Finite Group Databasebeta

← #24999816

Subgroups — #24999816

Order 11008.

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

normal subgroups only

This group has 438 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#19140792C211yesmaximal, characteristic, complemented
2#19135430C211yesmaximal, characteristic
3#19133125C211yesmaximal, characteristic
4#19133112C211yesmaximal, characteristic
5#19132480C211yesmaximal, characteristic, complemented
6#19132449C211yesmaximal, characteristic, complemented
7C43×#1305C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×#13063239—21no—
10C2×#13063239—21no—
11#14582835—21no—
12#14582832—21no—
13#14582832—21no—
14#14582822—21no—
15#14582796—21no—
16#14582782—21no—
17#14582762C2211yescharacteristic
18C4×C22⋊Dic43C2211yescharacteristic
19C4×C22⋊Dic43C2211yescharacteristic
20#14582634—21no—
21#14582634—21no—
22#14582634—21no—
23#14582634—21no—
24C43×#407C2211yescharacteristic
25C43×#407C2211yescharacteristic
26C43×#380C2211yescharacteristic
27C22×D172Q811yescharacteristic
28C22×C22⋊D43—21no—
29#13063299—21no—
30#13063299—21no—
31#13063299—21no—
32#13063299—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43Q811yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×C4×Dic43—21no—
45C2×C4×Dic43—21no—
46#13063239—42no—
47#13063239—42no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95D411yescharacteristic
53C43⋊#95D411yescharacteristic
54C43⋊#95D411yescharacteristic
55C43⋊#95D411yescharacteristic
56C23×C4×C43C2311yescharacteristic
57C2×M16×C43—21no—
58C2×M16×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C22⋊C4×C43D411yescharacteristic
61C2×C22⋊C4×C43D411yescharacteristic
62C22⋊C8×C43—21no—
63C22⋊C8×C43—21no—
64C22⋊C8×C43—21no—
65C22⋊C8×C43—21no—
66#95×C43—21no—
67C24×C43C2×D411yescharacteristic
68C23×D43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—81no—
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×Q811yescharacteristic
75C22×C4×C43#4111yescharacteristic
76C22×C4×C43#4111yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C2×C22⋊D43—41no—
79C2×C22⋊D43—41no—
80C2×C22⋊D43—41no—
81C2×C22⋊D43—41no—
82C2×C22⋊D43—41no—
83C2×C22⋊D43—41no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—41no—
90C2×D172—21no—
91C2×D172—21no—
92C2×D172—81no—
93M16×C43—81no—
94M16×C43—81no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C4⋊C4×C43—81no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊Dic43—22no—
101C22⋊Dic43—41no—
102C22⋊Dic43—42no—
103C22⋊Dic43—81no—
104(C2×D43)⋊C4—41no—
105(C2×D43)⋊C4—41no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43—42no—
109C4⋊Dic43—81no—
110Dic43⋊C4—42no—
111Dic43⋊C4—81no—
112Dic43⋊C4—81no—
113Dic43⋊C4—81no—
114C4×Dic43—81no—
115C4×Dic43—81no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43#12011yescharacteristic
121C23×C43C22⋊Q811yescharacteristic
122C23×C43#12411yescharacteristic
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43—81no—
127C22×D43—81no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43C22⋊Q811yescharacteristic
141C2×C4×C43C22⋊Q811yescharacteristic
142C2×C4×C43#12411yescharacteristic
143C2×C4×C43#12411yescharacteristic
144C22⋊D43—81no—
145C22⋊D43—81no—
146C22⋊D43—81no—
147C22⋊D43—81no—
148C2×Dic43—22no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—42no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—81no—
165C2×Dic43—81no—
166D172—81no—
167D172—81no—
168C8×C43—81no—
169C8×C43—81no—
170#10384—431nomaximal, Sylow
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43#39311yescharacteristic
182C22×C43#45311yescharacteristic
183C22×C43#45411yescharacteristic
184C2×D43—81no—
185C2×D43—81no—
186C2×D43—81no—
187C2×D43—161no—
188C2×D43—161no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—81no—
194C4×C43—81no—
195Dic43—42no—
196Dic43—81no—
197Dic43—81no—
198Dic43—81no—
199Dic43—82no—
200Dic43—81no—
201#2667—431no—
202#1964—431no—
203#1510—431no—
204#1507—431no—
205#1305D4311yescharacteristic, complemented
206#1297—431no—
