Finite Group Databasebeta

← C32×#1441 #11768490

Subgroups — C32×#1441 #11768490

Order 1152.

1692 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic
2C22×C32×C4⋊C4C211yesmaximal, characteristic
3C2×C32×#95C212yesmaximal
4C2×C32×#95C212yesmaximal
5C2×C32×#95C211yesmaximal, characteristic
6C3×#1441C314yesmaximal, direct product factor
7C23×C32×C4C2211yescharacteristic
8C23×C32×C4C2212yes—
9C23×C32×C4C2212yes—
10C23×C32×C4C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C2×C32×C4⋊C4—24no—
13C2×C32×C4⋊C4—22no—
14C2×C32×C4⋊C4—22no—
15C2×C32×C4⋊C4—22no—
16C2×C32×C4⋊C4C414yescomplemented
17C32×#95—24no—
18C32×#95—22no—
19C32×#95—24no—
20C22×C3×C4⋊C4C2×C314yes—
21C22×C3×C4⋊C4C2×C314yes—
22C2×C3×#95C2×C318yes—
23C2×C3×#95C2×C318yes—
24C2×C3×#95C2×C314yes—
25C24×C32C2311yescharacteristic
26C22×C32×C4—21no—
27C22×C32×C4—21no—
28C22×C32×C4—22no—
29C22×C32×C4—21no—
30C22×C32×C4—21no—
31C22×C32×C4—22no—
32C22×C32×C4—21no—
33C22×C32×C4—21no—
34C22×C32×C4—22no—
35C22×C32×C4—22no—
36C22×C32×C4—22no—
37C22×C32×C4—22no—
38C22×C32×C4—22no—
39C22×C32×C4—22no—
40C22×C32×C4—22no—
41C22×C32×C4—22no—
42C22×C32×C4—22no—
43C22×C32×C4—22no—
44C22×C32×C4—22no—
45C22×C32×C4—22no—
46C22×C32×C4—22no—
47C22×C32×C4—22no—
48C22×C32×C4C2×C412yes—
49C22×C32×C4C2×C412yes—
50C22×C32×C4C2×C412yes—
51C22×C32×C4D414yes—
52C22×C32×C4D412yes—
53C22×C32×C4D412yes—
54C22×C32×C4D412yes—
55C22×C32×C4Q814yes—
56C22×C32×C4Q812yes—
57C32×C4⋊C4—28no—
58C32×C4⋊C4—28no—
59#1441C3211yescharacteristic, direct product factor, Sylow
60C23×C3×C4C22×C314yes—
61C23×C3×C4C22×C318yes—
62C23×C3×C4C22×C318yes—
63C23×C3×C4C22×C314yes—
64C23×C3×C4C22×C314yes—
65C2×C3×C4⋊C4—216no—
66C2×C3×C4⋊C4—28no—
67C2×C3×C4⋊C4—28no—
68C2×C3×C4⋊C4—28no—
69C2×C3×C4⋊C4C3×C4116yescomplemented
70C3×#95—216no—
71C3×#95—28no—
72C3×#95—216no—
73C23×C32C22×C411yescharacteristic
74C23×C32C2×D411yescharacteristic
75C23×C32C2×D411yescharacteristic
76C23×C32C2×D411yescharacteristic
77C23×C32C2×D412yes—
78C23×C32C2×Q811yescharacteristic
79C23×C32C2×Q812yes—
80C23×C32#4111yescharacteristic
81C23×C32#4111yescharacteristic
82C23×C32#4112yes—
83C23×C32#4112yes—
84C2×C32×C4—22no—
85C2×C32×C4—22no—
86C2×C32×C4—24no—
87C2×C32×C4—22no—
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4—24no—
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4—24no—
96C2×C32×C4—24no—
97C2×C32×C4—24no—
98C2×C32×C4—24no—
99C2×C32×C4—24no—
100C2×C32×C4—24no—
101C2×C32×C4—24no—
102C2×C32×C4—41no—
103C2×C32×C4—42no—
104C2×C32×C4—42no—
105C2×C32×C4—42no—
106C2×C32×C4—42no—
107C2×C32×C4—42no—
108C2×C32×C4—42no—
109C2×C32×C4—41no—
110C2×C32×C4—42no—
111C2×C32×C4—42no—
112C2×C32×C4—42no—
113C2×C32×C4C22⋊C414yes—
114C2×C32×C4C4⋊C414yescomplemented
115C22×C4⋊C4C2×C3211yescharacteristic
116C22×C4⋊C4C2×C3211yescharacteristic
117C2×#95C2×C3212yes—
118C2×#95C2×C3212yes—
119C2×#95C2×C3211yescharacteristic
120C24×C3C23×C314yes—
121C22×C3×C4—24no—
122C22×C3×C4—24no—
123C22×C3×C4—28no—
124C22×C3×C4—24no—
125C22×C3×C4—24no—
126C22×C3×C4—28no—
127C22×C3×C4—28no—
128C22×C3×C4—28no—
129C22×C3×C4—28no—
