Finite Group Databasebeta

← C113×#16630 #43284650

Subgroups — C113×#16630 #43284650

Order 28928.

1310 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#395×C113C211yesmaximal, characteristic
2C2×#391×C113C211yesmaximal, characteristic
3C113×#1446C212yesmaximal
4C113×#1446C212yesmaximal
5C113×#1445C212yesmaximal
6C113×#1441C212yesmaximal
7C113×#1441C212yesmaximal
8C113×#1441C211yesmaximal, characteristic
9C113×#1436C212yesmaximal
10C23×Q8×C113C2211yescharacteristic
11C23×Q8×C113C2211yescharacteristic
12C22×C4⋊C4×C113C2212yes—
13C22×C4⋊C4×C113C2211yescharacteristic
14C22×C4⋊C4×C113C2211yescharacteristic
15C22×C4⋊C4×C113C2212yes—
16C22×C42×C113C2211yescharacteristic
17#395×C113—24no—
18#391×C113—24no—
19C2×#95×C113C2212yes—
20C2×#95×C113C2212yes—
21C2×#95×C113C2212yes—
22C2×#95×C113C2211yescharacteristic
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×C113C2212yes—
33C22×Q8×C113—22no—
34C22×Q8×C113—22no—
35C22×Q8×C113—22no—
36C22×Q8×C113—24no—
37C22×Q8×C113—41no—
38C22×Q8×C113—41no—
39C22×Q8×C113—41no—
40C22×Q8×C113—41no—
41C22×Q8×C113—42no—
42C22×Q8×C113—41no—
43C22×Q8×C113—41no—
44C22×Q8×C113Q814yescomplemented
45C23×C4×C113C2312yes—
46C23×C4×C113C2311yescharacteristic
47C23×C4×C113C2311yescharacteristic
48C23×C4×C113C2312yes—
49C23×C4×C113C2312yes—
50C23×C4×C113C2312yes—
51C23×C4×C113C2312yes—
52C23×C4×C113C2312yes—
53C23×C4×C113C2311yescharacteristic
54C2×C4⋊C4×C113—24no—
55C2×C4⋊C4×C113—24no—
56C2×C4⋊C4×C113—41no—
57C2×C4⋊C4×C113—41no—
58C2×C4⋊C4×C113—42no—
59C2×C4⋊C4×C113—42no—
60C2×C4⋊C4×C113—42no—
61C2×C4⋊C4×C113—41no—
62C2×C4⋊C4×C113—42no—
63C2×C4⋊C4×C113D414yes—
64C2×C4⋊C4×C113Q818yescomplemented
65C2×C42×C113—22no—
66C2×C42×C113—41no—
67C2×C42×C113—41no—
68#95×C113—24no—
69#95×C113—24no—
70#95×C113—22no—
71#95×C113—24no—
72#95×C113—24no—
73#95×C113—24no—
74#95×C113—41no—
75#95×C113—42no—
76#95×C113—42no—
77#95×C113—42no—
78#95×C113—42no—
79#95×C113—42no—
80#95×C113—42no—
81#95×C113—42no—
82C24×C113C2411yescharacteristic
83C2×Q8×C113—28no—
84C2×Q8×C113—44no—
85C2×Q8×C113—44no—
86C2×Q8×C113—48no—
87C2×Q8×C113—44no—
88C2×Q8×C113—44no—
89C2×Q8×C113—44no—
90C2×Q8×C113—44no—
91C2×Q8×C113—44no—
92C2×Q8×C113—44no—
93C2×Q8×C113—48no—
94C2×Q8×C113—44no—
95C22×C4×C113—21no—
96C22×C4×C113—21no—
97C22×C4×C113—21no—
98C22×C4×C113—21no—
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—22no—
112C22×C4×C113—22no—
113C22×C4×C113—22no—
114C22×C4×C113—21no—
115C22×C4×C113—22no—
116C22×C4×C113—22no—
117C22×C4×C113—22no—
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—21no—
129C22×C4×C113—22no—
130C22×C4×C113—22no—
131C22×C4×C113—21no—
132C22×C4×C113—21no—
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×C113—22no—
141C22×C4×C113—22no—
142C22×C4×C113—22no—
143C22×C4×C113—22no—
144C22×C4×C113C2×D412yes—
145C22×C4×C113C2×D412yes—
146C22×C4×C113C2×D412yes—
147C22×C4×C113C2×Q814yes—
148C22×C4×C113C2×Q814yes—
149C22×C4×C113C2×Q814yes—
150C22×C4×C113C2×Q814yes—
151C22×C4×C113C2×Q812yes—
152C22×C4×C113#4114yes—
153C22×C4×C113#4112yes—
154C4⋊C4×C113—44no—
155C4⋊C4×C113—48no—
156C4⋊C4×C113—48no—
157C4⋊C4×C113—44no—
158C42×C113—44no—
159C23×C113C22×D411yescharacteristic
160C23×C113C22×Q811yescharacteristic
161C23×C113C22×Q812yes—
162C23×C113C2×#4111yescharacteristic
163C23×C113C2×#4112yes—
164C23×C113H(5,𝔽2)11yescharacteristic
165C23×C113H(5,𝔽2)11yescharacteristic
166C23×C113H(5,𝔽2)11yescharacteristic
