Finite Group Databasebeta

← C2×#10593339 #11808364

Subgroups — C2×#10593339 #11808364

Order 1152.

1110 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 183 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×#3773C212yesmaximal
2C2×#63900C211yesmaximal, characteristic
3C2×#63883C211yesmaximal, characteristic
4C2×#63781C211yesmaximal, characteristic
5C2×#63737C212yesmaximal
6#10593339C218yesmaximal, direct product factor
7C23×#157C2212yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#624C2211yescharacteristic
10C22×#624C2212yes—
11C22×#624C2211yescharacteristic
12C2×#3773—28no—
13C2×#3773C2218yes—
14C2×C3×C4⋊Dic3—21no—
15C2×C3×Dic3⋊C4—21no—
16C2×#3724—21no—
17C2×Dic3⋊Dic3—21no—
18#63900—22no—
19#63900C2214yes—
20#63883—22no—
21#63883C2214yes—
22#63781C2214yes—
23#63737C2218yes—
24C2×D3×C4⋊C4—61no—
25C2×D3×C4⋊C4—61no—
26C23×C3⋊D3C2311yescharacteristic
27C22×#157—24no—
28C22×#157—24no—
29C22×#157Q818yes—
30C22×#157C2314yes—
31C22×C32×C4D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C2×C4×C3⋊D3—24no—
34C2×C4×C3⋊D3D412yes—
35C2×C4×C3⋊D3C2312yes—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C22×C3×Dic3—22no—
39C2×#624—21no—
40C2×#624—22no—
41C2×#624—24no—
42C2×#624—24no—
43C2×#624—24no—
44C2×#624—21no—
45C2×#624—22no—
46C2×#624D414yes—
47C2×#624C2312yes—
48C2×#624C2314yes—
49C2×#624C2312yes—
50#3773—216no—
51C3×C4⋊Dic3—24no—
52C3×Dic3⋊C4—24no—
53#3724—24no—
54Dic3⋊Dic3—24no—
55C2×#398—91nomaximal, Sylow
56C22×C4×D3—61no—
57C22×C4×D3—61no—
58C22×C4×D3—62no—
59C22×C4×D3—61no—
60C22×C4×D3—61no—
61C2×C3×C4⋊C4—61no—
62C2×C3×C4⋊C4—61no—
63C2×C4⋊Dic3—21no—
64C2×C4⋊Dic3—61no—
65C2×Dic3⋊C4—21no—
66C2×Dic3⋊C4—61no—
67C2×Dic3⋊C4—62no—
68D3×C4⋊C4—64no—
69D3×C4⋊C4—64no—
70D3×C4⋊C4—64no—
71D3×C4⋊C4—64no—
72C23×C32C2×D411yescharacteristic
73C22×C3⋊D3C2×D411yescharacteristic
74C22×C3⋊D3C2×D412yes—
75C22×C3⋊D3C2×Q814yes—
76C22×C3⋊D3#4112yes—
77C22×C3⋊D3#4114yes—
78C22×C3⋊D3C2411yescharacteristic
79C2×#157—216no—
80C2×#157—24no—
81C2×#157—24no—
82C2×#157C2×Q818yes—
83C2×C32×C4—22no—
84C2×C32×C4C2×D412yes—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3C2×D412yes—
87C4×C3⋊D3—24no—
88C4×C3⋊D3—24no—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—22no—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—44no—
94C2×C3×Dic3—42no—
95#624—24no—
96#624—22no—
97#624—24no—
98#624—24no—
99#624—24no—
100#624—44no—
101#624—42no—
102#624C2×D414yes—
103C22×C4⋊C4—91no—
104C22×C4⋊C4—91no—
105C22×C4⋊C4—92no—
106#398—98no—
107C2×#95—91no—
