Finite Group Databasebeta

← #24993934

Subgroups — #24993934

Order 11008.

532 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 93 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#19143012C211yesmaximal, characteristic
2#19140295C211yesmaximal, characteristic
3#19133197C211yesmaximal, characteristic, complemented
4#19132927C211yesmaximal, characteristic
5#19132489C211yesmaximal, characteristic, complemented
6#19132487C211yesmaximal, characteristic, complemented
7C43×#1528C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×#13063282C2211yescharacteristic
10#14582956C2211yescharacteristic
11#14582856—22no—
12#14582853—22no—
13C4×#10621877C2211yescharacteristic
14M16×Dic43—21no—
15#14582837C411yescharacteristic
16#14582834C411yescharacteristic
17#14582830C411yescharacteristic
18#14582825C411yescharacteristic
19#14582794—21no—
20#14582789—21no—
21#14582780—21no—
22#14582770—21no—
23#14582745C2211yescharacteristic
24#14582641—22no—
25#14582624—21no—
26#14582622—21no—
27C2×#125×C43C2211yescharacteristic
28C43×#432C2211yescharacteristic
29C4×M16×C43C2211yescharacteristic
30C43×#330—22no—
31C22×C4×D43D411yescharacteristic
32C2×#10621877—21no—
33C2×#10621872—22no—
34M16×D43—24no—
35M16×D43—24no—
36C2×C8×D43—22no—
37#13063282—21no—
38#13063282—21no—
39#13063282—21no—
40#13063282—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4C2×C411yescharacteristic
44C2×Dic43⋊C4D411yescharacteristic
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4C2×C411yescharacteristic
48C2×(C2×D43)⋊C4D411yescharacteristic
49C2×C4×Dic43—21no—
50C2×C4×Dic43D411yescharacteristic
51C4⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53#13063236—21no—
54#13063236D412yes—
55#13063235—22no—
56C4×C43⋊C8—21no—
57C8×Dic43—22no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95C2×C411yescharacteristic
64C43⋊#95C2×C411yescharacteristic
65C2×M16×C43—21no—
66#125×C43—21no—
67#125×C43—21no—
68#125×C43—21no—
69#125×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43C2×C411yescharacteristic
73C2×C4⋊C4×C43C2×C411yescharacteristic
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77#97×C43—21no—
78#97×C43D412yes—
79C4×C8×C43—21no—
80C23×D43C22⋊C411yescharacteristic
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43C22⋊C411yescharacteristic
89C22×Dic43C22⋊C411yescharacteristic
90C22×Dic43C22⋊C411yescharacteristic
91C2×C4×D43—21no—
92C2×C4×D43—21no—
93C2×C4×D43—22no—
94C2×C4×D43—22no—
95M16×C43—22no—
96M16×C43—22no—
97C2×C8×C43—22no—
98C2×C8×C43—41no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C42×C43C2×D411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43#4111yescharacteristic
110C42×C43#4111yescharacteristic
111(C2×D43)⋊C4—21no—
112(C2×D43)⋊C4—21no—
113(C2×D43)⋊C4—21no—
114(C2×D43)⋊C4—21no—
115(C2×D43)⋊C4—42no—
116(C2×D43)⋊C4—42no—
117Dic43⋊C4—21no—
118Dic43⋊C4—21no—
119Dic43⋊C4—21no—
120Dic43⋊C4—21no—
121Dic43⋊C4—42no—
122Dic43⋊C4—42no—
123C4×Dic43—21no—
124C4×Dic43—21no—
125C4×Dic43—42no—
126#10621877—22no—
127#10621877—22no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—41no—
130#10621872—28no—
131C8×D43—28no—
132C23×C43C2×C22⋊C411yescharacteristic
133C22×D43—21no—
134C22×D43—21no—
135C22×D43—41no—
136C22×D43—41no—
137C22×D43#10412yes—
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×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43#12011yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12311yescharacteristic
154C2×Dic43—21no—
155C2×Dic43—21no—
156C2×Dic43—22no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43#10412yes—
167C4×D43—22no—
168C4×D43—22no—
169C4×D43—24no—
170C8×C43—24no—
171C8×C43—81no—
172C43⋊C8—24no—
173C43⋊C8—81no—
174#9388—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43#38611yescharacteristic
178C22×C43C2×#10411yescharacteristic
179C22×C43C2×#10411yescharacteristic
180C2×D43—22no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—42no—
184C2×D43—81no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—81no—
192C4×C43—81no—
193Dic43—22no—
194Dic43—42no—
195Dic43—41no—
