Finite Group Databasebeta

← C41×#11174 #23787375

Subgroups — C41×#11174 #23787375

Order 10496.

1406 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C41C211yesmaximal, characteristic
2C41×#2308C211yesmaximal, characteristic
3C2×C41×#386C211yesmaximal, characteristic
4C2×C41×#342C212yesmaximal, complemented
5C41×C22⋊#95C212yesmaximal, complemented
6C23×D4×C41C2211yescharacteristic
7C24×C4×C41C2211yescharacteristic
8C22×C22⋊C4×C41—21no—
9C22×C22⋊C4×C41C2212yes—
10C22×C22⋊C4×C41C2211yescharacteristic
11C22×C22⋊C4×C41C2212yes—
12C2×#99×C41—22no—
13C2×#99×C41—24no—
14C41×#386—22no—
15C41×#386—24no—
16C41×#386C414yescomplemented
17C41×#381—21no—
18C41×#379—21no—
19C2×#95×C41—21no—
20C2×#95×C41—24no—
21C41×#342—24no—
22C25×C41D411yescharacteristic
23C25×C41C2311yescharacteristic
24C22×D4×C41—22no—
25C22×D4×C41—22no—
26C22×D4×C41—22no—
27C22×D4×C41—22no—
28C22×D4×C41—22no—
29C22×D4×C41—22no—
30C22×D4×C41C2×C412yes—
31C22×D4×C41D412yes—
32C23×C4×C41—21no—
33C23×C4×C41—22no—
34C23×C4×C41—21no—
35C23×C4×C41—22no—
36C23×C4×C41—21no—
37C23×C4×C41—22no—
38C23×C4×C41—44no—
39C23×C4×C41C2×C412yes—
40C23×C4×C41D411yescharacteristic
41C23×C4×C41D414yes—
42C2×C22⋊C4×C41—22no—
43C2×C22⋊C4×C41—22no—
44C2×C22⋊C4×C41—22no—
45C2×C22⋊C4×C41—22no—
46C2×C22⋊C4×C41—22no—
47C2×C22⋊C4×C41—22no—
48C2×C22⋊C4×C41—24no—
49C2×C22⋊C4×C41—22no—
50C2×C22⋊C4×C41—22no—
51C2×C22⋊C4×C41—21no—
52C2×C22⋊C4×C41—22no—
53C2×C22⋊C4×C41—22no—
54C2×C22⋊C4×C41—22no—
55C2×C22⋊C4×C41—22no—
56C2×C22⋊C4×C41—22no—
57C2×C22⋊C4×C41—22no—
58C2×C22⋊C4×C41—22no—
59C2×C22⋊C4×C41—44no—
60C2×C22⋊C4×C41C2×C412yes—
61C2×C22⋊C4×C41D414yes—
62#99×C41—28no—
63#95×C41—24no—
64#95×C41—24no—
65#95×C41—48no—
66C24×C41—21no—
67C24×C41—22no—
68C24×C41—22no—
69C24×C41—21no—
70C24×C41—42no—
71C24×C41—42no—
72C24×C41—42no—
73C24×C41—42no—
74C24×C41C22⋊C412yes—
75C24×C41C22×C411yescharacteristic
76C24×C41C2×D411yescharacteristic
77C24×C41C2×D412yes—
78C24×C41C2×D411yescharacteristic
79C24×C41C2×D412yes—
80C24×C41#4112yes—
81C24×C41#4112yes—
82C24×C41#4112yes—
83C24×C41#4112yes—
84C2×D4×C41—22no—
85C2×D4×C41—22no—
86C2×D4×C41—24no—
87C2×D4×C41—24no—
88C2×D4×C41—22no—
89C2×D4×C41—24no—
90C2×D4×C41—24no—
91C2×D4×C41—22no—
92C2×D4×C41—42no—
93C2×D4×C41—42no—
94C2×D4×C41—42no—
95C2×D4×C41—42no—
96C2×D4×C41—42no—
97C2×D4×C41—42no—
98C2×D4×C41—42no—
99C2×D4×C41—42no—
100C22×C4×C41—28no—
101C22×C4×C41—24no—
102C22×C4×C41—22no—
103C22×C4×C41—24no—
104C22×C4×C41—21no—
105C22×C4×C41—22no—
106C22×C4×C41—22no—
107C22×C4×C41—21no—
108C22×C4×C41—22no—
109C22×C4×C41—24no—
110C22×C4×C41—24no—
111C22×C4×C41—24no—
112C22×C4×C41—24no—
113C22×C4×C41—44no—
114C22×C4×C41—44no—
115C22×C4×C41—48no—
116C22×C4×C41—44no—
117C22×C4×C41—42no—
118C22×C4×C41—41no—
119C22×C4×C41—42no—
