Finite Group Databasebeta

← C43×#13358 #24933375

Subgroups — C43×#13358 #24933375

Order 11008.

722 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 98 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×C43×#456C211yesmaximal, characteristic, complemented
2C2×C43×#454C211yesmaximal, characteristic
3C43×#2731C211yesmaximal, characteristic, complemented
4C2×C43×#356C211yesmaximal, characteristic, complemented
5C2×C43×#355C211yesmaximal, characteristic, complemented
6C43×#1793C211yesmaximal, characteristic, complemented
7C43×#1394C211yesmaximal, characteristic, complemented
8C2×2−1+4×C43C2211yescharacteristic
9C2×#137×C43—21no—
10C2×AGL(1,ℤ/8)×C43—21no—
11C2×C4⋊Q8×C43C2211yescharacteristic
12C2×#124×C43C2211yescharacteristic
13C43×#456—22no—
14C43×#456—22no—
15C43×#454—22no—
16C43×#454—22no—
17C2×#104×C43—21no—
18C2×#104×C43—21no—
19C2×#104×C43—21no—
20C43×#417—21no—
21C2×#101×C43C2211yescharacteristic
22C2×#101×C43C2211yescharacteristic
23C2×#101×C43C2211yescharacteristic
24C43×#396—21no—
25C43×#394—21no—
26C43×#393—21no—
27C43×#391C2211yescharacteristic
28C43×#388—21no—
29C43×#388—21no—
30C43×#387—21no—
31C43×#356—22no—
32C43×#355—22no—
332−1+4×C43—21no—
342−1+4×C43—21no—
352−1+4×C43—21no—
362−1+4×C43—42no—
372−1+4×C43D412yes—
38C2×#41×C43—21no—
39C2×#41×C43—21no—
40C2×#41×C43—21no—
41C2×#41×C43—41no—
42C22×Q8×C43—41no—
43C22×Q8×C43D411yescharacteristic
44C22×Q8×C43C2311yescharacteristic
45C22×D4×C43D411yescharacteristic
46#137×C43—24no—
47#137×C43—42no—
48AGL(1,ℤ/8)×C43—24no—
49AGL(1,ℤ/8)×C43—42no—
50C2×Q16×C43—41no—
51C2×SD16×C43—41no—
52C2×SD16×C43—41no—
53C2×D8×C43—41no—
54C2×M16×C43—21no—
55C2×M16×C43—21no—
56C2×M16×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—21no—
59C4⋊Q8×C43—21no—
60C4⋊Q8×C43—21no—
61#124×C43—21no—
62#124×C43—21no—
63#124×C43—21no—
64#124×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C42×C43D411yescharacteristic
76C2×C42×C43D411yescharacteristic
77C2×C42×C43D411yescharacteristic
78#104×C43—24no—
79#104×C43—24no—
80#104×C43—42no—
81#103×C43—41no—
82#102×C43—41no—
83#101×C43—21no—
84#101×C43—21no—
85#101×C43—21no—
86#101×C43—21no—
87#101×C43D412yes—
88#101×C43D412yes—
89#95×C43—21no—
90#95×C43—21no—
91#95×C43—21no—
92#95×C43—21no—
93#95×C43—21no—
94C24×C43—21no—
95#41×C43—22no—
96#41×C43—22no—
97#41×C43—22no—
98#41×C43—22no—
99#41×C43—22no—
100#41×C43—22no—
101#41×C43—41no—
102#41×C43—41no—
103#41×C43—41no—
104#41×C43—42no—
105#41×C43—42no—
106#41×C43—42no—
107#41×C43—42no—
108#41×C43—41no—
109#41×C43—41no—
110#41×C43—41no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×Q8×C43—41no—
117C2×Q8×C43—41no—
118C2×Q8×C43—41no—
119C2×Q8×C43—41no—
120C2×Q8×C43—42no—
121C2×Q8×C43—42no—
122C2×Q8×C43—42no—
123C2×Q8×C43—42no—
124C2×Q8×C43C2×D411yescharacteristic
125C2×Q8×C43C2×D411yescharacteristic
126C2×Q8×C43C2×D411yescharacteristic
127C2×Q8×C43#4111yescharacteristic
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—41no—
134C2×D4×C43—41no—
135C2×D4×C43—41no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—41no—
142C22×C4×C43—41no—
143C22×C4×C43—41no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147Q16×C43—44no—
148SD16×C43—44no—
149SD16×C43—44no—
150D8×C43—44no—
151M16×C43—22no—
152M16×C43—22no—
153M16×C43—41no—
154M16×C43—41no—
