Finite Group Databasebeta

← C2×#10591488 #11873540

Subgroups — C2×#10591488 #11873540

Order 1152.

973 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#936C211yesmaximal, characteristic
2C2×#63918C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic
4C2×C3×#832C211yesmaximal, characteristic
5#10591488C218yesmaximal, direct product factor
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5055—31nomaximal
10C2×#4765—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×#627—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×#217—21no—
17C2×C3×#217—21no—
18C3×#936—22no—
19C3×#936C2214yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×Dic3⋊Dic3—21no—
24#63918—22no—
25#63918C2214yescomplemented
26#63659C2214yes—
27C3×#832C2214yes—
28#63566C2214yescomplemented
29#63565C2214yescomplemented
30#63554C2214yescomplemented
31C2×C3×#124—31no—
32C2×#936D311yescharacteristic
33C2×#888—31no—
34C2×#869—31no—
35C2×C3×#102—31no—
36C2×#835—31no—
37C2×#835—31no—
38C2×#832—31no—
39C2×#832—31no—
40C2×#832—61no—
41C2×#832D311yescharacteristic
42C2×#816—31no—
43C2×#815—31no—
44#5055—38no—
45C2×#810—31no—
46C2×#803—31no—
47#4765—38no—
48C24×C32—21no—
49C2×C32×D4—21no—
50C2×C32×D4—22no—
51C2×C32×D4—22no—
52C2×C32×D4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C2×#627—24no—
64C2×#627—44no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×#217—24no—
70C3×#217—24no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×C4×Dic3D412yes—
74C3×C4×Dic3C2312yes—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8C2312yes—
77Dic3⋊Dic3—24no—
78C2×#489—91noSylow
79C22×C3×Q8—31no—
80C22×C3×D4—21no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C2×D311yescharacteristic
83C22×Dic6—61no—
84C22×Dic6—61no—
85C22×Dic6C2×D311yescharacteristic
86C22×C3×C8—31no—
87C3×#124—34no—
88C3×#124—62no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C22⋊C4—61no—
91C2×C3×C22⋊C4—61no—
92C2×C3×C42—31no—
93C2×#217—21no—
94C2×#217—21no—
95#936—22no—
96#936C2×D314yes—
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×C4×Dic3C2×D311yescharacteristic
104C22×C3⋊C8—31no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108#888—34no—
109#888—62no—
110#869—34no—
111#869—62no—
112C3×#102—34no—
113#835—34no—
114#835—34no—
115#832—34no—
116#832—34no—
117#832—64no—
118#832C2×D314yes—
119#816—34no—
120#815—34no—
121#810—34no—
122#803—34no—
123C23×C32—22no—
124C23×C32—42no—
125C23×C32—42no—
126C23×C32—42no—
127C23×C32C2×D411yescharacteristic
128C32×D4—22no—
129C32×D4—22no—
130C32×D4—42no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4112yes—
133C2×C32×C4#4112yes—
134C2×C32×C4C2411yescharacteristic
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—42no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3C2×D412yes—
144C2×C3×Dic3C2×D412yes—
145C3×Dic6—22no—
146C3×Dic6—22no—
147C3×Dic6—42no—
148#627—48no—
149C3⋊(C3⋊C8)—22no—
150C3×C3⋊C8—22no—
151C2×C4⋊Q8—91no—
152C2×#124—31no—
153#489—98no—
154C2×#103—91no—
155C2×#103—91no—
156C2×#102—31no—
157C2×#102—91no—
158C2×#97—91no—
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—41no—
162C2×C3×Q8—32no—
163C2×C3×Q8—61no—
164C2×C3×Q8—62no—
165C2×C3×Q8—62no—
166C2×C3×D4—24no—
167C2×C3×D4—22no—
168C2×C3×D4—21no—
169C2×C3×D4—22no—
170C2×C3×D4—22no—
171C2×C3×D4—22no—
172C2×C3×D4—21no—
