Finite Group Databasebeta

← #25006115

Subgroups — #25006115

Order 11008.

460 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 69 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#19138866C211yesmaximal, characteristic
2#19132926C211yesmaximal, characteristic, complemented
3#19132906C211yesmaximal, characteristic, complemented
4#19132544C211yesmaximal, characteristic, complemented
5#19132542C211yesmaximal, characteristic, complemented
6#19132523C211yesmaximal, characteristic
7C43×#1316C211yesmaximal, characteristic
8C2×#13063281C2211yescharacteristic
9C22×C22⋊Dic43C411yescharacteristic
10#14582953—21no—
11#14582949—21no—
12#14582835—21no—
13#14582827—21no—
14#14582793—21no—
15#14582792—21no—
16#14582774C411yescharacteristic
17#14582771C2211yescharacteristic
18#14582760C411yescharacteristic
19#14582755C411yescharacteristic
20#14582624—21no—
21#14582624—21no—
22#14582623C2211yescharacteristic
23#14582623C2211yescharacteristic
24C43×#379C2211yescharacteristic
25C43×#323C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C23×Dic43C2×C411yescharacteristic
28C23×Dic43C2×C411yescharacteristic
29#13063281—41no—
30#13063281—41no—
31C2×C4⋊Dic43—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4D411yescharacteristic
34C2×Dic43⋊C4D411yescharacteristic
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—41no—
40C2×C22⋊Dic43—41no—
41C2×C22⋊Dic43C2×C411yescharacteristic
42C2×C22⋊Dic43C2×C411yescharacteristic
43C2×C4×Dic43D411yescharacteristic
44C2×C4×Dic43D411yescharacteristic
45Dic43⋊C8—41no—
46Dic43⋊C8—41no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49#13063235—41no—
50C8×Dic43—41no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C25×C43C2×C411yescharacteristic
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43C2×C411yescharacteristic
59C2×C22⋊C4×C43C2311yescharacteristic
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62C24×C43—21no—
63C24×C43—21no—
64C24×C43—21no—
65C24×C43—42no—
66C24×C43—41no—
67C24×C43—41no—
68C24×C43—81no—
69C24×C43C22×C411yescharacteristic
70C22×C4×C43—21no—
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—41no—
80C22×Dic43—41no—
81C22×Dic43—81no—
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C22×Dic43C22⋊C411yescharacteristic
85C22×Dic43C22⋊C411yescharacteristic
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C22⋊C4×C43—42no—
91C22⋊C4×C43—81no—
92C22⋊Dic43—21no—
93C22⋊Dic43—21no—
94C22⋊Dic43—41no—
95C22⋊Dic43—42no—
96C22⋊Dic43—42no—
97C22⋊Dic43—41no—
98C22⋊Dic43—41no—
99C22⋊Dic43—81no—
100C4⋊Dic43—81no—
101Dic43⋊C4—41no—
102Dic43⋊C4—41no—
103Dic43⋊C4—81no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—22no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—42no—
119C23×C43—42no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—81no—
124C23×C43—81no—
125C23×C43—82no—
126C23×C43—82no—
127C23×C43—84no—
128C23×C43—81no—
129C23×C43—81no—
130C23×C43C2×C22⋊C411yescharacteristic
131C23×C43#13111yescharacteristic
132C23×C43#13111yescharacteristic
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—82no—
160C2×Dic43#9911yescharacteristic
161C2×Dic43#9911yescharacteristic
162C8×C43—81no—
163C8×C43—81no—
164C43⋊C8—81no—
165C43⋊C8—81no—
166#11542—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—42no—
174C22×C43—42no—
175C22×C43—42no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—42no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43—82no—
182C22×C43—82no—
183C22×C43—82no—
184C22×C43—82no—
185C22×C43—81no—
186C22×C43—81no—
187C22×C43#40811yescharacteristic
188C22×C43C2×#9911yescharacteristic
189C22×C43#41311yescharacteristic
190C4×C43—41no—
191C4×C43—41no—
192C4×C43—81no—
193Dic43—21no—
194Dic43—21no—
195Dic43—41no—
196Dic43—41no—
197Dic43—41no—
198Dic43—81no—
199Dic43—81no—
200#2482—431no—
201#1464—431no—
202#1458—431no—
203#1326—431no—
204#1326—431no—
205#1316—431no—
206#1316D4311yescharacteristic
207C2×C43—21no—
