Finite Group Databasebeta

← #24993781

Subgroups — #24993781

Order 11008.

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

normal subgroups only

This group has 732 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
1#19137436C211yesmaximal, characteristic
2#19135581C211yesmaximal, characteristic, complemented
3#19134539C211yesmaximal, characteristic
4#19133115C211yesmaximal, characteristic, complemented
5#19132500C211yesmaximal, characteristic, complemented
6#19132480C211yesmaximal, characteristic, complemented
7C43×#3007C211yesmaximal, characteristic
8C2×Q8×Dic43—21no—
9C2×#13063252—22no—
10#14582863C2211yescharacteristic
11#14582802—22no—
12#14582802—21no—
13#14582759—21no—
14#14582759C2211yescharacteristic
15C4×C22⋊Dic43—21no—
16C4×C22⋊Dic43C2211yescharacteristic
17C4×C22⋊Dic43C2211yescharacteristic
18#14582666—22no—
19#14582636—21no—
20#14582636—21no—
21C22×#41×C43C2211yescharacteristic
22C2×#137×C43C412yescomplemented
23C2×C22⋊Q8×C43C2211yescharacteristic
24C43×#452—22no—
25C43×#451—21no—
26C43×#450—21no—
27C43×#417C412yescomplemented
28C43×#407C2211yescharacteristic
29C2×#10621877—21no—
30Q8×Dic43—44no—
31C2×C4⋊Dic43—22no—
32C2×C4⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—22no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—22no—
37C2×C22⋊Dic43D412yes—
38C2×C4×Dic43—22no—
39C2×C4×Dic43—21no—
40C2×C4×Dic43—21no—
41#13063252—44no—
42C22⋊(C43⋊C8)—21no—
43C22⋊(C43⋊C8)—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95D411yescharacteristic
47C43⋊#95D411yescharacteristic
48C2×#41×C43—21no—
49C2×#41×C43—21no—
50C2×#41×C43—44no—
51C2×#41×C43C2×C412yes—
52C2×#41×C43D412yes—
53C22×Q8×C43C2×C411yescharacteristic
54C22×Q8×C43D411yescharacteristic
55C22×D4×C43—21no—
56C22×D4×C43D411yescharacteristic
57C23×C4×C43—21no—
58C23×C4×C43C2311yescharacteristic
59#137×C43—44no—
60C2×Q16×C43—22no—
61C2×SD16×C43—22no—
62C2×M16×C43C2×C412yes—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C22⋊Q8×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43C2×C411yescharacteristic
69C2×C22⋊C4×C43—21no—
70#103×C43—22no—
71#102×C43—22no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C24×C43—21no—
75C24×C43C2×D411yescharacteristic
76#41×C43—24no—
77#41×C43—24no—
78#41×C43—42no—
79#41×C43—42no—
80#41×C43—44no—
81#41×C43—44no—
82C2×Q8×C43—24no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—42no—
87C2×Q8×C43C22⋊C412yes—
88C2×D4×C43—21no—
89C2×D4×C43—22no—
90C2×D4×C43—22no—
91C2×D4×C43—42no—
92C2×D4×C43—44no—
93C2×D4×C43C22⋊C412yes—
94C22×C4×C43—22no—
95C22×C4×C43—22no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—42no—
100C22×C4×C43—44no—
101C22×C4×C43C22×C411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×Dic43—21no—
108C22×Dic43—22no—
109C22×Dic43—21no—
110C22×Dic43—41no—
111Q16×C43—44no—
112SD16×C43—44no—
113M16×C43—42no—
114C2×C8×C43—22no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—41no—
118C4⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊Dic43—22no—
122C22⋊Dic43—42no—
123C22⋊Dic43—41no—
124C22⋊Dic43—42no—
125C22⋊Dic43—44no—
126C22⋊Dic43—82no—
127C4⋊Dic43—44no—
128C4⋊Dic43—42no—
129C4×Dic43—44no—
