Finite Group Databasebeta

← C113×#23985 #43292005

Subgroups — C113×#23985 #43292005

Order 28928.

1474 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3490C211yesmaximal, characteristic
2C113×#2849C212yesmaximal, complemented
3C2×#381×C113C211yesmaximal, characteristic, complemented
4C113×#2030C212yesmaximal, complemented
5C113×#2022C212yesmaximal, complemented
6C113×#1898C212yesmaximal, complemented
7C113×#1890C214yesmaximal, complemented
8C113×#1819C211yesmaximal, characteristic, complemented
9C24×C4×C113C2211yescharacteristic
10#551×C113—24no—
11#546×C113—24no—
12#543×C113C2211yescharacteristic
13#538×C113—22no—
14#534×C113C2211yescharacteristic
15#525×C113—22no—
16C2×#123×C113C2214yes—
17C2×#120×C113C2212yes—
18#518×C113C2212yes—
19C22×C22⋊C4×C113C2211yescharacteristic
20C22×C22⋊C4×C113C2211yescharacteristic
21C2×#99×C113C2214yes—
22#386×C113—24no—
23#385×C113—24no—
24#381×C113—22no—
25#381×C113C2212yes—
26#381×C113C2212yes—
27#381×C113C2214yes—
28#379×C113C2212yes—
29C2×#95×C113—22no—
30#342×C113C2212yes—
31#342×C113C2214yes—
32#342×C113C2212yes—
33C25×C113C2311yescharacteristic
34C2×#41×C113—22no—
35C22×D4×C113D414yes—
36C22×D4×C113C2312yes—
37C23×C4×C113—21no—
38C23×C4×C113—21no—
39C23×C4×C113—24no—
40C23×C4×C113—21no—
41C23×C4×C113—24no—
42C23×C4×C113—42no—
43C23×C4×C113D412yes—
44C23×C4×C113C2312yes—
45#126×C113—24no—
46#124×C113—24no—
47#123×C113—24no—
48#123×C113—24no—
49#123×C113—22no—
50#123×C113—28no—
51#123×C113—44no—
52C22⋊Q8×C113—22no—
53C22⋊Q8×C113—22no—
54C22⋊Q8×C113—24no—
55#121×C113—22no—
56#121×C113—24no—
57#121×C113—22no—
58#120×C113—22no—
59#120×C113—22no—
60#120×C113—24no—
61#120×C113—22no—
62C4×D4×C113—24no—
63C4×D4×C113—24no—
64C4×D4×C113—24no—
65#117×C113—22no—
66#117×C113—22no—
67C2×C4⋊C4×C113—24no—
68C2×C22⋊C4×C113—24no—
69C2×C22⋊C4×C113—22no—
70C2×C22⋊C4×C113—21no—
71C2×C22⋊C4×C113—24no—
72C2×C22⋊C4×C113—24no—
73C2×C22⋊C4×C113—42no—
74C2×C22⋊C4×C113D412yes—
75C2×C22⋊C4×C113D414yes—
76C2×C22⋊C4×C113C2312yes—
77C2×C22⋊C4×C113C2314yes—
78C2×C22⋊C4×C113C2311yescharacteristic
79C2×C22⋊C4×C113C2311yescharacteristic
80C2×C22⋊C4×C113C2312yes—
81#99×C113—44no—
82#95×C113—24no—
83#95×C113—24no—
84#95×C113—28no—
85C24×C113—22no—
86C24×C113—22no—
87C24×C113—44no—
88C24×C113C2×D411yescharacteristic
89C24×C113C2×D414yes—
90C24×C113C2×D412yes—
91C24×C113C2×D411yescharacteristic
92C24×C113C2411yescharacteristic
93#41×C113—84no—
94C2×Q8×C113—22no—
95C2×D4×C113—24no—
96C2×D4×C113—22no—
97C2×D4×C113—22no—
98C2×D4×C113—24no—
99C2×D4×C113—24no—
100C2×D4×C113—22no—
101C2×D4×C113—24no—
102C2×D4×C113—48no—
103C22×C4×C113—24no—
104C22×C4×C113—24no—
105C22×C4×C113—22no—
106C22×C4×C113—22no—
107C22×C4×C113—24no—
108C22×C4×C113—22no—
109C22×C4×C113—24no—
110C22×C4×C113—24no—
111C22×C4×C113—22no—
112C22×C4×C113—22no—
113C22×C4×C113—24no—
114C22×C4×C113—416no—
115C22×C4×C113—42no—
116C22×C4×C113—42no—
117C22×C4×C113—42no—
118C22×C4×C113—42no—
119C22×C4×C113—44no—
120C22×C4×C113—42no—
121C22×C4×C113—44no—
122C22×C4×C113C2×D412yes—
123C22×C4×C113C2×D412yes—
124C22×C4×C113C2×D414yes—
125C22×C4×C113C2×D412yes—
126C22×C4×C113#4114yescomplemented
127C4⋊C4×C113—24no—
128C4⋊C4×C113—22no—
129C4⋊C4×C113—22no—
130C4⋊C4×C113—24no—
131C4⋊C4×C113—48no—
132C22⋊C4×C113—24no—
133C22⋊C4×C113—24no—
134C22⋊C4×C113—24no—
135C22⋊C4×C113—24no—
136C22⋊C4×C113—24no—
137C22⋊C4×C113—22no—
138C22⋊C4×C113—22no—
