Finite Group Databasebeta

← C2×#10591561 #11869505

Subgroups — C2×#10591561 #11869505

Order 1152.

993 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64155C211yesmaximal, characteristic
2C2×#63849C211yesmaximal, characteristic
3C2×C3×#835C211yesmaximal, characteristic, complemented
4C2×C3×#835C211yesmaximal, characteristic, complemented
5#10591561C218yesmaximal, direct product factor
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63573C211yesmaximal, characteristic, complemented
8C2×#63557C211yesmaximal, characteristic
9C2×#4815—31nomaximal
10C2×#4814—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13#64155—22no—
14#64155C2214yes—
15C2×#3752—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×#3722—21no—
23C2×Dic32—21no—
24#63849—22no—
25#63849C2214yes—
26C3×#835C2214yescomplemented
27C3×#835C2214yescomplemented
28#63575C2214yescomplemented
29#63573C2214yescomplemented
30#63557C2214yes—
31C2×#946—31no—
32C2×#946—31no—
33C2×#946—61no—
34C2×#892—31no—
35C2×#892—31no—
36C2×C3×#103—31no—
37C2×C3×#103—31no—
38C2×#835D311yescharacteristic, complemented
39C2×#835D311yescharacteristic, complemented
40C2×(C2×D3)⋊C8—31no—
41C2×(C2×D3)⋊C8—31no—
42C2×#818—31no—
43C2×#817—31no—
44C2×#808—31no—
45C2×#807—31no—
46#4815—38no—
47#4814—38no—
48C23×C3⋊D3D411yescharacteristic
49C2×C32×Q8—21no—
50C2×C32×Q8—22no—
51C2×C32×Q8—22no—
52C2×C32×Q8C2312yes—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3D411yescharacteristic
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3D412yes—
60C2×C4×C3⋊D3C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63#3752—24no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)C2312yes—
66#3750—24no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3C2312yes—
70C3×C4⋊Dic3C2312yes—
71C2×C3×C3⋊C8—22no—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8C2312yes—
74C2×C3×C3⋊C8C2312yes—
75#3722—24no—
76Dic32—24no—
77C2×#485—91noSylow
78C22×C3×Q8—21no—
79C22×C3×Q8C2×D311yescharacteristic
80C22×C3×Q8C2×D311yescharacteristic
81C22×C4×D3—31no—
82C22×C4×D3—31no—
83C22×C4×D3—61no—
84C22×C3×C8—31no—
85C22×C3×C8—31no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—31no—
88#946—34no—
89#946—34no—
90#946—64no—
91#946—62no—
92#946—62no—
93#946—64no—
94C2×(C2×D3)⋊C4—61no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—62no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×Dic3⋊C4—61no—
105C2×Dic3⋊C4—61no—
106C2×Dic3⋊C4—62no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110C22×C3⋊C8C2×D311yescharacteristic
111#892—34no—
112#892—34no—
113#892—62no—
114#892—62no—
115C3×#103—34no—
116C3×#103—34no—
117#835C2×D314yescomplemented
118#835C2×D314yescomplemented
119(C2×D3)⋊C8—34no—
120(C2×D3)⋊C8—34no—
121#818—34no—
122#817—34no—
123#808—34no—
124#807—34no—
125C23×C32C2×D411yescharacteristic
126C22×C3⋊D3—22no—
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3C2×D412yes—
130C32×Q8—22no—
131C32×Q8—22no—
132C32×Q8—42no—
133C2×C32×C4—22no—
134C2×C32×C4—42no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4112yes—
137C2×C32×C4#4112yes—
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—42no—
142C2×C3⋊Dic3C2×D412yes—
143C4×C3⋊D3—24no—
144C4×C3⋊D3—22no—
145C4×C3⋊D3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—42no—
149C2×C3×Dic3—42no—
150C3×C3⋊C8—22no—
151C3×C3⋊C8—22no—
152C2×C22⋊Q8—91no—
153C2×#117—91no—
154#485—98no—
155C2×#107—91no—
156C2×#106—91no—
157C2×#103—31no—
158C2×#103—31no—
159C2×C22⋊C8—91no—
160C23×D3—31no—
161C23×D3—31no—
