Finite Group Databasebeta

← C2×#10591049 #11899523

Subgroups — C2×#10591049 #11899523

Order 1152.

869 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 869 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64128C211yesmaximal, characteristic, complemented
2C2×#63810C211yesmaximal, characteristic, complemented
3C2×C3×#829C211yesmaximal, characteristic, complemented
4C2×C3×#828C211yesmaximal, characteristic, complemented
5#10591049C218yesmaximal, direct product factor
6C2×#63549C211yesmaximal, characteristic, complemented
7C2×#63546C211yesmaximal, characteristic, complemented
8C2×#63542C211yesmaximal, characteristic, complemented
9C2×#4919—31nomaximal
10C2×#4916—31nomaximal
11C2×#3832—21no—
12C2×#3796—21no—
13C2×C32×Q16C2211yescharacteristic
14C2×#3755—21no—
15#64128—22no—
16#64128C2214yescomplemented
17C2×#3745C2211yescharacteristic
18C2×C8×C3⋊D3C2211yescharacteristic
19C2×C3×Dic12C2211yescharacteristic
20C2×C3×D24C2211yescharacteristic
21C2×#3715—21no—
22#63810—22no—
23#63810C2214yescomplemented
24C3×#829C2214yescomplemented
25C3×#828C2214yescomplemented
26C2×C3×C3⋊C16C2211yescharacteristic
27C2×C3×C3⋊C16C2211yescharacteristic
28#63549C2214yescomplemented
29#63546C2214yescomplemented
30#63542C2214yescomplemented
31C2×#919—31no—
32C2×#919—31no—
33C2×#919—31no—
34C2×#919—61no—
35C2×#912—31no—
36C2×C3×Q32—31no—
37C2×C3×SD32—31no—
38C2×#829D311yescharacteristic, complemented
39C2×#828—31no—
40C2×#828D311yescharacteristic, complemented
41C2×#826—31no—
42#4919—38no—
43#4916—38no—
44C2×#800—31no—
45C2×D48—31no—
46C2×D3×C16—31no—
47C2×D3×C16—31no—
48C2×C32×Q8—21no—
49#3832—24no—
50#3832—42no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—41no—
53C2×C4×C3⋊D3—41no—
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C3×D12—21no—
56C2×C3×Dic6—21no—
57C2×#626—41no—
58C2×D3×Dic3—41no—
59#3796—24no—
60#3796—42no—
61C32×Q16—21no—
62C32×Q16C2312yes—
63C2×C32×C8C2311yescharacteristic
64#3755—24no—
65C2×C3⋊(C3⋊C8)D411yescharacteristic
66#3745—21no—
67#3745C2312yes—
68C8×C3⋊D3D412yes—
69C8×C3⋊D3C2312yes—
70C3×Dic12—21no—
71C3×Dic12C2312yes—
72C3×D24—21no—
73C3×D24C2312yes—
74#3715—24no—
75C3×C3⋊C16C2312yes—
76C3×C3⋊C16C2312yes—
77C2×#508—91noSylow
78C2×#239—61no—
79C2×#239—61no—
80C2×#239—61no—
81C2×#239—62no—
82C2×#237—61no—
83C2×C3×Q16—21no—
84C2×C3×Q16—31no—
85C2×C3×Q16C2×D311yescharacteristic
86C2×C3×Q16C2×D311yescharacteristic
87C2×C3×D8—31no—
88C2×#215—61no—
89C2×#215—61no—
90C2×#215—61no—
91C2×#215—62no—
92C2×#214—61no—
93#919—34no—
94#919—34no—
95#919—34no—
96#919—64no—
97#919—62no—
98#919—62no—
99#919—62no—
100#919—64no—
101#912—34no—
102#912—62no—
103C2×Dic12C2×D311yescharacteristic
104C2×D24—31no—
105C2×D24—31no—
106C2×D24—61no—
107C2×D24C2×D311yescharacteristic
108C2×D3×C8—31no—
109C2×D3×C8—31no—
110C2×D3×C8—61no—
111C3×Q32—34no—
112C3×SD32—34no—
113C2×C3×C16—31no—
114C2×C3×C16—31no—
115#829C2×D314yescomplemented
116#828—34no—
117#828C2×D314yescomplemented
118#826—34no—
119C2×C3⋊C16C2×D311yescharacteristic
120C2×C3⋊C16C2×D311yescharacteristic
121#800—34no—
122D48—34no—
123D3×C16—34no—
124D3×C16—34no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3D811yescharacteristic
127C22×C3×D3—41no—
128C32×Q8—22no—
129C32×Q8—41no—
130C2×C32×C4—41no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C3⋊Dic3D811yescharacteristic
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—44no—
