Finite Group Databasebeta

← #24989110

Subgroups — #24989110

Order 11008.

690 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#14583509C211yesmaximal, characteristic
2#19134676C211yesmaximal, characteristic
3#19134670C211yesmaximal, characteristic
4#19133129C211yesmaximal, characteristic
5#19133128C211yesmaximal, characteristic
6#19133127C211yesmaximal, characteristic
7C43×#1511C211yesmaximal, characteristic
8#14583509—22no—
9#14583509—22no—
10#14583509—22no—
11#14583509—22no—
12C2×#13063323C411yescharacteristic, complemented
13C2×#13063318—21no—
14C2×#13063318—21no—
15C2×#13063316—21no—
16C2×#13063316C411yescharacteristic, complemented
17C2×#13063315—21no—
18C2×#13063304C2211yescharacteristic
19C2×Q8×Dic43C411yescharacteristic, complemented
20C2×#13063290C411yescharacteristic, complemented
21C2×#13063284C2211yescharacteristic
22#14582863C2211yescharacteristic
23#14582762C2211yescharacteristic
24#14582667—21no—
25#14582667—21no—
26#14582665—21no—
27#14582665—21no—
28#14582637—22no—
29#14582636—22no—
30#14582635—22no—
31C2×C22⋊Q8×C43C2211yescharacteristic
32C43×#407C2211yescharacteristic
33C43×#381C2211yescharacteristic
34C43×#328—22no—
35C22×Dic86C2×C411yescharacteristic
36C2×#10621877—21no—
37#13063323—22no—
38#13063323—22no—
39#13063318—24no—
40#13063318—24no—
41#13063318—24no—
42#13063318—24no—
43#13063316—24no—
44#13063316—24no—
45#13063316—22no—
46#13063316—22no—
47#13063315—24no—
48#13063315—24no—
49#13063304—21no—
50#13063304—21no—
51#13063304D412yes—
52#13063304D412yes—
53Q8×Dic43—22no—
54Q8×Dic43—22no—
55#13063290—22no—
56#13063290—22no—
57#13063284—21no—
58#13063284—21no—
59#13063284—21no—
60#13063284—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43C2×C411yescharacteristic
64C2×C4⋊Dic43D411yescharacteristic
65C2×C4⋊Dic43D411yescharacteristic
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×C22⋊Dic43—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43D411yescharacteristic
74C2×C22⋊Dic43D411yescharacteristic
75C2×C4×Dic43—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43C2×C411yescharacteristic
78C2×C4×Dic43C2×C411yescharacteristic
79C22⋊(C43⋊C8)—21no—
80C22⋊(C43⋊C8)—21no—
81C43⋊#95—21no—
82C43⋊#95—21no—
83C22×Q8×C43C2×C411yescharacteristic
84C23×C4×C43C2311yescharacteristic
85C2×M16×C43—21no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43D412yes—
89C22⋊Q8×C43D412yes—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43C2×C411yescharacteristic
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C22⋊C8×C43—21no—
95C22⋊C8×C43—21no—
96#95×C43—21no—
97#95×C43—21no—
98C24×C43C2×D411yescharacteristic
99C2×Q8×C43—21no—
100C2×Q8×C43—42no—
101C2×Q8×C43C22⋊C412yes—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—42no—
105C22×C4×C43—41no—
106C22×C4×C43C22×C411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×Dic43—21no—
113C22×Dic43—21no—
114C22×Dic43—41no—
115C22×Dic43C22⋊C411yescharacteristic
116C22×Dic43C22⋊C411yescharacteristic
117C22×Dic43C22⋊C411yescharacteristic
118C22×Dic43C22⋊C411yescharacteristic
119C2×Dic86—21no—
120C2×Dic86—42no—
121C2×Dic86C22⋊C412yes—
122M16×C43—42no—
123C2×C8×C43—41no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—22no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43C22⋊C412yes—
128C22⋊C4×C43—22no—
129C22⋊C4×C43—22no—