155M16×C43—41no—
156M16×C43—41no—
157C2×C8×C43—41no—
158C2×C8×C43—41no—
159C2×C8×C43—41no—
160C4⋊C4×C43—41no—
161C4⋊C4×C43—42no—
162C4⋊C4×C43—41no—
163C4⋊C4×C43—41no—
164C4⋊C4×C43—41no—
165C4⋊C4×C43—41no—
166C22⋊C4×C43—42no—
167C22⋊C4×C43—42no—
168C22⋊C4×C43—41no—
169C22⋊C4×C43—41no—
170C22⋊C4×C43—41no—
171C22⋊C4×C43—41no—
172C22⋊C4×C43—81no—
173C22⋊C4×C43—81no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43#12011yescharacteristic
188Q8×C43—22no—
189Q8×C43—22no—
190Q8×C43—22no—
191Q8×C43—41no—
192Q8×C43—41no—
193Q8×C43—41no—
194Q8×C43—41no—
195Q8×C43—41no—
196Q8×C43—41no—
197Q8×C43—41no—
198Q8×C43—42no—
199Q8×C43—81no—
200D4×C43—22no—
201D4×C43—22no—
202D4×C43—22no—
203D4×C43—41no—
204D4×C43—41no—
205D4×C43—41no—
206D4×C43—42no—
207D4×C43—42no—
208D4×C43—42no—
209D4×C43—81no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43#12011yescharacteristic
239C2×C4×C43#12011yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12711yescharacteristic
244C8×C43—42no—
245C8×C43—42no—
246C8×C43—81no—
247#13358C4311yesmaximal, characteristic, direct product factor, Sylow
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—42no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43—81no—
254C22×C43—81no—
255C22×C43—81no—
256C22×C43—81no—
257C22×C43—81no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43#39211yescharacteristic
261C22×C43B(4,𝔽2)11yescharacteristic
262C22×C43B(4,𝔽2)11yescharacteristic
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—42no—
270C4×C43—42no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43—81no—
275C2×#456C2×C4311yescharacteristic, complemented
276C2×#454C2×C4311yescharacteristic
277#2731C2×C4311yescharacteristic, complemented
278C2×#356C2×C4311yescharacteristic, complemented
279C2×#355C2×C4311yescharacteristic, complemented
280#1793C2×C4311yescharacteristic, complemented
281#1394C2×C4311yescharacteristic, complemented
282C2×C43—21no—
283C2×C43—21no—
284C2×C43—82no—
285C2×C43—161no—
286C2×C43#202111yescharacteristic
287C2×C43#220311yescharacteristic
288C2×C43#220411yescharacteristic
289C2×2−1+4C22×C4311yescharacteristic
290C2×#137—21no—
291C2×AGL(1,ℤ/8)—21no—
292C2×C4⋊Q8C22×C4311yescharacteristic
293C2×#124C22×C4311yescharacteristic
294#456—22no—
295#456—22no—
296#454—22no—
297#454—22no—
298C2×#104—21no—
299C2×#104—21no—
300C2×#104—21no—
301#417—21no—
302C2×#101C22×C4311yescharacteristic
303C2×#101C22×C4311yescharacteristic
304C2×#101C22×C4311yescharacteristic
305#396—21no—
306#394—21no—
307#393—21no—
308#391C22×C4311yescharacteristic
309#388—21no—
310#388—21no—
311#387—21no—
312#356—22no—
313#355—22no—
314C43#1335811yescharacteristic, direct product factor, Sylow
3152−1+4—21no—
3162−1+4—21no—
3172−1+4—21no—
3182−1+4—42no—
3192−1+4D4×C4312yes—
320C2×#41—21no—
321C2×#41—21no—
322C2×#41—21no—
323C2×#41—41no—
324C22×Q8—41no—
325C22×Q8D4×C4311yescharacteristic
326C22×Q8C23×C4311yescharacteristic
327C22×D4D4×C4311yescharacteristic
328#137—24no—
329#137—42no—
330AGL(1,ℤ/8)—24no—
331AGL(1,ℤ/8)—42no—
332C2×Q16—41no—
333C2×SD16—41no—
334C2×SD16—41no—
335C2×D8—41no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343#124—21no—
344#124—21no—
345#124—21no—
346#124—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4D4×C4311yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C42D4×C4311yescharacteristic
