Finite Group Databasebeta

← #24992910

Subgroups — #24992910

Order 11008.

452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#14583241C211yesmaximal, characteristic
2#19143249C211yesmaximal, characteristic
3#19134695C211yesmaximal, characteristic
4#19133114C211yesmaximal, characteristic
5#19132958C211yesmaximal, characteristic
6#19132472C211yesmaximal, characteristic
7C43×#1282C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10#14583241—21no—
11#14583241—21no—
12#14583241—21no—
13#14583241—21no—
14#14582957—22no—
15#14582953—21no—
16#14582949—21no—
17C2×#13063259C411yescharacteristic, complemented
18C2×#13063257C411yescharacteristic, complemented
19#14582925—21no—
20C2×#13063250C411yescharacteristic, complemented
21C2×#13063250C411yescharacteristic, complemented
22#14582863C2211yescharacteristic
23#14582863C2211yescharacteristic
24#14582854—21no—
25#14582659—21no—
26#14582659—21no—
27#14582635—22no—
28#14582624—21no—
29#14582624—21no—
30C2×C22⋊C8×C43C2211yescharacteristic
31C2×C22⋊C8×C43C2211yescharacteristic
32C4×C22⋊C4×C43C2211yescharacteristic
33C22×Dic86C2×C411yescharacteristic
34C2×#10621877—21no—
35C2×#10621877—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40#13063284—21no—
41#13063284—21no—
42#13063284D411yescharacteristic
43#13063284D411yescharacteristic
44#13063284D411yescharacteristic
45#13063284D411yescharacteristic
46C2×C4⋊Dic43C2×C411yescharacteristic
47C2×C4⋊Dic43C2×C411yescharacteristic
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×Dic43⋊C4—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43—21no—
52C2×C4×Dic43—21no—
53#13063259—21no—
54#13063259—21no—
55#13063257—21no—
56#13063257—21no—
57Dic43⋊C8—22no—
58Dic43⋊C8—22no—
59#13063250—21no—
60#13063250—21no—
61#13063250—21no—
62#13063250—21no—
63C22⋊(C43⋊C8)—21no—
64C22⋊(C43⋊C8)—21no—
65C22⋊(C43⋊C8)—21no—
66C22⋊(C43⋊C8)D412yes—
67#13063235—22no—
68C8×Dic43—22no—
69C23×C4×C43C2311yescharacteristic
70C22×C8×C43—21no—
71C22×C8×C43C2×C411yescharacteristic
72C22×C8×C43C2×C411yescharacteristic
73C2×C22⋊C4×C43—21no—
74C2×C42×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43D411yescharacteristic
79C22⋊C8×C43D411yescharacteristic
80#95×C43—21no—
81C24×C43#4111yescharacteristic
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C2×Dic86—21no—
96C2×Dic86—21no—
97C2×Dic86—41no—
98C2×Dic86—41no—
99C2×C8×C43—21no—
100C2×C8×C43—21no—
101C2×C8×C43—21no—
102C2×C8×C43—21no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C2×C8×C43—41no—
107C22⋊C4×C43—22no—
108C22⋊C4×C43—41no—
109C42×C43—41no—
110C42×C43—41no—
111C22⋊Dic43—21no—
112C22⋊Dic43—21no—
113C22⋊Dic43—21no—
114C22⋊Dic43—21no—
115C22⋊Dic43—41no—
116C22⋊Dic43—41no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43C22⋊C411yescharacteristic
122C4⋊Dic43C22⋊C411yescharacteristic
123C4⋊Dic43C22⋊C411yescharacteristic
124C4⋊Dic43C22⋊C411yescharacteristic
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127C4×Dic43—21no—
128C4×Dic43—21no—
129C4×Dic43—21no—
130C4×Dic43—21no—
131#10621877—41no—
132#10621877—41no—
133#10621877—41no—
134#10621877—41no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8—41no—
137C23×C43—21no—
138C23×C43—21no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43C4×D411yescharacteristic
142C23×C43#12111yescharacteristic
143C23×C43#12311yescharacteristic
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43C2×C22⋊C411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43#12011yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—81no—
171C2×Dic43—81no—
172Dic86—41no—
173Dic86—41no—
174Dic86—81no—
175C8×C43—41no—
176C8×C43—41no—
177C8×C43—41no—
178C8×C43—41no—
179C43⋊C8—42no—
180C43⋊C8—81no—
181#9240—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43#38611yescharacteristic
193C22×C43#44311yescharacteristic
194C22×C43#44411yescharacteristic
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—82no—
199C4×C43#41011yescharacteristic
200C4×C43#41011yescharacteristic
201Dic43—41no—
202Dic43—41no—
203Dic43—41no—
204Dic43—41no—
205Dic43—81no—
206Dic43—81no—
207C2×#485—431no—
208#2924—431no—
209#1826—431no—
210#1508—431no—
211#1472—431no—
212#1293—431no—
