Finite Group Databasebeta

← #25252110

Subgroups — #25252110

Order 11008.

474 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145132C211yesmaximal, characteristic
2#19145128C211yesmaximal, characteristic
3#19136881C211yesmaximal, characteristic, complemented
4#19136880C211yesmaximal, characteristic, complemented
5#19136879C211yesmaximal, characteristic, complemented
6#19136876C211yesmaximal, characteristic, complemented
7#19136875C211yesmaximal, characteristic, complemented
8#19136872C211yesmaximal, characteristic, complemented
9#19136871C211yesmaximal, characteristic, complemented
10#19136382C211yesmaximal, characteristic
11#19136380C211yesmaximal, characteristic
12#19136376C211yesmaximal, characteristic
13#367×D43C211yesmaximal, characteristic
14#19136193C211yesmaximal, characteristic
15C43×#2255C211yesmaximal, characteristic, complemented
16#14583529—21no—
17#14583526—21no—
18C2×#13063264C2211yescharacteristic
19C2×C16×D43C2211yescharacteristic
20#14583309—21no—
21#14583307—21no—
22#14583306—21no—
23#14583305—21no—
24#14583304C2211yescharacteristic
25#14583303C2211yescharacteristic
26#14583303C2211yescharacteristic
27#14583301C2211yescharacteristic
28#14583300C2211yescharacteristic
29#14583300C2211yescharacteristic
30#14582940—21no—
31#14582938—21no—
32#14582936C2211yescharacteristic
33#14582936C2211yescharacteristic
34#107×D43C2211yescharacteristic
35#107×D43C2211yescharacteristic
36#14582853C2211yescharacteristic
37#14582727C2211yescharacteristic
38#14582727C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582726C2211yescharacteristic
41#14582726C2211yescharacteristic
42#14582726C2211yescharacteristic
43#14582726C2211yescharacteristic
44#14582726C2211yescharacteristic
45#14582725C2211yescharacteristic
46#14582725C2211yescharacteristic
47#14582724C2211yescharacteristic
48#14582724C2211yescharacteristic
49#14582674C2211yescharacteristic
50C4×C43⋊C16C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C43×#500C2211yescharacteristic
53C43×#499C2211yescharacteristic
54C43×#367C2211yescharacteristic
55C43×#367C2211yescharacteristic
56C43×#366C2211yescharacteristic
57C43×#366C2211yescharacteristic
58C43×#346C2211yescharacteristic
59C2×#10621872D411yescharacteristic
60C2×C8×D43C2311yescharacteristic
61#13063325—21no—
62#13063324—21no—
63#13063324—21no—
64#13063324—41no—
65#13063323—41no—
66#13063317—21no—
67#13063316—21no—
68#13063316—21no—
69#13063315—41no—
70#13063315—41no—
71#13063305—41no—
72#13063303—41no—
73#13063303—41no—
74#13063301—41no—
75#13063283—21no—
76#13063283—21no—
77#13063282D411yescharacteristic
78C4⋊C4×D43—21no—
79C4⋊C4×D43—21no—
80#13063264Q814yescomplemented
81C2×C43⋊C16C2311yescharacteristic
82C2×C43⋊C16C2311yescharacteristic
83C16×D43Q814yescomplemented
84#13063259—21no—
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063257—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256—21no—
97#13063256—21no—
98#13063236D411yescharacteristic
99#13063235D411yescharacteristic
100C8×Dic43C2311yescharacteristic
101C4⋊Q8×C43—21no—
102#125×C43—21no—
103C2×C16×C43C2311yescharacteristic
104C2×C16×C43C2311yescharacteristic
105#107×C43—21no—
106#107×C43C2311yescharacteristic
107#107×C43C2311yescharacteristic
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#106×C43—21no—
111C4×C8×C43C2311yescharacteristic
112C2×Q8×C43—41no—
113C2×C4×D43—41no—
114C2×C4×D43—41no—
115C2×C4×D43C2×D411yescharacteristic
116C2×Dic86—41no—
