Finite Group Databasebeta

← #24994385

Subgroups — #24994385

Order 11008.

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

normal subgroups only

This group has 556 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#19143621C211yesmaximal, characteristic
2#19138913C211yesmaximal, characteristic
3#19134686C211yesmaximal, characteristic, complemented
4#19134683C211yesmaximal, characteristic, complemented
5#19134580C211yesmaximal, characteristic
6#19132462C211yesmaximal, characteristic, complemented
7C43×#1289C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D43C2211yescharacteristic
9C22×C4⋊Dic43C2211yescharacteristic
10#14582970—22no—
11#14582967—22no—
12#14582953—21no—
13C2×#13063239—21no—
14#14582861—21no—
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16#14582839C412yescomplemented
17#14582836C412yescomplemented
18#14582798—21no—
19#14582776—21no—
20#14582774—21no—
21#14582759C2211yescharacteristic
22#14582756—21no—
23#14582665—21no—
24#14582662—22no—
25#14582661—22no—
26C2×C22⋊C8×C43C2211yescharacteristic
27C43×#380C2211yescharacteristic
28C43×#380C2211yescharacteristic
29C22×C22⋊D43D411yescharacteristic
30C23×Dic43—21no—
31C22×C4×D43D411yescharacteristic
32C2×#10621872—22no—
33C22×C43⋊C8D412yes—
34C4×C22⋊D43—21no—
35C4×C22⋊D43—21no—
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—22no—
45C2×C4⋊Dic43C2×C412yes—
46C2×Dic43⋊C4C2×C411yescharacteristic
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43D411yescharacteristic
49C2×(C2×D43)⋊C4—22no—
50C2×(C2×D43)⋊C4C2×C411yescharacteristic
51C2×C4×Dic43D411yescharacteristic
52Dic43⋊C8—22no—
53#13063239—42no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56(C2×D43)⋊C8—22no—
57#13063235—22no—
58C43⋊#95—22no—
59C43⋊#95—22no—
60C43⋊#95—21no—
61C23×C4×C43C2311yescharacteristic
62C22×C8×C43D412yes—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C22⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69#95×C43—21no—
70#95×C43C2×C412yes—
71C24×C43C2×D411yescharacteristic
72C23×D43C22⋊C411yescharacteristic
73C22×C4×C43—22no—
74C22×C4×C43—42no—
75C22×C4×C43—41no—
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C2×C22⋊D43—21no—
83C2×C22⋊D43—21no—
84C2×C22⋊D43—21no—
85C2×C22⋊D43—21no—
86C2×C22⋊D43—21no—
87C2×C22⋊D43—21no—
88C22×Dic43—22no—
89C22×Dic43—41no—
90C22×Dic43—41no—
91C22×Dic43—41no—
92C22×Dic43—82no—
93C22×Dic43C22⋊C411yescharacteristic
94C22×Dic43C22⋊C411yescharacteristic
95C22×Dic43C22⋊C411yescharacteristic
96C2×C4×D43—21no—
97C2×C4×D43—21no—
98C2×C4×D43—42no—
99C2×C8×C43—22no—
100C2×C8×C43—42no—
101C4⋊C4×C43—42no—
102C4⋊C4×C43—42no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C22⋊Dic43—21no—
108C22⋊Dic43—21no—
109C22⋊Dic43—41no—
110C22⋊Dic43—41no—
111(C2×D43)⋊C4—21no—
112(C2×D43)⋊C4—21no—
113(C2×D43)⋊C4—82no—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43—41no—
117C4⋊Dic43—41no—
118C4⋊Dic43—42no—
119C4⋊Dic43—82no—
120Dic43⋊C4—21no—
121Dic43⋊C4—21no—
122C4×Dic43—21no—
123C4×Dic43—21no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—42no—
126#10621872—82no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43C2×C22⋊C411yescharacteristic
130C23×C43#12111yescharacteristic
131C23×C43#12111yescharacteristic
132C23×C43AGL(1,ℤ/8)11yescharacteristic
133C23×C43#13711yescharacteristic
134C23×C43#13711yescharacteristic
135C23×C43#13711yescharacteristic
136C22×D43—21no—
137C22×D43—21no—
138C22×D43—21no—
139C22×D43—41no—
140C22×D43—41no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43#12011yescharacteristic
156C2×C4×C43#12311yescharacteristic
157C22⋊D43—41no—
158C22⋊D43—41no—
159C22⋊D43—41no—
160C22⋊D43—41no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43—82no—
172C2×Dic43—82no—
173C2×Dic43—81no—
174C2×Dic43—81no—
175C2×Dic43—81no—
176C4×D43—42no—
177C4×D43—81no—
178C8×C43—42no—
179C43⋊C8—42no—
180#9473—431nomaximal, Sylow
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43#38611yescharacteristic
192C22×C43#41711yescharacteristic
193C22×C43#41911yescharacteristic
194C22×C43#46811yescharacteristic
195C22×C43#46811yescharacteristic
196C22×C43#47011yescharacteristic
197C22×C43#47011yescharacteristic
198C2×D43—42no—
199C2×D43—41no—
200C2×D43—41no—
201C2×D43—41no—
202C2×D43—81no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—82no—
207C4×C43—161no—
208C4×C43#45812yes—
209Dic43—41no—
210Dic43—41no—
211Dic43—41no—
212Dic43—82no—
213Dic43—161no—
214#2973—431no—
215#2487—431no—
216#1824—431no—
217#1824—431no—
218#1799—431no—
219#1289—431no—
220#1289D4311yescharacteristic, complemented
221C2×C43—21no—
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—21no—
225C2×C43—21no—
226C2×C43—21no—
