Finite Group Databasebeta

← #25013648

Subgroups — #25013648

Order 11008.

476 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583331C211yesmaximal, characteristic
2C2×#14583015C211yesmaximal, characteristic, complemented
3C2×#14582705C211yesmaximal, characteristic, complemented
4C2×#14582705C211yesmaximal, characteristic, complemented
5#19135481C211yesmaximal, characteristic, complemented
6#19132672C211yesmaximal, characteristic, complemented
7C43×#1381C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9C2×#13063347C2211yescharacteristic
10C2×#13063333—21no—
11#14583331—22no—
12#14583331—22no—
13C2×Dic344C411yescharacteristic, complemented
14C2×#13063270C411yescharacteristic, complemented
15C2×#13063270C411yescharacteristic, complemented
16C2×D688C411yescharacteristic, complemented
17C22×C43⋊C16C2211yescharacteristic
18#14583015—22no—
19#14583015—22no—
20C2×#13063251—21no—
21C2×#13063251—21no—
22#14582867—21no—
23C2×C8×Dic43C2211yescharacteristic
24#14582705—22no—
25#14582705—22no—
26C22×C16×C43C2211yescharacteristic
27C2×#108×C43C2211yescharacteristic
28C2×#108×C43C2211yescharacteristic
29C2×#10621898—21no—
30C2×#10621898—21no—
31#13063347—21no—
32#13063347—21no—
33#13063347—21no—
34#13063347—21no—
35#13063347—21no—
36#13063347—21no—
37#13063347D412yes—
38#13063347D412yes—
39C2×Dic172C2×C411yescharacteristic
40C2×Dic172C2×C411yescharacteristic
41C2×#10621873—21no—
42C2×#10621873—21no—
43C2×D344C2×C411yescharacteristic
44C2×D344C2×C411yescharacteristic
45#13063333—24no—
46#13063333—42no—
47C2×#10621872—41no—
48C22×C43⋊C8D411yescharacteristic
49C2×C8×D43—41no—
50C2×C4×Dic43D411yescharacteristic
51Dic344—22no—
52#13063270—22no—
53#13063270—22no—
54D688—22no—
55C2×C43⋊C16—21no—
56C2×C43⋊C16—21no—
57C2×C43⋊C16—21no—
58#13063251—24no—
59#13063251—42no—
60(C2×D43)⋊C8—41no—
61(C2×D43)⋊C8—41no—
62C8×Dic43—21no—
63C8×Dic43—21no—
64C2×M16×C43—21no—
65C2×M16×C43—21no—
66C22×C8×C43C2311yescharacteristic
67C2×C16×C43—21no—
68C2×C16×C43—21no—
69C2×C16×C43C2×C411yescharacteristic
70C2×C16×C43C2×C411yescharacteristic
71#108×C43—21no—
72#108×C43—21no—
73#108×C43—21no—
74#108×C43D412yes—
75C22×C4×C43C2×D411yescharacteristic
76C2×C22⋊D43—41no—
77C2×C22⋊D43—41no—
78C22×Dic43—21no—
79#10621898—22no—
80#10621898—22no—
81#10621898—41no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85#10621898—41no—
86#10621898—41no—
87C2×D172—21no—
88C2×D172—21no—
89C2×C4×D43—41no—
90C2×C4×D43—41no—
91C2×Dic86—21no—
92C2×Dic86—21no—
93M16×C43—22no—
94M16×C43—41no—
95M16×C43—41no—
96M16×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C2×C8×C43C22×C411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43C2×D411yescharacteristic
102C2×C8×C43C2×D411yescharacteristic
103C2×C8×C43#4111yescharacteristic
104C2×C8×C43#4111yescharacteristic
105C4×Dic43—21no—
106C4×Dic43—21no—
107C2×C43⋊C8—21no—
108C2×C43⋊C8—21no—
109C2×C43⋊C8D811yescharacteristic
110C2×C43⋊C8D811yescharacteristic
111Dic172—21no—
112Dic172—21no—
113Dic172—21no—
114Dic172C22⋊C412yes—
115D344—21no—
