Finite Group Databasebeta

← #24994265

Subgroups — #24994265

Order 11008.

490 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 91 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#19143623C211yesmaximal, characteristic
2#19139795C211yesmaximal, characteristic
3#19133221C211yesmaximal, characteristic, complemented
4#19133221C211yesmaximal, characteristic, complemented
5#19132935C211yesmaximal, characteristic
6#19132451C211yesmaximal, characteristic, complemented
7C43×#1285C211yesmaximal, characteristic, complemented
8C2×#13063317C2211yescharacteristic
9C2×C4×D172C2211yescharacteristic
10#14582972—22no—
11#14582969—22no—
12#14582956C2211yescharacteristic
13#14582956C2211yescharacteristic
14#14582861—21no—
15C22⋊C8×D43—21no—
16#14582821—21no—
17#14582821—21no—
18#14582801C411yescharacteristic
19#14582801C411yescharacteristic
20#14582773—21no—
21#14582773—21no—
22#14582769C411yescharacteristic
23#14582765C411yescharacteristic
24#14582640—22no—
25#14582640—22no—
26#14582622—21no—
27#14582622—21no—
28C43×#432C2211yescharacteristic
29C43×#432C2211yescharacteristic
30C4×C4⋊C4×C43C2211yescharacteristic
31C22×D172C2×C411yescharacteristic
32C22×C4×D43D411yescharacteristic
33C22×C4×D43D411yescharacteristic
34C2×#10621872—22no—
35C2×C8×D43—22no—
36#13063317—21no—
37#13063317—21no—
38#13063317—21no—
39#13063317—21no—
40C4×D172—21no—
41C4×D172—21no—
42C4×D172—21no—
43C4×D172—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43C2×C411yescharacteristic
47C2×C4⋊Dic43C2×C411yescharacteristic
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×Dic43⋊C4—21no—
50C2×Dic43⋊C4—21no—
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—21no—
55C2×(C2×D43)⋊C4D411yescharacteristic
56C2×(C2×D43)⋊C4D411yescharacteristic
57C4⋊(C43⋊C8)—21no—
58C4⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)—21no—
61(C2×D43)⋊C8—22no—
62(C2×D43)⋊C8—22no—
63#13063236—21no—
64#13063236D412yes—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C2×C4⋊C4×C43—21no—
68C2×C42×C43C2×C411yescharacteristic
69C2×C42×C43C2×C411yescharacteristic
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75#97×C43—21no—
76#97×C43D412yes—
77#95×C43—21no—
78C23×D43C22⋊C411yescharacteristic
79C23×D43C22⋊C411yescharacteristic
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43C22×C411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43C22⋊C411yescharacteristic
88C22×Dic43C22⋊C411yescharacteristic
89C2×D172—21no—
90C2×D172—21no—
91C2×D172—22no—
92C2×D172—41no—
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97C2×C4×D43—81no—
98C2×C4×D43—81no—
99C2×C8×C43—22no—
100C2×C8×C43—41no—
101C4⋊C4×C43—42no—
102C42×C43—41no—
103C42×C43—41no—
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43#4111yescharacteristic
107C42×C43#4111yescharacteristic
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4—21no—
112(C2×D43)⋊C4—42no—
113(C2×D43)⋊C4—42no—
114(C2×D43)⋊C4—81no—
115(C2×D43)⋊C4—81no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—81no—
123C4⋊Dic43—81no—
124Dic43⋊C4—41no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127Dic43⋊C4—41no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—41no—
130#10621872—82no—
131C8×D43—82no—
132C23×C43C2×C22⋊C411yescharacteristic
133C22×D43—21no—
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—21no—
137C22×D43—21no—
138C22×D43—41no—
139C22×D43—41no—
140C22×D43—41no—
141C22×D43—41no—
142C22×D43#10112yes—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—22no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43#12011yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12311yescharacteristic
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169D172—42no—
170D172—42no—
171C4×D43—42no—
172C4×D43—42no—
173C4×D43—81no—
174C4×D43—81no—
175C8×C43—42no—
176C8×C43—81no—
177C43⋊C8—42no—
178C43⋊C8—81no—
179#9449—431nomaximal, Sylow
180C22×C43—21no—
181C22×C43—21no—
182C22×C43#38611yescharacteristic
183C22×C43C2×#10111yescharacteristic
184C22×C43#41311yescharacteristic
185C2×D43—22no—
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—42no—
189C2×D43—42no—
190C2×D43—41no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—81no—
194C2×D43—81no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—42no—
202C4×C43—81no—
203Dic43—41no—
204Dic43—41no—
205Dic43—81no—
206Dic43—81no—
207#2973—431no—
208#2566—431no—
209#1534—431no—
210#1534—431no—
