Finite Group Databasebeta

← #25015010

Subgroups — #25015010

Order 11008.

410 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×#14583329C211yesmaximal, characteristic
2#19136377C211yesmaximal, characteristic, complemented
3#19136331C211yesmaximal, characteristic, complemented
4#19136330C211yesmaximal, characteristic, complemented
5#19136192C211yesmaximal, characteristic, complemented
6#19135493C211yesmaximal, characteristic, complemented
7C43×#1976C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9#14583329—21no—
10#14583329—21no—
11#14583329—21no—
12#14583329—21no—
13C2×#13063271C411yescharacteristic, complemented
14C2×#13063269C411yescharacteristic, complemented
15C2×#13063268C411yescharacteristic, complemented
16C2×#13063266C411yescharacteristic, complemented
17C2×#13063265C2211yescharacteristic
18C22×C43⋊C16C2211yescharacteristic
19#14582937C2211yescharacteristic
20#14582915—21no—
21#14582872—21no—
22#14582726—21no—
23#14582724—21no—
24#14582709—22no—
25#14582708—22no—
26#14582675—21no—
27C4×C43⋊C16—21no—
28C2×#135×C43C2211yescharacteristic
29C43×#427C2211yescharacteristic
30C43×#421—21no—
31C43×#410—21no—
32C43×#405C2211yescharacteristic
33C2×#10621898—21no—
34#13063347—21no—
35#13063347—21no—
36#13063347—21no—
37#13063347—21no—
38C2×Dic172C2×C411yescharacteristic
39C2×#10621873—21no—
40C2×D344C2×C411yescharacteristic
41#13063284—21no—
42#13063271—21no—
43#13063271—21no—
44#13063269—21no—
45#13063269—21no—
46#13063268—21no—
47#13063268—21no—
48#13063266—21no—
49#13063266—21no—
50#13063265—21no—
51#13063265D412yes—
52C2×C43⋊C16—21no—
53C2×C43⋊C16C2×C411yescharacteristic
54C2×C43⋊C16C2×C411yescharacteristic
55C2×C43⋊C16D411yescharacteristic
56C2×C43⋊C16D411yescharacteristic
57C2×C43⋊C16D411yescharacteristic
58C2×C43⋊C16D411yescharacteristic
59#13063259—21no—
60#13063257—21no—
61#13063251—42no—
62#13063239—42no—
63C2×#41×C43—21no—
64#135×C43—21no—
65#135×C43—21no—
66#135×C43—21no—
67#135×C43—21no—
68C2×Q16×C43C2×C411yescharacteristic
69C2×SD16×C43—21no—
70C2×D8×C43C2×C411yescharacteristic
71C2×M16×C43D411yescharacteristic
72C22×C8×C43C2311yescharacteristic
73#117×C43—21no—
74#117×C43D411yescharacteristic
75#107×C43—21no—
76#106×C43—21no—
77#104×C43—42no—
78#99×C43—42no—
79#97×C43—21no—
80C4×C8×C43—21no—
81#41×C43—41no—
82#41×C43—41no—
83#41×C43—41no—
84#41×C43—41no—
85C2×Q8×C43—21no—
86C2×D4×C43—21no—
87C2×D4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43C2×D411yescharacteristic
90C2×C22⋊D43—41no—
91#10621898—41no—
92#10621898—41no—
93#10621898—41no—
94#10621898—41no—
95C2×D172—21no—
96C2×C4×D43—41no—
97C2×Dic86—21no—
98Q16×C43—21no—
99Q16×C43—21no—
100SD16×C43—41no—
101SD16×C43—41no—
102D8×C43—21no—
103D8×C43—21no—
104M16×C43—21no—
105M16×C43D812yes—
106C2×C8×C43—21no—
107C2×C8×C43C22×C411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43#4111yescharacteristic
112C2×C8×C43#4111yescharacteristic
113C4⋊C4×C43—21no—
114C4⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43D812yes—
117C42×C43—21no—
118C42×C43—41no—
119C22⋊Dic43—41no—
