Finite Group Databasebeta

← #25015273

Subgroups — #25015273

Order 11008.

492 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 91 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#19139797C211yesmaximal, characteristic
2#19134581C211yesmaximal, characteristic
3#99×Dic43C211yesmaximal, characteristic
4#19132720C211yesmaximal, characteristic
5#19132719C211yesmaximal, characteristic
6#19132719C211yesmaximal, characteristic
7C43×#1393C211yesmaximal, characteristic
8C2×#13063316C411yescharacteristic, complemented
9C2×D4×Dic43C2211yescharacteristic
10C2×#13063240C2211yescharacteristic
11C2×#13063240C2211yescharacteristic
12#14582822—21no—
13#14582822—21no—
14#14582802C2211yescharacteristic
15#14582774—21no—
16#14582774—21no—
17#14582769C411yescharacteristic, complemented
18#14582764C411yescharacteristic, complemented
19#14582757—21no—
20C4×Dic43⋊C4C411yescharacteristic, complemented
21C22⋊C4×Dic43—21no—
22#14582665—21no—
23#14582665—21no—
24C2×#99×C43C2211yescharacteristic
25C2×#99×C43C2211yescharacteristic
26C43×#390C2211yescharacteristic
27C23×Dic43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29#13063316—41no—
30#13063316—41no—
31D4×Dic43—41no—
32D4×Dic43—41no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—41no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43D411yescharacteristic
46C2×C22⋊Dic43D411yescharacteristic
47C2×C4×Dic43—41no—
48C2×C4×Dic43C2×C411yescharacteristic
49C2×C4×Dic43C2×C411yescharacteristic
50#13063240—21no—
51#13063240—21no—
52#13063240—21no—
53#13063240Q812yes—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—41no—
58C43⋊#95—41no—
59C22×D4×C43C2311yescharacteristic
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—21no—
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43—21no—
65C2×C42×C43C2×C411yescharacteristic
66#99×C43—21no—
67#99×C43—21no—
68#99×C43—21no—
69#99×C43Q812yes—
70C24×C43C2×D411yescharacteristic
71C24×C43C2×D411yescharacteristic
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43C2×Q811yescharacteristic
75C2×D4×C43C2×Q811yescharacteristic
76C2×D4×C43#4111yescharacteristic
77C2×D4×C43#4111yescharacteristic
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43C22×C411yescharacteristic
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—41no—
90C22×Dic43—41no—
91C22×Dic43—81no—
92C22×Dic43—81no—
93C22×Dic43C22⋊C411yescharacteristic
94C22×Dic43C22⋊C411yescharacteristic
95C22×Dic43C22⋊C411yescharacteristic
96C22×Dic43C22⋊C411yescharacteristic
97C4⋊C4×C43—41no—
98C22⋊C4×C43—22no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—41no—
101C22⋊C4×C43—42no—
102C22⋊C4×C43—42no—
103C22⋊C4×C43—41no—
104C42×C43—41no—
105C22⋊Dic43—22no—
106C22⋊Dic43—41no—
107C22⋊Dic43—41no—
108C22⋊Dic43—41no—
109C22⋊Dic43—41no—
110C22⋊Dic43—41no—
111C22⋊Dic43—81no—
112C22⋊Dic43—81no—
113C4⋊Dic43—41no—
114C4⋊Dic43—41no—
115C4⋊Dic43—41no—
116C4⋊Dic43—41no—
117C4⋊Dic43—81no—
118C4⋊Dic43—81no—
119Dic43⋊C4—42no—
120Dic43⋊C4—42no—
121Dic43⋊C4—82no—
122C4×Dic43—21no—
123C4×Dic43—21no—
124C4×Dic43—41no—
125C4×Dic43—82no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43—21no—
129C23×C43—21no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43C2×C22⋊C411yescharacteristic
135C23×C43C22⋊Q811yescharacteristic
136C23×C43C22⋊Q811yescharacteristic
137C23×C43#12411yescharacteristic
138C23×C43C4⋊Q811yescharacteristic
139D4×C43—41no—
140D4×C43—41no—
141D4×C43—41no—
142D4×C43—41no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—22no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—81no—
153C2×C4×C43—81no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43—81no—
157C2×C4×C43C4×Q811yescharacteristic
158C2×C4×C43C4×Q811yescharacteristic
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—41no—
163C2×Dic43—42no—
164C2×Dic43—42no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—42no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—81no—
176C2×Dic43—81no—
177C2×Dic43—81no—
178C2×Dic43—81no—
179C2×Dic43—81no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182C2×Dic43#9911yescharacteristic
183C2×Dic43#9911yescharacteristic
184#13300—431nomaximal, Sylow
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—41no—
194C22×C43—41no—
195C22×C43—41no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43—41no—
199C22×C43—81no—
200C22×C43—81no—
201C22×C43#39111yescharacteristic
202C22×C43C2×#9911yescharacteristic
203C22×C43#41011yescharacteristic
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—42no—
