Finite Group Databasebeta

← #25014839

Subgroups — #25014839

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145019C211yesmaximal, characteristic
2C2×#14582707C211yesmaximal, characteristic, complemented
3C2×#14582706C211yesmaximal, characteristic, complemented
4C2×#14582705C211yesmaximal, characteristic, complemented
5C2×#14582674C211yesmaximal, characteristic, complemented
6#19134765C211yesmaximal, characteristic, complemented
7C2×C43×#359C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9C2×#13063345—21no—
10#14583445—21no—
11C22×C43⋊C16C2211yescharacteristic
12#14583284C411yescharacteristic
13#14583282C411yescharacteristic
14#14583280—21no—
15#14583277C411yescharacteristic
16#14583274C411yescharacteristic
17#14583270—21no—
18C2×#13063261C2211yescharacteristic
19C2×#13063260—21no—
20#14582922—21no—
21C2×C8×Dic43C2211yescharacteristic
22#14582707—22no—
23#14582706—22no—
24#14582705—22no—
25#14582674—21no—
26#14582674—21no—
27C2×#135×C43C2211yescharacteristic
28C22×C16×C43C2211yescharacteristic
29C2×#108×C43C2211yescharacteristic
30C43×#359—22no—
31C2×#10621898—21no—
32#13063347—21no—
33#13063347—21no—
34#13063347—21no—
35#13063347—21no—
36#13063345—42no—
37#13063345—42no—
38C2×Dic172C2×C411yescharacteristic
39C2×#10621885—21no—
40C2×#10621873—21no—
41C2×#10621883—21no—
42C2×#10621884—21no—
43C2×D344C2×C411yescharacteristic
44C2×#10621882—21no—
45C2×#10621877—21no—
46C22×C43⋊C8D411yescharacteristic
47#13063323—21no—
48#13063321—21no—
49#13063314—21no—
50#13063312—21no—
51#13063297—42no—
52C4×C22⋊D43—42no—
53C2×C4×Dic43D411yescharacteristic
54C2×C43⋊C16—21no—
55C2×C43⋊C16—21no—
56C2×C43⋊C16D412yescomplemented
57#13063261—21no—
58#13063261—21no—
59#13063260—42no—
60Dic43⋊C8—42no—
61C8×Dic43C2×C411yescharacteristic
62C8×Dic43C2×C411yescharacteristic
63C8×Dic43D411yescharacteristic
64C8×Dic43D411yescharacteristic
65C2×#41×C43—21no—
66#135×C43—21no—
67#135×C43—21no—
68#135×C43—21no—
69#135×C43—21no—
70C2×Q16×C43C2×C411yescharacteristic
71C2×SD16×C43—21no—
72C2×D8×C43C2×C411yescharacteristic
73C2×M16×C43—21no—
74C22×C8×C43C2311yescharacteristic
75C2×C16×C43—21no—
76C2×C16×C43—21no—
77C2×C16×C43D412yescomplemented
78#108×C43—21no—
79#108×C43—21no—
80#41×C43—41no—
81#41×C43—41no—
82#41×C43—41no—
83#41×C43—41no—
84C2×Q8×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43C2×D411yescharacteristic
89C2×C22⋊D43—42no—
90C2×C22⋊D43—41no—
91C22×Dic43SD1612yes—
92#10621898—41no—
93#10621898—41no—
94#10621898—41no—
95#10621898—41no—
96C2×D172—21no—
97C2×C4×D43—41no—
98C2×Dic86—21no—
99Q16×C43—21no—
100Q16×C43—21no—
101SD16×C43—41no—
102SD16×C43—41no—
103D8×C43—21no—
104D8×C43—21no—
105M16×C43—41no—
106M16×C43—41no—
107C2×C8×C43—41no—
108C2×C8×C43C22×C411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43C2×D411yescharacteristic
112C2×C8×C43#4111yescharacteristic
113C2×C8×C43#4111yescharacteristic
114C22⋊Dic43—42no—
115#10621885—42no—
116#10621884—42no—
117#10621883—42no—
118#10621882—42no—
119(C2×D43)⋊C4—42no—
120Dic43⋊C4—42no—
121C4×Dic43C22⋊C411yescharacteristic
122C4×Dic43C22⋊C411yescharacteristic
123C4×Dic43D812yes—
124#10621877—41no—