130C22⋊C4×C43—42no—
131C22⋊Dic43—22no—
132C22⋊Dic43—22no—
133C22⋊Dic43—21no—
134C22⋊Dic43—21no—
135C22⋊Dic43—21no—
136C22⋊Dic43—21no—
137C22⋊Dic43—42no—
138C4⋊Dic43—24no—
139C4⋊Dic43—24no—
140C4⋊Dic43—21no—
141C4⋊Dic43—21no—
142C4⋊Dic43—21no—
143C4⋊Dic43—21no—
144C4⋊Dic43—21no—
145C4⋊Dic43C22⋊C412yes—
146Dic43⋊C4—24no—
147Dic43⋊C4—24no—
148Dic43⋊C4—24no—
149Dic43⋊C4—24no—
150Dic43⋊C4—22no—
151Dic43⋊C4—22no—
152C4×Dic43—24no—
153C4×Dic43—24no—
154C4×Dic43—21no—
155C4×Dic43—21no—
156C4×Dic43—21no—
157C4×Dic43—21no—
158#10621877—42no—
159C2×C43⋊C8—41no—
160C23×C43—22no—
161C23×C43—41no—
162C23×C43—41no—
163C23×C43C2×C22⋊C411yescharacteristic
164C23×C43#12011yescharacteristic
165C23×C43#12011yescharacteristic
166Q8×C43—42no—
167Q8×C43—42no—
168C2×C4×C43—22no—
169C2×C4×C43—22no—
170C2×C4×C43—22no—
171C2×C4×C43—22no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—42no—
177C2×C4×C43—42no—
178C2×C4×C43—81no—
179C2×C4×C43—81no—
180C2×C4×C43—81no—
181C2×C4×C43C2×C22⋊C411yescharacteristic
182C2×C4×C43C2×C22⋊C411yescharacteristic
183C2×C4×C43#12011yescharacteristic
184C2×C4×C43#12011yescharacteristic
185C2×Dic43—21no—
186C2×Dic43—21no—
187C2×Dic43—21no—
188C2×Dic43—22no—
189C2×Dic43—21no—
190C2×Dic43—22no—
191C2×Dic43—42no—
192C2×Dic43—42no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—81no—
198C2×Dic43—81no—
199C2×Dic43—81no—
200Dic86—42no—
201Dic86—42no—
202C8×C43—81no—
203C43⋊C8—81no—
204#8521—431nomaximal, Sylow
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—82no—
214C22×C43#37911yescharacteristic
215C22×C43#41012yes—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—21no—
220C4×C43—42no—
221C4×C43—42no—
222C4×C43—161no—
223Dic43—41no—
224Dic43—41no—
225Dic43—41no—
226Dic43—41no—
227Dic43—42no—
228Dic43—42no—
229Dic43—161no—
230C2×#541—431no—
231#1822—431no—
232#1820—431no—
233#1511—431no—
234#1511—431no—
235#1511—431no—
236#1511D4311yescharacteristic
237C2×C43—22no—
238C2×C43—41no—
239C2×C43—41no—
240C2×C43#178211yescharacteristic
241C2×C43#179611yescharacteristic
242C2×C43#179611yescharacteristic
243#541—862no—
244#541—862no—
245#541—862no—
246#541—862no—
247C2×C4⋊Q8—431no—
248C2×#126—861no—
249C2×#126—861no—
250C2×#125—431no—
251C2×#125—861no—
252C2×#125—861no—
253C2×C22⋊Q8—431no—
254C2×C22⋊Q8C2×D4311yescharacteristic
255C2×C4×Q8—431no—
256C2×C4×Q8—431no—
257C2×#117—431no—
258#407—431no—
259#407C2×D4311yescharacteristic
260#381—431no—
261#381C2×D4311yescharacteristic
262#343—861no—
263#343—861no—
264#342—861no—
265#342—861no—
266#328—22no—
267#328—862no—
268#328—862no—
269#328—862no—
270C43#852111yescharacteristic, complemented, Sylow
271C22×Q8—431no—
272C22×Q8C4×D4311yescharacteristic
273C23×C4C22×D4311yescharacteristic
274C2×M16—21no—
275C2×M16—861no—
276C4⋊Q8—862no—
277C4⋊Q8—862no—
278#126—864no—
279#126—864no—
280#126—864no—
281#126—864no—
282#125—862no—
283#125—864no—
284#125—864no—
285#125—864no—
286#125—864no—
287#125—862no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—432no—
291C22⋊Q8—432no—
292C22⋊Q8—861no—
293C22⋊Q8—861no—
294C22⋊Q8D17212yes—
295C22⋊Q8C22⋊D4312yes—
296C4×Q8—862no—
297C4×Q8—862no—
298C4×Q8—862no—
299C4×Q8—862no—
300#117—861no—
301#117—861no—
302#117—861no—
303#117—861no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—431no—
306C2×C4⋊C4—431no—