196Dic43—41no—
197Dic43—81no—
198#2873—431no—
199#2611—431no—
200#1528—431no—
201#1528D4311yescharacteristic, complemented
202#1464—431no—
203#1300—431no—
204#1300—431no—
205C2×C43—21no—
206C2×C43—21no—
207C2×C43#188411yescharacteristic
208C2×C43#189611yescharacteristic
209C2×C43#191511yescharacteristic
210D43—42no—
211C22×M16—861no—
212C2×#125C2×D4311yescharacteristic
213C2×#117—431no—
214#432—431no—
215#432C2×D4311yescharacteristic
216#405—862no—
217#405—862no—
218C4×M16—431no—
219C4×M16—861no—
220C4×M16C2×D4311yescharacteristic
221#400—431no—
222#399—431no—
223#398—431no—
224#397—431no—
225#389—861no—
226#388—861no—
227#387—861no—
228#385—861no—
229#376—431no—
230#330—22no—
231#330—862no—
232#324—861no—
233#323—861no—
234C43#938811yescharacteristic, complemented, Sylow
235C23×C4—431no—
236C2×M16—21no—
237C2×M16—862no—
238C2×M16—864no—
239C2×M16—864no—
240C2×M16—861no—
241C22×C8—862no—
242#125—21no—
243#125—21no—
244#125—21no—
245#125—21no—
246#117—861no—
247#117—861no—
248#117—861no—
249#117—861no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—431no—
253C2×C4⋊C4—431no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4C4×D4311yescharacteristic
257C2×C4⋊C4C4×D4311yescharacteristic
258C2×C22⋊C4—431no—
259C2×C22⋊C4—431no—
260C2×C22⋊C4—861no—
261C2×C22⋊C4—861no—
262C2×C42—431no—
263C2×C42—861no—
264C2×C42C22×D4311yescharacteristic
265C4⋊C8—21no—
266C4⋊C8—861no—
267C22⋊C8—21no—
268C22⋊C8—861no—
269#97—21no—
270#97—432no—
271#97—862no—
272#97—861no—
273#97C22⋊D4312yes—
274C4×C8—21no—
275C4×C8—862no—
276C4×C8—861no—
277#95—431no—
278#95—431no—
279#95—861no—
280#95—861no—
281#95—861no—
282#95—861no—
283#95—861no—
284C24—431no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—431no—
290C22×C4—862no—
291C22×C4—862no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4C2×C4×D4311yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4D4×D4311yescharacteristic
299M16—22no—
300M16—22no—
301M16—868no—
302M16—862no—
303M16—862no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—868no—
307C2×C8—862no—
308C2×C8—1721no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4—861no—
320C4⋊C4—861no—
321C4⋊C4—1722no—
322C4⋊C4—1722no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—1722no—
328C22⋊C4—1722no—
329C42—861no—
330C42—861no—
331C42—1722no—
332C42#1062189811yescharacteristic
333C42D4×D4311yescharacteristic
334C42#1062190011yescharacteristic
335C42C2×C22⋊D4311yescharacteristic
336C23—432no—
337C23—861no—
338C23—861no—
339C23—1721no—
340C23—1721no—
341C23C22⋊C4×D4311yescharacteristic
342C2×C4—21no—
343C2×C4—21no—
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—432no—
353C2×C4—862no—
354C2×C4—862no—
355C2×C4—864no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—862no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4(C22⋊D43)⋊C411yescharacteristic
369C2×C4C4×C22⋊D4311yescharacteristic
370C2×C4#1306329311yescharacteristic
371C2×C4#1306329611yescharacteristic
372C2×C4#1306329811yescharacteristic
373C2×C4#1306330711yescharacteristic
374C8—24no—
375C8—81no—
376C8—864no—
377C8—3441no—
378C22—21no—
379C22—21no—
380C22—862no—
381C22—3441no—
382C22—1722no—
383C22—1721no—
384C22—1721no—
385C22#1458277511yescharacteristic
386C22#104×D4311yescharacteristic
387C22#104×D4311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—862no—
397C4—3441no—
398C4—1722no—
399C4—1721no—
400C4—1721no—
401C2—21no—
402C2—21no—
403C2—1722no—
404C2#1913497511yescharacteristic
405C2#1913503511yescharacteristic
406C2#1913514411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1528C2
socleC22×C43#386
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1528D43
hypocenterC43#9388
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
3. #19133197C2semidirect
5. #19132489C2semidirect
6. #19132487C2semidirect
7. C43×#1528C2semidirect
201. #1528D43semidirect
234. C43#9388semidirect

Maximal subgroups

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

subgroupindex
#191430122
#191402952
#191331972
#191329272
#191324892
#191324872
C43×#15282
#938843