Finite Group Databasebeta

← #24990129

Subgroups — #24990129

Order 11008.

546 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 87 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#19137208C211yesmaximal, characteristic
2#19132921C211yesmaximal, characteristic
3#19132921C211yesmaximal, characteristic
4#19132502C211yesmaximal, characteristic, complemented
5#19132501C211yesmaximal, characteristic, complemented
6#19132500C211yesmaximal, characteristic, complemented
7C43×#1305C211yesmaximal, characteristic, complemented
8C22×(C2×D43)⋊C4C2211yescharacteristic
9C2×C22⋊C4×D43C411yescharacteristic
10C2×C22⋊C4×D43C411yescharacteristic
11#14582863C2211yescharacteristic
12#14582863C2211yescharacteristic
13#14582773—21no—
14#14582773—21no—
15#14582770—21no—
16#14582770—21no—
17#14582759C2211yescharacteristic
18#14582757C411yescharacteristic
19#14582757C411yescharacteristic
20#14582622—21no—
21#14582622—21no—
22#14582622—21no—
23#14582622—21no—
24C43×#407C2211yescharacteristic
25C43×#407C2211yescharacteristic
26C43×#380C2211yescharacteristic
27C24×D43C2×C411yescharacteristic
28C23×Dic43C2×C411yescharacteristic
29C22×C4×D43—21no—
30C22×C4×D43—21no—
31C2×#10621877—21no—
32C2×#10621877—21no—
33C2×C4⋊Dic43—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×C22⋊Dic43C2×C411yescharacteristic
37C2×C22⋊Dic43C2×C411yescharacteristic
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4D411yescharacteristic
45C2×(C2×D43)⋊C4D411yescharacteristic
46C2×(C2×D43)⋊C4D411yescharacteristic
47C2×(C2×D43)⋊C4D411yescharacteristic
48C22⋊C4×D43—42no—
49C22⋊C4×D43—42no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C23×C4×C43C2311yescharacteristic
58C2×M16×C43—21no—
59C2×M16×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C22⋊C4×C43C2×C411yescharacteristic
62C2×C22⋊C4×C43C2×C411yescharacteristic
63C22⋊C8×C43—21no—
64C22⋊C8×C43—21no—
65C22⋊C8×C43—21no—
66C22⋊C8×C43—21no—
67#95×C43—21no—
68C24×C43C22×C411yescharacteristic
69C23×D43—21no—
70C23×D43—21no—
71C23×D43—22no—
72C23×D43—22no—
73C23×D43—81no—
74C23×D43—81no—
75C23×D43C22⋊C411yescharacteristic
76C23×D43C22⋊C411yescharacteristic
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—81no—
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×C4×C43#4111yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—81no—
91C22×Dic43C22⋊C411yescharacteristic
92C22×Dic43C22⋊C411yescharacteristic
93C2×C4×D43—42no—
94C2×C4×D43—42no—
95C2×C4×D43—81no—
96C2×C4×D43—81no—
97C2×C4×D43—81no—
98C2×C4×D43—81no—
99M16×C43—81no—
100M16×C43—81no—
101C2×C8×C43—41no—
102C2×C8×C43—41no—
103C4⋊C4×C43—81no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊Dic43—41no—
107C22⋊Dic43—41no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4—21no—
112(C2×D43)⋊C4—21no—
113(C2×D43)⋊C4—21no—
114(C2×D43)⋊C4—21no—
115(C2×D43)⋊C4—21no—
116(C2×D43)⋊C4—42no—
117(C2×D43)⋊C4—42no—
118C4⋊Dic43—81no—
119Dic43⋊C4—81no—
120Dic43⋊C4—81no—
121#10621877—81no—
122#10621877—81no—
123C2×C43⋊C8—41no—
124C2×C43⋊C8—41no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43C2×C22⋊C411yescharacteristic
130C23×C43#11711yescharacteristic
131C23×C43#11711yescharacteristic
132C22×D43—21no—
133C22×D43—21no—
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—24no—
137C22×D43—24no—
138C22×D43—41no—
139C22×D43—41no—
140C22×D43—41no—
141C22×D43—41no—
142C22×D43—81no—
143C22×D43—81no—
144C22×D43—81no—
145C22×D43—81no—
146C22×D43—84no—
147C22×D43—84no—
148C22×D43#10012yes—
149C22×D43#10112yes—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43#12311yescharacteristic
163C2×C4×C43#12311yescharacteristic
164C2×C4×C43#12311yescharacteristic
165C2×C4×C43#12311yescharacteristic
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—81no—
177C2×Dic43—81no—
178C4×D43—84no—
179C4×D43—84no—
180C8×C43—81no—
181C8×C43—81no—
182C43⋊C8—81no—
183C43⋊C8—81no—
184#8756—431nomaximal, Sylow
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—42no—
194C22×C43—42no—
195C22×C43#38111yescharacteristic
196C22×C43C2×#10011yescharacteristic
197C22×C43C2×#10111yescharacteristic
198C2×D43—22no—
199C2×D43—22no—
200C2×D43—42no—
201C2×D43—42no—
202C2×D43—41no—
203C2×D43—41no—
204C2×D43—41no—
205C2×D43—41no—
206C2×D43—42no—
207C2×D43—42no—
208C2×D43—84no—
209C2×D43—84no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—81no—
215C4×C43—81no—
216Dic43—41no—
217Dic43—41no—
218Dic43—81no—
219Dic43—81no—
220#2315—431no—
221#1462—431no—
222#1462—431no—
223#1305—431no—
224#1305—431no—
225#1305—431no—
226#1305D4311yescharacteristic, complemented
