Finite Group Databasebeta

← #25014891

Subgroups — #25014891

Order 11008.

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

normal subgroups only

This group has 540 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#19138900C211yesmaximal, characteristic
2C2×#14582690C211yesmaximal, characteristic
3C2×#14582689C211yesmaximal, characteristic
4C2×#14582688C211yesmaximal, characteristic
5#19134585C211yesmaximal, characteristic
6#99×Dic43C211yesmaximal, characteristic
7C2×C43×#352C211yesmaximal, characteristic
8C2×#13063306C2211yescharacteristic
9C2×D4×Dic43C2211yescharacteristic
10C22×Dic43⋊C4C411yescharacteristic, complemented
11#14582922—21no—
12C2×#13063242C2211yescharacteristic
13C2×#13063240C2211yescharacteristic
14#14582832—21no—
15#14582827—21no—
16#14582794—21no—
17#14582762C411yescharacteristic, complemented
18#14582760C411yescharacteristic, complemented
19#14582757—21no—
20#14582757C411yescharacteristic, complemented
21C22⋊C4×Dic43—21no—
22#14582690—22no—
23#14582689—22no—
24#14582688—22no—
25#14582667—21no—
26#14582665—21no—
27C2×#123×C43C2211yescharacteristic
28C2×#100×C43C2211yescharacteristic
29C2×#99×C43C2211yescharacteristic
30C43×#352—22no—
31C23×Dic43C2×C411yescharacteristic
32C23×Dic43C2×C411yescharacteristic
33C23×Dic43D411yescharacteristic
34C2×#10621877—21no—
35#13063306—21no—
36#13063306—21no—
37#13063306—21no—
38#13063306—21no—
39D4×Dic43—41no—
40D4×Dic43—41no—
41C2×C4⋊Dic43D411yescharacteristic
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—41no—
47C2×Dic43⋊C4—41no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43C2×C411yescharacteristic
51C2×C22⋊Dic43C2×C411yescharacteristic
52C2×C22⋊Dic43D411yescharacteristic
53C2×C4×Dic43—41no—
54C2×C4×Dic43D411yescharacteristic
55Dic43⋊C8—41no—
56Dic43⋊C8—41no—
57#13063242—21no—
58#13063242—21no—
59#13063240—21no—
60#13063240D412yes—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C43⋊#95—41no—
67C22×D4×C43C2311yescharacteristic
68C23×C4×C43C2×C411yescharacteristic
69C2×M16×C43—21no—
70#123×C43—21no—
71#123×C43—21no—
72#123×C43—21no—
73#123×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43C2×C411yescharacteristic
78#100×C43—21no—
79#100×C43—21no—
80#99×C43—21no—
81#99×C43D412yes—
82C24×C43C22×C411yescharacteristic
83C24×C43C2×D411yescharacteristic
84C2×D4×C43—41no—
85C2×D4×C43—41no—
86C2×D4×C43C2×D411yescharacteristic
87C2×D4×C43C2×D411yescharacteristic
88C2×D4×C43#4111yescharacteristic
89C2×D4×C43#4111yescharacteristic
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43C2×D411yescharacteristic
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—21no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—41no—
107C22×Dic43—41no—
108C22×Dic43—41no—
109C22×Dic43—42no—
110C22×Dic43—42no—
111C22×Dic43C22⋊C411yescharacteristic
112C22×Dic43C22⋊C411yescharacteristic
113C22×Dic43C22⋊C411yescharacteristic
114C22×Dic43C22⋊C411yescharacteristic
115M16×C43—41no—
116M16×C43—41no—
117C2×C8×C43—41no—
118C4⋊C4×C43—41no—
119C4⋊C4×C43—41no—
120C22⋊C4×C43—21no—
121C22⋊C4×C43—21no—
122C22⋊C4×C43—22no—
123C22⋊C4×C43—41no—
124C22⋊C4×C43—41no—
125C22⋊C4×C43—41no—
126C22⋊Dic43—21no—
127C22⋊Dic43—21no—
128C22⋊Dic43—22no—
129C22⋊Dic43—41no—
130C22⋊Dic43—41no—
131C22⋊Dic43—41no—
132C22⋊Dic43—41no—
133C22⋊Dic43—41no—
