Finite Group Databasebeta

← #24999859

Subgroups — #24999859

Order 11008.

526 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 73 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#19142859C211yesmaximal, characteristic
2#19134667C211yesmaximal, characteristic
3#19134667C211yesmaximal, characteristic
4#19134667C211yesmaximal, characteristic
5C43⋊#1304C211yesmaximal, characteristic
6C43⋊#1304C211yesmaximal, characteristic
7C43×#1304C211yesmaximal, characteristic
8C22×C22⋊Dic43C2211yescharacteristic
9#14582835—22no—
10#14582822—22no—
11#14582822—22no—
12#14582755C2211yescharacteristic
13#14582755C2211yescharacteristic
14#14582755C2211yescharacteristic
15#14582665—22no—
16#14582665—22no—
17#14582665—22no—
18C43×#379C2211yescharacteristic
19C43×#379C2211yescharacteristic
20C43×#379C2211yescharacteristic
21C23×Dic43Q811yescharacteristic
22C23×Dic43Q811yescharacteristic
23C2×C4⋊Dic43—22no—
24C2×Dic43⋊C4—22no—
25C2×Dic43⋊C4—22no—
26C2×C22⋊Dic43—21no—
27C2×C22⋊Dic43—21no—
28C2×C22⋊Dic43—21no—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43D412yes—
40C2×C22⋊Dic43D412yes—
41C43⋊#95—22no—
42C25×C43C2311yescharacteristic
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43—21no—
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43—21no—
48C2×C22⋊C4×C43—21no—
49C2×C22⋊C4×C43—21no—
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43D412yes—
52C24×C43—42no—
53C24×C43—81no—
54C24×C43—81no—
55C24×C43C2×D411yescharacteristic
56C24×C43C2×D411yescharacteristic
57C24×C43C2×D411yescharacteristic
58C24×C43C2×Q811yescharacteristic
59C24×C43#4111yescharacteristic
60C24×C43#4111yescharacteristic
61C24×C43#4111yescharacteristic
62C22×C4×C43—22no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×Dic43—22no—
66C22×Dic43—22no—
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—41no—
74C22×Dic43—81no—
75C22×Dic43—81no—
76C22⋊C4×C43—42no—
77C22⋊C4×C43—42no—
78C22⋊C4×C43—42no—
79C22⋊C4×C43—81no—
80C22⋊C4×C43—81no—
81C22⋊C4×C43—81no—
82C22⋊C4×C43—81no—
83C22⋊C4×C43—81no—
84C22⋊C4×C43—81no—
85C22⋊Dic43—42no—
86C22⋊Dic43—42no—
87C22⋊Dic43—42no—
88C22⋊Dic43—41no—
89C22⋊Dic43—41no—
90C22⋊Dic43—41no—
91C22⋊Dic43—41no—
92C22⋊Dic43—81no—
93C22⋊Dic43—81no—
94C22⋊Dic43—81no—
95C22⋊Dic43—81no—
96C22⋊Dic43—81no—
97C22⋊Dic43—81no—
98C4⋊Dic43—82no—
99Dic43⋊C4—82no—
100Dic43⋊C4—82no—
101C23×C43—22no—
102C23×C43—22no—
103C23×C43—22no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—88no—
123C23×C43#12011yescharacteristic
124C23×C43C22⋊Q811yescharacteristic
125C23×C43C22⋊Q811yescharacteristic
126C23×C43C22⋊Q811yescharacteristic
127C23×C43#12411yescharacteristic
128C23×C43#12411yescharacteristic
129C23×C43#12411yescharacteristic
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43—81no—
138C2×C4×C43—81no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—42no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—42no—
146C2×Dic43—42no—
147C2×Dic43—81no—
148C2×Dic43—81no—
149C2×Dic43—81no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153C2×Dic43—81no—
154C2×Dic43—81no—
155C2×Dic43—81no—
156#10393—431nomaximal, Sylow
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—44no—
178C22×C43—82no—
179C22×C43—82no—
180C22×C43—82no—
181C22×C43—82no—
182C22×C43—82no—
183C22×C43—82no—
184C22×C43#39311yescharacteristic
185C22×C43#45812yes—
186C4×C43—82no—
187C4×C43—161no—
188C4×C43—161no—
189Dic43—82no—
190Dic43—82no—
191Dic43—81no—
192Dic43—81no—
193Dic43—161no—
194#2842—431no—
195#1819—431no—
