Finite Group Databasebeta

← #24994256

Subgroups — #24994256

Order 11008.

568 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 103 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#19139562C211yesmaximal, characteristic
2#19133218C212yesmaximal, complemented
3#19132936C211yesmaximal, characteristic, complemented
4#19132450C212yesmaximal, complemented
5C43×#2973C211yesmaximal, characteristic, complemented
6C2×#13063321C411yescharacteristic
7C2×#13063313C2211yescharacteristic
8C2×#13063312C411yescharacteristic
9#14582956C2212yes—
10#14582815—21no—
11#14582815—21no—
12#14582804C411yescharacteristic
13#14582800C411yescharacteristic
14#14582778—21no—
15#14582778—21no—
16C4×C4⋊Dic43C2211yescharacteristic
17#14582638—24no—
18#14582623—21no—
19#14582623—21no—
20C2×C4×D4×C43C2211yescharacteristic
21C43×#435—24no—
22C43×#432C2212yes—
23C43×#407—21no—
24C2×C22⋊C8×C43—21no—
25C22×Dic86C2×C411yescharacteristic
26C22×D172C2×C411yescharacteristic
27C22×C22⋊D43—21no—
28C22×C22⋊D43—21no—
29#13063321—42no—
30#13063313—22no—
31#13063313—22no—
32#13063312—42no—
33C2×C4⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×C4×Dic43C2×C411yescharacteristic
41C2×C4×Dic43C2×C411yescharacteristic
42C4⋊(C43⋊C8)—22no—
43C22⋊(C43⋊C8)—22no—
44#13063236—22no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C22×D4×C43C2×C411yescharacteristic
49C23×C4×C43D411yescharacteristic
50C23×C4×C43D411yescharacteristic
51C2×M16×C43—22no—
52C22×C8×C43—22no—
53C4×D4×C43—22no—
54C4×D4×C43—22no—
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C22⋊C4×C43D411yescharacteristic
57C2×C22⋊C4×C43D411yescharacteristic
58C2×C42×C43C2311yescharacteristic
59C4⋊C8×C43—22no—
60C22⋊C8×C43—22no—
61C22⋊C8×C43—22no—
62C22⋊C8×C43—22no—
63#97×C43D414yescomplemented
64C24×C43C22⋊C411yescharacteristic
65C24×C43C22⋊C411yescharacteristic
66C23×D43—21no—
67C2×D4×C43—22no—
68C2×D4×C43—22no—
69C2×D4×C43—41no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—81no—
75C22×C4×C43—81no—
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43C22×C411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C2×C22⋊D43—42no—
82C2×C22⋊D43—42no—
83C2×C22⋊D43—42no—
84C2×C22⋊D43—42no—
85C2×C22⋊D43—81no—
86C2×C22⋊D43—81no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C2×D172—22no—
91C2×D172—41no—
92C2×D172—41no—
93C2×Dic86—22no—
94C2×Dic86—41no—
95C2×Dic86—41no—
96M16×C43—82no—
97C2×C8×C43—24no—
98C2×C8×C43—82no—
99C4⋊C4×C43—22no—
100C22⋊C4×C43—22no—
101C22⋊C4×C43—22no—
102C42×C43C2×D412yes—
103C42×C43#4112yes—
104C22⋊Dic43—42no—
105C22⋊Dic43—42no—
106(C2×D43)⋊C4—41no—
107(C2×D43)⋊C4—42no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—81no—
110(C2×D43)⋊C4—81no—
111C4⋊Dic43—42no—
112C4×Dic43—41no—
113C4×Dic43—41no—
114C2×C43⋊C8—42no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43#10012yes—
125C23×C43C2×C22⋊C411yescharacteristic
126C22×D43—41no—
127C22×D43—41no—
128C22×D43—41no—
129C22×D43—41no—
130C22×D43—41no—
131C22×D43—41no—
132C22×D43—41no—
133D4×C43—44no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—81no—
145C2×C4×C43—81no—
146C2×C4×C43C4×D412yes—
147C2×C4×C43#12011yescharacteristic
148C2×C4×C43#12112yes—
149C2×C4×C43#12311yescharacteristic
150C22⋊D43—84no—
151C22⋊D43—84no—
152C2×Dic43—22no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161D172—82no—
162Dic86—82no—
163C8×C43—44no—
164C43⋊C8—82no—
165#9447—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—22no—
169C22×C43—42no—
170C22×C43—42no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—81no—
177C22×C43—81no—
178C22×C43#38611yescharacteristic
179C22×C43C2×#10011yescharacteristic
180C22×C43#41311yescharacteristic
181C2×D43—81no—
182C2×D43—81no—
183C2×D43—81no—
184C2×D43—81no—
185C2×D43—81no—
186C2×D43—81no—
187C2×D43—81no—
188C4×C43—22no—
189C4×C43—22no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—41no—
193C4×C43—41no—
194Dic43—42no—
195Dic43—81no—
196Dic43—81no—
197#2973D4311yescharacteristic, complemented
198#2544—431no—
199#1533—432no—
