Finite Group Databasebeta

← C2×#10590529 #11869398

Subgroups — C2×#10590529 #11869398

Order 1152.

1129 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63871C211yesmaximal, characteristic
3C2×C3×#810C211yesmaximal, characteristic, complemented
4C2×C3×#808C211yesmaximal, characteristic, complemented
5C2×#63573C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63557C211yesmaximal, characteristic
8#10590529C218yesmaximal, direct product factor
9C2×#4862—31nomaximal
10C2×#4805—31nomaximal
11C22×C4×C3⋊D3—21no—
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750—21no—
17C4⋊C4×C3⋊D3—22no—
18C4⋊C4×C3⋊D3C2214yes—
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#63573C2214yescomplemented
29#63566C2214yescomplemented
30#63557C2214yes—
31C2×#946—31no—
32C2×#897—31no—
33C2×D3×C4⋊C4—31no—
34C2×D3×C4⋊C4—31no—
35C2×D3×C4⋊C4—61no—
36C2×C3×#106—31no—
37C2×C3×#103—31no—
38C2×#835—31no—
39C2×(C2×D3)⋊C8—31no—
40C2×(C2×D3)⋊C8—31no—
41C2×#817—31no—
42C2×#816—31no—
43C2×#810D311yescharacteristic, complemented
44C2×#808—31no—
45C2×#808D311yescharacteristic, complemented
46#4862—38no—
47#4805—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⋊D3—24no—
56C2×C4×C3⋊D3—44no—
57C2×C4×C3⋊D3D412yes—
58C2×C4×C3⋊D3C2312yes—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C2×C3×Dic6—22no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6C2312yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2312yes—
69#3750—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75C2×C3×C3⋊C8C2312yes—
76Dic3⋊Dic3—24no—
77#3722—24no—
78C2×#483—91noSylow
79C22×C3×Q8—31no—
80C22×C4×D3—31no—
81C22×C4×D3—31no—
82C22×C4×D3—61no—
83C22×C4×D3—61no—
84C22×C4×D3—61no—
85C22×C4×D3—62no—
86C22×Dic6C2×D311yescharacteristic
87C22×C3×C8—31no—
88C22×C3×C8—31no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C4⋊C4C2×D311yescharacteristic
93#946—34no—
94#946—62no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×Dic3⋊C4—61no—
103C2×Dic3⋊C4—61no—
104C2×Dic3⋊C4—61no—
105C2×Dic3⋊C4—62no—
106C22×C3⋊C8C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108#897—34no—
109#897—62no—
110D3×C4⋊C4—34no—
111D3×C4⋊C4—34no—
112D3×C4⋊C4—64no—
113D3×C4⋊C4—62no—
114D3×C4⋊C4—62no—
115D3×C4⋊C4—64no—
116C3×#106—34no—
117C3×#103—34no—
118#835—34no—
119(C2×D3)⋊C8—34no—
120(C2×D3)⋊C8—34no—
121#817—34no—
122#816—34no—
123#810C2×D314yescomplemented
124#808—34no—
125#808C2×D314yescomplemented
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3SD1614yes—
130C22×C3⋊D3C2×D412yes—
131C2×C32×C4—22no—
132C2×C32×C4—42no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4112yes—
135C2×C32×C4#4112yes—
136C2×C32×C4C2411yescharacteristic
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—42no—
140C2×C3⋊Dic3C2×D412yes—
141C4×C3⋊D3—24no—
142C4×C3⋊D3—22no—
143C4×C3⋊D3—22no—
144C4×C3⋊D3—48no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—42no—
148C2×C3×Dic3—42no—
149C3×Dic6—22no—
150C3×Dic6—22no—
151C3×Dic6—42no—
152C3×C3⋊C8—22no—
153C3×C3⋊C8—22no—
154C2×C22⋊Q8—91no—
155C22×C4⋊C4—91no—
156#483—98no—
157C2×#106—31no—
158C2×#106—91no—
159C2×#103—31no—
160C2×#103—91no—
161C2×C22⋊C8—91no—
162C23×D3—31no—
163C23×D3—31no—
164C23×D3—61no—
165C2×C3×Q8—32no—
166C2×C3×Q8—61no—
167C2×C3×Q8—62no—
168C2×C3×Q8—62no—
169C22×C3×C4—22no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—61no—
174C22×C3×C4—61no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—61no—