134C4⋊Dic43—41no—
135Dic43⋊C4—42no—
136Dic43⋊C4—42no—
137Dic43⋊C4—41no—
138Dic43⋊C4—41no—
139Dic43⋊C4—41no—
140Dic43⋊C4—41no—
141C4×Dic43—21no—
142C4×Dic43—21no—
143C4×Dic43—82no—
144#10621877—41no—
145#10621877—41no—
146C2×C43⋊C8—41no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43—41no—
154C23×C43—41no—
155C23×C43C2×C22⋊C411yescharacteristic
156C23×C43C4×D411yescharacteristic
157C23×C43C4×D411yescharacteristic
158C23×C43#12111yescharacteristic
159C23×C43#12111yescharacteristic
160D4×C43—41no—
161D4×C43—41no—
162D4×C43—41no—
163D4×C43—41no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—41no—
167C2×C4×C43—42no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—81no—
174C2×C4×C43—81no—
175C2×C4×C43—81no—
176C2×C4×C43—81no—
177C2×C4×C43#12411yescharacteristic
178C2×C4×C43#12711yescharacteristic
179C2×Dic43—22no—
180C2×Dic43—21no—
181C2×Dic43—21no—
182C2×Dic43—21no—
183C2×Dic43—42no—
184C2×Dic43—42no—
185C2×Dic43—42no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—42no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—81no—
197C2×Dic43—81no—
198C2×Dic43—81no—
199C2×Dic43—81no—
200C2×Dic43—81no—
201C2×Dic43#9911yescharacteristic
202C2×Dic43#9911yescharacteristic
203C8×C43—81no—
204C43⋊C8—81no—
205#13220—431nomaximal, Sylow
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43—41no—
216C22×C43—42no—
217C22×C43—41no—
218C22×C43—41no—
219C22×C43—41no—
220C22×C43—41no—
221C22×C43—81no—
222C22×C43#39011yescharacteristic
223C22×C43C2×#9911yescharacteristic
224C22×C43#41011yescharacteristic
225C4×C43—21no—
226C4×C43—21no—
227C4×C43—81no—
228C4×C43—82no—
229C4×C43—81no—
230Dic43—21no—
231Dic43—41no—
232Dic43—41no—
233Dic43—41no—
234Dic43—81no—
235Dic43—82no—
236Dic43—81no—
237Dic43#35212yescomplemented
238#2486—431no—
239C2×#352—431no—
240C2×#352—431no—
241C2×#352—431no—
242C2×#352D4311yescharacteristic
243#1800—431no—
244C4×#99—431no—
245C2×C43—21no—
246C2×C43—21no—
247C2×C43—41no—
248C2×C43—41no—
249C2×C43—41no—
250C2×C43—41no—
251C2×C43#196411yescharacteristic
252C2×C43C2×#35211yescharacteristic
253C2×C43#212311yescharacteristic
254C2×#123—431no—
255C2×#123C2×D4311yescharacteristic
256C2×C4×D4—431no—
257C22×C4⋊C4—431no—
258#423—861no—
259C2×#100—431no—
260C2×#100C2×D4311yescharacteristic
261C2×#99—431no—
262C2×#99C2×D4311yescharacteristic
263#398—861no—
264#397—861no—
265#389—861no—
266#381—431no—
267#381—431no—
268#380—431no—
269#380—861no—
270C4×C22⋊C4—861no—
271#352—22no—
272#352—862no—
273#352—862no—
274#352—862no—
275#343—861no—
276#342—861no—
277C43#1322011yescharacteristic, complemented, Sylow
278C22×D4C22×D4311yescharacteristic
279C23×C4—431no—
280C23×C4—431no—
281C23×C4—431no—
282C23×C4C4×D4311yescharacteristic
283C2×M16—21no—
284C2×M16—861no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—861no—
290#123—861no—
291#123—861no—
292#123—861no—
293C4×D4—1721no—
294C4×D4—1721no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—431no—
297C2×C4⋊C4—861no—
298C2×C4⋊C4—861no—
299C2×C4⋊C4—861no—
300C2×C4⋊C4—861no—
301C2×C4⋊C4—1721no—
302C2×C4⋊C4—1721no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—431no—
306C2×C22⋊C4—431no—
307C2×C22⋊C4—431no—
308C2×C22⋊C4—861no—
309C2×C22⋊C4—861no—
310C2×C22⋊C4C4×D4311yescharacteristic
311C2×C42—431no—
312C2×C42—1721no—
313C4⋊C8—1721no—
