Finite Group Databasebeta

← C113×#9062 #43277082

Subgroups — C113×#9062 #43277082

Order 28928.

618 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#486×C113C211yesmaximal, characteristic
2C113×#2365C211yesmaximal, characteristic, complemented
3C113×#1982C211yesmaximal, characteristic
4C113×#1982C211yesmaximal, characteristic
5C2×#332×C113C211yesmaximal, characteristic, complemented
6C113×#1279C211yesmaximal, characteristic, complemented
7C113×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C113C2211yescharacteristic
9C2×#127×C113C2211yescharacteristic
10C2×C4×Q8×C113—21no—
11#486×C113—22no—
12#486×C113C414yescomplemented
13C2×C4⋊C8×C113C2211yescharacteristic
14C2×C4⋊C8×C113C2211yescharacteristic
15C2×#102×C113—22no—
16C2×#102×C113—21no—
17C2×#102×C113—21no—
18C2×#102×C113—21no—
19C2×#102×C113—21no—
20C2×C4×C8×C113C2211yescharacteristic
21#391×C113—21no—
22#389×C113—21no—
23#387×C113—22no—
24C4×C4⋊C4×C113—21no—
25C4×C4⋊C4×C113C2211yescharacteristic
26C4×C4⋊C4×C113C2211yescharacteristic
27#332×C113—22no—
28C22×Q8×C113—21no—
29C22×D4×C113—21no—
30C22×D4×C113—21no—
31C22×D4×C113—21no—
32C22×C8×C113—21no—
33C22×C8×C113—21no—
34C22×C8×C113—21no—
35C4⋊Q8×C113—21no—
36C4⋊Q8×C113—21no—
37C4⋊Q8×C113C2×C412yes—
38C4⋊Q8×C113D412yes—
39#127×C113—21no—
40#127×C113—21no—
41#127×C113—21no—
42#127×C113C2×C412yes—
43C4×Q8×C113—42no—
44C4×Q8×C113—42no—
45C2×C4⋊C4×C113—21no—
46C2×C4⋊C4×C113—22no—
47C2×C4⋊C4×C113D411yescharacteristic
48C2×C4⋊C4×C113D411yescharacteristic
49C2×C4⋊C4×C113D412yes—
50C2×C4⋊C4×C113D411yescharacteristic
51C2×C4⋊C4×C113D411yescharacteristic
52C2×C42×C113—22no—
53C2×C42×C113—21no—
54C2×C42×C113—21no—
55C2×C42×C113C2311yescharacteristic
56C4⋊C8×C113—21no—
57C4⋊C8×C113—21no—
58C4⋊C8×C113—21no—
59C4⋊C8×C113—21no—
60#102×C113—28no—
61#102×C113—42no—
62#102×C113—42no—
63#102×C113—42no—
64#102×C113—42no—
65C4×C8×C113—21no—
66C4×C8×C113C2×C412yes—
67#95×C113—22no—
68#95×C113—22no—
69#95×C113—21no—
70#95×C113—21no—
71C24×C113—41no—
72C2×Q8×C113—22no—
73C2×Q8×C113—22no—
74C2×Q8×C113—41no—
75C2×Q8×C113—41no—
76C2×Q8×C113—41no—
77C2×Q8×C113—41no—
78C2×D4×C113—22no—
79C2×D4×C113—22no—
80C2×D4×C113—22no—
81C2×D4×C113—42no—
82C2×D4×C113—42no—
83C2×D4×C113—41no—
84C2×D4×C113—41no—
85C2×D4×C113—41no—
86C2×D4×C113—41no—
87C2×D4×C113—41no—
88C2×D4×C113—41no—
89C2×D4×C113—41no—
90C2×D4×C113—41no—
91C2×D4×C113—41no—
92C2×D4×C113—41no—
93C2×D4×C113—41no—
94C22×C4×C113—21no—
95C22×C4×C113—22no—
96C22×C4×C113—21no—
97C22×C4×C113—21no—
98C22×C4×C113—21no—
99C22×C4×C113C2×D411yescharacteristic
100C22×C4×C113C2×D411yescharacteristic
101C22×C4×C113C2×D411yescharacteristic
102C2×C8×C113—22no—
103C2×C8×C113—41no—
104C2×C8×C113—41no—
105C2×C8×C113—41no—
106C2×C8×C113—41no—
107C2×C8×C113—41no—
108C2×C8×C113—41no—
109C2×C8×C113—41no—
110C2×C8×C113—41no—
111C4⋊C4×C113—22no—
112C4⋊C4×C113—22no—
113C4⋊C4×C113—22no—
114C4⋊C4×C113—21no—
115C4⋊C4×C113—21no—
116C4⋊C4×C113—21no—
117C4⋊C4×C113—21no—
118C4⋊C4×C113—21no—
119C4⋊C4×C113—21no—
120C4⋊C4×C113—44no—
121C4⋊C4×C113C22⋊C414yes—
122C4⋊C4×C113D812yes—
123C4⋊C4×C113SD1612yes—
124C42×C113—44no—
125C42×C113—41no—
126C42×C113—41no—
127C42×C113—41no—
128C42×C113—41no—
129C42×C113C22×C411yescharacteristic
130C42×C113C2×D411yescharacteristic
131C42×C113#4111yescharacteristic
132C42×C113#4111yescharacteristic
133C23×C113—42no—
134C23×C113—81no—
135C23×C113—81no—
136C23×C113—81no—
137C23×C113—81no—
138C23×C113—81no—
139C23×C113—81no—
140C23×C113#12011yescharacteristic
141Q8×C113—42no—
142Q8×C113—42no—