182C22×Dic3—62no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C2×C4×D3—32no—
186C2×C4×D3—32no—
187C2×C4×D3—32no—
188C2×C4×D3—32no—
189C2×C4×D3—62no—
190C2×C4×D3—62no—
191C2×C4×D3—64no—
192C2×C4×D3—64no—
193C2×C4×D3—62no—
194C2×C4×D3—62no—
195C2×C4×D3—62no—
196C2×C4×D3—62no—
197C2×C4×D3—64no—
198C2×C4×D3—64no—
199C2×C4×D3—68no—
200C2×C4×D3—124no—
201C2×C4×D3—124no—
202C2×C4×D3—128no—
203C2×Dic6—22no—
204C2×Dic6—22no—
205C2×Dic6—21no—
206C2×Dic6C22×D312yes—
207C2×C3×C8—32no—
208C2×C3×C8—32no—
209C2×C3×C8—62no—
210C2×C3×C8—62no—
211C3×C4⋊C4—22no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4C22×D312yes—
218C3×C4⋊C4C22×D312yes—
219(C2×D3)⋊C4—64no—
220(C2×D3)⋊C4—64no—
221C4⋊Dic3—21no—
222C4⋊Dic3—32no—
223C4⋊Dic3—32no—
224C4⋊Dic3—62no—
225C4⋊Dic3—64no—
226C4⋊Dic3—62no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3C22×D312yes—
230Dic3⋊C4—64no—
231Dic3⋊C4—64no—
232Dic3⋊C4—64no—
233Dic3⋊C4—68no—
234C2×C3⋊C8—22no—
235C2×C3⋊C8—22no—
236C2×C3⋊C8C22×D312yes—
237C2×C3⋊C8C22×D312yes—
238C22×C32#12312yes—
239C22×C32C2×SD1612yes—
240C22×C32#13712yes—
241C22×C32C22×D411yescharacteristic
242C2×C3⋊D3—22no—
243C2×C3⋊D3—22no—
244C2×C3⋊D3—28no—
245C2×C3⋊D3C2×SD1614yes—
246C32×C4—42no—
247C32×C4#12312yes—
248C32×C4C2×#4111yescharacteristic
249C32×C4C2×#4111yescharacteristic
250C3⋊Dic3—22no—
251C3⋊Dic3—42no—
252C3×Dic3—42no—
253C3×Dic3—42no—
254C22×Q8—31no—
255C23×C4—91no—
256C23×C4—181no—
257C22×C8—31no—
258C22×C8—31no—
259C22⋊Q8—94no—
260C22⋊Q8—182no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—91no—
263C2×C4⋊C4—94no—
264C2×C4⋊C4—182no—
265C2×C4⋊C4—181no—
266C2×C4⋊C4—181no—
267C2×C4⋊C4D3211yescharacteristic
268C2×C22⋊C4—181no—
269#106—34no—
270#106—94no—
271#103—34no—
272#103—94no—
273C22⋊C8—94no—
274C23×C3—21no—
275C23×C3D3×D411yescharacteristic
276C23×C3D3×D411yescharacteristic
277C22×D3—34no—
278C22×D3—34no—
279C22×D3—32no—
280C22×D3—32no—
281C22×D3—64no—
282C22×D3—62no—
283C22×D3—64no—
284C22×D3—64no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—62no—
289C3×Q8—62no—
290C3×Q8—62no—
291C3×Q8—122no—
292C2×C3×C4—24no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—21no—
299C2×C3×C4—44no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—122no—
305C2×C3×C4—122no—
306C2×C3×C4#23512yes—
307C2×C3×C4#23512yes—
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4#23712yes—
311C2×C3×C4#23912yes—
312C2×C3×C4C23×D311yescharacteristic
313C2×C3×C4C23×D311yescharacteristic
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—32no—
317C2×Dic3—32no—
318C2×Dic3—42no—
319C2×Dic3—42no—
320C2×Dic3—62no—
321C2×Dic3—64no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—64no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—124no—
328C2×Dic3—122no—
329C2×Dic3—122no—
330C4×D3—64no—
331C4×D3—64no—
332C4×D3—68no—
333C4×D3—64no—
334C4×D3—64no—
335C4×D3—62no—
336C4×D3—62no—
337C4×D3—62no—
338C4×D3—62no—
339C4×D3—128no—
340C4×D3—128no—
341C4×D3—1216no—
342Dic6—22no—
343Dic6—22no—
344Dic6—42no—
345C3×C8—62no—
346C3×C8—62no—
347C3⋊C8—22no—
348C3⋊C8—22no—
349C2×C32#48314yescomplemented
350C2×C32C2×#12311yescharacteristic
351C2×C32C22×SD1611yescharacteristic
352C2×C32C2×#13711yescharacteristic
353C3⋊D3—24no—
354C24—91no—
355C2×Q8—32no—
356C2×Q8—61no—
357C2×Q8—62no—
358C2×Q8—62no—
359C22×C4—21no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4—91no—
363C22×C4—92no—
364C22×C4—92no—
365C22×C4—184no—
366C22×C4—182no—
