Finite Group Databasebeta

← #25070516

Subgroups — #25070516

Order 11008.

1002 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 187 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×#14583530C211yesmaximal, characteristic, complemented
2#19145353C212yesmaximal
3#19140337C211yesmaximal, characteristic
4#19133605C214yesmaximal, complemented
5#19133537C214yesmaximal, complemented
6#19133168C212yesmaximal, complemented
7C2×C43×#324C211yesmaximal, characteristic, complemented
8#14583530—24no—
9#14583530—22no—
10#14583530C2214yes—
11C2×#13063324—22no—
12C2×#13063316—22no—
13C2×#13063308—21no—
14C2×#13063304—21no—
15C2×#13063304C2212yes—
16C2×#13063299C2211yescharacteristic
17C2×#13063284—21no—
18#14583230C2214yes—
19#14583218—22no—
20#14583128—24no—
21#14583052C2214yes—
22#14583040—22no—
23#14582829C2212yes—
24#14582821—22no—
25#14582816C2212yes—
26#14582778—21no—
27#14582759C2211yescharacteristic
28#14582637C2218yes—
29C22×C4⋊C4×C43C2211yescharacteristic
30C2×C22⋊C8×C43C2212yes—
31C43×#324C2214yes—
32C22×Dic86—21no—
33C22×Dic86D412yes—
34C22×D172C2311yescharacteristic
35C22×C22⋊D43—21no—
36C2×#10621873—24no—
37#13063324—28no—
38#13063324—28no—
39#13063316—28no—
40#13063316—28no—
41#13063308—44no—
42#13063304—24no—
43#13063304—24no—
44#13063304—22no—
45#13063304—22no—
46#13063304D414yes—
47#13063304C2314yes—
48#13063299—22no—
49#13063299—22no—
50#13063284—24no—
51#13063284—24no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43D412yes—
57C2×C4⋊Dic43C2311yescharacteristic
58C2×Dic43⋊C4—22no—
59C2×Dic43⋊C4—22no—
60C2×Dic43⋊C4—22no—
61C2×C22⋊Dic43—22no—
62C2×C22⋊Dic43—21no—
63C2×(C2×D43)⋊C4—22no—
64C2×(C2×D43)⋊C4—21no—
65C2×(C2×D43)⋊C4—22no—
66C2×C4×Dic43—22no—
67#13063257—24no—
68#13063250—24no—
69#13063247—24no—
70C43⋊#95—22no—
71C43⋊#95C2312yes—
72C23×C4×C43D411yescharacteristic
73C23×C4×C43D411yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C22×C8×C43—22no—
76C2×C4⋊C4×C43—22no—
77C2×C4⋊C4×C43—22no—
78C2×C4⋊C4×C43D412yes—
79C2×C4⋊C4×C43C2312yes—
80C22⋊C8×C43—22no—
81C22⋊C8×C43C2314yes—
82C24×C43C2×D411yescharacteristic
83C23×D43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—22no—
89C22×C4×C43—81no—
90C22×C4×C43—81no—
91C22×C4×C43SD1614yescomplemented
92C22×C4×C43C2×D412yes—
93C22×C4×C43C2×D412yes—
94C22×C4×C43C2×D412yes—
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2411yescharacteristic
98C2×C22⋊D43—41no—
99C2×C22⋊D43—41no—
100C2×C22⋊D43—42no—
101C2×C22⋊D43—42no—
102C22×Dic43—22no—
103C22×Dic43—22no—
104C22×Dic43—21no—
105C22×Dic43—22no—
106C2×D172—22no—
107C2×D172—81no—
108C2×Dic86—24no—
109C2×Dic86—22no—
110C2×Dic86—82no—
111C2×Dic86—82no—
112C2×Dic86C2×D414yes—
113C2×C8×C43—24no—
114C2×C8×C43—82no—
115C4⋊C4×C43—24no—
116C4⋊C4×C43—24no—
117C22⋊Dic43—24no—
118C22⋊Dic43—24no—
119C22⋊Dic43—42no—
120(C2×D43)⋊C4—42no—
121(C2×D43)⋊C4—44no—
122(C2×D43)⋊C4—82no—
123C4⋊Dic43—24no—
124C4⋊Dic43—24no—
125C4⋊Dic43—24no—
126C4⋊Dic43—22no—
127C4⋊Dic43—22no—
128C4⋊Dic43—81no—