314C4⋊C8—1721no—
315#100—21no—
316#100—21no—
317#100—861no—
318#100—861no—
319#99—21no—
320#99—432no—
321#99—861no—
322#99C22⋊D4312yes—
323#95—861no—
324#95—861no—
325#95—861no—
326#95—861no—
327#95—861no—
328#95—1721no—
329C24C2×C4×D4311yescharacteristic
330C24D4×D4311yescharacteristic
331C2×D4—41no—
332C2×D4—41no—
333C2×D4#1062189811yescharacteristic
334C2×D4D4×D4311yescharacteristic
335C2×D4#1062190011yescharacteristic
336C2×D4C2×C22⋊D4311yescharacteristic
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—431no—
345C22×C4—431no—
346C22×C4—431no—
347C22×C4—431no—
348C22×C4—861no—
349C22×C4—861no—
350C22×C4—861no—
351C22×C4—861no—
352C22×C4—861no—
353C22×C4—861no—
354C22×C4—861no—
355C22×C4—861no—
356C22×C4—1722no—
357C22×C4—1722no—
358C22×C4—1721no—
359C22×C4—1721no—
360C22×C4—1721no—
361C22×C4D4×D4311yescharacteristic
362M16—41no—
363M16—41no—
364M16—1721no—
365M16—1721no—
366C2×C8—41no—
367C2×C8—1721no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—1721no—
371C4⋊C4—1721no—
372C4⋊C4—1721no—
373C4⋊C4—1722no—
374C4⋊C4—1722no—
375C4⋊C4—1721no—
376C4⋊C4—1721no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—22no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—861no—
384C22⋊C4—861no—
385C22⋊C4—862no—
386C22⋊C4—1721no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C42—861no—
392C42—861no—
393C42—3442no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23C22⋊C4×D4311yescharacteristic
403C23(C22⋊D43)⋊C411yescharacteristic
404C23C4×C22⋊D4311yescharacteristic
405C23#1306329711yescharacteristic
406C23#1306329811yescharacteristic
407D4—41no—
408D4—41no—
409D4—41no—
410D4—41no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—431no—
425C2×C4—431no—
426C2×C4—862no—
427C2×C4—861no—
428C2×C4—861no—
429C2×C4—861no—
430C2×C4—3441no—
431C2×C4—3441no—
432C2×C4—3441no—
433C2×C4—3441no—
434C2×C4—3441no—
435C2×C4—1722no—
436C2×C4—1722no—
437C2×C4—1722no—
438C2×C4—1722no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4—1721no—
443C2×C4—1721no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4—1721no—
448C2×C4#1306331111yescharacteristic
449C2×C4#1306332111yescharacteristic
450C8—81no—
451C8—3441no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—42no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—81no—
468C22#1458279911yescharacteristic
469C22#99×D4311yescharacteristic
470C22#1458287111yescharacteristic
471C4—21no—
472C4—21no—
473C4—81no—
474C4—82no—
475C4—81no—
476C4—432no—
477C4—861no—
478C4—3441no—
479C4—3442no—
480C4—3441no—
481C4—1721no—
482C4—1721no—
483C4—1721no—
484C2—21no—
485C2—21no—
486C2—41no—
487C2—41no—
488C2—41no—
489C2—41no—
490C2#1913542911yescharacteristic
491C2#352×D4311yescharacteristic
492C2#1913624711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
FittingC2×C43×#352C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenterC2×#352D43
hypocenterC43#13220
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
10. C22×Dic43⋊C4C4semidirect
17. #14582762C4semidirect
18. #14582760C4semidirect
20. #14582757C4semidirect
237. Dic43#352semidirect
277. C43#13220semidirect

Maximal subgroups

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

subgroupindex
#191389002
C2×#145826902
C2×#145826892
C2×#145826882
#191345852
#99×Dic432
C2×C43×#3522
#1322043