Finite Group Databasebeta

← #24990221

Subgroups — #24990221

Order 11008.

480 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 85 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#19137532C211yesmaximal, characteristic
2C4×#13063239C211yesmaximal, characteristic
3#19132931C211yesmaximal, characteristic
4#19132481C211yesmaximal, characteristic, complemented
5#19132480C211yesmaximal, characteristic, complemented
6#19132447C211yesmaximal, characteristic, complemented
7C43×#1284C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D43C2211yescharacteristic
9C2×#13063239—21no—
10#14582863C2211yescharacteristic
11#14582793—21no—
12#14582781—21no—
13#14582775—21no—
14#14582766C411yescharacteristic, complemented
15#14582758C411yescharacteristic, complemented
16C4×C22⋊Dic43C2211yescharacteristic
17C4×C22⋊Dic43C2211yescharacteristic
18#14582746—21no—
19#14582744C411yescharacteristic, complemented
20#95×D43C411yescharacteristic, complemented
21#14582665—21no—
22#14582624—21no—
23#14582622—21no—
24C43×#407C2211yescharacteristic
25C43×#381C2211yescharacteristic
26C4×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊D43D411yescharacteristic
28C22×C4×D43—21no—
29C22×C4×D43C2×C411yescharacteristic
30C2×#10621877—21no—
31C4×C22⋊D43—21no—
32C4×C22⋊D43—21no—
33C4×C22⋊D43—21no—
34C4×C22⋊D43—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4D411yescharacteristic
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43D411yescharacteristic
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4D411yescharacteristic
42C2×C4×Dic43—21no—
43C2×C4×Dic43—21no—
44C2×C4×Dic43—21no—
45C2×C4×Dic43C2×C411yescharacteristic
46#13063239—24no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95C2×C411yescharacteristic
55C43⋊#95C2×C411yescharacteristic
56C23×C4×C43C2311yescharacteristic
57C2×M16×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C42×C43—21no—
61C22⋊C8×C43—21no—
62C22⋊C8×C43—21no—
63#95×C43—21no—
64#95×C43—21no—
65#95×C43C2×C411yescharacteristic
66#95×C43C2×C411yescharacteristic
67C24×C43C2×D411yescharacteristic
68C23×D43C22⋊C411yescharacteristic
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—41no—
72C22×C4×C43—81no—
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43#4111yescharacteristic
76C22×C4×C43#4111yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C2×C22⋊D43—21no—
80C2×C22⋊D43—21no—
81C2×C22⋊D43—22no—
82C2×C22⋊D43—41no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—41no—
86C22×Dic43C22⋊C411yescharacteristic
87C22×Dic43C22⋊C411yescharacteristic
88C22×Dic43C22⋊C411yescharacteristic
89C2×C4×D43—21no—
90C2×C4×D43—21no—
91C2×C4×D43—42no—
92C2×C4×D43—42no—
93C2×C4×D43—81no—
94C2×C4×D43—81no—
95M16×C43—81no—
96C2×C8×C43—41no—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—81no—
100C42×C43—81no—
101C22⋊Dic43—22no—
102C22⋊Dic43—21no—
103C22⋊Dic43—21no—
104C22⋊Dic43—41no—
105C22⋊Dic43—42no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—42no—
109Dic43⋊C4—21no—
110Dic43⋊C4—21no—
111Dic43⋊C4—81no—
112C4×Dic43—21no—
113C4×Dic43—21no—
114C4×Dic43—42no—
115C4×Dic43—81no—
116C4×Dic43—81no—
117#10621877—81no—
118C2×C43⋊C8—41no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43C2×C22⋊C411yescharacteristic
124C23×C43#12311yescharacteristic
125C23×C43#12311yescharacteristic
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—41no—
129C22×D43—41no—
130C22×D43#10412yes—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—81no—
145C2×C4×C43—81no—
146C2×C4×C43#11711yescharacteristic
147C2×C4×C43#11711yescharacteristic
148C2×C4×C43#12311yescharacteristic
149C2×C4×C43#12311yescharacteristic
150C22⋊D43—42no—
151C22⋊D43—42no—
152C2×Dic43—22no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—21no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—42no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—81no—
167C2×Dic43—81no—
168C4×D43—81no—
169C4×D43—81no—
170C4×D43—84no—
171C8×C43—81no—
172C43⋊C8—81no—
173#8776—431nomaximal, Sylow
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—81no—
183C22×C43—81no—
184C22×C43#38111yescharacteristic
185C22×C43C2×#10411yescharacteristic
186C22×C43#42111yescharacteristic
187C2×D43—22no—
188C2×D43—42no—
189C2×D43—41no—
190C2×D43—41no—
191C2×D43—42no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—81no—
197C4×C43—81no—
198C4×C43—82no—
199Dic43—42no—
200Dic43—41no—
201Dic43—41no—
202Dic43—41no—
