Finite Group Databasebeta

← C2×#10591491 #11874406

Subgroups — C2×#10591491 #11874406

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3754C211yesmaximal, characteristic
2C2×C3×#936C211yesmaximal, characteristic
3C22×C3×#214C211yesmaximal, characteristic
4C2×#63866C211yesmaximal, characteristic, complemented
5C22×#3719C211yesmaximal, characteristic, complemented
6C22×#3718C211yesmaximal, characteristic, complemented
7#10591491C218yesmaximal, direct product factor
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5167—31nomaximal
10C2×#5060—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×#3754—24no—
16C2×#3754C2214yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—22no—
19C3×#936—22no—
20C3×#936C2214yes—
21C2×C3×#214—24no—
22C2×C3×#214C2214yes—
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×Dic3⋊Dic3—22no—
26#63866—22no—
27#63866C2214yescomplemented
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C2×#3718—24no—
31C2×#3718C2214yescomplemented
32#63554C2214yescomplemented
33C22×C3×SD16—31no—
34C2×C3×#124—31no—
35C2×#944—31no—
36C22×#216—31no—
37C22×#216—31no—
38C22×#216—31no—
39C2×#936D311yescharacteristic
40C22×#214—31no—
41C22×#214—31no—
42C22×#214—61no—
43C22×#214D311yescharacteristic
44C22×Dic12—31no—
45C2×#869—31no—
46#5167—38no—
47C2×#815—31no—
48#5060—38no—
49C2×#803—31no—
50C24×C32—21no—
51C2×C32×D4—22no—
52C2×C32×D4—22no—
53C2×C32×D4—21no—
54C2×C32×D4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C2×#634—22no—
58C2×#634—22no—
59C2×#634—21no—
60C2×#634C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D412yes—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2312yes—
72#3754—28no—
73C2×C3⋊(C3⋊C8)D414yes—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#217—28no—
76C3×#214—28no—
77C3×C4×Dic3D412yes—
78C3×C4×Dic3C2312yes—
79C2×C3×C3⋊C8D414yes—
80C2×C3×C3⋊C8C2312yes—
81Dic3⋊Dic3—28no—
82#3719—28no—
83#3718—28no—
84C2×#497—91noSylow
85C22×C3×Q8—31no—
86C22×C3×Q8—31no—
87C22×C3×D4—21no—
88C22×C3×D4C2×D311yescharacteristic
89C22×C3×D4C2×D311yescharacteristic
90C22×Dic6—31no—
91C22×Dic6—31no—
92C22×Dic6—61no—
93C22×Dic6C2×D311yescharacteristic
94C22×Dic6C2×D311yescharacteristic
95C2×C3×SD16—34no—
96C2×C3×SD16—64no—
97C22×C3×C8—31no—
98C3×#124—34no—
99C3×#124—62no—
100C2×C3×C22⋊C4—62no—
101C2×C3×C42—31no—
102C2×#217—22no—
103#944—34no—
104#944—62no—
105C2×#216—34no—
106C2×#216—34no—
107C2×#216—34no—
108C2×#216—64no—
109C2×#216—64no—
110C2×#216—64no—
111#936—22no—
112#936C2×D314yes—
113C2×#214—24no—
114C2×#214—34no—
115C2×#214—34no—
116C2×#214—64no—
117C2×#214—64no—
118C2×#214—64no—
119C2×#214—68no—
120C2×#214C2×D314yes—
121C2×C4⋊Dic3—62no—
122C2×Dic3⋊C4—62no—
123C2×C4×Dic3C2×D311yescharacteristic
124C22×C3⋊C8—31no—
125C22×C3⋊C8—31no—
126C22×C3⋊C8—61no—
127C22×C3⋊C8C2×D311yescharacteristic
128C2×Dic12—34no—
129C2×Dic12—64no—
130#869—34no—
131#869—62no—
132#815—34no—
133#803—34no—
134C23×C32—22no—
135C23×C32—42no—
136C23×C32—44no—
137C23×C32C2×D411yescharacteristic
138C32×D4—22no—
139C32×D4—22no—
140C32×D4—42no—
141C2×C32×C4C2×D412yes—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2411yescharacteristic
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—42no—
147#634—22no—
148#634—22no—
149#634—42no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—42no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3C2×D414yes—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—22no—
160C3×Dic6—42no—
161C3×Dic6—42no—