227C2×C43#189011yescharacteristic
228C2×C43#189411yescharacteristic
229C2×C43#191011yescharacteristic
230D43—81no—
231C2×C4×D4—431no—
232C22×C4⋊C4—431no—
233#435—862no—
234#435—862no—
235#432—861no—
236C2×#99—861no—
237#407—861no—
238C2×C22⋊C8—431no—
239C2×C22⋊C8C2×D4311yescharacteristic
240#400—432no—
241#399—432no—
242#389—861no—
243#386—861no—
244#385—861no—
245#380—431no—
246#380—861no—
247#380C2×D4311yescharacteristic
248#380C2×D4311yescharacteristic
249#342—861no—
250#340—862no—
251#340—862no—
252C43#947311yescharacteristic, complemented, Sylow
253C22×D4—431no—
254C23×C4—431no—
255C23×C4—861no—
256C23×C4C22×D4311yescharacteristic
257C2×M16—862no—
258C22×C8—432no—
259C22×C8D17212yes—
260C4×D4—861no—
261C4×D4—861no—
262C4×D4—861no—
263C4×D4—861no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—432no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—861no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4—861no—
272C2×C4⋊C4—862no—
273C2×C4⋊C4—861no—
274C2×C4⋊C4—861no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—431no—
278C2×C22⋊C4—431no—
279C2×C22⋊C4—862no—
280C2×C22⋊C4—861no—
281C2×C42—431no—
282C4⋊C8—862no—
283#99—1722no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—862no—
287C22⋊C8—861no—
288C22⋊C8—861no—
289#97—862no—
290#95—21no—
291#95—862no—
292#95—862no—
293#95—861no—
294#95C4×D4312yes—
295C24—431no—
296C24D4×D4311yescharacteristic
297C2×D4—861no—
298C2×D4—861no—
299C2×D4—861no—
300C2×D4—861no—
301C2×D4—861no—
302C2×D4—861no—
303C22×C4—22no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—431no—
307C22×C4—431no—
308C22×C4—431no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—862no—
312C22×C4—3442no—
313C22×C4—1722no—
314C22×C4—1721no—
315C22×C4—1721no—
316C22×C4—1721no—
317C22×C4C2×C4×D4311yescharacteristic
318C22×C4C2×D17211yescharacteristic
319C22×C4#1062189811yescharacteristic
320C22×C4D4×D4311yescharacteristic
321C22×C4D4×D4311yescharacteristic
322C22×C4#1062190211yescharacteristic
323M16—3442no—
324C2×C8—22no—
325C2×C8—42no—
326C2×C8—862no—
327C2×C8—1722no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—861no—
331C4⋊C4—861no—
332C4⋊C4—862no—
333C4⋊C4—862no—
334C4⋊C4—3442no—
335C4⋊C4—1722no—
336C4⋊C4—1721no—
337C4⋊C4—1721no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—861no—
343C22⋊C4—861no—
344C22⋊C4—861no—
345C22⋊C4—861no—
346C22⋊C4—3442no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
349C42—861no—
350C42—861no—
351C23—41no—
352C23—41no—
353C23—861no—
354C23—861no—
355C23—861no—
356C23—1721no—
357C23—1721no—
358C23C22⋊C4×D4311yescharacteristic
359C23#1306329811yescharacteristic
360C23#1306330011yescharacteristic
361C23#1306334911yescharacteristic
362C23#1306335411yescharacteristic
363C23#1306335411yescharacteristic
364C23#1306335711yescharacteristic
365D4—1721no—
366D4—1721no—
367D4—1721no—
368D4—1721no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—861no—
382C2×C4—861no—
383C2×C4—861no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—3441no—
387C2×C4—3442no—
388C2×C4—3442no—
389C2×C4—3441no—
390C2×C4—3441no—
391C2×C4—3441no—
392C2×C4—1722no—
393C2×C4—1722no—
394C2×C4—1722no—
395C2×C4—1722no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4#1306328711yescharacteristic
399C2×C4C4×D17211yescharacteristic
400C2×C4#1306329511yescharacteristic
401C2×C4#1306331011yescharacteristic
402C8—42no—
403C8—1722no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—3441no—
415C22—1722no—
416C22—1721no—
417C22—1721no—
418C22—1721no—
419C22#1458277711yescharacteristic
420C22#1458289711yescharacteristic
421C22#1458290611yescharacteristic
422C22#1458314411yescharacteristic
423C22#1458314611yescharacteristic
424C22#1458315611yescharacteristic
425C22#1458315811yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—82no—
430C4—161no—
431C4—3442no—
432C4—1721no—
433C4—1721no—
434C4—1721no—
435C4—6881no—
436C4#1458309012yes—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—3441no—
444C2#1913500711yescharacteristic
445C2#1913502711yescharacteristic
446C2#1913512111yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1289C2
socleC22×C43#386
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1289D43
hypocenterC43#9473
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
3. #19134686C2semidirect
4. #19134683C2semidirect
6. #19132462C2semidirect
7. C43×#1289C2semidirect
16. #14582839C4semidirect
17. #14582836C4semidirect
220. #1289D43semidirect
252. C43#9473semidirect

Maximal subgroups

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

subgroupindex
#191436212
#191389132
#191346862
#191346832
#191345802
#191324622
C43×#12892
#947343