Finite Group Databasebeta

← C2×#10591660 #11864921

Subgroups — C2×#10591660 #11864921

Order 1152.

1561 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 1561 conjugacy classes of subgroups — too many to draw. Only its 212 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×#64298C211yesmaximal, characteristic
2C2×#64153C211yesmaximal, characteristic, complemented
3C2×C3×#942C212yesmaximal, complemented
4#10591660C218yesmaximal, direct product factor
5C2×#63568C212yesmaximal, complemented
6C2×#63561C211yesmaximal, characteristic, complemented
7C2×#5205—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×#634C2211yescharacteristic
10C2×C3×#235C2212yes—
11C2×#3805—22no—
12#64298—22no—
13#64298—24no—
14#64298C2214yes—
15C2×#3795—22no—
16C2×D3×Dic6—22no—
17#64153—22no—
18#64153C2214yescomplemented
19C2×#3750—22no—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×#216—22no—
22C3×#942—24no—
23C3×#942C2218yescomplemented
24C2×C3×#215—22no—
25C2×C3×#208C2212yes—
26#63568C2218yescomplemented
27#63561C2214yescomplemented
28C2×#1010—32no—
29C2×C3×#137—32no—
30C2×#944—32no—
31C2×#944—61no—
32C2×#942D312yescomplemented
33C2×#837—32no—
34#5205—316no—
35C2×#825—32no—
36C2×#824—32no—
37C2×C32×Q8—21no—
38C2×C32×Q8—22no—
39C2×C32×Q8—22no—
40C2×C32×Q8C2312yes—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D412yes—
45C2×#634—22no—
46C2×#634—22no—
47C2×#634D412yes—
48C2×#634C2312yes—
49C2×C3×#67—22no—
50C3×#235—22no—
51C3×#235—22no—
52C3×#235D414yes—
53C3×#235C2314yes—
54C2×C3×D12D412yes—
55C2×C3×C4×D3—22no—
56C2×C3×Dic6D412yes—
57C2×#627—22no—
58C2×#625—22no—
59#3805—28no—
60#3805—28no—
61C2×D3×Dic3—24no—
62#3795—28no—
63#3795—28no—
64D3×Dic6—28no—
65D3×Dic6—28no—
66#3750—28no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3C2312yes—
69C3×#216—28no—
70C3×#215—28no—
71C3×#208—22no—
72C3×#208C2314yes—
73C2×C3×C3⋊C8—22no—
74C2×#456—91noSylow
75C2×C3×#41—32no—
76C22×C3×Q8—21no—
77C22×C3×Q8C2×D312yes—
78#1010—38no—
79#1010—64no—
80#1010—64no—
81#1010—64no—
82C2×D3×Q8—62no—
83C2×#237—62no—
84C2×#237—64no—
85C2×#235—62no—
86C2×#235C2×D312yes—
87C22×Dic6—32no—
88C22×Dic6—61no—
89C22×Dic6—62no—
90C3×#137—38no—
91C3×#137—64no—
92C2×C3×Q16—62no—
93C2×C3×SD16—62no—
94C2×C3×M16—32no—
95#944—38no—
96#944—64no—
97#944—64no—
98#944—64no—
99C2×#216—22no—
100#942—24no—
101#942C2×D318yescomplemented
102C2×#215—22no—
103C2×Dic3⋊C4—64no—
104C2×Dic3⋊C4—64no—
105C2×C4×Dic3—32no—
106C2×C4×Dic3—61no—
107C2×#208C2×D312yes—
108#837—38no—
109#825—38no—
110#824—38no—
111C23×C32C2×D411yescharacteristic
112C22×C3×D3—22no—
113C32×Q8—24no—
114C32×Q8—42no—
115C2×C32×C4—22no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2411yescharacteristic
122C2×C3⋊Dic3—24no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3C2×D414yes—
127#634—24no—
128#634—24no—
129C3×#67—24no—
130C3×#67—24no—
131C2×C3×Dic3—22no—
132C3×D12—22no—
133C3×D12C2×D414yes—
134C3×C4×D3—24no—
135C3×C4×D3—24no—
136C3×Dic6—22no—
137C3×Dic6C2×D414yes—
138#627—28no—
139#625—28no—
