Finite Group Databasebeta

← #25004208

Subgroups — #25004208

Order 11008.

870 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582873C211yesmaximal, characteristic
2#19143040C211yesmaximal, characteristic
3#19134314C212yesmaximal, complemented
4C2×#14582655C212yesmaximal, complemented
5C43×#2311C211yesmaximal, characteristic
6C22×#10621877C2212yes—
7C2×#13063284C2212yes—
8#14582873—24no—
9C2×#13063240—22no—
10#14582866—24no—
11#14582863—22no—
12#14582661—24no—
13#14582655—24no—
14C22×#41×C43C2211yescharacteristic
15C2×#117×C43C2211yescharacteristic
16C22×C4⋊C4×C43C2211yescharacteristic
17C43×#391C412yescomplemented
18C43×#390C412yescomplemented
19C43×#386—22no—
20C43×#380—22no—
21C2×#10621877—22no—
22C2×#10621877—22no—
23C2×#10621877—22no—
24C2×#10621877—22no—
25C2×#10621877—22no—
26C2×#10621877—22no—
27C22×C43⋊C8D414yes—
28#13063284—22no—
29#13063284—22no—
30#13063284—22no—
31#13063284D414yes—
32C2×C4⋊Dic43—22no—
33C2×C22⋊Dic43—22no—
34C2×C4×Dic43—22no—
35#13063240—28no—
36C22⋊(C43⋊C8)—28no—
37C2×#41×C43—22no—
38C2×#41×C43—22no—
39C2×#41×C43—22no—
40C2×#41×C43—22no—
41C2×#41×C43—22no—
42C2×#41×C43—22no—
43C22×Q8×C43C2×C411yescharacteristic
44C22×D4×C43C2×C411yescharacteristic
45C22×D4×C43D412yes—
46C23×C4×C43—21no—
47C23×C4×C43D412yes—
48C23×C4×C43C2311yescharacteristic
49#117×C43—22no—
50#117×C43—22no—
51C2×C4⋊C4×C43—22no—
52C2×C4⋊C4×C43—22no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43C2×C412yes—
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—24no—
58C2×C42×C43C2×C412yes—
59#95×C43—24no—
60C24×C43C22⋊C412yes—
61C24×C43C2×D411yescharacteristic
62#41×C43—42no—
63#41×C43—42no—
64#41×C43—42no—
65#41×C43—42no—
66#41×C43—42no—
67#41×C43—42no—
68#41×C43—42no—
69#41×C43—42no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C2×Q8×C43—22no—
73C2×Q8×C43—22no—
74C2×D4×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—22no—
77C2×D4×C43—22no—
78C2×D4×C43—22no—
79C2×D4×C43—24no—
80C2×D4×C43—24no—
81C2×D4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43—24no—
84C22×C4×C43—24no—
85C22×C4×C43—22no—
86C22×C4×C43—22no—
87C22×C4×C43—22no—
88C22×C4×C43—42no—
89C22×C4×C43—82no—
90C22×C4×C43C22⋊C412yes—
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D412yes—
94C22×C4×C43C2×D412yes—
95C22×C4×C43#4112yes—
96C22×C4×C43#4112yes—
97C22×C4×C43#4112yes—
98C22×C4×C43#4112yes—
99C22×Dic43—42no—
100C4⋊C4×C43—24no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—42no—
103C4⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—84no—
107C42×C43—24no—
108C22⋊Dic43—24no—
109C22⋊Dic43—42no—
110C4⋊Dic43—24no—
111C4⋊Dic43—42no—
112C4×Dic43—24no—
113C4×Dic43—42no—
114#10621877—42no—
115#10621877—42no—
116#10621877—42no—
117#10621877—42no—
118C2×C43⋊C8—24no—
119C2×C43⋊C8—24no—
120C2×C43⋊C8—24no—
121C23×C43—22no—
122C23×C43—22no—
123C23×C43—22no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—42no—
127C23×C43—42no—
128C23×C43C2×C22⋊C411yescharacteristic
129C23×C43#12011yescharacteristic
130C23×C43#12112yes—