135C4⋊(C3⋊D3)—41no—
136C4×C3⋊D3—44no—
137C4×C3⋊D3D812yes—
138C4×C3⋊D3C2×D412yes—
139C2×C3×Dic3—41no—
140C3×D12—22no—
141C3×D12—41no—
142C3×Dic6—22no—
143C3×Dic6—41no—
144#626—44no—
145D3×Dic3—44no—
146C32×C8C2×D411yescharacteristic
147C32×C8C2411yescharacteristic
148C3⋊(C3⋊C8)C2×D412yes—
149C2×#135—91no—
150C2×#135—91no—
151#508—98no—
152C2×Q32—31no—
153C2×SD32—31no—
154C2×SD32—91no—
155C2×D16—91no—
156C22×C16—91no—
157C2×C3×Q8—22no—
158C2×C3×Q8—21no—
159C2×C3×Q8—21no—
160C2×C3×Q8—61no—
161C2×C3×D4—61no—
162C2×#67—121no—
163C22×Dic3—121no—
164#239—64no—
165#239—64no—
166#239—64no—
167#239—68no—
168#239—122no—
169#239—122no—
170#239—122no—
171#239—124no—
172#237—64no—
173#237—122no—
174C2×D12—21no—
175C2×D12—62no—
176C2×D12—61no—
177C2×D12—61no—
178C2×D12—121no—
179C2×D12—121no—
180C2×D12—122no—
181C2×D12—121no—
182C2×C4×D3—31no—
183C2×C4×D3—31no—
184C2×C4×D3—61no—
185C2×C4×D3—121no—
186C2×C4×D3—121no—
187C2×C4×D3—121no—
188C2×C4×D3—122no—
189C2×Dic6—21no—
190C3×Q16—22no—
191C3×Q16—21no—
192C3×Q16—21no—
193C3×Q16—22no—
194C3×Q16—32no—
195C3×Q16—61no—
196C3×Q16C22×D312yes—
197C3×Q16C22×D312yes—
198C3×D8—32no—
199C3×D8—61no—
200C2×C3×C8—21no—
201C2×C3×C8C22×D311yescharacteristic
202C2×C3×C8C22×D311yescharacteristic
203#215—64no—
204#215—64no—
205#215—64no—
206#215—68no—
207#214—64no—
208C2×C3⋊C8—31no—
209C2×C3⋊C8—31no—
210C2×C3⋊C8—61no—
211Dic12—21no—
212Dic12C22×D312yes—
213D24—21no—
214D24—32no—
215D24—32no—
216D24—62no—
217D24—62no—
218D24—61no—
219D24—61no—
220D24C22×D312yes—
221D3×C8—32no—
222D3×C8—32no—
223D3×C8—32no—
224D3×C8—32no—
225D3×C8—62no—
226D3×C8—62no—
227C3×C16—32no—
228C3×C16—32no—
229C3⋊C16C22×D312yes—
230C3⋊C16C22×D312yes—
231C22×C32C2×D811yescharacteristic
232C2×C3⋊D3—22no—
233C2×C3⋊D3—42no—
234C2×C3⋊D3—82no—
235C2×C3⋊D3C2×D812yes—
236C2×C3×D3—42no—
237C2×C3×D3—82no—
238C32×C4—42no—
239C32×C4C2×D811yescharacteristic
240C32×C4C22×D411yescharacteristic
241C3⋊Dic3C2×D812yes—
242C3×Dic3—42no—
243C2×#41—181no—
244C2×#41—181no—
245#135—94no—
246#135—94no—
247#135—182no—
248#135—182no—
249C2×Q16—31no—
250C2×Q16D3211yescharacteristic
251C2×SD16—181no—
252C2×SD16—181no—
253C2×D8—31no—
254C2×D8—91no—
255C22×C8—91no—
256Q32—34no—
257SD32—34no—
258SD32—94no—
259D16—94no—
260C2×C16—31no—
261C2×C16—31no—
262C2×C16—94no—
263C23×C3—121no—
264C22×D3—31no—
265C22×D3—31no—
266C22×D3—41no—
267C22×D3—61no—
268C22×D3—122no—
269C22×D3—121no—
270C22×D3—121no—
271C3×Q8—24no—
272C3×Q8—22no—
273C3×Q8—22no—
274C3×Q8—42no—
275C3×Q8—41no—
276C3×Q8—41no—
277C3×Q8—62no—
278C3×Q8—121no—
279C3×D4—62no—
280C3×D4—121no—
281C2×C3×C4—21no—
282C2×C3×C4—42no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—121no—
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4D3×D411yescharacteristic
288#67—124no—
289C2×Dic3—31no—
290C2×Dic3—31no—
291C2×Dic3—41no—
292C2×Dic3—61no—
293C2×Dic3—124no—
294D12—22no—
295D12—41no—
296D12—64no—
297D12—62no—
298D12—62no—
299D12—122no—
300D12—124no—
301D12—124no—
302D12—128no—
303D12—124no—
304D12—121no—
305D12—121no—
306C4×D3—32no—
307C4×D3—32no—
308C4×D3—32no—
309C4×D3—32no—
310C4×D3—62no—
311C4×D3—62no—
312C4×D3—124no—
313C4×D3—124no—
314C4×D3—124no—
315C4×D3—128no—
316Dic6—22no—
317Dic6—41no—
318C3×C8—21no—
319C3×C8—21no—
320C3×C8D3×D411yescharacteristic
321C3×C8D3×D411yescharacteristic
322C3×C8C23×D311yescharacteristic
