Finite Group Databasebeta

← #24985018

Subgroups — #24985018

Order 11008.

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

normal subgroups only

This group has 550 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#19142925C211yesmaximal, characteristic
2#19134356C211yesmaximal, characteristic, complemented
3#19134352C211yesmaximal, characteristic, complemented
4#19132419C211yesmaximal, characteristic, complemented
5#19132417C211yesmaximal, characteristic, complemented
6#19132416C211yesmaximal, characteristic, complemented
7C43×#1270C211yesmaximal, characteristic, complemented
8C2×#13063307—21no—
9C2×#13063296C411yescharacteristic
10C2×C42×D43C2211yescharacteristic
11C2×(C2×D43)⋊C8—21no—
12C2×(C2×D43)⋊C8—21no—
13C2×#13063235—21no—
14C2×C8×Dic43—21no—
15#14582802C411yescharacteristic
16#14582798C411yescharacteristic
17#14582797C2211yescharacteristic
18#14582793—21no—
19#14582792—21no—
20#14582775—21no—
21#14582756C411yescharacteristic
22#14582654C2211yescharacteristic
23#14582654C2211yescharacteristic
24C43×#390C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C22⋊D43—21no—
28C22×C4×D43C2×C411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C22×C43⋊C8—21no—
32C22×C43⋊C8—21no—
33#13063307—42no—
34#13063307—42no—
35#13063296—42no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×Dic43⋊C4—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47C42×D43—42no—
48(C2×D43)⋊C8—24no—
49(C2×D43)⋊C8—24no—
50#13063235—42no—
51C8×Dic43—42no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C22×D4×C43C2×C411yescharacteristic
56C22×C8×C43—21no—
57C22×C8×C43—21no—
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C42×C43C2311yescharacteristic
62C24×C43—21no—
63C23×D43C22⋊C411yescharacteristic
64C2×D4×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C22×C4×C43—21no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C2×C22⋊D43—42no—
73C2×C22⋊D43—42no—
74C2×C22⋊D43—42no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43C22⋊C411yescharacteristic
78C22×Dic43C22⋊C411yescharacteristic
79C22×Dic43C22⋊C411yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—22no—
87C2×C4×D43—22no—
88C2×C4×D43—22no—
89C2×C4×D43—41no—
90C2×C4×D43—41no—
91C2×C4×D43—41no—
92C2×C8×C43—22no—
93C2×C8×C43—22no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C4⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—41no—
101C22⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C42×C43—41no—
104C22⋊Dic43—42no—
105C22⋊Dic43—42no—
106C22⋊Dic43—42no—
107(C2×D43)⋊C4—42no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—42no—
111C4⋊Dic43—41no—
112Dic43⋊C4—41no—
113Dic43⋊C4—41no—
114C4×Dic43—22no—
115C4×Dic43—22no—
116C4×Dic43—41no—
117C2×C43⋊C8—22no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43C2×C22⋊C411yescharacteristic
131C22×D43—21no—
132C22×D43—21no—
133C22×D43—21no—
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—21no—
137C22×D43#10412yes—
138D4×C43—81no—
139D4×C43—81no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43#13111yescharacteristic
150C2×C4×C43#13111yescharacteristic
151C2×C4×C43#13511yescharacteristic
152C2×C4×C43#13511yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
155C22⋊D43—84no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43#9912yes—
170C2×Dic43#10412yes—
171C4×D43—42no—
172C4×D43—42no—
173C4×D43—42no—
174C4×D43—42no—
175C4×D43—42no—
176C4×D43—42no—
177C8×C43—42no—
178C8×C43—42no—
179C43⋊C8—42no—
180C43⋊C8—42no—
181#7674—431nomaximal, Sylow
182C22×C43—81no—
183C22×C43—81no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43—81no—
187C22×C43—81no—
188C22×C43—81no—
189C22×C43#40811yescharacteristic
190C22×C43C2×#9911yescharacteristic
191C22×C43#41311yescharacteristic
192C22×C43#41611yescharacteristic
193C22×C43#41811yescharacteristic
194C22×C43C2×#10411yescharacteristic
195C22×C43C2×#10411yescharacteristic
196C2×D43—22no—
197C2×D43—22no—
198C2×D43—22no—
199C2×D43—41no—
200C2×D43—41no—
201C2×D43—41no—
202C2×D43—41no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—81no—
210Dic43—22no—
211Dic43—22no—
212Dic43—41no—
213Dic43—81no—
214Dic43—81no—
215#2854—431no—
216#1749—431no—
217C4×C22⋊C8—431no—
218#1271—431no—
219#1271—431no—
220#1270—431no—
221#1270D4311yescharacteristic, complemented
222C2×C43—161no—
223C2×C43#146811yescharacteristic
224C2×C43#148411yescharacteristic
