Finite Group Databasebeta

← #24997366

Subgroups — #24997366

Order 11008.

548 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 99 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#19144388C211yesmaximal, characteristic
2#19139953C211yesmaximal, characteristic
3#19133159C211yesmaximal, characteristic, complemented
4#19133024C211yesmaximal, characteristic, complemented
5#19132987C211yesmaximal, characteristic
6#19132454C211yesmaximal, characteristic, complemented
7C43×#3104C211yesmaximal, characteristic, complemented
8C2×C4×D172C2211yescharacteristic
9#14583196—22no—
10#14583186—21no—
11#14583176—21no—
12#14582952C2211yescharacteristic
13#14582942—21no—
14#14582923C2211yescharacteristic
15#14582903—21no—
16#14582834—21no—
17#14582810—21no—
18#14582801—21no—
19#14582797—21no—
20#14582770—22no—
21#14582765C2211yescharacteristic
22#14582636—22no—
23Q8⋊(C43⋊C8)—22no—
24#14582628—22no—
25C43×#533C2211yescharacteristic
26C2×C4×Q8×C43C2211yescharacteristic
27C43×#484—21no—
28C43×#477—21no—
29C43×#462—21no—
30C43×#451—21no—
31C4×Q16×C43—22no—
32C43×#431C2211yescharacteristic
33C22×D172D411yescharacteristic
34C22×C4×D43—21no—
35C2×#10621877—21no—
36C4×D172—21no—
37C4×D172—21no—
38C4×D172—21no—
39C4×D172—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43D411yescharacteristic
42C2×Dic43⋊C4—22no—
43C2×(C2×D43)⋊C4—22no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—22no—
46#13063258—22no—
47#13063256—22no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)D412yes—
51#13063245—22no—
52#13063245—22no—
53C22⋊(C43⋊C8)—21no—
54C4×C43⋊C8—21no—
55C43⋊#95—22no—
56C43⋊#95—21no—
57C43⋊#95D412yes—
58C22×Q8×C43D411yescharacteristic
59C2×Q16×C43—22no—
60C4⋊Q8×C43D411yescharacteristic
61C4⋊Q8×C43D411yescharacteristic
62#125×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C4×Q8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71#117×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76#107×C43—22no—
77C4⋊C8×C43—21no—
78#103×C43—22no—
79#103×C43—22no—
80C22⋊C8×C43—21no—
81C4×C8×C43D412yes—
82C23×D43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—21no—
87C2×Q8×C43—42no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×Dic43—22no—
94C22×Dic43—21no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172—21no—
100C2×D172Q1612yescomplemented
101C2×C4×D43—41no—
102C2×C4×D43—41no—
103C2×C4×D43—82no—
104Q16×C43—44no—
105C2×C8×C43—22no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C42×C43—41no—
118C42×C43—41no—
119C42×C43—41no—
120C42×C43C2×D411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43#4111yescharacteristic
124(C2×D43)⋊C4—44no—
125(C2×D43)⋊C4—41no—
126(C2×D43)⋊C4—41no—
127(C2×D43)⋊C4—82no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43—41no—
131C4⋊Dic43—41no—
132Dic43⋊C4—82no—
133#10621877—41no—
134#10621877—41no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8—41no—
137C23×C43#12011yescharacteristic
138C22×D43—22no—
139C22×D43—42no—
140C22×D43—42no—
141C22×D43—41no—
142C22×D43—41no—
143Q8×C43—22no—
144Q8×C43—22no—
145Q8×C43—41no—
146Q8×C43—41no—
147Q8×C43—42no—
148Q8×C43—81no—
149C2×C4×C43—22no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43#12011yescharacteristic
160C2×C4×C43#12011yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12711yescharacteristic
165C2×C4×C43C2×Q1611yescharacteristic
166C2×C4×C43#13511yescharacteristic
167C2×C4×C43#13711yescharacteristic
168C2×C4×C43#13711yescharacteristic
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C2×Dic43—41no—
173C2×Dic43—42no—
174D172—22no—
175D172—22no—
176D172—41no—
177D172—41no—
178C4×D43—82no—
179C4×D43—82no—
180C8×C43—42no—
181C43⋊C8—42no—
182C43⋊C8—81no—
183#10002—431nomaximal, Sylow
184C22×C43—21no—
185C22×C43—21no—
186C22×C43#39211yescharacteristic
187C22×C43#45111yescharacteristic
188C22×C43#45211yescharacteristic
189C2×D43—44no—
190C2×D43—42no—
191C2×D43—82no—
192C2×D43—81no—
193C2×D43—81no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—42no—
199C4×C43—81no—
200C4×C43—81no—
201C4×C43—81no—
202C4×C43#45111yescharacteristic
203C4×C43#45211yescharacteristic
204C4×C43#46711yescharacteristic
205C4×C43#47011yescharacteristic
206Dic43—82no—
207Dic43—81no—
208#3104D4311yescharacteristic, complemented
209#3077—431no—
210#2580—431no—
211#1518—431no—
212#1487—431no—
213#1478—431no—
