Finite Group Databasebeta

← #25007071

Subgroups — #25007071

Order 11008.

700 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 87 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#19139526C211yesmaximal, characteristic
2#19132922C211yesmaximal, characteristic, complemented
3#19132618C212yesmaximal, complemented
4#19132591C212yesmaximal, complemented
5C2×C43×#342C211yesmaximal, characteristic, complemented
6C2×#13063308—21no—
7C2×#13063299C411yescharacteristic, complemented
8C2×#13063294—21no—
9#14582863—21no—
10#14582835C411yescharacteristic, complemented
11#14582835C2211yescharacteristic
12#14582808C411yescharacteristic, complemented
13#14582808C2211yescharacteristic
14#14582799—21no—
15#14582799—21no—
16C4×C22⋊Dic43C411yescharacteristic, complemented
17#14582623—21no—
18#14582623C2212yes—
19C22×C22⋊C4×C43—21no—
20C22×C22⋊C4×C43C2211yescharacteristic
21C43×#342—21no—
22C43×#342C2212yes—
23C22×D172C2×C411yescharacteristic, complemented
24C22×C22⋊D43—21no—
25C22×C22⋊D43—21no—
26C22×C22⋊D43—21no—
27C2×#10621877—41no—
28#13063308—44no—
29#13063299—41no—
30#13063299—41no—
31#13063294—44no—
32C2×C4⋊Dic43C2×C411yescharacteristic, complemented
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×C4×Dic43—21no—
42C22⋊(C43⋊C8)—22no—
43C22⋊(C43⋊C8)—41no—
44C43⋊#95C2×C411yescharacteristic, complemented
45C43⋊#95C2×C411yescharacteristic, complemented
46C25×C43D411yescharacteristic
47C23×C4×C43—41no—
48C23×C4×C43C2×C411yescharacteristic
49C23×C4×C43D411yescharacteristic
50C2×C22⋊C4×C43—24no—
51C2×C22⋊C4×C43—22no—
52C2×C22⋊C4×C43—41no—
53C2×C22⋊C4×C43—41no—
54C2×C22⋊C4×C43—41no—
55C2×C22⋊C4×C43—42no—
56C2×C22⋊C4×C43C2×C411yescharacteristic
57C2×C22⋊C4×C43D411yescharacteristic
58C2×C22⋊C4×C43D411yescharacteristic
59C2×C22⋊C4×C43C2311yescharacteristic
60C24×C43—21no—
61C24×C43—21no—
62C24×C43—22no—
63C24×C43—21no—
64C24×C43—21no—
65C24×C43—42no—
66C24×C43—81no—
67C24×C43C22⋊C411yescharacteristic
68C24×C43C22⋊C411yescharacteristic
69C24×C43C2×D411yescharacteristic
70C23×D43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—42no—
76C22×C4×C43—44no—
77C22×C4×C43—42no—
78C22×C4×C43—81no—
79C22×C4×C43—82no—
80C22×C4×C43—82no—
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22⋊C411yescharacteristic
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C2×C22⋊D43—42no—
86C2×C22⋊D43—42no—
87C2×C22⋊D43—42no—
88C2×C22⋊D43—42no—
89C2×C22⋊D43—41no—
90C2×C22⋊D43—41no—
91C2×C22⋊D43—42no—
92C2×C22⋊D43—41no—
93C2×C22⋊D43—41no—
94C2×C22⋊D43—81no—
95C2×C22⋊D43—81no—
96C22×Dic43—21no—
97C22×Dic43—21no—
98C22×Dic43—21no—
99C2×D172—41no—
100C2×D172—81no—
101C22⋊C4×C43—24no—
102C22⋊C4×C43—41no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—44no—
107C22⋊C4×C43—42no—
108C22⋊Dic43—24no—
109C22⋊Dic43—42no—
110C22⋊Dic43—42no—
111(C2×D43)⋊C4—42no—
112(C2×D43)⋊C4—42no—
113(C2×D43)⋊C4—42no—
114C4⋊Dic43—41no—
115Dic43⋊C4—42no—
116Dic43⋊C4—42no—
117C4×Dic43—81no—
118#10621877—82no—
119C2×C43⋊C8—42no—
120C23×C43—22no—
121C23×C43—22no—
122C23×C43—22no—
123C23×C43—22no—
124C23×C43—22no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43—21no—
129C23×C43—21no—
130C23×C43—21no—
131C23×C43—41no—
132C23×C43—42no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43—42no—
138C23×C43—81no—
139C23×C43—81no—
140C23×C43—84no—
141C23×C43—82no—
142C23×C43—82no—
