Finite Group Databasebeta

← #24994316

Subgroups — #24994316

Order 11008.

904 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 904 conjugacy classes of subgroups — too many to draw. Only its 111 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#19138242C211yesmaximal, characteristic
2#19134516C211yesmaximal, characteristic
3#19133127C212yesmaximal, complemented
4#19132447C212yesmaximal, complemented
5C43×#2308C211yesmaximal, characteristic
6C2×#13063312C412yescomplemented
7C2×#13063304C2211yescharacteristic
8C2×#13063242—22no—
9#14582863C2212yes—
10#14582813—22no—
11#14582802C412yescomplemented
12#14582755—21no—
13#14582755—21no—
14C4×C22⋊Dic43C2211yescharacteristic
15#14582635—24no—
16C23×D4×C43C2211yescharacteristic
17C22×C22⋊C4×C43—21no—
18C43×#386—24no—
19C43×#381C2212yes—
20C43×#379—21no—
21C22×Dic86C2×C411yescharacteristic, complemented
22C2×#10621877—22no—
23#13063312—44no—
24#13063304—22no—
25#13063304—22no—
26C2×C4⋊Dic43C2×C411yescharacteristic, complemented
27C2×Dic43⋊C4—21no—
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—22no—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—22no—
33C2×C22⋊Dic43—22no—
34C2×C4×Dic43C2×C412yescomplemented
35#13063242—44no—
36C22⋊(C43⋊C8)—22no—
37C22⋊(C43⋊C8)—22no—
38C43⋊#95—21no—
39C25×C43D411yescharacteristic
40C25×C43D411yescharacteristic
41C22×D4×C43—22no—
42C22×D4×C43—22no—
43C22×D4×C43—44no—
44C22×D4×C43C2×C412yes—
45C22×D4×C43D412yes—
46C23×C4×C43—22no—
47C23×C4×C43C2311yescharacteristic
48C2×C22⋊C4×C43—22no—
49C2×C22⋊C4×C43—22no—
50C2×C22⋊C4×C43—22no—
51C2×C22⋊C4×C43—22no—
52C2×C22⋊C4×C43—44no—
53#95×C43—22no—
54#95×C43D414yes—
55C24×C43—21no—
56C24×C43—24no—
57C24×C43—21no—
58C24×C43—21no—
59C24×C43—21no—
60C24×C43—42no—
61C24×C43—42no—
62C24×C43—42no—
63C24×C43—81no—
64C24×C43—81no—
65C24×C43C22⋊C412yes—
66C24×C43C22⋊C412yes—
67C24×C43C2×D411yescharacteristic
68C2×D4×C43—24no—
69C2×D4×C43—24no—
70C2×D4×C43—24no—
71C2×D4×C43—24no—
72C2×D4×C43—42no—
73C2×D4×C43—42no—
74C2×D4×C43—44no—
75C2×D4×C43—44no—
76C2×D4×C43—48no—
77C22×C4×C43—24no—
78C22×C4×C43—42no—
79C22×C4×C43—44no—
80C22×C4×C43—82no—
81C22×C4×C43—82no—
82C22×C4×C43C22×C411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D412yes—
85C22×C4×C43#4112yes—
86C22×Dic43—22no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C2×Dic86—22no—
90C2×Dic86—42no—
91C22⋊C4×C43—44no—
92C22⋊C4×C43—44no—
93C22⋊C4×C43—82no—
94C22⋊C4×C43—82no—
95C22⋊Dic43—42no—
96C22⋊Dic43—44no—
97C22⋊Dic43—44no—
98C22⋊Dic43—41no—
99C22⋊Dic43—41no—
100C22⋊Dic43—82no—
101C22⋊Dic43—82no—
102C4⋊Dic43—22no—
103Dic43⋊C4—42no—
104C4×Dic43—42no—
105#10621877—44no—
106C2×C43⋊C8—42no—
107C23×C43—22no—
108C23×C43—22no—
109C23×C43—24no—
110C23×C43—22no—
111C23×C43—22no—
112C23×C43—22no—
113C23×C43—22no—
114C23×C43—22no—
115C23×C43—22no—
116C23×C43—22no—
117C23×C43—41no—
118C23×C43—42no—
119C23×C43—42no—
120C23×C43—42no—
121C23×C43—42no—
122C23×C43—42no—
123C23×C43—42no—
124C23×C43—42no—
125C23×C43—42no—
126C23×C43—42no—
127C23×C43—42no—
128C23×C43—81no—
129C23×C43—81no—
130C23×C43—81no—
131C23×C43—81no—
132C23×C43—88no—
133C23×C43—88no—
134C23×C43#9914yes—
135C23×C43C2×C22⋊C411yescharacteristic
136C23×C43#12011yescharacteristic
137C23×C43#12311yescharacteristic
138D4×C43—48no—
139D4×C43—48no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—44no—
145C2×C4×C43—44no—
146C2×C4×C43—44no—
147C2×C4×C43—88no—
148C2×C4×C43C4×D412yes—
149C2×C4×C43#12112yes—
150C2×Dic43—42no—
151C2×Dic43—42no—
152C2×Dic43—42no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157Dic86—82no—
158C43⋊C8—82no—
159#9459—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—24no—
167C22×C43—21no—
168C22×C43—44no—
169C22×C43—44no—
170C22×C43—44no—
171C22×C43—44no—
172C22×C43—44no—
173C22×C43—42no—
174C22×C43—42no—
175C22×C43—42no—
176C22×C43—42no—
177C22×C43—42no—
178C22×C43—82no—
179C22×C43—82no—
180C22×C43—84no—
181C22×C43—84no—
182C22×C43—84no—
183C22×C43#38611yescharacteristic
184C22×C43C2×#9912yes—
185C22×C43#45512yes—
186C4×C43—22no—
187C4×C43—22no—
188C4×C43—84no—
189Dic43—82no—
190Dic43—81no—