130C4×Dic43—42no—
131C4×Dic43—42no—
132#10621877—42no—
133C2×C43⋊C8—41no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—22no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—42no—
140C23×C43—42no—
141C23×C43—41no—
142C23×C43—41no—
143C23×C43C4×D411yescharacteristic
144C23×C43#12011yescharacteristic
145C23×C43#12111yescharacteristic
146Q8×C43—24no—
147Q8×C43—22no—
148Q8×C43—42no—
149Q8×C43—81no—
150Q8×C43#9914yes—
151D4×C43—22no—
152D4×C43—22no—
153D4×C43—44no—
154D4×C43—44no—
155D4×C43—42no—
156C2×C4×C43—24no—
157C2×C4×C43—22no—
158C2×C4×C43—22no—
159C2×C4×C43—22no—
160C2×C4×C43—22no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—44no—
165C2×C4×C43—44no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—81no—
169C2×C4×C43—81no—
170C2×C4×C43C2×C22⋊C411yescharacteristic
171C2×C4×C43C4×D411yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12311yescharacteristic
174C2×Dic43—22no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—42no—
178C2×Dic43—41no—
179C2×Dic43—42no—
180C2×Dic43—42no—
181C2×Dic43—41no—
182C2×Dic43—42no—
183C2×Dic43—41no—
184C2×Dic43—81no—
185C2×Dic43—81no—
186C8×C43—42no—
187C43⋊C8—81no—
188#9364—431nomaximal, Sylow
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—42no—
198C22×C43—42no—
199C22×C43—42no—
200C22×C43—81no—
201C22×C43—81no—
202C22×C43—82no—
203C22×C43—82no—
204C22×C43#38611yescharacteristic
205C22×C43#45511yescharacteristic
206C22×C43#45611yescharacteristic
207C4×C43—21no—
208C4×C43—24no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—81no—
212C4×C43—81no—
213C4×C43C2×#9912yes—
214Dic43—42no—
215Dic43—82no—
216Dic43—81no—
217Dic43—82no—
218#3007D4311yescharacteristic
219#2341—431no—
220#1996—431no—
221#1789—431no—
222#1508—431no—
223#1305—431no—
224#1297—431no—
225C2×C43—21no—
226C2×C43—21no—
227C2×C43—41no—
228C2×C43—41no—
229C2×C43—82no—
230C2×C43#188211yescharacteristic
231C2×C43#189811yescharacteristic
232C2×C43#190611yescharacteristic
233C22×#41C2×D4311yescharacteristic
234C2×#137Dic4312yescomplemented
235C2×C22⋊Q8C2×D4311yescharacteristic
236C2×C4×Q8—861no—
237#452—22no—
238#451—21no—
239#450—21no—
240C2×#104—862no—
241#417Dic4312yescomplemented
242#407—431no—
243#407C2×D4311yescharacteristic
244#390—862no—
245#390—861no—
246#380—431no—
247#380—861no—
248C4×C22⋊C4—431no—
249C4×C22⋊C4—431no—
250C4×C22⋊C4—861no—
251#342—862no—
252#328—861no—
253#328—861no—
254C43#936411yescharacteristic, complemented, Sylow
255C2×#41—21no—
256C2×#41—21no—
257C2×#41—44no—
258C2×#41C2×Dic4312yes—
259C2×#41C22⋊D4312yes—
260C22×Q8C2×Dic4311yescharacteristic
261C22×Q8C22⋊D4311yescharacteristic
262C22×D4—21no—
263C22×D4C22⋊D4311yescharacteristic
264C23×C4—21no—
265C23×C4C22×D4311yescharacteristic
266#137—44no—
267C2×Q16—22no—
268C2×SD16—22no—
269C2×M16—861no—
270C2×M16C2×Dic4312yes—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275C4×Q8—1724no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—862no—
278C2×C4⋊C4—861no—
279C2×C4⋊C4C2×Dic4311yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—432no—
282C2×C22⋊C4—861no—
283C2×C22⋊C4—862no—
284C2×C22⋊C4—862no—
285C2×C22⋊C4—861no—
286C2×C42—862no—
287C2×C42—861no—
