Finite Group Databasebeta

← #24994398

Subgroups — #24994398

Order 11008.

818 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 97 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#19137926C211yesmaximal, characteristic
2#19136950C211yesmaximal, characteristic, complemented
3#19134539C211yesmaximal, characteristic
4#19132924C211yesmaximal, characteristic, complemented
5#19132449C211yesmaximal, characteristic, complemented
6#19132448C211yesmaximal, characteristic, complemented
7C43×#1789C211yesmaximal, characteristic
8C2×#13063306—21no—
9C2×#13063281—21no—
10C22×Dic43⋊C4C2211yescharacteristic
11C2×#13063252—22no—
12#14582863C2211yescharacteristic
13#14582818C412yescomplemented
14#14582813C412yescomplemented
15#14582779—21no—
16#14582772—22no—
17#14582762C2211yescharacteristic
18C4×Dic43⋊C4—22no—
19#14582750—22no—
20C22⋊C4×Dic43—21no—
21C4×C22⋊Dic43C2211yescharacteristic
22#14582624—22no—
23C22×#41×C43C2211yescharacteristic
24C2×#104×C43—22no—
25C43×#407C2211yescharacteristic
26C4×C22⋊C4×C43C2211yescharacteristic
27C23×Dic43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C2×#10621877—21no—
30#13063306—44no—
31#13063281—28no—
32C2×Dic43⋊C4—22no—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—22no—
38C2×Dic43⋊C4C2×C412yes—
39C2×Dic43⋊C4D412yes—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—22no—
43C2×C22⋊Dic43—22no—
44C2×C4×Dic43—22no—
45C2×C4×Dic43—22no—
46C2×C4×Dic43D412yes—
47#13063252—44no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C43⋊#95—22no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—22no—
54C43⋊#95C2×C412yes—
55C2×#41×C43—21no—
56C2×#41×C43—21no—
57C2×#41×C43—21no—
58C2×#41×C43—21no—
59C2×#41×C43—44no—
60C22×Q8×C43C2×C411yescharacteristic
61C22×D4×C43—21no—
62C22×D4×C43C2×C411yescharacteristic
63C23×C4×C43—21no—
64C23×C4×C43C2311yescharacteristic
65C2×M16×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C42×C43D412yes—
68#104×C43—44no—
69C22⋊C8×C43—21no—
70C22⋊C8×C43—21no—
71#95×C43—21no—
72C24×C43—21no—
73C24×C43C2×D411yescharacteristic
74#41×C43—24no—
75#41×C43—24no—
76#41×C43—42no—
77#41×C43—42no—
78#41×C43—42no—
79#41×C43—42no—
80#41×C43—42no—
81#41×C43—42no—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—42no—
85C2×D4×C43—24no—
86C2×D4×C43—21no—
87C2×D4×C43—21no—
88C2×D4×C43—42no—
89C2×D4×C43—42no—
90C2×D4×C43—41no—
91C2×D4×C43—41no—
92C22×C4×C43—21no—
93C22×C4×C43—22no—
94C22×C4×C43—42no—
95C22×C4×C43—42no—
96C22×C4×C43—42no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43C22×C411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×Dic43—24no—
106C22×Dic43—22no—
107C22×Dic43—21no—
108C22×Dic43—22no—
109C22×Dic43—21no—
110C22×Dic43—21no—
111C22×Dic43—21no—
112C22×Dic43—42no—
113C22×Dic43C22⋊C412yes—
114C22×Dic43C22⋊C412yes—
115M16×C43—42no—
116C2×C8×C43—41no—
117C22⋊C4×C43—24no—
118C42×C43—42no—
119C22⋊Dic43—24no—
120C22⋊Dic43—42no—
121C22⋊Dic43—44no—
122C22⋊Dic43—44no—
123Dic43⋊C4—28no—
124Dic43⋊C4—22no—
125Dic43⋊C4—22no—
126Dic43⋊C4—22no—
127Dic43⋊C4—22no—
128Dic43⋊C4—44no—
129C4×Dic43—28no—