173C2×C3×D4—22no—
174C2×C3×D4—42no—
175C2×C3×D4—41no—
176C2×C3×D4C22×D312yes—
177C2×C3×D4C22×D312yes—
178C22×C3×C4—21no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—121no—
190C22×Dic3#6711yescharacteristic
191C22×Dic3#6711yescharacteristic
192C2×Dic6—22no—
193C2×Dic6—22no—
194C2×Dic6—21no—
195C2×Dic6—64no—
196C2×Dic6—64no—
197C2×Dic6—124no—
198C2×Dic6—124no—
199C2×Dic6C22×D312yes—
200C2×C3×C8—32no—
201C2×C3×C8—62no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—61no—
204C3×C22⋊C4—64no—
205C3×C22⋊C4—64no—
206C3×C42—32no—
207C3×C42—32no—
208#217—24no—
209#217—24no—
210C4⋊Dic3—21no—
211C4⋊Dic3—32no—
212C4⋊Dic3—32no—
213C4⋊Dic3—62no—
214C4⋊Dic3—64no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—121no—
218C4⋊Dic3C22×D312yes—
219Dic3⋊C4—64no—
220C4×Dic3#6712yes—
221C4×Dic3C22×D312yes—
222C2×C3⋊C8—22no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—32no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—62no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—122no—
229C2×C3⋊C8C22×D312yes—
230C22×C32—42no—
231C22×C32—42no—
232C22×C32—42no—
233C22×C32—84no—
234C22×C32#12412yes—
235C22×C32AGL(1,ℤ/8)12yes—
236C22×C32#13712yes—
237C22×C32C22×D411yescharacteristic
238C32×C4#12412yes—
239C32×C4C2×#4111yescharacteristic
240C32×C4C2×#4111yescharacteristic
241C3⋊Dic3—42no—
242C3×Dic3—22no—
243C3×Dic3—22no—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C22×Q8—31no—
247C22×Q8—181no—
248C22×D4D3211yescharacteristic
249C22×C8—31no—
250C22×C8—91no—
251C4⋊Q8—94no—
252C4⋊Q8—182no—
253#124—34no—
254#124—62no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—181no—
258C2×C22⋊C4—61no—
259C2×C22⋊C4—61no—
260C2×C42—31no—
261#103—94no—
262#103—94no—
263#102—34no—
264#102—94no—
265#97—94no—
266C23×C3—22no—
267C23×C3—22no—
268C23×C3—21no—
269C23×C3—42no—
270C23×C3—44no—
271C23×C3—42no—
272C23×C3—42no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—42no—
276C23×C3—42no—
277C23×C3—82no—
278C23×C3—82no—
279C23×C3D3×D411yescharacteristic
280C23×C3C2×#6711yescharacteristic
281C3×Q8—62no—
282C3×Q8—62no—
283C3×Q8—122no—
284C3×D4—24no—
285C3×D4—22no—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—22no—
289C3×D4—42no—
290C3×D4—44no—
291C3×D4—42no—
292C3×D4—42no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—32no—
298C2×C3×C4—32no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—122no—
304C2×C3×C4—122no—
305C2×C3×C4#23512yes—
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4#23712yes—
308C2×C3×C4#23712yes—
309C2×C3×C4#23712yes—
310C2×C3×C4C2×#6711yescharacteristic
311C2×C3×C4C23×D311yescharacteristic
312C2×C3×C4C23×D311yescharacteristic
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—42no—
318C2×Dic3—42no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—122no—
322C2×Dic3—122no—
323C2×Dic3—122no—
324C2×Dic3—242no—
325C2×Dic3C2×#6712yes—
326C2×Dic3C2×#6712yes—
327Dic6—22no—
328Dic6—22no—
329Dic6—42no—
330Dic6—128no—
331Dic6—128no—
332C3×C8—62no—
333C3⋊C8—22no—
334C3⋊C8—62no—
335C3⋊C8—62no—
336C3⋊C8—122no—
337C2×C32—82no—
338C2×C32#48914yescomplemented
339C2×C32C2×#12411yescharacteristic
340C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
341C2×C32C2×#13711yescharacteristic
342C24—21no—
343C2×Q8—32no—
344C2×Q8—61no—
345C2×Q8—62no—
346C2×Q8—62no—
347C2×Q8—184no—