162C23×D3—61no—
163C2×C3×Q8—22no—
164C2×C3×Q8—21no—
165C2×C3×Q8—21no—
166C2×C3×Q8—22no—
167C2×C3×Q8—22no—
168C2×C3×Q8—22no—
169C2×C3×Q8—22no—
170C2×C3×Q8—22no—
171C2×C3×Q8—42no—
172C2×C3×Q8—42no—
173C2×C3×Q8C22×D312yes—
174C2×C3×Q8C22×D312yes—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3—31no—
186C22×Dic3—31no—
187C22×Dic3—61no—
188C22×Dic3—62no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C2×C4×D3—32no—
192C2×C4×D3—32no—
193C2×C4×D3—32no—
194C2×C4×D3—32no—
195C2×C4×D3—62no—
196C2×C4×D3—62no—
197C2×C4×D3—62no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—122no—
202C2×C4×D3—122no—
203C2×C3×C8—32no—
204C2×C3×C8—32no—
205C2×C3×C8—62no—
206C2×C3×C8—62no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
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—21no—
218C4⋊Dic3—32no—
219C4⋊Dic3—32no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3C22×D312yes—
225C4⋊Dic3C22×D312yes—
226Dic3⋊C4—64no—
227Dic3⋊C4—64no—
228Dic3⋊C4—68no—
229C4×Dic3—64no—
230C4×Dic3—64no—
231C2×C3⋊C8—22no—
232C2×C3⋊C8—22no—
233C2×C3⋊C8C22×D312yes—
234C2×C3⋊C8C22×D312yes—
235C22×C32#12312yes—
236C22×C32#13512yes—
237C22×C32#13712yes—
238C22×C32C22×D411yescharacteristic
239C2×C3⋊D3—22no—
240C2×C3⋊D3—22no—
241C2×C3⋊D3—22no—
242C2×C3⋊D3—44no—
243C32×C4—42no—
244C32×C4#12312yes—
245C32×C4C2×#4111yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3⋊Dic3—22no—
248C3⋊Dic3—42no—
249C3×Dic3—42no—
250C3×Dic3—42no—
251C22×Q8D3211yescharacteristic
252C23×C4—91no—
253C22×C8—31no—
254C22×C8—31no—
255C22⋊Q8—94no—
256C22⋊Q8—182no—
257#117—94no—
258#117—182no—
259C2×C4⋊C4—31no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—181no—
263C2×C22⋊C4—181no—
264C2×C22⋊C4—181no—
265C2×C42—181no—
266#107—94no—
267#106—94no—
268#103—34no—
269#103—34no—
270C22⋊C8—94no—
271C23×C3—21no—
272C23×C3D3×D411yescharacteristic
273C23×C3D3×D411yescharacteristic
274C22×D3—32no—
275C22×D3—32no—
276C22×D3—62no—
277C22×D3—64no—
278C22×D3—62no—
279C22×D3—62no—
280C22×D3—62no—
281C22×D3—62no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—122no—
285C22×D3—122no—
286C3×Q8—22no—
287C3×Q8—22no—
288C3×Q8—22no—
289C3×Q8—22no—
290C3×Q8—42no—
291C3×Q8—42no—
292C3×Q8—44no—
293C3×Q8—42no—
294C3×Q8—42no—
295C2×C3×C4—24no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—21no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—21no—
302C2×C3×C4—44no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—122no—
308C2×C3×C4—122no—
309C2×C3×C4#23512yes—
310C2×C3×C4#23512yes—
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4#23712yes—
314C2×C3×C4#23712yes—
315C2×C3×C4C23×D311yescharacteristic
316C2×C3×C4C23×D311yescharacteristic
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—32no—
320C2×Dic3—32no—
321C2×Dic3—42no—
322C2×Dic3—42no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—64no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—122no—
330C2×Dic3—124no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333C4×D3—64no—
334C4×D3—64no—
335C4×D3—62no—
336C4×D3—62no—
337C4×D3—62no—
338C4×D3—62no—
339C4×D3—122no—
340C4×D3—122no—
341C4×D3—124no—
342C3×C8—62no—
343C3×C8—62no—
344C3⋊C8—22no—
345C3⋊C8—22no—
346C2×C32#48514yescomplemented
347C2×C32C2×#12311yescharacteristic
348C2×C32C2×#13511yescharacteristic
349C2×C32C2×#13711yescharacteristic
350C3⋊D3—42no—
351C24—91no—
352C2×Q8—21no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8C2×D3212yes—
356C22×C4—21no—
357C22×C4—61no—
358C22×C4—61no—
359C22×C4—91no—
