Finite Group Databasebeta

← #25006801

Subgroups — #25006801

Order 11008.

514 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 83 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#19140336C211yesmaximal, characteristic
2#343×D43C211yesmaximal, characteristic, complemented
3#324×D43C211yesmaximal, characteristic, complemented
4#19132602C211yesmaximal, characteristic, complemented
5#19132600C211yesmaximal, characteristic, complemented
6#19132598C211yesmaximal, characteristic, complemented
7C43×#1345C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×#13063307—21no—
10C2×#13063296C411yescharacteristic
11C2×C4⋊C4×D43C2211yescharacteristic
12C22⋊C8×D43—21no—
13#14582831C411yescharacteristic
14#14582829C2211yescharacteristic
15#14582822—21no—
16#14582822—21no—
17#14582813C411yescharacteristic
18#14582775—21no—
19#14582758C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#394C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C22⋊D43—21no—
28C22×C4×D43C2×C411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×#10621877—21no—
32C2×#10621872—41no—
33M16×D43—24no—
34M16×D43—42no—
35C2×C8×D43—41no—
36C2×C8×D43—41no—
37#13063307—42no—
38#13063307—42no—
39#13063296—41no—
40#13063296—41no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43C2×C411yescharacteristic
43C2×C4⋊Dic43D411yescharacteristic
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4C2×C411yescharacteristic
47C2×Dic43⋊C4D411yescharacteristic
48C4⋊C4×D43—41no—
49C4⋊C4×D43—41no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43—21no—
52C2×C22⋊Dic43—21no—
53C2×(C2×D43)⋊C4—21no—
54C22⋊(C43⋊C8)—21no—
55(C2×D43)⋊C8—41no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95C2×C411yescharacteristic
59C22×D4×C43C2×C411yescharacteristic
60C2×M16×C43—21no—
61C2×C4⋊C4×C43C2311yescharacteristic
62C2×C22⋊C4×C43—21no—
63C2×C22⋊C4×C43—21no—
64C22⋊C8×C43—21no—
65#95×C43C2×C411yescharacteristic
66C24×C43—21no—
67C23×D43C22⋊C411yescharacteristic
68C2×D4×C43—41no—
69C2×D4×C43—81no—
70C22×C4×C43—21no—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C2×C22⋊D43—41no—
75C2×C22⋊D43—41no—
76C2×C22⋊D43—42no—
77C2×C22⋊D43—42no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43C22⋊C411yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43—22no—
90C2×C4×D43—81no—
91C2×C4×D43—81no—
92C2×C4×D43D812yes—
93C2×C4×D43SD1612yes—
94M16×C43—22no—
95M16×C43—41no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C4⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—41no—
101C22⋊C4×C43—81no—
102C22⋊Dic43—42no—
103C22⋊Dic43—42no—
104C22⋊Dic43—81no—
105(C2×D43)⋊C4—42no—
106C4⋊Dic43—41no—
107C4⋊Dic43—42no—
108C4⋊Dic43—41no—
109Dic43⋊C4—41no—
110Dic43⋊C4—41no—
111Dic43⋊C4—41no—
112Dic43⋊C4—41no—
113Dic43⋊C4—81no—
114#10621877—22no—
115#10621877—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118#10621872—44no—
119C8×D43—44no—
120C8×D43—82no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43C2×C22⋊C411yescharacteristic
129C22×D43—41no—
130C22×D43—41no—
131C22×D43#9911yescharacteristic
132C22×D43#9911yescharacteristic
133C22×D43#10212yes—
134C22×D43#10412yes—
135D4×C43—82no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43C2×D811yescharacteristic
146C2×C4×C43C2×SD1611yescharacteristic
147C22⋊D43—82no—
148C22⋊D43—82no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43#10212yes—
162C4×D43—22no—
163C4×D43—22no—
164C4×D43—22no—
165C4×D43—22no—
166C4×D43—42no—
167C4×D43—81no—
168C4×D43—81no—
169C4×D43—81no—
170C8×C43—42no—
171C8×C43—81no—
172C43⋊C8—42no—
173C43⋊C8—81no—
174#11698—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—81no—
178C22×C43—81no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43—81no—
183C22×C43—81no—
184C22×C43C2×#9911yescharacteristic
185C22×C43C2×#10211yescharacteristic
186C22×C43C2×#10411yescharacteristic
187C2×D43—21no—
188C2×D43—21no—
189C2×D43—21no—
190C2×D43—21no—
191C2×D43—42no—
192C2×D43—42no—
193C2×D43#32712yes—
194C2×D43#32712yes—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—41no—
198C4×C43—41no—
199C4×C43—81no—
200Dic43—22no—
201Dic43—41no—
202Dic43—41no—
203Dic43—81no—
204Dic43—81no—
205#2618—431no—
206C2×#343—431no—
207C2×#324—431no—
208#1346—431no—
209#1346—431no—
210#1345—431no—