117C2×Dic86—41no—
118C2×Dic86—41no—
119C2×C8×C43C2×D411yescharacteristic
120C2×C8×C43C2411yescharacteristic
121C4⋊C4×C43—21no—
122C4⋊C4×C43—21no—
123C4⋊C4×C43—21no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—41no—
126C4⋊C4×C43—41no—
127C4⋊C4×C43—41no—
128C42×C43C2×D411yescharacteristic
129(C2×D43)⋊C4—41no—
130(C2×D43)⋊C4—41no—
131(C2×D43)⋊C4D811yescharacteristic
132(C2×D43)⋊C4D811yescharacteristic
133C4⋊Dic43—21no—
134C4⋊Dic43—21no—
135C4⋊Dic43—21no—
136C4⋊Dic43—21no—
137C4⋊Dic43—41no—
138C4⋊Dic43—41no—
139C4⋊Dic43—41no—
140Dic43⋊C4—41no—
141Dic43⋊C4—41no—
142Dic43⋊C4—41no—
143Dic43⋊C4—41no—
144Dic43⋊C4—41no—
145Dic43⋊C4—41no—
146Dic43⋊C4—41no—
147Dic43⋊C4—41no—
148Dic43⋊C4D811yescharacteristic
149Dic43⋊C4D811yescharacteristic
150C4×Dic43—41no—
151C4×Dic43—41no—
152C4×Dic43C2×D411yescharacteristic
153C2×C43⋊C8C2×D411yescharacteristic
154C2×C43⋊C8C2×D411yescharacteristic
155#10621872Q1614yes—
156C8×D43C2×Q812yes—
157C8×D43C2×Q812yes—
158C16×C43C2×Q812yes—
159C16×C43C2×Q812yes—
160C43⋊C16C2×Q812yes—
161C43⋊C16C2×Q812yes—
162C22×D43C2×D811yescharacteristic
163Q8×C43—161no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43C2×D811yescharacteristic
169C2×C4×C43C2×D811yescharacteristic
170C2×C4×C43C22×D411yescharacteristic
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43C2×D811yescharacteristic
176C2×Dic43C2×D811yescharacteristic
177C2×Dic43C2×D811yescharacteristic
178C4×D43—161no—
179C4×D43—161no—
180C4×D43C4⋊Q812yes—
181C4×D43C2×Q1612yes—
182Dic86—161no—
183Dic86—161no—
184Dic86—161no—
185C8×C43C2×Q1612yes—
186C8×C43C22×Q811yescharacteristic
187C8×C43C22×Q811yescharacteristic
188C43⋊C8C4⋊Q812yes—
189C43⋊C8C2×Q1612yes—
190#33730—431nomaximal, Sylow
191C22×C43C22×D811yescharacteristic
192C2×D43—21no—
193C2×D43—21no—
194C2×D43#50012yes—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—81no—
198C4×C43—81no—
199C4×C43—81no—
200C4×C43—81no—
201C4×C43C2×C4⋊Q811yescharacteristic
202C4×C43C22×Q1611yescharacteristic
203Dic43—21no—
204Dic43—21no—
205Dic43—81no—
206Dic43—81no—
207Dic43—81no—
208Dic43—81no—
209Dic43#50012yes—
210#3164—431no—
211#3164—431no—
212#2255—431no—
213#2255—431no—
214#2255—431no—
215#2255D4311yescharacteristic, complemented
216#2254—431no—
217#2254—431no—
218#2253—431no—
219#2253—431no—
220#2159—431no—
221#2159—431no—
222#2158—431no—
223C2×#367—431no—
224#2108—431no—
225C2×C43C2×#50011yescharacteristic
226C2×C43#341611yescharacteristic
227C2×C43#341611yescharacteristic
228D43—22no—
229#544—861no—
230#544—861no—
231C2×M32—431no—
232C22×C16—431no—
233#501—861no—
234#501—861no—
235#501—861no—
236#501—861no—
237#500—431no—
238#500—431no—
239#500—431no—
240#500C2×D4311yescharacteristic
241#499—431no—
242#499—431no—
243#499—431no—
244#499C2×D4311yescharacteristic
245#428—861no—
246#428—861no—
247#427—431no—
248#427—431no—
249C2×#107—431no—
250C2×#107—431no—
251#405—431no—
252#367—431no—
253#367—431no—
254#367—431no—
255#367—431no—
256#367—431no—
257#367—431no—
258#367—431no—
259#367—431no—
260#367C2×D4311yescharacteristic
261#367C2×D4311yescharacteristic
262#366—431no—
263#366—431no—
264#366—431no—
265#366—431no—
266#366C2×D4311yescharacteristic
267#366C2×D4311yescharacteristic
268#346—431no—
269#346C2×D4311yescharacteristic
270C4×C16—431no—
271C4×C16—431no—
272C43#3373011yescharacteristic, complemented, Sylow
273C2×M16—431no—
274C22×C8—431no—
275C4⋊Q8—21no—
276C4⋊Q8—861no—
277C4⋊Q8—861no—
278C4⋊Q8—861no—
279C4⋊Q8—1721no—