167C23×C113H(5,𝔽2)11yescharacteristic
168C23×C113H(5,𝔽2)12yes—
169C23×C1132−1+412yes—
170Q8×C113—416no—
171Q8×C113—416no—
172C2×C4×C113—22no—
173C2×C4×C113—22no—
174C2×C4×C113—22no—
175C2×C4×C113—22no—
176C2×C4×C113—22no—
177C2×C4×C113—22no—
178C2×C4×C113—24no—
179C2×C4×C113—24no—
180C2×C4×C113—22no—
181C2×C4×C113—22no—
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—24no—
195C2×C4×C113—24no—
196C2×C4×C113—24no—
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—42no—
214C2×C4×C113—42no—
215C2×C4×C113—42no—
216C2×C4×C113—41no—
217C2×C4×C113—41no—
218C2×C4×C113—41no—
219C2×C4×C113—41no—
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—42no—
228C2×C4×C113—42no—
229C2×C4×C113—42no—
230C2×C4×C113C22⋊Q814yes—
231C22×C113C2×C22⋊Q811yescharacteristic
232C22×C113#53312yes—
233C22×C113#53411yescharacteristic
234C22×C113#53511yescharacteristic
235C22×C113#53811yescharacteristic
236C22×C113#53811yescharacteristic
237C22×C113#53812yes—
238C22×C113#54212yes—
239C22×C113#54212yes—
240C22×C113#54311yescharacteristic
241C22×C113#54311yescharacteristic
242C22×C113#54312yes—
243C22×C113#54412yes—
244C22×C113#54612yes—
245C22×C113D4×Q812yes—
246C22×C113#55111yescharacteristic
247C22×C113#55412yes—
248C22×C113#55712yes—
249C22×C113Q8211yescharacteristic
250C22×C113Q8212yes—
251C22×C113H(3,𝔽4)11yescharacteristic
252C22×C113#56212yes—
253C22×C113#56311yescharacteristic
254C4×C113—24no—
255C4×C113—44no—
256C4×C113—44no—
257C4×C113—42no—
258C4×C113—42no—
259C4×C113—44no—
260C4×C113—44no—
261C4×C113—44no—
262C4×C113—82no—
263#16630C11311yesmaximal, characteristic, direct product factor, Sylow
264C2×C113#245112yes—
265C2×C113#258611yescharacteristic
266C2×C113#262611yescharacteristic
267C2×C113#266512yes—
268C2×C113#268411yescharacteristic
269C2×C113#269212yes—
270C2×C113#273411yescharacteristic
271C2×C113#279911yescharacteristic
272C2×C113#280612yes—
273C2×C113#281111yescharacteristic
274C2×C113#283211yescharacteristic
275C2×#395C2×C11311yescharacteristic
276C2×#391C2×C11311yescharacteristic
277#1446C2×C11312yes—
278#1446C2×C11312yes—
279#1445C2×C11312yes—
280#1441C2×C11312yes—
281#1441C2×C11312yes—
282#1441C2×C11311yescharacteristic
283#1436C2×C11312yes—
284C113#1663011yescharacteristic, direct product factor, Sylow
285C23×Q8C22×C11311yescharacteristic
286C23×Q8C22×C11311yescharacteristic
287C22×C4⋊C4C22×C11312yes—
288C22×C4⋊C4C22×C11311yescharacteristic
289C22×C4⋊C4C22×C11311yescharacteristic
290C22×C4⋊C4C22×C11312yes—
291C22×C42C22×C11311yescharacteristic
292#395—24no—
293#391—24no—
294C2×#95C22×C11312yes—
295C2×#95C22×C11311yescharacteristic
296C2×#95C22×C11312yes—
297C2×#95C22×C11312yes—
298C2×#95C22×C11312yes—
299C2×#95C22×C11312yes—
300C2×#95C22×C11312yes—
301C2×#95C22×C11312yes—
302C2×#95C22×C11311yescharacteristic
303C2×#95C22×C11312yes—
304C2×#95C22×C11312yes—
305C2×#95C22×C11312yes—
306C2×#95C22×C11312yes—
307C2×#95C22×C11312yes—
308C22×Q8—22no—
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—24no—
312C22×Q8—41no—
313C22×Q8—41no—
314C22×Q8—41no—
315C22×Q8—41no—
316C22×Q8—42no—
317C22×Q8—41no—
318C22×Q8—41no—
319C22×Q8Q8×C11314yescomplemented
320C23×C4C23×C11312yes—
321C23×C4C23×C11311yescharacteristic
322C23×C4C23×C11311yescharacteristic
323C23×C4C23×C11312yes—
324C23×C4C23×C11312yes—
325C23×C4C23×C11312yes—
326C23×C4C23×C11312yes—
327C23×C4C23×C11312yes—