225C2×C43#149411yescharacteristic
226C2×C43#150111yescharacteristic
227C2×C43#150711yescharacteristic
228C2×C43#152411yescharacteristic
229C2×C43#155311yescharacteristic
230D43—42no—
231C2×#123—861no—
232C2×#121—431no—
233C22×C42—431no—
234C2×C22⋊C8—861no—
235C2×C22⋊C8—861no—
236C2×#97—861no—
237C2×C4×C8—861no—
238#390—431no—
239#390C2×D4311yescharacteristic
240#389—431no—
241#389—431no—
242#388—861no—
243#388—861no—
244#386—861no—
245#380—431no—
246#336—431no—
247#336—431no—
248#336C2×D4311yescharacteristic
249#336C2×D4311yescharacteristic
250C43#767411yescharacteristic, complemented, Sylow
251C22×D4—861no—
252C22×D4C4×D4311yescharacteristic
253C23×C4—431no—
254C23×C4—431no—
255C23×C4—431no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—861no—
259C22×C8—861no—
260#123—1722no—
261#123—1722no—
262#121—1722no—
263C2×C4⋊C4—431no—
264C2×C4⋊C4—431no—
265C2×C4⋊C4—861no—
266C2×C4⋊C4—861no—
267C2×C4⋊C4C4×D4311yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C2×C22⋊C4—861no—
273C2×C22⋊C4—861no—
274C2×C42—431no—
275C2×C42—431no—
276C2×C42—431no—
277C2×C42—1722no—
278C2×C42C22×D4311yescharacteristic
279C22⋊C8—864no—
280C22⋊C8—864no—
281#97—1722no—
282C4×C8—1722no—
283#95—861no—
284#95—861no—
285#95—861no—
286C24—21no—
287C24—431no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—1722no—
293C2×D4—1722no—
294C2×D4—1722no—
295C22×C4—21no—
296C22×C4—431no—
297C22×C4—431no—
298C22×C4—431no—
299C22×C4—862no—
300C22×C4—862no—
301C22×C4—862no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4—861no—
307C22×C4—861no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4—1721no—
311C22×C4—1721no—
312C22×C4—1721no—
313C22×C4C2×C4×D4311yescharacteristic
314C22×C4D4×D4311yescharacteristic
315C22×C4D4×D4311yescharacteristic
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—862no—
323C2×C8—862no—
324C2×C8—1721no—
325C2×C8—1721no—
326C2×C8—1721no—
327C2×C8—1721no—
328C4⋊C4—41no—
329C4⋊C4—861no—
330C4⋊C4—861no—
331C4⋊C4—1721no—
332C4⋊C4—1722no—
333C4⋊C4—1721no—
334C4⋊C4—1721no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—1722no—
340C22⋊C4—1722no—
341C22⋊C4—1722no—
342C22⋊C4—1722no—
343C42—41no—
344C42—862no—
345C42—862no—
346C42—1721no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—432no—
355C23—861no—
356C23—861no—
357C23—861no—
358C23—861no—
359C23—861no—
360C23—861no—
361C23C22⋊C4×D4311yescharacteristic
362D4—81no—
363D4—81no—
364D4—3444no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—432no—
375C2×C4—432no—
376C2×C4—861no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—861no—
383C2×C4—1722no—
384C2×C4—1722no—
385C2×C4—1722no—
386C2×C4—1722no—
387C2×C4—1722no—
388C2×C4—1722no—
389C2×C4—1721no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4#1306333111yescharacteristic
396C2×C4#1306333311yescharacteristic
397C2×C4#1306334411yescharacteristic
398C2×C4#1306334611yescharacteristic
399C2×C4#1306334911yescharacteristic
400C2×C4#1306335211yescharacteristic
401C8—42no—
402C8—42no—
403C8—1722no—
404C8—1722no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—862no—
413C22—862no—
414C22—862no—
415C22—1721no—
416C22—1721no—
417C22—1721no—
418C22—1721no—
419C22#1458286411yescharacteristic
420C22#99×D4311yescharacteristic
421C22#1458288011yescharacteristic
422C22#1458289211yescharacteristic
423C22#1458290211yescharacteristic
424C22#104×D4311yescharacteristic
425C22#104×D4311yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—81no—
433C4—862no—
434C4—862no—
435C4—3441no—
436C4—3441no—
437C4—1721no—
438C2—161no—
439C2—1722no—
440C2#1913294011yescharacteristic
441C2#1913301011yescharacteristic
442C2#1913305211yescharacteristic
443C2#1913308311yescharacteristic
444C2#1913310911yescharacteristic
445C2#1913318011yescharacteristic
446C2#1913329711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063296C4
cosocleC2×C42×C43C23
hypercenter#1270D43
hypocenterC43#7674
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #19134356C2semidirect
3. #19134352C2semidirect
4. #19132419C2semidirect
5. #19132417C2semidirect
6. #19132416C2semidirect
7. C43×#1270C2semidirect
221. #1270D43semidirect
250. C43#7674semidirect

Maximal subgroups

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

subgroupindex
#191429252
#191343562
#191343522
#191324192
#191324172
#191324162
C43×#12702
#767443