D312yes—
110C22×Dic6C2×D312yes—
111C22×Dic6C2×D318yescomplemented
112C3×#117—38no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C42—32no—
116C2×#217C2×D312yes—
117#947—316no—
118#946—332no—
119#944—316no—
120#929—332no—
121C2×(C2×D3)⋊C4—38no—
122C2×(C2×D3)⋊C4—38no—
123#926C2×D318yescomplemented
124C2×C4⋊Dic3—38no—
125C2×C4⋊Dic3C2×D312yes—
126C2×Dic3⋊C4—38no—
127C2×C4×Dic3C2×D312yes—
128#897—332no—
129#886—332no—
130#875—316no—
131#869—316no—
132C23×C32—24no—
133C23×C32C2×D414yes—
134C23×C32C2412yes—
135C23×C32C2411yescharacteristic
136C22×C3⋊D3—24no—
137C22×C3⋊D3—28no—
138C22×C3⋊D3C2414yes—
139C2×C32×C4C2×D414yes—
140C2×C32×C4C2×D414yes—
141C2×C32×C4C2×D4116yes—
142C2×C32×C4C2412yes—
143C2×C32×C4C2412yes—
144#638—216no—
145C2×C3⋊Dic3—24no—
146C2×C3⋊Dic3C2414yes—
147C4⋊(C3⋊D3)—28no—
148C4×C3⋊D3—216no—
149#634—28no—
150C2×C3×Dic3—216no—
151C2×C3×Dic3—28no—
152C2×C3×Dic3—28no—
153C2×C3×Dic3C2418yes—
154C2×C3×Dic3C2418yes—
155C3×Dic6—216no—
156C3×Dic6—216no—
157C22×#41—91no—
158C23×Q8—31no—
159#536—916no—
160C2×C4⋊Q8—92no—
161C2×#124—92no—
162C2×#123—94no—
163C2×C22⋊Q8—94no—
164C2×#117—31no—
165C24×C3—21no—
166C24×C3C22×D311yescharacteristic
167C24×C3C22×D311yescharacteristic
168C23×D3—32no—
169C23×D3—32no—
170C23×D3—62no—
171C2×C3×Q8—38no—
172C2×C3×Q8—38no—
173C2×C3×Q8—68no—
174C2×C3×Q8—68no—
175C2×C3×Q8—632no—
176C22×C3×C4—28no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—24no—
180C22×C3×C4—34no—
181C22×C3×C4—34no—
182C22×C3×C4—38no—
183C22×C3×C4—68no—
184C22×C3×C4D1218yes—
185C22×C3×C4#6718yes—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D314yes—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D314yes—
192C2×#67—38no—
193C2×#67—38no—
194C2×#67—68no—
195C2×#67—616no—
196C2×#67—68no—
197C2×#67—68no—
198C22×Dic3—28no—
199C22×Dic3—32no—
200C22×Dic3—32no—
201C22×Dic3—62no—
202C22×Dic3C22×D318yes—
203C22×Dic3C22×D314yes—
204C22×Dic3C22×D314yes—
205#235—664no—
206#235—632no—
207#235—632no—
208C2×D12—34no—
209C2×D12—34no—
210C2×D12—64no—
211C2×D12—68no—
212C2×D12—64no—
213C2×D12—64no—
214C2×C4×D3—38no—
215C2×C4×D3—38no—
216C2×C4×D3—68no—
217C2×C4×D3—616no—
218C2×C4×D3—68no—
219C2×C4×D3—68no—
220C2×Dic6—28no—
221C2×Dic6—28no—
222C2×Dic6—232no—
223C2×Dic6—34no—
224C2×Dic6—34no—
225C2×Dic6—64no—
226C2×Dic6—68no—
227C2×Dic6—64no—
228C2×Dic6—64no—
229C2×Dic6C22×D318yes—
230C2×Dic6C22×D318yes—
231C3×C4⋊C4—38no—
232C3×C22⋊C4—38no—
233C3×C42—38no—
234#217C22×D318yes—
235(C2×D3)⋊C4—332no—
236(C2×D3)⋊C4—332no—
237C4⋊Dic3—332no—
238C4⋊Dic3C22×D318yes—
239Dic3⋊C4—332no—
240C4×Dic3C22×D318yes—
241C22×C32—28no—
242C22×C32—24no—
243C22×C32C22×D414yes—
244C22×C32C22×D412yes—
245C22×C322−1+414yes—
246C22×C32C2511yescharacteristic