360C22×C4—92no—
361C22×C4—92no—
362C22×C4—182no—
363C22×C4—182no—
364C22×C4—181no—
365C22×C4C2×D3211yescharacteristic
366C2×C8—32no—
367C2×C8—32no—
368C2×C8—62no—
369C2×C8—62no—
370C4⋊C4—32no—
371C4⋊C4—32no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—92no—
375C4⋊C4—184no—
376C4⋊C4—181no—
377C22⋊C4—184no—
378C22⋊C4—184no—
379C42—184no—
380C22×C3—21no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3#88312yes—
385C22×C3#88312yes—
386C22×C3#91512yes—
387C22×C3#91612yes—
388C22×C3#91812yes—
389C22×C3#91912yes—
390C22×C3C2×D3×D411yescharacteristic
391C22×C3C2×D3×D411yescharacteristic
392C2×D3—64no—
393C2×D3—62no—
394C2×D3—62no—
395C2×D3—62no—
396C2×D3—62no—
397C2×D3—62no—
398C2×D3—62no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—128no—
402C2×D3—124no—
403C2×D3—124no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—22no—
407C3×C4—44no—
408C3×C4—42no—
409C3×C4—42no—
410C3×C4—122no—
411C3×C4—122no—
412C3×C4#88312yes—
413C3×C4#88312yes—
414C3×C4C2×#23511yescharacteristic
415C3×C4C2×#23511yescharacteristic
416C3×C4C2×#23711yescharacteristic
417C3×C4C2×#23711yescharacteristic
418Dic3—42no—
419Dic3—42no—
420Dic3—62no—
421Dic3—62no—
422Dic3—122no—
423Dic3—124no—
424Dic3—122no—
425Dic3—122no—
426C32C2×#48511yescharacteristic, complemented, Sylow
427C23—92no—
428C23—182no—
429C23—182no—
430C23—182no—
431C23#381111yescharacteristic
432Q8—22no—
433Q8—22no—
434Q8—42no—
435C2×C4—22no—
436C2×C4—42no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—92no—
440C2×C4—122no—
441C2×C4—122no—
442C2×C4—182no—
443C2×C4—182no—
444C2×C4—182no—
445C2×C4—184no—
446C2×C4—182no—
447C2×C4—362no—
448C2×C4#380412yes—
449C2×C4#380412yes—
450C2×C4#381111yescharacteristic
451C2×C4C22×D3211yescharacteristic
452C8—62no—
453C8—62no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—24no—
457C2×C3—21no—
458C2×C3#481414yescomplemented
459C2×C3#481514yescomplemented
460C2×C3C2×#88311yescharacteristic
461C2×C3C2×#88311yescharacteristic
462C2×C3C2×#91511yescharacteristic
463C2×C3C2×#91611yescharacteristic
464C2×C3C2×#91811yescharacteristic
465C2×C3C2×#91911yescharacteristic
466D3—124no—
467D3—122no—
468D3—122no—
469C22—182no—
470C22—182no—
471C22—182no—
472C22—364no—
473C22#6395012yes—
474C22#6395112yes—
475C22#6397512yes—
476C22C2×#381111yescharacteristic
477C4—42no—
478C4—122no—
479C4—122no—
480C4—182no—
481C4—362no—
482C4#6397512yes—
483C4C2×#380411yescharacteristic
484C4C2×#380411yescharacteristic
485C3—21no—
486C3C2×#481411yescharacteristic, complemented
487C3C2×#481511yescharacteristic, complemented
488C2—362no—
489C2#1059156114yesdirect product factor
490C2C2×#6395011yescharacteristic
491C2C2×#6395111yescharacteristic
492C2C2×#6397511yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×Q8D32
hypocenterC32C2×#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#835C2semidirect
4. C2×C3×#835C2semidirect
5. #10591561C2direct (N × H)
6. C2×#63575C2semidirect
7. C2×#63573C2semidirect
26. C3×#835C22semidirect
27. C3×#835C22semidirect
28. #63575C22semidirect
29. #63573C22semidirect
38. C2×#835D3semidirect
39. C2×#835D3semidirect
117. #835C2×D3semidirect
118. #835C2×D3semidirect
346. C2×C32#485semidirect
426. C32C2×#485semidirect
458. C2×C3#4814semidirect
459. C2×C3#4815semidirect
486. C3C2×#4814semidirect
487. C3C2×#4815semidirect
489. C2#10591561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641552
C2×#638492
C2×C3×#8352
#105915612
C2×#635752
C2×#635732
C2×#635572
C2×#48153
C2×#48143