Finite Group Databasebeta

← #24997368

Subgroups — #24997368

Order 11008.

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

normal subgroups only

This group has 548 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#19144630C211yesmaximal, characteristic, complemented
2#19144388C211yesmaximal, characteristic
3#19139954C211yesmaximal, characteristic
4#19133025C211yesmaximal, characteristic, complemented
5#19132985C211yesmaximal, characteristic
6#19132453C211yesmaximal, characteristic, complemented
7C43×#1518C211yesmaximal, characteristic, complemented
8C2×C4×Dic86C2211yescharacteristic
9C2×C4×D172C2211yescharacteristic
10#14583232—21no—
11#14583196—22no—
12#14583191—21no—
13#14583186—21no—
14#14583176—21no—
15#14583106—21no—
16#14583054—21no—
17C4×#10621885—22no—
18#14582952C2211yescharacteristic
19#14582942—21no—
20#14582923C2211yescharacteristic
21#14582903—21no—
22#14582836—21no—
23#14582812—21no—
24#14582800—21no—
25#14582798—21no—
26#14582773—22no—
27#14582631—22no—
28#14582626—22no—
29C43×#533C2211yescharacteristic
30C43×#431C2211yescharacteristic
31C43×#382C2211yescharacteristic
32C43×#328—22no—
33C22×Dic86D411yescharacteristic
34C22×D172D411yescharacteristic
35C22×C4×D43—21no—
36C2×#10621885—22no—
37C2×#10621877—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40C4×Dic86—21no—
41C4×Dic86—21no—
42C4×D172—21no—
43C4×D172—21no—
44C4×D172—21no—
45C4×D172—21no—
46C2×C4⋊Dic43—22no—
47C2×C4⋊Dic43D411yescharacteristic
48C2×C4⋊Dic43D411yescharacteristic
49C2×Dic43⋊C4—21no—
50C2×(C2×D43)⋊C4—22no—
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4—22no—
53C2×C4×Dic43—21no—
54#13063258—22no—
55#13063258—22no—
56#13063256—22no—
57C4⋊(C43⋊C8)—21no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)D412yes—
60#13063249—22no—
61#13063248—22no—
62#13063245—22no—
63#13063245—22no—
64C22⋊(C43⋊C8)—21no—
65C4×C43⋊C8D412yes—
66C43⋊#95—22no—
67C4⋊Q8×C43D411yescharacteristic
68C4⋊Q8×C43D411yescharacteristic
69#125×C43—21no—
70C22⋊Q8×C43—21no—
71C22⋊Q8×C43—21no—
72C4×Q8×C43—21no—
73C4×Q8×C43—21no—
74#117×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C42×C43C2311yescharacteristic
77C4⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79C4×C8×C43—21no—
80#95×C43—21no—
81#95×C43D412yes—
82C23×D43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C22×C4×C43—22no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C2×D172—21no—
93C2×D172—21no—
94C2×D172—21no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172Q1612yescomplemented
98C2×C4×D43—41no—
99C2×C4×D43—41no—
100C2×C4×D43—82no—
101C2×Dic86—21no—
102C2×Dic86—21no—
103C2×Dic86—42no—
104C2×C8×C43—41no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C42×C43—41no—
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43#4111yescharacteristic
119#10621885—44no—
120(C2×D43)⋊C4—44no—
121(C2×D43)⋊C4—41no—
122(C2×D43)⋊C4—41no—
123(C2×D43)⋊C4—82no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43—82no—
129Dic43⋊C4—41no—
130Dic43⋊C4—41no—
131C4×Dic43—41no—
132C4×Dic43—41no—
133#10621877—41no—
134#10621877—41no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8—22no—
137C23×C43#12011yescharacteristic
138C22×D43—22no—
139C22×D43—42no—
140C22×D43—42no—
141C22×D43—41no—
142C22×D43—41no—
143Q8×C43—42no—
144Q8×C43—81no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—42no—
152C2×C4×C43#12011yescharacteristic
153C2×C4×C43#12011yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12711yescharacteristic
158C2×C4×C43C2×Q1611yescharacteristic
159C2×C4×C43#13511yescharacteristic
160C2×C4×C43#13711yescharacteristic
161C2×C4×C43#13711yescharacteristic
162C2×Dic43—22no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—42no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170D172—22no—
171D172—22no—
172D172—41no—
173D172—41no—
174C4×D43—82no—
175C4×D43—82no—
176Dic86—22no—
177Dic86—22no—
178Dic86—41no—
179Dic86—41no—
180C8×C43—81no—
181C43⋊C8—42no—
182C43⋊C8—42no—
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—82no—
199C4×C43—81no—
200C4×C43—81no—
201C4×C43#45111yescharacteristic
202C4×C43#45211yescharacteristic
203C4×C43#46711yescharacteristic