162C3⋊(C3⋊C8)C2×D414yes—
163C3×C3⋊C8C2×D414yes—
164C22×Q16—91no—
165C22×Q16—91no—
166C22×SD16—31no—
167C22×SD16—91no—
168C2×C4⋊Q8—91no—
169C2×#124—31no—
170#497—98no—
171C2×#97—91no—
172C24×C3—21no—
173C24×C3—21no—
174C24×C3—41no—
175C2×C3×Q8—32no—
176C2×C3×Q8—32no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×Q8—62no—
180C2×C3×Q8—62no—
181C2×C3×Q8—62no—
182C2×C3×Q8—62no—
183C2×C3×D4—24no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—21no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—22no—
191C2×C3×D4—42no—
192C2×C3×D4—41no—
193C2×C3×D4C22×D312yes—
194C2×C3×D4C22×D312yes—
195C22×C3×C4—21no—
196C22×C3×C4—32no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205C22×Dic3—121no—
206C22×Dic3#6712yes—
207C2×Dic6—22no—
208C2×Dic6—22no—
209C2×Dic6—22no—
210C2×Dic6—22no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—32no—
214C2×Dic6—32no—
215C2×Dic6—62no—
216C2×Dic6—64no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—61no—
222C2×Dic6—61no—
223C2×Dic6—121no—
224C2×Dic6—122no—
225C2×Dic6C22×D312yes—
226C2×Dic6C22×D312yes—
227C3×SD16—68no—
228C2×C3×C8—34no—
229C2×C3×C8—32no—
230C3×C22⋊C4—68no—
231C3×C42—32no—
232C3×C42—32no—
233#217—28no—
234#216—68no—
235#216—68no—
236#216—68no—
237#214—28no—
238#214—68no—
239#214—68no—
240#214—616no—
241C4⋊Dic3—68no—
242Dic3⋊C4—68no—
243C4×Dic3#6712yes—
244C4×Dic3C22×D312yes—
245C2×C3⋊C8—34no—
246C2×C3⋊C8—34no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—64no—
250C2×C3⋊C8—62no—
251C2×C3⋊C8#6714yes—
252C2×C3⋊C8C22×D312yes—
253Dic12—68no—
254C22×C32—42no—
255C22×C32—44no—
256C22×C32—84no—
257C22×C32#12712yes—
258C22×C32#13714yes—
259C22×C32C22×D411yescharacteristic
260C32×C4#12712yes—
261C32×C4C22×D411yescharacteristic
262C32×C4C22×D411yescharacteristic
263C3⋊Dic3—42no—
264C3×Dic3—24no—
265C3×Dic3—42no—
266C3×Dic3—42no—
267C22×Q8—31no—
268C22×Q8—31no—
269C22×Q8—91no—
270C22×D4D3211yescharacteristic
271C2×Q16—94no—
272C2×Q16—94no—
273C2×Q16—184no—
274C2×Q16—184no—
275C2×SD16—34no—
276C2×SD16—64no—
277C2×SD16—94no—
278C2×SD16—184no—
279C22×C8—31no—
280C22×C8—91no—
281C4⋊Q8—94no—
282C4⋊Q8—182no—
283#124—34no—
284#124—62no—
285C2×C4⋊C4—182no—
286C2×C22⋊C4—62no—
287C2×C42—31no—
288#97—94no—
289C23×C3—22no—
290C23×C3—22no—
291C23×C3—21no—
292C23×C3—42no—
293C23×C3—44no—
294C23×C3—44no—
295C23×C3—42no—
296C23×C3—42no—
297C23×C3—44no—
298C23×C3—84no—
299C23×C3D3×D411yescharacteristic
300C23×C3C2×#6711yescharacteristic
301C3×Q8—62no—
302C3×Q8—62no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—122no—
306C3×Q8—122no—
307C3×D4—24no—
308C3×D4—22no—
309C3×D4—22no—
310C3×D4—22no—
311C3×D4—22no—
312C3×D4—42no—
313C3×D4—44no—
314C3×D4—42no—
315C3×D4—42no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—34no—
321C2×C3×C4—64no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—122no—
325C2×C3×C4—122no—
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D412yes—
328C2×C3×C4D3×D412yes—
329C2×C3×C4D3×D412yes—
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C2×#6712yes—
332C2×C3×C4C23×D311yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334C2×Dic3—24no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—42no—
338C2×Dic3—42no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—122no—
342C2×Dic3—124no—
343C2×Dic3—122no—
344C2×Dic3—122no—
345C2×Dic3C2×#6714yes—
346Dic6—22no—
347Dic6—22no—
348Dic6—22no—
349Dic6—22no—
350Dic6—42no—
351Dic6—42no—
352Dic6—64no—
353Dic6—62no—
354Dic6—62no—
355Dic6—62no—
356Dic6—62no—