120C22×C4×C41—41no—
121C22×C4×C41—44no—
122C22×C4×C41—44no—
123C22×C4×C41—44no—
124C22×C4×C41—42no—
125C22×C4×C41—44no—
126C22×C4×C41—42no—
127C22×C4×C41—42no—
128C22×C4×C41—42no—
129C22×C4×C41—42no—
130C22×C4×C41C22⋊C412yes—
131C22⋊C4×C41—24no—
132C22⋊C4×C41—24no—
133C22⋊C4×C41—24no—
134C22⋊C4×C41—48no—
135C22⋊C4×C41—41no—
136C22⋊C4×C41—42no—
137C22⋊C4×C41—42no—
138C22⋊C4×C41—41no—
139C22⋊C4×C41—42no—
140C22⋊C4×C41—42no—
141C22⋊C4×C41—42no—
142C22⋊C4×C41—42no—
143C22⋊C4×C41—82no—
144C22⋊C4×C41—82no—
145C23×C41—24no—
146C23×C41—22no—
147C23×C41—24no—
148C23×C41—22no—
149C23×C41—22no—
150C23×C41—22no—
151C23×C41—22no—
152C23×C41—41no—
153C23×C41—41no—
154C23×C41—42no—
155C23×C41—41no—
156C23×C41—41no—
157C23×C41—44no—
158C23×C41—42no—
159C23×C41—44no—
160C23×C41—44no—
161C23×C41—44no—
162C23×C41—42no—
163C23×C41—42no—
164C23×C41—48no—
165C23×C41—42no—
166C23×C41—42no—
167C23×C41—42no—
168C23×C41—42no—
169C23×C41—81no—
170C23×C41—81no—
171C23×C41—84no—
172C23×C41C2×C22⋊C411yescharacteristic
173C23×C41#11711yescharacteristic
174C23×C41#11711yescharacteristic
175C23×C41C4×D412yes—
176C23×C41C4×D412yes—
177C23×C41#12011yescharacteristic
178C23×C41#12011yescharacteristic
179C23×C41#12112yes—
180C23×C41#12112yes—
181C23×C41#12112yes—
182C23×C41#12112yes—
183C23×C41#12312yes—
184C23×C41#12311yescharacteristic
185C23×C41#12312yes—
186C23×C41#12312yes—
187C23×C41#12311yescharacteristic
188C23×C41#12312yes—
189C23×C41#12412yes—
190C23×C41#12412yes—
191C23×C41#12612yes—
192C23×C41#12612yes—
193D4×C41—44no—
194D4×C41—44no—
195D4×C41—44no—
196D4×C41—44no—
197C2×C4×C41—24no—
198C2×C4×C41—28no—
199C2×C4×C41—22no—
200C2×C4×C41—22no—
201C2×C4×C41—22no—
202C2×C4×C41—42no—
203C2×C4×C41—44no—
204C2×C4×C41—48no—
205C2×C4×C41—44no—
206C2×C4×C41—42no—
207C2×C4×C41—42no—
208C2×C4×C41—42no—
209C2×C4×C41—44no—
210C2×C4×C41—42no—
211C2×C4×C41—42no—
212C2×C4×C41—48no—
213C2×C4×C41—48no—
214C2×C4×C41—42no—
215C2×C4×C41—44no—
216C2×C4×C41—44no—
217C2×C4×C41—44no—
218C2×C4×C41—44no—
219C2×C4×C41—82no—
220C2×C4×C41—82no—
221C2×C4×C41—84no—
222C2×C4×C41—84no—
223C2×C4×C41—84no—
224#11174C4111yesmaximal, characteristic, direct product factor, Sylow
225C22×C41—21no—
226C22×C41—22no—
227C22×C41—22no—
228C22×C41—21no—
229C22×C41—21no—
230C22×C41—22no—
231C22×C41—21no—
232C22×C41—22no—
233C22×C41—24no—
234C22×C41—24no—
235C22×C41—24no—
236C22×C41—24no—
237C22×C41—24no—
238C22×C41—24no—
239C22×C41—41no—
240C22×C41—41no—
241C22×C41—42no—
242C22×C41—41no—
243C22×C41—41no—
244C22×C41—42no—
245C22×C41—42no—
246C22×C41—42no—
247C22×C41—42no—
248C22×C41—42no—
249C22×C41—44no—
250C22×C41—42no—
251C22×C41—42no—
252C22×C41—42no—
253C22×C41—82no—
254C22×C41—84no—
255C22×C41—84no—
256C22×C41#38111yescharacteristic
257C22×C41#38611yescharacteristic
