Finite Group Databasebeta

← C2×#10590715 #11869523

Subgroups — C2×#10590715 #11869523

Order 1152.

933 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63871C211yesmaximal, characteristic
2C2×#63849C211yesmaximal, characteristic
3C2×#63647C211yesmaximal, characteristic
4C2×C3×#818C211yesmaximal, characteristic, complemented
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C2×#63574C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8#10590715C218yesmaximal, direct product factor
9C2×#4888—31nomaximal
10C2×#4814—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×Dic3⋊Dic3—21no—
19C2×#3722—21no—
20C2×#3722—21no—
21C2×Dic32—21no—
22#63871—22no—
23#63871C2214yes—
24#63849—22no—
25#63849C2214yes—
26#63647C2214yes—
27C3×#818C2214yescomplemented
28C3×#816C2214yescomplemented
29#63574C2214yescomplemented
30#63565C2214yescomplemented
31C2×#946—31no—
32C2×#897—31no—
33C2×#892—31no—
34C2×#892—31no—
35C2×C3×#107—31no—
36C2×C3×#103—31no—
37C2×#835—31no—
38C2×(C2×D3)⋊C8—31no—
39C2×(C2×D3)⋊C8—31no—
40C2×(C2×D3)⋊C8—61no—
41C2×#818D311yescharacteristic, complemented
42C2×#816D311yescharacteristic, complemented
43C2×#810—31no—
44C2×#808—31no—
45C2×#808—31no—
46#4888—38no—
47#4814—38no—
48C23×C3⋊D3D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C2×C4×C3⋊D3—22no—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3D412yes—
54C2×C4×C3⋊D3C2312yes—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C2×C32×C8—22no—
64C2×C32×C8C2312yes—
65C2×C3⋊(C3⋊C8)—22no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2312yes—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73Dic3⋊Dic3—24no—
74#3722—24no—
75#3722—24no—
76Dic32—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—21no—
84C22×C3×C8C2×D311yescharacteristic
85C22×C3×C8C2×D311yescharacteristic
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
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×C4⋊Dic3—61no—
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×Dic3⋊C4—61no—
100C2×C4×Dic3—61no—
101C2×C4×Dic3—61no—
102C22×C3⋊C8—31no—
103C22×C3⋊C8—31no—
104C22×C3⋊C8—61no—
105#897—34no—
106#897—62no—
107#892—34no—
108#892—34no—
109#892—62no—
110#892—62no—
111C3×#107—34no—
112C3×#103—34no—
113#835—34no—
114(C2×D3)⋊C8—34no—
115(C2×D3)⋊C8—34no—
116(C2×D3)⋊C8—64no—
117#818C2×D314yescomplemented
118#816C2×D314yescomplemented
119#810—34no—
120#808—34no—
121#808—34no—
122C23×C32C2×D411yescharacteristic
123C22×C3⋊D3—22no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3C2×D412yes—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4112yes—
129C2×C32×C4#4112yes—
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3C2×D412yes—
133C4×C3⋊D3—24no—
134C4×C3⋊D3—22no—
135C4×C3⋊D3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3—42no—
144C3×Dic6—22no—
145C3×Dic6—22no—
146C3×Dic6—42no—
147C32×C8—22no—
148C3⋊(C3⋊C8)—22no—
149C2×C22⋊Q8—91no—
150C2×#117—91no—
151#485—98no—
152C2×#107—31no—
153C2×#106—91no—
154C2×#103—31no—
155C2×#103—91no—
156C2×C22⋊C8—91no—
157C23×D3—31no—
158C23×D3—31no—
159C23×D3—61no—
160C2×C3×Q8—32no—
161C2×C3×Q8—61no—
162C2×C3×Q8—62no—
163C2×C3×Q8—62no—
164C22×C3×C4—21no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—61no—
178C2×C4×D3—32no—
179C2×C4×D3—32no—
180C2×C4×D3—32no—
181C2×C4×D3—32no—
