Finite Group Databasebeta

← C2×#10590450 #11869514

Subgroups — C2×#10590450 #11869514

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×#64106C211yesmaximal, characteristic
2C2×#63849C211yesmaximal, characteristic
3C2×C3×#808C211yesmaximal, characteristic, complemented
4C2×C3×#807C211yesmaximal, characteristic, complemented
5C2×#63567C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63557C211yesmaximal, characteristic
8#10590450C218yesmaximal, direct product factor
9C2×#4888—31nomaximal
10C2×#4868—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)—21no—
16#64106—22no—
17#64106C2214yes—
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×#808C2214yescomplemented
27C3×#807C2214yescomplemented
28#63567C2214yescomplemented
29#63567C2214yescomplemented
30#63557C2214yes—
31C2×#897—31no—
32C2×#897—31no—
33C2×#897—61no—
34C2×#892—31no—
35C2×#892—31no—
36C2×C3×#107—31no—
37C2×C3×#106—31no—
38C2×(C2×D3)⋊C8—31no—
39C2×(C2×D3)⋊C8—31no—
40C2×#816—31no—
41C2×#816—31no—
42C2×#810—31no—
43C2×#810—31no—
44C2×#808D311yescharacteristic, complemented
45C2×#807D311yescharacteristic, complemented
46#4888—38no—
47#4868—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—
57C2×#634—22no—
58C2×#634—22no—
59C2×#634—21no—
60C2×#634C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65#3752—24no—
66C4⋊(C3⋊Dic3)—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×C4×D3—31no—
79C22×C4×D3—31no—
80C22×C4×D3—61no—
81C22×Dic6—31no—
82C22×Dic6—31no—
83C22×Dic6—61no—
84C22×C3×C8—31no—
85C22×C3×C8—31no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C4⋊C4C2×D311yescharacteristic
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—61no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3—62no—
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4×Dic3—61no—
102C2×C4×Dic3—61no—
103C22×C3⋊C8C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105#897—34no—
106#897—34no—
107#897—64no—
108#897—62no—
109#897—62no—
110#897—64no—
111#892—34no—
112#892—34no—
113#892—62no—
114#892—62no—
115C3×#107—34no—
116C3×#106—34no—
117(C2×D3)⋊C8—34no—
118(C2×D3)⋊C8—34no—
119#816—34no—
120#816—34no—
121#810—34no—
122#810—34no—
123#808C2×D314yescomplemented
124#807C2×D314yescomplemented
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—
143#634—22no—
144#634—22no—
145#634—42no—
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—31no—
156C2×#106—31no—
157C2×#103—91no—
158C2×#103—91no—
159C2×C22⋊C8—91no—
160C23×D3—31no—
161C23×D3—31no—
162C23×D3—61no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—61no—
176C22×Dic3—62no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C2×C4×D3—32no—
180C2×C4×D3—32no—
181C2×C4×D3—32no—
182C2×C4×D3—32no—
183C2×C4×D3—62no—
184C2×C4×D3—62no—
185C2×C4×D3—62no—
186C2×C4×D3—62no—
187C2×C4×D3—62no—
188C2×C4×D3—62no—
189C2×C4×D3—122no—
190C2×C4×D3—122no—
191C2×Dic6—32no—
192C2×Dic6—32no—
193C2×Dic6—62no—
194C2×Dic6—62no—
195C2×Dic6—62no—
196C2×Dic6—62no—
197C2×Dic6—62no—
198C2×Dic6—62no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—122no—
202C2×Dic6—122no—
203C2×C3×C8—32no—
204C2×C3×C8—32no—
205C2×C3×C8—62no—
206C2×C3×C8—62no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—22no—
211C3×C4⋊C4—32no—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4C22×D312yes—
216C3×C4⋊C4C22×D312yes—
217(C2×D3)⋊C4—64no—
218(C2×D3)⋊C4—64no—
219(C2×D3)⋊C4—64no—
220(C2×D3)⋊C4—64no—
221(C2×D3)⋊C4—68no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224C4⋊Dic3—64no—
225C4⋊Dic3—64no—
226C4⋊Dic3—68no—
227C4⋊Dic3C22×D312yes—
228C4⋊Dic3C22×D312yes—
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×Q8—91no—
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—181no—
262C2×C4⋊C4D3211yescharacteristic
263C2×C22⋊C4—181no—