116D344—21no—
117D344—21no—
118D344C22⋊C412yes—
119#10621873—22no—
120#10621873—22no—
121#10621873—41no—
122#10621873—41no—
123#10621872—44no—
124C8×D43—44no—
125C16×C43—21no—
126C16×C43—21no—
127C43⋊C16—41no—
128C23×C43#13511yescharacteristic
129C22×D43—41no—
130C22×D43—41no—
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43C2×D811yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C22⋊D43—42no—
138C22⋊D43—42no—
139C22⋊D43—81no—
140C22⋊D43—81no—
141C2×Dic43—22no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146D172—22no—
147D172—41no—
148D172—41no—
149D172—41no—
150C4×D43—42no—
151C4×D43—42no—
152C4×D43—81no—
153C4×D43—81no—
154Dic86—22no—
155Dic86—41no—
156Dic86—41no—
157Dic86—41no—
158C8×C43—42no—
159C8×C43—81no—
160C8×C43C2×C22⋊C411yescharacteristic
161C8×C43C4×D411yescharacteristic
162C8×C43#12111yescharacteristic
163C8×C43#12311yescharacteristic
164C43⋊C8—21no—
165C43⋊C8—21no—
166#13011—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43C4×D811yescharacteristic
170C22×C43#44911yescharacteristic
171C22×C43#46311yescharacteristic
172C2×D43—42no—
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C4×C43#38611yescharacteristic
179C4×C43#44211yescharacteristic
180C4×C43#44711yescharacteristic
181C4×C43#45911yescharacteristic
182Dic43—42no—
183Dic43—42no—
184Dic43—81no—
185C2×#508—431no—
186C2×#443—431no—
187C2×#359—431no—
188C2×#359—431no—
189#1974—431no—
190#1381D4311yescharacteristic, complemented
191#1374—431no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43#187911yescharacteristic
195C2×C43#217811yescharacteristic
196C2×C43#217911yescharacteristic
197D43—82no—
198D43—161no—
199C2×#135—431no—
200C2×#135—431no—
201C2×#131—861no—
202#508—862no—
203#508—862no—
204C2×Q32—431no—
205C2×SD32—431no—
206C2×SD32—431no—
207C2×D16—431no—
208C22×C16—431no—
209C22×C16C2×D4311yescharacteristic
210#443—862no—
211#443—862no—
212C2×#108C2×D4311yescharacteristic
213C2×#108C2×D4311yescharacteristic
214C2×#104—861no—
215C2×#104—861no—
216#408—861no—
217C2×C4×C8—431no—
218#359—862no—
219#359—862no—
220C43#1301111yescharacteristic, complemented, Sylow
221C2×#41—861no—
222C2×#41—861no—
223#135—432no—
224#135—432no—
225#135—861no—
226#135—861no—
227#135—861no—
228#135—861no—
229#135—861no—
230#135—861no—
231C2×Q16—431no—
232C2×Q16—431no—
233C2×SD16—861no—
234C2×SD16—861no—
235C2×D8—431no—
236C2×D8—431no—
237#131—864no—
238#131—1722no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—1721no—
242C22×C8—431no—
243C22×C8—1721no—
244C22×C8C22×D4311yescharacteristic
245C2×C42—431no—
246Q32—862no—
247SD32—862no—
248SD32—862no—
249D16—862no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—861no—
253C2×C16—861no—
254C2×C16—861no—
255C2×C16C4×D4311yescharacteristic
256C2×C16C4×D4311yescharacteristic
257#108—21no—
258#108—21no—
259#108—21no—
260#108D17212yes—
261#104—864no—
262#104—1722no—
263C22⋊C8—1721no—
264C22⋊C8—1721no—
265C4×C8—861no—
266C4×C8—861no—
267#41—862no—
268#41—862no—
269#41—1721no—
270#41—1721no—
271#41—1721no—
272#41—1721no—