247C2×C3⋊D3—24no—
248C2×C3⋊D3—28no—
249C2×C3⋊D3—48no—
250C32×C4C22×D414yes—
251C32×C4C22×D414yes—
252C3⋊Dic3—24no—
253C3×Dic3—28no—
254C3×Dic3—28no—
255C2×#41—98no—
256C2×#41—188no—
257C22×Q8—32no—
258C22×Q8—32no—
259C22×Q8—38no—
260C22×Q8—68no—
261C22×Q8—91no—
262C22×D4—92no—
263C22×D4—91no—
264C23×C4—32no—
265C23×C4—92no—
266C23×C4D3211yescharacteristic
267C4⋊Q8—916no—
268#124—916no—
269#123—932no—
270C22⋊Q8—932no—
271#117—38no—
272C2×C4⋊C4—32no—
273C2×C4⋊C4—98no—
274C2×C22⋊C4—32no—
275C2×C22⋊C4—98no—
276C2×C42—32no—
277C23×C3—24no—
278C23×C3—24no—
279C23×C3—22no—
280C23×C3—21no—
281C23×C3—24no—
282C23×C3—44no—
283C23×C3C2×D1214yes—
284C23×C3C2×#6714yes—
285C23×C3C23×D312yes—
286C23×C3C23×D312yes—
287C23×C3C23×D311yescharacteristic
288C23×C3C23×D311yescharacteristic
289C22×D3—34no—
290C22×D3—34no—
291C22×D3—64no—
292C22×D3—68no—
293C22×D3—64no—
294C22×D3—68no—
295C22×D3—68no—
296C22×D3—64no—
297C22×D3—128no—
298C3×Q8—616no—
299C3×Q8—616no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—24no—
303C2×C3×C4—24no—
304C2×C3×C4—216no—
305C2×C3×C4—38no—
306C2×C3×C4—38no—
307C2×C3×C4—616no—
308C2×C3×C4—68no—
309C2×C3×C4—68no—
310C2×C3×C4C2×D1214yes—
311C2×C3×C4C2×D1214yes—
312C2×C3×C4C2×D12116yes—
313C2×C3×C4C2×#6714yes—
314C2×C3×C4C2×#6714yes—
315C2×C3×C4C2×#67116yes—
316C2×C3×C4C23×D312yes—
317C2×C3×C4C23×D312yes—
318C2×C3×C4C23×D312yes—
319C2×C3×C4C23×D312yes—
320#67—632no—
321#67—616no—
322#67—616no—
323C2×Dic3—28no—
324C2×Dic3—216no—
325C2×Dic3—28no—
326C2×Dic3—34no—
327C2×Dic3—34no—
328C2×Dic3—64no—
329C2×Dic3—68no—
330C2×Dic3—64no—
331C2×Dic3—64no—
332C2×Dic3C23×D318yes—
333C2×Dic3C23×D318yes—
334D12—616no—
335D12—68no—
336D12—68no—
337C4×D3—632no—
338C4×D3—616no—
339C4×D3—616no—
340Dic6—216no—
341Dic6—216no—
342Dic6—616no—
343Dic6—68no—
344Dic6—68no—
345C2×C32—24no—
346C2×C32#53614yescomplemented
347C2×C32C23×D411yescharacteristic
348C2×C32C2×2−1+412yes—
349C3⋊D3—44no—
350C24—92no—
351C24C2×D3211yescharacteristic
352#41—1832no—
353C2×Q8—38no—
354C2×Q8—38no—
355C2×Q8—68no—
356C2×Q8—68no—
357C2×Q8—632no—
358C2×Q8—94no—
359C2×Q8—184no—
360C2×D4—98no—
361C2×D4—94no—
362C2×D4—188no—
363C2×D4—184no—
364C22×C4—38no—
365C22×C4—34no—
366C22×C4—34no—
367C22×C4—68no—
368C22×C4—92no—
369C22×C4—98no—
370C22×C4—188no—
371C22×C4#62618yes—
372C22×C4C2×D3214yes—
373C22×C4C2×D3211yescharacteristic
374C22×C4C2×D3211yescharacteristic
375C4⋊C4—38no—
376C4⋊C4—932no—
377C22⋊C4—38no—
378C22⋊C4—932no—
379C42—38no—
380C22×C3—24no—
381C22×C3—24no—
382C22×C3—28no—
383C22×C3—28no—
384C22×C3—24no—
385C22×C3—22no—
386C22×C3—24no—
387C22×C3—21no—
388C22×C3—44no—
389C22×C3—48no—
390C22×C3C22×D1214yes—
391C22×C3C22×D1212yes—
