Finite Group Databasebeta

← #25251294

Subgroups — #25251294

Order 11008.

520 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145132C211yesmaximal, characteristic
2#19143458C211yesmaximal, characteristic
3#19136762C211yesmaximal, characteristic, complemented
4#19136757C211yesmaximal, characteristic, complemented
5#19136756C211yesmaximal, characteristic, complemented
6#19136747C211yesmaximal, characteristic, complemented
7#19136746C211yesmaximal, characteristic, complemented
8#19136738C211yesmaximal, characteristic, complemented
9#19136735C211yesmaximal, characteristic, complemented
10#19136380C211yesmaximal, characteristic
11#19136378C211yesmaximal, characteristic
12#19136352C211yesmaximal, characteristic
13#19136313C211yesmaximal, characteristic
14#358×D43C211yesmaximal, characteristic
15C43×#2229C211yesmaximal, characteristic, complemented
16C2×Q16×D43C2211yescharacteristic
17#14583529—21no—
18#14583375—21no—
19C2×#13063264C2211yescharacteristic
20C2×C16×D43C2211yescharacteristic
21#14583309—21no—
22#14583306—21no—
23#14583304C2211yescharacteristic
24#14583303C2211yescharacteristic
25#14583300C2211yescharacteristic
26#14583004—21no—
27#14583003—21no—
28C4×Dic172C2211yescharacteristic
29Q16×Dic43C2211yescharacteristic
30#14582993C2211yescharacteristic
31#14582938—21no—
32#14582936C2211yescharacteristic
33#14582936C2211yescharacteristic
34#107×D43C2211yescharacteristic
35#14582906—21no—
36#14582853C2211yescharacteristic
37#14582727C2211yescharacteristic
38#14582727C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582724C2211yescharacteristic
41#14582724C2211yescharacteristic
42#14582724C2211yescharacteristic
43C4⋊(C43⋊C16)C2211yescharacteristic
44Dic43⋊C16C2211yescharacteristic
45Dic43⋊C16C2211yescharacteristic
46#14582704C2211yescharacteristic
47#14582704C2211yescharacteristic
48#14582703C2211yescharacteristic
49#14582703C2211yescharacteristic
50#14582702C2211yescharacteristic
51#14582702C2211yescharacteristic
52C43×#499C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic
54C43×#367C2211yescharacteristic
55C43×#366C2211yescharacteristic
56C43×C4⋊C16C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#358C2211yescharacteristic
59C2×Q8×D43—21no—
60C2×Dic172C2311yescharacteristic
61C2×#10621885—21no—
62Q16×D43—22no—
63Q16×D43Q814yescomplemented
64C2×#10621872D411yescharacteristic
65C2×C8×D43C2311yescharacteristic
66#13063325—21no—
67#13063324—21no—
68#13063324—41no—
69#13063316—21no—
70#13063315—41no—
71#13063305—41no—
72#13063303—41no—
73Q8×Dic43—21no—
74C4×Dic86—21no—
75C4×Dic86—41no—
76#13063290—21no—
77#13063290—41no—
78#13063283—21no—
79#13063283—21no—
80#13063283—41no—
81#13063282—41no—
82#13063282D411yescharacteristic
83C4⋊C4×D43—21no—
84#13063264—22no—
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87C16×D43—22no—
88#13063259—21no—
89#13063259C2311yescharacteristic
90#13063259C2311yescharacteristic
91#13063259C2311yescharacteristic
92#13063258—21no—
93#13063258—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256—21no—
97#13063250—21no—
98#13063249—21no—
99#13063248—21no—
100#13063236D411yescharacteristic
101#13063235D411yescharacteristic
102C8×Dic43C2311yescharacteristic
103C2×Q16×C43C2311yescharacteristic
104#125×C43—21no—
105C4×Q8×C43—21no—
106C2×C16×C43C2311yescharacteristic
107C2×C16×C43C2311yescharacteristic
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#106×C43—21no—
112#103×C43—21no—
113C4×C8×C43C2311yescharacteristic
114C2×Q8×C43—21no—
115Q8×D43—24no—
116Q8×D43—42no—
117C2×C4×D43—41no—