129C4⋊Dic43C2×D414yes—
130Dic43⋊C4—28no—
131Dic43⋊C4—24no—
132Dic43⋊C4—24no—
133Dic43⋊C4—44no—
134C4×Dic43—28no—
135#10621873—84no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43#12011yescharacteristic
139C23×C43#12011yescharacteristic
140C23×C43C2×SD1612yes—
141C23×C43#13712yes—
142C23×C43C22×D411yescharacteristic
143C22×D43—42no—
144C22×D43—42no—
145C22×D43—41no—
146C22×D43—41no—
147C22×D43—41no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—24no—
151C2×C4×C43—24no—
152C2×C4×C43—22no—
153C2×C4×C43—41no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—41no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—81no—
160C2×C4×C43#12012yes—
161C2×C4×C43C2×SD1614yes—
162C2×C4×C43C22×D412yes—
163C22⋊D43—82no—
164C22⋊D43—82no—
165C2×Dic43—24no—
166C2×Dic43—24no—
167C2×Dic43—44no—
168C2×Dic43—44no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—42no—
174C2×Dic43—41no—
175D172—44no—
176Dic86—44no—
177Dic86—82no—
178Dic86—84no—
179C8×C43—44no—
180#18294—431nomaximal, Sylow
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—42no—
188C22×C43—42no—
189C22×C43#44812yes—
190C22×C43#44812yes—
191C22×C43C2×#12011yescharacteristic
192C22×C43C22×SD1611yescharacteristic
193C22×C43C2×#13711yescharacteristic
194C2×D43—82no—
195C2×D43—82no—
196C2×D43—81no—
197C2×D43—81no—
198C2×D43—81no—
199C4×C43—24no—
200C4×C43—22no—
201C4×C43—22no—
202C4×C43—42no—
203Dic43—44no—
204Dic43—44no—
205Dic43—82no—
206Dic43—81no—
207C2×#544—431no—
208#3187—432no—
209#2618—431no—
210#1611—434no—
211#1599—434no—
212#1520—432no—
213C2×#324D4311yescharacteristic, complemented
214C2×C43—21no—
215C2×C43—21no—
216C2×C43—22no—
217C2×C43—22no—
218C2×C43C2×#44811yescharacteristic
219C2×C43#302011yescharacteristic
220C2×C43#302611yescharacteristic
221D43—161no—
222#544—434no—
223#544—864no—
224#544—862no—
225C2×C4⋊Q8—862no—
226C2×#125—862no—
227C2×#123—861no—
228C2×C22⋊Q8—432no—
229C2×C22⋊Q8—861no—
230C2×#121—431no—
231C2×#117—861no—
232C22×C4⋊C4C2×D4311yescharacteristic
233#483—434no—
234#481—862no—
235#465—864no—
236#450—434no—
237#448—862no—
238C2×C22⋊C8C2×D4312yes—
239#398—432no—
240#396—862no—
241#394—432no—
242#386—861no—
243#380—431no—
244#328—438no—
245#324C2×D4314yes—
246C43#1829411yescharacteristic, complemented, Sylow
247C22×Q8—432no—
248C22×Q8—861no—
249C22×D4—431no—
250C22×D4—861no—
251C23×C4D17211yescharacteristic
252C23×C4D17211yescharacteristic
253C23×C4C22×D4311yescharacteristic
254C2×SD16—864no—
255C22×C8—22no—
256C4⋊Q8—868no—
257C4⋊Q8—868no—
258#125—868no—
259#125—868no—
260#123—1724no—
261C22⋊Q8—434no—
262C22⋊Q8—434no—
263C22⋊Q8—864no—
264C22⋊Q8—862no—
265C22⋊Q8—864no—
266C22⋊Q8—862no—
267#121—862no—
268#121—862no—
269#117—864no—
270#117—864no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—432no—
274C2×C4⋊C4—431no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4—861no—
278C2×C4⋊C4—862no—
279C2×C4⋊C4—862no—
280C2×C4⋊C4—861no—
281C2×C4⋊C4—862no—
282C2×C4⋊C4D17212yes—
283C2×C4⋊C4C22×D4312yes—
284C2×C22⋊C4—862no—
