Finite Group Databasebeta

← C2×#10590897 #11874402

Subgroups — C2×#10590897 #11874402

Order 1152.

1257 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3746C211yesmaximal, characteristic, complemented
2C22×C3×#204C211yesmaximal, characteristic
3C2×#63866C211yesmaximal, characteristic, complemented
4C2×#63860C211yesmaximal, characteristic
5C22×#3719C211yesmaximal, characteristic, complemented
6C22×#3716C211yesmaximal, characteristic
7C2×C3×#815C211yesmaximal, characteristic, complemented
8#10590897C218yesmaximal, direct product factor
9C2×#5167—31nomaximal
10C2×#4715—31nomaximal
11C22×#634C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×#3746—24no—
17C2×#3746C2214yescomplemented
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×C3×#204—24no—
21C2×C3×#204C2214yes—
22C2×Dic3⋊Dic3—22no—
23C2×(C2×D3)⋊Dic3—22no—
24#63866—22no—
25#63866C2214yescomplemented
26#63860—22no—
27#63860C2214yes—
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C2×#3716—24no—
31C2×#3716C2214yes—
32C3×#815C2214yescomplemented
33C22×C3×SD16—31no—
34C2×#944—31no—
35C22×#216—31no—
36C2×#936—31no—
37C22×#214—31no—
38C22×Dic12—31no—
39C22×Dic12—31no—
40C22×Dic12—31no—
41C22×Dic12—61no—
42C22×#204—31no—
43C22×#204D311yescharacteristic
44C2×#875—31no—
45C2×#869—31no—
46C2×C3×#97—31no—
47#5167—38no—
48C2×#815D311yescharacteristic, complemented
49#4715—38no—
50C23×C3×D3—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3—21no—
54C2×#634—22no—
55C2×#634—22no—
56C2×#634—22no—
57C2×#634—22no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634C2312yes—
61C2×#634C2312yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D412yes—
64C2×C3×D12—22no—
65C2×C3×D12—22no—
66C2×C3×D12—21no—
67C2×C3×D12C2312yes—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72C2×C32×C8D414yes—
73C2×C32×C8C2312yes—
74#3746—28no—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8D414yes—
78C2×C3×C3⋊C8C2312yes—
79C3×#204—28no—
80Dic3⋊Dic3—28no—
81(C2×D3)⋊Dic3—28no—
82#3719—28no—
83#3716—28no—
84C2×#497—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12C2×D311yescharacteristic
88C22×Dic6—31no—
89C22×Dic6—31no—
90C22×Dic6—31no—
91C22×Dic6—31no—
92C22×Dic6—61no—
93C22×Dic6—61no—
94C22×Dic6C2×D311yescharacteristic
95C2×C3×SD16—34no—
96C2×C3×SD16—64no—
97C22×C3×C8—21no—
98C22×C3×C8—31no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C2×C3×C42—31no—
102C2×#217—62no—
103#944—34no—
104#944—62no—
105C2×#216—34no—
106C2×#216—64no—
107#936—34no—
108#936—62no—
109C2×#214—34no—
110C2×#214—64no—
111C2×(C2×D3)⋊C4—62no—
112C2×C4⋊Dic3—62no—
113C2×Dic3⋊C4—62no—
114C2×C4×Dic3C2×D311yescharacteristic
115C22×C3⋊C8C2×D311yescharacteristic
116C2×Dic12—34no—
117C2×Dic12—34no—
118C2×Dic12—34no—
119C2×Dic12—64no—
120C2×Dic12—68no—
121C2×Dic12—64no—
122C2×Dic12—64no—
123C2×Dic12—64no—
124C2×#204—24no—
125C2×#204—34no—
126C2×#204—64no—
127C2×#204C2×D314yes—
128#875—34no—
129#875—62no—
130#869—34no—
131#869—62no—
132C3×#97—34no—
133#815C2×D314yescomplemented
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—42no—
137C22×C3×D3—44no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D412yes—
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—42no—
145C2×C3⋊Dic3—42no—
146#634—22no—
147#634—22no—
148#634—22no—
149#634—22no—
150#634—42no—
151#634—42no—
152C2×C3×Dic3—24no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3C2×D414yes—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—42no—
