Finite Group Databasebeta

← #25014954

Subgroups — #25014954

Order 11008.

432 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144247C211yesmaximal, characteristic
2#19136290C211yesmaximal, characteristic
3#19136289C211yesmaximal, characteristic
4#19136248C211yesmaximal, characteristic
5#19134643C211yesmaximal, characteristic
6#19134397C211yesmaximal, characteristic
7C43×#2123C211yesmaximal, characteristic
8C22×#10621885C411yescharacteristic, complemented
9C2×#13063332C2211yescharacteristic
10#14583470C2211yescharacteristic
11#14583155—21no—
12#14583155—21no—
13#14583138—21no—
14#14583138—21no—
15C2×#13063260—21no—
16#14582935C411yescharacteristic, complemented
17#14582908C411yescharacteristic, complemented
18#14582907C411yescharacteristic, complemented
19#14582883C2211yescharacteristic
20#14582883C2211yescharacteristic
21#14582855—21no—
22#14582698—22no—
23#14582697—22no—
24#14582688—22no—
25#14582669—21no—
26C43⋊#338—21no—
27C43×#536C2211yescharacteristic
28C43×#413C2211yescharacteristic
29C43×#410C2211yescharacteristic
30C43×#352—22no—
31C22×Dic86C2×C411yescharacteristic
32C2×#10621885—21no—
33C2×#10621885—21no—
34C2×#10621885—41no—
35C2×#10621885—41no—
36#13063332—41no—
37#13063332—41no—
38C2×#10621877—21no—
39C2×#10621877—21no—
40C2×#10621877C2×C411yescharacteristic
41C2×#10621877D411yescharacteristic
42C2×#10621877D411yescharacteristic
43C22×C43⋊C8C2×C411yescharacteristic
44C22×C43⋊C8D411yescharacteristic
45C22×C43⋊C8D411yescharacteristic
46#13063323—21no—
47#13063312—21no—
48#13063306—21no—
49#13063306—21no—
50#13063304—21no—
51#13063304—21no—
52#13063284C2×C411yescharacteristic
53#13063260—41no—
54#13063260—41no—
55#13063258—21no—
56#13063256—21no—
57#13063249—21no—
58#13063249—21no—
59#13063248—21no—
60#13063248—21no—
61#13063244—21no—
62#13063244D412yes—
63#13063242—21no—
64#13063242—21no—
65#13063236—41no—
66C4×C43⋊C8—41no—
67C2×#41×C43C2311yescharacteristic
68C22×Q8×C43C2×C411yescharacteristic
69C2×M16×C43—21no—
70C4⋊Q8×C43—21no—
71#124×C43—21no—
72#123×C43—21no—
73#123×C43—21no—
74C22⋊Q8×C43—21no—
75C22⋊Q8×C43—21no—
76#117×C43—21no—
77#117×C43C2×C411yescharacteristic
78#101×C43—21no—
79#100×C43—21no—
80#99×C43—21no—
81#99×C43D412yes—
82#41×C43—41no—
83#41×C43—41no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—41no—
87C2×Q8×C43—41no—
88C2×Q8×C43C2×D411yescharacteristic
89C2×D4×C43C2×D411yescharacteristic
90C2×D4×C43#4111yescharacteristic
91C2×D4×C43#4111yescharacteristic
92C22×C4×C43—21no—
93C22×C4×C43C22×C411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×Dic43—21no—
97C2×Dic86—21no—
98C2×Dic86—21no—
99C2×Dic86—41no—
100C2×Dic86—41no—
101M16×C43—41no—
102M16×C43—41no—
103C2×C8×C43—41no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C22⋊C4×C43—21no—
109C22⋊C4×C43—22no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—41no—
112C42×C43—21no—
113C42×C43—41no—
114C22⋊Dic43—21no—
115C22⋊Dic43—41no—
116C22⋊Dic43—41no—
117#10621885—42no—
118#10621885—41no—
119#10621885—41no—
120C4⋊Dic43—21no—
121Dic43⋊C4—41no—
122Dic43⋊C4—41no—
123C4×Dic43—21no—
124#10621877—22no—
125#10621877—41no—
126#10621877—41no—
127#10621877—41no—
128#10621877—41no—
129#10621877—41no—
130#10621877—41no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8—21no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—41no—
138C2×C43⋊C8—41no—
139C2×C43⋊C8C22⋊C411yescharacteristic
140C2×C43⋊C8C22⋊C411yescharacteristic
141C2×C43⋊C8C22⋊C411yescharacteristic
142C2×C43⋊C8C22⋊C411yescharacteristic
143C23×C43C4×D411yescharacteristic
144C23×C43#12111yescharacteristic
145C23×C43#12411yescharacteristic
146Q8×C43—41no—
147Q8×C43—41no—
148Q8×C43—41no—
149Q8×C43—81no—
150D4×C43—41no—
151D4×C43—41no—
152D4×C43—41no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—42no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—81no—
163C2×C4×C43C2×C22⋊C411yescharacteristic
164C2×C4×C43C4×D411yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43#12711yescharacteristic
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—81no—
170Dic86—41no—
171Dic86—41no—
172Dic86—81no—
173C8×C43—81no—
174C43⋊C8—21no—
175C43⋊C8—21no—
176C43⋊C8—21no—
177C43⋊C8—42no—
178C43⋊C8—81no—
179C43⋊C8#9911yescharacteristic
180C43⋊C8#9911yescharacteristic
181#13233—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—41no—
188C22×C43#39011yescharacteristic
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—81no—