140D3×Dic3—216no—
141C3×C3⋊C8—24no—
142C2×2−1+4—91no—
143C2×#137—32no—
144C2×C4⋊Q8—91no—
145#456—98no—
146C2×#104—92no—
147C2×#101—91no—
148C3×#41—34no—
149C3×#41—34no—
150C3×#41—62no—
151C3×#41—62no—
152C2×C3×Q8—22no—
153C2×C3×Q8—22no—
154C2×C3×Q8—22no—
155C2×C3×Q8—22no—
156C2×C3×Q8—22no—
157C2×C3×Q8—22no—
158C2×C3×Q8—22no—
159C2×C3×Q8—32no—
160C2×C3×Q8—42no—
161C2×C3×Q8—42no—
162C2×C3×Q8C22×D314yes—
163C2×C3×D4—32no—
164C2×C3×D4—62no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4—62no—
169C22×C3×C4C22×D312yes—
170C2×#67—22no—
171C2×#67—64no—
172C22×Dic3—34no—
173C22×Dic3—62no—
174C22×Dic3—64no—
175C22×Dic3—62no—
176C22×Dic3—62no—
177D3×Q8—68no—
178D3×Q8—68no—
179#237—68no—
180#237—68no—
181#237—616no—
182#237—616no—
183#235—22no—
184#235—22no—
185#235—68no—
186#235—68no—
187#235#6714yes—
188#235C22×D314yes—
189C2×D12#6712yes—
190C2×C4×D3—22no—
191C2×C4×D3—64no—
192C2×Dic6—34no—
193C2×Dic6—34no—
194C2×Dic6—62no—
195C2×Dic6—62no—
196C2×Dic6—68no—
197C2×Dic6—64no—
198C2×Dic6—62no—
199C2×Dic6—62no—
200C2×Dic6—62no—
201C2×Dic6—62no—
202C2×Dic6—68no—
203C2×Dic6—122no—
204C2×Dic6—122no—
205C2×Dic6#6712yes—
206C3×Q16—68no—
207C3×SD16—68no—
208C3×M16—34no—
209C3×M16—62no—
210C2×C3×C8—62no—
211#216—28no—
212#215—28no—
213Dic3⋊C4—616no—
214Dic3⋊C4—616no—
215C4×Dic3—34no—
216C4×Dic3—62no—
217C4×Dic3—62no—
218C4×Dic3—62no—
219#208—22no—
220#208C22×D314yes—
221C2×C3⋊C8—22no—
222C22×C32—22no—
223C22×C32#12011yescharacteristic
224C22×C32#12011yescharacteristic
225C22×C32C22×D411yescharacteristic
226C2×C3×D3—24no—
227C2×C3×D3—44no—
228C32×C4—42no—
229C32×C4#12012yes—
230C32×C4C22×D412yes—
231C3⋊Dic3—24no—
232C3⋊Dic3—24no—
233C3×Dic3—24no—
2342−1+4—94no—
2352−1+4—182no—
2362−1+4—184no—
237C2×#41—32no—
238C2×#41—182no—
239C2×#41—182no—
240C22×Q8—91no—
241C22×Q8—182no—
242C22×Q8D3211yescharacteristic
243#137—38no—
244#137—64no—
245C2×Q16—62no—
246C2×SD16—62no—
247C2×M16—32no—
248C4⋊Q8—94no—
249C4⋊Q8—182no—
250C2×C4⋊C4—182no—
251C2×C42—91no—
252#104—98no—
253#101—94no—
254C23×C3—21no—
255C23×C3—62no—
256C23×C3D3×D412yes—
257C22×D3—22no—
258C3×Q8—24no—
259C3×Q8—24no—
260C3×Q8—34no—
261C3×Q8—44no—
262C3×Q8—44no—
263C3×Q8—42no—
264C3×Q8—42no—
265C3×Q8—62no—
266C3×D4—34no—
267C3×D4—64no—
268C3×D4—64no—
269C3×D4—62no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—21no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—42no—
280C2×C3×C4—62no—
281C2×C3×C4—64no—
282C2×C3×C4—64no—
283C2×C3×C4D3×D412yes—
284C2×C3×C4D3×D412yes—
285C2×C3×C4D3×D412yes—
286C2×C3×C4C2×#6712yes—
287C2×C3×C4C2×#6712yes—
288C2×C3×C4C23×D312yes—
289#67—24no—
290#67—24no—
291#67—616no—
292C2×Dic3—22no—
293C2×Dic3—38no—
294C2×Dic3—64no—
295C2×Dic3—616no—
296C2×Dic3—64no—
297C2×Dic3—68no—
298C2×Dic3—68no—
299C2×Dic3—64no—
300C2×Dic3—64no—
301C2×Dic3—64no—
302C2×Dic3—122no—
303C2×Dic3—122no—
304D12—22no—
305D12C2×#6714yes—
306C4×D3—24no—
307C4×D3—24no—
308C4×D3—616no—
309Dic6—22no—
310Dic6—616no—
311Dic6—64no—
312Dic6—64no—
313Dic6—64no—
314Dic6—64no—
315Dic6—124no—