207C4×C43—82no—
208C4×C43—81no—
209C4×C43—161no—
210Dic43—21no—
211Dic43—21no—
212Dic43—41no—
213Dic43—41no—
214Dic43—41no—
215Dic43—81no—
216Dic43—82no—
217Dic43—81no—
218Dic43—161no—
219#2566—431no—
220#1799—431no—
221C4×#99—431no—
222#1393—431no—
223#1393—431no—
224#1393—431no—
225#1393D4311yescharacteristic
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—41no—
229C2×C43—41no—
230C2×C43—41no—
231C2×C43—41no—
232C2×C43#199611yescharacteristic
233C2×C43#212611yescharacteristic
234C2×C43#212711yescharacteristic
235C2×#125—431no—
236C2×C4×D4—431no—
237C2×#99—431no—
238C2×#99—431no—
239C2×#99C2×D4311yescharacteristic
240C2×#99C2×D4311yescharacteristic
241#396—861no—
242#396—861no—
243#390—431no—
244#390C2×D4311yescharacteristic
245#385—861no—
246#385—861no—
247#384—431no—
248#382—431no—
249#380—861no—
250C4×C4⋊C4—431no—
251C4×C22⋊C4—861no—
252#342—861no—
253#342—861no—
254C43#1330011yescharacteristic, complemented, Sylow
255C22×D4C22×D4311yescharacteristic
256C23×C4—431no—
257C23×C4—431no—
258#125—1721no—
259#125—1721no—
260C4×D4—1721no—
261C4×D4—1721no—
262C2×C4⋊C4—431no—
263C2×C4⋊C4—431no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4—861no—
266C2×C4⋊C4—861no—
267C2×C4⋊C4—861no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—1721no—
270C2×C4⋊C4C4×D4311yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—431no—
276C2×C22⋊C4—431no—
277C2×C22⋊C4—861no—
278C2×C22⋊C4—861no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C42—431no—
282C2×C42—431no—
283C2×C42—1721no—
284C2×C42C4×D4311yescharacteristic
285#99—21no—
286#99—21no—
287#99—21no—
288#99—432no—
289#99—861no—
290#99—861no—
291#99—861no—
292#99Dic8612yes—
293#95—861no—
294#95—861no—
295#95—861no—
296#95—1721no—
297#95—1721no—
298C24D4×D4311yescharacteristic
299C24D4×D4311yescharacteristic
300C2×D4—41no—
301C2×D4—41no—
302C2×D4C2×Dic8611yescharacteristic
303C2×D4#1062189811yescharacteristic
304C2×D4#1062190011yescharacteristic
305C2×D4Q8×D4311yescharacteristic
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—431no—
311C22×C4—431no—
312C22×C4—431no—
313C22×C4—431no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—3441no—
321C22×C4—3441no—
322C22×C4—1721no—
323C22×C4—1721no—
324C22×C4C2×C4×D4311yescharacteristic
325C4⋊C4—41no—
326C4⋊C4—3441no—
327C4⋊C4—3441no—
328C4⋊C4—3442no—
329C4⋊C4—1721no—
330C4⋊C4—1721no—
331C4⋊C4—1722no—
332C4⋊C4—1721no—
333C4⋊C4—1721no—
334C4⋊C4—1722no—
335C22⋊C4—22no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—862no—
342C22⋊C4—3441no—
343C22⋊C4—3441no—
344C22⋊C4—1721no—
345C22⋊C4—1721no—
346C22⋊C4—1721no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
349C42—41no—
350C42—861no—
351C42—861no—
352C42—3442no—
353C42—1721no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23C22⋊C4×D4311yescharacteristic
363C23#1306330211yescharacteristic
364C23#1306330311yescharacteristic
365C23#1306331111yescharacteristic
366C23#1306332411yescharacteristic
367D4—41no—
368D4—41no—
369D4—41no—
370D4—41no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—431no—
386C2×C4—431no—
387C2×C4—861no—
388C2×C4—861no—
389C2×C4—861no—
390C2×C4—3441no—
391C2×C4—3441no—
392C2×C4—3441no—
393C2×C4—3441no—
394C2×C4—3441no—
395C2×C4—3441no—
396C2×C4—3441no—
397C2×C4—1721no—
398C2×C4—1722no—
399C2×C4—1722no—
400C2×C4—1722no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4#1306329011yescharacteristic
411C2×C4C4×Dic8611yescharacteristic
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—81no—
427C22—81no—
428C22#1458280311yescharacteristic
429C22#99×D4311yescharacteristic
430C22#1458287111yescharacteristic
431C4—21no—
432C4—21no—
433C4—42no—
434C4—82no—
435C4—81no—
436C4—161no—
437C4—861no—
438C4—861no—
439C4—3441no—
440C4—3442no—
441C4—3441no—
442C4—1721no—
443C4—1721no—
444C4—1721no—
445C4—6881no—
446C2—21no—
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—41no—
452C2#1913557811yescharacteristic
453C2#1913625711yescharacteristic
454C2#1913626311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1393C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenter#1393D43
hypocenterC43#13300
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
8. C2×#13063316C4semidirect
17. #14582769C4semidirect
18. #14582764C4semidirect
20. C4×Dic43⋊C4C4semidirect
254. C43#13300semidirect

Maximal subgroups

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

subgroupindex
#191397972
#191345812
#99×Dic432
#191327202
#191327192
C43×#13932
#1330043