Finite Group Databasebeta

← #25006797

Subgroups — #25006797

Order 11008.

536 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 107 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#19137831C211yesmaximal, characteristic
2#19132909C211yesmaximal, characteristic, complemented
3#19132600C212yesmaximal, complemented
4#19132597C212yesmaximal, complemented
5C43×#1742C211yesmaximal, characteristic, complemented
6C2×C4×D172C411yescharacteristic
7C2×C4×C22⋊D43—21no—
8#14582952—21no—
9#14582829C2211yescharacteristic
10#14582824C411yescharacteristic
11#14582821—21no—
12#14582816C2211yescharacteristic
13#14582815—21no—
14#14582808C411yescharacteristic
15C4×C4⋊Dic43C411yescharacteristic
16C4×(C2×D43)⋊C4—21no—
17#14582625C2212yes—
18#14582623—21no—
19C22×M16×C43—21no—
20C2×#117×C43C2211yescharacteristic
21C43×#343—21no—
22C43×#343C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C22×C4×D43—21no—
26C4×D172—41no—
27C4×D172—41no—
28C4×C22⋊D43—42no—
29C4×C22⋊D43—42no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×C4×Dic43—21no—
39C4⋊(C43⋊C8)—41no—
40C22⋊(C43⋊C8)—22no—
41C4×C43⋊C8—41no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95C2×C411yescharacteristic
45C43⋊#95C2×C411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C2×M16×C43—24no—
48C2×M16×C43—22no—
49C2×M16×C43—41no—
50C2×M16×C43—42no—
51C22×C8×C43—41no—
52#117×C43—41no—
53#117×C43—41no—
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C4⋊C4×C43C2311yescharacteristic
56C2×C22⋊C4×C43C2×C411yescharacteristic
57C2×C22⋊C4×C43D411yescharacteristic
58C2×C42×C43C2×C411yescharacteristic
59C2×C42×C43D411yescharacteristic
60C24×C43C22⋊C411yescharacteristic
61C23×D43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—22no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43D812yes—
69C22×C4×C43SD1612yes—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C2×C22⋊D43—42no—
74C2×C22⋊D43—42no—
75C2×C22⋊D43—42no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C2×D172—42no—
80C2×D172—41no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C2×C4×D43—42no—
84C2×C4×D43—42no—
85M16×C43—24no—
86M16×C43—44no—
87M16×C43—42no—
88C2×C8×C43—42no—
89C2×C8×C43—44no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C42×C43—21no—
95C42×C43—21no—
96C42×C43—21no—
97C42×C43—21no—
98C22⋊Dic43—42no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—42no—
101(C2×D43)⋊C4—42no—
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—41no—
104C4⋊Dic43—42no—
105C4⋊Dic43—41no—
106Dic43⋊C4—41no—
107Dic43⋊C4—41no—
108C4×Dic43—42no—
109C2×C43⋊C8—42no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43#10212yes—
115C23×C43C2×C22⋊C411yescharacteristic
116C22×D43—22no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43#9911yescharacteristic
138C2×C4×C43#9911yescharacteristic
139C2×C4×C43#10212yes—
140C2×C4×C43#10412yes—
141C2×C4×C43C2×D811yescharacteristic
142C2×C4×C43C2×SD1611yescharacteristic
143C22⋊D43—48no—
144C2×Dic43—22no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153D172—42no—
154D172—42no—
155C4×D43—82no—
156C4×D43—82no—
157C8×C43—44no—
158C43⋊C8—82no—
159#11697—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—22no—
163C22×C43—42no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—81no—
167C22×C43C2×#9911yescharacteristic
168C22×C43C2×#10211yescharacteristic
169C22×C43C2×#10411yescharacteristic
170C2×D43—42no—
171C2×D43—42no—
172C2×D43—42no—
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C2×D43—81no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43#32712yes—
184C4×C43#32712yes—
185Dic43—42no—
186Dic43—81no—
187Dic43—81no—
188#2392—431no—
189#1742D4311yescharacteristic, complemented
190#1458—431no—
191#1346—432no—
192#1345—432no—
193C2×C43—21no—
194C2×C43—21no—
195C2×C43—42no—
196C2×C43C2×#32711yescharacteristic
197C2×C43#212011yescharacteristic
198C2×C43#213211yescharacteristic
199D43—82no—
200C22×M16—21no—
201C2×C4×D4—431no—