273#41—1721no—
274#41—1721no—
275C2×Q8—861no—
276C2×Q8—861no—
277C2×D4—861no—
278C2×D4—861no—
279C2×D4—1721no—
280C2×D4—1721no—
281C22×C4—861no—
282C22×C4—1721no—
283C22×C4—1721no—
284C22×C4D4×D4311yescharacteristic
285Q16—432no—
286Q16—861no—
287Q16—861no—
288Q16—861no—
289SD16—862no—
290SD16—862no—
291SD16—1721no—
292SD16—1721no—
293D8—432no—
294D8—861no—
295D8—861no—
296D8—861no—
297M16—22no—
298M16—41no—
299M16—41no—
300M16—41no—
301M16—1724no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—431no—
305C2×C8—431no—
306C2×C8—861no—
307C2×C8—861no—
308C2×C8—1724no—
309C2×C8C2×C4×D4311yescharacteristic
310C2×C8C2×D17211yescharacteristic
311C2×C8#1062189811yescharacteristic
312C2×C8D4×D4311yescharacteristic
313C2×C8D4×D4311yescharacteristic
314C2×C8#1062190211yescharacteristic
315C42—861no—
316C42—861no—
317C16—21no—
318C16—21no—
319C16—1721no—
320C23—1721no—
321C23—1721no—
322C23#1306334811yescharacteristic
323Q8—862no—
324Q8—1721no—
325Q8—1721no—
326Q8—1721no—
327D4—862no—
328D4—3441no—
329D4—3441no—
330D4—1722no—
331D4—1722no—
332D4—1721no—
333D4—1721no—
334D4—1721no—
335C2×C4—862no—
336C2×C4—3441no—
337C2×C4—3441no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1722no—
343C2×C4—1722no—
344C2×C4#1306328711yescharacteristic
345C2×C4#1306329511yescharacteristic
346C2×C4#1306329811yescharacteristic
347C2×C4D8×D4311yescharacteristic
348C2×C4#1306335211yescharacteristic
349C2×C4#1306335211yescharacteristic
350C8—42no—
351C8—81no—
352C8—861no—
353C8—861no—
354C8C22⋊C4×D4311yescharacteristic
355C8C4×D17211yescharacteristic
356C8#1306330011yescharacteristic
357C8#1306331011yescharacteristic
358C22—21no—
359C22—21no—
360C22—3441no—
361C22—3441no—
362C22—3441no—
363C22—3441no—
364C22—3441no—
365C22—1722no—
366C22#1458298111yescharacteristic
367C22#1458304711yescharacteristic
368C22#1458311711yescharacteristic
369C4—3441no—
370C4—1722no—
371C4—1722no—
372C4#1458277711yescharacteristic
373C4#1458301011yescharacteristic
374C4#1458303411yescharacteristic
375C4#1458309311yescharacteristic
376C2—21no—
377C2—21no—
378C2—3442no—
379C2—6881no—
380C2#1913494411yescharacteristic
381C2#1913647511yescharacteristic
382C2#1913648011yescharacteristic
subgroupG/H
centerC2×C4D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1381C2
socleC22×C43C4×D8
prime radicalC2×#14583331C2
cosocleC22×C8×C43C23
hypercenter#1381D43
hypocenterC43#13011
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1381

Complements

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

NH ≅ G/Ntype
2. C2×#14583015C2semidirect
3. C2×#14582705C2semidirect
4. C2×#14582705C2semidirect
5. #19135481C2semidirect
6. #19132672C2semidirect
7. C43×#1381C2semidirect
13. C2×Dic344C4semidirect
14. C2×#13063270C4semidirect
15. C2×#13063270C4semidirect
16. C2×D688C4semidirect
190. #1381D43semidirect
220. C43#13011semidirect

Maximal subgroups

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

subgroupindex
C2×#145833312
C2×#145830152
C2×#145827052
#191354812
#191326722
C43×#13812
#1301143