Finite Group Databasebeta

← #24993162

Subgroups — #24993162

Order 11008.

522 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 109 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#19145370C211yesmaximal, characteristic
2#19137678C211yesmaximal, characteristic
3#19135580C211yesmaximal, characteristic
4#19133168C211yesmaximal, characteristic
5C2×#14582637C211yesmaximal, characteristic
6#19132475C211yesmaximal, characteristic
7C43×#1282C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C2×#13063304C2211yescharacteristic
10#14583235—21no—
11#14583235C412yescomplemented
12#14583140—22no—
13#14583057—21no—
14#14583057C412yescomplemented
15#14582803—21no—
16#14582783—21no—
17#14582782—21no—
18#14582771—21no—
19#14582759C2211yescharacteristic
20C4×Dic43⋊C4—21no—
21C22⋊C4×Dic43—21no—
22C2×C43⋊#95C2211yescharacteristic
23#14582665—21no—
24#14582665—21no—
25#14582637—22no—
26#14582637—21no—
27#14582637—21no—
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×Dic86C2×C411yescharacteristic
32C22×Dic86D411yescharacteristic
33C23×Dic43—21no—
34C2×Dic172—22no—
35#13063304—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40#13063304—21no—
41#13063304C2×C412yes—
42#13063304D412yes—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43C2×C411yescharacteristic
45C2×C4⋊Dic43D411yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—21no—
48C2×Dic43⋊C4—21no—
49C2×Dic43⋊C4—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43—21no—
52C2×C22⋊Dic43—21no—
53C2×C4×Dic43—21no—
54C2×C4×Dic43—21no—
55#13063259—22no—
56#13063250—22no—
57#13063250—22no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95D411yescharacteristic
65C43⋊#95D411yescharacteristic
66C23×C4×C43C2311yescharacteristic
67C22×C8×C43—21no—
68C22×C8×C43—21no—
69C2×C22⋊C4×C43D411yescharacteristic
70C2×C22⋊C4×C43D411yescharacteristic
71C2×C42×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43C2×C412yes—
76#95×C43—21no—
77C24×C43C2×D411yescharacteristic
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—81no—
81C22×C4×C43C22×C411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—42no—
94C22×Dic43—41no—
95C22×Dic43—41no—
96C22×Dic43—41no—
97C22×Dic43—81no—
98C2×Dic86—21no—
99C2×Dic86—21no—
100C2×Dic86—21no—
101C2×Dic86—81no—
102C2×Dic86—81no—
103C2×Dic86C22⋊C412yes—
104C2×C8×C43—22no—
105C2×C8×C43—41no—
106C2×C8×C43—81no—
107C2×C8×C43—81no—
108C22⋊C4×C43—21no—
109C22⋊C4×C43—21no—
110C22⋊C4×C43—21no—
111C22⋊C4×C43Q1612yescomplemented
112C42×C43—81no—
113C22⋊Dic43—22no—
114C22⋊Dic43—22no—
115C22⋊Dic43—41no—
116C22⋊Dic43—41no—
117C22⋊Dic43—41no—
118C22⋊Dic43—41no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—81no—
123C4⋊Dic43C22⋊C412yes—
124Dic43⋊C4—22no—
125Dic43⋊C4—22no—
126Dic43⋊C4—42no—
127Dic43⋊C4—41no—
128Dic43⋊C4—41no—
129Dic43⋊C4—81no—
130C4×Dic43—42no—
131C4×Dic43—81no—
132Dic172—82no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43C4×D411yescharacteristic
136C23×C43#12011yescharacteristic
137C23×C43#12111yescharacteristic
138C23×C43C2×Q1611yescharacteristic
139C23×C43#13511yescharacteristic
140C23×C43#13711yescharacteristic
141C23×C43#13711yescharacteristic
142C2×C4×C43—22no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
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×C43—41no—
154C2×C4×C43C2×C22⋊C411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12311yescharacteristic
158C2×Dic43—22no—
159C2×Dic43—22no—
160C2×Dic43—22no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—82no—
173C2×Dic43—82no—
174C2×Dic43—81no—
175C2×Dic43—81no—
176C2×Dic43—81no—
177C2×Dic43—81no—
178C2×Dic43—81no—
179Dic86—42no—
180Dic86—42no—
181Dic86—81no—
182Dic86—81no—
183C8×C43—42no—
184C8×C43—81no—
185#9276—431nomaximal, Sylow
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—41no—
193C22×C43—41no—
194C22×C43—41no—
195C22×C43—41no—
196C22×C43#38611yescharacteristic
197C22×C43C4×Q1611yescharacteristic
198C22×C43#44111yescharacteristic
199C22×C43#45111yescharacteristic
200C22×C43#45211yescharacteristic
201C22×C43#46211yescharacteristic
202C22×C43#46411yescharacteristic
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—42no—
208C4×C43—81no—
209Dic43—42no—
210Dic43—42no—
211Dic43—42no—
212Dic43—81no—
213Dic43—81no—
214Dic43—81no—
215Dic43—161no—
216#3189—431no—
217#2368—431no—
218#1996—431no—
219#1520—431no—
220C2×#328—431no—
221#1294—431no—
222#1282D4311yescharacteristic
223C2×C43—21no—
224C2×C43—21no—