227C2×C43—21no—
228C2×C43—21no—
229C2×C43—41no—
230C2×C43—41no—
231C2×C43#182111yescharacteristic
232C2×C43#182811yescharacteristic
233C2×C43#182911yescharacteristic
234D43—42no—
235D43—42no—
236C22×C22⋊C4—431no—
237C22×C22⋊C4—431no—
238C22×C22⋊C4—431no—
239#407—431no—
240#407—431no—
241#407C2×D4311yescharacteristic
242#407C2×D4311yescharacteristic
243#385—861no—
244#385—861no—
245#385—861no—
246#385—861no—
247#380—431no—
248#380—431no—
249#380—431no—
250#380C2×D4311yescharacteristic
251#323—861no—
252#323—861no—
253#323—861no—
254#323—861no—
255C43#875611yescharacteristic, complemented, Sylow
256C25—431no—
257C23×C4—431no—
258C23×C4—861no—
259C23×C4—861no—
260C23×C4C22×D4311yescharacteristic
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—861no—
264C2×M16—861no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—861no—
267C2×C4⋊C4—861no—
268C2×C4⋊C4—861no—
269C2×C22⋊C4—431no—
270C2×C22⋊C4—431no—
271C2×C22⋊C4—431no—
272C2×C22⋊C4—431no—
273C2×C22⋊C4—431no—
274C2×C22⋊C4—431no—
275C2×C22⋊C4—861no—
276C2×C22⋊C4—861no—
277C2×C22⋊C4—861no—
278C2×C22⋊C4—861no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C22⋊C4—1722no—
282C2×C22⋊C4—1722no—
283C2×C22⋊C4C4×D4311yescharacteristic
284C2×C22⋊C4C4×D4311yescharacteristic
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—861no—
290C22⋊C8—861no—
291C22⋊C8—861no—
292C22⋊C8—861no—
293#95—21no—
294#95—861no—
295#95—861no—
296#95—861no—
297C24—431no—
298C24—431no—
299C24—862no—
300C24—862no—
301C24—861no—
302C24—861no—
303C24—3441no—
304C24—3441no—
305C24C2×C4×D4311yescharacteristic
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—81no—
309C22×C4—431no—
310C22×C4—431no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—3441no—
316C22×C4—3441no—
317C22×C4—3441no—
318C22×C4—3441no—
319C22×C4—3441no—
320C22×C4—1722no—
321C22×C4—1722no—
322C22×C4#1062189811yescharacteristic
323C22×C4#1062189811yescharacteristic
324C22×C4D4×D4311yescharacteristic
325C22×C4D4×D4311yescharacteristic
326C22×C4#1062190011yescharacteristic
327C22×C4#1062190211yescharacteristic
328M16—81no—
329M16—81no—
330M16—3441no—
331M16—3441no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—1721no—
335C2×C8—1721no—
336C4⋊C4—81no—
337C4⋊C4—3441no—
338C4⋊C4—3441no—
339C4⋊C4—3441no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—861no—
343C22⋊C4—861no—
344C22⋊C4—861no—
345C22⋊C4—861no—
346C22⋊C4—861no—
347C22⋊C4—861no—
348C22⋊C4—861no—
349C22⋊C4—861no—
350C22⋊C4—1722no—
351C22⋊C4—1722no—
352C22⋊C4—1721no—
353C22⋊C4—1721no—
354C23—21no—
355C23—21no—
356C23—41no—
357C23—41no—
358C23—432no—
359C23—432no—
360C23—864no—
361C23—864no—
362C23—861no—
363C23—861no—
364C23—861no—
365C23—861no—
366C23—3441no—
367C23—3441no—
368C23—3441no—
369C23—3441no—
370C23—3444no—
371C23—3444no—
372C23—1721no—
373C23—1721no—
374C23—1721no—
375C23—1721no—
376C23C22⋊C4×D4311yescharacteristic
377C23#1306328211yescharacteristic
378C23#1306328311yescharacteristic
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—861no—
392C2×C4—861no—
393C2×C4—3444no—
394C2×C4—3444no—
395C2×C4—3441no—
396C2×C4—3441no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4#1306330711yescharacteristic
406C2×C4#1306330711yescharacteristic
407C2×C4#1306331011yescharacteristic
408C2×C4#1306331011yescharacteristic
409C8—81no—
410C8—81no—
411C8—3441no—
412C8—3441no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22—862no—
424C22—862no—
425C22—3444no—
426C22—3444no—
427C22—1722no—
428C22—1722no—
429C22—1722no—
430C22—1722no—
431C22—1721no—
432C22—1721no—
433C22—1721no—
434C22—1721no—
435C22#1458276111yescharacteristic
436C22#100×D4311yescharacteristic
437C22#101×D4311yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—81no—
443C4—81no—
444C4—3441no—
445C4—3441no—
446C4—1721no—
447C4—1721no—
448C2—21no—
449C2—21no—
450C2—41no—
451C2—41no—
452C2—1722no—
453C2—1722no—
454C2#1913467411yescharacteristic
455C2#1913470211yescharacteristic
456C2#1913470511yescharacteristic
subgroupG/H
centerC22#14582761
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1305C2
socleC22×C43#381
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1305D43
hypocenterC43#8756
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
4. #19132502C2semidirect
5. #19132501C2semidirect
6. #19132500C2semidirect
7. C43×#1305C2semidirect
226. #1305D43semidirect
255. C43#8756semidirect

Maximal subgroups

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

subgroupindex
#191372082
#191329212
#191325022
#191325012
#191325002
C43×#13052
#875643