Finite Group Databasebeta

← #24997157

Subgroups — #24997157

Order 11008.

804 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14583057C211yesmaximal, characteristic
2C2×#14583054C211yesmaximal, characteristic
3#19140711C211yesmaximal, characteristic
4C2×#14582635C211yesmaximal, characteristic
5#19132865C211yesmaximal, characteristic
6#19132437C211yesmaximal, characteristic
7C2×C43×#328C211yesmaximal, characteristic
8C23×Dic86C2211yescharacteristic
9C22×Dic172—21no—
10C22×#10621885—21no—
11C2×#13063304C2211yescharacteristic
12#14583057—22no—
13#14583057—22no—
14#14583054—22no—
15#14583054—22no—
16C2×#13063250—21no—
17C2×#13063248—21no—
18C2×C22⋊(C43⋊C8)C2211yescharacteristic
19#14582830—21no—
20#14582829—21no—
21#14582819—21no—
22#14582818—21no—
23#14582757—22no—
24C2×C43⋊#95—22no—
25C2×C43⋊#95C2211yescharacteristic
26#14582635—22no—
27C2×C22⋊Q8×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×#95×C43C2211yescharacteristic
30C43×#328—22no—
31C22×Dic86—21no—
32C22×Dic86—21no—
33C22×Dic86—21no—
34C22×Dic86—21no—
35C22×Dic86—21no—
36C22×Dic86—44no—
37C22×Dic86D412yes—
38C22×Dic86D411yescharacteristic
39C23×Dic43—21no—
40C23×Dic43D412yes—
41C2×Dic172—24no—
42C2×Dic172—44no—
43C2×#10621885—24no—
44C2×#10621885—44no—
45C22×C43⋊C8—21no—
46#13063304—21no—
47#13063304—21no—
48#13063304—21no—
49#13063304—21no—
50C2×C4⋊Dic43D411yescharacteristic
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—22no—
53C2×Dic43⋊C4—22no—
54C2×C22⋊Dic43—21no—
55#13063250—24no—
56#13063248—24no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)D412yes—
59C43⋊#95—22no—
60C43⋊#95—22no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—44no—
64C22×Q8×C43D411yescharacteristic
65C23×C4×C43—21no—
66C23×C4×C43C2311yescharacteristic
67C22×C8×C43—21no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43—21no—
71C22⋊Q8×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43D412yes—
77#95×C43—21no—
78#95×C43—21no—
79C24×C43C2×D411yescharacteristic
80C2×Q8×C43—21no—
81C2×Q8×C43—21no—
82C2×Q8×C43—42no—
83C22×C4×C43—22no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—42no—
87C22×C4×C43—41no—
88C22×C4×C43—42no—
89C22×C4×C43—41no—
90C22×C4×C43—42no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C22×Dic43—24no—
98C22×Dic43—22no—
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—22no—
102C22×Dic43—22no—
103C22×Dic43—42no—
104C22×Dic43—42no—
105C22×Dic43—42no—
106C22×Dic43—41no—
107C22×Dic43—41no—
108C22×Dic43Q1614yescomplemented
109C2×Dic86—24no—
110C2×Dic86—24no—
111C2×Dic86—22no—
112C2×Dic86—22no—
113C2×Dic86—21no—
114C2×Dic86—21no—
115C2×Dic86—44no—
116C2×Dic86—44no—
117C2×Dic86—44no—
118C2×Dic86—44no—
119C2×Dic86—42no—
120C2×Dic86—42no—
121C2×Dic86—41no—
122C2×Dic86—41no—
123C2×Dic86—42no—
124C2×C8×C43—22no—
125C2×C8×C43—42no—
126C4⋊C4×C43—21no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43—41no—
129C4⋊C4×C43—41no—
130C22⋊C4×C43—41no—
131C22⋊C4×C43—41no—
132C22⋊Dic43—41no—
133C22⋊Dic43—41no—
134#10621885—48no—
135C4⋊Dic43—21no—
136C4⋊Dic43—21no—
137Dic43⋊C4—41no—
138Dic43⋊C4—41no—
139Dic43⋊C4—82no—
140Dic43⋊C4—82no—
141C2×C43⋊C8—22no—
142C2×C43⋊C8—42no—