120C4⋊Dic43—41no—
121C4×Dic43—41no—
122Dic172—21no—
123Dic172—21no—
124D344—21no—
125D344—21no—
126#10621873—41no—
127#10621873—41no—
128C43⋊C16—22no—
129C43⋊C16C22⋊C411yescharacteristic
130C43⋊C16C22⋊C411yescharacteristic
131C43⋊C16C22⋊C411yescharacteristic
132C43⋊C16C22⋊C411yescharacteristic
133C23×C43—41no—
134C23×C43C2×D811yescharacteristic
135C22×D43—41no—
136Q8×C43—41no—
137Q8×C43—41no—
138D4×C43—41no—
139D4×C43—41no—
140D4×C43—81no—
141D4×C43—81no—
142C2×C4×C43—22no—
143C2×C4×C43—41no—
144C2×C4×C43—81no—
145C2×C4×C43—81no—
146C2×C4×C43—81no—
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12711yescharacteristic
150C2×C4×C43C2×D811yescharacteristic
151C2×C4×C43#13511yescharacteristic
152C2×C4×C43#13511yescharacteristic
153C22⋊D43—81no—
154C22⋊D43—81no—
155C2×Dic43—41no—
156C2×Dic43—81no—
157D172—41no—
158D172—41no—
159C4×D43—81no—
160C4×D43—81no—
161Dic86—41no—
162Dic86—41no—
163C8×C43—22no—
164C8×C43C2×C22⋊C411yescharacteristic
165C8×C43C4×D411yescharacteristic
166C8×C43#12111yescharacteristic
167C8×C43#12411yescharacteristic
168#13243—431nomaximal, Sylow
169C22×C43—41no—
170C22×C43—81no—
171C22×C43—161no—
172C22×C43C4×D811yescharacteristic
173C22×C43#46611yescharacteristic
174C22×C43#49311yescharacteristic
175C2×D43—81no—
176C2×D43—161no—
177C4×C43—42no—
178C4×C43—81no—
179C4×C43—161no—
180C4×C43#39011yescharacteristic
181C4×C43C4×D811yescharacteristic
182C4×C43#46611yescharacteristic
183C4×C43#49511yescharacteristic
184Dic43—81no—
185Dic43—161no—
186C2×#508—431no—
187#2158—431no—
188#2145—431no—
189#2145—431no—
190#2108—431no—
191#1976—431no—
192#1976D4311yescharacteristic, complemented
193C2×C43—21no—
194C2×C43—21no—
195C2×C43—21no—
196C2×C43—161no—
197C2×C43#197011yescharacteristic
198D43—161no—
199C2×#135—431no—
200C2×#135C2×D4311yescharacteristic
201#508—861no—
202#508—861no—
203#508—861no—
204#508—861no—
205C2×Q32—431no—
206C2×SD32—431no—
207C2×SD32—431no—
208C2×D16—431no—
209C2×M32—431no—
210C22×C16—431no—
211#427—431no—
212#427C2×D4311yescharacteristic
213#421—21no—
214#421—861no—
215#410—21no—
216#410—861no—
217#405C2×D4311yescharacteristic
218#367—861no—
219#366—861no—
220#360—862no—
221#360—862no—
222#346—861no—
223C4×C16—861no—
224C43#1324311yescharacteristic, complemented, Sylow
225C2×#41—21no—
226C2×#41—861no—
227#135—21no—
228#135—21no—
229#135—21no—
230#135—21no—
231#135—861no—
232#135—861no—
233#135—861no—
234#135—861no—
235C2×Q16—431no—
236C2×Q16C4×D4311yescharacteristic
237C2×SD16—21no—
238C2×SD16—861no—
239C2×D8—431no—
240C2×D8C4×D4311yescharacteristic
241C2×M16C22⋊D4311yescharacteristic
242C22×C8C22×D4311yescharacteristic
243#117—21no—
244#117—861no—
245#117C22⋊D4311yescharacteristic
246Q32—861no—
247Q32—861no—
248SD32—861no—
249SD32—861no—
250SD32—861no—
251SD32—861no—
252D16—861no—
253D16—861no—
254M32—432no—
255M32—861no—
256C2×C16—431no—
257C2×C16—431no—
258C2×C16—431no—
259C2×C16—431no—
260C2×C16—431no—
261C2×C16—431no—
262C2×C16—861no—
263#107—21no—
264#107—861no—
265#106—21no—
266#106—861no—
267#104—42no—
268#104—1722no—
269#99—42no—
