Finite Group Databasebeta

← #24995522

Subgroups — #24995522

Order 11008.

510 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621882C211yesmaximal, characteristic
2#19133341C211yesmaximal, characteristic, complemented
3#19132985C211yesmaximal, characteristic, complemented
4#19132916C211yesmaximal, characteristic, complemented
5#19132915C211yesmaximal, characteristic, complemented
6#19132879C211yesmaximal, characteristic, complemented
7C43×#1478C211yesmaximal, characteristic, complemented
8C22×#10621882C411yescharacteristic
9C2×C4×D172C2211yescharacteristic
10C4×#10621882—21no—
11C4×#10621882—21no—
12C4×#10621882—21no—
13C4×#10621882—21no—
14#14582952C2211yescharacteristic
15#14582952C2211yescharacteristic
16C2×#13063258C411yescharacteristic
17C2×#13063246C411yescharacteristic
18C2×#13063245C411yescharacteristic
19C2×C4×C43⋊C8C2211yescharacteristic
20#14582651—21no—
21#14582649—21no—
22#14582626—22no—
23#14582623—22no—
24#14582622—22no—
25#14582621—21no—
26C8×C43⋊C8—21no—
27C2×C4×D4×C43C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C43×#431C2211yescharacteristic
30C43×D4⋊C8—22no—
31C22×D172C2×C411yescharacteristic
32C22×C4×D43—21no—
33C2×#10621882—21no—
34C2×#10621882—21no—
35C2×#10621882—22no—
36C2×#10621882C814yescomplemented
37C22×C43⋊C8C2×C411yescharacteristic
38C22×C43⋊C8C2×C411yescharacteristic
39C4×D172—21no—
40C4×D172—21no—
41C4×D172—21no—
42C4×D172—21no—
43C2×C4⋊Dic43C2×C411yescharacteristic
44C2×(C2×D43)⋊C4—21no—
45#13063258—21no—
46#13063258—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49#13063246—21no—
50#13063246—21no—
51#13063245—21no—
52#13063245—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)D412yes—
55C4×C43⋊C8—21no—
56C4×C43⋊C8—21no—
57C4×C43⋊C8D411yescharacteristic
58C4×C43⋊C8D411yescharacteristic
59C4×C43⋊C8D411yescharacteristic
60C4×C43⋊C8D411yescharacteristic
61C22×D4×C43C2×C411yescharacteristic
62C23×C4×C43—21no—
63C4×D4×C43—21no—
64C4×D4×C43—21no—
65C4×D4×C43—21no—
66C4×D4×C43—21no—
67C2×C4⋊C4×C43C2×C411yescharacteristic
68C2×C22⋊C4×C43—21no—
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—21no—
71C4⋊C8×C43D412yes—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C4×C8×C43—21no—
75C4×C8×C43—21no—
76C24×C43—21no—
77C23×D43—21no—
78C2×D4×C43—21no—
79C2×D4×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43C2×C812yes—
84C22×C4×C43—21no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—82no—
88C22×C4×C43C22×C411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C22×Dic43—21no—
92C2×D172—21no—
93C2×D172—21no—
94C2×D172—21no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172C2×C812yes—
98C2×C4×D43—41no—
99C2×C4×D43—41no—
100C2×C4×D43—82no—
101C2×C8×C43—22no—
102C2×C8×C43—41no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C42×C43C2×D411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43C2×D411yescharacteristic
110C42×C43#4111yescharacteristic
111#10621882—24no—
112#10621882—24no—
113(C2×D43)⋊C4—41no—
114(C2×D43)⋊C4—41no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C2×C43⋊C8—21no—
118C2×C43⋊C8—21no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8C22⋊C411yescharacteristic
122C2×C43⋊C8C22⋊C411yescharacteristic
123C2×C43⋊C8C22⋊C411yescharacteristic
124C2×C43⋊C8C22⋊C411yescharacteristic
125C2×C43⋊C8C2×C812yes—
126C2×C43⋊C8M1612yes—
127C23×C43—22no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43—81no—
131C23×C43—81no—
132C23×C43C4×D411yescharacteristic
133C22×D43—22no—
134C22×D43—41no—
135C22×D43—41no—
136C22×D43—81no—
137C22×D43—81no—
138D4×C43—22no—
139D4×C43—22no—
140D4×C43—41no—
141D4×C43—41no—
142C2×C4×C43—22no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—82no—
146C2×C4×C43—82no—
147C2×C4×C43—81no—
148C2×C4×C43C2×C22⋊C411yescharacteristic
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12411yescharacteristic
153C2×C4×C43#12711yescharacteristic
154C2×C4×C43C22×C811yescharacteristic
155C2×C4×C43C2×M1611yescharacteristic
156C2×C4×C43#13111yescharacteristic
157C2×C4×C43#13111yescharacteristic
158C2×Dic43—41no—
159C2×Dic43—81no—
160D172—22no—
161D172—22no—
162D172—41no—
163D172—41no—
164C4×D43—82no—
165C4×D43—82no—
166C8×C43—42no—
167C8×C43—81no—
168C43⋊C8—21no—
169C43⋊C8—21no—
170C43⋊C8—42no—
171C43⋊C8—81no—
172C43⋊C8C22⋊C812yes—
173C43⋊C8C22⋊C812yes—
174#9668—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—42no—
178C22×C43—82no—
179C22×C43—82no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43#39011yescharacteristic
183C22×C43C8×D411yescharacteristic
184C22×C43#43611yescharacteristic
185C2×D43—42no—
186C2×D43—82no—
187C2×D43—81no—
188C2×D43—81no—
189C2×D43—82no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—81no—
194C4×C43C2×C22⋊C811yescharacteristic