108C2×#95—92no—
109C23×D3—61no—
110C23×D3—61no—
111C22×C3×C4—21no—
112C22×C3×C4—21no—
113C22×C3×C4—61no—
114C22×C3×C4—61no—
115C22×C3×C4—62no—
116C22×Dic3—21no—
117C22×Dic3—21no—
118C22×Dic3—22no—
119C22×Dic3—61no—
120C22×Dic3—61no—
121C2×C4×D3—62no—
122C2×C4×D3—64no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—62no—
126C2×C4×D3—64no—
127C2×C4×D3—62no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C2×C4×D3—64no—
131C2×C4×D3—68no—
132C2×C4×D3—62no—
133C2×C4×D3—64no—
134C2×C4×D3—124no—
135C2×C4×D3—124no—
136C2×C4×D3—124no—
137C2×C4×D3—124no—
138C3×C4⋊C4—64no—
139C3×C4⋊C4—64no—
140C4⋊Dic3—24no—
141C4⋊Dic3—64no—
142Dic3⋊C4—24no—
143Dic3⋊C4—64no—
144Dic3⋊C4—68no—
145C22×C32#12112yes—
146C22×C32#12312yes—
147C22×C32C4⋊Q812yes—
148C22×C32C22×D411yescharacteristic
149C2×C3⋊D3#12112yes—
150C2×C3⋊D3C22⋊Q818yes—
151C2×C3⋊D3#12312yes—
152C2×C3⋊D3#12518yes—
153C2×C3⋊D3C4⋊Q812yes—
154C2×C3⋊D3C22×D411yescharacteristic
155C2×C3⋊D3C22×Q812yes—
156C2×C3⋊D3C2×#4112yes—
157C2×C3⋊D3C2×#4111yescharacteristic
158#157—28no—
159C32×C4—22no—
160C3⋊Dic3—22no—
161C3×Dic3—24no—
162C3×Dic3—44no—
163C3×Dic3—42no—
164C23×C4—91no—
165C23×C4—92no—
166C23×C4—91no—
167C23×C4—92no—
168C23×C4—91no—
169C2×C4⋊C4—61no—
170C2×C4⋊C4—61no—
171C2×C4⋊C4—94no—
172C2×C4⋊C4—94no—
173C2×C4⋊C4—98no—
174C2×C4⋊C4—182no—
175C2×C4⋊C4—182no—
176C2×C4⋊C4—181no—
177C2×C4⋊C4—181no—
178C2×C4⋊C4—188no—
179#95—94no—
180#95—98no—
181C23×C3—21no—
182C23×C3—21no—
183C22×D3—61no—
184C22×D3—61no—
185C22×D3—62no—
186C22×D3—62no—
187C22×D3—64no—
188C22×D3—64no—
189C22×D3—62no—
190C22×D3—64no—
191C22×D3—62no—
192C22×D3—64no—
193C22×D3—61no—
194C22×D3—61no—
195C2×C3×C4—24no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—42no—
199C2×C3×C4—62no—
200C2×C3×C4—64no—
201C2×C3×C4—62no—
202C2×C3×C4—64no—
203C2×C3×C4—124no—
204C2×C3×C4—122no—
205C2×Dic3—22no—
206C2×Dic3—24no—
207C2×Dic3—22no—
208C2×Dic3—24no—
209C2×Dic3—44no—
210C2×Dic3—42no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—64no—
214C2×Dic3—122no—
215C4×D3—64no—
216C4×D3—68no—
217C4×D3—64no—
218C4×D3—68no—
219C4×D3—68no—
220C4×D3—124no—
221C4×D3—124no—
222C4×D3—124no—
223C4×D3—124no—
224C4×D3—124no—
225C4×D3—128no—
226C4×D3—124no—
227C2×C32#39814yescomplemented
228C2×C32C2×#12111yescharacteristic
229C2×C32C2×#12311yescharacteristic
230C2×C32C2×C4⋊Q811yescharacteristic
231C3⋊D3#39814yescomplemented
232C3⋊D3C2×C22⋊Q812yes—
233C3⋊D3C2×#12512yes—
234C24—91no—
235C22×C4—61no—
236C22×C4—62no—
237C22×C4—61no—
238C22×C4—92no—