225C2×C43—21no—
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—21no—
229C2×C43#187811yescharacteristic
230C2×C43#190611yescharacteristic
231C2×C43#191311yescharacteristic
232C2×C22⋊Q8—431no—
233C2×C22⋊Q8—431no—
234#484—432no—
235#484—861no—
236#467—862no—
237#451—432no—
238#451—861no—
239C2×C22⋊C8C2×D4311yescharacteristic
240C2×C22⋊C8C2×D4311yescharacteristic
241#391—861no—
242#387—861no—
243#387—861no—
244#385—861no—
245#380—431no—
246C4×C4⋊C4—861no—
247C4×C22⋊C4—861no—
248C4×C22⋊C4C2×D4311yescharacteristic
249C2×#95—431no—
250#342—861no—
251#342—861no—
252#328—861no—
253#328—861no—
254#328—862no—
255C43#927611yescharacteristic, complemented, Sylow
256C22×Q8—431no—
257C22×Q8—431no—
258C23×C4—861no—
259C23×C4C22×D4311yescharacteristic
260C2×Q16—862no—
261C22×C8—21no—
262C22×C8—21no—
263C22⋊Q8—432no—
264C22⋊Q8—432no—
265C22⋊Q8—861no—
266C22⋊Q8—861no—
267C22⋊Q8—861no—
268C22⋊Q8—861no—
269C22⋊Q8—861no—
270C22⋊Q8—861no—
271C2×C4⋊C4—431no—
272C2×C4⋊C4—431no—
273C2×C4⋊C4—861no—
274C2×C4⋊C4—861no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4—861no—
278C2×C22⋊C4—861no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C22⋊C4D17211yescharacteristic
282C2×C22⋊C4D17211yescharacteristic
283C2×C42—21no—
284C2×C42—861no—
285C2×C42—861no—
286#107—862no—
287#103—862no—
288#103—862no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8C4×D4312yes—
293#95—21no—
294#95—431no—
295#95—431no—
296#95—861no—
297#95—861no—
298#95—861no—
299#95—861no—
300#95—861no—
301#95—861no—
302C24C2×D17211yescharacteristic
303C2×Q8—432no—
304C2×Q8—861no—
305C2×Q8—861no—
306C2×Q8—861no—
307C2×Q8—3441no—
308C2×Q8—3441no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—81no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—3441no—
319C22×C4—1722no—
320C22×C4—1721no—
321C22×C4—1721no—
322C22×C4—1721no—
323C22×C4C2×C4×D4311yescharacteristic
324C22×C4#1062189811yescharacteristic
325C22×C4D4×D4311yescharacteristic
326C22×C4D4×D4311yescharacteristic
327C22×C4D4×D4311yescharacteristic
328C22×C4#1062190211yescharacteristic
329Q16—3442no—
330C2×C8—22no—
331C2×C8—41no—
332C2×C8—81no—
333C2×C8—81no—
334C4⋊C4—432no—
335C4⋊C4—862no—
336C4⋊C4—862no—
337C4⋊C4—861no—
338C4⋊C4—861no—
339C4⋊C4—861no—
340C4⋊C4—3441no—
341C4⋊C4—3441no—
342C4⋊C4—1722no—
343C4⋊C4—1721no—
344C4⋊C4—1721no—
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—862no—
349C22⋊C4—862no—
350C22⋊C4—1721no—
351C22⋊C4—1721no—
352C22⋊C4—1721no—
353C22⋊C4—1721no—
354C22⋊C4Dic17212yescomplemented
355C42—81no—
356C42—3441no—
357C42—1722no—
358C23—41no—
359C23—41no—
360C23C4×D17211yescharacteristic
361C23#1306329511yescharacteristic
362C23#1306330011yescharacteristic
363C23C2×Dic17211yescharacteristic
364C23#1306334711yescharacteristic
365C23#1306335811yescharacteristic
366C23#1306335811yescharacteristic
367Q8—3441no—
368Q8—3441no—
369Q8—1722no—
370Q8—1722no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—862no—
384C2×C4—862no—
385C2×C4—862no—
386C2×C4—3442no—
387C2×C4—3442no—
388C2×C4—3441no—
389C2×C4—3441no—
390C2×C4—3441no—
391C2×C4—3441no—
392C2×C4—3441no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4C22⋊C4×D4311yescharacteristic
405C2×C4#1306328711yescharacteristic
406C2×C4#1306329811yescharacteristic
407C2×C4#1306331011yescharacteristic
408C8—42no—
409C8—81no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22#1458277711yescharacteristic
421C22C4×Dic17211yescharacteristic
422C22#1458300711yescharacteristic
423C22#1458305711yescharacteristic
424C22#1458306311yescharacteristic
425C22#1458311011yescharacteristic
426C22#1458312211yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—81no—
433C4—3441no—
434C4—3441no—
435C4—3441no—
436C4—1722no—
437C4—1722no—
438C4—1722no—
439C4—6881no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—21no—
444C2—21no—
445C2—21no—
446C2#1913493511yescharacteristic
447C2#1913509711yescharacteristic
448C2#1913513611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1282C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1282D43
hypocenterC43#9276
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
11. #14583235C4semidirect
14. #14583057C4semidirect
111. C22⋊C4×C43Q16semidirect
255. C43#9276semidirect
354. C22⋊C4Dic172semidirect

Maximal subgroups

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

subgroupindex
#191453702
#191376782
#191355802
#191331682
C2×#145826372
#191324752
C43×#12822
#927643