Finite Group Databasebeta

← #24991690

Subgroups — #24991690

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143232C211yesmaximal, characteristic
2#19137867C211yesmaximal, characteristic
3#19133025C211yesmaximal, characteristic, complemented
4#19133023C211yesmaximal, characteristic, complemented
5#19132907C211yesmaximal, characteristic
6#19132498C211yesmaximal, characteristic, complemented
7C43×#1303C211yesmaximal, characteristic, complemented
8C2×C4×Dic86C2211yescharacteristic
9C2×#13063282C2211yescharacteristic
10#14582959—22no—
11#14582959—22no—
12#14582952C2211yescharacteristic
13#14582923C2211yescharacteristic
14#14582862—21no—
15M16×Dic43—21no—
16#14582839C411yescharacteristic
17#14582836C411yescharacteristic
18#14582829—21no—
19#14582821—21no—
20#14582820C411yescharacteristic
21#14582812C411yescharacteristic
22C4×C4⋊Dic43—21no—
23C4×(C2×D43)⋊C4—21no—
24#14582631—22no—
25#14582629—22no—
26#14582624—21no—
27#14582622—21no—
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C4×C4⋊C4×C43C2211yescharacteristic
31C22×Dic86C2×C411yescharacteristic
32C22×C4×D43D411yescharacteristic
33C2×#10621877—21no—
34C4×Dic86—21no—
35C4×Dic86—21no—
36C4×Dic86—21no—
37C4×Dic86—21no—
38#13063282—21no—
39#13063282—21no—
40#13063282—21no—
41#13063282—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43C2×C411yescharacteristic
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4C2×C411yescharacteristic
47C2×Dic43⋊C4D411yescharacteristic
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4C2×C411yescharacteristic
51C2×(C2×D43)⋊C4D411yescharacteristic
52C2×C4×Dic43—21no—
53C2×C4×Dic43D411yescharacteristic
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56C4⋊(C43⋊C8)D412yes—
57C22⋊(C43⋊C8)—21no—
58(C2×D43)⋊C8—24no—
59#13063235—22no—
60C4×C43⋊C8—21no—
61C8×Dic43—22no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C2×M16×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C42×C43—21no—
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43D412yes—
73C22⋊C8×C43—21no—
74C4×C8×C43—21no—
75#95×C43C2×C411yescharacteristic
76#95×C43C2×C411yescharacteristic
77C23×D43C22⋊C411yescharacteristic
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43C22×C411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43C22⋊C411yescharacteristic
86C22×Dic43C22⋊C411yescharacteristic
87C22×Dic43C22⋊C411yescharacteristic
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43—21no—
93C2×C4×D43—21no—
94C2×Dic86—21no—
95C2×Dic86—21no—
96C2×Dic86—42no—
97M16×C43—41no—
98M16×C43—41no—
99C2×C8×C43—22no—
100C2×C8×C43—41no—
101C4⋊C4×C43—42no—
102C42×C43—41no—
103C42×C43—41no—
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43#4111yescharacteristic
107C42×C43#4111yescharacteristic
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4—21no—
112(C2×D43)⋊C4—42no—
113(C2×D43)⋊C4—42no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—42no—
117C4⋊Dic43—42no—
118Dic43⋊C4—21no—
119Dic43⋊C4—21no—
120Dic43⋊C4—21no—
121Dic43⋊C4—21no—
122Dic43⋊C4—41no—
123Dic43⋊C4—41no—
124C4×Dic43—21no—
125C4×Dic43—21no—
126C4×Dic43—41no—
127C4×Dic43—41no—
128#10621877—41no—
129#10621877—41no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—41no—
132C23×C43C2×C22⋊C411yescharacteristic
133C22×D43—21no—
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—41no—
137C22×D43—41no—
138C2×C4×C43—22no—
139C2×C4×C43—41no—
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×C43C4×D411yescharacteristic
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43#12011yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12311yescharacteristic
152C2×C4×C43#13511yescharacteristic
153C2×C4×C43#13511yescharacteristic
154C2×C4×C43#13711yescharacteristic
155C2×C4×C43#13711yescharacteristic
156C2×Dic43—22no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C4×D43—41no—
170C4×D43—41no—
171C4×D43—41no—
172C4×D43—41no—
173Dic86—22no—
174Dic86—22no—
175Dic86—41no—
176Dic86—41no—
177C8×C43—42no—
178C8×C43—81no—
179C43⋊C8—42no—
180C43⋊C8—81no—
181#9034—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—21no—
184C22×C43#38611yescharacteristic
185C22×C43#41611yescharacteristic
186C22×C43#41911yescharacteristic
187C2×D43—42no—
188C2×D43—41no—
189C2×D43—41no—
190C2×D43—41no—
191C2×D43—81no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—42no—
197C4×C43—81no—
198C4×C43#45211yescharacteristic
199C4×C43#45211yescharacteristic
200C4×C43#48511yescharacteristic
201C4×C43#48511yescharacteristic
