Finite Group Databasebeta

← C2×#10593640 #11922998

Subgroups — C2×#10593640 #11922998

Order 1152.

636 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 81 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×#64267C211yesmaximal, characteristic
2C2×#64265C211yesmaximal, characteristic, complemented
3C2×C3×#131⋊C3C211yesmaximal, characteristic, complemented
4#10593640C214yesmaximal, direct product factor
5C2×#5406—33nomaximal
6C2×#5141—31nomaximal
7C2×C3×#41⋊C3C2211yescharacteristic
8#64267—21no—
9#64267C2212yes—
10#64265—21no—
11#64265C2212yescomplemented
12C2×C3⋊GL(2,𝔽3)—21no—
13C2×C3⋊#226—21no—
14C2×#3744—41nomaximal
15C3×#131⋊C3C2212yescomplemented
16C2×#986—33no—
17C2×#984—33no—
18C2×C3×#131D311yescharacteristic, complemented
19C2×#951—31no—
20C2×#949—31no—
21C22×#204—31no—
22C2×#131⋊C3D313yescomplemented
23#5406—312no—
24#5141—34no—
25#5141—34no—
26C2×#824—31no—
27C2×#823—31no—
28C2×#819—31no—
29C2×C4⋊(C3⋊D3)—41no—
30C2×#634—41no—
31C3×#41⋊C3D411yescharacteristic
32C3×#41⋊C3C2311yescharacteristic
33C2×C3×SL(2,𝔽3)D411yescharacteristic
34C3⋊GL(2,𝔽3)—22no—
35C3⋊#226—22no—
36C2×C32×C8—41no—
37#3744—44no—
38C2×#471—91noSylow
39C2×C3×#41C2×D311yescharacteristic
40C22×D12—31no—
41C22×Dic6—31no—
42C2×#41⋊C3C2×D313yes—
43#986—36no—
44#986—63no—
45#984—36no—
46#984—63no—
47C2×GL(2,𝔽3)—63no—
48C2×#226—63no—
49C3×#131—32no—
50C3×#131C2×D312yescomplemented
51C2×C3×M16—31no—
52C22×C3×C8—31no—
53#951—32no—
54#951—32no—
55#951—61no—
56#951—61no—
57#949—32no—
58#949—32no—
59#949—61no—
60#949—61no—
61C2×#216—61no—
62C2×#215—61no—
63C2×#214—61no—
64C2×#213—61no—
65C2×#208—31no—
66C2×#208—31no—
67C2×#204—34no—
68C2×#204—61no—
69C2×#204—62no—
70C2×#204—61no—
71C2×#204—123no—
72#131⋊C3C2×D316yescomplemented
73#824—34no—
74#823—34no—
75#819—34no—
76C22×C3⋊D3—81no—
77C2×C32×C4—41no—
78C2×C3⋊Dic3—81no—
79C4⋊(C3⋊D3)—42no—
80C4⋊(C3⋊D3)—81no—
81#634—42no—
82#634—81no—
83C3×SL(2,𝔽3)C2×D411yescharacteristic
84C32×C8—42no—
85C2×#137—91no—
86C2×AGL(1,ℤ/8)—91no—
87C22×SD16—91no—
88C2×#131C3⋊D311yescharacteristic, complemented
89#471—94no—
90#471—94no—
91C2×#108—91no—
92C2×#101—91no—
93C2×#100—91no—
94C23×D3—61no—
95C3×#41—31no—
96C3×#41—31no—
97C3×#41D1211yescharacteristic
98C3×#41C22×D311yescharacteristic
99C2×C3×Q8D1211yescharacteristic
100C2×C3×D4—31no—
101C22×C3×C4—31no—
102C22×Dic3—61no—
103C2×D12—32no—
104C2×D12—61no—
105C2×D12—61no—
106C2×D12—61no—
107C2×D12—61no—
108C2×D12—61no—
