Finite Group Databasebeta

← C2×#10590527 #11869521

Subgroups — C2×#10590527 #11869521

Order 1152.

997 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×#63871C211yesmaximal, characteristic
3C2×C3×#810C211yesmaximal, characteristic, complemented
4C2×C3×#808C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63557C211yesmaximal, characteristic
8#10590527C218yesmaximal, direct product factor
9C2×#4868—31nomaximal
10C2×#4814—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4×C3⋊Dic3—21no—
17#64101—22no—
18#64101C2214yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×Dic3⋊Dic3—21no—
23C2×#3722—21no—
24#63871—22no—
25#63871C2214yes—
26C3×#810C2214yescomplemented
27C3×#808C2214yescomplemented
28#63575C2214yescomplemented
29#63566C2214yescomplemented
30#63557C2214yes—
31C2×#946—31no—
32C2×#897—31no—
33C2×#892—31no—
34C2×#892—31no—
35C2×#892—61no—
36C2×C3×#106—31no—
37C2×C3×#103—31no—
38C2×#835—31no—
39C2×(C2×D3)⋊C8—31no—
40C2×(C2×D3)⋊C8—31no—
41C2×#818—31no—
42C2×#816—31no—
43C2×#810D311yescharacteristic, complemented
44C2×#808D311yescharacteristic, complemented
45C2×#807—31no—
46#4868—38no—
47#4814—38no—
48C23×C3⋊D3D411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3D411yescharacteristic
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3D412yes—
56C2×C4×C3⋊D3C2312yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65#3752—24no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68C4×C3⋊Dic3—24no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2312yes—
71C2×C3×C3⋊C8—22no—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8C2312yes—
74C2×C3×C3⋊C8C2312yes—
75Dic3⋊Dic3—24no—
76#3722—24no—
77C2×#485—91noSylow
78C22×C3×Q8—31no—
79C22×C4×D3—31no—
80C22×C4×D3—31no—
81C22×C4×D3—61no—
82C22×Dic6C2×D311yescharacteristic
83C22×C3×C8—31no—
84C22×C3×C8—31no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C4⋊C4C2×D311yescharacteristic
89#946—34no—
90#946—62no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×(C2×D3)⋊C4—62no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×Dic3⋊C4—61no—
102C2×C4×Dic3—61no—
103C2×C4×Dic3—61no—
104C2×C4×Dic3—62no—
105C22×C3⋊C8C2×D311yescharacteristic
106C22×C3⋊C8C2×D311yescharacteristic
107#897—34no—
108#897—62no—
109#892—34no—
110#892—34no—
111#892—64no—
112#892—62no—
113#892—62no—
114#892—64no—
115C3×#106—34no—
116C3×#103—34no—
117#835—34no—
118(C2×D3)⋊C8—34no—
119(C2×D3)⋊C8—34no—
120#818—34no—
121#816—34no—
122#810C2×D314yescomplemented
123#808C2×D314yescomplemented
124#807—34no—
125C23×C32C2×D411yescharacteristic
126C22×C3⋊D3—22no—
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3C2×D412yes—
130C2×C32×C4—22no—
131C2×C32×C4—42no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4112yes—
134C2×C32×C4#4112yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—42no—
139C2×C3⋊Dic3C2×D412yes—
140C4×C3⋊D3—24no—
141C4×C3⋊D3—22no—
142C4×C3⋊D3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—42no—
147C3×Dic6—22no—
148C3×Dic6—22no—
149C3×Dic6—42no—
150C3×C3⋊C8—22no—
151C3×C3⋊C8—22no—
152C2×C22⋊Q8—91no—
153C2×#117—91no—
154#485—98no—
155C2×#107—91no—
156C2×#106—31no—
157C2×#103—31no—
158C2×#103—91no—
159C2×C22⋊C8—91no—
160C23×D3—31no—
161C23×D3—31no—
162C23×D3—61no—
163C2×C3×Q8—32no—
164C2×C3×Q8—61no—
165C2×C3×Q8—62no—
166C2×C3×Q8—62no—
167C22×C3×C4—22no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—21no—