143Dic172—48no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—22no—
147C23×C43#12011yescharacteristic
148C23×C43#12111yescharacteristic
149C23×C43#12711yescharacteristic
150C23×C43C2×Q1612yes—
151C23×C43#13712yes—
152Q8×C43—42no—
153Q8×C43—81no—
154C2×C4×C43—22no—
155C2×C4×C43—22no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—44no—
161C2×C4×C43—42no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—42no—
167C2×C4×C43—82no—
168C2×C4×C43—81no—
169C2×C4×C43—81no—
170C2×C4×C43#12011yescharacteristic
171C2×C4×C43#12011yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12111yescharacteristic
174C2×Dic43—24no—
175C2×Dic43—24no—
176C2×Dic43—42no—
177C2×Dic43—44no—
178C2×Dic43—42no—
179C2×Dic43—42no—
180C2×Dic43—42no—
181C2×Dic43—44no—
182C2×Dic43—44no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—42no—
188C2×Dic43—82no—
189Dic86—24no—
190Dic86—24no—
191Dic86—42no—
192Dic86—42no—
193Dic86—44no—
194Dic86—44no—
195Dic86—42no—
196Dic86—81no—
197C8×C43—42no—
198C43⋊C8—42no—
199#9967—431nomaximal, Sylow
200C22×C43—22no—
201C22×C43—22no—
202C22×C43—22no—
203C22×C43—22no—
204C22×C43—21no—
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—21no—
208C22×C43#39211yescharacteristic
209C22×C43#45112yes—
210C22×C43#45511yescharacteristic
211C22×C43#45611yescharacteristic
212C22×C43B(4,𝔽2)12yes—
213C22×C43#46212yes—
214C22×C43#49411yescharacteristic
215C22×C43#49711yescharacteristic
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—21no—
220C4×C43—82no—
221C4×C43—81no—
222C4×C43—81no—
223Dic43—44no—
224Dic43—44no—
225Dic43—81no—
226Dic43—81no—
227C2×#451—431no—
228C2×#451—431no—
229#2659—431no—
230C2×#328—431no—
231C2×#328D4311yescharacteristic
232#1446—431no—
233#1280—431no—
234C2×C43—21no—
235C2×C43—22no—
236C2×C43—21no—
237C2×C43#160212yes—
238C2×C43#160512yes—
239C2×C43#200711yescharacteristic
240C2×C43#201611yescharacteristic
241C2×C43#202111yescharacteristic
242C23×Q8—431no—
243C22×Q16—861no—
244C22×Q16—861no—
245C2×C22⋊Q8—431no—
246C2×C22⋊Q8C2×D4311yescharacteristic
247#451—862no—
248#451—862no—
249#451—862no—
250#451—862no—
251C2×#103—861no—
252C2×#103—861no—
253C2×C22⋊C8—431no—
254C2×C22⋊C8C2×D4311yescharacteristic
255#398—861no—
256#398—861no—
257#395—861no—
258#395—861no—
259#380—862no—
260C2×#95—431no—
261C2×#95—862no—
262C2×#95C2×D4311yescharacteristic
263#328—22no—
264#328—862no—
265C43#996711yescharacteristic, complemented, Sylow
266C22×Q8—431no—
267C22×Q8—432no—
268C22×Q8—861no—
269C22×Q8—861no—
270C22×Q8—861no—
271C22×Q8—861no—
272C22×Q8—861no—
273C22×Q8—1724no—
274C22×Q8D17211yescharacteristic
275C23×C4—21no—
276C23×C4—432no—
277C23×C4—861no—
278C23×C4C22×D4311yescharacteristic
279C2×Q16—864no—
280C2×Q16—864no—
281C2×Q16—1724no—
282C2×Q16—1724no—
283C22×C8—21no—
284C22×C8—861no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—861no—
290C22⋊Q8—861no—
291C22⋊Q8—861no—
292C22⋊Q8—861no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—431no—
295C2×C4⋊C4—862no—
296C2×C4⋊C4—862no—
297C2×C4⋊C4—861no—
298C2×C4⋊C4D17211yescharacteristic
299C2×C22⋊C4—21no—
300C2×C22⋊C4—861no—
301#103—864no—
302#103—864no—
303C22⋊C8—21no—
304C22⋊C8—432no—
305C22⋊C8—861no—
306C22⋊C8C22⋊D4312yes—
307#95—21no—