208C2×C43—21no—
209C2×C43—41no—
210C2×C43—41no—
211C2×C43—82no—
212C2×C43#146811yescharacteristic
213C2×C43#212011yescharacteristic
214C2×C43#212211yescharacteristic
215C2×#117—431no—
216C22×C22⋊C4—431no—
217#432—861no—
218#431—861no—
219#399—861no—
220#397—861no—
221#388—861no—
222#388—861no—
223#385—431no—
224#385—431no—
225#381—431no—
226#379—431no—
227#379C2×D4311yescharacteristic
228#324—861no—
229#324—861no—
230#323—431no—
231#323—431no—
232#323C2×D4311yescharacteristic
233#323C2×D4311yescharacteristic
234C43#1154211yescharacteristic, complemented, Sylow
235C25C4×D4311yescharacteristic
236C23×C4—431no—
237C23×C4—431no—
238#117—1721no—
239#117—1721no—
240C2×C4⋊C4—431no—
241C2×C4⋊C4—431no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4—861no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—431no—
247C2×C22⋊C4—431no—
248C2×C22⋊C4—861no—
249C2×C22⋊C4—861no—
250C2×C22⋊C4—861no—
251C2×C22⋊C4—861no—
252C2×C22⋊C4—1721no—
253C2×C22⋊C4—1721no—
254C2×C22⋊C4C4×D4311yescharacteristic
255C2×C22⋊C4C22×D4311yescharacteristic
256C2×C42—431no—
257C2×C42—431no—
258C4⋊C8—1721no—
259C4⋊C8—1721no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—861no—
263C22⋊C8—861no—
264#97—1721no—
265C4×C8—1721no—
266#95—861no—
267#95—861no—
268#95—861no—
269#95—861no—
270C24—21no—
271C24—21no—
272C24—21no—
273C24—41no—
274C24—42no—
275C24—41no—
276C24—81no—
277C24C2×C4×D4311yescharacteristic
278C22×C4—21no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—431no—
282C22×C4—431no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—3441no—
290C22×C4—1721no—
291C22×C4—1721no—
292C22×C4D4×D4311yescharacteristic
293C22×C4D4×D4311yescharacteristic
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—1721no—
297C2×C8—1721no—
298C4⋊C4—3441no—
299C4⋊C4—3441no—
300C4⋊C4—1721no—
301C4⋊C4—1721no—
302C22⋊C4—41no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—81no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C22⋊C4—3441no—
309C22⋊C4—1721no—
310C22⋊C4—1721no—
311C22⋊C4—1721no—
312C22⋊C4—1722no—
313C22⋊C4—1722no—
314C42—861no—
315C42—861no—
316C42—861no—
317C42—861no—
318C23—21no—
319C23—21no—
320C23—22no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—42no—
327C23—42no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—81no—
332C23—81no—
333C23—82no—
334C23—82no—
335C23—84no—
336C23—81no—
337C23—81no—
338C23C22⋊C4×D4311yescharacteristic
339C23#1306333111yescharacteristic
340C23#1306333311yescharacteristic
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—431no—
349C2×C4—431no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—3442no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1721no—
370C8—81no—
371C8—81no—
372C8—3441no—
373C8—3441no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—41no—
384C22—41no—
385C22—42no—
386C22—81no—
387C22—81no—
388C22—82no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—81no—
393C22—81no—
394C22#1458286411yescharacteristic
395C22#99×D4311yescharacteristic
396C22#1458288011yescharacteristic
397C4—41no—
398C4—41no—
399C4—81no—
400C4—861no—
401C4—861no—
402C4—3441no—
403C4—3441no—
404C4—1721no—
405C4—1721no—
406C4—1721no—
407C2—21no—
408C2—21no—
409C2—41no—
410C2—41no—
411C2—82no—
412C2#1913294011yescharacteristic
413C2#1913623311yescharacteristic
414C2#1913624311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1316C2
socleC22×C43C2×#99
prime radicalC25×C43C2×C4
cosocleC2×C22⋊C4×C43C23
hypercenter#1316D43
hypocenterC43#11542
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1316

Complements

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

NH ≅ G/Ntype
2. #19132926C2semidirect
3. #19132906C2semidirect
4. #19132544C2semidirect
5. #19132542C2semidirect
234. C43#11542semidirect

Maximal subgroups

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

subgroupindex
#191388662
#191329262
#191329062
#191325442
#191325422
#191325232
C43×#13162
#1154243