358C2×C42D4×C4311yescharacteristic
359C2×C42D4×C4311yescharacteristic
360#104—24no—
361#104—24no—
362#104—42no—
363#103—41no—
364#102—41no—
365#101—21no—
366#101—21no—
367#101—21no—
368#101—21no—
369#101D4×C4312yes—
370#101D4×C4312yes—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376C24—21no—
377#41—22no—
378#41—22no—
379#41—22no—
380#41—22no—
381#41—22no—
382#41—22no—
383#41—41no—
384#41—41no—
385#41—41no—
386#41—42no—
387#41—42no—
388#41—42no—
389#41—42no—
390#41—41no—
391#41—41no—
392#41—41no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—42no—
403C2×Q8—42no—
404C2×Q8—42no—
405C2×Q8—42no—
406C2×Q8C2×D4×C4311yescharacteristic
407C2×Q8C2×D4×C4311yescharacteristic
408C2×Q8C2×D4×C4311yescharacteristic
409C2×Q8#41×C4311yescharacteristic
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4C2×D4×C4311yescharacteristic
427C22×C4C2×D4×C4311yescharacteristic
428C22×C4C2×D4×C4311yescharacteristic
429Q16—44no—
430SD16—44no—
431SD16—44no—
432D8—44no—
433M16—22no—
434M16—22no—
435M16—41no—
436M16—41no—
437M16—41no—
438M16—41no—
439C2×C8—41no—
440C2×C8—41no—
441C2×C8—41no—
442C4⋊C4—41no—
443C4⋊C4—42no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C22⋊C4—42no—
449C22⋊C4—42no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4—81no—
455C22⋊C4—81no—
456C42—21no—
457C42—21no—
458C42—21no—
459C42—21no—
460C42—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23#120×C4311yescharacteristic
470Q8—22no—
471Q8—22no—
472Q8—22no—
473Q8—41no—
474Q8—41no—
475Q8—41no—
476Q8—41no—
477Q8—41no—
478Q8—41no—
479Q8—41no—
480Q8—42no—
481Q8—81no—
482D4—22no—
483D4—22no—
484D4—22no—
485D4—41no—
486D4—41no—
487D4—41no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—81no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4#120×C4311yescharacteristic
521C2×C4#120×C4311yescharacteristic
522C2×C4#121×C4311yescharacteristic
523C2×C4#121×C4311yescharacteristic
524C2×C4#121×C4311yescharacteristic
525C2×C4#127×C4311yescharacteristic
526C8—42no—
527C8—42no—
528C8—81no—
529C22—21no—
530C22—21no—
531C22—42no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22C43×#39211yescharacteristic
542C22C43×B(4,𝔽2)11yescharacteristic
543C22C43×B(4,𝔽2)11yescharacteristic
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—42no—
551C4—42no—
552C4—81no—
553C4—81no—
554C4—81no—
555C4—81no—
556C2—21no—
557C2—21no—
558C2—82no—
559C2—161no—
560C2C43×#202111yescharacteristic
561C2C43×#220311yescharacteristic
562C2C43×#220411yescharacteristic
subgroupG/H
center, socleC22×C43B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C43
prime radicalC2×C43×#454C2
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C43 ◁ C22×Q8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#456C2semidirect
3. C43×#2731C2semidirect
4. C2×C43×#356C2semidirect
5. C2×C43×#355C2semidirect
6. C43×#1793C2semidirect
7. C43×#1394C2semidirect
247. #13358C43direct (N × H)
275. C2×#456C2×C43semidirect
277. #2731C2×C43semidirect
278. C2×#356C2×C43semidirect
279. C2×#355C2×C43semidirect
280. #1793C2×C43semidirect
281. #1394C2×C43semidirect
314. C43#13358direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4562
C2×C43×#4542
C43×#27312
C2×C43×#3562
C2×C43×#3552
C43×#17932
C43×#13942
#1335843