Finite Group Databasebeta

← #24997094

Subgroups — #24997094

Order 11008.

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

normal subgroups only

This group has 744 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#19145367C211yesmaximal, characteristic
2C2×#14583055C211yesmaximal, characteristic
3#19135580C211yesmaximal, characteristic
4#19134530C211yesmaximal, characteristic
5#19133167C211yesmaximal, characteristic
6#19132443C211yesmaximal, characteristic
7C43×#2434C211yesmaximal, characteristic
8C22×#10621885—21no—
9C2×#13063304C2211yescharacteristic
10#14583234—21no—
11#14583232—21no—
12#14583138—22no—
13#14583055—22no—
14#14583055—22no—
15#14583055—21no—
16#14583054—21no—
17C2×#13063249—21no—
18C2×#13063249—22no—
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20C2×C22⋊(C43⋊C8)C2211yescharacteristic
21#14582759C2211yescharacteristic
22#14582665—22no—
23#14582636—22no—
24C23×Q8×C43C2211yescharacteristic
25C2×C4⋊Q8×C43—21no—
26C2×C22⋊Q8×C43C2211yescharacteristic
27C43×#395—22no—
28C43×#391—21no—
29C43×#385—22no—
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C2×#10621885—24no—
33C2×#10621885—22no—
34C2×#10621885—44no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8D412yes—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40#13063304—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43D411yescharacteristic
43C2×Dic43⋊C4—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46#13063258—22no—
47#13063249—24no—
48#13063249—22no—
49#13063249—44no—
50#13063248—22no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)D412yes—
55C43⋊#95—21no—
56C22×Q8×C43—21no—
57C22×Q8×C43—21no—
58C22×Q8×C43—21no—
59C22×Q8×C43—21no—
60C22×Q8×C43—21no—
61C22×Q8×C43—44no—
62C22×Q8×C43D411yescharacteristic
63C22×Q8×C43D412yes—
64C23×C4×C43—21no—
65C23×C4×C43C2311yescharacteristic
66C4⋊Q8×C43—44no—
67C22⋊Q8×C43—21no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43—21no—
71C2×C4⋊C4×C43—24no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43D412yes—
76C2×C42×C43—21no—
77#95×C43—24no—
78#95×C43—21no—
79C24×C43C2×D411yescharacteristic
80C2×Q8×C43—24no—
81C2×Q8×C43—24no—
82C2×Q8×C43—24no—
83C2×Q8×C43—22no—
84C2×Q8×C43—21no—
85C2×Q8×C43—22no—
86C2×Q8×C43—21no—
87C2×Q8×C43—44no—
88C2×Q8×C43—42no—
89C2×Q8×C43—42no—
90C2×Q8×C43—42no—
91C2×Q8×C43—42no—
92C2×Q8×C43—44no—
93C2×Q8×C43—44no—
94C2×Q8×C43—41no—
95C2×Q8×C43—41no—
96C22×C4×C43—22no—
97C22×C4×C43—22no—
98C22×C4×C43—21no—
99C22×C4×C43—21no—
100C22×C4×C43—42no—
101C22×C4×C43—44no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×Dic43—21no—
111C22×Dic43—21no—
112C22×Dic43—41no—
113C2×Dic86—21no—
114C2×Dic86—21no—
115C2×Dic86—42no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43—48no—
119C4⋊C4×C43—41no—
120C4⋊C4×C43—41no—
121C22⋊C4×C43—22no—
122C22⋊C4×C43—41no—
123C22⋊C4×C43—41no—
124C22⋊C4×C43Q1614yescomplemented
125C42×C43—42no—
126C22⋊Dic43—41no—
127C22⋊Dic43—41no—
128C22⋊Dic43—42no—
129#10621885—48no—
130#10621885—82no—
131C4⋊Dic43—21no—
132C4⋊Dic43—21no—
133C4⋊Dic43—42no—
134Dic43⋊C4—41no—
135Dic43⋊C4—41no—
136C2×C43⋊C8—22no—
137C2×C43⋊C8—22no—
138C2×C43⋊C8—42no—
139C2×C43⋊C8—42no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43#12011yescharacteristic
143C23×C43#12111yescharacteristic
144C23×C43#12711yescharacteristic
145C23×C43C2×Q1612yes—
146C23×C43#13712yes—
147Q8×C43—24no—
148Q8×C43—24no—
149Q8×C43—42no—
150Q8×C43—42no—
151Q8×C43—44no—
152Q8×C43—44no—
153Q8×C43—42no—
154Q8×C43—81no—
155C2×C4×C43—22no—
156C2×C4×C43—22no—
157C2×C4×C43—22no—
158C2×C4×C43—24no—
159C2×C4×C43—24no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—42no—
164C2×C4×C43—42no—
165C2×C4×C43—42no—
166C2×C4×C43—44no—
167C2×C4×C43—44no—
168C2×C4×C43—42no—
169C2×C4×C43—42no—
170C2×C4×C43—42no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43#12011yescharacteristic
174C2×C4×C43#12011yescharacteristic
175C2×C4×C43#12111yescharacteristic
176C2×C4×C43#12111yescharacteristic
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—81no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182C2×Dic43—81no—
183C2×Dic43—81no—
184Dic86—42no—
185Dic86—42no—
186C43⋊C8—42no—
187C43⋊C8—42no—
188#9957—431nomaximal, Sylow
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—42no—
196C22×C43—42no—
197C22×C43#39211yescharacteristic
198C22×C43#45112yes—
199C22×C43#46212yes—
200C22×C43#49411yescharacteristic
201C22×C43#49711yescharacteristic
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—44no—
206C4×C43—44no—
207C4×C43—81no—
208C4×C43—81no—
209C4×C43B(4,𝔽2)12yes—
