Finite Group Databasebeta

← C2×#10591518 #11863620

Subgroups — C2×#10591518 #11863620

Order 1152.

1797 conjugacy classes of subgroups; only the 252 normal subgroups are shown.

normal subgroups only

This group has 1797 conjugacy classes of subgroups — too many to draw. Only its 252 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
1C22×#3797C211yesmaximal, characteristic, complemented
2C2×#64147C211yesmaximal, characteristic
3C22×C3×#214C212yesmaximal, complemented
4#10591518C218yesmaximal, direct product factor
5C2×#63566C212yesmaximal, complemented
6C2×#63557C211yesmaximal, characteristic, complemented
7C2×#5170—32nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×#638—21no—
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×Dic6C2212yes—
12C22×#627—21no—
13C22×#624—21no—
14C2×#3797—22no—
15C2×#3797—28no—
16C2×#3797C2214yescomplemented
17C2×#3757—21no—
18#64147—22no—
19#64147C2214yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#214—28no—
22C2×C3×#214C2218yescomplemented
23C22×C3×C3⋊C8C2212yes—
24#63566C2218yescomplemented
25#63557C2214yescomplemented
26C22×D3×Q8—32no—
27C22×C3×SD16—32no—
28C2×#938—32no—
29C2×#938—61no—
30C22×#214D312yescomplemented
31C2×#835—32no—
32#5170—316no—
33C2×(C2×D3)⋊C8—32no—
34C2×#816—32no—
35C24×C32—21no—
36C23×C3⋊D3D411yescharacteristic
37C2×C32×D4—24no—
38C2×C32×D4—21no—
39C2×C32×D4C2312yes—
40C22×C32×C4C2311yescharacteristic
41C2×#638—24no—
42C2×#638—44no—
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D411yescharacteristic
45C2×C4×C3⋊D3—24no—
46C2×C4×C3⋊D3D412yes—
47C2×C4×C3⋊D3C2312yes—
48C22×C3×Dic3—22no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6—24no—
51C2×C3×Dic6D418yescomplemented
52C2×C3×Dic6C2314yes—
53C2×#627—28no—
54C2×#627—24no—
55C2×#624—28no—
56C2×#624—24no—
57#3797—216no—
58#3797—216no—
59#3757—24no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)C2312yes—
62C3×#214—216no—
63C2×C3×C3⋊C8—24no—
64C2×C3×C3⋊C8C2314yes—
65C2×#448—91noSylow
66C22×C3×Q8—32no—
67C22×C3×D4—21no—
68C22×C3×D4C2×D312yes—
69C22×#67—62no—
70C22×#67—62no—
71C2×D3×Q8—38no—
72C2×D3×Q8—64no—
73C2×D3×Q8—68no—
74C2×D3×Q8—68no—
75C22×C4×D3—32no—
76C22×C4×D3—61no—
77C22×C4×D3—62no—
78C22×Dic6—62no—
79C22×Dic6C2×D312yes—
80C2×C3×SD16—38no—
81C2×C3×SD16—68no—
82C22×C3×C8—32no—
83C2×#217—62no—
84C2×#217—62no—
85#938—38no—
86#938—64no—
87#938—64no—
88#938—64no—
89C2×#214—28no—
90C2×#214C2×D318yescomplemented
91C2×C4⋊Dic3—32no—
92C2×C4⋊Dic3—61no—
93C22×C3⋊C8C2×D312yes—
94#835—38no—
95(C2×D3)⋊C8—38no—
96#816—38no—
97C23×C32—22no—
98C23×C32—42no—
99C23×C32—42no—
100C23×C32—42no—
101C23×C32C2×D411yescharacteristic
102C22×C3⋊D3—22no—
103C22×C3⋊D3—22no—
104C22×C3⋊D3SD1614yescomplemented
105C22×C3⋊D3C2×D412yes—
106C32×D4—24no—
107C32×D4—42no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D414yes—
110C2×C32×C4C2411yescharacteristic
111#638—48no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—42no—
115C2×C3⋊Dic3C2×D412yes—
116C4×C3⋊D3—24no—
117C4×C3⋊D3—24no—
118C2×C3×Dic3—28no—
119C2×C3×Dic3—24no—
120C3×Dic6—28no—
121C3×Dic6—24no—
122C3×Dic6C2×D418yescomplemented
123#627—216no—