203Dic43—81no—
204Dic43—82no—
205#2353—431no—
206C4×#99—431no—
207#1465—431no—
208#1297—431no—
209#1297—431no—
210#1284—431no—
211#1284D4311yescharacteristic, complemented
212C2×C43—21no—
213C2×C43—21no—
214C2×C43—41no—
215C2×C43—41no—
216C2×C43#182611yescharacteristic
217C2×C43#182711yescharacteristic
218C2×C43#182811yescharacteristic
219D43—42no—
220C2×C4×D4—431no—
221C2×#99—861no—
222#407—431no—
223#407C2×D4311yescharacteristic
224#388—861no—
225#387—861no—
226#386—861no—
227#383—431no—
228#381C2×D4311yescharacteristic
229#380—431no—
230C4×C22⋊C4—431no—
231C4×C22⋊C4—431no—
232C4×C22⋊C4—861no—
233C4×C22⋊C4C2×D4311yescharacteristic
234#376—431no—
235C2×#95—431no—
236#342—861no—
237#324—861no—
238#323—861no—
239C43#877611yescharacteristic, complemented, Sylow
240C22×D4—431no—
241C23×C4—431no—
242C23×C4—861no—
243C23×C4C22×D4311yescharacteristic
244C2×M16—21no—
245C2×M16—861no—
246C4×D4—861no—
247C4×D4—861no—
248C4×D4—861no—
249C4×D4—861no—
250C2×C4⋊C4—431no—
251C2×C4⋊C4—861no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—431no—
255C2×C22⋊C4—431no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C42—21no—
260C2×C42—431no—
261C2×C42—861no—
262C2×C42—861no—
263C2×C42—861no—
264#99—864no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C22⋊C8—861no—
268C22⋊C8—861no—
269#95—21no—
270#95—21no—
271#95—431no—
272#95—431no—
273#95—861no—
274#95—861no—
275#95—861no—
276#95—861no—
277#95—861no—
278#95C4×D4311yescharacteristic
279#95C4×D4311yescharacteristic
280C24—431no—
281C24D4×D4311yescharacteristic
282C2×D4—862no—
283C2×D4—861no—
284C2×D4—861no—
285C2×D4—1721no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4—81no—
290C22×C4—431no—
291C22×C4—431no—
292C22×C4—431no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—3441no—
298C22×C4—3441no—
299C22×C4—1722no—
300C22×C4—1722no—
301C22×C4—1721no—
302C22×C4C2×C4×D4311yescharacteristic
303C22×C4#1062189811yescharacteristic
304C22×C4#1062189811yescharacteristic
305C22×C4D4×D4311yescharacteristic
306C22×C4#1062190011yescharacteristic
307C22×C4#1062190211yescharacteristic
308M16—81no—
309M16—3441no—
310C2×C8—41no—
311C2×C8—1721no—
312C4⋊C4—861no—
313C4⋊C4—861no—
314C4⋊C4—3441no—
315C22⋊C4—22no—
316C22⋊C4—41no—
317C22⋊C4—81no—
318C22⋊C4—861no—
319C22⋊C4—861no—
320C22⋊C4—861no—
321C22⋊C4—861no—
322C22⋊C4—862no—
323C22⋊C4—1722no—
324C22⋊C4—1722no—
325C22⋊C4—1721no—
326C42—81no—
327C42—861no—
328C42—861no—
329C42—3441no—
330C42—3441no—
331C42—1722no—
332C23—21no—
333C23—21no—
334C23—41no—
335C23—41no—
336C23—432no—
337C23—861no—
338C23—861no—
339C23—1721no—
340C23—1721no—
341C23C22⋊C4×D4311yescharacteristic
342C23#1306330711yescharacteristic
343C23#1306331011yescharacteristic
344D4—1722no—
345D4—1722no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—862no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—3441no—
368C2×C4—3441no—
369C2×C4—3444no—
370C2×C4—3441no—
371C2×C4—3441no—
372C2×C4—1721no—
373C2×C4—1722no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4#1306328211yescharacteristic
381C2×C4#1306328311yescharacteristic
382C2×C4#1306330711yescharacteristic
383C2×C4#1306331011yescharacteristic
384C8—81no—
385C8—3441no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—81no—
395C22—81no—
396C22—862no—
397C22—1722no—
398C22—1722no—
399C22—1721no—
400C22—1721no—
401C22#1458276111yescharacteristic
402C22#104×D4311yescharacteristic
403C22#1458291411yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—82no—
411C4—3441no—
412C4—3442no—
413C4—1722no—
414C4—1721no—
415C4—1721no—
416C4—1721no—
417C2—21no—
418C2—21no—
419C2—41no—
420C2—41no—
421C2—1722no—
422C2#1913469311yescharacteristic
423C2#1913469711yescharacteristic
424C2#1913470211yescharacteristic
subgroupG/H
centerC22#14582761
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1284C2
socleC22×C43#381
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1284D43
hypocenterC43#8776
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
4. #19132481C2semidirect
5. #19132480C2semidirect
6. #19132447C2semidirect
7. C43×#1284C2semidirect
14. #14582766C4semidirect
15. #14582758C4semidirect
19. #14582744C4semidirect
20. #95×D43C4semidirect
211. #1284D43semidirect
239. C43#8776semidirect

Maximal subgroups

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

subgroupindex
#191375322
C4×#130632392
#191329312
#191324812
#191324802
#191324472
C43×#12842
#877643