348C2×Q8—364no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4C2×D3212yes—
353C22×C4—31no—
354C22×C4—31no—
355C22×C4—61no—
356C22×C4—61no—
357C22×C4—181no—
358C22×C4C2×D3211yescharacteristic
359C2×C8—32no—
360C2×C8—62no—
361C2×C8—92no—
362C2×C8—182no—
363C4⋊C4—32no—
364C4⋊C4—61no—
365C4⋊C4—92no—
366C4⋊C4—184no—
367C4⋊C4—181no—
368C22⋊C4—64no—
369C22⋊C4—64no—
370C42—32no—
371C42—32no—
372C22×C3—21no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—44no—
377C22×C3—42no—
378C22×C3—42no—
379C22×C3—42no—
380C22×C3—42no—
381C22×C3—42no—
382C22×C3—42no—
383C22×C3—82no—
384C22×C3—82no—
385C22×C3—88no—
386C22×C3—84no—
387C22×C3—84no—
388C22×C3#88512yes—
389C22×C3#91112yes—
390C22×C3#91512yes—
391C22×C3#93612yes—
392C22×C3#94912yes—
393C22×C3#95112yes—
394C22×C3C2×D3×D411yescharacteristic
395C22×C3C22×#6711yescharacteristic
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—22no—
399C3×C4—62no—
400C3×C4—62no—
401C3×C4—122no—
402C3×C4—122no—
403C3×C4#88512yes—
404C3×C4#93612yes—
405C3×C4C2×#23511yescharacteristic
406C3×C4C2×#23711yescharacteristic
407C3×C4C2×#23711yescharacteristic
408C3×C4C2×#23711yescharacteristic
409Dic3—22no—
410Dic3—22no—
411Dic3—42no—
412Dic3—42no—
413Dic3—122no—
414Dic3—122no—
415Dic3—242no—
416C32C2×#48911yescharacteristic, complemented, Sylow
417C23—22no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23D3×#6711yescharacteristic
422Q8—62no—
423Q8—62no—
424Q8—122no—
425Q8—368no—
426D4—22no—
427D4—22no—
428D4—42no—
429C2×C4—32no—
430C2×C4—32no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—122no—
436C2×C4—122no—
437C2×C4—182no—
438C2×C4—362no—
439C2×C4#380412yes—
440C2×C4#380512yes—
441C2×C4D3×#6711yescharacteristic
442C2×C4C22×D3211yescharacteristic
443C8—62no—
444C8—182no—
445C2×C3—24no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—84no—
450C2×C3—82no—
451C2×C3—82no—
452C2×C3#476514yescomplemented
453C2×C3#505514yescomplemented
454C2×C3C2×#88511yescharacteristic
455C2×C3C2×#91111yescharacteristic
456C2×C3C2×#91511yescharacteristic
457C2×C3C2×#93611yescharacteristic
458C2×C3C2×#94911yescharacteristic
459C2×C3C2×#95111yescharacteristic
460C22—42no—
461C22—42no—
462C22—42no—
463C22—84no—
464C22#6392512yes—
465C22#6392912yes—
466C22#6395912yes—
467C22C2×D3×#6711yescharacteristic
468C4—62no—
469C4—62no—
470C4—122no—
471C4—122no—
472C4—362no—
473C4#6395912yes—
474C4C2×#380411yescharacteristic
475C4C2×#380511yescharacteristic
476C3—21no—
477C3C2×#476511yescharacteristic, complemented
478C3C2×#505511yescharacteristic, complemented
479C2—82no—
480C2#1059148814yesdirect product factor
481C2C2×#6392511yescharacteristic
482C2C2×#6392911yescharacteristic
483C2C2×#6395911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63918C2semidirect
5. #10591488C2direct (N × H)
6. C2×#63566C2semidirect
7. C2×#63565C2semidirect
8. C2×#63554C2semidirect
25. #63918C22semidirect
28. #63566C22semidirect
29. #63565C22semidirect
30. #63554C22semidirect
338. C2×C32#489semidirect
416. C32C2×#489semidirect
452. C2×C3#4765semidirect
453. C2×C3#5055semidirect
477. C3C2×#4765semidirect
478. C3C2×#5055semidirect
480. C2#10591488direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9362
C2×#639182
C2×#636592
C2×C3×#8322
#105914882
C2×#635662
C2×#635652
C2×#635542
C2×#50553
C2×#47653