125#10621877—41no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8C22⋊C411yescharacteristic
128C2×C43⋊C8C22⋊C411yescharacteristic
129C2×C43⋊C8D812yes—
130C2×C43⋊C8SD1612yes—
131Dic172—21no—
132Dic172—21no—
133D344—21no—
134D344—21no—
135#10621873—41no—
136#10621873—41no—
137C16×C43—22no—
138C43⋊C16—22no—
139C23×C43—41no—
140C23×C43C2×SD1611yescharacteristic
141C22×D43—41no—
142Q8×C43—41no—
143Q8×C43—41no—
144D4×C43—41no—
145D4×C43—41no—
146D4×C43—81no—
147D4×C43—81no—
148C2×C4×C43—41no—
149C2×C4×C43—81no—
150C2×C4×C43—81no—
151C2×C4×C43C2×C22⋊C411yescharacteristic
152C2×C4×C43#12411yescharacteristic
153C2×C4×C43#12711yescharacteristic
154C2×C4×C43C2×D811yescharacteristic
155C2×C4×C43C2×D811yescharacteristic
156C2×C4×C43C2×SD1611yescharacteristic
157C22⋊D43—84no—
158C22⋊D43—81no—
159C22⋊D43—81no—
160C2×Dic43—42no—
161C2×Dic43—41no—
162C2×Dic43#10212yes—
163C2×Dic43#10212yes—
164D172—41no—
165D172—41no—
166C4×D43—81no—
167C4×D43—81no—
168Dic86—41no—
169Dic86—41no—
170C8×C43—81no—
171C8×C43C4×D411yescharacteristic
172C8×C43C4×D411yescharacteristic
173C8×C43#12111yescharacteristic
174C8×C43#12111yescharacteristic
175C43⋊C8—81no—
176C43⋊C8#10212yes—
177C43⋊C8#10212yes—
178#13209—431nomaximal, Sylow
179C22×C43—22no—
180C22×C43—82no—
181C22×C43—81no—
182C22×C43C2×#10211yescharacteristic
183C22×C43#48611yescharacteristic
184C22×C43#49211yescharacteristic
185C2×D43—82no—
186C2×D43—81no—
187C4×C43—81no—
188C4×C43#39011yescharacteristic
189C4×C43C2×#10211yescharacteristic
190C4×C43#48611yescharacteristic
191C4×C43#49311yescharacteristic
192Dic43—22no—
193Dic43—22no—
194Dic43—81no—
195#3147—431no—
196C2×#359—431no—
197C2×#359—431no—
198C2×#359—431no—
199C2×#359D4311yescharacteristic, complemented
200C2×#346—431no—
201#1848—431no—
202C2×C43—21no—
203C2×C43—21no—
204C2×C43—161no—
205C2×C43#195711yescharacteristic
206C2×C43#214312yes—
207D43—161no—
208C2×#135—431no—
209C2×#135—861no—
210C2×#135C2×D4311yescharacteristic
211#532—861no—
212C22×C16—431no—
213C22×C16C2×D4311yescharacteristic
214#495—431no—
215#495—431no—
216#495—861no—
217#494—431no—
218#493—431no—
219#492—861no—
220C2×#108—431no—
221C2×#108—861no—
222C2×#108C2×D4311yescharacteristic
223#423—861no—
224C2×C4×C8—431no—
225#359—22no—
226#359—862no—
227#359—862no—
228#359—862no—
229#346—861no—
230#346—861no—
231C43#1320911yescharacteristic, complemented, Sylow
232C2×#41—21no—
233C2×#41—861no—
234#135—21no—
235#135—21no—
236#135—21no—
237#135—21no—
238#135—861no—
239#135—861no—
240#135—861no—
241#135—861no—
242#135—1722no—
243#135—1722no—
244C2×Q16—431no—
245C2×Q16—861no—
246C2×Q16C4×D4311yescharacteristic
247C2×SD16—21no—
248C2×SD16—861no—
249C2×SD16—861no—
250C2×SD16—861no—
251C2×D8—431no—
252C2×D8—861no—
253C2×D8C4×D4311yescharacteristic
254C2×M16—21no—
255C2×M16—861no—
256C22×C8—431no—
257C22×C8C22×D4311yescharacteristic
258C4⋊Q8—861no—
259#127—861no—
260#124—861no—
261#124—861no—
262#121—1722no—
263C4×D4—1722no—
264C2×C42—431no—
265C2×C16—21no—
266C2×C16—21no—
267C2×C16—432no—
268C2×C16—861no—
269C2×C16—861no—
270C2×C16C22⋊D4312yescomplemented
271#108—21no—
272#108—21no—