210Dic43—81no—
211Dic43—81no—
212Dic43—161no—
213#3189—431no—
214C2×#451—431no—
215#2434D4311yescharacteristic
216#1996—431no—
217#1787—431no—
218#1520—431no—
219#1282—431no—
220C2×C43—21no—
221C2×C43—22no—
222C2×C43—22no—
223C2×C43—21no—
224C2×C43#200911yescharacteristic
225C2×C43#201611yescharacteristic
226C2×C43#202111yescharacteristic
227C23×Q8C2×D4311yescharacteristic
228C22×Q16—861no—
229C2×C4⋊Q8—21no—
230C2×C22⋊Q8—431no—
231C2×C22⋊Q8C2×D4311yescharacteristic
232#484—861no—
233#484—861no—
234#467—862no—
235#451—862no—
236#451—861no—
237#451—861no—
238#451—862no—
239C2×#103—861no—
240C2×#103—862no—
241C2×C22⋊C8—431no—
242C2×C22⋊C8—431no—
243#395—22no—
244#391—21no—
245#385—22no—
246#380—431no—
247C4×C22⋊C4C2×D4311yescharacteristic
248#342—862no—
249#328—862no—
250C43#995711yescharacteristic, complemented, Sylow
251C22×Q8—21no—
252C22×Q8—21no—
253C22×Q8—21no—
254C22×Q8—21no—
255C22×Q8—21no—
256C22×Q8—44no—
257C22×Q8—431no—
258C22×Q8C22⋊D4311yescharacteristic
259C22×Q8C22⋊D4312yes—
260C23×C4—21no—
261C23×C4C22×D4311yescharacteristic
262C2×Q16—862no—
263C2×Q16—864no—
264C2×Q16—1724no—
265C22×C8—432no—
266C22×C8—861no—
267C4⋊Q8—44no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—861no—
273C22⋊Q8—861no—
274C22⋊Q8—861no—
275C22⋊Q8—861no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—431no—
279C2×C4⋊C4—861no—
280C2×C4⋊C4—861no—
281C2×C4⋊C4C22⋊D4311yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—861no—
284C2×C22⋊C4—861no—
285C2×C22⋊C4C22⋊D4312yes—
286C2×C42—21no—
287#107—862no—
288#103—862no—
289#103—864no—
290#103—862no—
291#103—1724no—
292C22⋊C8—432no—
293C22⋊C8—861no—
294C22⋊C8—861no—
295C22⋊C8—861no—
296#95—24no—
297#95—21no—
298#95—861no—
299C24C2×C22⋊D4311yescharacteristic
300C2×Q8—24no—
301C2×Q8—24no—
302C2×Q8—24no—
303C2×Q8—22no—
304C2×Q8—21no—
305C2×Q8—22no—
306C2×Q8—21no—
307C2×Q8—44no—
308C2×Q8—42no—
309C2×Q8—42no—
310C2×Q8—42no—
311C2×Q8—42no—
312C2×Q8—44no—
313C2×Q8—44no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—861no—
317C2×Q8—861no—
318C2×Q8—1722no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—42no—
324C22×C4—44no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—1721no—
330C22×C4D4×D4311yescharacteristic
331C22×C4D4×D4311yescharacteristic
332C22×C4D4×D4311yescharacteristic
333C22×C4#1062190011yescharacteristic
334C22×C4C2×C22⋊D4311yescharacteristic
335C22×C4C2×C22⋊D4311yescharacteristic
336Q16—3442no—
337Q16—1728no—
338C2×C8—862no—
339C2×C8—862no—
340C2×C8—1722no—
341C2×C8—1722no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—48no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—861no—
348C4⋊C4—861no—
349C4⋊C4—1722no—
350C4⋊C4—1721no—
351C4⋊C4—1721no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—1722no—
356C22⋊C4—1721no—
357C22⋊C4—1721no—
358C22⋊C4#1062188514yescomplemented
359C42—42no—
360C23—41no—
361C23—41no—
362C23#1306329411yescharacteristic
363C23#1306329611yescharacteristic
364C23#1306332111yescharacteristic
365C23C2×#1062188512yes—
366C23#1306335612yes—
367Q8—24no—
368Q8—24no—
369Q8—42no—
370Q8—42no—
371Q8—44no—
372Q8—44no—
373Q8—42no—
374Q8—81no—
375Q8—1722no—
376Q8—1722no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—3441no—
396C2×C4—3441no—
397C2×C4—3441no—
398C2×C4—3441no—
399C2×C4—3441no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4#1306329311yescharacteristic
403C2×C4#1306329311yescharacteristic
404C2×C4#1306329711yescharacteristic
405C2×C4#1306329711yescharacteristic
406C8—1722no—
407C8—1722no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—42no—
415C22—42no—
416C22#1458280711yescharacteristic
417C22#1458305512yes—
418C22#1458310612yes—
419C22#1458327811yescharacteristic
420C22#1458329111yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—44no—
425C4—44no—
426C4—81no—
427C4—81no—
428C4—3441no—
429C4—3441no—
430C4—6881no—
431C4#1458308512yes—
432C2—22no—
433C2—21no—
434C2—22no—
435C2—21no—
436C2#1913565511yescharacteristic
437C2#1913569511yescharacteristic
438C2#1913571811yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2434C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#2434D43
hypocenterC43#9957
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2434

Complements

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

NH ≅ G/Ntype
124. C22⋊C4×C43Q16semidirect
250. C43#9957semidirect
358. C22⋊C4#10621885semidirect

Maximal subgroups

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

subgroupindex
#191453672
C2×#145830552
#191355802
#191345302
#191331672
#191324432
C43×#24342
#995743