159C3×Dic6—22no—
160C3×Dic6—22no—
161C3×Dic6—42no—
162C32×C8C2×D414yes—
163C3×C3⋊C8C2×D414yes—
164C22×Q16—91no—
165C22×Q16—91no—
166C22×SD16—31no—
167C22×SD16—91no—
168C2×C4⋊Q8—91no—
169C2×#124—91no—
170#497—98no—
171C2×#97—31no—
172C24×C3—61no—
173C23×D3—21no—
174C2×C3×Q8—32no—
175C2×C3×Q8—61no—
176C2×C3×Q8—62no—
177C2×C3×Q8—62no—
178C2×C3×D4—32no—
179C2×C3×D4—62no—
180C2×C3×D4—62no—
181C2×C3×D4—61no—
182C22×C3×C4—21no—
183C22×C3×C4—32no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3—121no—
194C22×Dic3D1212yes—
195C2×D12—22no—
196C2×D12—22no—
197C2×D12—21no—
198C2×D12C22×D312yes—
199C2×Dic6—22no—
200C2×Dic6—22no—
201C2×Dic6—21no—
202C2×Dic6—32no—
203C2×Dic6—32no—
204C2×Dic6—32no—
205C2×Dic6—32no—
206C2×Dic6—62no—
207C2×Dic6—62no—
208C2×Dic6—64no—
209C2×Dic6—64no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×Dic6—62no—
213C2×Dic6—62no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—61no—
222C2×Dic6—121no—
223C2×Dic6—121no—
224C2×Dic6—122no—
225C2×Dic6—122no—
226C2×Dic6C22×D312yes—
227C3×SD16—68no—
228C2×C3×C8—24no—
229C2×C3×C8—22no—
230C2×C3×C8—34no—
231C2×C3×C8—32no—
232C2×C3×C8D1214yes—
233C2×C3×C8#6714yes—
234C2×C3×C8C22×D312yes—
235C2×C3×C8C22×D312yes—
236C3×C42—32no—
237C3×C42—32no—
238#217—68no—
239#216—68no—
240#214—68no—
241(C2×D3)⋊C4—68no—
242C4⋊Dic3—68no—
243Dic3⋊C4—68no—
244C4×Dic3D1212yes—
245C4×Dic3C22×D312yes—
246C2×C3⋊C8D1214yes—
247C2×C3⋊C8C22×D312yes—
248Dic12—616no—
249Dic12—68no—
250Dic12—68no—
251Dic12—68no—
252#204—28no—
253#204—68no—
254C22×C32#12712yes—
255C22×C32#13714yes—
256C22×C32C22×D411yescharacteristic
257C2×C3×D3—42no—
258C2×C3×D3—44no—
259C2×C3×D3—84no—
260C32×C4#12712yes—
261C32×C4C22×D411yescharacteristic
262C32×C4C22×D411yescharacteristic
263C3⋊Dic3—42no—
264C3⋊Dic3—42no—
265C3×Dic3—24no—
266C3×Dic3—42no—
267C22×Q8—31no—
268C22×Q8—91no—
269C22×Q8—91no—
270C22×D4—31no—
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×C8D3211yescharacteristic
281C4⋊Q8—94no—
282C4⋊Q8—182no—
283#124—94no—
284#124—182no—
285C2×C4⋊C4—182no—
286C2×C22⋊C4—182no—
287C2×C42—31no—
288#97—34no—
289C23×C3—21no—
290C23×C3—62no—
291C23×C3—122no—
292C23×C3—124no—
293C23×C3C2×D1211yescharacteristic
294C23×C3D3×D411yescharacteristic
295C22×D3—22no—
296C22×D3—44no—
297C22×D3—42no—
298C3×Q8—62no—
299C3×Q8—62no—
300C3×Q8—122no—
301C3×D4—62no—
302C3×D4—62no—
303C3×D4—122no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—34no—
309C2×C3×C4—64no—
310C2×C3×C4—62no—
311C2×C3×C4—122no—
312C2×C3×C4C2×D1211yescharacteristic
313C2×C3×C4C2×D1212yes—
314C2×C3×C4C2×D1212yes—
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D412yes—
317C2×C3×C4C2×#6712yes—
318C2×C3×C4C23×D311yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320C2×Dic3—24no—
321C2×Dic3—22no—
322C2×Dic3—42no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329C2×Dic3—124no—
330C2×Dic3—124no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333C2×Dic3—122no—
334C2×Dic3—122no—
335C2×Dic3C2×D1214yes—
336D12—22no—
337D12—22no—
338D12—42no—
339Dic6—22no—
340Dic6—22no—
341Dic6—42no—
342Dic6—64no—
343Dic6—64no—
344Dic6—62no—
345Dic6—62no—
346Dic6—62no—
347Dic6—62no—
348Dic6—62no—
349Dic6—62no—
350Dic6—62no—
351Dic6—62no—
352Dic6—122no—
353Dic6—122no—
354Dic6—124no—
355Dic6—124no—
356Dic6—122no—
357Dic6—122no—
358Dic6—122no—
359Dic6—122no—
360C3×C8—24no—
361C3×C8—34no—
362C3×C8C2×D1214yes—
