Finite Group Databasebeta

← #24988225

Subgroups — #24988225

Order 11008.

744 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063244C211yesmaximal, characteristic, complemented
2#19133193C212yesmaximal
3#19133042C212yesmaximal, complemented
4#19132939C211yesmaximal, characteristic, complemented
5C2×C43×#556C211yesmaximal, characteristic
6#14582956C2212yes—
7C2×#13063244—21no—
8C4×#10621877C2212yes—
9#14582668—21no—
10#14582639—24no—
11Q8⋊(C43⋊C8)—24no—
12#14582625—21no—
13#14582625—21no—
14C43×#556—24no—
15C43×#556—24no—
16C2×C4⋊Q8×C43C411yescharacteristic
17C2×#126×C43—21no—
18C2×#126×C43—21no—
19C2×#124×C43C411yescharacteristic
20C2×#124×C43C2211yescharacteristic
21C2×C22⋊Q8×C43—21no—
22C2×C4×Q8×C43C411yescharacteristic
23C2×C4×Q8×C43C2211yescharacteristic
24C2×C4×Q8×C43C2211yescharacteristic
25C2×C4×D4×C43C411yescharacteristic
26C2×#117×C43—21no—
27C2×#10621877—22no—
28C4⋊(C43⋊C8)—22no—
29#13063244—24no—
30C22⋊(C43⋊C8)—22no—
31#13063236—22no—
32#13063236—22no—
33C4×C43⋊C8—22no—
34C22×Q8×C43C2×C411yescharacteristic
35C22×Q8×C43C2×C411yescharacteristic
36C22×Q8×C43D411yescharacteristic
37C22×D4×C43C2×C411yescharacteristic
38C23×C4×C43—21no—
39C4⋊Q8×C43—22no—
40C4⋊Q8×C43—22no—
41#126×C43—28no—
42#126×C43—28no—
43#124×C43—22no—
44#124×C43—22no—
45#124×C43—22no—
46#124×C43D414yes—
47C22⋊Q8×C43—28no—
48C4×Q8×C43—22no—
49C4×Q8×C43—22no—
50C4×Q8×C43—22no—
51C4×Q8×C43—22no—
52C4×Q8×C43—22no—
53C4×Q8×C43D414yes—
54C4×D4×C43—22no—
55C4×D4×C43—22no—
56#117×C43—28no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43C2×C411yescharacteristic
62C2×C4⋊C4×C43D411yescharacteristic
63C2×C4⋊C4×C43D411yescharacteristic
64C2×C4⋊C4×C43D411yescharacteristic
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43—21no—
69C2×C22⋊C4×C43—21no—
70C2×C42×C43—21no—
71C2×C42×C43—21no—
72C2×C42×C43C2×C411yescharacteristic
73C2×C42×C43C2×C411yescharacteristic
74C2×C42×C43C2311yescharacteristic
75C24×C43—21no—
76C2×Q8×C43—22no—
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43—22no—
80C2×Q8×C43—41no—
81C2×Q8×C43—42no—
82C2×Q8×C43—42no—
83C2×Q8×C43C22⋊C412yes—
84C2×Q8×C43C22⋊C412yes—
85C2×D4×C43—21no—
86C2×D4×C43—42no—
87C2×D4×C43C22⋊C412yes—
88C22×C4×C43—24no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—42no—
93C22×C4×C43—42no—
94C22×C4×C43C22⋊C411yescharacteristic
95C22×C4×C43C22⋊C411yescharacteristic
96C22×C4×C43C22⋊C411yescharacteristic
97C22×C4×C43C22⋊C411yescharacteristic
98C22×C4×C43C22×C411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C4⋊C4×C43—24no—
102C4⋊C4×C43—24no—
103C4⋊C4×C43—24no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—24no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43C22⋊C412yes—
110C22⋊C4×C43—24no—
111C22⋊C4×C43—24no—
112C22⋊C4×C43—24no—
113C22⋊C4×C43—24no—
114C22⋊C4×C43—24no—
115C42×C43—24no—
116C42×C43—21no—
117C42×C43—21no—
118C42×C43—21no—
119C42×C43—21no—
120C42×C43—24no—
121C42×C43C2×D412yes—
122C42×C43C2×D412yes—
123#10621877—24no—
124#10621877—42no—
125C2×C43⋊C8—42no—
126C2×C43⋊C8—42no—
127C23×C43—22no—
128C23×C43—42no—
129C23×C43—42no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43C2×C22⋊C411yescharacteristic
133Q8×C43—24no—
134Q8×C43—44no—
135Q8×C43—42no—
136Q8×C43—42no—
137Q8×C43—42no—
138D4×C43—42no—
139D4×C43—42no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—22no—
145C2×C4×C43—21no—
146C2×C4×C43—22no—
147C2×C4×C43—21no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—41no—
154C2×C4×C43—48no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43#10412yes—
162C2×C4×C43C2×C22⋊C411yescharacteristic
163C2×C4×C43C2×C22⋊C411yescharacteristic
164C2×C4×C43#12012yes—
165C2×C4×C43#12012yes—
166C43⋊C8—44no—
167C43⋊C8—82no—
168#8368—431nomaximal, Sylow
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—42no—
172C22×C43—42no—
173C22×C43—42no—
174C22×C43—82no—
175C22×C43—82no—
176C22×C43#37911yescharacteristic
177C22×C43C2×#10411yescharacteristic
178C22×C43#42111yescharacteristic
179C4×C43—22no—
180C4×C43—21no—
181C4×C43—22no—
182C4×C43—22no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43—42no—
186C4×C43—42no—
187C4×C43—41no—
188C4×C43—42no—
