Finite Group Databasebeta

← #25012119

Subgroups — #25012119

Order 11008.

962 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 962 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14583470C211yesmaximal, characteristic
2C2×#14582697C214yesmaximal, complemented
3#19134523C211yesmaximal, characteristic
4C43×#1785C211yesmaximal, characteristic
5C23×Dic86C411yescharacteristic
6#14583470—28no—
7C2×#13063323C2212yes—
8C2×#13063312C412yes—
9C2×#13063306—21no—
10C2×#13063306—21no—
11C2×#13063304—21no—
12C2×#13063304—21no—
13C2×#13063284C411yescharacteristic
14C2×#13063244C2212yes—
15C2×#13063242—21no—
16#14582863—21no—
17#14582697—28no—
18C22×#41×C43C2211yescharacteristic
19C2×#101×C43C2212yes—
20C2×#100×C43—21no—
21C43×#407—21no—
22C22×Dic86—21no—
23C22×Dic86—24no—
24C22×Dic86—42no—
25C22×Dic86—42no—
26C22×Dic86C2×C412yes—
27C23×Dic43—21no—
28C2×#10621877—22no—
29#13063323—24no—
30#13063323D418yes—
31#13063312—24no—
32#13063312—24no—
33#13063306—28no—
34#13063306—28no—
35#13063304—28no—
36#13063304—28no—
37#13063284—24no—
38C2×C4⋊Dic43—21no—
39C2×Dic43⋊C4—22no—
40C2×Dic43⋊C4—22no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—22no—
43C2×C22⋊Dic43—22no—
44C2×C4×Dic43C2×C412yes—
45#13063244—24no—
46#13063242—42no—
47C22⋊(C43⋊C8)—42no—
48C2×#41×C43—24no—
49C2×#41×C43—42no—
50C2×#41×C43—42no—
51C22×Q8×C43C2311yescharacteristic
52C22×D4×C43C2×C411yescharacteristic
53C22×D4×C43D411yescharacteristic
54C22×D4×C43D411yescharacteristic
55C23×C4×C43C2×C411yescharacteristic
56C23×C4×C43D411yescharacteristic
57C23×C4×C43D411yescharacteristic
58C2×M16×C43—22no—
59#101×C43—24no—
60#100×C43—42no—
61C22⋊C8×C43—42no—
62C24×C43C22⋊C411yescharacteristic
63C24×C43C22⋊C411yescharacteristic
64C24×C43C22⋊C411yescharacteristic
65#41×C43—416no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43C2×D414yes—
69C2×D4×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43—22no—
72C2×D4×C43—22no—
73C2×D4×C43—22no—
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43—41no—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43—22no—
84C22×C4×C43—22no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43C22⋊C411yescharacteristic
88C22×C4×C43C22×C411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×Dic43—24no—
92C22×Dic43—22no—
93C22×Dic43—22no—
94C22×Dic43—42no—
95C22×Dic43—42no—
96C2×Dic86—24no—
97C2×Dic86—22no—
98C2×Dic86—42no—
99C2×Dic86—416no—
100C2×Dic86—42no—
101C2×Dic86—42no—
102C2×Dic86—42no—
103C2×Dic86C22⋊C414yes—
104M16×C43—42no—
105M16×C43—42no—
106C2×C8×C43—42no—
107C22⋊Dic43—24no—
108C22⋊Dic43—28no—
109C22⋊Dic43—28no—
110C4⋊Dic43—24no—
111Dic43⋊C4—28no—
112Dic43⋊C4—28no—
113C4×Dic43—22no—
114C4×Dic43C22⋊C414yes—
115#10621877—42no—
116#10621877—42no—
117C2×C43⋊C8—42no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—42no—
127C23×C43—42no—
128C23×C43—42no—
129C23×C43#9912yes—
130C23×C43C2×C22⋊C411yescharacteristic
131Q8×C43—44no—
132D4×C43—44no—
133D4×C43—44no—
134D4×C43—44no—
135C2×C4×C43—28no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—44no—
145C2×C4×C43—44no—
146C2×C4×C43#9912yes—
147C2×C4×C43C2×C22⋊C412yes—
148C2×C4×C43#12012yes—
149C2×C4×C43#12012yes—
150C2×Dic43—24no—
151C2×Dic43—24no—
152C2×Dic43—48no—
153C2×Dic43—44no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156Dic86—48no—
157Dic86—44no—
158Dic86—44no—
159C8×C43—82no—
160C43⋊C8—82no—
161#12704—431nomaximal, Sylow
162C22×C43—22no—
163C22×C43—22no—
164C22×C43—42no—
165C22×C43—42no—
166C22×C43—42no—
167C22×C43—42no—
168C22×C43—42no—
169C22×C43—42no—
170C22×C43—42no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—81no—
174C22×C43—81no—
175C22×C43#37911yescharacteristic
176C22×C43C2×#9911yescharacteristic
177C22×C43C2×#9911yescharacteristic
178C4×C43—22no—
179C4×C43—22no—
180C4×C43—22no—