288C2×C42—861no—
289#104—1724no—
290#103—22no—
291#102—22no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—861no—
295C22⋊C8—861no—
296#95—431no—
297#95—431no—
298#95—861no—
299#95—861no—
300C24—21no—
301C24D4×D4311yescharacteristic
302#41—24no—
303#41—24no—
304#41—42no—
305#41—42no—
306#41—44no—
307#41—44no—
308C2×Q8—24no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—42no—
313C2×Q8C22⋊Dic4312yes—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—42no—
318C2×D4—44no—
319C2×D4C22⋊Dic4312yes—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—42no—
326C22×C4—44no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—862no—
330C22×C4—1721no—
331C22×C4D4×D4311yescharacteristic
332C22×C4#1062190011yescharacteristic
333C22×C4#1062190011yescharacteristic
334C22×C4C22×Dic4311yescharacteristic
335C22×C4C2×C22⋊D4311yescharacteristic
336C22×C4C2×C22⋊D4311yescharacteristic
337Q16—44no—
338SD16—44no—
339M16—42no—
340M16—1722no—
341C2×C8—22no—
342C2×C8—1721no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—1724no—
348C4⋊C4—1722no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—862no—
352C22⋊C4—3442no—
353C22⋊C4—1722no—
354C22⋊C4—1724no—
355C22⋊C4—1721no—
356C22⋊C4—1722no—
357C42—1722no—
358C42—1724no—
359C42—1722no—
360C23—21no—
361C23—21no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—42no—
367C23—41no—
368C23—41no—
369C23D4×Dic4311yescharacteristic
370C23#1306329311yescharacteristic
371C23#1306329711yescharacteristic
372Q8—24no—
373Q8—22no—
374Q8—42no—
375Q8—81no—
376Q8#1306324014yes—
377D4—22no—
378D4—22no—
379D4—44no—
380D4—44no—
381D4—42no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—862no—
397C2×C4—3441no—
398C2×C4—3441no—
399C2×C4—1721no—
400C2×C4—1722no—
401C2×C4—1722no—
402C2×C4—1721no—
403C2×C4—1722no—
404C2×C4—1721no—
405C2×C4—1722no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4C2×C22⋊Dic4311yescharacteristic
409C2×C4D4×Dic4311yescharacteristic
410C2×C4#1306329711yescharacteristic
411C2×C4#1306330611yescharacteristic
412C8—42no—
413C8—3441no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—82no—
428C22—82no—
429C22#1458277911yescharacteristic
430C22#1458307511yescharacteristic
431C22#1458308011yescharacteristic
432C4—21no—
433C4—24no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—3441no—
439C4—3442no—
440C4—3442no—
441C4—1722no—
442C4C2×#1306324012yes—
443C2—21no—
444C2—21no—
445C2—41no—
446C2—41no—
447C2—82no—
448C2#1913496611yescharacteristic
449C2#1913504911yescharacteristic
450C2#1913509811yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#3007C2
socleC22×C43#386
prime radicalC22×#41×C43C22
cosocleC23×C4×C43C23
hypercenter#3007D43
hypocenterC43#9364
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
2. #19135581C2semidirect
4. #19133115C2semidirect
5. #19132500C2semidirect
6. #19132480C2semidirect
22. C2×#137×C43C4semidirect
27. C43×#417C4semidirect
234. C2×#137Dic43semidirect
241. #417Dic43semidirect
254. C43#9364semidirect

Maximal subgroups

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

subgroupindex
#191374362
#191355812
#191345392
#191331152
#191325002
#191324802
C43×#30072
#936443