Finite Group Databasebeta

← #24988239

Subgroups — #24988239

Order 11008.

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

normal subgroups only

This group has 750 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
1C2×#14583590C211yesmaximal, characteristic
2C4×#13063241C211yesmaximal, characteristic
3#19133198C211yesmaximal, characteristic, complemented
4#19133196C211yesmaximal, characteristic, complemented
5#19133042C211yesmaximal, characteristic, complemented
6#19132935C211yesmaximal, characteristic
7C43×#1491C211yesmaximal, characteristic, complemented
8#14583590—22no—
9#14583590—22no—
10#14583590—22no—
11#14583590—22no—
12C2×#13063319—21no—
13C2×#13063317C2211yescharacteristic
14C2×#13063315—21no—
15C2×#13063310—21no—
16C2×#13063301C411yescharacteristic
17C2×#13063301C411yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063283C411yescharacteristic
20C2×#13063282—21no—
21C2×C4⋊C4×D43C411yescharacteristic
22#14582956C2211yescharacteristic
23C2×#13063241—21no—
24C4×#10621877C2211yescharacteristic
25#14582667—21no—
26#14582640—22no—
27#14582640—22no—
28Q8⋊(C43⋊C8)—22no—
29#14582622—21no—
30#14582622—21no—
31C2×C4×Q8×C43C2211yescharacteristic
32C43×#432C2211yescharacteristic
33C4×M16×C43C2211yescharacteristic
34C43×Q8⋊C8—22no—
35C22×D172D411yescharacteristic
36C22×C4×D43—21no—
37C22×C4×D43C2×C411yescharacteristic
38C22×C4×D43C2×C411yescharacteristic
39C2×#10621877—21no—
40#13063319—24no—
41#13063319—24no—
42#13063317—21no—
43#13063317—21no—
44#13063317D412yes—
45#13063317D412yes—
46#13063315—24no—
47#13063315—24no—
48#13063310—24no—
49#13063310—24no—
50#13063301—22no—
51#13063301—22no—
52#13063301—22no—
53#13063301—22no—
54C4×D172—21no—
55C4×D172—21no—
56C4×D172—21no—
57C4×D172—21no—
58#13063283—22no—
59#13063283—22no—
60#13063282—24no—
61#13063282—24no—
62C2×C4⋊Dic43C2×C411yescharacteristic
63C2×C4⋊Dic43C2×C411yescharacteristic
64C2×C4⋊Dic43D411yescharacteristic
65C2×Dic43⋊C4—21no—
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4—21no—
70C4⋊C4×D43—22no—
71C4⋊C4×D43—22no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4D411yescharacteristic
76C2×(C2×D43)⋊C4D411yescharacteristic
77C2×C4×Dic43—21no—
78C4⋊(C43⋊C8)—21no—
79#13063241—24no—
80C22⋊(C43⋊C8)—21no—
81#13063236—21no—
82#13063236—21no—
83C4×C43⋊C8—21no—
84C22×Q8×C43C2×C411yescharacteristic
85C2×M16×C43—21no—
86C4×Q8×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43D412yes—
89C4×Q8×C43D412yes—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43C2×C411yescharacteristic
92C2×C42×C43—21no—
93C2×C42×C43C2311yescharacteristic
94C4⋊C8×C43—21no—
95C22⋊C8×C43—21no—
96#97×C43—21no—
97#97×C43—21no—
98C4×C8×C43—21no—
99C23×D43C22⋊C411yescharacteristic
100C23×D43C22⋊C411yescharacteristic
101C2×Q8×C43—21no—
102C2×Q8×C43—42no—
103C2×Q8×C43C22⋊C412yes—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43C22×C411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×Dic43—21no—
110C22×Dic43—21no—
111C22×Dic43C22⋊C411yescharacteristic
112C22×Dic43C22⋊C411yescharacteristic
113C2×D172—21no—
114C2×D172—21no—
115C2×D172—22no—
116C2×D172—41no—
117C2×C4×D43—24no—
118C2×C4×D43—21no—
119C2×C4×D43—21no—
120C2×C4×D43—21no—
121C2×C4×D43—21no—
122C2×C4×D43—42no—
123C2×C4×D43—42no—
124C2×C4×D43—42no—
125C2×C4×D43—42no—
126M16×C43—22no—
127M16×C43—41no—
128C2×C8×C43—41no—
129C2×C8×C43—41no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—22no—
132C4⋊C4×C43—22no—
133C4⋊C4×C43C22⋊C412yes—
134C42×C43—22no—
135C42×C43—22no—
136C42×C43C2×D411yescharacteristic
137C42×C43C2×D411yescharacteristic
138C42×C43C2×D411yescharacteristic