130C4×Dic43—42no—
131C4×Dic43—82no—
132#10621877—42no—
133C2×C43⋊C8—41no—
134C23×C43—22no—
135C23×C43—22no—
136C23×C43—22no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—42no—
140C23×C43—41no—
141C23×C43—42no—
142C23×C43C2×C22⋊C411yescharacteristic
143C23×C43#12011yescharacteristic
144C23×C43#12311yescharacteristic
145Q8×C43—22no—
146Q8×C43—22no—
147Q8×C43—41no—
148Q8×C43—41no—
149D4×C43—22no—
150D4×C43—22no—
151D4×C43—41no—
152D4×C43—41no—
153D4×C43—44no—
154D4×C43—44no—
155C2×C4×C43—22no—
156C2×C4×C43—22no—
157C2×C4×C43—24no—
158C2×C4×C43—22no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—44no—
164C2×C4×C43—44no—
165C2×C4×C43—42no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—42no—
169C2×C4×C43C4×D411yescharacteristic
170C2×C4×C43C4×D411yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×Dic43—22no—
174C2×Dic43—22no—
175C2×Dic43—24no—
176C2×Dic43—22no—
177C2×Dic43—22no—
178C2×Dic43—24no—
179C2×Dic43—22no—
180C2×Dic43—42no—
181C2×Dic43—42no—
182C2×Dic43—42no—
183C2×Dic43—42no—
184C2×Dic43—42no—
185C2×Dic43—42no—
186C2×Dic43—42no—
187C2×Dic43—81no—
188C2×Dic43#10414yescomplemented
189C8×C43—81no—
190C43⋊C8—81no—
191#9476—431nomaximal, Sylow
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—44no—
200C22×C43—44no—
201C22×C43—42no—
202C22×C43—82no—
203C22×C43—81no—
204C22×C43—81no—
205C22×C43#38611yescharacteristic
206C22×C43C2×#10412yes—
207C22×C43B(4,𝔽2)12yes—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—44no—
213C4×C43—42no—
214Dic43—24no—
215Dic43—44no—
216Dic43—42no—
217Dic43—82no—
218#2406—431no—
219#2274—431no—
220#1789—431no—
221#1789D4311yescharacteristic
222#1463—431no—
223#1284—431no—
224#1284—431no—
225C2×C43—22no—
226C2×C43—22no—
227C2×C43—41no—
228C2×C43—82no—
229C2×C43#188911yescharacteristic
230C2×C43#189611yescharacteristic
231C2×C43#191211yescharacteristic
232C22×#41C2×D4311yescharacteristic
233C2×#123—861no—
234C2×#117—861no—
235C22×C4⋊C4—431no—
236C2×#104—22no—
237C2×#104—862no—
238#407—431no—
239#407C2×D4311yescharacteristic
240#395—432no—
241#394—432no—
242#386—861no—
243#385—862no—
244#381—431no—
245C4×C4⋊C4—862no—
246C4×C4⋊C4—862no—
247C4×C22⋊C4—431no—
248C4×C22⋊C4—861no—
249C4×C22⋊C4C2×D4311yescharacteristic
250#324—862no—
251C43#947611yescharacteristic, complemented, Sylow
252C2×#41—21no—
253C2×#41—21no—
254C2×#41—21no—
255C2×#41—21no—
256C2×#41—44no—
257C22×Q8C4×D4311yescharacteristic
258C22×D4—21no—
259C22×D4C4×D4311yescharacteristic
260C23×C4—21no—
261C23×C4—431no—
262C23×C4—431no—
263C23×C4C22×D4311yescharacteristic
264C2×M16—21no—
265C2×M16—861no—
266#123—1724no—
267#117—868no—
268C2×C4⋊C4—432no—
269C2×C4⋊C4—432no—
270C2×C4⋊C4—862no—
271C2×C4⋊C4—861no—
272C2×C4⋊C4—861no—
273C2×C4⋊C4—861no—
274C2×C4⋊C4—861no—
275C2×C4⋊C4—862no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—861no—
278C2×C22⋊C4—862no—
279C2×C22⋊C4—862no—
280C2×C22⋊C4—861no—
281C2×C42—432no—
282C2×C42—862no—
283C2×C42—862no—
284C2×C42C22⋊D4312yes—
285#104—44no—
286#104—1724no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—861no—
