Finite Group Databasebeta

← #25012579

Subgroups — #25012579

Order 11008.

680 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 95 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
1#19137159C211yesmaximal, characteristic
2C2×#14582691C212yesmaximal
3#19134581C212yesmaximal, complemented
4#19132720C211yesmaximal, characteristic, complemented
5C43×#1393C211yesmaximal, characteristic, complemented
6C2×#13063321C2211yescharacteristic
7C2×D4×Dic43C2211yescharacteristic
8C2×#13063287C411yescharacteristic, complemented
9C2×(C22⋊D43)⋊C4—22no—
10C2×#13063240C2212yes—
11#14582801C411yescharacteristic, complemented
12#14582799—22no—
13#14582768C411yescharacteristic, complemented
14#14582757—22no—
15C42×Dic43C411yescharacteristic, complemented
16#14582691—24no—
17#14582665—22no—
18C2×#99×C43C2212yes—
19C43×#390C2211yescharacteristic
20C22×D172C2×C411yescharacteristic
21C22×C22⋊D43—22no—
22C23×Dic43D412yes—
23C22×C4×D43—21no—
24#13063321—22no—
25#13063321D412yes—
26#13063321Q812yes—
27D4×Dic43—41no—
28D4×Dic43—41no—
29#13063287—41no—
30#13063287—41no—
31(C22⋊D43)⋊C4—48no—
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×Dic43⋊C4—22no—
34C2×Dic43⋊C4—42no—
35C2×C22⋊Dic43—22no—
36C2×C22⋊Dic43D412yes—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—22no—
39C2×C4×Dic43—21no—
40C2×C4×Dic43—21no—
41C2×C4×Dic43C2×C411yescharacteristic
42C2×C4×Dic43C2×C411yescharacteristic
43#13063240—22no—
44#13063240—22no—
45C43⋊#95—42no—
46C22×D4×C43C2311yescharacteristic
47C2×C4⋊C4×C43C2×C411yescharacteristic
48C2×C22⋊C4×C43—22no—
49C2×C22⋊C4×C43—22no—
50C2×C42×C43C2×C411yescharacteristic
51#99×C43—22no—
52#99×C43—22no—
53C24×C43C2×D412yes—
54C23×D43—21no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×D4×C43C2×D411yescharacteristic
58C2×D4×C43C2×Q811yescharacteristic
59C2×D4×C43#4112yes—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—42no—
63C22×C4×C43C22×C411yescharacteristic
64C2×C22⋊D43—24no—
65C2×C22⋊D43—24no—
66C2×C22⋊D43—44no—
67C2×C22⋊D43—44no—
68C22×Dic43—22no—
69C22×Dic43—22no—
70C22×Dic43—21no—
71C22×Dic43—42no—
72C22×Dic43—44no—
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C412yes—
76C2×D172—21no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172C4⋊C412yescomplemented
80C2×C4×D43—44no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C4⋊C4×C43—41no—
84C22⋊C4×C43—42no—
85C22⋊C4×C43—44no—
86C22⋊C4×C43—42no—
87C42×C43—41no—
88C22⋊Dic43—42no—
89C22⋊Dic43—42no—
90C22⋊Dic43—42no—
91(C2×D43)⋊C4—42no—
92(C2×D43)⋊C4—44no—
93C4⋊Dic43—41no—
94Dic43⋊C4—44no—
95Dic43⋊C4—84no—
96C4×Dic43—24no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—42no—
101C4×Dic43C4⋊C412yescomplemented
102C23×C43—22no—
103C23×C43—22no—
104C23×C43—42no—
105C23×C43—42no—
106C23×C43C2×C22⋊C411yescharacteristic
107C23×C43#12112yes—
108C23×C43C22⋊Q812yes—
109C22×D43—22no—
110C22×D43—42no—
111C22×D43—42no—
112C22×D43—41no—
113C22×D43—41no—
114D4×C43—41no—
115D4×C43—41no—
116D4×C43—42no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—22no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—42no—
123C2×C4×C43—41no—
124C2×C4×C43—82no—
125C2×C4×C43—82no—
126C2×C4×C43—82no—
127C2×C4×C43C2×C4⋊C411yescharacteristic
128C2×C4×C43#11711yescharacteristic
129C22⋊D43—48no—
130C22⋊D43—48no—
131C2×Dic43—22no—
132C2×Dic43—22no—
133C2×Dic43—22no—
134C2×Dic43—22no—
135C2×Dic43—21no—
136C2×Dic43—22no—
137C2×Dic43—44no—
138C2×Dic43—41no—
139C2×Dic43—42no—
140C2×Dic43—82no—
141C2×Dic43—82no—
142C2×Dic43—82no—
143C2×Dic43—82no—
144C2×Dic43#9911yescharacteristic
145C2×Dic43#9911yescharacteristic
146D172—42no—
147D172—42no—
148C4×D43—82no—
149C4×D43—82no—
150#12797—431nomaximal, Sylow
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—22no—
154C22×C43—22no—
155C22×C43—42no—
156C22×C43—42no—
157C22×C43—42no—
158C22×C43—42no—
159C22×C43—82no—
160C22×C43#38011yescharacteristic
161C22×C43C2×#9911yescharacteristic
162C22×C43#41011yescharacteristic
163C2×D43—44no—
164C2×D43—42no—
165C2×D43—82no—
166C2×D43—81no—
167C2×D43—81no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—42no—
171C4×C43—81no—
172C4×C43—162no—
173Dic43—24no—
174Dic43—21no—
175Dic43—42no—
176Dic43—41no—
177Dic43—162no—