139C42×C43C2×D411yescharacteristic
140(C2×D43)⋊C4—24no—
141(C2×D43)⋊C4—24no—
142(C2×D43)⋊C4—24no—
143(C2×D43)⋊C4—21no—
144(C2×D43)⋊C4—21no—
145(C2×D43)⋊C4—21no—
146(C2×D43)⋊C4—21no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43—21no—
150C4⋊Dic43—21no—
151C4⋊Dic43C22⋊C412yes—
152C4⋊Dic43C22⋊C412yes—
153Dic43⋊C4—24no—
154Dic43⋊C4—24no—
155Dic43⋊C4—24no—
156Dic43⋊C4—22no—
157Dic43⋊C4—22no—
158Dic43⋊C4—22no—
159Dic43⋊C4—22no—
160C4×Dic43—24no—
161#10621877—22no—
162#10621877—41no—
163C2×C43⋊C8—41no—
164C2×C43⋊C8—41no—
165C23×C43C2×C22⋊C411yescharacteristic
166C22×D43—21no—
167C22×D43—21no—
168C22×D43—21no—
169C22×D43—21no—
170C22×D43—21no—
171C22×D43—41no—
172C22×D43—41no—
173C22×D43—41no—
174C22×D43—41no—
175C22×D43#10412yes—
176Q8×C43—24no—
177Q8×C43—42no—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—22no—
181C2×C4×C43—22no—
182C2×C4×C43—22no—
183C2×C4×C43—41no—
184C2×C4×C43—42no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43C2×C22⋊C411yescharacteristic
188C2×C4×C43C2×C22⋊C411yescharacteristic
189C2×C4×C43#12011yescharacteristic
190C2×C4×C43#12011yescharacteristic
191C2×C4×C43#12011yescharacteristic
192C2×C4×C43#12011yescharacteristic
193C2×Dic43—21no—
194C2×Dic43—22no—
195C2×Dic43—21no—
196C2×Dic43—22no—
197C2×Dic43—42no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202D172—42no—
203D172—42no—
204C4×D43—42no—
205C4×D43—42no—
206C4×D43—48no—
207C4×D43—42no—
208C4×D43—42no—
209C8×C43—42no—
210C8×C43—81no—
211C43⋊C8—42no—
212C43⋊C8—81no—
213#8371—431nomaximal, Sylow
214C22×C43—21no—
215C22×C43—21no—
216C22×C43#37911yescharacteristic
217C22×C43C2×#10411yescharacteristic
218C22×C43#42111yescharacteristic
219C2×D43—22no—
220C2×D43—42no—
221C2×D43—41no—
222C2×D43—41no—
223C2×D43—42no—
224C2×D43—41no—
225C2×D43—41no—
226C2×D43—41no—
227C2×D43—81no—
228C2×D43—81no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—42no—
235C4×C43—42no—
236C4×C43#41312yes—
237Dic43—42no—
238Dic43—41no—
239Dic43—41no—
240Dic43—42no—
241C2×#552—431no—
242C4×#100—431no—
243#1528—431no—
244#1528—431no—
245#1491—431no—
246#1491D4311yescharacteristic, complemented
247#1466—431no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43#178511yescharacteristic
251C2×C43#178911yescharacteristic
252C2×C43#179611yescharacteristic
253D43—42no—
254D43—81no—
255#552—862no—
256#552—862no—
257#552—862no—
258#552—862no—
259C2×#126—861no—
260C2×#125—431no—
261C2×#125—861no—
262C2×#123—861no—
263C2×C22⋊Q8—431no—
264C2×C22⋊Q8—431no—
265C2×C4×Q8C2×D4311yescharacteristic
266C2×C4×D4—431no—
267C2×#117—431no—
268C2×#117—861no—
269C22×C4⋊C4—431no—
270#432—431no—
271#432C2×D4311yescharacteristic
272C2×#100—861no—
273C4×M16—431no—
274C4×M16C2×D4311yescharacteristic
275#343—861no—
276#330—862no—
277#330—862no—
278Q8⋊C8—22no—
279Q8⋊C8—862no—
280#323—861no—
281#323—861no—
282C43#837111yescharacteristic, complemented, Sylow
283C22×Q8C4×D4311yescharacteristic
284C22×D4—431no—
285C23×C4—431no—
286C23×C4—431no—
287C23×C4—861no—
288C2×M16—21no—
289C2×M16—861no—
290#126—864no—
291#126—864no—
292#125—432no—
293#125—432no—
294#125—864no—
295#125—864no—
296#125—861no—
297#125—861no—
298#123—864no—
299#123—864no—
300C22⋊Q8—862no—
301C22⋊Q8—862no—
302C22⋊Q8—862no—
303C22⋊Q8—862no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8D17212yes—
307C4×Q8C22⋊D4312yes—
308C4×D4—861no—
309C4×D4—861no—
310C4×D4—861no—
311C4×D4—861no—
312#117—864no—
313#117—864no—
314#117—862no—
315#117—862no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—431no—
318C2×C4⋊C4—431no—
319C2×C4⋊C4—431no—
320C2×C4⋊C4—862no—
321C2×C4⋊C4—861no—
322C2×C4⋊C4—861no—
