Finite Group Databasebeta

← #25014901

Subgroups — #25014901

Order 11008.

628 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 91 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#19139482C211yesmaximal, characteristic
2C2×#14582690C211yesmaximal, characteristic, complemented
3C2×#14582688C211yesmaximal, characteristic, complemented
4C2×#14582686C211yesmaximal, characteristic
5#19134585C211yesmaximal, characteristic, complemented
6#99×Dic43C211yesmaximal, characteristic, complemented
7C2×C43×AΣL(1,𝔽16)C211yesmaximal, characteristic
8C2×#13063306C2211yescharacteristic
9C2×D4×Dic43C2211yescharacteristic
10C22×C22⋊Dic43C411yescharacteristic, complemented
11#14582922—21no—
12C2×#13063242C2211yescharacteristic
13C2×#13063240C2211yescharacteristic
14#14582822—21no—
15#14582813—21no—
16#14582793—21no—
17#14582779—21no—
18#14582760C411yescharacteristic, complemented
19#14582757C411yescharacteristic, complemented
20#14582755C411yescharacteristic, complemented
21C22⋊C4×Dic43—21no—
22#14582690—22no—
23#14582688—22no—
24#14582686—22no—
25#14582667—21no—
26#14582665—21no—
27C2×#120×C43C2211yescharacteristic
28C2×#100×C43C2211yescharacteristic
29C2×#99×C43C2211yescharacteristic
30C43×AΣL(1,𝔽16)—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×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—41no—
51C2×C22⋊Dic43—41no—
52C2×C22⋊Dic43C2×C411yescharacteristic
53C2×C22⋊Dic43C2×C411yescharacteristic
54C2×C22⋊Dic43D411yescharacteristic
55C2×C4×Dic43—41no—
56C2×C4×Dic43D411yescharacteristic
57Dic43⋊C8—41no—
58Dic43⋊C8—41no—
59#13063242—21no—
60#13063242—21no—
61#13063240—21no—
62#13063240D412yes—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C43⋊#95—41no—
67C25×C43C2×C411yescharacteristic
68C22×D4×C43—21no—
69C22×D4×C43C2311yescharacteristic
70C2×M16×C43—21no—
71#120×C43—21no—
72#120×C43—21no—
73#120×C43—21no—
74#120×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×C43—21no—
83C24×C43—21no—
84C24×C43—21no—
85C24×C43—42no—
86C24×C43—41no—
87C24×C43—41no—
88C24×C43—81no—
89C24×C43C22×C411yescharacteristic
90C24×C43C2×D411yescharacteristic
91C2×D4×C43—41no—
92C2×D4×C43—41no—
93C2×D4×C43—42no—
94C2×D4×C43—41no—
95C2×D4×C43—41no—
96C2×D4×C43—81no—
97C2×D4×C43C2×D411yescharacteristic
98C2×D4×C43C2×D411yescharacteristic
99C2×D4×C43#4111yescharacteristic
100C2×D4×C43#4111yescharacteristic
101C22×C4×C43—21no—
102C22×C4×C43—41no—
103C22×C4×C43C2×D411yescharacteristic
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—21no—
109C22×Dic43—21no—
110C22×Dic43—21no—
111C22×Dic43—21no—
112C22×Dic43—41no—
113C22×Dic43—41no—
114C22×Dic43—41no—
115C22×Dic43—81no—
116C22×Dic43—81no—
117C22×Dic43C22⋊C411yescharacteristic
118C22×Dic43C22⋊C411yescharacteristic
119C22×Dic43C22⋊C411yescharacteristic
120C22×Dic43C22⋊C411yescharacteristic
121M16×C43—41no—
122M16×C43—41no—
123C2×C8×C43—41no—
124C22⋊C4×C43—21no—
125C22⋊C4×C43—21no—
126C22⋊C4×C43—22no—
127C22⋊C4×C43—41no—
128C22⋊C4×C43—41no—
129C22⋊C4×C43—41no—
130C22⋊Dic43—21no—
131C22⋊Dic43—21no—
132C22⋊Dic43—22no—
133C22⋊Dic43—41no—
134C22⋊Dic43—41no—
135C22⋊Dic43—41no—
136C22⋊Dic43—42no—
137C22⋊Dic43—42no—
138C22⋊Dic43—41no—
139C22⋊Dic43—41no—
140C22⋊Dic43—41no—
141C22⋊Dic43—41no—
142C22⋊Dic43—81no—
143C4⋊Dic43—41no—
144Dic43⋊C4—41no—
145Dic43⋊C4—41no—
146Dic43⋊C4—81no—
147C4×Dic43—21no—
148C4×Dic43—21no—
149C4×Dic43—82no—
150#10621877—41no—
151#10621877—41no—
152C2×C43⋊C8—41no—
153C23×C43—21no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—22no—
158C23×C43—41no—
159C23×C43—41no—
160C23×C43—41no—
161C23×C43—41no—
162C23×C43—41no—
163C23×C43—41no—
164C23×C43—41no—
165C23×C43—42no—
166C23×C43—42no—
