Finite Group Databasebeta

← #24991467

Subgroups — #24991467

Order 11008.

476 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144377C211yesmaximal, characteristic
2#19143164C211yesmaximal, characteristic
3#19132998C211yesmaximal, characteristic, complemented
4#19132978C211yesmaximal, characteristic
5#19132490C211yesmaximal, characteristic, complemented
6#19132430C211yesmaximal, characteristic, complemented
7C43×#1493C211yesmaximal, characteristic, complemented
8C2×#13063333—21no—
9C4×#10621898C2211yescharacteristic
10#14583203—21no—
11#14583196—21no—
12#14583191C411yescharacteristic
13#14583186C411yescharacteristic
14#14583181C411yescharacteristic
15#14583176C411yescharacteristic
16#14582952C2211yescharacteristic
17#14582935—21no—
18#14582927—21no—
19#14582924—22no—
20#14582921—21no—
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C4⋊C8×D43—21no—
24#14582893—21no—
25#14582631—21no—
26Q8⋊(C43⋊C8)—21no—
27Q8⋊(C43⋊C8)—21no—
28#14582628—21no—
29C43×#533C2211yescharacteristic
30C43×#423C2211yescharacteristic
31C2×C4×C8×C43C2211yescharacteristic
32C43×Q8⋊C8—22no—
33C2×#10621898D411yescharacteristic
34#13063333—42no—
35#13063333—42no—
36C2×#10621872—22no—
37C22×C43⋊C8—21no—
38C22×C43⋊C8—21no—
39C2×C8×D43—22no—
40C4×Dic86C2×C411yescharacteristic
41C4×Dic86D411yescharacteristic
42C4×D172C2×C411yescharacteristic
43C4×D172D411yescharacteristic
44C4×C22⋊D43—21no—
45C4×C22⋊D43—21no—
46#13063284D411yescharacteristic
47#13063282—21no—
48C42×D43—21no—
49#13063258—21no—
50#13063258—21no—
51#13063256—21no—
52#13063256—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56C4⋊(C43⋊C8)C2×C411yescharacteristic
57C4⋊(C43⋊C8)C2×C411yescharacteristic
58C4⋊(C43⋊C8)D411yescharacteristic
59C4⋊(C43⋊C8)D411yescharacteristic
60Dic43⋊C8—22no—
61Dic43⋊C8—22no—
62#13063248—21no—
63#13063248—21no—
64#13063245—21no—
65#13063245—21no—
66C22⋊(C43⋊C8)—21no—
67C4×C43⋊C8—21no—
68C2×M16×C43—21no—
69C22×C8×C43—21no—
70C4⋊Q8×C43C2×C411yescharacteristic
71C4⋊Q8×C43C2×C411yescharacteristic
72#125×C43—21no—
73C22⋊Q8×C43—21no—
74C22⋊Q8×C43—21no—
75C4×Q8×C43—21no—
76C4×Q8×C43—21no—
77#117×C43—21no—
78C2×C42×C43C2311yescharacteristic
79C4⋊C8×C43—21no—
80C4⋊C8×C43D412yes—
81C4×C8×C43—21no—
82C4×C8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C2×C22⋊D43—21no—
89#10621898—21no—
90#10621898—21no—
91#10621898SD1612yes—
92#10621898Q1612yes—
93C2×D172C22⋊C411yescharacteristic
94C2×C4×D43—21no—
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97C2×Dic86C22⋊C411yescharacteristic
98M16×C43—41no—
99M16×C43—41no—
100C2×C8×C43—22no—
101C2×C8×C43—22no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C42×C43—41no—
112C42×C43C22×C411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C22⋊Dic43—21no—
117(C2×D43)⋊C4—21no—
118(C2×D43)⋊C4—21no—
119C4⋊Dic43C22⋊C411yescharacteristic
120C4⋊Dic43C22⋊C411yescharacteristic
121Dic43⋊C4—21no—
122Dic43⋊C4—21no—
123C4×Dic43—21no—
124C4×Dic43—21no—
125C4×Dic43—21no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—21no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—41no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8—41no—
134C2×C43⋊C8—41no—
135#10621872—44no—
136C8×D43—44no—
137C23×C43#12311yescharacteristic
138C22×D43—21no—
139Q8×C43—42no—
140Q8×C43—41no—
141Q8×C43—41no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43C2×C22⋊C411yescharacteristic
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43#12011yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43C2×SD1611yescharacteristic
154C2×C4×C43C2×Q1611yescharacteristic
155C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C43#13711yescharacteristic
157C22⋊D43—22no—
158C22⋊D43—22no—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162D172—21no—
163D172#10312yes—
164C4×D43—22no—
165C4×D43—22no—
166C4×D43—41no—
167C4×D43—41no—
168C4×D43—81no—
169Dic86—21no—
170Dic86#10312yes—
171C8×C43—42no—
172C8×C43—42no—
173C43⋊C8—41no—
174C43⋊C8—41no—
175C43⋊C8—41no—
176C43⋊C8—41no—
177C43⋊C8—81no—
178#8993—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43#38611yescharacteristic
182C22×C43#48311yescharacteristic
183C22×C43#48411yescharacteristic
184C2×D43—22no—
185C2×D43—41no—
186C2×D43—41no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—81no—
191C4×C43—81no—
192C4×C43C2×#10311yescharacteristic
193C4×C43#41711yescharacteristic
194C4×C43#44311yescharacteristic
195C4×C43#44411yescharacteristic
196C4×C43#45011yescharacteristic
197C4×C43#45111yescharacteristic
198Dic43—22no—
199Dic43—41no—
200Dic43—41no—
