Finite Group Databasebeta

← #24992939

Subgroups — #24992939

Order 11008.

464 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583121C211yesmaximal, characteristic
2#19133194C211yesmaximal, characteristic
3#19133042C211yesmaximal, characteristic, complemented
4#19132946C211yesmaximal, characteristic
5#19132464C211yesmaximal, characteristic, complemented
6#19132444C211yesmaximal, characteristic, complemented
7C43×#2984C211yesmaximal, characteristic, complemented
8C22×#10621885C411yescharacteristic
9C22×#10621884C411yescharacteristic
10C2×#13063313C2211yescharacteristic
11#14583121—21no—
12#14583121—21no—
13#14583121—21no—
14#14583121—21no—
15#14582956C2211yescharacteristic
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×#13063248C411yescharacteristic
18C2×#13063245C411yescharacteristic
19C4×#10621877C2211yescharacteristic
20#14582638—22no—
21Q8⋊(C43⋊C8)—21no—
22Q8⋊(C43⋊C8)—21no—
23#14582622—21no—
24#14582622—21no—
25C2×C4×Q8×C43C2211yescharacteristic
26C43×#446—21no—
27C43×#446—22no—
28C8×Q8×C43—21no—
29C43×#432—21no—
30C43×#432C2211yescharacteristic
31C43×#431—21no—
32C43×#431C2211yescharacteristic
33C22×Dic86C2×C411yescharacteristic
34C22×D172C2×C411yescharacteristic
35C2×#10621885—21no—
36C2×#10621885—21no—
37C2×#10621885—42no—
38C2×#10621884—21no—
39C2×#10621884—21no—
40C2×#10621884—42no—
41C2×#10621877—21no—
42C22×C43⋊C8C2×C411yescharacteristic
43C22×C43⋊C8C2×C411yescharacteristic
44#13063313—21no—
45#13063313—21no—
46#13063313—21no—
47#13063313—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53#13063248—21no—
54#13063248—21no—
55#13063245—21no—
56#13063245—21no—
57C22⋊(C43⋊C8)—21no—
58#13063236—21no—
59#13063236—21no—
60C4×C43⋊C8—21no—
61C22×Q8×C43C2×C411yescharacteristic
62C4×Q8×C43—21no—
63C4×Q8×C43—21no—
64C4×Q8×C43D411yescharacteristic
65C4×Q8×C43D411yescharacteristic
66C4×Q8×C43D411yescharacteristic
67C4×Q8×C43D411yescharacteristic
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43C2×C411yescharacteristic
70C2×C42×C43—21no—
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—22no—
73C4⋊C8×C43—22no—
74C4⋊C8×C43—21no—
75C4⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43D411yescharacteristic
78C22⋊C8×C43D411yescharacteristic
79#97×C43—22no—
80#97×C43D412yes—
81C4×C8×C43—22no—
82C4×C8×C43—21no—
83C23×D43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—22no—
86C2×Q8×C43—41no—
87C2×Q8×C43C22⋊C411yescharacteristic
88C2×Q8×C43C22⋊C411yescharacteristic
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C22×Dic43—21no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172—41no—
98C2×D172—41no—
99C2×Dic86—21no—
100C2×Dic86—21no—
101C2×Dic86—41no—
102C2×Dic86—41no—
103C2×C8×C43—21no—
104C2×C8×C43—21no—
105C2×C8×C43—22no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43C22⋊C411yescharacteristic
112C4⋊C4×C43C22⋊C411yescharacteristic
113C42×C43—21no—
114C42×C43—21no—
115C42×C43—21no—
116C42×C43—21no—
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43#4111yescharacteristic
121#10621885—42no—
122#10621885—42no—
123#10621884—42no—
124#10621884—42no—
