Finite Group Databasebeta

← C113×#16629 #43284649

Subgroups — C113×#16629 #43284649

Order 28928.

1286 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C113C211yesmaximal, characteristic
2C2×#395×C113C212yesmaximal
3C2×#391×C113C211yesmaximal, characteristic
4C113×#1444C212yesmaximal
5C113×#1443C212yesmaximal
6C113×#1442C212yesmaximal
7C113×#1441C212yesmaximal
8C113×#1441C211yesmaximal, characteristic
9C113×#1436C212yesmaximal
10C23×Q8×C113C2211yescharacteristic
11C22×C4⋊C4×C113C2212yes—
12C22×C4⋊C4×C113C2211yescharacteristic
13C22×C4⋊C4×C113C2212yes—
14C22×C4⋊C4×C113C2212yes—
15C22×C4⋊C4×C113C2211yescharacteristic
16C22×C4⋊C4×C113C2211yescharacteristic
17C22×C42×C113C2211yescharacteristic
18#398×C113—24no—
19#395×C113—28no—
20#391×C113—24no—
21C2×#95×C113C2212yes—
22C2×#95×C113C2212yes—
23C2×#95×C113C2212yes—
24C2×#95×C113C2212yes—
25C2×#95×C113C2212yes—
26C2×#95×C113C2212yes—
27C2×#95×C113C2211yescharacteristic
28C2×#95×C113C2212yes—
29C2×#95×C113C2212yes—
30C2×#95×C113C2212yes—
31C2×#95×C113C2212yes—
32C2×#95×C113C2211yescharacteristic
33C2×#95×C113C2212yes—
34C22×Q8×C113—22no—
35C22×Q8×C113—22no—
36C22×Q8×C113—41no—
37C22×Q8×C113—41no—
38C22×Q8×C113—41no—
39C22×Q8×C113—41no—
40C22×Q8×C113D414yes—
41C23×C4×C113C2312yes—
42C23×C4×C113C2312yes—
43C23×C4×C113C2311yescharacteristic
44C23×C4×C113C2311yescharacteristic
45C23×C4×C113C2312yes—
46C23×C4×C113C2312yes—
47C23×C4×C113C2312yes—
48C23×C4×C113C2312yes—
49C23×C4×C113C2311yescharacteristic
50C2×C4⋊C4×C113—24no—
51C2×C4⋊C4×C113—24no—
52C2×C4⋊C4×C113—24no—
53C2×C4⋊C4×C113—22no—
54C2×C4⋊C4×C113—24no—
55C2×C4⋊C4×C113—24no—
56C2×C4⋊C4×C113—24no—
57C2×C4⋊C4×C113—41no—
58C2×C4⋊C4×C113—41no—
59C2×C4⋊C4×C113—41no—
60C2×C4⋊C4×C113—42no—
61C2×C4⋊C4×C113—42no—
62C2×C4⋊C4×C113—42no—
63C2×C4⋊C4×C113—42no—
64C2×C4⋊C4×C113—41no—
65C2×C4⋊C4×C113—41no—
66C2×C4⋊C4×C113D414yes—
67C2×C42×C113—22no—
68C2×C42×C113—41no—
69C2×C42×C113—41no—
70#95×C113—24no—
71#95×C113—24no—
72#95×C113—24no—
73#95×C113—24no—
74#95×C113—24no—
75#95×C113—22no—
76#95×C113—24no—
77#95×C113—24no—
78#95×C113—24no—
79#95×C113—42no—
80#95×C113—42no—
81#95×C113—41no—
82#95×C113Q818yescomplemented
83C24×C113C2411yescharacteristic
84C2×Q8×C113—28no—
85C2×Q8×C113—44no—
86C2×Q8×C113—44no—
87C2×Q8×C113—44no—
88C2×Q8×C113—44no—
89C2×Q8×C113—44no—
90C2×Q8×C113—44no—
91C22×C4×C113—21no—
92C22×C4×C113—21no—
93C22×C4×C113—21no—
94C22×C4×C113—21no—
95C22×C4×C113—22no—
96C22×C4×C113—22no—
97C22×C4×C113—22no—
98C22×C4×C113—22no—
99C22×C4×C113—22no—
100C22×C4×C113—22no—
101C22×C4×C113—22no—
102C22×C4×C113—22no—
103C22×C4×C113—22no—
104C22×C4×C113—22no—
105C22×C4×C113—22no—
106C22×C4×C113—22no—
107C22×C4×C113—22no—