139C22⋊C4×C113—22no—
140C22⋊C4×C113—22no—
141C22⋊C4×C113—24no—
142C22⋊C4×C113—24no—
143C22⋊C4×C113—24no—
144C22⋊C4×C113—48no—
145C22⋊C4×C113—48no—
146C22⋊C4×C113—42no—
147C42×C113—24no—
148C23×C113—21no—
149C23×C113—21no—
150C23×C113—24no—
151C23×C113—21no—
152C23×C113—21no—
153C23×C113—28no—
154C23×C113—28no—
155C23×C113—22no—
156C23×C113—24no—
157C23×C113—42no—
158C23×C113—44no—
159C23×C113—42no—
160C23×C113—48no—
161C23×C113—48no—
162C23×C113—44no—
163C23×C113#12012yes—
164C23×C113#12012yes—
165C23×C113C22×D411yescharacteristic
166C23×C113C22×D412yes—
167C23×C113C2×#4112yes—
168C23×C113H(5,𝔽2)12yes—
169Q8×C113—82no—
170D4×C113—42no—
171D4×C113—42no—
172D4×C113—44no—
173D4×C113—48no—
174D4×C113—84no—
175D4×C113—82no—
176C2×C4×C113—22no—
177C2×C4×C113—22no—
178C2×C4×C113—24no—
179C2×C4×C113—22no—
180C2×C4×C113—24no—
181C2×C4×C113—28no—
182C2×C4×C113—24no—
183C2×C4×C113—48no—
184C2×C4×C113—48no—
185C2×C4×C113—42no—
186C2×C4×C113—42no—
187C2×C4×C113—44no—
188C2×C4×C113—44no—
189C2×C4×C113—42no—
190C2×C4×C113—42no—
191C2×C4×C113—44no—
192C2×C4×C113—48no—
193C2×C4×C113—44no—
194C2×C4×C113—42no—
195C2×C4×C113—44no—
196C2×C4×C113—82no—
197C2×C4×C113—84no—
198C2×C4×C113—84no—
199C22×C113—24no—
200C22×C113—24no—
201C22×C113—22no—
202C22×C113—22no—
203C22×C113—24no—
204C22×C113—22no—
205C22×C113—22no—
206C22×C113—24no—
207C22×C113—42no—
208C22×C113—42no—
209C22×C113—416no—
210C22×C113—42no—
211C22×C113—42no—
212C22×C113—42no—
213C22×C113—44no—
214C22×C113—84no—
215C22×C113#45814yes—
216C22×C113C2×#12011yescharacteristic
217C22×C113#52511yescharacteristic
218C22×C113#53511yescharacteristic
219C22×C113#54614yes—
220C4×C113—44no—
221C4×C113—42no—
222C4×C113—42no—
223C4×C113—42no—
224C4×C113—44no—
225C4×C113—84no—
226C4×C113—82no—
227#23985C11311yesmaximal, characteristic, direct product factor, Sylow
228C2×C113—21no—
229C2×C113—24no—
230C2×C113—21no—
231C2×C113—24no—
232C2×C113—42no—
233C2×C113—82no—
234C2×C113#240411yescharacteristic
235C2×C113C2×#45812yes—
236#3490C2×C11311yescharacteristic
237#2849C2×C11312yescomplemented
238C2×#381C2×C11311yescharacteristic, complemented
239#2030C2×C11312yescomplemented
240#2022C2×C11312yescomplemented
241#1898C2×C11312yescomplemented
242#1890C2×C11314yescomplemented
243#1819C2×C11311yescharacteristic, complemented
244C113#2398511yescharacteristic, direct product factor, Sylow
245C24×C4C22×C11311yescharacteristic
246#551—24no—
247#546—24no—
248#543C22×C11311yescharacteristic
249#538—22no—
250#534C22×C11311yescharacteristic
251#525—22no—
252C2×#123C22×C11314yes—
253C2×#120C22×C11312yes—
254#518C22×C11312yes—
255C22×C22⋊C4C22×C11311yescharacteristic
256C22×C22⋊C4C22×C11311yescharacteristic
257C2×#99C22×C11314yes—
258#386—24no—
259#385—24no—
260#381—22no—
261#381C22×C11314yes—
262#381C22×C11312yes—
263#381C22×C11312yes—
264#379C22×C11312yes—
265C2×#95—22no—
266#342C22×C11312yes—
267#342C22×C11312yes—
268#342C22×C11314yes—
269C25C23×C11311yescharacteristic
270C2×#41—22no—
271C22×D4D4×C11314yes—
272C22×D4C23×C11312yes—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—24no—
276C23×C4—21no—
277C23×C4—24no—
278C23×C4—42no—
279C23×C4D4×C11312yes—
280C23×C4C23×C11312yes—
281#126—24no—
282#124—24no—
283#123—24no—
284#123—24no—
285#123—22no—
286#123—28no—
287#123—44no—
288C22⋊Q8—22no—
289C22⋊Q8—22no—
290C22⋊Q8—24no—
291#121—22no—
292#121—24no—
293#121—22no—
294#120—22no—
295#120—22no—