323C2×C4⋊C4—861no—
324C2×C4⋊C4—861no—
325C2×C4⋊C4—861no—
326C2×C4⋊C4—862no—
327C2×C4⋊C4C4×D4311yescharacteristic
328C2×C22⋊C4—431no—
329C2×C22⋊C4—431no—
330C2×C22⋊C4—861no—
331C2×C22⋊C4—861no—
332C2×C22⋊C4—861no—
333C2×C42—21no—
334C2×C42—861no—
335C2×C42C22×D4311yescharacteristic
336C4⋊C8—21no—
337C4⋊C8—861no—
338#100—864no—
339C22⋊C8—21no—
340C22⋊C8—861no—
341#97—21no—
342#97—21no—
343#97—861no—
344#97—861no—
345C4×C8—21no—
346C4×C8—861no—
347C24—431no—
348C24—431no—
349C2×Q8—21no—
350C2×Q8—42no—
351C2×Q8(C2×D43)⋊C412yes—
352C2×D4—862no—
353C2×D4—861no—
354C2×D4—861no—
355C2×D4—1721no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—431no—
359C22×C4—431no—
360C22×C4—864no—
361C22×C4—861no—
362C22×C4—861no—
363C22×C4—861no—
364C22×C4—861no—
365C22×C4—861no—
366C22×C4—861no—
367C22×C4—1722no—
368C22×C4—1722no—
369C22×C4—1722no—
370C22×C4—1722no—
371C22×C4C2×C4×D4311yescharacteristic
372C22×C4D4×D4311yescharacteristic
373C22×C4D4×D4311yescharacteristic
374M16—22no—
375M16—41no—
376M16—862no—
377M16—1721no—
378C2×C8—41no—
379C2×C8—41no—
380C2×C8—1721no—
381C2×C8—1721no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—432no—
386C4⋊C4—432no—
387C4⋊C4—864no—
388C4⋊C4—864no—
389C4⋊C4—864no—
390C4⋊C4—861no—
391C4⋊C4—861no—
392C4⋊C4—861no—
393C4⋊C4—862no—
394C4⋊C4—862no—
395C4⋊C4—861no—
396C4⋊C4—862no—
397C4⋊C4—862no—
398C4⋊C4(C2×D43)⋊C412yes—
399C22⋊C4—864no—
400C22⋊C4—864no—
401C22⋊C4—864no—
402C22⋊C4—861no—
403C22⋊C4—861no—
404C22⋊C4—861no—
405C22⋊C4—861no—
406C42—22no—
407C42—22no—
408C42—864no—
409C42C2×D17211yescharacteristic
410C42D4×D4311yescharacteristic
411C42D4×D4311yescharacteristic
412C42C2×C22⋊D4311yescharacteristic
413C23—432no—
414C23—861no—
415C23—861no—
416C23—861no—
417C23—861no—
418C23—861no—
419C23—1721no—
420C23—1721no—
421C23—1721no—
422C23—1721no—
423C23C22⋊C4×D4311yescharacteristic
424Q8—24no—
425Q8—42no—
426D4—1722no—
427D4—1722no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—861no—
438C2×C4—862no—
439C2×C4—862no—
440C2×C4—861no—
441C2×C4—1722no—
442C2×C4—1722no—
443C2×C4—1728no—
444C2×C4—1722no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4—1722no—
448C2×C4—1722no—
449C2×C4—1721no—
450C2×C4—1721no—
451C2×C4C22⋊C4×D4311yescharacteristic
452C2×C4C2×(C2×D43)⋊C411yescharacteristic
453C2×C4#1306329311yescharacteristic
454C2×C4#1306329311yescharacteristic
455C2×C4#1306329511yescharacteristic
456C2×C4#1306329511yescharacteristic
457C8—42no—
458C8—81no—
459C8—3441no—
460C8—1722no—
461C22—21no—
462C22—21no—
463C22—862no—
464C22—3441no—
465C22—3441no—
466C22—1722no—
467C22—1722no—
468C22—1721no—
469C22—1721no—
470C22—1721no—
471C22—1721no—
472C22—1721no—
473C22#1458275411yescharacteristic
474C22#104×D4311yescharacteristic
475C22#1458291411yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—42no—
482C4—42no—
483C4—1721no—
484C4—1721no—
485C4—1722no—
486C4—1722no—
487C4#1458288112yes—
488C2—21no—
489C2—21no—
490C2—3441no—
491C2—1722no—
492C2#1913452111yescharacteristic
493C2#1913453711yescharacteristic
494C2#1913456711yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1491C2
socleC22×C43#379
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenter#1491D43
hypocenterC43#8371
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
3. #19133198C2semidirect
4. #19133196C2semidirect
5. #19133042C2semidirect
7. C43×#1491C2semidirect
246. #1491D43semidirect
282. C43#8371semidirect

Maximal subgroups

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

subgroupindex
C2×#145835902
C4×#130632412
#191331982
#191331962
#191330422
#191329352
C43×#14912
#837143