285C2×C22⋊C4—862no—
286C2×C22⋊C4—861no—
287C2×C22⋊C4—861no—
288C2×C22⋊C4—862no—
289C2×C42—862no—
290#106—864no—
291#103—864no—
292#102—864no—
293C22⋊C8—22no—
294C22⋊C8C22×D4314yes—
295#95—432no—
296#95—862no—
297C24—861no—
298C24C2×D17211yescharacteristic
299C2×Q8—434no—
300C2×Q8—864no—
301C2×Q8—862no—
302C2×Q8—3442no—
303C2×Q8—3442no—
304C2×D4—862no—
305C2×D4—3441no—
306C2×D4—1721no—
307C2×D4—1721no—
308C2×D4—1722no—
309C2×D4—1722no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—81no—
316C22×C4—81no—
317C22×C4—862no—
318C22×C4—862no—
319C22×C4—862no—
320C22×C4—861no—
321C22×C4#1062187314yescomplemented
322C22×C4C2×D17212yes—
323C22×C4C2×D17212yes—
324C22×C4C2×D17211yescharacteristic
325C22×C4D4×D4312yes—
326C22×C4D4×D4312yes—
327C22×C4C23×D4311yescharacteristic
328SD16—3444no—
329C2×C8—24no—
330C2×C8—82no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—434no—
334C4⋊C4—864no—
335C4⋊C4—864no—
336C4⋊C4—864no—
337C4⋊C4—868no—
338C4⋊C4—862no—
339C4⋊C4—864no—
340C4⋊C4—864no—
341C4⋊C4—862no—
342C4⋊C4—3441no—
343C4⋊C4—1724no—
344C22⋊C4—864no—
345C22⋊C4—864no—
346C22⋊C4—3442no—
347C22⋊C4—1722no—
348C22⋊C4—1722no—
349C22⋊C4—1724no—
350C42—868no—
351C23—41no—
352C23—41no—
353C23—1722no—
354C23—1722no—
355C23—1721no—
356C23—1721no—
357C23—1721no—
358C23#1306329511yescharacteristic
359C23#1306329511yescharacteristic
360C23C2×#1062187312yes—
361C23#1306335812yes—
362C23C22×D17211yescharacteristic
363Q8—3442no—
364Q8—3444no—
365Q8—1724no—
366D4—3442no—
367D4—3442no—
368D4—1724no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—864no—
382C2×C4—864no—
383C2×C4—1722no—
384C2×C4—1722no—
385C2×C4—1721no—
386C2×C4—1722no—
387C2×C4—1721no—
388C2×C4—1721no—
389C2×C4—1724no—
390C2×C4—1724no—
391C2×C4#1306329512yes—
392C2×C4C2×#1062187314yes—
393C2×C4C2×D4×D4312yes—
394C8—44no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—3442no—
404C22—3442no—
405C22—3441no—
406C22—3441no—
407C22—3441no—
408C22#1458304012yes—
409C22#1458304012yes—
410C22C2×#1306329511yescharacteristic
411C22C22×#1062187311yescharacteristic
412C22C2×#1306335811yescharacteristic
413C4—22no—
414C4—22no—
415C4—24no—
416C4—42no—
417C4—3442no—
418C4—3441no—
419C4—1724no—
420C4—1724no—
421C2—21no—
422C2—21no—
423C2—22no—
424C2—22no—
425C2—6881no—
426C2C2×#1458304011yescharacteristic
427C2#1914396211yescharacteristic
428C2#1914399411yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#324C2
socleC22×C43C2×#120
prime radicalC2×#13063299C22
hypercenterC2×#324D43
hypocenterC43#18294
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
1. C2×#14583530C2semidirect
4. #19133605C2semidirect
5. #19133537C2semidirect
6. #19133168C2semidirect
7. C2×C43×#324C2semidirect
91. C22×C4×C43SD16semidirect
213. C2×#324D43semidirect
246. C43#18294semidirect
321. C22×C4#10621873semidirect

Maximal subgroups

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

subgroupindex
C2×#145835302
#191453532
#191403372
#191336052
#191335372
#191331682
C2×C43×#3242
#1829443