316Dic6—124no—
317Dic6C2×#6714yes—
318C3×C8—64no—
319C3⋊C8—24no—
320C2×C32—21no—
321C2×C32—21no—
322C2×C32#45612yescomplemented
323C2×C32C2×#12011yescharacteristic
324C3×D3—44no—
325#41—34no—
326#41—34no—
327#41—62no—
328#41—62no—
329#41—188no—
330#41—188no—
331#41—188no—
332#41—188no—
333C2×Q8—21no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—32no—
337C2×Q8—92no—
338C2×Q8—92no—
339C2×Q8—182no—
340C2×Q8—188no—
341C2×Q8—188no—
342C2×Q8—182no—
343C2×Q8—182no—
344C2×Q8C2×D3212yes—
345C2×D4—32no—
346C2×D4—62no—
347C2×D4—182no—
348C22×C4—21no—
349C22×C4—62no—
350C22×C4—92no—
351C22×C4—184no—
352C22×C4—181no—
353C22×C4C2×D3211yescharacteristic
354Q16—68no—
355SD16—68no—
356M16—34no—
357M16—62no—
358C2×C8—62no—
359C4⋊C4—188no—
360C42—92no—
361C42—181no—
362C22×C3—24no—
363C22×C3—24no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—64no—
368C22×C3—124no—
369C22×C3#93712yes—
370C22×C3#93712yes—
371C22×C3C2×D3×D412yes—
372C2×D3—24no—
373C2×D3—44no—
374C3×C4—22no—
375C3×C4—22no—
376C3×C4—44no—
377C3×C4—44no—
378C3×C4—64no—
379C3×C4#93712yes—
380C3×C4#93712yes—
381C3×C4C2×D3×D412yes—
382C3×C4C22×#6712yes—
383Dic3—24no—
384Dic3—68no—
385Dic3—68no—
386Dic3—68no—
387Dic3—124no—
388C32C2×#45611yescharacteristic, complemented, Sylow
389C23—62no—
390C23#381111yescharacteristic
391Q8—24no—
392Q8—34no—
393Q8—42no—
394Q8—62no—
395Q8—188no—
396Q8—184no—
397Q8—184no—
398D4—34no—
399D4—64no—
400D4—64no—
401D4—62no—
402D4—188no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—62no—
407C2×C4—64no—
408C2×C4—64no—
409C2×C4—94no—
410C2×C4—1816no—
411C2×C4—184no—
412C2×C4—182no—
413C2×C4—182no—
414C2×C4—182no—
415C2×C4D3×#6712yes—
416C2×C4D3×#6712yes—
417C2×C4#381111yescharacteristic
418C2×C4C22×D3211yescharacteristic
419C8—64no—
420C2×C3—22no—
421C2×C3—22no—
422C2×C3—22no—
423C2×C3—22no—
424C2×C3—22no—
425C2×C3—21no—
426C2×C3—124no—
427C2×C3#520514yescomplemented
428C2×C3C2×#93712yes—
429D3—44no—
430C22—22no—
431C22—64no—
432C22—124no—
433C22#6398311yescharacteristic
434C22#6398311yescharacteristic
435C22C2×#381111yescharacteristic
436C4—42no—
437C4—64no—
438C4—184no—
439C4—184no—
440C4#6398312yes—
441C4C2×D3×#6712yes—
442C3—21no—
443C3C2×#520512yescomplemented
444C2—21no—
445C2—21no—
446C2—124no—
447C2#1059166012yesdirect product factor
448C2C2×#6398311yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radicalC2×#64298C2
hypercenterC22×Q8D32
hypocenterC32C2×#456
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#64153C2semidirect
3. C2×C3×#942C2semidirect
4. #10591660C2direct (N × H)
5. C2×#63568C2semidirect
6. C2×#63561C2semidirect
18. #64153C22semidirect
23. C3×#942C22semidirect
26. #63568C22semidirect
27. #63561C22semidirect
32. C2×#942D3semidirect
101. #942C2×D3semidirect
322. C2×C32#456semidirect
388. C32C2×#456semidirect
427. C2×C3#5205semidirect
443. C3C2×#5205semidirect
447. C2#10591660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642982
C2×#641532
C2×C3×#9422
#105916602
C2×#635682
C2×#635612
C2×#52053