202Dic43—41no—
203Dic43—41no—
204Dic43—42no—
205Dic43—41no—
206Dic43—81no—
207#2921—431no—
208#2396—431no—
209#1487—431no—
210#1487—431no—
211#1458—431no—
212#1303—431no—
213#1303D4311yescharacteristic, complemented
214C2×C43—21no—
215C2×C43—21no—
216C2×C43#187311yescharacteristic
217C2×C43#188411yescharacteristic
218C2×C43#189111yescharacteristic
219D43—81no—
220C2×C4×Q8—431no—
221C2×#117—431no—
222#433—862no—
223#433—862no—
224#431—431no—
225#431C2×D4311yescharacteristic
226#423—431no—
227#423C2×D4311yescharacteristic
228#407—861no—
229C4×M16—861no—
230#400—431no—
231#399—431no—
232#398—861no—
233#396—861no—
234#395—431no—
235#393—431no—
236C4×C4⋊C4—861no—
237C4×C4⋊C4C2×D4311yescharacteristic
238C4×C22⋊C4—861no—
239Q8⋊C8—862no—
240Q8⋊C8—862no—
241#324—861no—
242#323—861no—
243C43#903411yescharacteristic, complemented, Sylow
244C22×Q8—431no—
245C23×C4—431no—
246C2×M16—21no—
247C2×M16—861no—
248C4×Q8—861no—
249C4×Q8—861no—
250C4×Q8—861no—
251C4×Q8—861no—
252#117—861no—
253#117—861no—
254#117—861no—
255#117—861no—
256C2×C4⋊C4—21no—
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×C22⋊C4—431no—
264C2×C22⋊C4—431no—
265C2×C22⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C42—21no—
268C2×C42—431no—
269C2×C42—861no—
270C2×C42C22×D4311yescharacteristic
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—432no—
274C4⋊C8—861no—
275C4⋊C8—861no—
276C4⋊C8D17212yes—
277C22⋊C8—21no—
278C22⋊C8—864no—
279C22⋊C8—861no—
280#97—862no—
281C4×C8—21no—
282C4×C8—862no—
283C4×C8—861no—
284#95—861no—
285#95—861no—
286#95—861no—
287#95—861no—
288#95C4×D4311yescharacteristic
289#95C4×D4311yescharacteristic
290C24—431no—
291C2×Q8—861no—
292C2×Q8—861no—
293C2×Q8—1722no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—431no—
297C22×C4—431no—
298C22×C4—431no—
299C22×C4—861no—
300C22×C4—861no—
301C22×C4—861no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4—861no—
307C22×C4C2×C4×D4311yescharacteristic
308C22×C4D4×D4311yescharacteristic
309C22×C4D4×D4311yescharacteristic
310M16—41no—
311M16—41no—
312M16—1721no—
313M16—1721no—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—862no—
317C2×C8—1721no—
318C4⋊C4—42no—
319C4⋊C4—861no—
320C4⋊C4—861no—
321C4⋊C4—861no—
322C4⋊C4—861no—
323C4⋊C4—861no—
324C4⋊C4—861no—
325C4⋊C4—1722no—
326C4⋊C4—1722no—
327C4⋊C4—1721no—
328C4⋊C4—1721no—
329C22⋊C4—861no—
330C22⋊C4—861no—
331C22⋊C4—861no—
332C22⋊C4—861no—
333C22⋊C4—1722no—
334C22⋊C4—1722no—
335C42—41no—
336C42—41no—
337C42—861no—
338C42—861no—
339C42—1721no—
340C42—1721no—
341C42C2×D17211yescharacteristic
342C42#1062189811yescharacteristic
343C42D4×D4311yescharacteristic
344C42#1062190211yescharacteristic
345C23—861no—
346C23—861no—
347C23—861no—
348C23—1721no—
349C23—1721no—
350C23C22⋊C4×D4311yescharacteristic
351Q8—862no—
352Q8—862no—
353Q8—1721no—
354Q8—1721no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—862no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4#1306328711yescharacteristic
381C2×C4C4×D17211yescharacteristic
382C2×C4#1306329511yescharacteristic
383C2×C4#1306329811yescharacteristic
384C2×C4#1306330011yescharacteristic
385C2×C4#1306331011yescharacteristic
386C2×C4#1306334411yescharacteristic
387C2×C4#1306334611yescharacteristic
388C2×C4#1306335411yescharacteristic
389C2×C4#1306335711yescharacteristic
390C8—42no—
391C8—81no—
392C8—3441no—
393C8—1722no—
394C22—21no—
395C22—21no—
396C22—3441no—
397C22—1722no—
398C22—1721no—
399C22—1721no—
400C22—1721no—
401C22#1458277711yescharacteristic
402C22#1458289211yescharacteristic
403C22#1458290611yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—3441no—
411C4—1721no—
412C4—1722no—
413C4—1721no—
414C4—1721no—
415C4#1458306211yescharacteristic
416C4#1458306411yescharacteristic
417C4#1458324211yescharacteristic
418C4#1458324311yescharacteristic
419C2—21no—
420C2—21no—
421C2—3441no—
422C2#1913490611yescharacteristic
423C2#1913497711yescharacteristic
424C2#1913501211yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1303C2
socleC22×C43#386
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1303D43
hypocenterC43#9034
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #19133025C2semidirect
4. #19133023C2semidirect
6. #19132498C2semidirect
7. C43×#1303C2semidirect
213. #1303D43semidirect
243. C43#9034semidirect

Maximal subgroups

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

subgroupindex
#191432322
#191378672
#191330252
#191330232
#191329072
#191324982
C43×#13032
#903443