258C22×C41#38611yescharacteristic
259C22×C41#38812yes—
260C22×C41#38812yes—
261C22×C41#39412yes—
262C22×C41#39412yes—
263C22×C41#39712yes—
264C22×C41#39712yes—
265C22×C41B(4,𝔽2)12yes—
266C22×C41#45812yes—
267C4×C41—44no—
268C4×C41—42no—
269C4×C41—82no—
270C4×C41—84no—
271C4×C41—84no—
272C22×#99C2×C4111yescharacteristic
273#2308C2×C4111yescharacteristic
274C2×#386C2×C4111yescharacteristic
275C2×#342C2×C4112yescomplemented
276C22⋊#95C2×C4112yescomplemented
277C2×C41—21no—
278C2×C41—22no—
279C2×C41—21no—
280C2×C41—22no—
281C2×C41—22no—
282C2×C41—22no—
283C2×C41—22no—
284C2×C41—82no—
285C2×C41#144011yescharacteristic
286C2×C41#188911yescharacteristic
287C2×C41#189011yescharacteristic
288C2×C41#204414yes—
289C23×D4C22×C4111yescharacteristic
290C24×C4C22×C4111yescharacteristic
291C22×C22⋊C4—21no—
292C22×C22⋊C4C22×C4112yes—
293C22×C22⋊C4C22×C4111yescharacteristic
294C22×C22⋊C4C22×C4112yes—
295C2×#99—22no—
296C2×#99—24no—
297#386—22no—
298#386—24no—
299#386C4×C4114yescomplemented
300#381—21no—
301#379—21no—
302C2×#95—21no—
303C2×#95—24no—
304#342—24no—
305C41#1117411yescharacteristic, direct product factor, Sylow
306C25D4×C4111yescharacteristic
307C25C23×C4111yescharacteristic
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4C2×C4×C4112yes—
315C22×D4D4×C4112yes—
316C23×C4—21no—
317C23×C4—22no—
318C23×C4—21no—
319C23×C4—22no—
320C23×C4—21no—
321C23×C4—22no—
322C23×C4—44no—
323C23×C4C2×C4×C4112yes—
324C23×C4D4×C4111yescharacteristic
325C23×C4D4×C4114yes—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4C2×C4×C4112yes—
345C2×C22⋊C4D4×C4114yes—
346#99—28no—
347#95—24no—
348#95—24no—
349#95—48no—
350C24—21no—
351C24—22no—
352C24—22no—
353C24—21no—
354C24—42no—
355C24—42no—
356C24—42no—
357C24—42no—
358C24C22⋊C4×C4112yes—
359C24C22×C4×C4111yescharacteristic
360C24C2×D4×C4111yescharacteristic
361C24C2×D4×C4112yes—
362C24C2×D4×C4111yescharacteristic
363C24C2×D4×C4112yes—
364C24#41×C4112yes—
365C24#41×C4112yes—
366C24#41×C4112yes—
367C24#41×C4112yes—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—22no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C22×C4—28no—
385C22×C4—24no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—44no—
398C22×C4—44no—
399C22×C4—48no—
400C22×C4—44no—
401C22×C4—42no—
402C22×C4—41no—
403C22×C4—42no—
404C22×C4—41no—
405C22×C4—44no—
406C22×C4—44no—
407C22×C4—44no—
408C22×C4—42no—
409C22×C4—44no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4C22⋊C4×C4112yes—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C22⋊C4—48no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—42no—
422C22⋊C4—41no—
423C22⋊C4—42no—
424C22⋊C4—42no—
425C22⋊C4—42no—
426C22⋊C4—42no—
427C22⋊C4—82no—
428C22⋊C4—82no—
429C23—24no—
430C23—22no—