182C2×C4×D3—62no—
183C2×C4×D3—62no—
184C2×C4×D3—62no—
185C2×C4×D3—62no—
186C2×C4×D3—62no—
187C2×C4×D3—62no—
188C2×C4×D3—122no—
189C2×C4×D3—122no—
190C2×Dic6—22no—
191C2×Dic6—22no—
192C2×Dic6—21no—
193C2×Dic6C22×D312yes—
194C2×C3×C8—22no—
195C2×C3×C8—22no—
196C2×C3×C8—22no—
197C2×C3×C8—42no—
198C2×C3×C8C22×D312yes—
199C2×C3×C8C22×D312yes—
200C3×C4⋊C4—32no—
201C3×C4⋊C4—32no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206(C2×D3)⋊C4—64no—
207(C2×D3)⋊C4—64no—
208(C2×D3)⋊C4—64no—
209(C2×D3)⋊C4—64no—
210C4⋊Dic3—21no—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213C4⋊Dic3—64no—
214C4⋊Dic3C22×D312yes—
215C4⋊Dic3C22×D312yes—
216C4⋊Dic3C22×D312yes—
217Dic3⋊C4—64no—
218C4×Dic3—64no—
219C4×Dic3—64no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—32no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8—62no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—122no—
226C22×C32#12312yes—
227C22×C32#13512yes—
228C22×C32#13712yes—
229C22×C32C22×D411yescharacteristic
230C2×C3⋊D3—22no—
231C2×C3⋊D3—22no—
232C2×C3⋊D3—22no—
233C2×C3⋊D3—44no—
234C32×C4#12312yes—
235C32×C4C2×#4111yescharacteristic
236C32×C4C2×#4111yescharacteristic
237C3⋊Dic3—22no—
238C3×Dic3—42no—
239C3×Dic3—42no—
240C3×Dic3—42no—
241C3×Dic3—42no—
242C22×Q8—31no—
243C23×C4—91no—
244C22×C8—91no—
245C22×C8D3211yescharacteristic
246C22⋊Q8—94no—
247C22⋊Q8—182no—
248#117—94no—
249#117—182no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—31no—
253C2×C4⋊C4—181no—
254C2×C22⋊C4—181no—
255C2×C22⋊C4—181no—
256C2×C42—181no—
257#107—34no—
258#106—94no—
259#103—34no—
260#103—94no—
261C22⋊C8—94no—
262C23×C3—21no—
263C23×C3D3×D411yescharacteristic
264C23×C3D3×D411yescharacteristic
265C22×D3—32no—
266C22×D3—32no—
267C22×D3—62no—
268C22×D3—64no—
269C22×D3—62no—
270C22×D3—62no—
271C22×D3—62no—
272C22×D3—62no—
273C22×D3—62no—
274C22×D3—62no—
275C22×D3—122no—
276C22×D3—122no—
277C3×Q8—62no—
278C3×Q8—62no—
279C3×Q8—122no—
280C2×C3×C4—21no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—22no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—122no—
289C2×C3×C4—122no—
290C2×C3×C4—122no—
291C2×C3×C4—122no—
292C2×C3×C4#23512yes—
293C2×C3×C4#23512yes—
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4#23712yes—
297C2×C3×C4#23912yes—
298C2×C3×C4C23×D311yescharacteristic
299C2×C3×C4C23×D311yescharacteristic
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—32no—
305C2×Dic3—32no—
306C2×Dic3—42no—
307C2×Dic3—42no—
308C2×Dic3—42no—
309C2×Dic3—42no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—122no—
314C4×D3—64no—
315C4×D3—64no—
316C4×D3—62no—
317C4×D3—62no—
318C4×D3—62no—
319C4×D3—62no—
320C4×D3—122no—
321C4×D3—122no—
322C4×D3—124no—
323Dic6—22no—
324Dic6—22no—
325Dic6—42no—
326C3×C8—22no—
327C3×C8—22no—
328C3×C8—42no—
329C3⋊C8—62no—
330C3⋊C8—62no—
331C3⋊C8—122no—
332C2×C32#48514yescomplemented
333C2×C32C2×#12311yescharacteristic
334C2×C32C2×#13511yescharacteristic
335C2×C32C2×#13711yescharacteristic
336C3⋊D3—42no—
337C24—91no—
338C2×Q8—32no—
339C2×Q8—61no—
340C2×Q8—62no—
341C2×Q8—62no—
342C22×C4—61no—
343C22×C4—61no—
344C22×C4—61no—
345C22×C4—61no—
346C22×C4—91no—
347C22×C4—92no—
348C22×C4—92no—
349C22×C4—182no—
350C22×C4—182no—
351C22×C4C2×D3211yescharacteristic
352C2×C8—22no—
353C2×C8—92no—