167C23×C43—41no—
168C23×C43—41no—
169C23×C43—41no—
170C23×C43—81no—
171C23×C43—81no—
172C23×C43—82no—
173C23×C43—82no—
174C23×C43—84no—
175C23×C43—81no—
176C23×C43—81no—
177C23×C43C2×C22⋊C411yescharacteristic
178C23×C43C4×D411yescharacteristic
179C23×C43C4×D411yescharacteristic
180C23×C43#12111yescharacteristic
181C23×C43#12111yescharacteristic
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—41no—
186D4×C43—82no—
187D4×C43—82no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—41no—
191C2×C4×C43—42no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—81no—
195C2×C4×C43—81no—
196C2×C4×C43#12411yescharacteristic
197C2×C4×C43#12711yescharacteristic
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43—21no—
201C2×Dic43—41no—
202C2×Dic43—42no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—42no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—81no—
214C2×Dic43—81no—
215C2×Dic43—81no—
216C2×Dic43—81no—
217C2×Dic43—81no—
218C2×Dic43—81no—
219C2×Dic43—81no—
220C2×Dic43#9911yescharacteristic
221C2×Dic43#9911yescharacteristic
222C8×C43—81no—
223C43⋊C8—81no—
224#13222—431nomaximal, Sylow
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—41no—
232C22×C43—41no—
233C22×C43—41no—
234C22×C43—41no—
235C22×C43—42no—
236C22×C43—42no—
237C22×C43—42no—
238C22×C43—41no—
239C22×C43—41no—
240C22×C43—41no—
241C22×C43—41no—
242C22×C43—42no—
243C22×C43—81no—
244C22×C43—81no—
245C22×C43—81no—
246C22×C43—82no—
247C22×C43—82no—
248C22×C43—82no—
249C22×C43—82no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43#39011yescharacteristic
253C22×C43C2×#9911yescharacteristic
254C22×C43#41011yescharacteristic
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—81no—
258C4×C43—82no—
259Dic43—21no—
260Dic43—21no—
261Dic43—41no—
262Dic43—41no—
263Dic43—41no—
264Dic43—81no—
265Dic43—82no—
266Dic43—81no—
267#2534—431no—
268C2×#352—431no—
269C2×#352—431no—
270C2×AΣL(1,𝔽16)—431no—
271C2×AΣL(1,𝔽16)D4311yescharacteristic
272#1800—431no—
273C4×#99—431no—
274C2×C43—21no—
275C2×C43—21no—
276C2×C43—41no—
277C2×C43—41no—
278C2×C43—41no—
279C2×C43—41no—
280C2×C43—82no—
281C2×C43#196411yescharacteristic
282C2×C43#212011yescharacteristic
283C2×C43#212111yescharacteristic
284C2×#123—431no—
285C2×#120C2×D4311yescharacteristic
286C2×C4×D4—431no—
287C22×C22⋊C4—431no—
288#423—861no—
289C2×#100—431no—
290C2×#100C2×D4311yescharacteristic
291C2×#99—431no—
292C2×#99C2×D4311yescharacteristic
293#396—861no—
294#394—861no—
295#388—861no—
296#386—861no—
297#381—431no—
298#380—431no—
299#379—431no—
300C4×C22⋊C4—861no—
301#352—862no—
302#352—862no—
303AΣL(1,𝔽16)—22no—
304AΣL(1,𝔽16)—862no—
305#343—861no—
306#342—861no—
307C43#1322211yescharacteristic, complemented, Sylow
308C25C4×D4311yescharacteristic
309C22×D4—21no—
310C22×D4C22×D4311yescharacteristic
311C23×C4—431no—
312C23×C4—431no—
313C23×C4—431no—
314C2×M16—21no—
315C2×M16—861no—
316#123—861no—
317#123—861no—
318#123—861no—
319#123—861no—
320#120—21no—
321#120—21no—
322#120—21no—
323#120—21no—
324C4×D4—1721no—
325C4×D4—1721no—
326C2×C4⋊C4—431no—
327C2×C4⋊C4—861no—
328C2×C4⋊C4—861no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—431no—
332C2×C22⋊C4—431no—
333C2×C22⋊C4—431no—
334C2×C22⋊C4—861no—
335C2×C22⋊C4—861no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4—861no—
340C2×C22⋊C4—1721no—
341C2×C22⋊C4—1721no—
342C2×C22⋊C4C4×D4311yescharacteristic
343C2×C42—431no—
344C2×C42—1721no—
345C4⋊C8—1721no—
346C4⋊C8—1721no—
347#100—21no—
348#100—21no—
349#100—861no—
350#100—861no—
351#99—21no—
352#99—432no—
353#99—861no—
354#99C22⋊D4312yes—
355#95—861no—
356#95—861no—
357#95—861no—
358#95—1721no—
359C24—21no—
360C24—21no—