130C22×C3×C4—28no—
131C22×C3×C4—28no—
132C22×C3×C4—24no—
133C22×C3×C4—24no—
134C22×C3×C4—28no—
135C22×C3×C4—28no—
136C22×C3×C4—28no—
137C22×C3×C4—28no—
138C22×C3×C4—28no—
139C22×C3×C4—28no—
140C22×C3×C4—28no—
141C22×C3×C4—28no—
142C22×C3×C4—28no—
143C22×C3×C4C2×C3×C418yes—
144C22×C3×C4C2×C3×C418yes—
145C22×C3×C4C2×C3×C418yes—
146C22×C3×C4C3×D4116yes—
147C22×C3×C4C3×D418yes—
148C22×C3×C4C3×D418yes—
149C22×C3×C4C3×D418yes—
150C22×C3×C4C3×Q8116yes—
151C22×C3×C4C3×Q818yes—
152C3×C4⋊C4—232no—
153C3×C4⋊C4—232no—
154C22×C32C2×C22⋊C411yescharacteristic
155C22×C32C2×C4⋊C411yescharacteristic
156C22×C32#11711yescharacteristic
157C22×C32C4×D412yes—
158C22×C32C4×Q812yes—
159C22×C32#12011yescharacteristic
160C22×C32#12111yescharacteristic
161C22×C32#12111yescharacteristic
162C22×C32#12112yes—
163C22×C32#12112yes—
164C22×C32C22⋊Q811yescharacteristic
165C22×C32C22⋊Q811yescharacteristic
166C22×C32C22⋊Q812yes—
167C22×C32C22⋊Q812yes—
168C22×C32C22⋊Q812yes—
169C22×C32#12311yescharacteristic
170C22×C32#12312yes—
171C22×C32#12411yescharacteristic
172C22×C32#12512yes—
173C22×C32#12512yes—
174C22×C32#12612yes—
175C22×C32C4⋊Q812yes—
176C22×C32C4⋊Q811yescharacteristic
177C32×C4—24no—
178C32×C4—24no—
179C32×C4—42no—
180C32×C4—44no—
181C32×C4—44no—
182C23×C4C22×C3211yescharacteristic
183C23×C4C22×C3212yes—
184C23×C4C22×C3212yes—
185C23×C4C22×C3211yescharacteristic
186C23×C4C22×C3211yescharacteristic
187C2×C4⋊C4—24no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4C32×C414yescomplemented
192#95—24no—
193#95—22no—
194#95—24no—
195C23×C3C22×C3×C414yes—
196C23×C3C2×C3×D414yes—
197C23×C3C2×C3×D414yes—
198C23×C3C2×C3×D414yes—
199C23×C3C2×C3×D418yes—
200C23×C3C2×C3×Q814yes—
201C23×C3C2×C3×Q818yes—
202C23×C3C3×#4114yes—
203C23×C3C3×#4114yes—
204C23×C3C3×#4118yes—
205C23×C3C3×#4118yes—
206C2×C3×C4—28no—
207C2×C3×C4—28no—
208C2×C3×C4—216no—
209C2×C3×C4—28no—
210C2×C3×C4—28no—
211C2×C3×C4—28no—
212C2×C3×C4—216no—
213C2×C3×C4—28no—
214C2×C3×C4—28no—
215C2×C3×C4—28no—
216C2×C3×C4—28no—
217C2×C3×C4—216no—
218C2×C3×C4—216no—
219C2×C3×C4—216no—
220C2×C3×C4—216no—
221C2×C3×C4—216no—
222C2×C3×C4—216no—
223C2×C3×C4—216no—
224C2×C3×C4—44no—
225C2×C3×C4—48no—
226C2×C3×C4—48no—
227C2×C3×C4—48no—
228C2×C3×C4—48no—
229C2×C3×C4—48no—
230C2×C3×C4—48no—
231C2×C3×C4—44no—
232C2×C3×C4—48no—
233C2×C3×C4—48no—
234C2×C3×C4—48no—
235C2×C3×C4C3×C22⋊C4116yes—
236C2×C3×C4C3×C4⋊C4116yescomplemented
237C2×C32#38011yescharacteristic
238C2×C32#38611yescharacteristic
239C2×C32#38712yes—
240C2×C32#38912yes—
241C2×C32#39111yescharacteristic
242C2×C32#39411yescharacteristic
243C2×C32#39511yescharacteristic
244C2×C32#39612yes—
245C2×C32#39811yescharacteristic
246C2×C32#39812yes—
247C2×C32#40011yescharacteristic
248C24C23×C3211yescharacteristic
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4C2×C32×C412yes—
272C22×C4C2×C32×C412yes—
273C22×C4C2×C32×C412yes—
274C22×C4C32×D414yes—
275C22×C4C32×D412yes—
276C22×C4C32×D412yes—
277C22×C4C32×D412yes—
278C22×C4C32×Q814yes—
279C22×C4C32×Q812yes—
280C4⋊C4—28no—
281C4⋊C4—28no—
282C22×C3C2×C3×C22⋊C414yes—