201#3076—431no—
202#2906—431no—
203#1493D4311yescharacteristic, complemented
204#1481—431no—
205#1476—431no—
206#1301—431no—
207#1277—431no—
208C2×C43—21no—
209C2×C43—21no—
210C2×C43#187211yescharacteristic
211C2×C43#187611yescharacteristic
212C2×C43#188111yescharacteristic
213D43—42no—
214C2×#131—861no—
215#533C2×D4311yescharacteristic
216C4×#41—431no—
217#479—861no—
218#478—861no—
219#477—431no—
220#476—431no—
221#475—431no—
222#474—431no—
223#431—431no—
224#427—861no—
225#424—861no—
226#424—862no—
227#423—861no—
228#423C2×D4311yescharacteristic
229C2×C4⋊C8—431no—
230C2×C4⋊C8—431no—
231C2×C4⋊C8—861no—
232#416—861no—
233C2×C4×C8C2×D4311yescharacteristic
234Q8⋊C8—22no—
235Q8⋊C8—861no—
236Q8⋊C8—861no—
237Q8⋊C8—861no—
238D4⋊C8—861no—
239C43#899311yescharacteristic, complemented, Sylow
240C2×#41—431no—
241#131—1722no—
242#131—1722no—
243C2×M16—21no—
244C2×M16—862no—
245C22×C8—21no—
246C22×C8—862no—
247C22×C8—861no—
248C22×C8—861no—
249C4⋊Q8C4×D4311yescharacteristic
250C4⋊Q8C4×D4311yescharacteristic
251#125—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—431no—
257C4×Q8—431no—
258C4×D4—431no—
259C4×D4—431no—
260C4×D4—861no—
261C4×D4—861no—
262#117—21no—
263#117—431no—
264#117—861no—
265C2×C42—861no—
266C2×C42C22×D4311yescharacteristic
267#107—861no—
268#107—861no—
269#106—861no—
270#106—861no—
271C4⋊C8—21no—
272C4⋊C8—431no—
273C4⋊C8—431no—
274C4⋊C8—431no—
275C4⋊C8—431no—
276C4⋊C8—862no—
277C4⋊C8—862no—
278C4⋊C8—861no—
279C4⋊C8—861no—
280C4⋊C8—861no—
281C4⋊C8C22⋊D4312yes—
282#103—861no—
283#103—861no—
284#102—861no—
285#102—861no—
286C22⋊C8—861no—
287C4×C8—21no—
288C4×C8—21no—
289C4×C8—861no—
290#41—432no—
291#41—432no—
292#41—861no—
293#41—861no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—431no—
297C2×D4—431no—
298C2×D4—861no—
299C22×C4—861no—
300C22×C4—861no—
301C22×C4—861no—
302C22×C4#1062189811yescharacteristic
303C22×C4D4×D4311yescharacteristic
304C22×C4#1062190011yescharacteristic
305M16—41no—
306M16—41no—
307M16—1724no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—861no—
313C2×C8—861no—
314C2×C8—861no—
315C2×C8—861no—
316C2×C8—1724no—
317C2×C8—1721no—
318C2×C8—1721no—
319C2×C8—1721no—
320C2×C8—1721no—
321C2×C8—1721no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—431no—
329C4⋊C4—431no—
330C4⋊C4—861no—
331C4⋊C4—861no—
332C22⋊C4—41no—
333C22⋊C4—861no—
334C22⋊C4—861no—
335C22⋊C4—861no—
336C42—41no—
337C42—861no—
338C42—861no—
339C42—861no—
340C42C2×C4×D4311yescharacteristic
341C42D4×D4311yescharacteristic
342C42D4×D4311yescharacteristic
343C42C2×C22⋊D4311yescharacteristic
344C23—861no—
345C23#1306330711yescharacteristic
346Q8—42no—
347Q8—41no—
348Q8—41no—
349Q8—432no—
350Q8—861no—
351D4—432no—
352D4—862no—
353D4—862no—
354D4—861no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—861no—
361C2×C4—862no—
362C2×C4—862no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—3441no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4C22⋊C4×D4311yescharacteristic
369C2×C4(C22⋊D43)⋊C411yescharacteristic
370C2×C4C4×C22⋊D4311yescharacteristic
371C2×C4#1306329311yescharacteristic
372C2×C4#1306329611yescharacteristic
373C2×C4#1306329811yescharacteristic
374C2×C4SD16×D4311yescharacteristic
375C2×C4Q16×D4311yescharacteristic
376C2×C4#1306335211yescharacteristic
377C2×C4#1306335711yescharacteristic
378C8—42no—
379C8—42no—
380C8—3441no—
381C8—1721no—
382C8—1721no—
383C8—1721no—
384C8—1721no—
385C22—21no—
386C22—21no—
387C22—862no—
388C22—1721no—
389C22—1721no—
390C22#1458277511yescharacteristic
391C22#1458322811yescharacteristic
392C22#1458323311yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—81no—
397C4—81no—
398C4—862no—
399C4—1721no—
400C4—1721no—
401C4#103×D4311yescharacteristic
402C4#1458289911yescharacteristic
403C4#1458301311yescharacteristic
404C4#1458301811yescharacteristic
405C4#1458304811yescharacteristic
406C4#1458305311yescharacteristic
407C2—21no—
408C2—21no—
409C2—1722no—
410C2#1913489911yescharacteristic
411C2#1913491911yescharacteristic
412C2#1913496011yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1493C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1493D43
hypocenterC43#8993
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
3. #19132998C2semidirect
5. #19132490C2semidirect
6. #19132430C2semidirect
7. C43×#1493C2semidirect
203. #1493D43semidirect
239. C43#8993semidirect

Maximal subgroups

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

subgroupindex
#191443772
#191431642
#191329982
#191329782
#191324902
#191324302
C43×#14932
#899343