124#624—216no—
125C3×C3⋊C8—24no—
126C23×Q8—91no—
127C22×SD16—32no—
128C2×#121—91no—
129#448—98no—
130C2×#103—92no—
131C2×C22⋊C8—91no—
132C24×C3—22no—
133C24×C3—22no—
134C23×D3—32no—
135C23×D3—61no—
136C2×C3×Q8—38no—
137C2×C3×Q8—34no—
138C2×C3×Q8—62no—
139C2×C3×Q8—64no—
140C2×C3×D4—22no—
141C2×C3×D4—24no—
142C2×C3×D4—22no—
143C2×C3×D4—24no—
144C2×C3×D4—22no—
145C2×C3×D4—44no—
146C2×C3×D4C22×D314yes—
147C22×C3×C4—21no—
148C22×C3×C4—62no—
149C22×C3×C4C22×D312yes—
150C2×#67—68no—
151C2×#67—68no—
152C2×#67—128no—
153C2×#67—128no—
154C22×Dic3—22no—
155C22×Dic3—32no—
156C22×Dic3—61no—
157C22×Dic3—62no—
158C22×Dic3—62no—
159D3×Q8—616no—
160D3×Q8—632no—
161D3×Q8—616no—
162C2×C4×D3—34no—
163C2×C4×D3—34no—
164C2×C4×D3—62no—
165C2×C4×D3—62no—
166C2×C4×D3—68no—
167C2×C4×D3—616no—
168C2×C4×D3—64no—
169C2×C4×D3—64no—
170C2×C4×D3—124no—
171C2×Dic6—24no—
172C2×Dic6—22no—
173C2×Dic6—68no—
174C2×Dic6—616no—
175C2×Dic6#6718yescomplemented
176C2×Dic6C22×D314yes—
177C3×SD16—616no—
178C2×C3×C8—34no—
179C2×C3×C8—64no—
180#217—68no—
181#217—68no—
182#214—216no—
183C4⋊Dic3—34no—
184C4⋊Dic3—62no—
185C4⋊Dic3—62no—
186C4⋊Dic3—62no—
187C2×C3⋊C8—24no—
188C2×C3⋊C8C22×D314yes—
189C22×C32—42no—
190C22×C32—42no—
191C22×C32—42no—
192C22×C32—84no—
193C22×C32#12012yes—
194C22×C32C2×SD1612yes—
195C22×C32#13712yes—
196C22×C32C22×D411yescharacteristic
197C2×C3⋊D3—22no—
198C2×C3⋊D3—22no—
199C2×C3⋊D3—28no—
200C2×C3⋊D3C2×SD1614yescomplemented
201C32×C4#12012yes—
202C32×C4C22×D412yes—
203C3⋊Dic3—22no—
204C3⋊Dic3—42no—
205C3×Dic3—28no—
206C22×Q8—32no—
207C22×Q8—94no—
208C22×Q8—181no—
209C22×Q8—182no—
210C22×Q8—188no—
211C22×D4—181no—
212C22×D4D3211yescharacteristic
213C23×C4—91no—
214C23×C4—181no—
215C2×SD16—38no—
216C2×SD16—68no—
217C22×C8—32no—
218#121—94no—
219#121—182no—
220C2×C4⋊C4—91no—
221C2×C22⋊C4—181no—
222#103—98no—
223C22⋊C8—94no—
224C23×C3—24no—
225C23×C3—24no—
226C23×C3—21no—
227C23×C3—44no—
228C23×C3—44no—
229C23×C3—44no—
230C23×C3—44no—
231C23×C3—44no—
232C23×C3—44no—
233C23×C3D3×D412yes—
234C22×D3—38no—
235C22×D3—34no—
236C22×D3—64no—
237C22×D3—62no—
238C22×D3—64no—
239C22×D3—64no—
240C22×D3—122no—
241C22×D3—122no—
242C3×Q8—38no—
243C3×Q8—68no—
244C3×Q8—64no—
245C3×D4—24no—
246C3×D4—24no—
247C3×D4—44no—
248C3×D4—44no—
249C3×D4—44no—
250C2×C3×C4—21no—
251C2×C3×C4—24no—
252C2×C3×C4—21no—
253C2×C3×C4—68no—
254C2×C3×C4—64no—
255C2×C3×C4D3×D414yes—
256C2×C3×C4D3×D412yes—
257C2×C3×C4C2×#6714yes—
258C2×C3×C4C23×D312yes—
259#67—1216no—
260#67—1216no—
261C2×Dic3—28no—
262C2×Dic3—24no—
263C2×Dic3—34no—
264C2×Dic3—62no—
265C2×Dic3—64no—
266C2×Dic3—64no—
267C2×Dic3—64no—
268C2×Dic3—122no—
269C2×Dic3—124no—
270C2×Dic3—124no—
271C4×D3—632no—
272C4×D3—68no—
273C4×D3—64no—
274C4×D3—64no—
275C4×D3—124no—
276C4×D3—124no—
277Dic6—28no—
278Dic6—24no—
279Dic6—632no—
280Dic6C2×#6718yescomplemented
281C3×C8—64no—
282C3⋊C8—24no—
283C2×C32—82no—
284C2×C32#44814yescomplemented
285C2×C32C2×#12011yescharacteristic
286C2×C32C22×SD1611yescharacteristic
287C2×C32C2×#13711yescharacteristic
288C3⋊D3—24no—
289C24—21no—
290C24—91no—
291C2×Q8—34no—
292C2×Q8—38no—
293C2×Q8—64no—