323C3×C8C23×D311yescharacteristic
324C3⋊C8—32no—
325C3⋊C8—32no—
326C3⋊C8—62no—
327C2×C32#50812yescomplemented
328C2×C32C22×D811yescharacteristic
329C3⋊D3—22no—
330C3⋊D3—82no—
331C3×D3—82no—
332#41—184no—
333#41—184no—
334#41—362no—
335#41—362no—
336C2×Q8—21no—
337C2×Q8—61no—
338C2×D4—61no—
339C2×D4—181no—
340C2×D4—361no—
341C2×D4—361no—
342C22×C4—91no—
343C22×C4—361no—
344C22×C4—361no—
345Q16—21no—
346Q16—32no—
347Q16—61no—
348Q16C2×D3212yes—
349SD16—184no—
350SD16—184no—
351D8—32no—
352D8—61no—
353D8—92no—
354D8—181no—
355C2×C8—91no—
356C2×C8—92no—
357C2×C8—92no—
358C2×C8C2×D3211yescharacteristic
359C16—32no—
360C16—32no—
361C22×C3—21no—
362C22×C3—122no—
363C22×C3—242no—
364C22×C3D3×D811yescharacteristic
365C22×C3D3×D811yescharacteristic
366C2×D3—32no—
367C2×D3—32no—
368C2×D3—42no—
369C2×D3—62no—
370C2×D3—62no—
371C2×D3—62no—
372C2×D3—82no—
373C2×D3—122no—
374C2×D3—124no—
375C2×D3—122no—
376C2×D3—122no—
377C2×D3—244no—
378C2×D3—242no—
379C2×D3—242no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—44no—
383C3×C4—42no—
384C3×C4—42no—
385C3×C4—122no—
386C3×C4D3×D811yescharacteristic
387C3×C4D3×D811yescharacteristic
388C3×C4C2×D3×D411yescharacteristic
389C3×C4C2×D3×D411yescharacteristic
390Dic3—32no—
391Dic3—32no—
392Dic3—42no—
393Dic3—62no—
394C32C2×#50811yescharacteristic, complemented, Sylow
395C23—91no—
396C23—121no—
397C23—361no—
398Q8—22no—
399Q8—41no—
400Q8—62no—
401Q8—121no—
402D4—62no—
403D4—121no—
404D4—182no—
405D4—364no—
406D4—364no—
407D4—361no—
408C2×C4—41no—
409C2×C4—91no—
410C2×C4—92no—
411C2×C4—92no—
412C2×C4—121no—
413C2×C4—364no—
414C2×C4—364no—
415C2×C4#381111yescharacteristic
416C8—92no—
417C8#381111yescharacteristic
418C8C22×D3211yescharacteristic
419C2×C3—21no—
420C2×C3—22no—
421C2×C3—242no—
422C2×C3#491612yescomplemented
423C2×C3#491912yescomplemented
424C2×C3C2×D3×D811yescharacteristic
425C2×C3C2×D3×D811yescharacteristic
426D3—62no—
427D3—62no—
428D3—82no—
429D3—122no—
430D3—244no—
431D3—242no—
432D3—242no—
433C22—92no—
434C22—122no—
435C22—182no—
436C22—242no—
437C22—362no—
438C22—722no—
439C22#6392611yescharacteristic
440C4—42no—
441C4—92no—
442C4—122no—
443C4#6392611yescharacteristic
444C4C2×#381111yescharacteristic
445C3—21no—
446C3C2×#491611yescharacteristic, complemented
447C3C2×#491911yescharacteristic, complemented
448C2—182no—
449C2—242no—
450C2—722no—
451C2#1059104912yesdirect product factor
452C2C2×#6392611yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
hypercenterC2×Q16D32
hypocenterC32C2×#508
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#64128C2semidirect
2. C2×#63810C2semidirect
3. C2×C3×#829C2semidirect
4. C2×C3×#828C2semidirect
5. #10591049C2direct (N × H)
6. C2×#63549C2semidirect
7. C2×#63546C2semidirect
8. C2×#63542C2semidirect
16. #64128C22semidirect
23. #63810C22semidirect
24. C3×#829C22semidirect
25. C3×#828C22semidirect
28. #63549C22semidirect
29. #63546C22semidirect
30. #63542C22semidirect
38. C2×#829D3semidirect
40. C2×#828D3semidirect
115. #829C2×D3semidirect
117. #828C2×D3semidirect
327. C2×C32#508semidirect
394. C32C2×#508semidirect
422. C2×C3#4916semidirect
423. C2×C3#4919semidirect
446. C3C2×#4916semidirect
447. C3C2×#4919semidirect
451. C2#10591049direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641282
C2×#638102
C2×C3×#8292
C2×C3×#8282
#105910492
C2×#635492
C2×#635462
C2×#635422
C2×#49193
C2×#49163