204C4×C43#47011yescharacteristic
205Dic43—42no—
206Dic43—81no—
207Dic43—81no—
208#3104—431no—
209#3077—431no—
210#2580—431no—
211#1518D4311yescharacteristic, complemented
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×Q8—431no—
223C2×C4×D4—431no—
224#484—861no—
225#478—862no—
226#477—861no—
227#476—861no—
228#474—861no—
229#462—861no—
230#451—861no—
231C4×Q16—862no—
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#382C2×D4311yescharacteristic
243#328—22no—
244Q8⋊C8—862no—
245D4⋊C8—862no—
246C43#1000211yescharacteristic, complemented, Sylow
247C22×Q8—431no—
248C22×D4—431no—
249C23×C4—861no—
250C2×Q16—862no—
251C2×M16—861no—
252C4⋊Q8D17211yescharacteristic
253C4⋊Q8D17211yescharacteristic
254#125—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—861no—
260C4×Q8—861no—
261C4×Q8—861no—
262C4×Q8—861no—
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—431no—
271C2×C4⋊C4—862no—
272C2×C4⋊C4—861no—
273C2×C22⋊C4—862no—
274C2×C22⋊C4—862no—
275C2×C22⋊C4—861no—
276C2×C42—861no—
277C2×C42C22×D4311yescharacteristic
278#107—862no—
279#107—862no—
280#106—862no—
281C4⋊C8—21no—
282C4⋊C8—432no—
283C4⋊C8—861no—
284C4⋊C8—861no—
285#103—862no—
286#103—862no—
287#102—862no—
288#102—862no—
289C22⋊C8—21no—
290C22⋊C8—861no—
291C4×C8—21no—
292C4×C8—432no—
293#95—21no—
294#95—862no—
295#95C22⋊D4312yes—
296C24—861no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—861no—
300C2×Q8—861no—
301C2×Q8—1722no—
302C2×D4—432no—
303C2×D4—861no—
304C2×D4—861no—
305C2×D4—861no—
306C2×D4—861no—
307C2×D4—861no—
308C22×C4—22no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4—3442no—
313C22×C4—1721no—
314C22×C4—1721no—
315C22×C4D4×D4311yescharacteristic
316C22×C4D4×D4311yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318Q16—1724no—
319M16—1721no—
320M16—1721no—
321C2×C8—41no—
322C2×C8—862no—
323C2×C8—862no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—861no—
333C4⋊C4—861no—
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—1721no—
346C42—1721no—
347C42C2×D17211yescharacteristic
348C42#1062189811yescharacteristic
349C42D4×D4311yescharacteristic
350C42D4×D4311yescharacteristic
351C23—862no—
352C23—1722no—
353C23—1722no—
354C23—1721no—
355C23—1721no—
356C23#1306329311yescharacteristic
357Q8—42no—
358Q8—81no—
359Q8—862no—
360Q8—862no—
361Q8—1721no—
362Q8—1721no—
363D4—862no—
364D4—862no—
365D4—1721no—
366D4—1721no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—862no—
375C2×C4—3442no—
376C2×C4—3442no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1722no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4#1306329511yescharacteristic
385C2×C4#1306329511yescharacteristic
386C2×C4#1306329811yescharacteristic
387C2×C4#1306329811yescharacteristic
388C2×C4#1306329911yescharacteristic
389C2×C4#1306332111yescharacteristic
390C2×C4Q16×D4311yescharacteristic
391C2×C4#1306334611yescharacteristic
392C2×C4#1306335411yescharacteristic
393C2×C4#1306335711yescharacteristic
394C8—81no—
395C8—1722no—
396C8—1722no—
397C22—21no—
398C22—21no—
399C22—3442no—
400C22—3441no—
401C22—3441no—
402C22—1724no—
403C22—1722no—
404C22#1458280811yescharacteristic
405C22#1458305311yescharacteristic
406C22#1458305811yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—81no—
413C4—81no—
414C4—3441no—
415C4—3441no—
416C4—1722no—
417C4#1458305611yescharacteristic
418C4#1458306411yescharacteristic
419C4#1458313911yescharacteristic
420C4#1458315611yescharacteristic
421C2—21no—
422C2—21no—
423C2—3442no—
424C2#1913560411yescharacteristic
425C2#1913564711yescharacteristic
426C2#1913566111yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1518C2
socleC22×C43#392
prime radicalC22×D172D4
hypercenter#1518D43
hypocenterC43#10002
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
1. #19144630C2semidirect
4. #19133025C2semidirect
6. #19132453C2semidirect
7. C43×#1518C2semidirect
97. C2×D172Q16semidirect
211. #1518D43semidirect
246. C43#10002semidirect

Maximal subgroups

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

subgroupindex
#191446302
#191443882
#191399542
#191330252
#191329852
#191324532
C43×#15182
#1000243