367C22×C4—182no—
368C22×C4—181no—
369C22×C4—364no—
370C22×C4C2×D3211yescharacteristic
371C2×C8—32no—
372C2×C8—32no—
373C2×C8—62no—
374C2×C8—62no—
375C4⋊C4—21no—
376C4⋊C4—32no—
377C4⋊C4—61no—
378C4⋊C4—92no—
379C4⋊C4—184no—
380C4⋊C4—184no—
381C4⋊C4—181no—
382C4⋊C4C2×D3212yes—
383C22⋊C4—184no—
384C22×C3—21no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3#88312yes—
389C22×C3#89412yes—
390C22×C3D3×SD1612yes—
391C22×C3D3×SD1612yes—
392C22×C3#91512yes—
393C22×C3#91812yes—
394C22×C3C2×D3×D411yescharacteristic
395C22×C3C2×D3×D411yescharacteristic
396C2×D3—34no—
397C2×D3—34no—
398C2×D3—64no—
399C2×D3—64no—
400C2×D3—64no—
401C2×D3—616no—
402C2×D3—62no—
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—62no—
406C2×D3—68no—
407C2×D3—68no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—22no—
411C3×C4—44no—
412C3×C4—42no—
413C3×C4—42no—
414C3×C4—122no—
415C3×C4—122no—
416C3×C4#88312yes—
417C3×C4#89412yes—
418C3×C4C2×#23511yescharacteristic
419C3×C4C2×#23511yescharacteristic
420C3×C4C2×#23711yescharacteristic
421C3×C4C2×#23911yescharacteristic
422Dic3—42no—
423Dic3—42no—
424Dic3—64no—
425Dic3—62no—
426Dic3—62no—
427Dic3—124no—
428Dic3—122no—
429Dic3—122no—
430C32C2×#48311yescharacteristic, complemented, Sylow
431C23—92no—
432C23—94no—
433C23—182no—
434C23—182no—
435C23#381111yescharacteristic
436Q8—62no—
437Q8—62no—
438Q8—122no—
439C2×C4—22no—
440C2×C4—42no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—92no—
444C2×C4—122no—
445C2×C4—122no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—182no—
449C2×C4—184no—
450C2×C4—182no—
451C2×C4—368no—
452C2×C4—362no—
453C2×C4#379612yes—
454C2×C4#379812yes—
455C2×C4#381111yescharacteristic
456C2×C4C22×D3211yescharacteristic
457C8—62no—
458C8—62no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—24no—
463C2×C3#480514yescomplemented
464C2×C3#486214yescomplemented
465C2×C3C2×#88311yescharacteristic
466C2×C3C2×#89411yescharacteristic
467C2×C3C2×D3×SD1611yescharacteristic
468C2×C3C2×D3×SD1611yescharacteristic
469C2×C3C2×#91511yescharacteristic
470C2×C3C2×#91811yescharacteristic
471D3—68no—
472D3—64no—
473D3—64no—
474C22—94no—
475C22—182no—
476C22—182no—
477C22—188no—
478C22#6385312yes—
479C22#6393012yes—
480C22#6395112yes—
481C22C2×#381111yescharacteristic
482C4—42no—
483C4—122no—
484C4—122no—
485C4—182no—
486C4—362no—
487C4#6385312yes—
488C4C2×#379611yescharacteristic
489C4C2×#379811yescharacteristic
490C3—21no—
491C3C2×#480511yescharacteristic, complemented
492C3C2×#486211yescharacteristic, complemented
493C2—184no—
494C2#1059052914yesdirect product factor
495C2C2×#6385311yescharacteristic
496C2C2×#6393011yescharacteristic
497C2C2×#6395111yescharacteristic
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×#483
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×#63573C2semidirect
6. C2×#63566C2semidirect
8. #10590529C2direct (N × H)
26. C3×#810C22semidirect
27. C3×#808C22semidirect
28. #63573C22semidirect
29. #63566C22semidirect
43. C2×#810D3semidirect
45. C2×#808D3semidirect
123. #810C2×D3semidirect
125. #808C2×D3semidirect
349. C2×C32#483semidirect
430. C32C2×#483semidirect
463. C2×C3#4805semidirect
464. C2×C3#4862semidirect
491. C3C2×#4805semidirect
492. C3C2×#4862semidirect
494. C2#10590529direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#638712
C2×C3×#8102
C2×C3×#8082
C2×#635732
C2×#635662
C2×#635572
#105905292
C2×#48623
C2×#48053