290C22⋊C8—861no—
291#95—21no—
292#95—432no—
293#95—862no—
294#95—862no—
295#95—861no—
296#95—861no—
297C24—21no—
298C24D4×D4311yescharacteristic
299#41—24no—
300#41—24no—
301#41—42no—
302#41—42no—
303#41—42no—
304#41—42no—
305#41—42no—
306#41—42no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—42no—
310C2×D4—24no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—41no—
316C2×D4—41no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—432no—
325C22×C4—432no—
326C22×C4—864no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—862no—
331C22×C4—861no—
332C22×C4—862no—
333C22×C4—1722no—
334C22×C4C2×C4×D4311yescharacteristic
335C22×C4#1062189811yescharacteristic
336C22×C4D4×D4311yescharacteristic
337C22×C4D4×D4311yescharacteristic
338C22×C4#1062190011yescharacteristic
339C22×C4C2×C22⋊D4311yescharacteristic
340M16—42no—
341M16—1722no—
342C2×C8—41no—
343C2×C8—1721no—
344C4⋊C4—868no—
345C4⋊C4—862no—
346C4⋊C4—862no—
347C4⋊C4—862no—
348C4⋊C4—862no—
349C4⋊C4—1724no—
350C22⋊C4—24no—
351C22⋊C4—864no—
352C22⋊C4—1724no—
353C22⋊C4—1722no—
354C22⋊C4—1724no—
355C42—42no—
356C42—868no—
357C42—3442no—
358C42—1722no—
359C23—22no—
360C23—22no—
361C23—22no—
362C23—41no—
363C23—41no—
364C23—42no—
365C23—42no—
366C23—41no—
367C23C22⋊C4×D4311yescharacteristic
368C23#1306329311yescharacteristic
369C23#1306330711yescharacteristic
370Q8—22no—
371Q8—22no—
372Q8—41no—
373Q8—41no—
374D4—22no—
375D4—22no—
376D4—41no—
377D4—41no—
378D4—44no—
379D4—44no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—434no—
395C2×C4—862no—
396C2×C4—862no—
397C2×C4—864no—
398C2×C4—862no—
399C2×C4—862no—
400C2×C4—864no—
401C2×C4—862no—
402C2×C4—3441no—
403C2×C4—1722no—
404C2×C4—1722no—
405C2×C4—1722no—
406C2×C4—1722no—
407C2×C4—1722no—
408C2×C4—1722no—
409C2×C4—1722no—
410C2×C4(C22⋊D43)⋊C411yescharacteristic
411C2×C4C4×C22⋊D4311yescharacteristic
412C2×C4#1306329611yescharacteristic
413C2×C4#1306329811yescharacteristic
414C8—81no—
415C8—3441no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—44no—
424C22—44no—
425C22—42no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22#1458277511yescharacteristic
430C22#104×D4312yes—
431C22#1458308512yes—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—44no—
437C4—42no—
438C4—864no—
439C4—3442no—
440C4—1724no—
441C4—1722no—
442C2—22no—
443C2—22no—
444C2—41no—
445C2—82no—
446C2#1913500011yescharacteristic
447C2#1913503511yescharacteristic
448C2#1913512911yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1789C2
socleC22×C43#386
prime radicalC22×#41×C43C22
cosocleC23×C4×C43C23
hypercenter#1789D43
hypocenterC43#9476
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #19136950C2semidirect
4. #19132924C2semidirect
5. #19132449C2semidirect
6. #19132448C2semidirect
13. #14582818C4semidirect
14. #14582813C4semidirect
188. C2×Dic43#104semidirect
251. C43#9476semidirect

Maximal subgroups

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

subgroupindex
#191379262
#191369502
#191345392
#191329242
#191324492
#191324482
C43×#17892
#947643