357Dic6—122no—
358Dic6—124no—
359Dic6—122no—
360Dic6—122no—
361C3×C8—34no—
362C3⋊C8—34no—
363C3⋊C8—34no—
364C3⋊C8—64no—
365C3⋊C8C2×#6714yes—
366C2×C32—82no—
367C2×C32#49714yescomplemented
368C2×C32C2×#12711yescharacteristic
369C2×C32C2×#13712yes—
370C24—21no—
371C2×Q8—32no—
372C2×Q8—32no—
373C2×Q8—61no—
374C2×Q8—61no—
375C2×Q8—62no—
376C2×Q8—62no—
377C2×Q8—62no—
378C2×Q8—62no—
379C2×Q8—92no—
380C2×Q8—181no—
381C2×Q8—182no—
382C2×Q8—182no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4C2×D3212yes—
387C22×C4—32no—
388C22×C4—61no—
389C22×C4—61no—
390C22×C4—181no—
391C22×C4C2×D3211yescharacteristic
392Q16—188no—
393Q16—188no—
394SD16—68no—
395SD16—188no—
396C2×C8—32no—
397C2×C8—34no—
398C2×C8—92no—
399C2×C8—94no—
400C4⋊C4—188no—
401C22⋊C4—68no—
402C42—32no—
403C42—32no—
404C22×C3—21no—
405C22×C3—24no—
406C22×C3—22no—
407C22×C3—44no—
408C22×C3—44no—
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—44no—
412C22×C3—84no—
413C22×C3—88no—
414C22×C3—84no—
415C22×C3—84no—
416C22×C3#91514yes—
417C22×C3#94012yes—
418C22×C3#94012yes—
419C22×C3#95114yes—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C22×#6711yescharacteristic
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—64no—
426C3×C4—122no—
427C3×C4—122no—
428C3×C4#94012yes—
429C3×C4#94012yes—
430C3×C4C2×D3×D411yescharacteristic
431C3×C4C2×D3×D411yescharacteristic
432C3×C4C2×D3×D411yescharacteristic
433C3×C4C22×#6711yescharacteristic
434Dic3—24no—
435Dic3—42no—
436Dic3—42no—
437Dic3—124no—
438Dic3—122no—
439Dic3—122no—
440C32C2×#49711yescharacteristic, complemented, Sylow
441C23—22no—
442C23—44no—
443C23—42no—
444C23D3×#6711yescharacteristic
445Q8—62no—
446Q8—62no—
447Q8—62no—
448Q8—62no—
449Q8—122no—
450Q8—122no—
451Q8—182no—
452Q8—182no—
453Q8—362no—
454D4—22no—
455D4—22no—
456D4—42no—
457C2×C4—34no—
458C2×C4—64no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—122no—
462C2×C4—122no—
463C2×C4—182no—
464C2×C4—362no—
465C2×C4D3×#6712yes—
466C2×C4D3×#6711yescharacteristic
467C2×C4#381112yes—
468C2×C4C22×D3211yescharacteristic
469C8—34no—
470C8—94no—
471C2×C3—24no—
472C2×C3—22no—
473C2×C3—21no—
474C2×C3—84no—
475C2×C3—82no—
476C2×C3—82no—
477C2×C3#506014yescomplemented
478C2×C3#516714yescomplemented
479C2×C3C2×#91512yes—
480C2×C3C2×#94011yescharacteristic
481C2×C3C2×#94011yescharacteristic
482C2×C3C2×#95112yes—
483C22—44no—
484C22—42no—
485C22—84no—
486C22#6392914yes—
487C22#6397912yes—
488C22C2×D3×#6711yescharacteristic
489C4—64no—
490C4—122no—
491C4—122no—
492C4—362no—
493C4#6397912yes—
494C4C2×D3×#6711yescharacteristic
495C4C2×#381111yescharacteristic
496C3—21no—
497C3C2×#506011yescharacteristic, complemented
498C3C2×#516711yescharacteristic, complemented
499C2—82no—
500C2#1059149114yesdirect product factor
501C2C2×#6392912yes—
502C2C2×#6397911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#497
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
4. C2×#63866C2semidirect
5. C22×#3719C2semidirect
6. C22×#3718C2semidirect
7. #10591491C2direct (N × H)
8. C2×#63554C2semidirect
27. #63866C22semidirect
29. C2×#3719C22semidirect
31. C2×#3718C22semidirect
32. #63554C22semidirect
367. C2×C32#497semidirect
440. C32C2×#497semidirect
477. C2×C3#5060semidirect
478. C2×C3#5167semidirect
497. C3C2×#5060semidirect
498. C3C2×#5167semidirect
500. C2#10591491direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37542
C2×C3×#9362
C22×C3×#2142
C2×#638662
C22×#37192
C22×#37182
#105914912
C2×#635542
C2×#51673
C2×#50603