Finite Group Databasebeta

← #24994634

Subgroups — #24994634

Order 11008.

472 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 93 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#19144518C211yesmaximal, characteristic
2#19143640C211yesmaximal, characteristic
3#19134675C211yesmaximal, characteristic, complemented
4#19133136C211yesmaximal, characteristic
5#19132501C211yesmaximal, characteristic, complemented
6#19132472C211yesmaximal, characteristic, complemented
7C43×#1823C211yesmaximal, characteristic, complemented
8#14583410C2211yescharacteristic
9#14583234C412yescomplemented
10#14583229—21no—
11#14583217C412yescomplemented
12#14583212—21no—
13#14582974—21no—
14#14582973—21no—
15#14582970—21no—
16C8×C22⋊D43—21no—
17#14582957—21no—
18#14582939—21no—
19#14582898—21no—
20#14582864—21no—
21#14582863C2211yescharacteristic
22#14582863C2211yescharacteristic
23#14582863C2211yescharacteristic
24#14582668—21no—
25#14582668—21no—
26#14582635—21no—
27#14582632—21no—
28C22×C4⋊C4×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#380C2211yescharacteristic
31C43×#340—21no—
32C43×#340—21no—
33C2×#10621898D411yescharacteristic
34C2×#10621877—21no—
35C2×#10621877—21no—
36C2×#10621877D411yescharacteristic
37C2×#10621877D411yescharacteristic
38C2×#10621872—21no—
39C2×C8×D43—21no—
40#13063308—21no—
41#13063304C2×C411yescharacteristic
42#13063304D411yescharacteristic
43#13063299C2×C411yescharacteristic
44#13063299D411yescharacteristic
45#13063294—21no—
46C4×C22⋊D43—21no—
47C4×C22⋊D43—21no—
48#13063284D411yescharacteristic
49#13063258—22no—
50#13063256—22no—
51Dic43⋊C8—21no—
52Dic43⋊C8—21no—
53#13063248—22no—
54#13063245—22no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)C2×C412yes—
61(C2×D43)⋊C8—21no—
62(C2×D43)⋊C8—21no—
63#13063235—21no—
64C8×Dic43—21no—
65C23×C4×C43—21no—
66C23×C4×C43C2311yescharacteristic
67C22×C8×C43D411yescharacteristic
68C22×C8×C43D411yescharacteristic
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43C2×C412yes—
76C2×C22⋊C4×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79#95×C43—21no—
80C24×C43#4111yescharacteristic
81C22×C4×C43—22no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—81no—
88C22×C4×C43—81no—
89C22×C4×C43C22×C411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43#4111yescharacteristic
95C2×C22⋊D43—21no—
96C2×C22⋊D43—21no—
97C2×C22⋊D43—21no—
98#10621898—41no—
99#10621898—41no—
100C2×D172C22⋊C411yescharacteristic
101C2×C4×D43—21no—
102C2×Dic86C22⋊C411yescharacteristic
103C2×C8×C43—21no—
104C2×C8×C43—21no—
105C2×C8×C43—41no—
106C2×C8×C43—41no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C22⋊C4×C43—81no—
114C22⋊Dic43—21no—
115C22⋊Dic43—21no—
116C22⋊Dic43—21no—
117(C2×D43)⋊C4—21no—
118(C2×D43)⋊C4—21no—
119C4⋊Dic43C22⋊C411yescharacteristic
120C4⋊Dic43C22⋊C411yescharacteristic
121Dic43⋊C4—21no—
122Dic43⋊C4—21no—
123C4×Dic43—21no—
124#10621877—41no—
125#10621877—41no—
126#10621877—41no—
127#10621877—41no—
128#10621877—41no—
129#10621877—41no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—41no—
134#10621872—81no—
135C8×D43—81no—
136C23×C43—21no—
137C23×C43—21no—
138C23×C43—41no—
139C23×C43—41no—
140C23×C43C4×D411yescharacteristic
141C23×C43#12111yescharacteristic
142C23×C43#12311yescharacteristic
143C22×D43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—82no—
155C2×C4×C43—81no—
156C2×C4×C43—81no—
157C2×C4×C43—82no—
158C2×C4×C43—81no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43C2×C22⋊C411yescharacteristic
162C2×C4×C43C4×D411yescharacteristic
163C2×C4×C43#12011yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C22⋊D43—41no—
166C22⋊D43—41no—
167C22⋊D43—81no—
168C22⋊D43—81no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—21no—
172D172—41no—
173C4×D43—41no—
174C4×D43—41no—
175Dic86—41no—
176C8×C43—41no—
177C8×C43—41no—
178C43⋊C8—42no—
179C43⋊C8—41no—
180C43⋊C8—41no—
181C43⋊C8—81no—
182#9522—431nomaximal, Sylow
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—42no—
192C22×C43—42no—
193C22×C43#38611yescharacteristic
194C22×C43#47111yescharacteristic
195C22×C43#47211yescharacteristic
196C2×D43—41no—
197C2×D43—41no—
198C2×D43—41no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—82no—
203C4×C43—161no—
204C4×C43#45811yescharacteristic
205C4×C43#45811yescharacteristic
206Dic43—41no—
207Dic43—41no—
208Dic43—41no—
209#3092—431no—