270#99—1722no—
271#97—21no—
272C4×C8—21no—
273#41—41no—
274#41—41no—
275#41—41no—
276#41—41no—
277#41—1721no—
278#41—1721no—
279#41—1721no—
280#41—1721no—
281C2×Q8—21no—
282C2×Q8—861no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—861no—
286C2×D4—1721no—
287C22×C4—41no—
288C22×C4—1721no—
289C22×C4C2×C22⋊D4311yescharacteristic
290Q16—21no—
291Q16—21no—
292Q16—861no—
293Q16—861no—
294SD16—41no—
295SD16—41no—
296SD16—1721no—
297SD16—1721no—
298D8—21no—
299D8—21no—
300D8—861no—
301D8—861no—
302M16—21no—
303M16#1062188212yes—
304C2×C8—21no—
305C2×C8C2×C4×D4311yescharacteristic
306C2×C8#1062189811yescharacteristic
307C2×C8D4×D4311yescharacteristic
308C2×C8D4×D4311yescharacteristic
309C2×C8D4×D4311yescharacteristic
310C2×C8#1062190011yescharacteristic
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—1721no—
314C22⋊C4—41no—
315C22⋊C4—1721no—
316C22⋊C4#1062188212yes—
317C42—21no—
318C42—41no—
319C42—1721no—
320C16—431no—
321C16—431no—
322C16—431no—
323C16—431no—
324C16—862no—
325C23—41no—
326C23—1721no—
327C23C2×#1062188211yescharacteristic
328Q8—41no—
329Q8—41no—
330Q8—1721no—
331Q8—1721no—
332D4—41no—
333D4—41no—
334D4—81no—
335D4—81no—
336D4—3441no—
337D4—3441no—
338D4—1721no—
339D4—1721no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—3441no—
346C2×C4—3441no—
347C2×C4—3441no—
348C2×C4—1721no—
349C2×C4C4×C22⋊D4311yescharacteristic
350C2×C4#1306329711yescharacteristic
351C2×C4#1306332111yescharacteristic
352C2×C4C2×#1062188211yescharacteristic
353C2×C4#1306334511yescharacteristic
354C2×C4#1306334511yescharacteristic
355C8—22no—
356C8C22⋊C4×D4311yescharacteristic
357C8(C22⋊D43)⋊C411yescharacteristic
358C8#1306329811yescharacteristic
359C8#1306331111yescharacteristic
360C22—41no—
361C22—81no—
362C22—161no—
363C22—3441no—
364C22—6881no—
365C22C4×#1062188211yescharacteristic
366C22#1458313311yescharacteristic
367C22#1458327511yescharacteristic
368C4—42no—
369C4—81no—
370C4—161no—
371C4—3441no—
372C4—6881no—
373C4#1458279911yescharacteristic
374C4C4×#1062188211yescharacteristic
375C4#1458313311yescharacteristic
376C4#1458328111yescharacteristic
377C2—21no—
378C2—21no—
379C2—21no—
380C2—161no—
381C2—6881no—
382C2#1913546011yescharacteristic
subgroupG/H
centerC4#14583133
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1976C2
socleC2×C43#1970
prime radicalC2×#14583329C2
cosocleC22×C8×C43C23
hypercenter#1976D43
hypocenterC43#13243
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #405 ◁ #1976

Complements

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

NH ≅ G/Ntype
2. #19136377C2semidirect
3. #19136331C2semidirect
4. #19136330C2semidirect
5. #19136192C2semidirect
6. #19135493C2semidirect
7. C43×#1976C2semidirect
13. C2×#13063271C4semidirect
14. C2×#13063269C4semidirect
15. C2×#13063268C4semidirect
16. C2×#13063266C4semidirect
192. #1976D43semidirect
224. C43#13243semidirect

Maximal subgroups

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

subgroupindex
C2×#145833292
#191363772
#191363312
#191363302
#191361922
#191354932
C43×#19762
#1324343