189C4×C43#41312yes—
190C2×#556D4311yescharacteristic
191C4×#101—431no—
192#1527—432no—
193#1491—432no—
194#1467—431no—
195C2×C43—21no—
196C2×C43—21no—
197C2×C43—82no—
198C2×C43#178511yescharacteristic
199C2×C43#178911yescharacteristic
200C2×C43#179611yescharacteristic
201#556—24no—
202#556—24no—
203C2×C4⋊Q8Dic4311yescharacteristic
204C2×#126—21no—
205C2×#126—21no—
206C2×#124Dic4311yescharacteristic
207C2×#124C2×D4311yescharacteristic
208C2×C22⋊Q8—21no—
209C2×C4×Q8Dic4311yescharacteristic
210C2×C4×Q8C2×D4311yescharacteristic
211C2×C4×Q8C2×D4311yescharacteristic
212C2×C4×D4Dic4311yescharacteristic
213C2×#117—21no—
214#432—432no—
215C2×#101—861no—
216C4×M16—432no—
217#343—861no—
218#329—864no—
219Q8⋊C8—864no—
220#324—861no—
221#324—861no—
222C43#836811yescharacteristic, complemented, Sylow
223C22×Q8C2×Dic4311yescharacteristic
224C22×Q8C2×Dic4311yescharacteristic
225C22×Q8C22⋊D4311yescharacteristic
226C22×D4C2×Dic4311yescharacteristic
227C23×C4—21no—
228C2×M16—862no—
229C4⋊Q8—22no—
230C4⋊Q8—22no—
231#126—28no—
232#126—28no—
233#124—22no—
234#124—22no—
235#124—22no—
236#124C22⋊D4314yes—
237C22⋊Q8—28no—
238C4×Q8—22no—
239C4×Q8—22no—
240C4×Q8—22no—
241C4×Q8—22no—
242C4×Q8—22no—
243C4×Q8C22⋊D4314yes—
244C4×D4—22no—
245C4×D4—22no—
246#117—28no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C2×Dic4311yescharacteristic
252C2×C4⋊C4C22⋊D4311yescharacteristic
253C2×C4⋊C4C22⋊D4311yescharacteristic
254C2×C4⋊C4C22⋊D4311yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C42—21no—
261C2×C42—21no—
262C2×C42C2×Dic4311yescharacteristic
263C2×C42C2×Dic4311yescharacteristic
264C2×C42C22×D4311yescharacteristic
265C4⋊C8—862no—
266#101—864no—
267C22⋊C8—862no—
268#97—862no—
269#97—862no—
270C4×C8—862no—
271C24—21no—
272C2×Q8—22no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—42no—
278C2×Q8—42no—
279C2×Q8C22⋊Dic4312yes—
280C2×Q8C22⋊Dic4312yes—
281C2×D4—21no—
282C2×D4—42no—
283C2×D4C22⋊Dic4312yes—
284C22×C4—24no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4C22⋊Dic4311yescharacteristic
291C22×C4C22⋊Dic4311yescharacteristic
292C22×C4C22⋊Dic4311yescharacteristic
293C22×C4C22⋊Dic4311yescharacteristic
294C22×C4C22×Dic4311yescharacteristic
295C22×C4C2×C22⋊D4311yescharacteristic
296C22×C4C2×C22⋊D4311yescharacteristic
297M16—864no—
298M16—1722no—
299C2×C8—1722no—
300C2×C8—1722no—
301C4⋊C4—24no—
302C4⋊C4—24no—
303C4⋊C4—24no—
304C4⋊C4—21no—
305C4⋊C4—24no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4C22⋊Dic4312yes—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—24no—
313C22⋊C4—24no—
314C22⋊C4—24no—
315C42—24no—
316C42—21no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—24no—
321C42C2×C22⋊D4312yes—
322C42C2×C22⋊D4312yes—
323C23—22no—
324C23—42no—
325C23—42no—
326C23—41no—
327C23—41no—
328C23C2×C22⋊Dic4311yescharacteristic
329Q8—24no—
330Q8—44no—
331Q8—42no—
332Q8—42no—
333Q8—42no—
334D4—42no—
335D4—42no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—48no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4#1306325212yes—
358C2×C4C2×C22⋊Dic4311yescharacteristic
359C2×C4C2×C22⋊Dic4311yescharacteristic
360C2×C4#1306329412yes—
361C2×C4#1306329412yes—
362C8—3442no—
363C8—1724no—
364C22—21no—
365C22—21no—
366C22—42no—
367C22—42no—
368C22—42no—
369C22—82no—
370C22—82no—
371C22#1458275511yescharacteristic
372C22C2×#1306325211yescharacteristic
373C22#1458291611yescharacteristic
374C4—21no—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—42no—
379C4—42no—
380C4—41no—
381C4—42no—
382C4—41no—
383C4—41no—
384C4#1458288312yes—
385C2—21no—
386C2—21no—
387C2—82no—
388C2#1913452311yescharacteristic
389C2#1913453911yescharacteristic
390C2#1913457011yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#556C2
socleC22×C43#379
prime radicalC22×D4×C43C2×C4
cosocleC2×C42×C43C23
hypercenterC2×#556D43
hypocenterC43#8368
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C4×#13063244C2semidirect
3. #19133042C2semidirect
4. #19132939C2semidirect
222. C43#8368semidirect

Maximal subgroups

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

subgroupindex
C4×#130632442
#191331932
#191330422
#191329392
C2×C43×#5562
#836843