143Q8×C113—42no—
144Q8×C113—42no—
145D4×C113—44no—
146D4×C113—42no—
147D4×C113—42no—
148D4×C113—42no—
149D4×C113—42no—
150D4×C113—82no—
151D4×C113—81no—
152D4×C113—81no—
153D4×C113—81no—
154D4×C113—81no—
155C2×C4×C113—21no—
156C2×C4×C113—21no—
157C2×C4×C113—24no—
158C2×C4×C113—22no—
159C2×C4×C113—22no—
160C2×C4×C113—41no—
161C2×C4×C113—42no—
162C2×C4×C113—41no—
163C2×C4×C113—42no—
164C2×C4×C113—41no—
165C2×C4×C113—41no—
166C2×C4×C113—41no—
167C2×C4×C113—41no—
168C2×C4×C113—41no—
169C2×C4×C113—41no—
170C2×C4×C113—41no—
171C2×C4×C113—41no—
172C2×C4×C113C2×C22⋊C411yescharacteristic
173C2×C4×C113C4×D411yescharacteristic
174C2×C4×C113C4×D411yescharacteristic
175C2×C4×C113#12111yescharacteristic
176C2×C4×C113#12111yescharacteristic
177C2×C4×C113#12311yescharacteristic
178C2×C4×C113C2×D811yescharacteristic
179C2×C4×C113C2×SD1611yescharacteristic
180C2×C4×C113#13511yescharacteristic
181C2×C4×C113#13511yescharacteristic
182C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C113#13711yescharacteristic
186C8×C113—42no—
187C8×C113—81no—
188C8×C113—81no—
189C22×C113—82no—
190C22×C113—82no—
191C22×C113—82no—
192C22×C113—161no—
193C22×C113—161no—
194C22×C113—161no—
195C22×C113—161no—
196C22×C113#38611yescharacteristic
197C22×C113#44711yescharacteristic
198C22×C113#44811yescharacteristic
199C22×C113#44911yescharacteristic
200C22×C113#44911yescharacteristic
201C22×C113#45411yescharacteristic
202C22×C113#45411yescharacteristic
203C4×C113—21no—
204C4×C113—21no—
205C4×C113—44no—
206C4×C113—42no—
207C4×C113—42no—
208C4×C113—81no—
209C4×C113—81no—
210C4×C113C4×D811yescharacteristic
211C4×C113C4×SD1611yescharacteristic
212C4×C113#44011yescharacteristic
213C4×C113#44211yescharacteristic
214C4×C113#45911yescharacteristic
215C4×C113#46011yescharacteristic
216C4×C113#46311yescharacteristic
217C4×C113#46411yescharacteristic
218#9062C11311yesmaximal, characteristic, direct product factor, Sylow
219C2×C113—162no—
220C2×C113#162511yescharacteristic
221C2×C113#162611yescharacteristic
222C2×C113#162711yescharacteristic
223C2×C113#162811yescharacteristic
224C2×C113#187911yescharacteristic
225C2×C113#188011yescharacteristic
226C2×C113#188811yescharacteristic
227C2×#486C2×C11311yescharacteristic
228#2365C2×C11311yescharacteristic, complemented
229#1982C2×C11311yescharacteristic
230#1982C2×C11311yescharacteristic
231C2×#332C2×C11311yescharacteristic, complemented
232#1279C2×C11311yescharacteristic, complemented
233#1279C2×C11311yescharacteristic, complemented
234C113#906211yescharacteristic, direct product factor, Sylow
235C2×C4⋊Q8C22×C11311yescharacteristic
236C2×#127C22×C11311yescharacteristic
237C2×C4×Q8—21no—
238#486—22no—
239#486C4×C11314yescomplemented
240C2×C4⋊C8C22×C11311yescharacteristic
241C2×C4⋊C8C22×C11311yescharacteristic
242C2×#102—22no—
243C2×#102—21no—
244C2×#102—21no—
245C2×#102—21no—
246C2×#102—21no—
247C2×C4×C8C22×C11311yescharacteristic
248#391—21no—
249#389—21no—
250#387—22no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4C22×C11311yescharacteristic
253C4×C4⋊C4C22×C11311yescharacteristic
254#332—22no—
255C22×Q8—21no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8C2×C4×C11312yes—
265C4⋊Q8D4×C11312yes—
266#127—21no—
267#127—21no—
268#127—21no—
269#127C2×C4×C11312yes—
270C4×Q8—42no—
271C4×Q8—42no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4D4×C11311yescharacteristic
275C2×C4⋊C4D4×C11311yescharacteristic
276C2×C4⋊C4D4×C11312yes—
277C2×C4⋊C4D4×C11311yescharacteristic
278C2×C4⋊C4D4×C11311yescharacteristic