143C23×C43#9911yescharacteristic
144C23×C43#9911yescharacteristic
145C23×C43#10412yes—
146C23×C43C2×C22⋊C411yescharacteristic
147C23×C43AGL(1,ℤ/8)11yescharacteristic
148C23×C43#13711yescharacteristic
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—41no—
152C22×D43—41no—
153C22×D43—41no—
154C22×D43—41no—
155C22×D43—41no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—42no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—44no—
166C2×C4×C43—81no—
167C2×C4×C43—81no—
168C2×C4×C43—81no—
169C2×C4×C43—88no—
170C2×C4×C43—82no—
171C2×C4×C43—82no—
172C22⋊D43—84no—
173C22⋊D43—82no—
174C22⋊D43—82no—
175C22⋊D43—82no—
176C22⋊D43—82no—
177C2×Dic43—22no—
178C2×Dic43—22no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186D172—82no—
187C43⋊C8—82no—
188#11757—431nomaximal, Sylow
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—22no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—42no—
200C22×C43—42no—
201C22×C43—42no—
202C22×C43—41no—
203C22×C43—41no—
204C22×C43—44no—
205C22×C43—44no—
206C22×C43—41no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43—81no—
211C22×C43—81no—
212C22×C43—82no—
213C22×C43—82no—
214C22×C43#35312yes—
215C22×C43C2×#9911yescharacteristic
216C22×C43#41711yescharacteristic
217C22×C43C2×#10411yescharacteristic
218C2×D43—81no—
219C2×D43—81no—
220C2×D43—81no—
221C2×D43—81no—
222C2×D43—81no—
223C2×D43—81no—
224C2×D43—81no—
225C4×C43—41no—
226C4×C43—41no—
227C4×C43—41no—
228C4×C43—41no—
229C4×C43—84no—
230Dic43—42no—
231Dic43—42no—
232Dic43—81no—
233#2539—431no—
234C2×#342D4311yescharacteristic, complemented
235#1462—431no—
236#1352—432no—
237#1343—432no—
238C2×C43—21no—
239C2×C43—21no—
240C2×C43—22no—
241C2×C43—41no—
242C2×C43—41no—
243C2×C43—42no—
244C2×C43—41no—
245C2×C43#150411yescharacteristic
246C2×C43#212111yescharacteristic
247C2×C43C2×#35311yescharacteristic
248D43—161no—
249C2×#123—861no—
250C2×#121—431no—
251C2×#120—861no—
252C22×C22⋊C4—21no—
253C22×C22⋊C4C2×D4311yescharacteristic
254#407—861no—
255#399—431no—
256#399—431no—
257#392—431no—
258#392—431no—
259#390—861no—
260#390—861no—
261C4×C22⋊C4—431no—
262#342—21no—
263#342C2×D4312yes—
264#323—432no—
265#323—861no—
266C43#1175711yescharacteristic, complemented, Sylow
267C25C22⋊D4311yescharacteristic
268C22×D4—431no—
269C22×D4—861no—
270C22×D4—861no—
271C22×D4—861no—
272C23×C4—41no—
273C23×C4C4×D4311yescharacteristic
274C23×C4D17211yescharacteristic
275C2×M16—1721no—
276#123—1724no—
277#121—1721no—
278#121—1721no—
279#120—1724no—
280C2×C4⋊C4—431no—
281C2×C4⋊C4—861no—
282C2×C4⋊C4—861no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—41no—
286C2×C22⋊C4—41no—
287C2×C22⋊C4—41no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4—861no—
290C2×C22⋊C4—861no—
291C2×C22⋊C4—861no—
292C2×C22⋊C4—861no—
293C2×C22⋊C4—861no—
294C2×C22⋊C4—861no—
295C2×C22⋊C4C4×D4311yescharacteristic
296C2×C22⋊C4D17211yescharacteristic
297C2×C22⋊C4C22⋊D4311yescharacteristic
298C2×C22⋊C4C22×D4311yescharacteristic
299C2×C42—861no—
300C22⋊C8—862no—
301C22⋊C8—1721no—
302#95—431no—
303#95—431no—
304C24—21no—
305C24—21no—
306C24—22no—
307C24—21no—
308C24—21no—
309C24—42no—
310C24—81no—
311C24—861no—
312C24(C2×D43)⋊C411yescharacteristic
313C24(C2×D43)⋊C411yescharacteristic
314C24C2×C22⋊D4311yescharacteristic
315C2×D4—3441no—
316C2×D4—3441no—
317C2×D4—3441no—
318C2×D4—1721no—