214#1286—431no—
215C2×C43—21no—
216C2×C43—21no—
217C2×C43#200111yescharacteristic
218C2×C43#200811yescharacteristic
219C2×C43#201011yescharacteristic
220D43—82no—
221#533C2×D4311yescharacteristic
222C2×C4×Q8C2×D4311yescharacteristic
223C2×C4×D4—431no—
224#484—21no—
225#478—862no—
226#477—21no—
227#476—861no—
228#474—861no—
229#462—21no—
230#451—21no—
231C4×Q16—22no—
232#431—431no—
233#431C2×D4311yescharacteristic
234#428—861no—
235#423—431no—
236#418—861no—
237#399—861no—
238#393—861no—
239#390—861no—
240#389—861no—
241#385—862no—
242#382—431no—
243#328—862no—
244Q8⋊C8—862no—
245D4⋊C8—862no—
246C43#1000211yescharacteristic, complemented, Sylow
247C22×Q8C22⋊D4311yescharacteristic
248C22×D4—431no—
249C23×C4—861no—
250C2×Q16—22no—
251C2×M16—861no—
252C4⋊Q8C22⋊D4311yescharacteristic
253C4⋊Q8C22⋊D4311yescharacteristic
254#125—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×D4—861no—
264C4×D4—861no—
265C4×D4—861no—
266C4×D4—861no—
267#117—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—431no—
270C2×C4⋊C4—862no—
271C2×C4⋊C4—861no—
272C2×C4⋊C4C22⋊D4311yescharacteristic
273C2×C22⋊C4—862no—
274C2×C22⋊C4—862no—
275C2×C22⋊C4—861no—
276C2×C42—21no—
277C2×C42C22×D4311yescharacteristic
278#107—22no—
279#107—862no—
280#106—862no—
281C4⋊C8—21no—
282C4⋊C8—432no—
283C4⋊C8—861no—
284C4⋊C8—861no—
285#103—22no—
286#103—22no—
287#102—862no—
288#102—862no—
289C22⋊C8—21no—
290C22⋊C8—861no—
291C4×C8—861no—
292C4×C8C22⋊D4312yes—
293#95—432no—
294#95—862no—
295#95—861no—
296C24—861no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8—42no—
302C2×D4—432no—
303C2×D4—861no—
304C2×D4—861no—
305C2×D4—861no—
306C2×D4—861no—
307C2×D4—861no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—862no—
311C22×C4—861no—
312C22×C4—3442no—
313C22×C4—1721no—
314C22×C4—1721no—
315C22×C4D4×D4311yescharacteristic
316C22×C4D4×D4311yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318Q16—44no—
319M16—1721no—
320M16—1721no—
321C2×C8—22no—
322C2×C8—862no—
323C2×C8—1721no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—861no—
335C4⋊C4—861no—
336C4⋊C4—3442no—
337C4⋊C4—1721no—
338C4⋊C4—1721no—
339C22⋊C4—41no—
340C22⋊C4—3442no—
341C22⋊C4—1724no—
342C22⋊C4—1721no—
343C22⋊C4—1721no—
344C42—41no—
345C42—41no—
346C42—41no—
347C42D4×D4311yescharacteristic
348C42#1062190011yescharacteristic
349C42C2×C22⋊D4311yescharacteristic
350C42C2×C22⋊D4311yescharacteristic
351C23—862no—
352C23—1722no—
353C23—1722no—
354C23—1721no—
355C23—1721no—
356C23#1306329311yescharacteristic
357Q8—22no—
358Q8—22no—
359Q8—41no—
360Q8—41no—
361Q8—42no—
362Q8—81no—
363D4—862no—
364D4—862no—
365D4—1721no—
366D4—1721no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—3442no—
378C2×C4—3442no—
379C2×C4—1722no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4—1721no—
384C2×C4#1306329311yescharacteristic
385C2×C4#1306329411yescharacteristic
386C2×C4#1306329611yescharacteristic
387C2×C4#1306329711yescharacteristic
388C2×C4#1306329711yescharacteristic
389C2×C4#1306332111yescharacteristic
390C2×C4Q16×D4311yescharacteristic
391C2×C4#1306334811yescharacteristic
392C2×C4#1306335711yescharacteristic
393C2×C4#1306335711yescharacteristic
394C8—42no—
395C8—3441no—
396C8—1722no—
397C22—21no—
398C22—21no—
399C22—3442no—
400C22—3441no—
401C22—3441no—
402C22—1724no—
403C22—1722no—
404C22#1458280711yescharacteristic
405C22#1458305311yescharacteristic
406C22#1458306011yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—42no—
412C4—81no—
413C4—81no—
414C4—81no—
415C4—3442no—
416C4—3441no—
417C4#1458305311yescharacteristic
418C4#1458306011yescharacteristic
419C4#1458313711yescharacteristic
420C4#1458315411yescharacteristic
421C2—21no—
422C2—21no—
423C2—3442no—
424C2#1913560211yescharacteristic
425C2#1913564511yescharacteristic
426C2#1913566011yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3104C2
socleC22×C43#392
prime radicalC22×D172D4
hypercenter#3104D43
hypocenterC43#10002
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
3. #19133159C2semidirect
4. #19133024C2semidirect
6. #19132454C2semidirect
7. C43×#3104C2semidirect
100. C2×D172Q16semidirect
208. #3104D43semidirect
246. C43#10002semidirect

Maximal subgroups

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

subgroupindex
#191443882
#191399532
#191331592
#191330242
#191329872
#191324542
C43×#31042
#1000243