307C2×C4⋊C4—431no—
308C2×C4⋊C4—861no—
309C2×C4⋊C4—861no—
310C2×C4⋊C4—861no—
311C2×C4⋊C4—861no—
312C2×C4⋊C4—861no—
313C2×C4⋊C4—861no—
314C2×C4⋊C4—861no—
315C2×C4⋊C4C4×D4311yescharacteristic
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—431no—
319C2×C22⋊C4—431no—
320C2×C22⋊C4—861no—
321C2×C22⋊C4—861no—
322C2×C42—431no—
323C2×C42—431no—
324C2×C42—861no—
325C2×C42—861no—
326C22⋊C8—21no—
327C22⋊C8—21no—
328C22⋊C8—861no—
329C22⋊C8—861no—
330#95—21no—
331#95—21no—
332#95—861no—
333#95—861no—
334C24D4×D4311yescharacteristic
335C2×Q8—21no—
336C2×Q8—42no—
337C2×Q8—432no—
338C2×Q8—861no—
339C2×Q8—1722no—
340C2×Q8(C2×D43)⋊C412yes—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—41no—
345C22×C4—431no—
346C22×C4—431no—
347C22×C4—431no—
348C22×C4—431no—
349C22×C4—861no—
350C22×C4—861no—
351C22×C4—1721no—
352C22×C4C2×C4×D4311yescharacteristic
353C22×C4C2×D17211yescharacteristic
354C22×C4D4×D4311yescharacteristic
355C22×C4D4×D4311yescharacteristic
356C22×C4D4×D4311yescharacteristic
357C22×C4C2×C22⋊D4311yescharacteristic
358M16—42no—
359M16—1722no—
360C2×C8—41no—
361C2×C8—1721no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—432no—
366C4⋊C4—864no—
367C4⋊C4—864no—
368C4⋊C4—864no—
369C4⋊C4—864no—
370C4⋊C4—864no—
371C4⋊C4—864no—
372C4⋊C4—861no—
373C4⋊C4—861no—
374C4⋊C4—861no—
375C4⋊C4—862no—
376C4⋊C4—861no—
377C4⋊C4—861no—
378C4⋊C4—862no—
379C4⋊C4(C2×D43)⋊C412yes—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—42no—
383C22⋊C4—861no—
384C22⋊C4—861no—
385C22⋊C4—862no—
386C22⋊C4—861no—
387C22⋊C4—861no—
388C22⋊C4—862no—
389C22⋊C4—1722no—
390C42—864no—
391C42—864no—
392C42—861no—
393C42—861no—
394C42—861no—
395C42—861no—
396C23—22no—
397C23—41no—
398C23—41no—
399C23C22⋊C4×D4311yescharacteristic
400C23#1306329311yescharacteristic
401C23#1306329511yescharacteristic
402Q8—42no—
403Q8—42no—
404Q8—1722no—
405Q8—1722no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—861no—
420C2×C4—861no—
421C2×C4—862no—
422C2×C4—861no—
423C2×C4—861no—
424C2×C4—862no—
425C2×C4—3441no—
426C2×C4—3441no—
427C2×C4—3441no—
428C2×C4—1722no—
429C2×C4—1722no—
430C2×C4—1721no—
431C2×C4—1721no—
432C2×C4—1721no—
433C2×C4—1721no—
434C2×C4C22⋊C4×D4311yescharacteristic
435C2×C4C2×(C2×D43)⋊C411yescharacteristic
436C2×C4#1306329311yescharacteristic
437C2×C4#1306329511yescharacteristic
438C8—81no—
439C8—3441no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—82no—
449C22#1458275411yescharacteristic
450C22#1458287112yes—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—42no—
456C4—42no—
457C4—161no—
458C4—1722no—
459C4—1722no—
460C4—1721no—
461C4—1721no—
462C4—1721no—
463C4—1721no—
464C4—6881no—
465C2—22no—
466C2—41no—
467C2—41no—
468C2#1913451111yescharacteristic
469C2#1913456711yescharacteristic
470C2#1913456911yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1511C2
socleC22×C43#379
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1511D43
hypocenterC43#8521
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
12. C2×#13063323C4semidirect
16. C2×#13063316C4semidirect
19. C2×Q8×Dic43C4semidirect
20. C2×#13063290C4semidirect
270. C43#8521semidirect

Maximal subgroups

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

subgroupindex
C2×#145835092
#191346762
#191346702
#191331292
#191331282
#191331272
C43×#15112
#852143