319C2×D4—1722no—
320C2×D4—1722no—
321C2×D4—1722no—
322C2×D4—1722no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4—1722no—
326C2×D4—1721no—
327C2×D4—1721no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—42no—
333C22×C4—44no—
334C22×C4—42no—
335C22×C4—81no—
336C22×C4—82no—
337C22×C4—82no—
338C22×C4—861no—
339C22×C4—861no—
340C22×C4—861no—
341C22×C4(C2×D43)⋊C411yescharacteristic
342C22×C4(C2×D43)⋊C411yescharacteristic
343C22×C4C2×C4×D4311yescharacteristic
344C22×C4C2×D17211yescharacteristic
345M16—3442no—
346C2×C8—1722no—
347C4⋊C4—1721no—
348C4⋊C4—1722no—
349C4⋊C4—1722no—
350C22⋊C4—24no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—44no—
356C22⋊C4—42no—
357C22⋊C4—864no—
358C22⋊C4—1722no—
359C22⋊C4—1722no—
360C22⋊C4—1722no—
361C22⋊C4—1722no—
362C22⋊C4—1722no—
363C42—3441no—
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—22no—
373C23—21no—
374C23—21no—
375C23—41no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—42no—
382C23—81no—
383C23—81no—
384C23—84no—
385C23—82no—
386C23—82no—
387C23—1721no—
388C23—1721no—
389C23—1721no—
390C23—1721no—
391C23—1721no—
392C23—1721no—
393C23—1721no—
394C23#1306323911yescharacteristic
395C23#1306323911yescharacteristic
396C23#1306325312yes—
397C23C2×(C2×D43)⋊C411yescharacteristic
398C23#1306335111yescharacteristic
399C23#1306335611yescharacteristic
400D4—3442no—
401D4—3442no—
402D4—3442no—
403D4—3444no—
404D4—3442no—
405D4—3442no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—44no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—88no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—862no—
423C2×C4—862no—
424C2×C4—1721no—
425C2×C4—1721no—
426C2×C4—1721no—
427C2×C4—1721no—
428C2×C4—1721no—
429C2×C4—1721no—
430C2×C4—1721no—
431C8—3442no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—22no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—41no—
446C22—41no—
447C22—44no—
448C22—44no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—81no—
454C22—81no—
455C22—82no—
456C22—82no—
457C22—3441no—
458C22—3441no—
459C22—3441no—
460C22—3441no—
461C22—3441no—
462C22—3441no—
463C22—3441no—
464C22#1458269112yes—
465C22C2×#1306323911yescharacteristic
466C22#1458289811yescharacteristic
467C22C2×#1306325311yescharacteristic
468C4—41no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—84no—
473C4—3441no—
474C4—1722no—
475C4—1722no—
476C2—21no—
477C2—21no—
478C2—22no—
479C2—41no—
480C2—41no—
481C2—42no—
482C2—41no—
483C2—6881no—
484C2#1913309711yescharacteristic
485C2#1913623911yescharacteristic
486C2C2×#1458269111yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC2×C43×#342C2
socleC22×C43C2×#99
prime radical#19139526C2
cosocleC2×C22⋊C4×C43C23
hypercenterC2×#342D43
hypocenterC43#11757
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
2. #19132922C2semidirect
3. #19132618C2semidirect
4. #19132591C2semidirect
5. C2×C43×#342C2semidirect
7. C2×#13063299C4semidirect
10. #14582835C4semidirect
12. #14582808C4semidirect
16. C4×C22⋊Dic43C4semidirect
23. C22×D172C2×C4semidirect
32. C2×C4⋊Dic43C2×C4semidirect
44. C43⋊#95C2×C4semidirect
45. C43⋊#95C2×C4semidirect
234. C2×#342D43semidirect
266. C43#11757semidirect

Maximal subgroups

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

subgroupindex
#191395262
#191329222
#191326182
#191325912
C2×C43×#3422
#1175743