328C23×C4C23×C11311yescharacteristic
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4—41no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4D4×C11314yes—
339C2×C4⋊C4Q8×C11318yescomplemented
340C2×C42—22no—
341C2×C42—41no—
342C2×C42—41no—
343#95—24no—
344#95—24no—
345#95—22no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—41no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95—42no—
357C24C24×C11311yescharacteristic
358C2×Q8—28no—
359C2×Q8—44no—
360C2×Q8—44no—
361C2×Q8—48no—
362C2×Q8—44no—
363C2×Q8—44no—
364C2×Q8—44no—
365C2×Q8—44no—
366C2×Q8—44no—
367C2×Q8—44no—
368C2×Q8—48no—
369C2×Q8—44no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
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—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
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—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4C2×D4×C11312yes—
420C22×C4C2×D4×C11312yes—
421C22×C4C2×D4×C11312yes—
422C22×C4C2×Q8×C11314yes—
423C22×C4C2×Q8×C11314yes—
424C22×C4C2×Q8×C11314yes—
425C22×C4C2×Q8×C11314yes—
426C22×C4C2×Q8×C11312yes—
427C22×C4#41×C11314yes—
428C22×C4#41×C11312yes—
429C4⋊C4—44no—
430C4⋊C4—48no—
431C4⋊C4—48no—
432C4⋊C4—44no—
433C42—44no—
434C23C22×D4×C11311yescharacteristic
435C23C22×Q8×C11311yescharacteristic
436C23C22×Q8×C11312yes—
437C23C2×#41×C11311yescharacteristic
438C23C2×#41×C11312yes—
439C23H(5,𝔽2)×C11311yescharacteristic
440C23H(5,𝔽2)×C11311yescharacteristic
441C23H(5,𝔽2)×C11311yescharacteristic
442C23H(5,𝔽2)×C11311yescharacteristic
443C23H(5,𝔽2)×C11312yes—
444C232−1+4×C11312yes—
445Q8—416no—
446Q8—416no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
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—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
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—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4C22⋊Q8×C11314yes—
506C22C2×C22⋊Q8×C11311yescharacteristic
507C22#533×C11312yes—
508C22#534×C11311yescharacteristic
509C22#535×C11311yescharacteristic
510C22#538×C11312yes—
511C22#538×C11311yescharacteristic
512C22#538×C11311yescharacteristic
513C22#542×C11312yes—
514C22#542×C11312yes—
515C22#543×C11311yescharacteristic
516C22#543×C11311yescharacteristic
517C22#543×C11312yes—
518C22#544×C11312yes—
519C22#546×C11312yes—
520C22D4×Q8×C11312yes—
521C22#551×C11311yescharacteristic
522C22#554×C11312yes—
523C22#557×C11312yes—
524C22Q82×C11312yes—
525C22Q82×C11311yescharacteristic
526C22H(3,𝔽4)×C11311yescharacteristic
527C22#562×C11312yes—
528C22#563×C11311yescharacteristic
529C4—24no—
530C4—44no—
531C4—44no—
532C4—42no—
533C4—44no—
534C4—42no—
535C4—44no—
536C4—44no—
537C4—82no—
538C2C113×#245112yes—
539C2C113×#258611yescharacteristic
540C2C113×#262611yescharacteristic
541C2C113×#266512yes—
542C2C113×#268411yescharacteristic
543C2C113×#269212yes—
544C2C113×#273411yescharacteristic
545C2C113×#279911yescharacteristic
546C2C113×#280612yes—
547C2C113×#281111yescharacteristic
548C2C113×#283211yescharacteristic
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
44. C22×Q8×C113Q8semidirect
64. C2×C4⋊C4×C113Q8semidirect
263. #16630C113direct (N × H)
284. C113#16630direct (N × H)
319. C22×Q8Q8×C113semidirect
339. C2×C4⋊C4Q8×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#395×C1132
C2×#391×C1132
C113×#14462
C113×#14452
C113×#14412
C113×#14362
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