202C2×C4×D4—861no—
203C2×#117C2×D4311yescharacteristic
204#431—861no—
205#398—431no—
206#397—431no—
207#396—861no—
208#394—431no—
209#394—861no—
210#392—431no—
211C4×C4⋊C4—431no—
212C4×C22⋊C4—861no—
213#343—21no—
214#343C2×D4312yes—
215#324—432no—
216#323—861no—
217C43#1169711yescharacteristic, complemented, Sylow
218C22×D4—431no—
219C22×D4—861no—
220C23×C4—861no—
221C23×C4C22⋊D4311yescharacteristic
222C2×M16—24no—
223C2×M16—22no—
224C2×M16—41no—
225C2×M16—42no—
226C22×C8—41no—
227C4×D4—1721no—
228C4×D4—1721no—
229C4×D4—1722no—
230C4×D4—1722no—
231#117—41no—
232#117—41no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4C22⋊D4311yescharacteristic
237C2×C4⋊C4C22×D4311yescharacteristic
238C2×C22⋊C4—861no—
239C2×C22⋊C4—861no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4C4×D4311yescharacteristic
244C2×C22⋊C4D17211yescharacteristic
245C2×C42—861no—
246C2×C42C4×D4311yescharacteristic
247C2×C42D17211yescharacteristic
248C4⋊C8—1721no—
249C22⋊C8—862no—
250C4×C8—1721no—
251#95—431no—
252#95—431no—
253#95—861no—
254#95—861no—
255C24—861no—
256C24(C2×D43)⋊C411yescharacteristic
257C2×D4—1721no—
258C2×D4—1722no—
259C2×D4—1722no—
260C2×D4—1722no—
261C2×D4—1722no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—1721no—
269C22×C4—1721no—
270C22×C4—1722no—
271C22×C4—1722no—
272C22×C4(C2×D43)⋊C411yescharacteristic
273C22×C4(C2×D43)⋊C411yescharacteristic
274C22×C4(C2×D43)⋊C411yescharacteristic
275C22×C4#1062188212yes—
276C22×C4#1062188412yes—
277C22×C4C2×C4×D4311yescharacteristic
278C22×C4C2×D17211yescharacteristic
279C22×C4C2×C22⋊D4311yescharacteristic
280M16—24no—
281M16—44no—
282M16—42no—
283C2×C8—42no—
284C2×C8—44no—
285C2×C8—1722no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—1721no—
289C4⋊C4—1722no—
290C4⋊C4—1721no—
291C4⋊C4—1721no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—1722no—
295C22⋊C4—1722no—
296C22⋊C4—1722no—
297C22⋊C4—1722no—
298C22⋊C4—1721no—
299C22⋊C4—1721no—
300C42—21no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42—1722no—
305C23—21no—
306C23—21no—
307C23—41no—
308C23—41no—
309C23—862no—
310C23—1721no—
311C23—1721no—
312C23—1721no—
313C23—1721no—
314C23—1721no—
315C23—1721no—
316C23#1306324512yes—
317C23C2×(C2×D43)⋊C411yescharacteristic
318D4—1722no—
319D4—1722no—
320D4—1728no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—862no—
336C2×C4—3442no—
337C2×C4—3442no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4#1306323911yescharacteristic
347C2×C4#1306323911yescharacteristic
348C2×C4#1306324512yes—
349C2×C4#1306325312yes—
350C2×C4C2×#1062188211yescharacteristic
351C2×C4C2×#1062188411yescharacteristic
352C8—44no—
353C8—3442no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—42no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—3441no—
362C22—3441no—
363C22—3441no—
364C22—3441no—
365C22—1722no—
366C22—1722no—
367C22—1722no—
368C22C2×#1306323911yescharacteristic
369C22C2×#1306324511yescharacteristic
370C22C2×#1306325311yescharacteristic
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—3441no—
378C4—3441no—
379C4—1722no—
380C4#1458263212yes—
381C4#1458263212yes—
382C2—21no—
383C2—21no—
384C2—42no—
385C2—3442no—
386C2C2×#1458263211yescharacteristic
387C2#1913623711yescharacteristic
388C2#1913627811yescharacteristic
subgroupG/H
centerC2×C4#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1742C2
socleC22×C43C2×#99
prime radical#14582808C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1742D43
hypocenterC43#11697
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#117 ◁ #1742

Complements

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

NH ≅ G/Ntype
2. #19132909C2semidirect
3. #19132600C2semidirect
4. #19132597C2semidirect
5. C43×#1742C2semidirect
189. #1742D43semidirect
217. C43#11697semidirect

Maximal subgroups

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

subgroupindex
#191378312
#191329092
#191326002
#191325972
C43×#17422
#1169743