118C2×C4×D43—41no—
119C2×C4×D43C2×D411yescharacteristic
120C2×Dic86—21no—
121C2×Dic86—41no—
122C2×Dic86—41no—
123C2×Dic86—41no—
124Q16×C43—21no—
125Q16×C43C2×Q812yes—
126C2×C8×C43C2×D411yescharacteristic
127C2×C8×C43C2411yescharacteristic
128C4⋊C4×C43—21no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—41no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43—41no—
134C42×C43—41no—
135C42×C43C2×D411yescharacteristic
136#10621885—24no—
137(C2×D43)⋊C4—41no—
138(C2×D43)⋊C4—41no—
139(C2×D43)⋊C4D811yescharacteristic
140(C2×D43)⋊C4D811yescharacteristic
141C4⋊Dic43—21no—
142C4⋊Dic43—21no—
143C4⋊Dic43—21no—
144C4⋊Dic43—41no—
145C4⋊Dic43—41no—
146C4⋊Dic43—41no—
147Dic43⋊C4—41no—
148Dic43⋊C4—41no—
149Dic43⋊C4—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4D811yescharacteristic
153Dic43⋊C4D811yescharacteristic
154C4×Dic43—41no—
155C4×Dic43—41no—
156C4×Dic43—41no—
157C4×Dic43—41no—
158C4×Dic43—41no—
159C4×Dic43C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162Dic172—21no—
163Dic172C2×Q812yes—
164#10621872—22no—
165C8×D43C2×Q812yes—
166C8×D43#4112yes—
167C16×C43—21no—
168C16×C43—21no—
169C43⋊C16—21no—
170C43⋊C16—21no—
171C22×D43C2×D811yescharacteristic
172Q8×C43—22no—
173Q8×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43C2×D811yescharacteristic
179C2×C4×C43C2×D811yescharacteristic
180C2×C4×C43C22×D411yescharacteristic
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43C2×D811yescharacteristic
186C2×Dic43C2×D811yescharacteristic
187C2×Dic43C2×D811yescharacteristic
188C4×D43—44no—
189C4×D43—161no—
190C4×D43C22⋊Q812yes—
191C4×D43#13712yes—
192Dic86—22no—
193Dic86—41no—
194Dic86—44no—
195Dic86—161no—
196Dic86—161no—
197C8×C43—21no—
198C8×C43C22×Q811yescharacteristic
199C8×C43C2×#4111yescharacteristic
200C43⋊C8—21no—
201C43⋊C8C22⋊Q812yes—
202#33632—431nomaximal, Sylow
203C22×C43C22×D811yescharacteristic
204C2×D43—21no—
205C2×D43—21no—
206C2×D43#47412yes—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—42no—
210C4×C43—81no—
211C4×C43—81no—
212C4×C43—81no—
213C4×C43C2×C22⋊Q811yescharacteristic
214C4×C43C2×#13711yescharacteristic
215Dic43—21no—
216Dic43—21no—
217Dic43—42no—
218Dic43—81no—
219Dic43—81no—
220Dic43—81no—
221Dic43#47412yes—
222#3164—431no—
223#2950—431no—
224#2229—431no—
225#2229—431no—
226#2229—431no—
227#2229D4311yescharacteristic, complemented
228#2227—431no—
229#2227—431no—
230#2225—431no—
231#2225—431no—
232#2159—431no—
233#2158—431no—
234#2151—431no—
235#2141—431no—
236C2×#358—431no—
237C2×C43C2×#47411yescharacteristic
238C2×C43#341611yescharacteristic
239C2×C43#341711yescharacteristic
240D43—22no—
241C22×Q16—431no—
242#544—861no—
243#519—861no—
244C2×M32—431no—
245C22×C16—431no—
246#501—861no—
247#501—861no—
248#500—431no—
249#500—431no—
250#499—431no—
251#499C2×D4311yescharacteristic
252#441—861no—
253#441—861no—
254C4×Q16—431no—
255C4×Q16—431no—
256C4×Q16—431no—
257C4×Q16C2×D4311yescharacteristic
258#428—861no—
259#427—431no—
260#427—431no—
261C2×#107—431no—
262#419—861no—
263#405—431no—
264#367—431no—
265#367—431no—
266#367—431no—
267#367C2×D4311yescharacteristic
268#366—431no—
269#366—431no—
270#366—431no—
271#366C2×D4311yescharacteristic
272C4⋊C16—431no—
273C4⋊C16—431no—
274C4⋊C16—431no—
275C4⋊C16C2×D4311yescharacteristic
276#358—431no—
277#358—431no—
278#358—431no—
279#358—431no—
280#358—431no—
281#358—431no—
282#358C2×D4311yescharacteristic
283#358C2×D4311yescharacteristic
284C43#3363211yescharacteristic, complemented, Sylow
285C22×Q8—861no—
286C2×Q16—434no—
287C2×Q16—431no—
288C2×Q16—862no—