193C4×C43—82no—
194C4×C43—81no—
195C4×C43C2×#9911yescharacteristic
196C4×C43#41011yescharacteristic
197Dic43—81no—
198Dic43—81no—
199#3059—431no—
200#2135—431no—
201#2135—431no—
202#2123—431no—
203#2123D4311yescharacteristic
204#1813—431no—
205#1757—431no—
206C2×C43—21no—
207C2×C43—41no—
208C2×C43—41no—
209C2×C43—41no—
210C2×C43#196411yescharacteristic
211C22×Q16—431no—
212C2×#131—431no—
213#536—431no—
214#536C2×D4311yescharacteristic
215#470—861no—
216#470—861no—
217#467—861no—
218#467—861no—
219C2×#108—861no—
220#427—431no—
221#419—431no—
222#419—431no—
223#413—431no—
224#413—431no—
225#413C2×D4311yescharacteristic
226#410C2×D4311yescharacteristic
227#405—861no—
228#356—862no—
229#356—862no—
230#352—22no—
231#352—862no—
232#344—861no—
233#338—861no—
234C43#1323311yescharacteristic, complemented, Sylow
235C2×#41C22×D4311yescharacteristic
236C22×Q8—431no—
237C22×Q8C4×D4311yescharacteristic
238C2×Q16—861no—
239C2×Q16—861no—
240C2×Q16—1721no—
241C2×Q16—1721no—
242#131—1721no—
243#131—1721no—
244C2×M16—21no—
245C2×M16—431no—
246C2×M16—431no—
247C2×M16—431no—
248C2×M16—861no—
249C2×M16—861no—
250C22×C8—431no—
251C22×C8—431no—
252C22×C8—431no—
253C4⋊Q8—21no—
254C4⋊Q8—861no—
255#124—21no—
256#124—861no—
257#123—21no—
258#123—21no—
259#123—861no—
260#123—861no—
261C22⋊Q8—21no—
262C22⋊Q8—21no—
263C22⋊Q8—861no—
264C22⋊Q8—861no—
265#117—21no—
266#117—431no—
267#117C4×D4311yescharacteristic
268#108—1721no—
269#108—1721no—
270#107—861no—
271#106—861no—
272#103—861no—
273#103—861no—
274#103—861no—
275#103—861no—
276#101—21no—
277#101—432no—
278#101—861no—
279#100—21no—
280#100—861no—
281#100—861no—
282#99—21no—
283#99C22⋊D4312yes—
284#97—1721no—
285C4×C8—1721no—
286#41—41no—
287#41—41no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—861no—
293C2×Q8—861no—
294C2×Q8—1721no—
295C2×Q8—1721no—
296C2×Q8D4×D4311yescharacteristic
297C2×D4#1062189811yescharacteristic
298C2×D4#1062190011yescharacteristic
299C2×D4C2×C22⋊D4311yescharacteristic
300C22×C4—21no—
301C22×C4—861no—
302C22×C4C2×C4×D4311yescharacteristic
303C22×C4D4×D4311yescharacteristic
304C22×C4D4×D4311yescharacteristic
305Q16—1721no—
306Q16—1721no—
307Q16—1722no—
308M16—41no—
309M16—41no—
310M16—862no—
311M16—1721no—
312M16—1721no—
313M16—1721no—
314M16—1721no—
315M16—1721no—
316M16—1721no—
317C2×C8—41no—
318C2×C8—431no—
319C2×C8—431no—
320C2×C8—431no—
321C2×C8—431no—
322C2×C8—861no—
323C2×C8—861no—
324C2×C8—861no—
325C2×C8—861no—
326C2×C8—861no—
327C2×C8—861no—
328C2×C8—1721no—
329C2×C8—1721no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—861no—
335C4⋊C4—1721no—
336C4⋊C4—1721no—
337C22⋊C4—21no—
338C22⋊C4—22no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—861no—
342C22⋊C4—1721no—
343C22⋊C4—1721no—
344C42—21no—
345C42—41no—
346C42—861no—
347C23C4×C22⋊D4311yescharacteristic
348C23#1306329711yescharacteristic
349C23#1306331111yescharacteristic
350Q8—41no—
351Q8—41no—
352Q8—41no—
353Q8—81no—
354Q8—3441no—
355Q8—1721no—
356Q8—1721no—
357D4—41no—
358D4—41no—
359D4—41no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—81no—
370C2×C4—3441no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4C22⋊C4×D4311yescharacteristic
374C2×C4(C22⋊D43)⋊C411yescharacteristic
375C2×C4#1306329811yescharacteristic
376C2×C4#1306332111yescharacteristic
377C8—81no—
378C8—431no—
379C8—431no—
380C8—861no—
381C8—861no—
382C8—861no—
383C8—3441no—
384C8—1722no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22#1458279911yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—81no—
396C4—82no—
397C4—81no—
398C4—3441no—
399C4—3441no—
400C4#99×D4311yescharacteristic
401C4#1458287111yescharacteristic
402C2—21no—
403C2—41no—
404C2—41no—
405C2—41no—
406C2#1913542911yescharacteristic
subgroupG/H
centerC2#19135429
commutatorC22×C4×C43C22×C4
FrattiniC2×#41C22×D43
FittingC43×#2123C2
socleC2×C43#1964
prime radical, cosocleC2×#41×C43C23
hypercenter#2123D43
hypocenterC43#13233
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2123

Complements

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

NH ≅ G/Ntype
8. C22×#10621885C4semidirect
16. #14582935C4semidirect
17. #14582908C4semidirect
18. #14582907C4semidirect
234. C43#13233semidirect

Maximal subgroups

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

subgroupindex
#191442472
#191362902
#191362892
#191362482
#191346432
#191343972
C43×#21232
#1323343