273#108—861no—
274#108—861no—
275#108—1722no—
276C4⋊C8—1722no—
277C4×C8—431no—
278C4×C8—431no—
279C4×C8—431no—
280C4×C8—431no—
281#41—41no—
282#41—41no—
283#41—41no—
284#41—41no—
285#41—1721no—
286#41—1721no—
287#41—1721no—
288#41—1721no—
289C2×Q8—21no—
290C2×Q8—861no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—861no—
294C2×D4—1722no—
295C2×D4—1721no—
296C22×C4—41no—
297C22×C4—432no—
298C22×C4—1721no—
299C22×C4D4×D4311yescharacteristic
300Q16—21no—
301Q16—21no—
302Q16—861no—
303Q16—861no—
304Q16—1722no—
305SD16—41no—
306SD16—41no—
307SD16—1722no—
308SD16—1722no—
309SD16—1721no—
310SD16—1721no—
311D8—21no—
312D8—21no—
313D8—861no—
314D8—861no—
315D8—1722no—
316M16—41no—
317M16—41no—
318M16—1721no—
319M16—1721no—
320C2×C8—41no—
321C2×C8—431no—
322C2×C8—431no—
323C2×C8—432no—
324C2×C8—432no—
325C2×C8—1721no—
326C2×C8C2×C4×D4311yescharacteristic
327C2×C8#1062189811yescharacteristic
328C2×C8D4×D4311yescharacteristic
329C2×C8D4×D4311yescharacteristic
330C2×C8#1062190011yescharacteristic
331C2×C8C2×C22⋊D4311yescharacteristic
332C4⋊C4—1722no—
333C22⋊C4—1722no—
334C22⋊C4—1722no—
335C42—431no—
336C42—431no—
337C42—432no—
338C16—22no—
339C16—862no—
340C23—41no—
341C23—1721no—
342C23SD16×D4311yescharacteristic
343Q8—41no—
344Q8—41no—
345Q8—1721no—
346Q8—1721no—
347D4—41no—
348D4—41no—
349D4—81no—
350D4—81no—
351D4—3444no—
352D4—3441no—
353D4—3441no—
354D4—1721no—
355D4—1721no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—432no—
360C2×C4—432no—
361C2×C4—3441no—
362C2×C4—3441no—
363C2×C4—1722no—
364C2×C4—1721no—
365C2×C4C22⋊C4×D4311yescharacteristic
366C2×C4#1306331111yescharacteristic
367C2×C4#1306332111yescharacteristic
368C2×C4D8×D4311yescharacteristic
369C2×C4D8×D4311yescharacteristic
370C2×C4SD16×D4311yescharacteristic
371C8—81no—
372C8—432no—
373C8—432no—
374C8—3441no—
375C8(C22⋊D43)⋊C411yescharacteristic
376C8C4×C22⋊D4311yescharacteristic
377C8#1306329711yescharacteristic
378C8#1306329811yescharacteristic
379C22—22no—
380C22—82no—
381C22—81no—
382C22—3442no—
383C22—3441no—
384C22#102×D4311yescharacteristic
385C22#1458324411yescharacteristic
386C22#1458327011yescharacteristic
387C4—81no—
388C4—862no—
389C4—862no—
390C4—3441no—
391C4#1458279911yescharacteristic
392C4#102×D4311yescharacteristic
393C4#1458324411yescharacteristic
394C4#1458327411yescharacteristic
395C2—21no—
396C2—21no—
397C2—161no—
398C2—6881no—
399C2#1913539911yescharacteristic
400C2#1913632112yes—
subgroupG/H
centerC2×C4D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#359C2
socleC22×C43C2×#102
prime radical#19145019C2
cosocleC22×C8×C43C23
hypercenterC2×#359D43
hypocenterC43#13209
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C2×#14582707C2semidirect
3. C2×#14582706C2semidirect
4. C2×#14582705C2semidirect
5. C2×#14582674C2semidirect
6. #19134765C2semidirect
7. C2×C43×#359C2semidirect
56. C2×C43⋊C16D4semidirect
77. C2×C16×C43D4semidirect
199. C2×#359D43semidirect
231. C43#13209semidirect
270. C2×C16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191450192
C2×#145827072
C2×#145827062
C2×#145827052
C2×#145826742
#191347652
C2×C43×#3592
#1320943