191Dic43—81no—
192#2435—431no—
193#2308D4311yescharacteristic
194#1783—431no—
195#1511—432no—
196#1284—432no—
197C2×C43—22no—
198C2×C43—22no—
199C2×C43—41no—
200C2×C43—44no—
201C2×C43—82no—
202C2×C43#188511yescharacteristic
203C2×C43#189811yescharacteristic
204C2×C43#191111yescharacteristic
205C23×D4C2×D4311yescharacteristic
206C2×#124—432no—
207C2×C22⋊Q8—431no—
208C22×C22⋊C4—21no—
209C2×#100—862no—
210#407—432no—
211#394—862no—
212#390—432no—
213#386—24no—
214#381C2×D4312yes—
215#379—21no—
216#379—861no—
217#379—861no—
218C4×C22⋊C4—431no—
219#328—864no—
220C43#945911yescharacteristic, complemented, Sylow
221C25C22⋊D4311yescharacteristic
222C25C22⋊D4311yescharacteristic
223C22×Q8—431no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—44no—
227C22×D4C4×D4312yes—
228C22×D4D17212yes—
229C23×C4—22no—
230C23×C4C22×D4311yescharacteristic
231C2×M16—862no—
232#124—1724no—
233C22⋊Q8—862no—
234C22⋊Q8—862no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—861no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—44no—
242C2×C22⋊C4—862no—
243C2×C22⋊C4—862no—
244C2×C22⋊C4—862no—
245C2×C22⋊C4—862no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C42—432no—
249#100—1724no—
250C22⋊C8—862no—
251C22⋊C8—862no—
252#95—22no—
253#95—861no—
254#95C22⋊D4314yes—
255C24—21no—
256C24—24no—
257C24—21no—
258C24—21no—
259C24—21no—
260C24—42no—
261C24—42no—
262C24—42no—
263C24—81no—
264C24—81no—
265C24(C2×D43)⋊C412yes—
266C24(C2×D43)⋊C412yes—
267C24C2×C22⋊D4311yescharacteristic
268C2×Q8—862no—
269C2×Q8—1722no—
270C2×D4—24no—
271C2×D4—24no—
272C2×D4—24no—
273C2×D4—24no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—48no—
277C2×D4—44no—
278C2×D4—44no—
279C22×C4—24no—
280C22×C4—42no—
281C22×C4—44no—
282C22×C4—82no—
283C22×C4—82no—
284C22×C4—862no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4C2×C4×D4311yescharacteristic
288C22×C4C2×D17211yescharacteristic
289C22×C4#1062189812yes—
290C22×C4C2×C22⋊D4312yes—
291M16—1724no—
292C2×C8—1722no—
293C4⋊C4—862no—
294C4⋊C4—1722no—
295C22⋊C4—44no—
296C22⋊C4—44no—
297C22⋊C4—82no—
298C22⋊C4—82no—
299C22⋊C4—3442no—
300C22⋊C4—3442no—
301C22⋊C4—1724no—
302C22⋊C4—1722no—
303C22⋊C4—1724no—
304C22⋊C4—1721no—
305C22⋊C4—1721no—
306C42—1722no—
307C23—22no—
308C23—22no—
309C23—24no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—41no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—88no—
333C23—88no—
334C23#1306323914yes—
335C23C2×(C2×D43)⋊C411yescharacteristic
336C23#1306329411yescharacteristic
337C23#1306330811yescharacteristic
338Q8—3442no—
339D4—48no—
340D4—48no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—88no—
349C2×C4—1722no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4—1722no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4C4×C22⋊D4312yes—
357C2×C4#1306329912yes—
358C8—3442no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—24no—
366C22—21no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—44no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—42no—
376C22—42no—
377C22—82no—
378C22—82no—
379C22—84no—
380C22—84no—
381C22—84no—
382C22#1458277811yescharacteristic
383C22C2×#1306323912yes—
384C22#1458307712yes—
385C4—22no—
386C4—22no—
387C4—84no—
388C4—3442no—
389C4—3441no—
390C4—3441no—
391C2—22no—
392C2—22no—
393C2—41no—
394C2—44no—
395C2—82no—
396C2#1913498311yescharacteristic
397C2#1913504811yescharacteristic
398C2#1913512711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2308C2
socleC22×C43#386
prime radicalC23×D4×C43C22
cosocleC23×C4×C43C23
hypercenter#2308D43
hypocenterC43#9459
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2308

Complements

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

NH ≅ G/Ntype
3. #19133127C2semidirect
4. #19132447C2semidirect
6. C2×#13063312C4semidirect
11. #14582802C4semidirect
21. C22×Dic86C2×C4semidirect
26. C2×C4⋊Dic43C2×C4semidirect
34. C2×C4×Dic43C2×C4semidirect
220. C43#9459semidirect

Maximal subgroups

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

subgroupindex
#191382422
#191345162
#191331272
#191324472
C43×#23082
#945943