211#1466—431no—
212#1285—431no—
213#1285D4311yescharacteristic, complemented
214C2×C43—21no—
215C2×C43—21no—
216C2×C43#188411yescharacteristic
217C2×C43#190111yescharacteristic
218C2×C43#191111yescharacteristic
219D43—42no—
220D43—81no—
221C2×#125—431no—
222C2×C4×D4—431no—
223#435—862no—
224#435—862no—
225#432—431no—
226#432—431no—
227#432C2×D4311yescharacteristic
228#432C2×D4311yescharacteristic
229#407—861no—
230C2×C22⋊C8—861no—
231#396—861no—
232#396—861no—
233#390—431no—
234#390—431no—
235#385—861no—
236#385—861no—
237#384—431no—
238#382—431no—
239C4×C4⋊C4C2×D4311yescharacteristic
240#330—862no—
241#330—862no—
242#323—861no—
243#323—861no—
244C43#944911yescharacteristic, complemented, Sylow
245C22×D4—431no—
246C23×C4—431no—
247C23×C4—431no—
248C2×M16—862no—
249C22×C8—862no—
250#125—861no—
251#125—861no—
252#125—861no—
253#125—861no—
254C4×D4—861no—
255C4×D4—861no—
256C4×D4—861no—
257C4×D4—861no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—431no—
260C2×C4⋊C4—431no—
261C2×C4⋊C4—431no—
262C2×C4⋊C4—861no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4—861no—
266C2×C22⋊C4—431no—
267C2×C22⋊C4—431no—
268C2×C22⋊C4—861no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C2×C42C4×D4311yescharacteristic
273C2×C42C4×D4311yescharacteristic
274C2×C42C22×D4311yescharacteristic
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—861no—
278C4⋊C8—861no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—862no—
282C22⋊C8—862no—
283C22⋊C8—861no—
284C22⋊C8—861no—
285#97—21no—
286#97—432no—
287#97—861no—
288#97D17212yes—
289#95—21no—
290#95—861no—
291#95—861no—
292C24—431no—
293C24—431no—
294C2×D4—862no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—1721no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—431no—
301C22×C4—431no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4—861no—
307C22×C4—861no—
308C22×C4—3441no—
309C22×C4—3441no—
310C22×C4C2×C4×D4311yescharacteristic
311C22×C4D4×D4311yescharacteristic
312C22×C4D4×D4311yescharacteristic
313M16—3442no—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—862no—
317C2×C8—3442no—
318C2×C8—1721no—
319C4⋊C4—42no—
320C4⋊C4—861no—
321C4⋊C4—861no—
322C4⋊C4—861no—
323C4⋊C4—861no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C4⋊C4—3441no—
327C4⋊C4—3441no—
328C4⋊C4—1721no—
329C4⋊C4—1721no—
330C4⋊C4—1721no—
331C4⋊C4—1721no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C22⋊C4—861no—
335C22⋊C4—861no—
336C22⋊C4—3441no—
337C22⋊C4—3441no—
338C22⋊C4—1722no—
339C22⋊C4—1722no—
340C42—41no—
341C42—41no—
342C42C2×D17211yescharacteristic
343C42#1062189811yescharacteristic
344C42D4×D4311yescharacteristic
345C42#1062190211yescharacteristic
346C23—432no—
347C23—861no—
348C23—861no—
349C23—861no—
350C23—861no—
351C23—861no—
352C23—1721no—
353C23—1721no—
354C23—1721no—
355C23—1721no—
356C23C22⋊C4×D4311yescharacteristic
357D4—1722no—
358D4—1722no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—3441no—
372C2×C4—3441no—
373C2×C4—1722no—
374C2×C4—1722no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4#1306328711yescharacteristic
384C2×C4C4×D17211yescharacteristic
385C2×C4#1306329511yescharacteristic
386C2×C4#1306329811yescharacteristic
387C2×C4#1306330011yescharacteristic
388C2×C4#1306331011yescharacteristic
389C8—42no—
390C8—81no—
391C8—3441no—
392C8—1722no—
393C22—21no—
394C22—21no—
395C22—862no—
396C22—3441no—
397C22—3441no—
398C22—1722no—
399C22—1722no—
400C22—1721no—
401C22—1721no—
402C22—1721no—
403C22—1721no—
404C22—1721no—
405C22#1458277711yescharacteristic
406C22#101×D4311yescharacteristic
407C22#1458288011yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—42no—
415C4—81no—
416C4—3441no—
417C4—3441no—
418C4—1721no—
419C4—1721no—
420C2—21no—
421C2—21no—
422C2—3441no—
423C2—1722no—
424C2#1913497711yescharacteristic
425C2#1913506211yescharacteristic
426C2#1913512611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1285C2
socleC22×C43#386
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1285D43
hypocenterC43#9449
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
3. #19133221C2semidirect
4. #19133221C2semidirect
6. #19132451C2semidirect
7. C43×#1285C2semidirect
213. #1285D43semidirect
244. C43#9449semidirect

Maximal subgroups

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

subgroupindex
#191436232
#191397952
#191332212
#191329352
#191324512
C43×#12852
#944943