181C4×C43—22no—
182Dic43—44no—
183Dic43—44no—
184C2×#536—431no—
185C2×#356—434no—
186#1785—431no—
187#1785D4311yescharacteristic
188C2×C43—21no—
189C2×C43—21no—
190C2×C43—42no—
191C2×C43—81no—
192C2×C43—81no—
193C2×C43#178111yescharacteristic
194C2×C43#213512yes—
195C22×#41C2×D4311yescharacteristic
196C23×Q8—431no—
197#536—868no—
198C2×C4⋊Q8—432no—
199C2×#124—432no—
200C2×#123—861no—
201C2×#123—861no—
202C2×C22⋊Q8—861no—
203C2×C22⋊Q8—861no—
204C2×#117—431no—
205C2×#101—432no—
206C2×#101C2×D4312yes—
207C2×#100—21no—
208C2×#100—861no—
209#407—21no—
210#407—861no—
211#356—868no—
212C43#1270411yescharacteristic, complemented, Sylow
213C2×#41—24no—
214C2×#41—42no—
215C2×#41—42no—
216C22×Q8—432no—
217C22×Q8—864no—
218C22×Q8—861no—
219C22×Q8—1722no—
220C22×Q8—1722no—
221C22×Q8C22×D4311yescharacteristic
222C22×D4C4×D4311yescharacteristic
223C22×D4D17211yescharacteristic
224C22×D4C22⋊D4311yescharacteristic
225C23×C4—861no—
226C23×C4C4×D4311yescharacteristic
227C23×C4D17211yescharacteristic
228C23×C4C22⋊D4311yescharacteristic
229C2×M16—22no—
230C2×M16—862no—
231C4⋊Q8—438no—
232C4⋊Q8—864no—
233#124—864no—
234#124—864no—
235#123—868no—
236#123—868no—
237C22⋊Q8—868no—
238C22⋊Q8—868no—
239#117—864no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—862no—
242C2×C4⋊C4—862no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—862no—
245C2×C22⋊C4—862no—
246C2×C42—432no—
247#101—24no—
248#101—864no—
249#100—42no—
250#100—1722no—
251C22⋊C8—42no—
252C22⋊C8—1722no—
253C24(C2×D43)⋊C411yescharacteristic
254C24(C2×D43)⋊C411yescharacteristic
255C24(C2×D43)⋊C411yescharacteristic
256#41—416no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—434no—
260C2×Q8—864no—
261C2×Q8—862no—
262C2×Q8—17216no—
263C2×Q8—1722no—
264C2×Q8—1722no—
265C2×Q8—1722no—
266C2×Q8—1722no—
267C2×Q8D4×D4314yes—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—864no—
287C22×C4—862no—
288C22×C4—862no—
289C22×C4—1722no—
290C22×C4—1722no—
291C22×C4(C2×D43)⋊C411yescharacteristic
292C22×C4C2×C4×D4311yescharacteristic
293C22×C4C2×D17211yescharacteristic
294C22×C4C2×C22⋊D4311yescharacteristic
295M16—42no—
296M16—42no—
297M16—1722no—
298M16—1722no—
299C2×C8—42no—
300C2×C8—1722no—
301C4⋊C4—864no—
302C4⋊C4—868no—
303C4⋊C4—868no—
304C22⋊C4—864no—
305C22⋊C4—868no—
306C22⋊C4—868no—
307C42—434no—
308C42—862no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23#1306323912yes—
321C23C2×(C2×D43)⋊C411yescharacteristic
322Q8—44no—
323Q8—1724no—
324Q8—1728no—
325Q8—1724no—
326D4—44no—
327D4—44no—
328D4—44no—
329C2×C4—28no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—864no—
341C2×C4—864no—
342C2×C4—1728no—
343C2×C4—1724no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4#1306323912yes—
347C2×C4C22⋊C4×D4312yes—
348C2×C4#1306329312yes—
349C2×C4#1306329512yes—
350C8—82no—
351C8—3442no—
352C22—22no—
353C22—22no—
354C22—42no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—41no—
362C22—41no—
363C22—81no—
364C22—81no—
365C22#1458275411yescharacteristic
366C22C2×#1306323911yescharacteristic
367C22C2×#1306323911yescharacteristic
368C4—22no—
369C4—22no—
370C4—22no—
371C4—22no—
372C4—1724no—
373C4—1724no—
374C2—21no—
375C2—21no—
376C2—42no—
377C2—81no—
378C2—81no—
379C2#1913450911yescharacteristic
380C2#1913628912yes—
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC43×#1785C2
socleC22×C43C2×#99
prime radicalC22×#41×C43C22
cosocleC22×Q8×C43C23
hypercenter#1785D43
hypocenterC43#12704
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1785

Complements

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

NH ≅ G/Ntype
2. C2×#14582697C2semidirect
212. C43#12704semidirect

Maximal subgroups

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

subgroupindex
C2×#145834702
C2×#145826972
#191345232
C43×#17852
#1270443