195C4×C43#40811yescharacteristic
196C4×C43C8×D411yescharacteristic
197C4×C43#43611yescharacteristic
198C4×C43#47212yes—
199Dic43—81no—
200C2×C4×D8—431no—
201#1564—431no—
202#1478—431no—
203#1478D4311yescharacteristic, complemented
204#1460—431no—
205#1460—431no—
206#1450—431no—
207C2×C43—21no—
208C2×C43—21no—
209C2×C43—82no—
210C2×C43#195411yescharacteristic
211C2×C43#197611yescharacteristic
212C2×C43#197811yescharacteristic
213D43—82no—
214C22×D8—431no—
215C2×C4×D4—431no—
216C2×C4×D4C2×D4311yescharacteristic
217C4×D8—861no—
218C4×D8—861no—
219C4×D8—861no—
220C4×D8—861no—
221#431—431no—
222#431—431no—
223#431C2×D4311yescharacteristic
224#431C2×D4311yescharacteristic
225C2×#107—431no—
226C2×#102—431no—
227C2×#102—431no—
228C2×C4×C8—431no—
229#335—861no—
230#334—861no—
231D4⋊C8—22no—
232D4⋊C8—862no—
233#323—862no—
234#323—862no—
235#322—861no—
236C82—861no—
237C43#966811yescharacteristic, complemented, Sylow
238C22×D4—431no—
239C22×D4C4×D4311yescharacteristic
240C23×C4—21no—
241C23×C4—861no—
242C2×D8—434no—
243C2×D8—862no—
244C2×D8—861no—
245C2×D8—861no—
246C22×C8—431no—
247C22×C8—431no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—861no—
253C4×D4—861no—
254C4×D4—861no—
255C4×D4—861no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4C4×D4311yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—861no—
260C2×C42C22×D4311yescharacteristic
261#107—861no—
262#107—861no—
263C4⋊C8—21no—
264C4⋊C8—861no—
265C4⋊C8—861no—
266C4⋊C8C22⋊D4312yes—
267#102—861no—
268#102—861no—
269#102—861no—
270#102—861no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—432no—
274C22⋊C8—861no—
275C4×C8—21no—
276C4×C8—21no—
277C4×C8—431no—
278C4×C8—431no—
279C4×C8—431no—
280C4×C8—431no—
281C4×C8—861no—
282C4×C8—861no—
283C24—21no—
284C24—861no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—432no—
291C2×D4—861no—
292C2×D4—861no—
293C2×D4—861no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4C8×D4312yes—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—82no—
301C22×C4—861no—
302C22×C4—3442no—
303C22×C4—1721no—
304C22×C4—1721no—
305C22×C4C2×C4×D4311yescharacteristic
306C22×C4D4×D4311yescharacteristic
307C22×C4#1062190011yescharacteristic
308D8—864no—
309D8—864no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—431no—
313C2×C8—431no—
314C2×C8—432no—
315C2×C8—432no—
316C2×C8—431no—
317C2×C8—431no—
318C2×C8—861no—
319C2×C8—861no—
320C2×C8—862no—
321C2×C8—1721no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—1721no—
329C22⋊C4—1721no—
330C42#1062189811yescharacteristic
331C42D4×D4311yescharacteristic
332C42D4×D4311yescharacteristic
333C42C2×C22⋊D4311yescharacteristic
334C23—22no—
335C23—41no—
336C23—41no—
337C23—81no—
338C23—81no—
339C23—862no—
340C23—3441no—
341C23—3441no—
342C23—1721no—
343C23—1721no—
344C23(C22⋊D43)⋊C411yescharacteristic
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349D4—862no—
350D4—862no—
351D4—1721no—
352D4—1721no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—3442no—
360C2×C4—3442no—
361C2×C4—3441no—
362C2×C4—1721no—
363C2×C4C22⋊C4×D4311yescharacteristic
364C2×C4C4×C22⋊D4311yescharacteristic
365C2×C4#1306329711yescharacteristic
366C2×C4#1306329811yescharacteristic
367C2×C4#1306331111yescharacteristic
368C2×C4#1306332111yescharacteristic
369C2×C4C2×C8×D4311yescharacteristic
370C2×C4M16×D4311yescharacteristic
371C2×C4#1306333111yescharacteristic
372C2×C4#1306333311yescharacteristic
373C8—42no—
374C8—81no—
375C8—432no—
376C8—432no—
377C8—861no—
378C8—861no—
379C8—3441no—
380C8—1722no—
381C22—21no—
382C22—21no—
383C22—42no—
384C22—82no—
385C22—82no—
386C22—81no—
387C22—81no—
388C22—3442no—
389C22—3442no—
390C22—3441no—
391C22—3441no—
392C22—1722no—
393C22#1458279911yescharacteristic
394C22(C22⋊D43)⋊C811yescharacteristic
395C22#1458297411yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—3441no—
401C4C22⋊C8×D4311yescharacteristic
402C4#1458286411yescharacteristic
403C4C8×C22⋊D4311yescharacteristic
404C4#1458297511yescharacteristic
405C4#1458316712yes—
406C2—21no—
407C2—21no—
408C2—82no—
409C2—3442no—
410C2#1913538711yescharacteristic
411C2#1913549211yescharacteristic
412C2#1913550411yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1478C2
socleC22×C43#390
prime radicalC22×#10621882C4
cosocleC2×C42×C43C23
hypercenter#1478D43
hypocenterC43#9668
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #19133341C2semidirect
3. #19132985C2semidirect
4. #19132916C2semidirect
5. #19132915C2semidirect
6. #19132879C2semidirect
7. C43×#1478C2semidirect
36. C2×#10621882C8semidirect
203. #1478D43semidirect
237. C43#9668semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106218822
#191333412
#191329852
#191329162
#191329152
#191328792
C43×#14782
#966843