431C23—24no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—22no—
436C23—41no—
437C23—41no—
438C23—42no—
439C23—41no—
440C23—44no—
441C23—41no—
442C23—44no—
443C23—44no—
444C23—44no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—48no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23—81no—
454C23—81no—
455C23—84no—
456C23C2×C22⋊C4×C4111yescharacteristic
457C23#117×C4111yescharacteristic
458C23#117×C4111yescharacteristic
459C23C4×D4×C4112yes—
460C23C4×D4×C4112yes—
461C23#120×C4111yescharacteristic
462C23#120×C4111yescharacteristic
463C23#121×C4112yes—
464C23#121×C4112yes—
465C23#121×C4112yes—
466C23#121×C4112yes—
467C23#123×C4112yes—
468C23#123×C4111yescharacteristic
469C23#123×C4112yes—
470C23#123×C4112yes—
471C23#123×C4111yescharacteristic
472C23#123×C4112yes—
473C23#124×C4112yes—
474C23#124×C4112yes—
475C23#126×C4112yes—
476C23#126×C4112yes—
477D4—44no—
478D4—44no—
479D4—44no—
480D4—44no—
481C2×C4—24no—
482C2×C4—28no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—48no—
489C2×C4—44no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—44no—
494C2×C4—42no—
495C2×C4—48no—
496C2×C4—42no—
497C2×C4—48no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—84no—
504C2×C4—84no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4—84no—
508C22—24no—
509C22—24no—
510C22—24no—
511C22—24no—
512C22—24no—
513C22—24no—
514C22—21no—
515C22—22no—
516C22—22no—
517C22—21no—
518C22—21no—
519C22—22no—
520C22—21no—
521C22—22no—
522C22—41no—
523C22—41no—
524C22—42no—
525C22—41no—
526C22—41no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—44no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—82no—
537C22—84no—
538C22—84no—
539C22C41×#38111yescharacteristic
540C22C41×#38611yescharacteristic
541C22C41×#38611yescharacteristic
542C22C41×#38812yes—
543C22C41×#38812yes—
544C22C41×#39412yes—
545C22C41×#39412yes—
546C22C41×#39712yes—
547C22C41×#39712yes—
548C22C41×B(4,𝔽2)12yes—
549C22C41×#45812yes—
550C4—44no—
551C4—42no—
552C4—82no—
553C4—84no—
554C4—84no—
555C2—21no—
556C2—22no—
557C2—21no—
558C2—22no—
559C2—22no—
560C2—22no—
561C2—22no—
562C2—82no—
563C2C41×#144011yescharacteristic
564C2C41×#188911yescharacteristic
565C2C41×#189011yescharacteristic
566C2C41×#204414yes—
subgroupG/H
center, socleC23×C41#120
commutatorC24C22×C4×C41
Frattini, cosocleC25C23×C41
prime radicalC23×D4×C41C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C25×C41 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C41×#342C2semidirect
5. C41×C22⋊#95C2semidirect
16. C41×#386C4semidirect
224. #11174C41direct (N × H)
275. C2×#342C2×C41semidirect
276. C22⋊#95C2×C41semidirect
299. #386C4×C41semidirect
305. C41#11174direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#99×C412
C41×#23082
C2×C41×#3862
C2×C41×#3422
C41×C22⋊#952
#1117441