108C22×C4×C113—22no—
109C22×C4×C113—22no—
110C22×C4×C113—22no—
111C22×C4×C113—21no—
112C22×C4×C113—22no—
113C22×C4×C113—22no—
114C22×C4×C113—22no—
115C22×C4×C113—21no—
116C22×C4×C113—21no—
117C22×C4×C113—21no—
118C22×C4×C113—22no—
119C22×C4×C113—22no—
120C22×C4×C113—22no—
121C22×C4×C113—22no—
122C22×C4×C113—22no—
123C22×C4×C113—22no—
124C22×C4×C113—22no—
125C22×C4×C113—22no—
126C22×C4×C113—22no—
127C22×C4×C113—22no—
128C22×C4×C113—22no—
129C22×C4×C113—22no—
130C22×C4×C113—22no—
131C22×C4×C113—22no—
132C22×C4×C113—22no—
133C22×C4×C113—22no—
134C22×C4×C113—22no—
135C22×C4×C113—22no—
136C22×C4×C113—22no—
137C22×C4×C113—22no—
138C22×C4×C113—22no—
139C22×C4×C113—22no—
140C22×C4×C113C2×D412yes—
141C22×C4×C113C2×D412yes—
142C22×C4×C113C2×D414yes—
143C22×C4×C113C2×D412yes—
144C22×C4×C113C2×D412yes—
145C22×C4×C113C2×Q814yes—
146C22×C4×C113C2×Q814yes—
147C22×C4×C113C2×Q814yes—
148C22×C4×C113#4114yes—
149C22×C4×C113#4112yes—
150C4⋊C4×C113—44no—
151C4⋊C4×C113—44no—
152C4⋊C4×C113—44no—
153C4⋊C4×C113—48no—
154C4⋊C4×C113—48no—
155C4⋊C4×C113—48no—
156C42×C113—44no—
157C23×C113C22×D411yescharacteristic
158C23×C113C22×D411yescharacteristic
159C23×C113C22×Q812yes—
160C23×C113C2×#4111yescharacteristic
161C23×C113C2×#4112yes—
162C23×C113H(5,𝔽2)11yescharacteristic
163C23×C113H(5,𝔽2)11yescharacteristic
164C23×C113H(5,𝔽2)11yescharacteristic
165C23×C113H(5,𝔽2)11yescharacteristic
166C23×C1132−1+412yes—
167C23×C1132−1+412yes—
168Q8×C113—416no—
169C2×C4×C113—22no—
170C2×C4×C113—22no—
171C2×C4×C113—22no—
172C2×C4×C113—22no—
173C2×C4×C113—22no—
174C2×C4×C113—22no—
175C2×C4×C113—24no—
176C2×C4×C113—24no—
177C2×C4×C113—22no—
178C2×C4×C113—22no—
179C2×C4×C113—24no—
180C2×C4×C113—24no—
181C2×C4×C113—24no—
182C2×C4×C113—24no—
183C2×C4×C113—24no—
184C2×C4×C113—24no—
185C2×C4×C113—24no—
186C2×C4×C113—24no—
187C2×C4×C113—24no—
188C2×C4×C113—24no—
189C2×C4×C113—24no—
190C2×C4×C113—24no—
191C2×C4×C113—24no—
192C2×C4×C113—24no—
193C2×C4×C113—24no—
194C2×C4×C113—42no—
195C2×C4×C113—42no—
196C2×C4×C113—42no—
197C2×C4×C113—42no—
198C2×C4×C113—42no—
199C2×C4×C113—42no—
200C2×C4×C113—42no—
201C2×C4×C113—42no—
202C2×C4×C113—42no—
203C2×C4×C113—42no—
204C2×C4×C113—42no—
205C2×C4×C113—42no—
206C2×C4×C113—42no—
207C2×C4×C113—42no—
208C2×C4×C113—42no—
209C2×C4×C113—42no—
210C2×C4×C113—42no—
211C2×C4×C113—42no—
212C2×C4×C113—42no—
213C2×C4×C113—41no—
214C2×C4×C113—41no—
215C2×C4×C113—41no—
216C2×C4×C113—41no—
217C2×C4×C113—42no—
218C2×C4×C113—42no—
219C2×C4×C113—42no—
220C2×C4×C113—42no—
221C2×C4×C113—42no—
222C2×C4×C113—42no—
223C2×C4×C113—42no—
224C2×C4×C113—42no—
225C2×C4×C113—42no—
226C2×C4×C113—42no—
227C2×C4×C113#12114yes—
228C22×C113C2×#12111yescharacteristic
