Finite Group Databasebeta

← #24988728

Subgroups — #24988728

Order 11008.

838 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 838 conjugacy classes of subgroups — too many to draw. Only its 115 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#19148304C211yesmaximal, characteristic
2#19134675C211yesmaximal, characteristic, complemented
3#19133097C212yesmaximal, complemented
4#19133097C212yesmaximal, complemented
5C43×#1445C211yesmaximal, characteristic, complemented
6#14583604—22no—
7#14583597—22no—
8#14583584—22no—
9#14583550—22no—
10#14583530C411yescharacteristic, complemented
11#14583496—22no—
12#14583480C411yescharacteristic, complemented
13#14583410—22no—
14#14583410C2212yes—
15#14583380C412yescomplemented
16#14582863C2212yes—
17#14582668—22no—
18#14582635—22no—
19#14582635—22no—
20#14582632—22no—
21#14582632—22no—
22C22×C4⋊C4×C43C2211yescharacteristic
23C2×#95×C43—22no—
24C2×#95×C43C2211yescharacteristic
25C2×#95×C43C2211yescharacteristic
26C2×#10621898—22no—
27C2×#10621898C2×C412yes—
28C2×#10621877—22no—
29#13063324—22no—
30#13063320—24no—
31#13063316—22no—
32#13063315—24no—
33#13063310—24no—
34#13063308—24no—
35#13063308—22no—
36#13063305—22no—
37#13063304—22no—
38#13063304—22no—
39#13063304D412yes—
40#13063304D412yes—
41#13063303—24no—
42#13063300—22no—
43#13063299—22no—
44#13063299—22no—
45#13063299D412yes—
46#13063299D412yes—
47#13063294—22no—
48#13063290—22no—
49#13063287—22no—
50C4×C22⋊D43—24no—
51C4×C22⋊D43—24no—
52C4×C22⋊D43—22no—
53C4×C22⋊D43—22no—
54#13063284—22no—
55#13063284C2×C412yes—
56#13063283—22no—
57C4⋊C4×D43—22no—
58C22⋊(C43⋊C8)—22no—
59C22⋊(C43⋊C8)—22no—
60C23×C4×C43—21no—
61C23×C4×C43—21no—
62C23×C4×C43D412yes—
63C23×C4×C43C2311yescharacteristic
64C2×C4⋊C4×C43—22no—
65C2×C4⋊C4×C43—22no—
66C2×C4⋊C4×C43C2×C411yescharacteristic
67C2×C4⋊C4×C43C2×C411yescharacteristic
68C2×C4⋊C4×C43D412yes—
69#95×C43—22no—
70#95×C43—22no—
71#95×C43—44no—
72C24×C43C2×D411yescharacteristic
73C22×C4×C43—22no—
74C22×C4×C43—22no—
75C22×C4×C43—22no—
76C22×C4×C43—22no—
77C22×C4×C43—42no—
78C22×C4×C43—42no—
79C22×C4×C43—42no—
80C22×C4×C43—42no—
81C22×C4×C43—42no—
82C22×C4×C43—42no—
83C22×C4×C43—41no—
84C22×C4×C43—42no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43C22⋊C412yes—
89C22×C4×C43C22⋊C412yes—
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D412yes—
93C22×C4×C43C2×D412yes—
94C2×C22⋊D43—22no—
95C2×C22⋊D43—22no—
96C2×C22⋊D43—22no—
97#10621898—44no—
98#10621898—82no—
99#10621898—82no—
100C2×D172—22no—
101C2×D172C22⋊C412yes—
102C2×C4×D43—22no—
103C2×C4×D43—24no—
104C2×Dic86—22no—
105C2×Dic86C22⋊C412yes—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—24no—
109C22⋊Dic43—22no—
110C22⋊Dic43—22no—
111C22⋊Dic43—22no—
112(C2×D43)⋊C4—24no—
113(C2×D43)⋊C4—24no—
114(C2×D43)⋊C4—22no—
115(C2×D43)⋊C4—22no—
116C4⋊Dic43—22no—
117C4⋊Dic43—22no—
118C4⋊Dic43C22⋊C412yes—
119C4⋊Dic43C22⋊C412yes—
120Dic43⋊C4—24no—
121Dic43⋊C4—24no—
122Dic43⋊C4—22no—
123Dic43⋊C4—22no—
124C4×Dic43—24no—
125C4×Dic43—22no—
126#10621877—44no—
127C2×C43⋊C8—42no—
128C23×C43—22no—
129C23×C43—21no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43C2×C22⋊C411yescharacteristic
134C23×C43#12011yescharacteristic
135C23×C43#12011yescharacteristic
136C22×D43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—44no—
148C2×C4×C43—44no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—82no—
152C2×C4×C43—82no—
153C2×C4×C43—82no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43—81no—
157C2×C4×C43—81no—
158C2×C4×C43C2×C22⋊C412yes—
159C2×C4×C43#12012yes—
160C22⋊D43—44no—
161C22⋊D43—42no—
162C22⋊D43—42no—
163C22⋊D43—42no—
164C22⋊D43—42no—
165C2×Dic43—22no—
166C2×Dic43—22no—
167C2×Dic43—22no—
168D172—42no—
169D172—82no—
170C4×D43—44no—
171C4×D43—84no—
172Dic86—42no—
173Dic86—82no—
174C43⋊C8—82no—
175#8454—431nomaximal, Sylow
176C22×C43—22no—
177C22×C43—22no—
178C22×C43—22no—
179C22×C43—22no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43#37911yescharacteristic
187C22×C43#41012yes—
188C22×C43#45311yescharacteristic
189C22×C43#45411yescharacteristic
190C22×C43#45511yescharacteristic
191C22×C43#45611yescharacteristic
192C2×D43—42no—
193C2×D43—42no—
194C2×D43—42no—