210#2976—431no—
211#1823D4311yescharacteristic, complemented
212#1821—431no—
213#1513—431no—
214#1305—431no—
215#1293—431no—
216C2×C43—21no—
217C2×C43—21no—
218C2×C43—41no—
219C2×C43—41no—
220C2×C43#189011yescharacteristic
221C2×C43#190211yescharacteristic
222C2×C43#190711yescharacteristic
223D43—81no—
224#525—431no—
225C22×C4⋊C4C2×D4311yescharacteristic
226#484—432no—
227#483—861no—
228#481—432no—
229#480—861no—
230#436—861no—
231#435—861no—
232#435—861no—
233C8×D4—861no—
234#433—861no—
235#428—861no—
236#417—861no—
237#408—861no—
238#407—431no—
239#407—431no—
240#407—431no—
241C2×C22⋊C8C2×D4311yescharacteristic
242#380C2×D4311yescharacteristic
243#343—861no—
244#343—861no—
245#340—21no—
246#340—21no—
247#328—861no—
248#327—861no—
249C43#952211yescharacteristic, complemented, Sylow
250C2×#41—431no—
251C23×C4—21no—
252C23×C4C22×D4311yescharacteristic
253C2×M16—431no—
254C2×M16—431no—
255C2×M16—861no—
256C2×M16—861no—
257C2×M16—861no—
258C22×C8—861no—
259C22×C8C22⋊D4311yescharacteristic
260C22×C8C22⋊D4311yescharacteristic
261#123—861no—
262C22⋊Q8—431no—
263C22⋊Q8—431no—
264#121—431no—
265#121—431no—
266#120—861no—
267C4×D4—861no—
268C4×D4—861no—
269#117—431no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4C4×D4312yes—
277C2×C22⋊C4—21no—
278#107—862no—
279#106—862no—
280C4⋊C8—861no—
281C4⋊C8—861no—
282#103—862no—
283#102—862no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—432no—
287C22⋊C8—861no—
288C22⋊C8—861no—
289C22⋊C8—861no—
290C22⋊C8—861no—
291C22⋊C8—861no—
292C22⋊C8—861no—
293C22⋊C8—861no—
294#97—861no—
295C4×C8—861no—
296#95—21no—
297C24#1062190011yescharacteristic
298#41—1721no—
299#41—1721no—
300C2×Q8—431no—
301C2×D4—431no—
302C2×D4—861no—
303C2×D4—861no—
304C2×D4—861no—
305C22×C4—22no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—81no—
312C22×C4—81no—
313C22×C4—861no—
314C22×C4C2×C4×D4311yescharacteristic
315C22×C4#1062189811yescharacteristic
316C22×C4D4×D4311yescharacteristic
317C22×C4D4×D4311yescharacteristic
318C22×C4D4×D4311yescharacteristic
319C22×C4C2×C22⋊D4311yescharacteristic
320M16—3441no—
321M16—1721no—
322M16—1721no—
323M16—1721no—
324M16—1721no—
325M16—1721no—
326M16—1721no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—862no—
332C2×C8—861no—
333C2×C8—861no—
334C2×C8—3441no—
335C2×C8—1721no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—431no—
343C4⋊C4—431no—
344C4⋊C4—861no—
345C4⋊C4—861no—
346C22⋊C4—81no—
347C22⋊C4—861no—
348C22⋊C4—861no—
349C22⋊C4—861no—
350C22⋊C4—861no—
351C22⋊C4—861no—
352C42—861no—
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23—861no—
358C23(C22⋊D43)⋊C411yescharacteristic
359C23#1306329611yescharacteristic
360C23#1306330711yescharacteristic
361Q8—1721no—
362D4—3441no—
363D4—3441no—
364D4—1721no—
365D4—1721no—
366D4—1721no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—82no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—82no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—1721no—
388C2×C4—1721no—
389C2×C4C22⋊C4×D4311yescharacteristic
390C2×C4C4×C22⋊D4311yescharacteristic
391C2×C4#1306329311yescharacteristic
392C2×C4#1306329811yescharacteristic
393C8—41no—
394C8—41no—
395C8—3441no—
396C8—1722no—
397C8—1721no—
398C8—1721no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—42no—
408C22—42no—
409C22—1721no—
410C22—1721no—
411C22—1721no—
412C22#1458277511yescharacteristic
413C22#1458315911yescharacteristic
414C22#1458316611yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—82no—
419C4—161no—
420C4—1721no—
421C4—1721no—
422C4—1721no—
423C4#1458308811yescharacteristic
424C4#1458308811yescharacteristic
425C2—21no—
426C2—21no—
427C2—41no—
428C2—41no—
429C2—3441no—
430C2#1913500511yescharacteristic
431C2#1913506511yescharacteristic
432C2#1913510611yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1823C2
socleC22×C43#386
prime radical#14583410C22
cosocleC23×C4×C43C23
hypercenter#1823D43
hypocenterC43#9522
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
3. #19134675C2semidirect
5. #19132501C2semidirect
6. #19132472C2semidirect
7. C43×#1823C2semidirect
9. #14583234C4semidirect
11. #14583217C4semidirect
211. #1823D43semidirect
249. C43#9522semidirect

Maximal subgroups

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

subgroupindex
#191445182
#191436402
#191346752
#191331362
#191325012
#191324722
C43×#18232
#952243