294C2×Q8—62no—
295C2×Q8—184no—
296C2×Q8—188no—
297C2×Q8—1816no—
298C2×Q8—1816no—
299C2×D4—24no—
300C2×D4—21no—
301C2×D4—184no—
302C2×D4—364no—
303C2×D4C2×D3212yes—
304C22×C4—62no—
305C22×C4—91no—
306C22×C4—92no—
307C22×C4—92no—
308C22×C4—184no—
309C22×C4—188no—
310C22×C4—184no—
311C22×C4—181no—
312C22×C4C2×D3211yescharacteristic
313SD16—616no—
314C2×C8—34no—
315C2×C8—64no—
316C4⋊C4—92no—
317C4⋊C4—181no—
318C22⋊C4—184no—
319C22×C3—21no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—44no—
324C22×C3—44no—
325C22×C3—44no—
326C22×C3—44no—
327C22×C3—44no—
328C22×C3—44no—
329C22×C3—88no—
330C22×C3—88no—
331C22×C3D3×SD1614yes—
332C22×C3#91514yes—
333C22×C3#93714yes—
334C22×C3C2×D3×D412yes—
335C2×D3—38no—
336C2×D3—64no—
337C2×D3—616no—
338C2×D3—64no—
339C2×D3—64no—
340C2×D3—122no—
341C2×D3—128no—
342C2×D3—122no—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—68no—
346C3×C4#93714yes—
347C3×C4C2×D3×D412yes—
348C3×C4C22×#6712yes—
349Dic3—28no—
350Dic3—64no—
351Dic3—122no—
352Dic3—124no—
353Dic3—124no—
354C32C2×#44811yescharacteristic, complemented, Sylow
355C23—22no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—92no—
360C23—94no—
361C23—182no—
362C23—182no—
363C23#381111yescharacteristic
364Q8—38no—
365Q8—64no—
366Q8—68no—
367Q8—1816no—
368D4—24no—
369D4—42no—
370D4—368no—
371C2×C4—64no—
372C2×C4—68no—
373C2×C4—92no—
374C2×C4—1816no—
375C2×C4—182no—
376C2×C4—184no—
377C2×C4—184no—
378C2×C4—182no—
379C2×C4—362no—
380C2×C4D3×#6714yes—
381C2×C4#381111yescharacteristic
382C2×C4C22×D3211yescharacteristic
383C8—64no—
384C2×C3—24no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—84no—
389C2×C3—84no—
390C2×C3#517018yescomplemented
391C2×C3C2×D3×SD1612yes—
392C2×C3C2×#91512yes—
393C2×C3C2×#93712yes—
394D3—68no—
395D3—124no—
396C22—42no—
397C22—42no—
398C22—42no—
399C22—84no—
400C22—94no—
401C22—188no—
402C22—182no—
403C22—182no—
404C22#6393012yes—
405C22#6393112yes—
406C22#6398312yes—
407C22C2×#381111yescharacteristic
408C4—68no—
409C4—182no—
410C4—362no—
411C4#6398312yes—
412C4C2×D3×#6712yes—
413C3—21no—
414C3C2×#517012yescomplemented
415C2—82no—
416C2—184no—
417C2#1059151814yesdirect product factor
418C2C2×#6393011yescharacteristic
419C2C2×#6393111yescharacteristic
420C2C2×#6398311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×#64147C2
hypercenterC22×D4D32
hypocenterC32C2×#448
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
1. C22×#3797C2semidirect
3. C22×C3×#214C2semidirect
4. #10591518C2direct (N × H)
5. C2×#63566C2semidirect
6. C2×#63557C2semidirect
16. C2×#3797C22semidirect
22. C2×C3×#214C22semidirect
24. #63566C22semidirect
25. #63557C22semidirect
30. C22×#214D3semidirect
51. C2×C3×Dic6D4semidirect
90. C2×#214C2×D3semidirect
104. C22×C3⋊D3SD16semidirect
122. C3×Dic6C2×D4semidirect
175. C2×Dic6#67semidirect
200. C2×C3⋊D3C2×SD16semidirect
280. Dic6C2×#67semidirect
284. C2×C32#448semidirect
354. C32C2×#448semidirect
390. C2×C3#5170semidirect
414. C3C2×#5170semidirect
417. C2#10591518direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C2×#641472
C22×C3×#2142
#105915182
C2×#635662
C2×#635572
C2×#51703