361C24—21no—
362C24—41no—
363C24—42no—
364C24—41no—
365C24—81no—
366C24C2×C4×D4311yescharacteristic
367C24D4×D4311yescharacteristic
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—42no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—81no—
374C2×D4#1062189811yescharacteristic
375C2×D4D4×D4311yescharacteristic
376C2×D4#1062190011yescharacteristic
377C2×D4C2×C22⋊D4311yescharacteristic
378C22×C4—21no—
379C22×C4—41no—
380C22×C4—431no—
381C22×C4—431no—
382C22×C4—431no—
383C22×C4—431no—
384C22×C4—861no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—861no—
388C22×C4—861no—
389C22×C4—861no—
390C22×C4—861no—
391C22×C4—861no—
392C22×C4—3441no—
393C22×C4—3441no—
394C22×C4—1721no—
395C22×C4—1721no—
396C22×C4—1721no—
397C22×C4D4×D4311yescharacteristic
398M16—41no—
399M16—41no—
400M16—1721no—
401M16—1721no—
402C2×C8—41no—
403C2×C8—1721no—
404C4⋊C4—3441no—
405C4⋊C4—1721no—
406C4⋊C4—1721no—
407C4⋊C4—1721no—
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—22no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—861no—
415C22⋊C4—861no—
416C22⋊C4—862no—
417C22⋊C4—3441no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C22⋊C4—1721no—
421C22⋊C4—1721no—
422C22⋊C4—1722no—
423C22⋊C4—1721no—
424C22⋊C4—1722no—
425C22⋊C4—1721no—
426C22⋊C4—1721no—
427C42—861no—
428C42—861no—
429C42—3442no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—42no—
443C23—42no—
444C23—41no—
445C23—41no—
446C23—41no—
447C23—81no—
448C23—81no—
449C23—82no—
450C23—82no—
451C23—84no—
452C23—81no—
453C23—81no—
454C23C22⋊C4×D4311yescharacteristic
455C23(C22⋊D43)⋊C411yescharacteristic
456C23C4×C22⋊D4311yescharacteristic
457C23#1306329711yescharacteristic
458C23#1306329811yescharacteristic
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—82no—
464D4—82no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—431no—
474C2×C4—431no—
475C2×C4—861no—
476C2×C4—861no—
477C2×C4—861no—
478C2×C4—3441no—
479C2×C4—3441no—
480C2×C4—3441no—
481C2×C4—3441no—
482C2×C4—3441no—
483C2×C4—3441no—
484C2×C4—3441no—
485C2×C4—1721no—
486C2×C4—1722no—
487C2×C4—1722no—
488C2×C4—1721no—
489C2×C4—1721no—
490C2×C4—1721no—
491C2×C4—1721no—
492C2×C4—1721no—
493C2×C4—1721no—
494C2×C4—1721no—
495C2×C4—1721no—
496C2×C4—1721no—
497C2×C4#1306331111yescharacteristic
498C2×C4#1306332111yescharacteristic
499C8—81no—
500C8—3441no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—42no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—82no—
523C22—82no—
524C22—82no—
525C22—82no—
526C22—81no—
527C22—81no—
528C22#1458279911yescharacteristic
529C22#99×D4311yescharacteristic
530C22#1458287111yescharacteristic
531C4—21no—
532C4—21no—
533C4—81no—
534C4—82no—
535C4—861no—
536C4—861no—
537C4—3441no—
538C4—3442no—
539C4—3441no—
540C4—1721no—
541C4—1721no—
542C4—1721no—
543C2—21no—
544C2—21no—
545C2—41no—
546C2—41no—
547C2—41no—
548C2—41no—
549C2—82no—
550C2#1913542911yescharacteristic
551C2#1913623311yescharacteristic
552C2#1913623811yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
FittingC2×C43×AΣL(1,𝔽16)C2
socleC22×C43C2×#99
prime radicalC2×#120×C43C22
cosocleC22×D4×C43C23
hypercenterC2×AΣL(1,𝔽16)D43
hypocenterC43#13222
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. C2×#14582690C2semidirect
3. C2×#14582688C2semidirect
5. #19134585C2semidirect
6. #99×Dic43C2semidirect
10. C22×C22⋊Dic43C4semidirect
18. #14582760C4semidirect
19. #14582757C4semidirect
20. #14582755C4semidirect
307. C43#13222semidirect

Maximal subgroups

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

subgroupindex
#191394822
C2×#145826902
C2×#145826882
C2×#145826862
#191345852
#99×Dic432
C2×C43×AΣL(1,𝔽16)2
#1322243