239C22×C4—94no—
240C22×C4—92no—
241C22×C4—94no—
242C22×C4—98no—
243C22×C4—94no—
244C22×C4—91no—
245C22×C4—92no—
246C22×C4—92no—
247C22×C4—184no—
248C22×C4—181no—
249C22×C4—182no—
250C22×C4—182no—
251C22×C4—181no—
252C22×C4—184no—
253C22×C4—184no—
254C22×C4—184no—
255C22×C4—184no—
256C22×C4—184no—
257C22×C4GO+(4,𝔽2)11yescharacteristic
258C4⋊C4—64no—
259C4⋊C4—64no—
260C4⋊C4—184no—
261C4⋊C4—184no—
262C4⋊C4—1816no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—22no—
271C2×D3—62no—
272C2×D3—62no—
273C2×D3—61no—
274C2×D3—61no—
275C2×D3—62no—
276C2×D3—62no—
277C2×D3—62no—
278C2×D3—61no—
279C2×D3—61no—
280C2×D3—62no—
281C2×D3—68no—
282C2×D3—68no—
283C2×D3—68no—
284C2×D3—68no—
285C2×D3—62no—
286C2×D3—62no—
287C2×D3—62no—
288C2×D3—62no—
289C3×C4—24no—
290C3×C4—42no—
291C3×C4—64no—
292C3×C4—124no—
293C3×C4—122no—
294Dic3—24no—
295Dic3—44no—
296Dic3—42no—
297Dic3—64no—
298Dic3—122no—
299C32C2×#39811yescharacteristic, complemented, Sylow
300C23—91no—
301C23—91no—
302C23—94no—
303C23—92no—
304C23—92no—
305C23—94no—
306C23C2×GO+(4,𝔽2)11yescharacteristic
307C2×C4—22no—
308C2×C4—62no—
309C2×C4—64no—
310C2×C4—64no—
311C2×C4—62no—
312C2×C4—94no—
313C2×C4—98no—
314C2×C4—92no—
315C2×C4—124no—
316C2×C4—122no—
317C2×C4—184no—
318C2×C4—184no—
319C2×C4—182no—
320C2×C4—184no—
321C2×C4—184no—
322C2×C4—184no—
323C2×C4—184no—
324C2×C4—184no—
325C2×C4—1816no—
326C2×C4—184no—
327C2×C4—182no—
328C2×C4—364no—
329C2×C4—362no—
330C2×C4C2×GO+(4,𝔽2)12yes—
331C2×C3—24no—
332C2×C3—24no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339D3—62no—
340D3—62no—
341D3—62no—
342D3—62no—
343D3—64no—
344D3—64no—
345C22—98no—
346C22—98no—
347C22—92no—
348C22—92no—
349C22—91no—
350C22—91no—
351C22—92no—
352C22—92no—
353C22—92no—
354C22#6422212yes—
355C22#6423012yes—
356C22#6423312yes—
357C22C22×GO+(4,𝔽2)11yescharacteristic
358C4—22no—
359C4—64no—
360C4—124no—
361C4—122no—
362C4—188no—
363C4—182no—
364C3—21no—
365C3—21no—
366C2—92no—
367C2—94no—
368C2—92no—
369C2#1059333914yesdirect product factor
370C2C2×#6422211yescharacteristic
371C2C2×#6423011yescharacteristic
372C2C2×#6423311yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊D3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#398
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #10593339C2direct (N × H)
227. C2×C32#398semidirect
231. C3⋊D3#398semidirect
299. C32C2×#398semidirect
369. C2#10593339direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37732
C2×#639002
C2×#638832
C2×#637812
C2×#637372
#105933392
C2×#3989