280C4⋊Q8—1721no—
281#125—21no—
282#125—861no—
283#125—861no—
284#125—861no—
285#125—1721no—
286#125—1721no—
287C22⋊Q8—1721no—
288C22⋊Q8—1721no—
289C22⋊Q8—1721no—
290C22⋊Q8—1721no—
291#117—431no—
292#117—861no—
293#117—861no—
294C2×C4⋊C4—861no—
295C2×C4⋊C4—861no—
296M32—434no—
297C2×C16—431no—
298C2×C16—431no—
299C2×C16—434no—
300C2×C16C22×D4311yescharacteristic
301C2×C16C22×D4311yescharacteristic
302#107—21no—
303#107—431no—
304#107—431no—
305#107—431no—
306#107—431no—
307#107—861no—
308#107—861no—
309#107—861no—
310#107—861no—
311#107—861no—
312#107C22×D4311yescharacteristic
313#107C22×D4311yescharacteristic
314#107C22×D4311yescharacteristic
315#107C22×D4311yescharacteristic
316#106—21no—
317#106—861no—
318#106—861no—
319#106—861no—
320#106—861no—
321#106—861no—
322#97—431no—
323#97—431no—
324C4×C8—431no—
325C4×C8C22×D4311yescharacteristic
326C2×Q8—41no—
327C2×Q8—1721no—
328C2×Q8—1721no—
329C2×Q8—1721no—
330C22×C4—431no—
331C22×C4—1721no—
332C22×C4—1721no—
333M16—434no—
334C2×C8—431no—
335C2×C8—431no—
336C2×C8—432no—
337C2×C8—432no—
338C2×C8D4×D4311yescharacteristic
339C2×C8C23×D4311yescharacteristic
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—431no—
348C4⋊C4—431no—
349C4⋊C4—861no—
350C4⋊C4—861no—
351C4⋊C4—861no—
352C4⋊C4—861no—
353C4⋊C4—1721no—
354C4⋊C4—1721no—
355C4⋊C4—1721no—
356C4⋊C4—1721no—
357C4⋊C4—1721no—
358C4⋊C4—1721no—
359C4⋊C4—1721no—
360C4⋊C4—1721no—
361C4⋊C4—1721no—
362C4⋊C4—1721no—
363C4⋊C4—1721no—
364C22⋊C4—431no—
365C22⋊C4—431no—
366C22⋊C4—1721no—
367C22⋊C4—1721no—
368C42—431no—
369C42—1721no—
370C42—1721no—
371C42D4×D4311yescharacteristic
372C16—432no—
373C16—432no—
374C16Q8×D4312yes—
375C16Q8×D4312yes—
376C23—431no—
377Q8—161no—
378Q8—6881no—
379Q8—6881no—
380Q8—6881no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—431no—
386C2×C4—432no—
387C2×C4—432no—
388C2×C4—431no—
389C2×C4—431no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4—1721no—
394C2×C4—6881no—
395C2×C4—6881no—
396C2×C4D8×D4311yescharacteristic
397C2×C4D8×D4311yescharacteristic
398C2×C4C2×D4×D4311yescharacteristic
399C8—432no—
400C8—432no—
401C8Q16×D4312yes—
402C8C2×Q8×D4311yescharacteristic
403C8C2×Q8×D4311yescharacteristic
404C22—432no—
405C22—861no—
406C22—861no—
407C22C2×D8×D4311yescharacteristic
408C4—21no—
409C4—21no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4—81no—
414C4—432no—
415C4—861no—
416C4—861no—
417C4—3441no—
418C4—3441no—
419C4—3441no—
420C4—3441no—
421C4C4⋊Q8×D4311yescharacteristic
422C4C2×Q16×D4311yescharacteristic
423C2—862no—
424C2#500×D4311yescharacteristic
425C2#1914774011yescharacteristic
426C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2255C2
socleC22×C43C22×D8
prime radicalC22×D43C2×D8
hypercenter#2255D43
hypocenterC43#33730
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2255

Complements

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

NH ≅ G/Ntype
3. #19136881C2semidirect
4. #19136880C2semidirect
5. #19136879C2semidirect
6. #19136876C2semidirect
7. #19136875C2semidirect
8. #19136872C2semidirect
9. #19136871C2semidirect
15. C43×#2255C2semidirect
80. #13063264Q8semidirect
83. C16×D43Q8semidirect
215. #2255D43semidirect
272. C43#33730semidirect

Maximal subgroups

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

subgroupindex
#191451322
#191451282
#191368812
#191368802
#191368792
#191368762
#191368752
#191368722
#191368712
#191363822
#191363802
#191363762
#367×D432
#191361932
C43×#22552
#3373043