211#1345D4311yescharacteristic, complemented
212C2×C43—21no—
213C2×C43—21no—
214C2×C43—161no—
215C2×C43C2×#32711yescharacteristic
216C2×C43#212111yescharacteristic
217C2×C43#213311yescharacteristic
218D43—22no—
219D43—22no—
220C22×M16—861no—
221C2×#123—861no—
222C2×#121—431no—
223C22×C4⋊C4—431no—
224C2×C22⋊C8—861no—
225#398—431no—
226#398—431no—
227#396—861no—
228#396—861no—
229#394—431no—
230#394C2×D4311yescharacteristic
231#386—861no—
232#380—431no—
233#343—431no—
234#343—861no—
235#343C2×D4311yescharacteristic
236#324—431no—
237#324—861no—
238#324C2×D4311yescharacteristic
239C43#1169811yescharacteristic, complemented, Sylow
240C22×D4—861no—
241C22×D4C4×D4311yescharacteristic
242C23×C4—431no—
243C23×C4—431no—
244C23×C4—431no—
245C2×M16—21no—
246C2×M16—864no—
247C2×M16—861no—
248C2×M16—1721no—
249C2×M16—1722no—
250C22×C8—1721no—
251C22×C8—1721no—
252#123—1722no—
253#123—1722no—
254#121—1721no—
255#121—1721no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4—431no—
258C2×C4⋊C4—431no—
259C2×C4⋊C4—431no—
260C2×C4⋊C4—861no—
261C2×C4⋊C4—861no—
262C2×C4⋊C4—861no—
263C2×C4⋊C4—1721no—
264C2×C4⋊C4—1721no—
265C2×C4⋊C4C22×D4311yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—861no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C22⋊C8—21no—
273C22⋊C8—861no—
274C22⋊C8—1721no—
275#95—431no—
276#95—861no—
277#95—861no—
278#95C4×D4311yescharacteristic
279C24—21no—
280C24—431no—
281C2×D4—41no—
282C2×D4—81no—
283C2×D4—1721no—
284C2×D4—1721no—
285C2×D4—1722no—
286C2×D4—1722no—
287C22×C4—21no—
288C22×C4—431no—
289C22×C4—432no—
290C22×C4—432no—
291C22×C4—431no—
292C22×C4—431no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—862no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4—861no—
299C22×C4—861no—
300C22×C4—861no—
301C22×C4—861no—
302C22×C4—3441no—
303C22×C4—3441no—
304C22×C4C2×C4×D4311yescharacteristic
305C22×C4D4×D4311yescharacteristic
306C22×C4D4×D4311yescharacteristic
307M16—22no—
308M16—41no—
309M16—862no—
310M16—1724no—
311M16—1721no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—3442no—
315C2×C8—1724no—
316C2×C8—1721no—
317C2×C8—1721no—
318C4⋊C4—41no—
319C4⋊C4—3441no—
320C4⋊C4—1721no—
321C4⋊C4—1721no—
322C4⋊C4—1721no—
323C4⋊C4—1721no—
324C4⋊C4—1722no—
325C4⋊C4—1721no—
326C4⋊C4—1721no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—81no—
330C22⋊C4—3441no—
331C22⋊C4—1722no—
332C22⋊C4—1722no—
333C22⋊C4—1722no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—431no—
342C23—431no—
343C23—432no—
344C23—432no—
345C23—1721no—
346C23—1721no—
347C23C22⋊C4×D4311yescharacteristic
348D4—82no—
349D4—3442no—
350D4—3442no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—432no—
361C2×C4—862no—
362C2×C4—862no—
363C2×C4—862no—
364C2×C4—862no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—3441no—
370C2×C4—3441no—
371C2×C4—3441no—
372C2×C4—1722no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4D8×D4311yescharacteristic
382C2×C4SD16×D4311yescharacteristic
383C8—42no—
384C8—81no—
385C8—3441no—
386C8—1722no—
387C22—21no—
388C22—21no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—432no—
397C22—432no—
398C22—861no—
399C22—861no—
400C22—861no—
401C22—861no—
402C22—1722no—
403C22—1722no—
404C22#99×D4311yescharacteristic
405C22#102×D4311yescharacteristic
406C22#104×D4311yescharacteristic
407C4—21no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—81no—
412C4—862no—
413C4—3441no—
414C4—3441no—
415C4—1721no—
416C4—1721no—
417C2—21no—
418C2—21no—
419C2—161no—
420C2—862no—
421C2—862no—
422C2#327×D4311yescharacteristic
423C2#1913623811yescharacteristic
424C2#1913628111yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1345C2
socleC22×C43C2×#99
prime radicalC2×#13063296C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1345D43
hypocenterC43#11698
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #343×D43C2semidirect
3. #324×D43C2semidirect
4. #19132602C2semidirect
5. #19132600C2semidirect
6. #19132598C2semidirect
7. C43×#1345C2semidirect
211. #1345D43semidirect
239. C43#11698semidirect

Maximal subgroups

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

subgroupindex
#191403362
#343×D432
#324×D432
#191326022
#191326002
#191325982
C43×#13452
#1169843