264C2×C22⋊C4—181no—
265C2×C42—181no—
266#107—34no—
267#106—34no—
268#103—94no—
269#103—94no—
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—
286C2×C3×C4—24no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—44no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—122no—
299C2×C3×C4—122no—
300C2×C3×C4#23512yes—
301C2×C3×C4#23512yes—
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4#23912yes—
305C2×C3×C4#23912yes—
306C2×C3×C4C23×D311yescharacteristic
307C2×C3×C4C23×D311yescharacteristic
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—32no—
311C2×Dic3—32no—
312C2×Dic3—42no—
313C2×Dic3—42no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—64no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—122no—
321C2×Dic3—124no—
322C2×Dic3—122no—
323C2×Dic3—122no—
324C4×D3—64no—
325C4×D3—64no—
326C4×D3—62no—
327C4×D3—62no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—122no—
331C4×D3—122no—
332C4×D3—124no—
333Dic6—62no—
334Dic6—62no—
335Dic6—62no—
336Dic6—62no—
337Dic6—122no—
338Dic6—122no—
339Dic6—124no—
340Dic6—122no—
341Dic6—122no—
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—92no—
353C2×Q8—181no—
354C2×Q8—182no—
355C2×Q8—182no—
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—21no—
371C4⋊C4—32no—
372C4⋊C4—32no—
373C4⋊C4—61no—
374C4⋊C4—61no—
375C4⋊C4—184no—
376C4⋊C4C2×D3212yes—
377C22⋊C4—184no—
378C22⋊C4—184no—
379C42—184no—
380C22×C3—21no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3#89412yes—
385C22×C3#89412yes—
386C22×C3#91212yes—
387C22×C3#91512yes—
388C22×C3#91612yes—
389C22×C3#91812yes—
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#89412yes—
413C3×C4#89412yes—
414C3×C4C2×#23511yescharacteristic
415C3×C4C2×#23511yescharacteristic
416C3×C4C2×#23911yescharacteristic
417C3×C4C2×#23911yescharacteristic
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—182no—
433Q8—182no—
434Q8—362no—
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#379912yes—
449C2×C4#379912yes—
450C2×C4#381111yescharacteristic
451C2×C4C22×D3211yescharacteristic
452C8—62no—
453C8—62no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—24no—
458C2×C3#486814yescomplemented
459C2×C3#488814yescomplemented
460C2×C3C2×#89411yescharacteristic
461C2×C3C2×#89411yescharacteristic
462C2×C3C2×#91211yescharacteristic
463C2×C3C2×#91511yescharacteristic
464C2×C3C2×#91611yescharacteristic
465C2×C3C2×#91811yescharacteristic
466D3—124no—
467D3—122no—
468D3—122no—
469C22—182no—
470C22—182no—
471C22—182no—
472C22—364no—
473C22#6389712yes—
474C22#6393612yes—
475C22#6395112yes—
476C22C2×#381111yescharacteristic
477C4—42no—
478C4—122no—
479C4—122no—
480C4—182no—
481C4—362no—
482C4#6389712yes—
483C4C2×#379911yescharacteristic
484C4C2×#379911yescharacteristic
485C3—21no—
486C3C2×#486811yescharacteristic, complemented
487C3C2×#488811yescharacteristic, complemented
488C2—362no—
489C2#1059045014yesdirect product factor
490C2C2×#6389711yescharacteristic
491C2C2×#6393611yescharacteristic
492C2C2×#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×#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×#808C2semidirect
4. C2×C3×#807C2semidirect
5. C2×#63567C2semidirect
6. C2×#63567C2semidirect
8. #10590450C2direct (N × H)
26. C3×#808C22semidirect
27. C3×#807C22semidirect
28. #63567C22semidirect
29. #63567C22semidirect
44. C2×#808D3semidirect
45. C2×#807D3semidirect
123. #808C2×D3semidirect
124. #807C2×D3semidirect
346. C2×C32#485semidirect
426. C32C2×#485semidirect
458. C2×C3#4868semidirect
459. C2×C3#4888semidirect
486. C3C2×#4868semidirect
487. C3C2×#4888semidirect
489. C2#10590450direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641062
C2×#638492
C2×C3×#8082
C2×C3×#8072
C2×#635672
C2×#635572
#105904502
C2×#48883
C2×#48683