Finite Group Databasebeta

← #24992664

Subgroups — #24992664

Order 11008.

622 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 113 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#19140340C211yesmaximal, characteristic
2#19137212C211yesmaximal, characteristic, complemented
3#19133164C211yesmaximal, characteristic
4#19133162C211yesmaximal, characteristic
5C2×#14582624C211yesmaximal, characteristic, complemented
6#19132462C211yesmaximal, characteristic, complemented
7C43×#1289C211yesmaximal, characteristic, complemented
8C2×#13063309—21no—
9C2×#13063299C2211yescharacteristic
10C2×#13063281—21no—
11C22×Dic43⋊C4C2211yescharacteristic
12C2×C22⋊(C43⋊C8)C2211yescharacteristic
13#14582831C412yescomplemented
14#14582821—22no—
15#14582817C412yescomplemented
16#14582796—22no—
17#14582794—22no—
18#14582776—21no—
19#14582759C2211yescharacteristic
20#14582757—21no—
21#14582634—22no—
22#14582632—22no—
23#14582624—22no—
24C2×C22⋊C8×C43C2211yescharacteristic
25C43×#380C2211yescharacteristic
26C43×#380C2211yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C22⋊D43—21no—
29C23×Dic43D411yescharacteristic
30C23×Dic43D411yescharacteristic
31C22×C43⋊C8—21no—
32#13063309—42no—
33#13063309—42no—
34#13063299—21no—
35#13063299—21no—
36#13063299—21no—
37#13063299—21no—
38#13063281—42no—
39#13063281—42no—
40C2×C4⋊Dic43—22no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43C2×C411yescharacteristic
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—22no—
48C2×Dic43⋊C4—22no—
49C2×Dic43⋊C4C2×C412yes—
50C2×Dic43⋊C4D412yes—
51C2×C22⋊Dic43—21no—
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—22no—
54C2×(C2×D43)⋊C4—22no—
55C2×C4×Dic43—22no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58C43⋊#95—22no—
59C43⋊#95—22no—
60C43⋊#95D412yes—
61C23×C4×C43C2311yescharacteristic
62C22×C8×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C22⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69#95×C43C2×C412yes—
70#95×C43D412yes—
71C24×C43C2×D411yescharacteristic
72C23×D43—21no—
73C22×C4×C43—22no—
74C22×C4×C43—22no—
75C22×C4×C43—81no—
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C2×C22⋊D43—41no—
83C2×C22⋊D43—41no—
84C2×C22⋊D43—41no—
85C2×C22⋊D43—41no—
86C2×C22⋊D43—41no—
87C2×C22⋊D43—41no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—22no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—81no—
97C22×Dic43C22⋊C412yes—
98C22×Dic43C22⋊C412yes—
99C22×Dic43D812yes—
100C22×Dic43SD1612yes—
101C2×D172—21no—
102C2×D172—21no—
103C2×D172—81no—
104C2×C8×C43—41no—
105C2×C8×C43—81no—
106C4⋊C4×C43—81no—
107C4⋊C4×C43—81no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—41no—
112C22⋊Dic43—41no—
113C22⋊Dic43—41no—
114(C2×D43)⋊C4—41no—
115(C2×D43)⋊C4—41no—
116(C2×D43)⋊C4—44no—
117(C2×D43)⋊C4—82no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—44no—
121C4⋊Dic43—81no—
122Dic43⋊C4—22no—
123Dic43⋊C4—22no—
124Dic43⋊C4—22no—
125Dic43⋊C4—22no—
126Dic43⋊C4—44no—
127Dic43⋊C4—82no—
128C4×Dic43—44no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—81no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43C2×C22⋊C411yescharacteristic
134C23×C43#12011yescharacteristic
135C23×C43#12311yescharacteristic
136C23×C43C2×D811yescharacteristic
137C23×C43C2×SD1611yescharacteristic
138C23×C43AGL(1,ℤ/8)11yescharacteristic
139C23×C43#13711yescharacteristic
140C22×D43—42no—
141C22×D43—42no—
142C22×D43—41no—
143C22×D43—41no—
144C22×D43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—42no—
152C2×C4×C43—42no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C22⋊D43—81no—
162C22⋊D43—81no—
163C22⋊D43—81no—
164C22⋊D43—81no—
165C2×Dic43—22no—
166C2×Dic43—22no—
167C2×Dic43—22no—
168C2×Dic43—22no—
169C2×Dic43—22no—
170C2×Dic43—22no—
171C2×Dic43—22no—
172C2×Dic43—42no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—42no—
180C2×Dic43—81no—
181C2×Dic43#10214yes—
182D172—81no—
183D172—81no—
184C8×C43—81no—
185C43⋊C8—81no—
186#9204—431nomaximal, Sylow
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—41no—
194C22×C43—41no—
195C22×C43—41no—
196C22×C43—41no—
197C22×C43#38611yescharacteristic
198C22×C43C2×#10211yescharacteristic
199C22×C43#41711yescharacteristic
200C22×C43#44711yescharacteristic
201C22×C43#44811yescharacteristic
202C22×C43#48011yescharacteristic
203C22×C43#48111yescharacteristic
204C2×D43—82no—
205C2×D43—82no—
206C2×D43—81no—
207C2×D43—81no—
208C2×D43—81no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—82no—
214C4×C43—82no—
215Dic43—24no—
216Dic43—42no—
217Dic43—82no—
218Dic43—81no—
219#2618—431no—
220#2316—431no—
221#1519—431no—
222#1519—431no—
223C2×#324—431no—
224#1289—431no—
225#1289D4311yescharacteristic, complemented