279C2×C42—22no—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42C23×C11311yescharacteristic
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287#102—28no—
288#102—42no—
289#102—42no—
290#102—42no—
291#102—42no—
292C4×C8—21no—
293C4×C8C2×C4×C11312yes—
294#95—22no—
295#95—22no—
296#95—21no—
297#95—21no—
298C24—41no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—42no—
309C2×D4—42no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4C2×D4×C11311yescharacteristic
327C22×C4C2×D4×C11311yescharacteristic
328C22×C4C2×D4×C11311yescharacteristic
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—44no—
348C4⋊C4C22⋊C4×C11314yes—
349C4⋊C4D8×C11312yes—
350C4⋊C4SD16×C11312yes—
351C42—44no—
352C42—41no—
353C42—41no—
354C42—41no—
355C42—41no—
356C42C22×C4×C11311yescharacteristic
357C42C2×D4×C11311yescharacteristic
358C42#41×C11311yescharacteristic
359C42#41×C11311yescharacteristic
360C23—42no—
361C23—81no—
362C23—81no—
363C23—81no—
364C23—81no—
365C23—81no—
366C23—81no—
367C23#120×C11311yescharacteristic
368Q8—42no—
369Q8—42no—
370Q8—42no—
371Q8—42no—
372D4—44no—
373D4—42no—
374D4—42no—
375D4—42no—
376D4—42no—
377D4—82no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—81no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—24no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4C2×C22⋊C4×C11311yescharacteristic
400C2×C4C4×D4×C11311yescharacteristic
401C2×C4C4×D4×C11311yescharacteristic
402C2×C4#121×C11311yescharacteristic
403C2×C4#121×C11311yescharacteristic
404C2×C4#123×C11311yescharacteristic
405C2×C4C2×D8×C11311yescharacteristic
406C2×C4C2×SD16×C11311yescharacteristic
407C2×C4#135×C11311yescharacteristic
408C2×C4#135×C11311yescharacteristic
409C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
410C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
411C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
412C2×C4#137×C11311yescharacteristic
413C8—42no—
414C8—81no—
415C8—81no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22—161no—
420C22—161no—
421C22—161no—
422C22—161no—
423C22#386×C11311yescharacteristic
424C22#447×C11311yescharacteristic
425C22#448×C11311yescharacteristic
426C22#449×C11311yescharacteristic
427C22#449×C11311yescharacteristic
428C22#454×C11311yescharacteristic
429C22#454×C11311yescharacteristic
430C4—21no—
431C4—21no—
432C4—44no—
433C4—42no—
434C4—42no—
435C4—81no—
436C4—81no—
437C4C4×D8×C11311yescharacteristic
438C4C4×SD16×C11311yescharacteristic
439C4#440×C11311yescharacteristic
440C4#442×C11311yescharacteristic
441C4#459×C11311yescharacteristic
442C4#460×C11311yescharacteristic
443C4#463×C11311yescharacteristic
444C4#464×C11311yescharacteristic
445C2—162no—
446C2C113×#162511yescharacteristic
447C2C113×#162611yescharacteristic
448C2C113×#162711yescharacteristic
449C2C113×#162811yescharacteristic
450C2C113×#187911yescharacteristic
451C2C113×#188011yescharacteristic
452C2C113×#188811yescharacteristic
subgroupG/H
center, socleC23×C113#120
commutatorC42C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC2×#127×C113C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2365C2semidirect
5. C2×#332×C113C2semidirect
6. C113×#1279C2semidirect
7. C113×#1279C2semidirect
12. #486×C113C4semidirect
218. #9062C113direct (N × H)
228. #2365C2×C113semidirect
231. C2×#332C2×C113semidirect
232. #1279C2×C113semidirect
233. #1279C2×C113semidirect
234. C113#9062direct (N × H)
239. #486C4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#486×C1132
C113×#23652
C113×#19822
C2×#332×C1132
C113×#12792
#9062113