308#95—21no—
309#95—862no—
310#95—862no—
311#95—861no—
312#95—861no—
313#95—1724no—
314C24D4×D4311yescharacteristic
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—42no—
318C2×Q8—864no—
319C2×Q8—864no—
320C2×Q8—862no—
321C2×Q8—861no—
322C2×Q8—862no—
323C2×Q8—861no—
324C2×Q8—1722no—
325C2×Q8—1722no—
326C2×Q8—1722no—
327C2×Q8—1724no—
328C2×Q8—1724no—
329C2×Q8—1724no—
330C2×Q8—1724no—
331C2×Q8—1721no—
332C2×Q8—1721no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—42no—
341C22×C4—434no—
342C22×C4—862no—
343C22×C4—864no—
344C22×C4—862no—
345C22×C4—862no—
346C22×C4—861no—
347C22×C4—861no—
348C22×C4—1722no—
349C22×C4—1722no—
350C22×C4—1722no—
351C22×C4—1721no—
352C22×C4—1721no—
353C22×C4C2×D17211yescharacteristic
354C22×C4#1062189811yescharacteristic
355C22×C4D4×D4311yescharacteristic
356C22×C4D4×D4311yescharacteristic
357C22×C4D4×D4311yescharacteristic
358C22×C4C2×C22⋊D4311yescharacteristic
359Q16—1728no—
360Q16—1728no—
361C2×C8—22no—
362C2×C8—42no—
363C2×C8—862no—
364C2×C8—1722no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—861no—
370C4⋊C4—861no—
371C4⋊C4—3442no—
372C4⋊C4—3442no—
373C4⋊C4—1721no—
374C4⋊C4—1721no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—1721no—
378C22⋊C4—1721no—
379C23—21no—
380C23—21no—
381C23—22no—
382C23#1306329511yescharacteristic
383C23#1306329811yescharacteristic
384C23#1306332111yescharacteristic
385C23Q16×D4312yes—
386C23#1306335412yes—
387Q8—42no—
388Q8—81no—
389Q8—864no—
390Q8—864no—
391Q8—3441no—
392Q8—1722no—
393Q8—1722no—
394Q8—1722no—
395Q8—1724no—
396Q8—1724no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—44no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—82no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—864no—
414C2×C4—864no—
415C2×C4—3442no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4—1721no—
419C2×C4—1721no—
420C2×C4—1722no—
421C2×C4—1724no—
422C2×C4—1722no—
423C2×C4—1722no—
424C2×C4—1722no—
425C2×C4—1722no—
426C2×C4—1724no—
427C2×C4—1724no—
428C2×C4#1306329311yescharacteristic
429C2×C4#1306329511yescharacteristic
430C2×C4#1306329811yescharacteristic
431C2×C4#1306329911yescharacteristic
432C8—42no—
433C8—1722no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22#1458280811yescharacteristic
443C22#1458305612yes—
444C22#1458307811yescharacteristic
445C22#1458308311yescharacteristic
446C22#1458308712yes—
447C22#1458310812yes—
448C22#1458327711yescharacteristic
449C22#1458329011yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—82no—
455C4—81no—
456C4—81no—
457C4—3441no—
458C4—3441no—
459C4—1724no—
460C4—1724no—
461C2—21no—
462C2—22no—
463C2—21no—
464C2#1913355312yes—
465C2#1913357012yes—
466C2#1913564311yescharacteristic
467C2#1913569611yescharacteristic
468C2#1913572011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#328C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenterC2×#328D43
hypocenterC43#9967
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
108. C22×Dic43Q16semidirect
265. C43#9967semidirect

Maximal subgroups

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

subgroupindex
C2×#145830572
C2×#145830542
#191407112
C2×#145826352
#191328652
#191324372
C2×C43×#3282
#996743