176C22×Dic3—21no—
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—61no—
180C22×Dic3—62no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C2×C4×D3—32no—
184C2×C4×D3—32no—
185C2×C4×D3—32no—
186C2×C4×D3—32no—
187C2×C4×D3—62no—
188C2×C4×D3—62no—
189C2×C4×D3—64no—
190C2×C4×D3—64no—
191C2×C4×D3—62no—
192C2×C4×D3—62no—
193C2×C4×D3—62no—
194C2×C4×D3—62no—
195C2×Dic6—22no—
196C2×Dic6—22no—
197C2×Dic6—21no—
198C2×Dic6C22×D312yes—
199C2×C3×C8—32no—
200C2×C3×C8—32no—
201C2×C3×C8—62no—
202C2×C3×C8—62no—
203C3×C4⋊C4—22no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—22no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4C22×D312yes—
210C3×C4⋊C4C22×D312yes—
211(C2×D3)⋊C4—64no—
212(C2×D3)⋊C4—64no—
213(C2×D3)⋊C4—64no—
214(C2×D3)⋊C4—64no—
215(C2×D3)⋊C4—68no—
216C4⋊Dic3—21no—
217C4⋊Dic3—32no—
218C4⋊Dic3—32no—
219C4⋊Dic3—62no—
220C4⋊Dic3—64no—
221C4⋊Dic3—62no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3C22×D312yes—
225Dic3⋊C4—64no—
226C4×Dic3—64no—
227C4×Dic3—64no—
228C4×Dic3—68no—
229C2×C3⋊C8—22no—
230C2×C3⋊C8—22no—
231C2×C3⋊C8C22×D312yes—
232C2×C3⋊C8C22×D312yes—
233C22×C32#12312yes—
234C22×C32#13512yes—
235C22×C32#13712yes—
236C22×C32C22×D411yescharacteristic
237C2×C3⋊D3—22no—
238C2×C3⋊D3—22no—
239C2×C3⋊D3—22no—
240C2×C3⋊D3—44no—
241C32×C4—42no—
242C32×C4#12312yes—
243C32×C4C2×#4111yescharacteristic
244C32×C4C2×#4111yescharacteristic
245C3⋊Dic3—22no—
246C3⋊Dic3—42no—
247C3×Dic3—42no—
248C3×Dic3—42no—
249C22×Q8—31no—
250C23×C4—91no—
251C22×C8—31no—
252C22×C8—31no—
253C22⋊Q8—94no—
254C22⋊Q8—182no—
255#117—94no—
256#117—182no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—91no—
259C2×C4⋊C4—181no—
260C2×C4⋊C4D3211yescharacteristic
261C2×C22⋊C4—181no—
262C2×C22⋊C4—181no—
263C2×C42—181no—
264#107—94no—
265#106—34no—
266#103—34no—
267#103—94no—
268C22⋊C8—94no—
269C23×C3—21no—
270C23×C3D3×D411yescharacteristic
271C23×C3D3×D411yescharacteristic
272C22×D3—32no—
273C22×D3—32no—
274C22×D3—62no—
275C22×D3—64no—
276C22×D3—62no—
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—62no—
280C22×D3—62no—
281C22×D3—62no—
282C22×D3—122no—
283C22×D3—122no—
284C3×Q8—62no—
285C3×Q8—62no—
286C3×Q8—122no—
287C2×C3×C4—24no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—44no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—122no—
300C2×C3×C4—122no—
301C2×C3×C4#23512yes—
302C2×C3×C4#23512yes—
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4#23712yes—
306C2×C3×C4#23912yes—
307C2×C3×C4C23×D311yescharacteristic
308C2×C3×C4C23×D311yescharacteristic
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—32no—
312C2×Dic3—32no—
313C2×Dic3—42no—
314C2×Dic3—42no—
315C2×Dic3—62no—
316C2×Dic3—64no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—64no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—124no—
323C2×Dic3—122no—
324C2×Dic3—122no—
325C4×D3—64no—
326C4×D3—64no—
327C4×D3—68no—
328C4×D3—64no—
329C4×D3—64no—
330C4×D3—62no—
331C4×D3—62no—
332C4×D3—62no—
333C4×D3—62no—
334Dic6—22no—
335Dic6—22no—
336Dic6—42no—
337C3×C8—62no—
338C3×C8—62no—
339C3⋊C8—22no—
340C3⋊C8—22no—
341C2×C32#48514yescomplemented
342C2×C32C2×#12311yescharacteristic
343C2×C32C2×#13511yescharacteristic
344C2×C32C2×#13711yescharacteristic
345C3⋊D3—42no—
346C24—91no—
347C2×Q8—32no—
348C2×Q8—61no—
349C2×Q8—62no—
350C2×Q8—62no—
351C22×C4—21no—
352C22×C4—61no—
353C22×C4—61no—
354C22×C4—91no—