109C2×D12—123no—
110C2×Dic6—32no—
111C2×Dic6—61no—
112C2×Dic6—61no—
113C2×Dic6—61no—
114C2×Dic6—61no—
115C2×Dic6—61no—
116C2×Dic6—123no—
117#41⋊C3D1213yes—
118#41⋊C3C22×D313yes—
119C2×SL(2,𝔽3)D1213yes—
120GL(2,𝔽3)—66no—
121#226—66no—
122C3×M16—32no—
123C3×M16—61no—
124C2×C3×C8—31no—
125C2×C3×C8—32no—
126C2×C3×C8—32no—
127C2×C3×C8—43no—
128C2×C3×C8S411yescharacteristic
129#216—62no—
130#216—62no—
131#215—62no—
132#215—62no—
133#214—62no—
134#214—62no—
135#213—62no—
136#213—62no—
137#208—32no—
138#208—32no—
139#208—61no—
140#208—61no—
141C2×C3⋊C8—61no—
142C2×C3⋊C8—61no—
143#204—64no—
144#204—64no—
145#204—1212no—
146C22×C32—41no—
147C2×C3⋊D3—82no—
148C2×C3⋊D3—162no—
149C32×C4—41no—
150C32×C4—41no—
151C3⋊Dic3—82no—
152C2×#41C2×C3⋊D311yescharacteristic
153C22×Q8—91no—
154C22×D4—91no—
155#137—92no—
156#137—92no—
157#137—181no—
158#137—181no—
159AGL(1,ℤ/8)—92no—
160AGL(1,ℤ/8)—92no—
161AGL(1,ℤ/8)—181no—
162AGL(1,ℤ/8)—181no—
163C2×Q16—181no—
164C2×SD16—94no—
165C2×SD16—181no—
166C2×SD16—182no—
167C2×SD16—181no—
168C2×SD16—181no—
169C2×SD16—181no—
170C2×D8—181no—
171#131—32no—
172#131C2×C3⋊D312yescomplemented
173C2×M16—31no—
174C2×M16—91no—
175C2×M16—91no—
176C22×C8—31no—
177#108—94no—
178#101—94no—
179#100—94no—
180C23×C3—31no—
181C22×D3—62no—
182C22×D3—121no—
183C22×D3—121no—
184C22×D3—243no—
185C22×D3—242no—
186C3×Q8—31no—
187C3×Q8C2×D1211yescharacteristic
188C3×D4—31no—
189C3×D4—31no—
190C3×D4—61no—
191C2×C3×C4—31no—
192C2×C3×C4—31no—
193C2×C3×C4—31no—
194C2×C3×C4—31no—
195C2×C3×C4—31no—
196C2×C3×C4—43no—
197C2×C3×C4C2×S411yescharacteristic
198C2×Dic3—62no—
199C2×Dic3—121no—
200C2×Dic3—121no—
201C2×Dic3—243no—
202D12—62no—
203D12—62no—
204D12—126no—
205D12—121no—
206D12—121no—
207D12—243no—
208Dic6—62no—
209Dic6—62no—
210Dic6—126no—
211Dic6—121no—
212Dic6—121no—
213Dic6—243no—
214SL(2,𝔽3)C2×D1213yes—
215C3×C8—32no—
216C3×C8—46no—
217C3×C8C2×S412yes—
218C3⋊C8—62no—
219C3⋊C8—62no—
220C2×C32—41no—
221C2×C32—42no—
222C3⋊D3—162no—
223C24—181no—
224#41—31no—
225#41—31no—
226#41C4⋊(C3⋊D3)11yescharacteristic
227#41C22×C3⋊D311yescharacteristic
228C2×Q8—92no—
229C2×Q8—181no—
230C2×Q8—181no—
231C2×Q8—181no—
232C2×Q8—181no—
233C2×Q8—181no—
234C2×Q8C4⋊(C3⋊D3)11yescharacteristic
235C2×D4—31no—
236C2×D4—92no—
237C2×D4—181no—
238C2×D4—181no—
239C2×D4—181no—
240C2×D4—181no—
241C2×D4—181no—
242C22×C4—31no—
243C22×C4—181no—
244Q16—182no—
245Q16—182no—
246SD16—184no—
247SD16—182no—