195C4×C43—22no—
196C4×C43—22no—
197C4×C43—42no—
198C4×C43—42no—
199C4×C43—82no—
200C4×C43—82no—
201Dic43—42no—
202Dic43—42no—
203Dic43—42no—
204#3492—431no—
205#1821—431no—
206#1504—432no—
207#1504—432no—
208#1445D4311yescharacteristic, complemented
209C2×C43—21no—
210C2×C43—21no—
211C2×C43—22no—
212C2×C43—21no—
213C2×C43—21no—
214C2×C43#178211yescharacteristic
215C2×C43#179211yescharacteristic
216C2×C43#179311yescharacteristic
217D43—82no—
218#554—862no—
219#553—862no—
220#552—862no—
221#547—862no—
222#544—431no—
223#539—862no—
224#537—431no—
225#525—432no—
226#525—862no—
227#520—432no—
228C22×C4⋊C4C2×D4311yescharacteristic
229#407—432no—
230C2×#95—22no—
231C2×#95C2×D4311yescharacteristic
232C2×#95C2×D4311yescharacteristic
233#343—862no—
234#328—862no—
235#328—862no—
236#327—862no—
237#327—862no—
238C43#845411yescharacteristic, complemented, Sylow
239C2×#41—432no—
240C2×#41—862no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4C22⋊D4312yes—
244C23×C4C22×D4311yescharacteristic
245C2×M16—862no—
246C4⋊Q8—862no—
247#126—864no—
248#125—862no—
249#125—864no—
250#123—864no—
251#123—864no—
252#123—862no—
253C22⋊Q8—432no—
254C22⋊Q8—432no—
255C22⋊Q8—862no—
256C22⋊Q8—864no—
257C22⋊Q8—862no—
258C22⋊Q8—862no—
259#121—432no—
260#121—432no—
261#121—862no—
262#121—862no—
263#121—862no—
264#120—862no—
265C4×Q8—862no—
266C4×D4—862no—
267C4×D4—864no—
268C4×D4—864no—
269C4×D4—862no—
270C4×D4—862no—
271#117—432no—
272#117—862no—
273#117—862no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—862no—
277C2×C4⋊C4C4×D4311yescharacteristic
278C2×C4⋊C4C4×D4311yescharacteristic
279C2×C4⋊C4D17212yes—
280C22⋊C8—862no—
281C22⋊C8—862no—
282#95—22no—
283#95—22no—
284#95—44no—
285C24C2×C22⋊D4311yescharacteristic
286#41—3442no—
287#41—3442no—
288#41—1724no—
289C2×Q8—432no—
290C2×Q8—862no—
291C2×D4—432no—
292C2×D4—862no—
293C2×D4—862no—
294C2×D4—862no—
295C2×D4—862no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—864no—
312C22×C4—862no—
313C22×C4(C2×D43)⋊C412yes—
314C22×C4(C2×D43)⋊C412yes—
315C22×C4C2×C4×D4311yescharacteristic
316C22×C4C2×D17211yescharacteristic
317C22×C4D4×D4312yes—
318C22×C4D4×D4312yes—
319M16—1724no—
320C2×C8—1722no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—24no—
324C4⋊C4—432no—
325C4⋊C4—432no—
326C4⋊C4—864no—
327C4⋊C4—862no—
328C4⋊C4—862no—
329C4⋊C4—864no—
330C4⋊C4—862no—
331C4⋊C4—862no—
332C22⋊C4—864no—
333C22⋊C4—864no—
334C22⋊C4—862no—
335C22⋊C4—862no—
336C22⋊C4—862no—
337C22⋊C4—862no—
338C22⋊C4—862no—
339C42—864no—
340C42—862no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—22no—
346C23—862no—
347C23C2×(C2×D43)⋊C411yescharacteristic
348C23#1306329311yescharacteristic
349C23#1306329311yescharacteristic
350Q8—3442no—
351Q8—1722no—
352D4—3442no—
353D4—1722no—
354D4—1722no—
355D4—1722no—
356D4—1722no—
357D4—1722no—
358D4—1724no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—862no—
381C2×C4—862no—
382C2×C4—862no—
383C2×C4—3444no—
384C2×C4—1724no—
385C2×C4C22⋊C4×D4312yes—
386C2×C4#1306329512yes—
387C8—3442no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—1722no—
399C22—1722no—
400C22—1722no—
401C22#1458275411yescharacteristic
402C22#1458287212yes—
403C22#1458306611yescharacteristic
404C22#1458307111yescharacteristic
405C22#1458307611yescharacteristic
406C22#1458308111yescharacteristic
407C4—22no—
408C4—22no—
409C4—42no—
410C4—42no—
411C4—82no—
412C4—82no—
413C4—1722no—
414C4—1722no—
415C4—1722no—
416C2—21no—
417C2—21no—
418C2—21no—
419C2—21no—
420C2—22no—
421C2—3442no—
422C2#1913451211yescharacteristic
423C2#1913454811yescharacteristic
424C2#1913455311yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1445C2
socleC22×C43#379
prime radical#19148304C2
cosocleC23×C4×C43C23
hypercenter#1445D43
hypocenterC43#8454
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. #19134675C2semidirect
3. #19133097C2semidirect
4. #19133097C2semidirect
5. C43×#1445C2semidirect
10. #14583530C4semidirect
12. #14583480C4semidirect
15. #14583380C4semidirect
208. #1445D43semidirect
238. C43#8454semidirect

Maximal subgroups

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

subgroupindex
#191483042
#191346752
#191330972
C43×#14452
#845443