296#120—24no—
297#120—22no—
298C4×D4—24no—
299C4×D4—24no—
300C4×D4—24no—
301#117—22no—
302#117—22no—
303C2×C4⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4D4×C11312yes—
311C2×C22⋊C4D4×C11314yes—
312C2×C22⋊C4C23×C11312yes—
313C2×C22⋊C4C23×C11314yes—
314C2×C22⋊C4C23×C11311yescharacteristic
315C2×C22⋊C4C23×C11311yescharacteristic
316C2×C22⋊C4C23×C11312yes—
317#99—44no—
318#95—24no—
319#95—24no—
320#95—28no—
321C24—22no—
322C24—22no—
323C24—44no—
324C24C2×D4×C11311yescharacteristic
325C24C2×D4×C11314yes—
326C24C2×D4×C11312yes—
327C24C2×D4×C11311yescharacteristic
328C24C24×C11311yescharacteristic
329#41—84no—
330C2×Q8—22no—
331C2×D4—24no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—22no—
337C2×D4—24no—
338C2×D4—48no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—416no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—44no—
356C22×C4—42no—
357C22×C4—44no—
358C22×C4C2×D4×C11312yes—
359C22×C4C2×D4×C11312yes—
360C22×C4C2×D4×C11314yes—
361C22×C4C2×D4×C11312yes—
362C22×C4#41×C11314yescomplemented
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—24no—
367C4⋊C4—48no—
368C22⋊C4—24no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—24no—
378C22⋊C4—24no—
379C22⋊C4—24no—
380C22⋊C4—48no—
381C22⋊C4—42no—
382C22⋊C4—48no—
383C42—24no—
384C23—21no—
385C23—21no—
386C23—24no—
387C23—21no—
388C23—21no—
389C23—28no—
390C23—28no—
391C23—22no—
392C23—24no—
393C23—42no—
394C23—44no—
395C23—42no—
396C23—48no—
397C23—48no—
398C23—44no—
399C23#120×C11312yes—
400C23#120×C11312yes—
401C23C22×D4×C11311yescharacteristic
402C23C22×D4×C11312yes—
403C23C2×#41×C11312yes—
404C23H(5,𝔽2)×C11312yes—
405Q8—82no—
406D4—42no—
407D4—42no—
408D4—44no—
409D4—48no—
410D4—84no—
411D4—82no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—28no—
418C2×C4—24no—
419C2×C4—48no—
420C2×C4—48no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—48no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—82no—
433C2×C4—84no—
434C2×C4—84no—
435C22—24no—
436C22—24no—
437C22—22no—
438C22—22no—
439C22—24no—
440C22—22no—
441C22—22no—
442C22—24no—
443C22—42no—
444C22—42no—
445C22—416no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—44no—
450C22—84no—
451C22#458×C11314yes—
452C22C2×#120×C11311yescharacteristic
453C22#525×C11311yescharacteristic
454C22#535×C11311yescharacteristic
455C22#546×C11314yes—
456C4—44no—
457C4—42no—
458C4—42no—
459C4—42no—
460C4—44no—
461C4—82no—
462C4—84no—
463C2—21no—
464C2—24no—
465C2—21no—
466C2—24no—
467C2—42no—
468C2—82no—
469C2C113×#240411yescharacteristic
470C2C2×#458×C11312yes—
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC24C24×C113
prime radicalC113×#3490C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C25×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2849C2semidirect
3. C2×#381×C113C2semidirect
4. C113×#2030C2semidirect
5. C113×#2022C2semidirect
6. C113×#1898C2semidirect
7. C113×#1890C2semidirect
8. C113×#1819C2semidirect
126. C22×C4×C113#41semidirect
227. #23985C113direct (N × H)
237. #2849C2×C113semidirect
238. C2×#381C2×C113semidirect
239. #2030C2×C113semidirect
240. #2022C2×C113semidirect
241. #1898C2×C113semidirect
242. #1890C2×C113semidirect
243. #1819C2×C113semidirect
244. C113#23985direct (N × H)
362. C22×C4#41×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34902
C113×#28492
C2×#381×C1132
C113×#20302
C113×#20222
C113×#18982
C113×#18902
C113×#18192
#23985113