131C23×C43#12311yescharacteristic
132C23×C43#12312yes—
133Q8×C43—42no—
134Q8×C43—42no—
135D4×C43—44no—
136D4×C43—44no—
137D4×C43—42no—
138D4×C43—42no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—44no—
143C2×C4×C43—44no—
144C2×C4×C43—42no—
145C2×C4×C43—44no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—84no—
150C2×C4×C43#11711yescharacteristic
151C2×C4×C43#11711yescharacteristic
152C2×C4×C43C4×D412yes—
153C2×C4×C43C4×D412yes—
154C2×C4×C43#12011yescharacteristic
155C2×C4×C43#12112yes—
156C2×C4×C43#12112yes—
157C2×C4×C43#12112yes—
158C2×C4×C43#12311yescharacteristic
159C2×C4×C43#12312yes—
160C2×C4×C43#12312yes—
161C2×C4×C43#12312yes—
162C2×C4×C43#12412yes—
163C2×C4×C43#12412yes—
164C2×C4×C43#12612yes—
165C2×C4×C43#12612yes—
166C2×Dic43—44no—
167C2×Dic43—82no—
168C2×Dic43—82no—
169C43⋊C8—44no—
170#11154—431nomaximal, Sylow
171C22×C43—21no—
172C22×C43—22no—
173C22×C43—21no—
174C22×C43—22no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—42no—
178C22×C43—44no—
179C22×C43—42no—
180C22×C43—42no—
181C22×C43—42no—
182C22×C43—82no—
183C22×C43#38111yescharacteristic
184C22×C43#38611yescharacteristic
185C22×C43#38611yescharacteristic
186C22×C43#39412yes—
187C22×C43#39712yes—
188C4×C43—42no—
189C4×C43—82no—
190C4×C43—82no—
191C4×C43#38812yes—
192C4×C43#38812yes—
193C4×C43#39412yes—
194C4×C43#39712yes—
195Dic43—84no—
196C2×#410—431no—
197#2879—431no—
198#2311D4311yescharacteristic
199#1736—432no—
200C2×H(3,ℤ/4)—432no—
201C2×C43—22no—
202C2×C43—21no—
203C2×C43—21no—
204C2×C43—22no—
205C2×C43—82no—
206C2×C43#144011yescharacteristic
207C2×C43#190911yescharacteristic
208C2×C43#191011yescharacteristic
209C22×#41C2×D4311yescharacteristic
210C22×M16—432no—
211C2×#117—432no—
212C2×#117C2×D4311yescharacteristic
213C22×C4⋊C4C2×D4311yescharacteristic
214#410—864no—
215C2×#99—862no—
216#408—864no—
217#407—862no—
218#391Dic4312yescomplemented
219#390Dic4312yescomplemented
220#386—22no—
221#380—22no—
222#340—864no—
223H(3,ℤ/4)—864no—
224C43#1115411yescharacteristic, complemented, Sylow
225C2×#41—22no—
226C2×#41—22no—
227C2×#41—22no—
228C2×#41—22no—
229C2×#41—22no—
230C2×#41—22no—
231C22×Q8C2×Dic4311yescharacteristic
232C22×D4C2×Dic4311yescharacteristic
233C22×D4C22⋊D4312yes—
234C23×C4—21no—
235C23×C4C22⋊D4312yes—
236C23×C4C22×D4311yescharacteristic
237C2×M16—862no—
238C2×M16—862no—
239C2×M16—862no—
240C2×M16—862no—
241C2×M16—862no—
242C2×M16—862no—
243C22×C8—434no—
244#117—22no—
245#117—22no—
246#117—434no—
247#117—862no—
248#117—862no—
249#117—862no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—862no—
255C2×C4⋊C4C2×Dic4312yes—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—24no—
258C2×C22⋊C4—862no—
259C2×C42—862no—
260C2×C42C2×Dic4312yes—
261#99—868no—
262C22⋊C8—868no—
263#95—24no—
264C24C22⋊Dic4312yes—
265C24C2×C22⋊D4311yescharacteristic
266#41—42no—
267#41—42no—
268#41—42no—
269#41—42no—
270#41—42no—
271#41—42no—
272#41—42no—
273#41—42no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×D4—22no—