392C22×C3#100714yes—
393C22×C3#101014yes—
394C22×C3C22×#6714yes—
395C22×C3C22×#6712yes—
396C22×C3C24×D311yescharacteristic
397C22×C3C24×D311yescharacteristic
398C2×D3—68no—
399C2×D3—64no—
400C2×D3—68no—
401C2×D3—68no—
402C2×D3—64no—
403C2×D3—128no—
404C2×D3—1216no—
405C2×D3—128no—
406C2×D3—128no—
407C3×C4—24no—
408C3×C4—24no—
409C3×C4—68no—
410C3×C4—68no—
411C3×C4C22×D1214yes—
412C3×C4C22×D1214yes—
413C3×C4C22×#6714yes—
414C3×C4C22×#6714yes—
415Dic3—28no—
416Dic3—28no—
417Dic3—68no—
418Dic3—64no—
419Dic3—64no—
420C32C2×#53611yescharacteristic, complemented, Sylow
421C23—24no—
422C23—94no—
423C23—188no—
424C23—184no—
425C23C2×#62614yes—
426C23C22×D3212yes—
427C23C22×D3211yescharacteristic
428Q8—616no—
429Q8—616no—
430Q8—188no—
431D4—1816no—
432D4—188no—
433C2×C4—38no—
434C2×C4—38no—
435C2×C4—68no—
436C2×C4—616no—
437C2×C4—68no—
438C2×C4—94no—
439C2×C4—184no—
440C2×C4—1816no—
441C2×C4C2×#62614yes—
442C2×C4C2×#62614yes—
443C2×C4C2×#626116yes—
444C2×C4C22×D3212yes—
445C2×C4C22×D3212yes—
446C2×C3—24no—
447C2×C3—24no—
448C2×C3—22no—
449C2×C3—24no—
450C2×C3—21no—
451C2×C3—44no—
452C2×C3#552614yescomplemented
453C2×C3#581614yescomplemented
454C2×C3C23×D1211yescharacteristic
455C2×C3C2×#100712yes—
456C2×C3C2×#101012yes—
457C2×C3C23×#6711yescharacteristic
458D3—128no—
459D3—124no—
460D3—124no—
461C22—24no—
462C22—28no—
463C22—188no—
464C22—184no—
465C22—368no—
466C22#6429714yes—
467C22C22×#62614yes—
468C22C22×#62612yes—
469C22C23×D3211yescharacteristic
470C4—68no—
471C4—68no—
472C4—184no—
473C4C22×#62614yes—
474C4C22×#62614yes—
475C3—21no—
476C3C2×#552611yescharacteristic, complemented
477C3C2×#581611yescharacteristic, complemented
478C2—24no—
479C2—364no—
480C2#1059486614yesdirect product factor
481C2C2×#6429712yes—
482C2C23×#62611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×#3828C2
hypercenterC23×C4D32
hypocenterC32C2×#536
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C23×C3×Dic6C2semidirect
3. C2×C3×#926C2semidirect
4. C2×#63966C2semidirect
5. #10594866C2direct (N × H)
6. C2×#63871C2semidirect
7. C2×#63866C2semidirect
8. C2×#63864C2semidirect
22. C22×C3×Dic6C22semidirect
24. C3×#926C22semidirect
27. #63966C22semidirect
30. #63871C22semidirect
31. #63866C22semidirect
32. #63864C22semidirect
37. C23×Dic6D3semidirect
44. C2×#926D3semidirect
111. C22×Dic6C2×D3semidirect
123. #926C2×D3semidirect
346. C2×C32#536semidirect
420. C32C2×#536semidirect
452. C2×C3#5526semidirect
453. C2×C3#5816semidirect
476. C3C2×#5526semidirect
477. C3C2×#5816semidirect
480. C2#10594866direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C23×C3×Dic62
C2×C3×#9262
C2×#639662
#105948662
C2×#638712
C2×#638662
C2×#638642
C2×#58163
C2×#55263