283C22×C3C2×C3×C4⋊C414yes—
284C22×C3C3×#11714yes—
285C22×C3C3×C4×D418yes—
286C22×C3C3×C4×Q818yes—
287C22×C3C3×#12014yes—
288C22×C3C3×#12114yes—
289C22×C3C3×#12114yes—
290C22×C3C3×#12118yes—
291C22×C3C3×#12118yes—
292C22×C3C3×C22⋊Q814yes—
293C22×C3C3×C22⋊Q814yes—
294C22×C3C3×C22⋊Q818yes—
295C22×C3C3×C22⋊Q818yes—
296C22×C3C3×C22⋊Q818yes—
297C22×C3C3×#12314yes—
298C22×C3C3×#12318yes—
299C22×C3C3×#12414yes—
300C22×C3C3×#12518yes—
301C22×C3C3×#12518yes—
302C22×C3C3×#12618yes—
303C22×C3C3×C4⋊Q818yes—
304C22×C3C3×C4⋊Q814yes—
305C3×C4—216no—
306C3×C4—216no—
307C3×C4—48no—
308C3×C4—416no—
309C3×C4—416no—
310C32#144111yescharacteristic, direct product factor, Sylow
311C23C22×C32×C411yescharacteristic
312C23C2×C32×D411yescharacteristic
313C23C2×C32×D411yescharacteristic
314C23C2×C32×D411yescharacteristic
315C23C2×C32×D412yes—
316C23C2×C32×Q811yescharacteristic
317C23C2×C32×Q812yes—
318C23C32×#4111yescharacteristic
319C23C32×#4111yescharacteristic
320C23C32×#4112yes—
321C23C32×#4112yes—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—24no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4C32×C22⋊C414yes—
352C2×C4C32×C4⋊C414yescomplemented
353C2×C3C3×#38014yes—
354C2×C3C3×#38614yes—
355C2×C3C3×#38718yes—
356C2×C3C3×#38918yes—
357C2×C3C3×#39114yes—
358C2×C3C3×#39414yes—
359C2×C3C3×#39514yes—
360C2×C3C3×#39618yes—
361C2×C3C3×#39814yes—
362C2×C3C3×#39818yes—
363C2×C3C3×#40014yes—
364C22C2×C32×C22⋊C411yescharacteristic
365C22C2×C32×C4⋊C411yescharacteristic
366C22C32×#11711yescharacteristic
367C22C32×C4×D412yes—
368C22C32×C4×Q812yes—
369C22C32×#12011yescharacteristic
370C22C32×#12111yescharacteristic
371C22C32×#12111yescharacteristic
372C22C32×#12112yes—
373C22C32×#12112yes—
374C22C32×C22⋊Q811yescharacteristic
375C22C32×C22⋊Q811yescharacteristic
376C22C32×C22⋊Q812yes—
377C22C32×C22⋊Q812yes—
378C22C32×C22⋊Q812yes—
379C22C32×#12311yescharacteristic
380C22C32×#12312yes—
381C22C32×#12411yescharacteristic
382C22C32×#12512yes—
383C22C32×#12512yes—
384C22C32×#12612yes—
385C22C32×C4⋊Q812yes—
386C22C32×C4⋊Q811yescharacteristic
387C4—24no—
388C4—24no—
389C4—42no—
390C4—44no—
391C4—44no—
392C3C3×#144114yesdirect product factor
393C2C32×#38011yescharacteristic
394C2C32×#38611yescharacteristic
395C2C32×#38712yes—
396C2C32×#38912yes—
397C2C32×#39111yescharacteristic
398C2C32×#39411yescharacteristic
399C2C32×#39511yescharacteristic
400C2C32×#39612yes—
401C2C32×#39811yescharacteristic
402C2C32×#39812yes—
403C2C32×#40011yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C32C23
commutatorC23C22×C32×C4
Frattini, cosocleC24C23×C32
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C32 ◁ G

Complements

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

NH ≅ G/Ntype
6. C3×#1441C3direct (N × H)
16. C2×C32×C4⋊C4C4semidirect
59. #1441C32direct (N × H)
69. C2×C3×C4⋊C4C3×C4semidirect
114. C2×C32×C4C4⋊C4semidirect
191. C2×C4⋊C4C32×C4semidirect
236. C2×C3×C4C3×C4⋊C4semidirect
310. C32#1441direct (N × H)
352. C2×C4C32×C4⋊C4semidirect
392. C3C3×#1441direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C2×C32×#952
C3×#14413