Finite Group Databasebeta

← C2×#10593226 #11922271

Subgroups — C2×#10593226 #11922271

Order 1152.

521 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 521 conjugacy classes of subgroups — too many to draw. Only its 59 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×#64265C211yesmaximal, characteristic
2C2×C3×#984C211yesmaximal, characteristic
3C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic
4#10593226C214yesmaximal, direct product factor
5C2×#5403—31nomaximal
6C2×#5204—31nomaximal
7C2×C3×#41⋊C3C2211yescharacteristic
8#64265—21no—
9#64265C2212yes—
10C2×C3⋊#226—21no—
11C3×#984—21no—
12C3×#984C2212yes—
13C2×C3×#226—21no—
14C2×#3719—41nomaximal
15C3⋊(#131⋊C3)C2212yes—
16C2×#984—31no—
17C2×#984—61no—
18C2×#984D311yescharacteristic
19C2×C3×#137—31no—
20C2×#951—31no—
21C2×#948D311yescharacteristic
22C22×#216—31no—
23C2×#131⋊C3—31no—
24#5403—34no—
25C2×#836—31no—
26#5204—34no—
27#5204—34no—
28C2×#824—31no—
29C2×#822—31no—
30C2×#634—41no—
31C2×C3×Dic6—41no—
32C3×#41⋊C3D411yescharacteristic
33C3×#41⋊C3C2311yescharacteristic
34C2×C3×SL(2,𝔽3)D411yescharacteristic
35C3⋊#226—22no—
36C3×#226—22no—
37C2×C3×C3⋊C8—41no—
38#3719—44no—
39C2×#473—91noSylow
40C2×C3×#41C2×D311yescharacteristic
41C22×C3×Q8—31no—
42C22×Dic6—31no—
43C2×#41⋊C3—21no—
44C2×#41⋊C3C2×D311yescharacteristic
45#984—21no—
46#984—32no—
47#984—62no—
48#984—62no—
49#984—61no—
50#984C2×D312yes—
51C2×#226—21no—
52C2×#226—62no—
53C2×#226—61no—
54C3×#137—32no—
55C3×#137—32no—
56C3×#137—61no—
57C3×#137—61no—
58C2×C3×Q16—61no—
59C2×C3×SD16—61no—
60C2×C3×M16—31no—
61#951—32no—
62#951—32no—
63#951—61no—
64#951—61no—
65#948—32no—
66#948C2×D312yes—
67C2×#216—34no—
68C2×#216—61no—
69C2×#216—62no—
70C2×#216—61no—
71C2×#216—61no—
72C2×#214—61no—
73C2×#208—31no—
74C2×#208—31no—
75C22×C3⋊C8—31no—
76C2×Dic12—121no—
77#131⋊C3—32no—
78#836—34no—
79#824—34no—
80#822—34no—
81C2×C32×C4—41no—
82C2×C3⋊Dic3—81no—
83#634—42no—
84#634—81no—
85C2×C3×Dic3—81no—
86C3×Dic6—42no—
87C3×Dic6—81no—
88C3×SL(2,𝔽3)C2×D411yescharacteristic
89C3×C3⋊C8—42no—
90C2×#137—31no—
91C2×#137—91no—
92C22×Q16—91no—
93C2×#131—31no—
94#473—94no—
95#473—94no—
96C2×#108—91no—
97C2×#101—91no—
98C2×#101—91no—
99C3×#41—31no—
100C3×#41—31no—
101C3×#41D1211yescharacteristic
102C3×#41C22×D311yescharacteristic
103C2×C3×Q8—32no—
104C2×C3×Q8—61no—
105C2×C3×Q8—61no—
106C2×C3×Q8—61no—
107C2×C3×Q8—61no—
108C2×C3×Q8—61no—
109C2×C3×Q8D1211yescharacteristic
110C2×C3×D4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—61no—
113C22×Dic3—61no—
114C2×Dic6—32no—
115C2×Dic6—41no—
116C2×Dic6—61no—
117C2×Dic6—61no—
118C2×Dic6—61no—
119C2×Dic6—61no—
120C2×Dic6—61no—
121C2×Dic6—121no—
122C2×Dic6—241no—
123#41⋊C3—21no—
124#41⋊C3—21no—
125#41⋊C3#6711yescharacteristic
126#41⋊C3C22×D311yescharacteristic
127C2×SL(2,𝔽3)—21no—
128C2×SL(2,𝔽3)#6711yescharacteristic
129#226—22no—
130#226—64no—
131#226—62no—
132C3×Q16—62no—
133C3×Q16—62no—
134C3×SD16—62no—
135C3×SD16—62no—
136C3×M16—32no—
137C3×M16—61no—
138C2×C3×C8—61no—
139C2×C3×C8—121no—
140#216—64no—
141#216—62no—
142#216—62no—
143#216—64no—
144#214—62no—
145#214—62no—
146#208—32no—
147#208—32no—
148#208—61no—
149#208—61no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—32no—
152C2×C3⋊C8—32no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8S411yescharacteristic
155Dic12—124no—
156C22×C32—41no—
157C32×C4—41no—
158C32×C4—41no—
159C3⋊Dic3—82no—
160C3×Dic3—82no—
161C2×#41D3211yescharacteristic
162C22×Q8—31no—
163C22×Q8—91no—
164#137—32no—
165#137—32no—
166#137—61no—
167#137—61no—
168#137—92no—
169#137—92no—
170#137—181no—
171#137—181no—
172C2×Q16—61no—