207#1284—431no—
208C2×C43—21no—
209C2×C43—21no—
210C2×C43—41no—
211C2×C43—41no—
212C2×C43#202711yescharacteristic
213C2×C43#203111yescharacteristic
214C2×C43#203211yescharacteristic
215D43—161no—
216C2×#121—431no—
217C2×#99—861no—
218C2×#99—861no—
219#407C2×D4311yescharacteristic
220#407C2×D4311yescharacteristic
221#399—861no—
222#398—861no—
223#398—861no—
224#396—861no—
225#389—861no—
226#387—861no—
227#381—431no—
228#380C2×D4311yescharacteristic
229C4×C22⋊C4—431no—
230C4×C22⋊C4—431no—
231#327—861no—
232#327—861no—
233#327—861no—
234#327—861no—
235C43#1038411yescharacteristic, complemented, Sylow
236C22×D4—431no—
237C22×D4—861no—
238C23×C4C22×D4311yescharacteristic
239C2×M16—21no—
240C2×M16—21no—
241#121—861no—
242#121—861no—
243#121—861no—
244#121—861no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4—861no—
252C2×C4⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4D17211yescharacteristic
258C2×C22⋊C4D17211yescharacteristic
259C2×C42—861no—
260C2×C42—861no—
261#99—1722no—
262#99—1722no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267#95—21no—
268#95—431no—
269#95—431no—
270#95—431no—
271#95—431no—
272#95—861no—
273#95—861no—
274#95—861no—
275#95—861no—
276C24—861no—
277C24C2×D17211yescharacteristic
278C2×D4—861no—
279C2×D4—861no—
280C2×D4—3441no—
281C2×D4—1721no—
282C2×D4—1721no—
283C2×D4—1721no—
284C2×D4—1721no—
285C2×D4—1721no—
286C2×D4—1721no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—81no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—1721no—
296C22×C4#1062189811yescharacteristic
297C22×C4#1062189811yescharacteristic
298C22×C4D4×D4311yescharacteristic
299C22×C4D4×D4311yescharacteristic
300C22×C4#1062190011yescharacteristic
301C22×C4Q8×D4311yescharacteristic
302M16—81no—
303M16—81no—
304C2×C8—41no—
305C2×C8—41no—
306C4⋊C4—81no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—3441no—
310C4⋊C4—3441no—
311C4⋊C4—3441no—
312C4⋊C4—3441no—
313C4⋊C4—1722no—
314C4⋊C4—1722no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—862no—
318C22⋊C4—3441no—
319C22⋊C4—1722no—
320C22⋊C4—1721no—
321C22⋊C4—1721no—
322C22⋊C4—1721no—
323C42—3441no—
324C42—3441no—
325C23—21no—
326C23—21no—
327C23—41no—
328C23—41no—
329C23—3441no—
330C23—3441no—
331C23—1721no—
332C23—1721no—
333C23—1721no—
334C23#1306329511yescharacteristic
335C23#1306330511yescharacteristic
336C23#1306331311yescharacteristic
337D4—3441no—
338D4—3441no—
339D4—3441no—
340D4—3441no—
341D4—3441no—
342D4—3441no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—862no—
356C2×C4—3441no—
357C2×C4—3441no—
358C2×C4—1721no—
359C2×C4—1722no—
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—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4#1306330311yescharacteristic
374C2×C4#1306330311yescharacteristic
375C2×C4#1306331111yescharacteristic
376C2×C4#1306331111yescharacteristic
377C8—81no—
378C8—81no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—81no—
388C22—81no—
389C22—3441no—
390C22—3441no—
391C22—3441no—
392C22—6881no—
393C22—6881no—
394C22#1458281211yescharacteristic
395C22#1458306911yescharacteristic
396C22#1458307411yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—81no—
402C4—81no—
403C4—3441no—
404C4—3441no—
405C4—3441no—
406C4—3442no—
407C4—3441no—
408C4—1722no—
409C2—21no—
410C2—21no—
411C2—41no—
412C2—41no—
413C2—6881no—
414C2#1913575211yescharacteristic
415C2#1913577011yescharacteristic
416C2#1913577311yescharacteristic
subgroupG/H
centerC22#14582812
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1305C2
socleC22×C43#393
prime radicalC2×#13063299C22
hypercenter#1305D43
hypocenterC43#10384
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
1. #19140792C2semidirect
5. #19132480C2semidirect
6. #19132449C2semidirect
7. C43×#1305C2semidirect
205. #1305D43semidirect
235. C43#10384semidirect

Maximal subgroups

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

subgroupindex
#191407922
#191354302
#191331252
#191331122
#191324802
#191324492
C43×#13052
#1038443