289C2×Q16—861no—
290C2×Q16C22×D4311yescharacteristic
291C2×M16—431no—
292C22×C8—431no—
293C4⋊Q8—861no—
294C4⋊Q8—861no—
295C4⋊Q8—1721no—
296#125—21no—
297#125—861no—
298#125—1721no—
299C22⋊Q8—1721no—
300C22⋊Q8—1721no—
301C4×Q8—21no—
302C4×Q8—861no—
303C4×Q8—861no—
304C4×Q8—861no—
305C4×Q8—1721no—
306C4×Q8—1721no—
307#117—431no—
308#117—861no—
309#117—861no—
310#117—1721no—
311#117—1721no—
312C2×C4⋊C4—861no—
313M32—862no—
314C2×C16—431no—
315C2×C16—431no—
316C2×C16—862no—
317C2×C16C22×D4311yescharacteristic
318C2×C16C22×D4311yescharacteristic
319#107—431no—
320#107—431no—
321#107—431no—
322#107—861no—
323#107—861no—
324#107—861no—
325#107C22×D4311yescharacteristic
326#107C22×D4311yescharacteristic
327#107C22×D4311yescharacteristic
328#106—21no—
329#106—861no—
330#106—861no—
331#106—861no—
332#103—21no—
333#103—861no—
334#103—861no—
335#103—861no—
336#97—431no—
337#97—431no—
338C4×C8—431no—
339C4×C8C22×D4311yescharacteristic
340C2×Q8—21no—
341C2×Q8—864no—
342C2×Q8—861no—
343C2×Q8—1721no—
344C2×Q8—1721no—
345C2×Q8—1722no—
346C2×Q8—1721no—
347C22×C4—431no—
348C22×C4—1721no—
349C22×C4—1721no—
350Q16—21no—
351Q16—432no—
352Q16—864no—
353Q16—861no—
354Q16Q8×D4312yes—
355M16—862no—
356C2×C8—431no—
357C2×C8—432no—
358C2×C8—432no—
359C2×C8—431no—
360C2×C8D4×D4311yescharacteristic
361C2×C8C23×D4311yescharacteristic
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—431no—
369C4⋊C4—431no—
370C4⋊C4—861no—
371C4⋊C4—861no—
372C4⋊C4—861no—
373C4⋊C4—1721no—
374C4⋊C4—1721no—
375C4⋊C4—1721no—
376C4⋊C4—1721no—
377C4⋊C4—1721no—
378C4⋊C4—1721no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C22⋊C4—431no—
382C22⋊C4—431no—
383C22⋊C4—1721no—
384C22⋊C4—1721no—
385C42—41no—
386C42—431no—
387C42—1721no—
388C42—1721no—
389C42—1721no—
390C42—1721no—
391C42—1721no—
392C42D4×D4311yescharacteristic
393C16—21no—
394C16—21no—
395C16—861no—
396C16—861no—
397C23—431no—
398Q8—22no—
399Q8—41no—
400Q8—862no—
401Q8—1724no—
402Q8—1721no—
403Q8—6881no—
404Q8—6881no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—431no—
410C2×C4—432no—
411C2×C4—432no—
412C2×C4—431no—
413C2×C4—431no—
414C2×C4—1724no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4—1721no—
419C2×C4—6881no—
420C2×C4D8×D4311yescharacteristic
421C2×C4D8×D4311yescharacteristic
422C2×C4C2×D4×D4311yescharacteristic
423C8—21no—
424C8—432no—
425C8—861no—
426C8C2×Q8×D4311yescharacteristic
427C8#41×D4311yescharacteristic
428C22—432no—
429C22—861no—
430C22—861no—
431C22C2×D8×D4311yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—432no—
439C4—861no—
440C4—861no—
441C4—3441no—
442C4—3441no—
443C4—3441no—
444C4—1722no—
445C4C22⋊Q8×D4311yescharacteristic
446C4#137×D4311yescharacteristic
447C2—862no—
448C2#474×D4311yescharacteristic
449C2#1914773811yescharacteristic
450C2#1914774711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2229C2
socleC22×C43C22×D8
prime radicalC22×D43C2×D8
hypercenter#2229D43
hypocenterC43#33632
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
3. #19136762C2semidirect
4. #19136757C2semidirect
5. #19136756C2semidirect
6. #19136747C2semidirect
7. #19136746C2semidirect
8. #19136738C2semidirect
9. #19136735C2semidirect
15. C43×#2229C2semidirect
63. Q16×D43Q8semidirect
227. #2229D43semidirect
284. C43#33632semidirect

Maximal subgroups

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

subgroupindex
#191451322
#191434582
#191367622
#191367572
#191367562
#191367472
#191367462
#191367382
#191367352
#191363802
#191363782
#191363522
#191363132
#358×D432
C43×#22292
#3363243