363C3×C8C2×#6714yes—
364C3⋊C8C2×D1214yes—
365C2×C32#49714yescomplemented
366C2×C32C2×#12711yescharacteristic
367C2×C32C2×#13712yes—
368C3×D3—82no—
369C24—61no—
370C2×Q8—32no—
371C2×Q8—61no—
372C2×Q8—62no—
373C2×Q8—62no—
374C2×Q8—92no—
375C2×Q8—92no—
376C2×Q8—181no—
377C2×Q8—181no—
378C2×Q8—182no—
379C2×Q8—182no—
380C2×Q8—182no—
381C2×Q8—182no—
382C2×D4—32no—
383C2×D4—62no—
384C2×D4—61no—
385C2×D4—62no—
386C22×C4—32no—
387C22×C4—61no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4C2×D3211yescharacteristic
391Q16—188no—
392Q16—188no—
393SD16—68no—
394SD16—188no—
395C2×C8—32no—
396C2×C8—34no—
397C2×C8#62614yes—
398C2×C8C2×D3212yes—
399C4⋊C4—188no—
400C22⋊C4—188no—
401C42—32no—
402C42—32no—
403C22×C3—21no—
404C22×C3—24no—
405C22×C3—22no—
406C22×C3—122no—
407C22×C3—124no—
408C22×C3—244no—
409C22×C3#87412yes—
410C22×C3#90914yes—
411C22×C3#91514yes—
412C22×C3#94012yes—
413C22×C3C22×D1211yescharacteristic
414C22×C3C2×D3×D411yescharacteristic
415C2×D3—44no—
416C2×D3—42no—
417C2×D3—84no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—22no—
421C3×C4—64no—
422C3×C4—122no—
423C3×C4#87412yes—
424C3×C4#94012yes—
425C3×C4C22×D1211yescharacteristic
426C3×C4C22×D1211yescharacteristic
427C3×C4C2×D3×D411yescharacteristic
428C3×C4C22×#6711yescharacteristic
429Dic3—24no—
430Dic3—42no—
431Dic3—124no—
432Dic3—124no—
433Dic3—122no—
434Dic3—122no—
435Dic3—122no—
436Dic3—122no—
437C32C2×#49711yescharacteristic, complemented, Sylow
438C23—62no—
439C23—124no—
440C23—122no—
441C23D3×D1211yescharacteristic
442Q8—62no—
443Q8—62no—
444Q8—122no—
445Q8—182no—
446Q8—182no—
447Q8—182no—
448Q8—182no—
449Q8—362no—
450Q8—362no—
451D4—62no—
452D4—62no—
453D4—122no—
454C2×C4—34no—
455C2×C4—64no—
456C2×C4—62no—
457C2×C4—122no—
458C2×C4—182no—
459C2×C4—182no—
460C2×C4—362no—
461C2×C4—362no—
462C2×C4D3×D1212yes—
463C2×C4D3×D1211yescharacteristic
464C2×C4C2×#62612yes—
465C2×C4C22×D3211yescharacteristic
466C8—34no—
467C8C2×#62614yes—
468C2×C3—22no—
469C2×C3—24no—
470C2×C3—21no—
471C2×C3—242no—
472C2×C3#471514yescomplemented
473C2×C3#516714yescomplemented
474C2×C3C2×#87411yescharacteristic
475C2×C3C2×#90912yes—
476C2×C3C2×#91512yes—
477C2×C3C2×#94011yescharacteristic
478D3—82no—
479C22—124no—
480C22—122no—
481C22—244no—
482C22#6380014yes—
483C22#6391112yes—
484C22C2×D3×D1211yescharacteristic
485C4—64no—
486C4—122no—
487C4—362no—
488C4—362no—
489C4#6391112yes—
490C4C2×D3×D1211yescharacteristic
491C4C22×#62611yescharacteristic
492C3—21no—
493C3C2×#471511yescharacteristic, complemented
494C3C2×#516711yescharacteristic, complemented
495C2—242no—
496C2#1059089714yesdirect product factor
497C2C2×#6380012yes—
498C2C2×#6391111yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32C2×#497
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
1. C22×#3746C2semidirect
3. C2×#63866C2semidirect
5. C22×#3719C2semidirect
7. C2×C3×#815C2semidirect
8. #10590897C2direct (N × H)
17. C2×#3746C22semidirect
25. #63866C22semidirect
29. C2×#3719C22semidirect
32. C3×#815C22semidirect
48. C2×#815D3semidirect
133. #815C2×D3semidirect
365. C2×C32#497semidirect
437. C32C2×#497semidirect
472. C2×C3#4715semidirect
473. C2×C3#5167semidirect
493. C3C2×#4715semidirect
494. C3C2×#5167semidirect
496. C2#10590897direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37462
C22×C3×#2042
C2×#638662
C2×#638602
C22×#37192
C22×#37162
C2×C3×#8152
#105908972
C2×#51673
C2×#47153