Finite Group Databasebeta

← #24994548

Subgroups — #24994548

Order 11008.

682 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 95 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#19143634C211yesmaximal, characteristic
2#19137954C211yesmaximal, characteristic
3#19134519C211yesmaximal, characteristic, complemented
4#19132931C211yesmaximal, characteristic
5#19132502C211yesmaximal, characteristic, complemented
6#19132500C211yesmaximal, characteristic, complemented
7C43×#1784C211yesmaximal, characteristic, complemented
8C2×#13063301—21no—
9C2×C4×C22⋊D43C2211yescharacteristic
10#14582975—22no—
11#14582974—22no—
12#14582949—21no—
13C2×#13063244—22no—
14#14582863C2211yescharacteristic
15#14582863C2211yescharacteristic
16#14582861—21no—
17#14582818—21no—
18#14582810—21no—
19#14582806—21no—
20#14582778C412yes—
21#14582772C412yes—
22#14582759C2211yescharacteristic
23#14582624—21no—
24#14582622—21no—
25C23×Q8×C43C2211yescharacteristic
26C2×#101×C43—22no—
27C43×#407C2211yescharacteristic
28C43×#407C2211yescharacteristic
29C22×C22⋊D43C2×C411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×#10621877—21no—
32C2×#10621877D412yes—
33C2×#10621872—22no—
34#13063301—44no—
35C4×C22⋊D43—21no—
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38C4×C22⋊D43—21no—
39C2×C4⋊Dic43—21no—
40C2×Dic43⋊C4—22no—
41C2×Dic43⋊C4D411yescharacteristic
42C2×C22⋊Dic43C2×C411yescharacteristic
43C2×C22⋊Dic43C2×C412yes—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4D411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47Dic43⋊C8—22no—
48#13063244—44no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53(C2×D43)⋊C8—22no—
54C8×Dic43—22no—
55C43⋊#95—21no—
56C43⋊#95—22no—
57C43⋊#95—22no—
58C22×Q8×C43—21no—
59C22×Q8×C43—21no—
60C22×Q8×C43—21no—
61C22×Q8×C43—21no—
62C22×Q8×C43—21no—
63C22×Q8×C43—21no—
64C22×Q8×C43—44no—
65C23×C4×C43C2×C412yes—
66C23×C4×C43C2311yescharacteristic
67C2×M16×C43—21no—
68C2×M16×C43D412yes—
69#101×C43—44no—
70C22⋊C8×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C24×C43C22×C411yescharacteristic
75C23×D43C22⋊C411yescharacteristic
76C2×Q8×C43—24no—
77C2×Q8×C43—24no—
78C2×Q8×C43—24no—
79C2×Q8×C43—42no—
80C2×Q8×C43—42no—
81C2×Q8×C43—42no—
82C2×Q8×C43—44no—
83C2×Q8×C43—44no—
84C2×Q8×C43—44no—
85C2×Q8×C43—41no—
86C2×Q8×C43—41no—
87C2×Q8×C43—41no—
88C2×Q8×C43—41no—
89C22×C4×C43—22no—
90C22×C4×C43—22no—
91C22×C4×C43—22no—
92C22×C4×C43—44no—
93C22×C4×C43—42no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43#4111yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C2×C22⋊D43—22no—
101C2×C22⋊D43—21no—
102C2×C22⋊D43—21no—
103C2×C22⋊D43—41no—
104C22×Dic43—22no—
105C22×Dic43C22⋊C411yescharacteristic
106C22×Dic43C22⋊C411yescharacteristic
107C22×Dic43C22⋊C411yescharacteristic
108C2×C4×D43—21no—
109C2×C4×D43—21no—
110C2×C4×D43—42no—
111M16×C43—42no—
112M16×C43—42no—
113C2×C8×C43—22no—
114C2×C8×C43—41no—
115C22⋊Dic43—21no—
116C22⋊Dic43—21no—
117C22⋊Dic43—42no—
118(C2×D43)⋊C4—21no—
119(C2×D43)⋊C4—21no—
120(C2×D43)⋊C4—44no—
121C4⋊Dic43—42no—
122Dic43⋊C4—21no—
123Dic43⋊C4—21no—
124Dic43⋊C4—44no—
125C4×Dic43—21no—
126C4×Dic43—21no—
127#10621877—42no—
128#10621877—42no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—41no—
131#10621872—82no—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43C2×C22⋊C411yescharacteristic
137C23×C43C4×D411yescharacteristic
138C23×C43C4×D411yescharacteristic
139C22×D43—21no—
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—41no—
143C22×D43—41no—
144Q8×C43—44no—
145Q8×C43—44no—
146Q8×C43—44no—
147Q8×C43—44no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—24no—
152C2×C4×C43—24no—
153C2×C4×C43—24no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43—42no—
161C2×C4×C43#12011yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12311yescharacteristic
165C22⋊D43—42no—
166C22⋊D43—42no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43#10112yescomplemented
177C4×D43—42no—
178C4×D43—81no—
179C8×C43—42no—
180C8×C43—81no—
181C43⋊C8—42no—
182C43⋊C8—81no—
183#9506—431nomaximal, Sylow
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—42no—
193C22×C43—42no—
194C22×C43#38611yescharacteristic
195C22×C43C2×#10111yescharacteristic
196C22×C43#41311yescharacteristic
197C2×D43—42no—
198C2×D43—41no—
199C2×D43—41no—
200C2×D43—41no—
201C2×D43—81no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—44no—
206C4×C43B(4,𝔽2)12yes—
207Dic43—22no—
208Dic43—41no—
209Dic43—41no—
210Dic43—82no—
211#2975—431no—
212#2409—431no—
213#1784—431no—