200#1466—431no—
201#1285—432no—
202C2×C43—21no—
203C2×C43—21no—
204C2×C43—42no—
205C2×C43—81no—
206C2×C43#188411yescharacteristic
207C2×C43#190011yescharacteristic
208C2×C43#191111yescharacteristic
209D43—161no—
210C2×#127—431no—
211C2×#124—431no—
212C2×#124—431no—
213C2×C4×D4C2×D4311yescharacteristic
214#435—24no—
215#432—432no—
216#432C2×D4312yes—
217#407—21no—
218C2×C22⋊C8—21no—
219#394—861no—
220#394—861no—
221#391—431no—
222#390—431no—
223#386—861no—
224#386—861no—
225C4×C4⋊C4—431no—
226#329—864no—
227#323—861no—
228#323—861no—
229C43#944711yescharacteristic, complemented, Sylow
230C22×Q8—431no—
231C22×D4—431no—
232C22×D4—861no—
233C22×D4—861no—
234C22×D4C4×D4311yescharacteristic
235C23×C4C22⋊D4311yescharacteristic
236C23×C4C22⋊D4311yescharacteristic
237C2×M16—22no—
238C22×C8—22no—
239#127—1722no—
240#124—862no—
241#124—862no—
242#124—1722no—
243C4×D4—22no—
244C4×D4—22no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4C4×D4311yescharacteristic
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⋊C4D17211yescharacteristic
254C2×C22⋊C4D17211yescharacteristic
255C2×C42—431no—
256C2×C42—431no—
257C2×C42C22×D4311yescharacteristic
258C4⋊C8—22no—
259C4⋊C8—862no—
260C22⋊C8—22no—
261C22⋊C8—22no—
262C22⋊C8—22no—
263C22⋊C8—862no—
264#97—862no—
265#97C22⋊D4314yescomplemented
266#95—861no—
267#95—861no—
268#95—861no—
269C24—861no—
270C24(C2×D43)⋊C411yescharacteristic
271C24(C2×D43)⋊C411yescharacteristic
272C2×Q8—862no—
273C2×Q8—1721no—
274C2×Q8—1721no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—41no—
278C2×D4—862no—
279C2×D4—3441no—
280C2×D4—3441no—
281C2×D4—1721no—
282C2×D4—1721no—
283C2×D4—1722no—
284C2×D4—1722no—
285C2×D4—1722no—
286C2×D4—1722no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—81no—
292C22×C4—81no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4(C2×D43)⋊C411yescharacteristic
297C22×C4(C2×D43)⋊C411yescharacteristic
298C22×C4C2×C4×D4311yescharacteristic
299C22×C4C2×D17211yescharacteristic
300C22×C4C2×C22⋊D4311yescharacteristic
301M16—82no—
302C2×C8—24no—
303C2×C8—82no—
304C2×C8—1722no—
305C4⋊C4—22no—
306C4⋊C4—1722no—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—3441no—
310C22⋊C4—3441no—
311C22⋊C4—1722no—
312C22⋊C4—1722no—
313C22⋊C4—1721no—
314C22⋊C4—1722no—
315C22⋊C4—1721no—
316C42—1721no—
317C42—1721no—
318C42#1062189812yes—
319C42C2×C22⋊D4312yes—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—1721no—
330C23—1721no—
331C23—1721no—
332C23—1721no—
333C23—1721no—
334C23—1721no—
335C23—1721no—
336C23#1306324112yes—
337C23C2×(C2×D43)⋊C411yescharacteristic
338Q8—3442no—
339D4—44no—
340D4—3442no—
341D4—3444no—
342D4—3444no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—862no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4C4×C22⋊D4312yes—
365C2×C4#1306329411yescharacteristic
366C2×C4#1306329912yes—
367C2×C4#1306330811yescharacteristic
368C8—44no—
369C8—3442no—
370C22—21no—
371C22—21no—
372C22—22no—
373C22—42no—
374C22—42no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—3441no—
383C22—3441no—
384C22—3441no—
385C22—3441no—
386C22—3441no—
387C22—3441no—
388C22—3441no—
389C22#1458277811yescharacteristic
390C22C2×#1306324111yescharacteristic
391C22#1458288111yescharacteristic
392C4—22no—
393C4—22no—
394C4—21no—
395C4—21no—
396C4—41no—
397C4—41no—
398C4—3441no—
399C4—3441no—
400C4—1722no—
401C2—21no—
402C2—21no—
403C2—42no—
404C2—81no—
405C2—6881no—
406C2#1913497811yescharacteristic
407C2#1913505811yescharacteristic
408C2#1913512711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2973C2
socleC22×C43#386
prime radicalC2×#13063321C4
cosocleC2×C42×C43C23
hypercenter#2973D43
hypocenterC43#9447
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #19133218C2semidirect
3. #19132936C2semidirect
4. #19132450C2semidirect
5. C43×#2973C2semidirect
63. #97×C43D4semidirect
197. #2973D43semidirect
229. C43#9447semidirect
265. #97C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191395622
#191332182
#191329362
#191324502
C43×#29732
#944743