213#1282D4311yescharacteristic
214C2×C43—21no—
215C2×C43—21no—
216C2×C43—41no—
217C2×C43—41no—
218C2×C43#187611yescharacteristic
219C2×C43#189911yescharacteristic
220C2×C43#190211yescharacteristic
221C2×C22⋊Q8—431no—
222C2×#117—431no—
223#485—861no—
224#485—861no—
225#485—861no—
226#485—861no—
227#433—862no—
228#432—861no—
229#431—861no—
230C2×#107—431no—
231C2×#106—431no—
232#424—861no—
233C2×#103—431no—
234C2×#103—431no—
235#407—431no—
236#407—431no—
237C2×C22⋊C8C2×D4311yescharacteristic
238C2×C22⋊C8C2×D4311yescharacteristic
239#405—861no—
240C4×C22⋊C4C2×D4311yescharacteristic
241#339—861no—
242#339—861no—
243#328—862no—
244#324—861no—
245#324—861no—
246C43#924011yescharacteristic, complemented, Sylow
247C22×Q8—431no—
248C23×C4C22×D4311yescharacteristic
249C2×M16—861no—
250C2×M16—861no—
251C22×C8—21no—
252C22×C8C4×D4311yescharacteristic
253C22×C8C4×D4311yescharacteristic
254C22⋊Q8—861no—
255C22⋊Q8—861no—
256C22⋊Q8—861no—
257C22⋊Q8—861no—
258#117—431no—
259#117—431no—
260#117—431no—
261#117—431no—
262#117—861no—
263#117—861no—
264C2×C4⋊C4—431no—
265C2×C4⋊C4—431no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—861no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4—861no—
271C2×C42—21no—
272C2×C42—861no—
273#107—861no—
274#107—861no—
275#106—861no—
276#106—861no—
277C4⋊C8—862no—
278C4⋊C8—862no—
279#103—861no—
280#103—861no—
281#103—861no—
282#103—861no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—432no—
287C22⋊C8—861no—
288C22⋊C8—861no—
289C22⋊C8—861no—
290C22⋊C8D17211yescharacteristic
291C22⋊C8D17211yescharacteristic
292#97—862no—
293C4×C8—862no—
294#95—21no—
295C24#1062189811yescharacteristic
296C2×Q8—861no—
297C2×Q8—861no—
298C2×Q8—1721no—
299C2×Q8—1721no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4—861no—
307C22×C4C2×C4×D4311yescharacteristic
308C22×C4C2×D17211yescharacteristic
309C22×C4D4×D4311yescharacteristic
310C22×C4D4×D4311yescharacteristic
311C22×C4D4×D4311yescharacteristic
312C22×C4#1062190211yescharacteristic
313M16—1721no—
314M16—1721no—
315M16—1721no—
316M16—1721no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—862no—
326C2×C8—1721no—
327C4⋊C4—431no—
328C4⋊C4—431no—
329C4⋊C4—431no—
330C4⋊C4—431no—
331C4⋊C4—861no—
332C4⋊C4—861no—
333C4⋊C4—861no—
334C4⋊C4—861no—
335C4⋊C4—1721no—
336C4⋊C4—1721no—
337C22⋊C4—22no—
338C22⋊C4—41no—
339C22⋊C4—861no—
340C22⋊C4—861no—
341C22⋊C4—861no—
342C22⋊C4—861no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C42—41no—
346C42—41no—
347C42—861no—
348C42—861no—
349C42—861no—
350C42—861no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23C4×D17211yescharacteristic
356C23#1306329811yescharacteristic
357C23#1306331011yescharacteristic
358Q8—3441no—
359Q8—1721no—
360Q8—1721no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—861no—
374C2×C4—861no—
375C2×C4—861no—
376C2×C4—861no—
377C2×C4—3441no—
378C2×C4—3441no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4C22⋊C4×D4311yescharacteristic
386C2×C4#1306328711yescharacteristic
387C2×C4#1306329511yescharacteristic
388C2×C4#1306330011yescharacteristic
389C8—41no—
390C8—41no—
391C8—41no—
392C8—41no—
393C8—3441no—
394C8—1722no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22#1458277711yescharacteristic
406C22#1458301711yescharacteristic
407C22#1458302211yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—3441no—
413C4—3441no—
414C4—1721no—
415C4—1721no—
416C4—1721no—
417C4—1721no—
418C4#1458287111yescharacteristic
419C4#1458287111yescharacteristic
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2#1913492111yescharacteristic
425C2#1913505211yescharacteristic
426C2#1913506711yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1282C2
socleC22×C43#386
prime radicalC24×C43#41
cosocleC23×C4×C43C23
hypercenter#1282D43
hypocenterC43#9240
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
17. C2×#13063259C4semidirect
18. C2×#13063257C4semidirect
20. C2×#13063250C4semidirect
21. C2×#13063250C4semidirect
246. C43#9240semidirect

Maximal subgroups

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

subgroupindex
C2×#145832412
#191432492
#191346952
#191331142
#191329582
#191324722
C43×#12822
#924043