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—21no—
231C2×C43—21no—
232C2×C43#187411yescharacteristic
233C2×C43#191211yescharacteristic
234C2×C43#191311yescharacteristic
235D43—161no—
236C2×#123—861no—
237C2×#121—431no—
238C2×#117—861no—
239C22×C4⋊C4—431no—
240C2×C22⋊C8—431no—
241C2×C22⋊C8C2×D4311yescharacteristic
242#398—432no—
243#396—862no—
244#394—432no—
245#389—862no—
246#389—862no—
247#386—861no—
248#380—431no—
249#380—861no—
250#380C2×D4311yescharacteristic
251#380C2×D4311yescharacteristic
252#327—862no—
253#327—862no—
254#324—862no—
255C43#920411yescharacteristic, complemented, Sylow
256C22×D4—431no—
257C22×D4—861no—
258C23×C4—431no—
259C23×C4—431no—
260C23×C4C22×D4311yescharacteristic
261C22×C8—21no—
262C22×C8—861no—
263#123—1722no—
264#123—1722no—
265#121—861no—
266#121—861no—
267#121—861no—
268#121—861no—
269#117—1722no—
270#117—1722no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—432no—
274C2×C4⋊C4—432no—
275C2×C4⋊C4—431no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4—861no—
278C2×C4⋊C4—861no—
279C2×C4⋊C4—861no—
280C2×C4⋊C4—862no—
281C2×C4⋊C4—861no—
282C2×C4⋊C4—862no—
283C2×C4⋊C4—862no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—862no—
287C2×C22⋊C4—862no—
288C2×C22⋊C4—861no—
289C2×C22⋊C4—861no—
290C2×C42—862no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—861no—
294C22⋊C8—861no—
295#95—432no—
296#95—862no—
297#95—862no—
298#95C4×D4312yes—
299#95D17212yes—
300C24—861no—
301C24D4×D4311yescharacteristic
302C2×D4—861no—
303C2×D4—861no—
304C2×D4—3441no—
305C2×D4—1721no—
306C2×D4—1721no—
307C2×D4—1721no—
308C2×D4—1721no—
309C2×D4—1721no—
310C2×D4—1721no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—81no—
314C22×C4—432no—
315C22×C4—432no—
316C22×C4—432no—
317C22×C4—432no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4—861no—
324C22×C4—861no—
325C22×C4—862no—
326C22×C4—3441no—
327C22×C4C2×C4×D4311yescharacteristic
328C22×C4C2×D17211yescharacteristic
329C22×C4#1062189811yescharacteristic
330C22×C4D4×D4311yescharacteristic
331C22×C4D4×D4311yescharacteristic
332C22×C4#1062190211yescharacteristic
333C2×C8—41no—
334C2×C8—81no—
335C2×C8—3441no—
336C2×C8—1721no—
337C4⋊C4—81no—
338C4⋊C4—81no—
339C4⋊C4—862no—
340C4⋊C4—862no—
341C4⋊C4—862no—
342C4⋊C4—862no—
343C4⋊C4—861no—
344C4⋊C4—861no—
345C4⋊C4—3442no—
346C4⋊C4—3441no—
347C4⋊C4—1724no—
348C4⋊C4—1724no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—3442no—
354C22⋊C4—1724no—
355C22⋊C4—1721no—
356C22⋊C4—1721no—
357C22⋊C4—1721no—
358C22⋊C4—1721no—
359C42—1724no—
360C23—41no—
361C23—41no—
362C23—1722no—
363C23—1722no—
364C23—1721no—
365C23—1721no—
366C23—1721no—
367C23C22⋊C4×D4311yescharacteristic
368C23#1306329511yescharacteristic
369C23#1306331011yescharacteristic
370C23D8×D4311yescharacteristic
371C23SD16×D4311yescharacteristic
372C23#1306335211yescharacteristic
373C23#1306335711yescharacteristic
374D4—3441no—
375D4—3441no—
376D4—3441no—
377D4—3441no—
378D4—3441no—
379D4—3441no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—434no—
393C2×C4—862no—
394C2×C4—862no—
395C2×C4—862no—
396C2×C4—862no—
397C2×C4—862no—
398C2×C4—862no—
399C2×C4—862no—
400C2×C4—3441no—
401C2×C4—1722no—
402C2×C4—1722no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4—1722no—
407C2×C4—1722no—
408C2×C4—1722no—
409C2×C4#1306328711yescharacteristic
410C2×C4C4×D17211yescharacteristic
411C2×C4#1306329811yescharacteristic
412C2×C4#1306330011yescharacteristic
413C8—81no—
414C8—3441no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—3442no—
426C22—3442no—
427C22—3441no—
428C22—3441no—
429C22—3441no—
430C22#1458277711yescharacteristic
431C22#102×D4311yescharacteristic
432C22#1458289911yescharacteristic
433C22#1458303411yescharacteristic
434C22#1458303911yescharacteristic
435C22#1458321411yescharacteristic
436C22#1458321911yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—82no—
443C4—864no—
444C4—3442no—
445C4—3441no—
446C4—1722no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—6881no—
454C2#1913491111yescharacteristic
455C2#1913513111yescharacteristic
456C2#1913513611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1289C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1289D43
hypocenterC43#9204
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #19137212C2semidirect
5. C2×#14582624C2semidirect
6. #19132462C2semidirect
7. C43×#1289C2semidirect
13. #14582831C4semidirect
15. #14582817C4semidirect
225. #1289D43semidirect
255. C43#9204semidirect

Maximal subgroups

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

subgroupindex
#191403402
#191372122
#191331642
#191331622
C2×#145826242
#191324622
C43×#12892
#920443