173C2×Q16—94no—
174C2×Q16—181no—
175C2×Q16—182no—
176C2×Q16—181no—
177C2×Q16—181no—
178C2×SD16—61no—
179C2×SD16—181no—
180#131—32no—
181#131—92no—
182C2×M16—31no—
183C2×M16—91no—
184C2×M16—91no—
185C22×C8—91no—
186#108—94no—
187#101—94no—
188#101—94no—
189C23×C3—31no—
190C3×Q8—31no—
191C3×Q8—62no—
192C3×Q8—62no—
193C3×Q8—121no—
194C3×Q8—121no—
195C3×Q8C2×D1211yescharacteristic
196C3×D4—31no—
197C3×D4—31no—
198C3×D4—61no—
199C2×C3×C4—31no—
200C2×C3×C4—31no—
201C2×C3×C4—31no—
202C2×C3×C4—31no—
203C2×C3×C4—31no—
204C2×C3×C4—41no—
205C2×C3×C4—62no—
206C2×C3×C4—81no—
207C2×C3×C4—121no—
208C2×C3×C4—121no—
209C2×C3×C4C2×S411yescharacteristic
210C2×Dic3—62no—
211C2×Dic3—81no—
212C2×Dic3—121no—
213C2×Dic3—121no—
214C2×Dic3—241no—
215C2×Dic3—242no—
216Dic6—42no—
217Dic6—62no—
218Dic6—62no—
219Dic6—81no—
220Dic6—122no—
221Dic6—121no—
222Dic6—121no—
223Dic6—242no—
224Dic6—241no—
225Dic6—242no—
226SL(2,𝔽3)—21no—
227SL(2,𝔽3)C2×#6711yescharacteristic
228C3×C8—62no—
229C3×C8—122no—
230C3⋊C8—32no—
231C3⋊C8—62no—
232C3⋊C8C2×S412yes—
233C2×C32—41no—
234C2×C32—42no—
235#41—31no—
236#41—31no—
237#41#62611yescharacteristic
238#41C2×D3211yescharacteristic
239C2×Q8—32no—
240C2×Q8—61no—
241C2×Q8—61no—
242C2×Q8—61no—
243C2×Q8—61no—
244C2×Q8—61no—
245C2×Q8—92no—
246C2×Q8—181no—
247C2×Q8—181no—
248C2×Q8—181no—
249C2×Q8—181no—
250C2×Q8—181no—
251C2×Q8#62611yescharacteristic
252C2×D4—31no—
253C22×C4—31no—
254C22×C4—61no—
255C22×C4—181no—
256Q16—62no—
257Q16—62no—
258Q16—184no—
259Q16—184no—
260Q16—182no—
261Q16—182no—
262SD16—62no—
263SD16—62no—
264SD16—182no—
265SD16—182no—
266M16—32no—
267M16—61no—
268M16—92no—
269M16—92no—
270M16—181no—
271M16—181no—
272C2×C8—31no—
273C2×C8—61no—
274C2×C8—92no—
275C2×C8—92no—
276C2×C8—91no—
277C2×C8—181no—
278C22×C3—31no—
279C22×C3—31no—
280C22×C3—41no—
281C22×C3—62no—
282C22×C3—81no—
283C22×C3C4⋊S411yescharacteristic
284C3×C4—31no—
285C3×C4—31no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—81no—
289C3×C4—81no—
290C3×C4—122no—
291C3×C4C4⋊S411yescharacteristic
292C3×C4C22×S411yescharacteristic
293Dic3—82no—
294Dic3—122no—
295Dic3—242no—
296Dic3—244no—
297C32—41noSylow
298C23—31no—
299Q8—31no—
300Q8—62no—
301Q8—62no—
302Q8—121no—
303Q8—121no—
304Q8—182no—
305Q8—182no—
306Q8—361no—
307Q8—361no—
308Q8C2×#62611yescharacteristic
309D4—31no—
310D4—31no—
311D4—61no—
312C2×C4—31no—
313C2×C4—31no—
314C2×C4—31no—
315C2×C4—31no—
316C2×C4—31no—
317C2×C4—62no—
318C2×C4—121no—
319C2×C4—121no—
320C2×C4—182no—
321C2×C4—361no—
322C2×C4—361no—
323C2×C4D3×S411yescharacteristic
324C8—32no—
325C8—62no—
326C8—92no—
327C8—182no—
328C2×C3—41no—
329C2×C3—42no—
330C2×C3—61no—
331C2×C3—61no—
332C2×C3—81no—
333C2×C3—82no—
334C2×C3#540312yescomplemented
335C2×C3C2×C4⋊S411yescharacteristic
336C22—31no—
337C22—31no—
338C22—62no—
339C22#6420711yescharacteristic
340C4—31no—
341C4—31no—
342C4—122no—
343C4—362no—
344C4#6420711yescharacteristic
345C4C2×D3×S411yescharacteristic
346C3—41no—
347C3—81no—
348C3C2×#540311yescharacteristic, complemented
349C2—61no—
350C2—61no—
351C2#1059322612yesdirect product factor
352C2C2×#6420711yescharacteristic
subgroupG/H
centerC22#64207
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C2×D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3C4⋊S4
prime radicalC2×C3×#41⋊C3C22
hypercenterC2×C4D3×S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #10593226C2direct (N × H)
334. C2×C3#5403semidirect
348. C3C2×#5403semidirect
351. C2#10593226direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642652
C2×C3×#9842
C2×C3⋊(#131⋊C3)2
#105932262
C2×#54033
C2×#52043
C2×#37194