125(C2×D43)⋊C4—41no—
126(C2×D43)⋊C4—41no—
127(C2×D43)⋊C4—41no—
128(C2×D43)⋊C4—41no—
129#10621877—22no—
130#10621877—41no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—41no—
134C2×C43⋊C8—41no—
135C2×C43⋊C8—41no—
136C2×C43⋊C8—41no—
137C23×C43C4×D411yescharacteristic
138C22×D43—41no—
139C22×D43—41no—
140C22×D43—41no—
141C22×D43—81no—
142C22×D43—81no—
143Q8×C43—21no—
144Q8×C43—21no—
145Q8×C43—21no—
146Q8×C43—42no—
147Q8×C43#10012yes—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—41no—
157C2×C4×C43—42no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43C2×C22⋊C411yescharacteristic
161C2×C4×C43C4×D411yescharacteristic
162C2×C4×C43#12011yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×C4×C43#12311yescharacteristic
166C2×Dic43—41no—
167C2×Dic43—81no—
168D172—41no—
169D172—41no—
170D172—81no—
171Dic86—41no—
172Dic86—41no—
173Dic86—81no—
174C8×C43—41no—
175C8×C43—41no—
176C8×C43—42no—
177C43⋊C8—42no—
178C43⋊C8—41no—
179C43⋊C8—41no—
180C43⋊C8—81no—
181#9244—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—21no—
184C22×C43#38611yescharacteristic
185C22×C43#44311yescharacteristic
186C22×C43#44411yescharacteristic
187C2×D43—81no—
188C2×D43—81no—
189C2×D43—81no—
190C2×D43—161no—
191C2×D43—161no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—22no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—41no—
199C4×C43—41no—
200C4×C43—41no—
201C4×C43C2×#10011yescharacteristic
202C4×C43#41311yescharacteristic
203Dic43—81no—
204C2×#464—431no—
205#2984D4311yescharacteristic, complemented
206#1527—431no—
207#1491—431no—
208#1469—431no—
209#1290—431no—
210#1283—431no—
211C2×C43—21no—
212C2×C43—21no—
213C2×C43#187611yescharacteristic
214C2×C43#190011yescharacteristic
215C2×C43#190511yescharacteristic
216D43—161no—
217C22×Q16—431no—
218C22×SD16—431no—
219C2×#124—431no—
220C2×C4×Q8C2×D4311yescharacteristic
221#464—861no—
222#464—861no—
223#464—861no—
224#464—861no—
225#446—21no—
226#446—22no—
227C8×Q8—21no—
228#432—21no—
229#432—431no—
230#432C2×D4311yescharacteristic
231#431—21no—
232#431C2×D4311yescharacteristic
233C2×C4⋊C8—431no—
234C2×#103—431no—
235C2×#102—431no—
236C4×M16—431no—
237#329—862no—
238Q8⋊C8—861no—
239Q8⋊C8—861no—
240#323—861no—
241#323—861no—
242C43#924411yescharacteristic, complemented, Sylow
243C22×Q8—431no—
244C22×Q8C4×D4311yescharacteristic
245C22×D4—431no—
246C2×Q16—861no—
247C2×Q16—861no—
248C2×Q16—1722no—
249C2×SD16—861no—
250C2×SD16—861no—
251C2×SD16—1722no—
252C2×M16—861no—
253C22×C8—431no—
254C22×C8—431no—
255#124—861no—
256#124—861no—
257#124—861no—
258#124—861no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8D17211yescharacteristic
262C4×Q8D17211yescharacteristic
263C4×Q8C22⋊D4311yescharacteristic
264C4×Q8C22⋊D4311yescharacteristic
265C2×C4⋊C4—21no—
266C2×C4⋊C4C4×D4311yescharacteristic
267C2×C22⋊C4—861no—
268C2×C22⋊C4—861no—
269C2×C42—21no—
270C2×C42C22×D4311yescharacteristic
271C4⋊C8—22no—
272C4⋊C8—22no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—861no—
276C4⋊C8—861no—
277C4⋊C8—861no—
278#103—861no—
279#103—861no—
280#102—861no—
281#102—861no—
282C22⋊C8—21no—
