Finite Group Databasebeta

← #24985222

Subgroups — #24985222

Order 11008.

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

normal subgroups only

This group has 506 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#19142925C211yesmaximal, characteristic
2#19134662C211yesmaximal, characteristic, complemented
3#19134662C211yesmaximal, 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—
13#14582802C411yescharacteristic
14#14582798C411yescharacteristic
15#14582797C2211yescharacteristic
16#14582793—21no—
17#14582792—21no—
18#14582775—21no—
19#14582756C411yescharacteristic
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22#14582653—21no—
23#14582653—21no—
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—42no—
49(C2×D43)⋊C8—42no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C22×D4×C43C2×C411yescharacteristic
54C22×C8×C43—21no—
55C22×C8×C43—21no—
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C42×C43C2311yescharacteristic
60C24×C43—21no—
61C23×D43C22⋊C411yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43—41no—
65C2×D4×C43—41no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C2×C22⋊D43—42no—
71C2×C22⋊D43—42no—
72C2×C22⋊D43—42no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43C22⋊C411yescharacteristic
76C22×Dic43C22⋊C411yescharacteristic
77C22×Dic43C22⋊C411yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—22no—
85C2×C4×D43—22no—
86C2×C4×D43—22no—
87C2×C4×D43—41no—
88C2×C4×D43—41no—
89C2×C4×D43—41no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C4⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—41no—
101C42×C43—41no—
102C22⋊Dic43—42no—
103C22⋊Dic43—42no—
104C22⋊Dic43—42no—
105(C2×D43)⋊C4—42no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43—42no—
109C4⋊Dic43—41no—
110Dic43⋊C4—41no—
111Dic43⋊C4—41no—
112C4×Dic43—41no—
113C4×Dic43—41no—
114C4×Dic43—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43C2×C22⋊C411yescharacteristic
129C22×D43—21no—
130C22×D43—21no—
131C22×D43—21no—
132C22×D43—21no—
133C22×D43—21no—
134C22×D43—21no—
135C22×D43#9912yes—
136D4×C43—81no—
137D4×C43—81no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43#13111yescharacteristic
148C2×C4×C43#13111yescharacteristic
149C2×C4×C43#13511yescharacteristic
150C2×C4×C43#13511yescharacteristic
151C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
153C22⋊D43—84no—
154C2×Dic43—21no—
155C2×Dic43—21no—
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—
169C4×D43—42no—
170C4×D43—42no—
171C4×D43—42no—
172C4×D43—42no—
173C4×D43—42no—
174C4×D43—42no—
175C8×C43—81no—
176C8×C43—81no—
177C43⋊C8—81no—
178C43⋊C8—81no—
179#7718—431nomaximal, Sylow
180C22×C43—81no—
181C22×C43—81no—
182C22×C43—81no—
183C22×C43—81no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43—81no—
187C22×C43#40811yescharacteristic
188C22×C43C2×#9911yescharacteristic
189C22×C43#41311yescharacteristic
190C22×C43#41611yescharacteristic
191C22×C43#41811yescharacteristic
192C22×C43#42111yescharacteristic
193C22×C43#42111yescharacteristic
194C2×D43—22no—
195C2×D43—22no—
196C2×D43—22no—
197C2×D43—41no—
198C2×D43—41no—
199C2×D43—41no—
200C2×D43—41no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—81no—
208Dic43—41no—
209Dic43—41no—
210Dic43—41no—
211Dic43—81no—
212Dic43—81no—
213#2854—431no—
214#1817—431no—
215#1817—431no—
216#1271—431no—
217#1271—431no—
218#1270—431no—
219#1270D4311yescharacteristic, complemented
220C2×C43—161no—
221C2×C43#146811yescharacteristic
222C2×C43#148211yescharacteristic
223C2×C43#149611yescharacteristic
224C2×C43#151011yescharacteristic
225C2×C43#151611yescharacteristic
226C2×C43#153511yescharacteristic
227C2×C43#155311yescharacteristic
228D43—42no—
229C2×#123—861no—
230C2×#121—431no—
231C22×C42—431no—
232C2×C22⋊C8—861no—
233C2×C22⋊C8—861no—
234#390—431no—
235#390C2×D4311yescharacteristic
236#389—431no—
237#389—431no—
238#388—861no—
239#388—861no—
240#386—861no—