178Dic43#35312yescomplemented
179C4×#127—431no—
180C2×#353—432no—
181#1799—432no—
182#1393—431no—
183#1393D4311yescharacteristic, complemented
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—42no—
187C2×C43—42no—
188C2×C43#179911yescharacteristic
189C2×C43C2×#35311yescharacteristic
190C2×C43#212611yescharacteristic
191D43—82no—
192C2×#127—431no—
193C2×C4×D4—431no—
194C2×C4×D4—431no—
195C2×C4×D4—862no—
196C2×#99—432no—
197C2×#99C2×D4312yes—
198#390—431no—
199#390—862no—
200#390C2×D4311yescharacteristic
201#384—431no—
202#380—862no—
203C43—431no—
204#353—864no—
205#342—862no—
206C43#1279711yescharacteristic, complemented, Sylow
207C22×D4—431no—
208C22×D4—862no—
209C22×D4C22×D4311yescharacteristic
210C23×C4—432no—
211C23×C4—861no—
212#127—432no—
213#127—432no—
214#127—862no—
215C4×D4—1728no—
216C4×D4—1721no—
217C4×D4—1721no—
218C4×D4—1721no—
219C4×D4—1721no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—862no—
222C2×C4⋊C4—1722no—
223C2×C4⋊C4C4×D4311yescharacteristic
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—432no—
227C2×C22⋊C4—861no—
228C2×C22⋊C4—862no—
229C2×C22⋊C4—862no—
230C2×C42—431no—
231C2×C42—431no—
232C2×C42—861no—
233C2×C42—861no—
234C2×C42C4×D4311yescharacteristic
235#99—22no—
236#99—22no—
237#99—862no—
238#99—862no—
239#95—1722no—
240C24—861no—
241C24D4×D4312yes—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—432no—
245C2×D4—864no—
246C2×D4—864no—
247C2×D4—861no—
248C2×D4—1721no—
249C2×D4—1721no—
250C2×D4—1724no—
251C2×D4—1724no—
252C2×D4#1062189812yes—
253C2×D4D4×D4311yescharacteristic
254C2×D4Q8×D4311yescharacteristic
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—42no—
258C22×C4—431no—
259C22×C4—431no—
260C22×C4—432no—
261C22×C4—862no—
262C22×C4—862no—
263C22×C4—861no—
264C22×C4—1721no—
265C22×C4—1721no—
266C22×C4—1724no—
267C22×C4—1724no—
268C22×C4—1722no—
269C22×C4C2×C4×D4311yescharacteristic
270C4⋊C4—41no—
271C4⋊C4—3444no—
272C4⋊C4—1721no—
273C4⋊C4—1724no—
274C22⋊C4—44no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—1724no—
278C22⋊C4—1722no—
279C22⋊C4—1722no—
280C22⋊C4—1722no—
281C22⋊C4—1722no—
282C42—41no—
283C42—432no—
284C42—861no—
285C42—861no—
286C42—864no—
287C42—861no—
288C42—1722no—
289C23—22no—
290C23—22no—
291C23—42no—
292C23—42no—
293C23—862no—
294C23—1722no—
295C23—1722no—
296C23—1721no—
297C23—1721no—
298C23C22⋊C4×D4311yescharacteristic
299C23#1306329812yes—
300C23#1306330312yes—
301D4—42no—
302D4—41no—
303D4—41no—
304D4—1722no—
305D4—1722no—
306D4—1728no—
307D4—1728no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—431no—
319C2×C4—431no—
320C2×C4—862no—
321C2×C4—862no—
322C2×C4—862no—
323C2×C4—862no—
324C2×C4—861no—
325C2×C4—862no—
326C2×C4—3442no—
327C2×C4—3442no—
328C2×C4—3442no—
329C2×C4—3442no—
330C2×C4—3442no—
331C2×C4—3442no—
332C2×C4—1724no—
333C2×C4—1721no—
334C2×C4—1722no—
335C2×C4C4⋊C4×D4311yescharacteristic
336C2×C4#1306328211yescharacteristic
337C22—21no—
338C22—21no—
339C22—22no—
340C22—22no—
341C22—42no—
342C22—42no—
343C22—42no—
344C22—42no—
345C22—82no—
346C22—3442no—
347C22—3441no—
348C22—3441no—
349C22—1724no—
350C22—1722no—
351C22#1458275811yescharacteristic
352C22#99×D4311yescharacteristic
353C22#1458287111yescharacteristic
354C4—21no—
355C4—21no—
356C4—42no—
357C4—81no—
358C4—162no—
359C4—432no—
360C4—864no—
361C4—861no—
362C4—1721no—
363C4—1722no—
364C4—6882no—
365C2—21no—
366C2—21no—
367C2—42no—
368C2—42no—
369C2—3442no—
370C2#1913458211yescharacteristic
371C2#353×D4311yescharacteristic
372C2#1913625911yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1393C2
socleC22×C43C2×#99
prime radicalC2×#13063321C22
cosocleC22×D4×C43C23
hypercenter#1393D43
hypocenterC43#12797
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
3. #19134581C2semidirect
4. #19132720C2semidirect
5. C43×#1393C2semidirect
8. C2×#13063287C4semidirect
11. #14582801C4semidirect
13. #14582768C4semidirect
15. C42×Dic43C4semidirect
79. C2×D172C4⋊C4semidirect
101. C4×Dic43C4⋊C4semidirect
178. Dic43#353semidirect
183. #1393D43semidirect
206. C43#12797semidirect

Maximal subgroups

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

subgroupindex
#191371592
C2×#145826912
#191345812
#191327202
C43×#13932
#1279743