283C22⋊C8—861no—
284C22⋊C8C22⋊D4311yescharacteristic
285C22⋊C8C22⋊D4311yescharacteristic
286#97—22no—
287#97—861no—
288#97—861no—
289#97C22⋊D4312yes—
290C4×C8—22no—
291C4×C8—21no—
292C4×C8—861no—
293C24—861no—
294C2×Q8—21no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—861no—
298C2×Q8—861no—
299C2×Q8—1721no—
300C2×Q8—1721no—
301C2×Q8(C2×D43)⋊C411yescharacteristic
302C2×Q8(C2×D43)⋊C411yescharacteristic
303C2×D4—861no—
304C2×D4—861no—
305C2×D4—1721no—
306C2×D4—1721no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—861no—
310C22×C4C2×C4×D4311yescharacteristic
311C22×C4#1062189811yescharacteristic
312C22×C4C2×C22⋊D4311yescharacteristic
313Q16—1722no—
314Q16—1722no—
315SD16—1722no—
316SD16—1722no—
317M16—862no—
318M16—1721no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—22no—
322C2×C8—861no—
323C2×C8—861no—
324C2×C8—1721no—
325C2×C8—1721no—
326C2×C8—1721no—
327C2×C8—1721no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4(C2×D43)⋊C411yescharacteristic
334C4⋊C4(C2×D43)⋊C411yescharacteristic
335C22⋊C4—1721no—
336C22⋊C4—1721no—
337C22⋊C4—1721no—
338C22⋊C4—1721no—
339C42—21no—
340C42—21no—
341C42—21no—
342C42—21no—
343C42C2×D17211yescharacteristic
344C42#1062189811yescharacteristic
345C42C2×C22⋊D4311yescharacteristic
346C42C2×C22⋊D4311yescharacteristic
347C23—3441no—
348C23—3441no—
349C23—1721no—
350C23—1721no—
351C23—1721no—
352C23C4×C22⋊D4311yescharacteristic
353Q8—21no—
354Q8—21no—
355Q8—21no—
356Q8—42no—
357Q8—3441no—
358Q8—1721no—
359Q8—1721no—
360Q8#1306324112yes—
361D4—3441no—
362D4—1721no—
363D4—1721no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—3441no—
377C2×C4—1721no—
378C2×C4C2×(C2×D43)⋊C411yescharacteristic
379C2×C4C4×C22⋊D4311yescharacteristic
380C2×C4#1306329411yescharacteristic
381C2×C4#1306329911yescharacteristic
382C2×C4#1306329911yescharacteristic
383C2×C4#1306330811yescharacteristic
384C8—41no—
385C8—41no—
386C8—42no—
387C8—3441no—
388C8—1722no—
389C8—1721no—
390C8—1721no—
391C22—21no—
392C22—21no—
393C22—3441no—
394C22—3441no—
395C22—3441no—
396C22—6881no—
397C22—6881no—
398C22#1458277811yescharacteristic
399C22#1458301411yescharacteristic
400C22#1458301911yescharacteristic
401C4—21no—
402C4—22no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—3441no—
411C4C2×#1306324111yescharacteristic
412C4#1458288111yescharacteristic
413C2—21no—
414C2—21no—
415C2—6881no—
416C2#1913492211yescharacteristic
417C2#1913505811yescharacteristic
418C2#1913508911yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2984C2
socleC22×C43#386
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#2984D43
hypocenterC43#9244
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2984

Complements

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

NH ≅ G/Ntype
3. #19133042C2semidirect
5. #19132464C2semidirect
6. #19132444C2semidirect
7. C43×#2984C2semidirect
205. #2984D43semidirect
242. C43#9244semidirect

Maximal subgroups

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

subgroupindex
C2×#145831212
#191331942
#191330422
#191329462
#191324642
#191324442
C43×#29842
#924443