279C2×D4—24no—
280C2×D4—22no—
281C2×D4—24no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—22no—
285C2×D4—22no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—22no—
289C22×C4—24no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—42no—
293C22×C4—82no—
294C22×C4—1722no—
295C22×C4C22⋊Dic4312yes—
296C22×C4#1062189812yes—
297C22×C4#1062189812yes—
298C22×C4D4×D4312yes—
299C22×C4D4×D4312yes—
300C22×C4#1062190012yes—
301C22×C4#1062190012yes—
302C22×C4C22×Dic4311yescharacteristic
303C22×C4C2×C22⋊D4311yescharacteristic
304M16—1722no—
305M16—1722no—
306M16—1722no—
307M16—1722no—
308C2×C8—864no—
309C2×C8—864no—
310C2×C8—864no—
311C4⋊C4—24no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C4⋊C4—864no—
316C4⋊C4—1722no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—84no—
320C22⋊C4—864no—
321C22⋊C4—1722no—
322C42—24no—
323C42—864no—
324C42—1722no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—41no—
329C23—41no—
330C23—42no—
331C23—42no—
332C23C2×C22⋊Dic4311yescharacteristic
333C23#1306329311yescharacteristic
334C23#1306329712yes—
335C23#1306330611yescharacteristic
336C23#1306330812yes—
337Q8—42no—
338Q8—42no—
339D4—44no—
340D4—44no—
341D4—42no—
342D4—42no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—84no—
354C2×C4—3442no—
355C2×C4—3442no—
356C2×C4—1724no—
357C2×C4#1306328411yescharacteristic
358C2×C4#1306328411yescharacteristic
359C2×C4D4×Dic4312yes—
360C2×C4D4×Dic4312yes—
361C2×C4#1306329311yescharacteristic
362C2×C4#1306329712yes—
363C2×C4#1306329812yes—
364C2×C4#1306329812yes—
365C2×C4#1306330611yescharacteristic
366C2×C4#1306330712yes—
367C2×C4#1306330712yes—
368C2×C4#1306330812yes—
369C2×C4#1306331112yes—
370C2×C4#1306331112yes—
371C2×C4#1306331812yes—
372C2×C4#1306331812yes—
373C8—1724no—
374C22—21no—
375C22—22no—
376C22—21no—
377C22—22no—
378C22—41no—
379C22—41no—
380C22—42no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—82no—
386C22#1458276211yescharacteristic
387C22#1458277911yescharacteristic
388C22#1458277911yescharacteristic
389C22#1458281412yes—
390C22#1458282712yes—
391C4—42no—
392C4—82no—
393C4—82no—
394C4—3444no—
395C4#1458279212yes—
396C4#1458279212yes—
397C4#1458281412yes—
398C4#1458282712yes—
399C2—21no—
400C2—22no—
401C2—21no—
402C2—22no—
403C2—82no—
404C2#1913284411yescharacteristic
405C2#1913511811yescharacteristic
406C2#1913512311yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2311C2
socleC22×C43#386
prime radicalC22×#41×C43C22
cosocleC23×C4×C43C23
hypercenter#2311D43
hypocenterC43#11154
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2311

Complements

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

NH ≅ G/Ntype
3. #19134314C2semidirect
4. C2×#14582655C2semidirect
17. C43×#391C4semidirect
18. C43×#390C4semidirect
218. #391Dic43semidirect
219. #390Dic43semidirect
224. C43#11154semidirect

Maximal subgroups

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

subgroupindex
C2×#145828732
#191430402
#191343142
C2×#145826552
C43×#23112
#1115443