229C22×C113#53312yes—
230C22×C113#53411yescharacteristic
231C22×C113#53411yescharacteristic
232C22×C113#53411yescharacteristic
233C22×C113#53511yescharacteristic
234C22×C113#53811yescharacteristic
235C22×C113#53811yescharacteristic
236C22×C113#53912yes—
237C22×C113#54112yes—
238C22×C113#54212yes—
239C22×C113#54412yes—
240C22×C113#54412yes—
241C22×C113#54712yes—
242C22×C113#54812yes—
243C22×C113D4×Q812yes—
244C22×C113D4×Q812yes—
245C22×C113#55111yescharacteristic
246C22×C113#55412yes—
247C22×C113Q8211yescharacteristic
248C22×C113#56311yescharacteristic
249C22×C113#56312yes—
250C22×C113#56311yescharacteristic
251C4×C113—24no—
252C4×C113—44no—
253C4×C113—44no—
254C4×C113—42no—
255C4×C113—42no—
256C4×C113—44no—
257C4×C113—44no—
258C4×C113—44no—
259C4×C113—82no—
260#16629C11311yesmaximal, characteristic, direct product factor, Sylow
261C2×C113#242912yes—
262C2×C113#258611yescharacteristic
263C2×C113#261711yescharacteristic
264C2×C113#266612yes—
265C2×C113#271711yescharacteristic
266C2×C113#272012yes—
267C2×C113#272811yescharacteristic
268C2×C113#272912yes—
269C2×C113#273411yescharacteristic
270C2×C113#273411yescharacteristic
271C2×C113#283311yescharacteristic
272C2×#398C2×C11311yescharacteristic
273C2×#395C2×C11312yes—
274C2×#391C2×C11311yescharacteristic
275#1444C2×C11312yes—
276#1443C2×C11312yes—
277#1442C2×C11312yes—
278#1441C2×C11312yes—
279#1441C2×C11311yescharacteristic
280#1436C2×C11312yes—
281C113#1662911yescharacteristic, direct product factor, Sylow
282C23×Q8C22×C11311yescharacteristic
283C22×C4⋊C4C22×C11312yes—
284C22×C4⋊C4C22×C11311yescharacteristic
285C22×C4⋊C4C22×C11312yes—
286C22×C4⋊C4C22×C11312yes—
287C22×C4⋊C4C22×C11311yescharacteristic
288C22×C4⋊C4C22×C11311yescharacteristic
289C22×C42C22×C11311yescharacteristic
290#398—24no—
291#395—28no—
292#391—24no—
293C2×#95C22×C11312yes—
294C2×#95C22×C11312yes—
295C2×#95C22×C11312yes—
296C2×#95C22×C11312yes—
297C2×#95C22×C11311yescharacteristic
298C2×#95C22×C11312yes—
299C2×#95C22×C11312yes—
300C2×#95C22×C11312yes—
301C2×#95C22×C11312yes—
302C2×#95C22×C11312yes—
303C2×#95C22×C11312yes—
304C2×#95C22×C11311yescharacteristic
305C2×#95C22×C11312yes—
306C22×Q8—22no—
307C22×Q8—22no—
308C22×Q8—41no—
309C22×Q8—41no—
310C22×Q8—41no—
311C22×Q8—41no—
312C22×Q8D4×C11314yes—
313C23×C4C23×C11312yes—
314C23×C4C23×C11312yes—
315C23×C4C23×C11311yescharacteristic
316C23×C4C23×C11311yescharacteristic
317C23×C4C23×C11312yes—
318C23×C4C23×C11312yes—
319C23×C4C23×C11312yes—
320C23×C4C23×C11312yes—
321C23×C4C23×C11311yescharacteristic
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—41no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4D4×C11314yes—
339C2×C42—22no—
340C2×C42—41no—