248SD16—182no—
249SD16—182no—
250SD16—182no—
251SD16—184no—
252D8—182no—
253D8—182no—
254M16—32no—
255M16—61no—
256M16—92no—
257M16—92no—
258M16—181no—
259M16—181no—
260C2×C8—31no—
261C2×C8—32no—
262C2×C8—32no—
263C2×C8—181no—
264C2×C8—181no—
265C2×C8C3⋊S411yescharacteristic
266C22×C3—31no—
267C22×C3—31no—
268C22×C3—43no—
269C22×C3—62no—
270C22×C3C4⋊S411yescharacteristic
271C2×D3—122no—
272C2×D3—246no—
273C2×D3—242no—
274C2×D3—242no—
275C2×D3—242no—
276C2×D3—486no—
277C3×C4—31no—
278C3×C4—31no—
279C3×C4—43no—
280C3×C4—43no—
281C3×C4C4⋊S411yescharacteristic
282C3×C4C22×S411yescharacteristic
283Dic3—122no—
284Dic3—246no—
285C32—41noSylow
286C23—31no—
287C23—182no—
288C23—361no—
289C23—361no—
290C23—722no—
291Q8—31no—
292Q8—182no—
293Q8—182no—
294Q8—361no—
295Q8—361no—
296Q8C2×C4⋊(C3⋊D3)11yescharacteristic
297D4—31no—
298D4—31no—
299D4—61no—
300D4—182no—
301D4—182no—
302D4—361no—
303D4—361no—
304C2×C4—31no—
305C2×C4—31no—
306C2×C4—31no—
307C2×C4—31no—
308C2×C4—31no—
309C2×C4—182no—
310C2×C4—361no—
311C2×C4—361no—
312C2×C4C2×C3⋊S411yescharacteristic
313C8—32no—
314C8—182no—
315C8—182no—
316C8C2×C3⋊S412yes—
317C2×C3—46no—
318C2×C3—43no—
319C2×C3—61no—
320C2×C3—61no—
321C2×C3#540612yescomplemented
322C2×C3C2×C4⋊S411yescharacteristic
323D3—242no—
324D3—486no—
325C22—31no—
326C22—31no—
327C22—62no—
328C22—362no—
329C22—722no—
330C22—722no—
331C22—722no—
332C22C4⋊(C3⋊S4)11yescharacteristic
333C4—31no—
334C4—31no—
335C4—362no—
336C4C4⋊(C3⋊S4)11yescharacteristic
337C4C22×C3⋊S411yescharacteristic
338C3—43no—
339C3C2×#540611yescharacteristic, complemented
340C2—61no—
341C2—61no—
342C2—722no—
343C2#1059364012yesdirect product factor
344C2C2×C4⋊(C3⋊S4)11yescharacteristic
subgroupG/H
centerC22C4⋊(C3⋊S4)
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C22×C3⋊S4
FittingC2×C3×#131D3
socleC22×C3C4⋊S4
prime radicalC2×#64267C2
hypercenterC2×C8C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#64265C2semidirect
3. C2×C3×#131⋊C3C2semidirect
4. #10593640C2direct (N × H)
11. #64265C22semidirect
15. C3×#131⋊C3C22semidirect
18. C2×C3×#131D3semidirect
22. C2×#131⋊C3D3semidirect
50. C3×#131C2×D3semidirect
72. #131⋊C3C2×D3semidirect
88. C2×#131C3⋊D3semidirect
172. #131C2×C3⋊D3semidirect
321. C2×C3#5406semidirect
339. C3C2×#5406semidirect
343. C2#10593640direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642672
C2×#642652
C2×C3×#131⋊C32
#105936402
C2×#54063
C2×#51413
C2×#37444