354C2×C8—182no—
355C2×C8C2×D3212yes—
356C4⋊C4—32no—
357C4⋊C4—32no—
358C4⋊C4—32no—
359C4⋊C4—61no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—184no—
363C22⋊C4—184no—
364C22⋊C4—184no—
365C42—184no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3#88312yes—
371C22×C3#89412yes—
372C22×C3#91212yes—
373C22×C3#91512yes—
374C22×C3#91812yes—
375C22×C3#91912yes—
376C22×C3C2×D3×D411yescharacteristic
377C22×C3C2×D3×D411yescharacteristic
378C2×D3—64no—
379C2×D3—62no—
380C2×D3—62no—
381C2×D3—62no—
382C2×D3—62no—
383C2×D3—62no—
384C2×D3—62no—
385C2×D3—122no—
386C2×D3—122no—
387C2×D3—128no—
388C2×D3—124no—
389C2×D3—124no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—22no—
393C3×C4—122no—
394C3×C4—122no—
395C3×C4—122no—
396C3×C4—122no—
397C3×C4#88312yes—
398C3×C4#89412yes—
399C3×C4C2×#23511yescharacteristic
400C3×C4C2×#23511yescharacteristic
401C3×C4C2×#23711yescharacteristic
402C3×C4C2×#23911yescharacteristic
403Dic3—42no—
404Dic3—42no—
405Dic3—42no—
406Dic3—42no—
407Dic3—62no—
408Dic3—62no—
409Dic3—122no—
410C32C2×#48511yescharacteristic, complemented, Sylow
411C23—92no—
412C23—182no—
413C23—182no—
414C23—182no—
415C23#380211yescharacteristic
416Q8—62no—
417Q8—62no—
418Q8—122no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—92no—
424C2×C4—122no—
425C2×C4—122no—
426C2×C4—122no—
427C2×C4—122no—
428C2×C4—182no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—184no—
432C2×C4#379912yes—
433C2×C4#380211yescharacteristic
434C2×C4#380412yes—
435C2×C4C22×D3211yescharacteristic
436C8—22no—
437C8—182no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—24no—
442C2×C3#481414yescomplemented
443C2×C3#488814yescomplemented
444C2×C3C2×#88311yescharacteristic
445C2×C3C2×#89411yescharacteristic
446C2×C3C2×#91211yescharacteristic
447C2×C3C2×#91511yescharacteristic
448C2×C3C2×#91811yescharacteristic
449C2×C3C2×#91911yescharacteristic
450D3—124no—
451D3—122no—
452D3—122no—
453C22—182no—
454C22—182no—
455C22—182no—
456C22—364no—
457C22#6381012yes—
458C22#6381112yes—
459C22#6385412yes—
460C22C2×#380211yescharacteristic
461C4—122no—
462C4—122no—
463C4—122no—
464C4—122no—
465C4—182no—
466C4#6385412yes—
467C4C2×#379911yescharacteristic
468C4C2×#380411yescharacteristic
469C3—21no—
470C3C2×#481411yescharacteristic, complemented
471C3C2×#488811yescharacteristic, complemented
472C2—362no—
473C2#1059071514yesdirect product factor
474C2C2×#6381011yescharacteristic
475C2C2×#6381111yescharacteristic
476C2C2×#6385411yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×C8D32
hypocenterC32C2×#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×C3×#818C2semidirect
5. C2×C3×#816C2semidirect
6. C2×#63574C2semidirect
7. C2×#63565C2semidirect
8. #10590715C2direct (N × H)
27. C3×#818C22semidirect
28. C3×#816C22semidirect
29. #63574C22semidirect
30. #63565C22semidirect
41. C2×#818D3semidirect
42. C2×#816D3semidirect
117. #818C2×D3semidirect
118. #816C2×D3semidirect
332. C2×C32#485semidirect
410. C32C2×#485semidirect
442. C2×C3#4814semidirect
443. C2×C3#4888semidirect
470. C3C2×#4814semidirect
471. C3C2×#4888semidirect
473. C2#10590715direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638712
C2×#638492
C2×#636472
C2×C3×#8182
C2×C3×#8162
C2×#635742
C2×#635652
#105907152
C2×#48883
C2×#48143