341C2×C42—41no—
342#95—24no—
343#95—24no—
344#95—24no—
345#95—24no—
346#95—24no—
347#95—22no—
348#95—24no—
349#95—24no—
350#95—24no—
351#95—42no—
352#95—42no—
353#95—41no—
354#95Q8×C11318yescomplemented
355C24C24×C11311yescharacteristic
356C2×Q8—28no—
357C2×Q8—44no—
358C2×Q8—44no—
359C2×Q8—44no—
360C2×Q8—44no—
361C2×Q8—44no—
362C2×Q8—44no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4C2×D4×C11312yes—
413C22×C4C2×D4×C11312yes—
414C22×C4C2×D4×C11314yes—
415C22×C4C2×D4×C11312yes—
416C22×C4C2×D4×C11312yes—
417C22×C4C2×Q8×C11314yes—
418C22×C4C2×Q8×C11314yes—
419C22×C4C2×Q8×C11314yes—
420C22×C4#41×C11314yes—
421C22×C4#41×C11312yes—
422C4⋊C4—44no—
423C4⋊C4—44no—
424C4⋊C4—44no—
425C4⋊C4—48no—
426C4⋊C4—48no—
427C4⋊C4—48no—
428C42—44no—
429C23C22×D4×C11311yescharacteristic
430C23C22×D4×C11311yescharacteristic
431C23C22×Q8×C11312yes—
432C23C2×#41×C11311yescharacteristic
433C23C2×#41×C11312yes—
434C23H(5,𝔽2)×C11311yescharacteristic
435C23H(5,𝔽2)×C11311yescharacteristic
436C23H(5,𝔽2)×C11311yescharacteristic
437C23H(5,𝔽2)×C11311yescharacteristic
438C232−1+4×C11312yes—
439C232−1+4×C11312yes—
440Q8—416no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4#121×C11314yes—
500C22C2×#121×C11311yescharacteristic
501C22#533×C11312yes—
502C22#534×C11311yescharacteristic
503C22#534×C11311yescharacteristic
504C22#534×C11311yescharacteristic
505C22#535×C11311yescharacteristic
506C22#538×C11311yescharacteristic
507C22#538×C11311yescharacteristic
508C22#539×C11312yes—
509C22#541×C11312yes—
510C22#542×C11312yes—
511C22#544×C11312yes—
512C22#544×C11312yes—
513C22#547×C11312yes—
514C22#548×C11312yes—
515C22D4×Q8×C11312yes—
516C22D4×Q8×C11312yes—
517C22#551×C11311yescharacteristic
518C22#554×C11312yes—
519C22Q82×C11311yescharacteristic
520C22#563×C11311yescharacteristic
521C22#563×C11312yes—
522C22#563×C11311yescharacteristic
523C4—24no—
524C4—44no—
525C4—44no—
526C4—42no—
527C4—42no—
528C4—44no—
529C4—44no—
530C4—44no—
531C4—82no—
532C2C113×#242912yes—
533C2C113×#258611yescharacteristic
534C2C113×#261711yescharacteristic
535C2C113×#266612yes—
536C2C113×#271711yescharacteristic
537C2C113×#272012yes—
538C2C113×#272811yescharacteristic
539C2C113×#272912yes—
540C2C113×#273411yescharacteristic
541C2C113×#273411yescharacteristic
542C2C113×#283311yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C113C24
commutator, Frattini, cosocleC24C24×C113
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
82. #95×C113Q8semidirect
260. #16629C113direct (N × H)
281. C113#16629direct (N × H)
354. #95Q8×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#398×C1132
C2×#395×C1132
C2×#391×C1132
C113×#14442
C113×#14432
C113×#14422
C113×#14412
C113×#14362
#16629113