355C22×C4—92no—
356C22×C4—92no—
357C22×C4—182no—
358C22×C4—182no—
359C22×C4—181no—
360C22×C4C2×D3211yescharacteristic
361C2×C8—32no—
362C2×C8—32no—
363C2×C8—62no—
364C2×C8—62no—
365C4⋊C4—21no—
366C4⋊C4—32no—
367C4⋊C4—61no—
368C4⋊C4—92no—
369C4⋊C4—184no—
370C4⋊C4—181no—
371C4⋊C4C2×D3212yes—
372C22⋊C4—184no—
373C22⋊C4—184no—
374C42—184no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3#88312yes—
380C22×C3#89412yes—
381C22×C3#91512yes—
382C22×C3#91512yes—
383C22×C3#91612yes—
384C22×C3#91912yes—
385C22×C3C2×D3×D411yescharacteristic
386C22×C3C2×D3×D411yescharacteristic
387C2×D3—64no—
388C2×D3—62no—
389C2×D3—62no—
390C2×D3—62no—
391C2×D3—62no—
392C2×D3—62no—
393C2×D3—62no—
394C2×D3—122no—
395C2×D3—122no—
396C2×D3—128no—
397C2×D3—124no—
398C2×D3—124no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—22no—
402C3×C4—44no—
403C3×C4—42no—
404C3×C4—42no—
405C3×C4—122no—
406C3×C4—122no—
407C3×C4#88312yes—
408C3×C4#89412yes—
409C3×C4C2×#23511yescharacteristic
410C3×C4C2×#23511yescharacteristic
411C3×C4C2×#23711yescharacteristic
412C3×C4C2×#23911yescharacteristic
413Dic3—42no—
414Dic3—42no—
415Dic3—64no—
416Dic3—62no—
417Dic3—62no—
418Dic3—124no—
419Dic3—122no—
420Dic3—122no—
421C32C2×#48511yescharacteristic, complemented, Sylow
422C23—92no—
423C23—182no—
424C23—182no—
425C23—182no—
426C23#381111yescharacteristic
427Q8—62no—
428Q8—62no—
429Q8—122no—
430C2×C4—22no—
431C2×C4—42no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—92no—
435C2×C4—122no—
436C2×C4—122no—
437C2×C4—182no—
438C2×C4—182no—
439C2×C4—182no—
440C2×C4—184no—
441C2×C4—182no—
442C2×C4—362no—
443C2×C4#379612yes—
444C2×C4#379812yes—
445C2×C4#381111yescharacteristic
446C2×C4C22×D3211yescharacteristic
447C8—62no—
448C8—62no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—24no—
453C2×C3#481414yescomplemented
454C2×C3#486814yescomplemented
455C2×C3C2×#88311yescharacteristic
456C2×C3C2×#89411yescharacteristic
457C2×C3C2×#91511yescharacteristic
458C2×C3C2×#91511yescharacteristic
459C2×C3C2×#91611yescharacteristic
460C2×C3C2×#91911yescharacteristic
461D3—124no—
462D3—122no—
463D3—122no—
464C22—182no—
465C22—182no—
466C22—182no—
467C22—364no—
468C22#6385312yes—
469C22#6393112yes—
470C22#6395012yes—
471C22C2×#381111yescharacteristic
472C4—42no—
473C4—122no—
474C4—122no—
475C4—182no—
476C4—362no—
477C4#6385312yes—
478C4C2×#379611yescharacteristic
479C4C2×#379811yescharacteristic
480C3—21no—
481C3C2×#481411yescharacteristic, complemented
482C3C2×#486811yescharacteristic, complemented
483C2—362no—
484C2#1059052714yesdirect product factor
485C2C2×#6385311yescharacteristic
486C2C2×#6393111yescharacteristic
487C2C2×#6395011yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×#810C2semidirect
4. C2×C3×#808C2semidirect
5. C2×#63575C2semidirect
6. C2×#63566C2semidirect
8. #10590527C2direct (N × H)
26. C3×#810C22semidirect
27. C3×#808C22semidirect
28. #63575C22semidirect
29. #63566C22semidirect
43. C2×#810D3semidirect
44. C2×#808D3semidirect
122. #810C2×D3semidirect
123. #808C2×D3semidirect
341. C2×C32#485semidirect
421. C32C2×#485semidirect
453. C2×C3#4814semidirect
454. C2×C3#4868semidirect
481. C3C2×#4814semidirect
482. C3C2×#4868semidirect
484. C2#10590527direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#638712
C2×C3×#8102
C2×C3×#8082
C2×#635752
C2×#635662
C2×#635572
#105905272
C2×#48683
C2×#48143