196#1819—431no—
197#1819—431no—
198#1304—431no—
199#1304—431no—
200#1304D4311yescharacteristic
201C2×C43—22no—
202C2×C43—41no—
203C2×C43—41no—
204C2×C43—41no—
205C2×C43—41no—
206C2×C43—41no—
207C2×C43—41no—
208C2×C43#203011yescharacteristic
209C2×C43#203211yescharacteristic
210C2×C43#203211yescharacteristic
211C22×C22⋊C4—431no—
212#399—862no—
213#396—862no—
214#396—862no—
215#379—431no—
216#379—431no—
217#379—431no—
218#379C2×D4311yescharacteristic
219#379C2×D4311yescharacteristic
220#379C2×D4311yescharacteristic
221#342—862no—
222#342—862no—
223#342—862no—
224C43#1039311yescharacteristic, complemented, Sylow
225C25C22×D4311yescharacteristic
226C23×C4—431no—
227C23×C4—431no—
228C2×C4⋊C4—862no—
229C2×C4⋊C4—862no—
230C2×C4⋊C4—862no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—432no—
240C2×C22⋊C4—432no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—861no—
249C2×C22⋊C4—861no—
250C2×C22⋊C4—861no—
251C2×C22⋊C4—861no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4D17212yes—
255#95—862no—
256C24—42no—
257C24—81no—
258C24—81no—
259C24C2×D17211yescharacteristic
260C24#1062189811yescharacteristic
261C24#1062189811yescharacteristic
262C24D4×D4311yescharacteristic
263C24D4×D4311yescharacteristic
264C24#1062190011yescharacteristic
265C24Q8×D4311yescharacteristic
266C22×C4—22no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—862no—
276C22×C4—862no—
277C22×C4—3441no—
278C22×C4—3441no—
279C22×C4—1721no—
280C4⋊C4—3442no—
281C4⋊C4—3442no—
282C4⋊C4—3442no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—81no—
287C22⋊C4—81no—
288C22⋊C4—81no—
289C22⋊C4—81no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C22⋊C4—3441no—
293C22⋊C4—3441no—
294C22⋊C4—3441no—
295C22⋊C4—3441no—
296C22⋊C4—3441no—
297C22⋊C4—3441no—
298C22⋊C4—1722no—
299C22⋊C4—1721no—
300C22⋊C4—1721no—
301C22⋊C4—1721no—
302C22⋊C4—1721no—
303C22⋊C4—1722no—
304C22⋊C4—1722no—
305C23—22no—
306C23—22no—
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—88no—
327C23#1306329511yescharacteristic
328C23#1306330311yescharacteristic
329C23#1306330311yescharacteristic
330C23#1306330511yescharacteristic
331C23#1306331111yescharacteristic
332C23#1306331111yescharacteristic
333C23#1306331311yescharacteristic
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—3441no—
344C2×C4—3441no—
345C2×C4—3441no—
346C2×C4—3441no—
347C2×C4—3441no—
348C2×C4—3441no—
349C2×C4—3441no—
350C2×C4—3441no—
351C2×C4—3441no—
352C2×C4—1722no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1722no—
359C2×C4—1722no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—44no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—82no—
387C22#1458281211yescharacteristic
388C22#1458309012yes—
389C4—82no—
390C4—161no—
391C4—161no—
392C4—3442no—
393C4—3442no—
394C4—3441no—
395C4—3441no—
396C4—6881no—
397C2—22no—
398C2—41no—
399C2—41no—
400C2—41no—
401C2—41no—
402C2—41no—
403C2—41no—
404C2#1913576311yescharacteristic
405C2#1913577311yescharacteristic
406C2#1913577311yescharacteristic
subgroupG/H
centerC22#14582812
commutator, prime radical, cosocleC25×C43C23
FrattiniC25C22×D43
FittingC43×#1304C2
socleC22×C43#393
hypercenter#1304D43
hypocenterC43#10393
LCSG ▷ C25×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #1304

Complements

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

NH ≅ G/Ntype
224. C43#10393semidirect

Maximal subgroups

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

subgroupindex
#191428592
#191346672
C43⋊#13042
C43×#13042
#1039343