214#1784D4311yescharacteristic, complemented
215#1465—431no—
216#1305—431no—
217#1305—431no—
218C2×C43—21no—
219C2×C43—21no—
220C2×C43—41no—
221C2×C43—41no—
222C2×C43#188911yescharacteristic
223C2×C43#190111yescharacteristic
224C2×C43#191511yescharacteristic
225D43—81no—
226C23×Q8C2×D4311yescharacteristic
227C2×C22⋊Q8—861no—
228C2×C4×D4—431no—
229#436—862no—
230#436—862no—
231#431—861no—
232C2×#101—22no—
233C2×#101—862no—
234#407—431no—
235#407—431no—
236#407—861no—
237#407C2×D4311yescharacteristic
238#407C2×D4311yescharacteristic
239#395—861no—
240#393—861no—
241#391—861no—
242#386—432no—
243#385—432no—
244#380—431no—
245#324—861no—
246#323—861no—
247C43#950611yescharacteristic, complemented, Sylow
248C22×Q8—21no—
249C22×Q8—21no—
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8—21no—
253C22×Q8—21no—
254C22×Q8—44no—
255C22×D4—431no—
256C23×C4—431no—
257C23×C4C4×D4312yes—
258C23×C4C22×D4311yescharacteristic
259C2×M16—21no—
260C2×M16—432no—
261C2×M16—862no—
262C2×M16—861no—
263C2×M16C22⋊D4312yes—
264C22⋊Q8—1724no—
265C4×D4—861no—
266C4×D4—861no—
267C4×D4—861no—
268C4×D4—861no—
269C2×C4⋊C4—431no—
270C2×C4⋊C4—862no—
271C2×C4⋊C4—861no—
272C2×C22⋊C4—431no—
273C2×C22⋊C4—431no—
274C2×C22⋊C4—432no—
275C2×C22⋊C4—862no—
276C2×C42—431no—
277C4⋊C8—862no—
278#101—44no—
279#101—1724no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—862no—
285C22⋊C8—861no—
286C22⋊C8—861no—
287C22⋊C8—861no—
288C22⋊C8—861no—
289C4×C8—862no—
290#95—862no—
291#95—862no—
292#95—861no—
293C24—431no—
294C24C2×C4×D4311yescharacteristic
295C2×Q8—24no—
296C2×Q8—24no—
297C2×Q8—24no—
298C2×Q8—42no—
299C2×Q8—42no—
300C2×Q8—42no—
301C2×Q8—44no—
302C2×Q8—44no—
303C2×Q8—44no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×D4—862no—
309C2×D4—861no—
310C2×D4—861no—
311C2×D4—1721no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—42no—
316C22×C4—44no—
317C22×C4—431no—
318C22×C4—431no—
319C22×C4—431no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—862no—
323C22×C4—1722no—
324C22×C4#1062189811yescharacteristic
325C22×C4D4×D4311yescharacteristic
326C22×C4D4×D4311yescharacteristic
327C22×C4D4×D4311yescharacteristic
328C22×C4#1062190011yescharacteristic
329C22×C4C2×C22⋊D4311yescharacteristic
330M16—42no—
331M16—42no—
332M16—3442no—
333M16—1722no—
334M16—1722no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—862no—
338C2×C8—1721no—
339C4⋊C4—861no—
340C4⋊C4—861no—
341C4⋊C4—1724no—
342C4⋊C4—1722no—
343C22⋊C4—861no—
344C22⋊C4—861no—
345C22⋊C4—861no—
346C22⋊C4—861no—
347C22⋊C4—1724no—
348C22⋊C4—1722no—
349C42—861no—
350C42—861no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23—861no—
356C23—861no—
357C23—861no—
358C23—1721no—
359C23—1721no—
360C23C22⋊C4×D4311yescharacteristic
361C23(C22⋊D43)⋊C411yescharacteristic
362C23C4×C22⋊D4311yescharacteristic
363Q8—44no—
364Q8—44no—
365Q8—44no—
366Q8—44no—
367D4—1722no—
368D4—1722no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—432no—
383C2×C4—861no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—3441no—
388C2×C4—1722no—
389C2×C4—1722no—
390C2×C4—1722no—
391C2×C4—1722no—
392C2×C4—1721no—
393C2×C4—1721no—
394C2×C4#1306329311yescharacteristic
395C2×C4#1306329611yescharacteristic
396C2×C4#1306329811yescharacteristic
397C2×C4#1306330711yescharacteristic
398C8—42no—
399C8—81no—
400C8—3441no—
401C8—1722no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—42no—
411C22—42no—
412C22—3441no—
413C22—1722no—
414C22—1721no—
415C22—1721no—
416C22—1721no—
417C22#1458277511yescharacteristic
418C22#101×D4311yescharacteristic
419C22#1458288211yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—44no—
424C4—862no—
425C4—3442no—
426C4—1721no—
427C4—1721no—
428C4#1458308512yes—
429C2—21no—
430C2—21no—
431C2—41no—
432C2—41no—
433C2—3441no—
434C2#1913500011yescharacteristic
435C2#1913506011yescharacteristic
436C2#1913514411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1784C2
socleC22×C43#386
prime radicalC22×C22⋊D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1784D43
hypocenterC43#9506
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

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

NH ≅ G/Ntype
3. #19134519C2semidirect
5. #19132502C2semidirect
6. #19132500C2semidirect
7. C43×#1784C2semidirect
176. C2×Dic43#101semidirect
214. #1784D43semidirect
247. C43#9506semidirect

Maximal subgroups

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

subgroupindex
#191436342
#191379542
#191345192
#191329312
#191325022
#191325002
C43×#17842
#950643