241#380—431no—
242#336—431no—
243#336—431no—
244#336—861no—
245#336—861no—
246#336C2×D4311yescharacteristic
247#336C2×D4311yescharacteristic
248C43#771811yescharacteristic, complemented, Sylow
249C22×D4—861no—
250C22×D4C4×D4311yescharacteristic
251C23×C4—431no—
252C23×C4—431no—
253C23×C4—431no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—861no—
257C22×C8—861no—
258#123—1722no—
259#123—1722no—
260#121—1722no—
261C2×C4⋊C4—431no—
262C2×C4⋊C4—431no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4C4×D4311yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—861no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C2×C42—431no—
273C2×C42—431no—
274C2×C42—431no—
275C2×C42—1722no—
276C2×C42C22×D4311yescharacteristic
277C22⋊C8—1722no—
278C22⋊C8—1722no—
279#95—861no—
280#95—861no—
281#95—861no—
282C24—21no—
283C24—431no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—1722no—
289C2×D4—1722no—
290C2×D4—1722no—
291C22×C4—21no—
292C22×C4—431no—
293C22×C4—431no—
294C22×C4—431no—
295C22×C4—862no—
296C22×C4—862no—
297C22×C4—862no—
298C22×C4—861no—
299C22×C4—861no—
300C22×C4—861no—
301C22×C4—861no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4—1721no—
307C22×C4—1721no—
308C22×C4—1721no—
309C22×C4C2×C4×D4311yescharacteristic
310C22×C4D4×D4311yescharacteristic
311C22×C4D4×D4311yescharacteristic
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—1721no—
319C2×C8—1721no—
320C2×C8—1721no—
321C2×C8—1721no—
322C2×C8—1721no—
323C2×C8—1721no—
324C4⋊C4—41no—
325C4⋊C4—861no—
326C4⋊C4—861no—
327C4⋊C4—1721no—
328C4⋊C4—1722no—
329C4⋊C4—1721no—
330C4⋊C4—1721no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—1722no—
336C22⋊C4—1722no—
337C22⋊C4—1722no—
338C22⋊C4—1722no—
339C42—41no—
340C42—1721no—
341C42—1721no—
342C42—1721no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—432no—
351C23—861no—
352C23—861no—
353C23—861no—
354C23—861no—
355C23—861no—
356C23—861no—
357C23C22⋊C4×D4311yescharacteristic
358D4—81no—
359D4—81no—
360D4—3444no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—861no—
371C2×C4—861no—
372C2×C4—861no—
373C2×C4—861no—
374C2×C4—861no—
375C2×C4—861no—
376C2×C4—861no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—1722no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4—1722no—
384C2×C4—1722no—
385C2×C4—1721no—
386C2×C4—1721no—
387C2×C4—1721no—
388C2×C4—1721no—
389C2×C4—1721no—
390C2×C4—1721no—
391C2×C4#1306333111yescharacteristic
392C2×C4#1306333311yescharacteristic
393C2×C4#1306334411yescharacteristic
394C2×C4#1306334611yescharacteristic
395C2×C4#1306334911yescharacteristic
396C2×C4#1306335211yescharacteristic
397C8—81no—
398C8—81no—
399C8—3441no—
400C8—3441no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—862no—
409C22—862no—
410C22—862no—
411C22—1721no—
412C22—1721no—
413C22—1721no—
414C22—1721no—
415C22#1458286411yescharacteristic
416C22#99×D4311yescharacteristic
417C22#1458288011yescharacteristic
418C22#1458289211yescharacteristic
419C22#1458290211yescharacteristic
420C22#1458291411yescharacteristic
421C22#1458291411yescharacteristic
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—81no—
429C4—3441no—
430C4—3441no—
431C4—1721no—
432C4—1721no—
433C4—1721no—
434C2—161no—
435C2—1722no—
436C2#1913294011yescharacteristic
437C2#1913300011yescharacteristic
438C2#1913306211yescharacteristic
439C2#1913312211yescharacteristic
440C2#1913314811yescharacteristic
441C2#1913322311yescharacteristic
442C2#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#7718
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. #19134662C2semidirect
3. #19134662C2semidirect
4. #19132419C2semidirect
5. #19132417C2semidirect
6. #19132416C2semidirect
7. C43×#1270C2semidirect
219. #1270D43semidirect
248. C43#7718semidirect

Maximal subgroups

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

subgroupindex
#191429252
#191346622
#191324192
#191324172
#191324162
C43×#12702
#771843