Finite Group Databasebeta

← C113×#9243 #43277263

Subgroups — C113×#9243 #43277263

Order 28928.

514 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×#463×C113C211yesmaximal, characteristic
2C113×#2974C211yesmaximal, characteristic, complemented
3C113×#1527C211yesmaximal, characteristic, complemented
4C113×#1490C211yesmaximal, characteristic, complemented
5C113×#1469C211yesmaximal, characteristic, complemented
6C113×#1290C211yesmaximal, characteristic, complemented
7C113×#1283C211yesmaximal, characteristic, complemented
8C22×SD16×C113C411yescharacteristic
9C22×D8×C113C411yescharacteristic
10C2×#124×C113C2211yescharacteristic
11C2×C4×D4×C113C2211yescharacteristic
12#463×C113—21no—
13#463×C113—21no—
14#463×C113—21no—
15#463×C113—21no—
16#436×C113—21no—
17#435×C113—22no—
18C8×D4×C113—21no—
19#432×C113C2211yescharacteristic
20#432×C113C2211yescharacteristic
21#431×C113C2211yescharacteristic
22C2×C4⋊C8×C113C2211yescharacteristic
23C2×#103×C113C411yescharacteristic
24C2×#102×C113C411yescharacteristic
25#407×C113—21no—
26C2×C22⋊C8×C113—21no—
27C4×M16×C113C2211yescharacteristic
28#329×C113—22no—
29D4⋊C8×C113—21no—
30D4⋊C8×C113—21no—
31#323×C113—21no—
32#323×C113—21no—
33C22×Q8×C113C2×C411yescharacteristic
34C22×D4×C113C2×C411yescharacteristic
35C22×D4×C113C2×C411yescharacteristic
36C23×C4×C113—21no—
37C2×SD16×C113—21no—
38C2×SD16×C113—21no—
39C2×SD16×C113—42no—
40C2×D8×C113—21no—
41C2×D8×C113—21no—
42C2×D8×C113—42no—
43C2×M16×C113—22no—
44C2×M16×C113—21no—
45C22×C8×C113—22no—
46C22×C8×C113C2×C411yescharacteristic
47C22×C8×C113C2×C411yescharacteristic
48#124×C113—21no—
49#124×C113—21no—
50#124×C113—21no—
51#124×C113—21no—
52C4×D4×C113—21no—
53C4×D4×C113—21no—
54C4×D4×C113D411yescharacteristic
55C4×D4×C113D411yescharacteristic
56C4×D4×C113D411yescharacteristic
57C4×D4×C113D411yescharacteristic
58C2×C4⋊C4×C113C2×C411yescharacteristic
59C2×C22⋊C4×C113—21no—
60C2×C22⋊C4×C113—21no—
61C2×C22⋊C4×C113—21no—
62C2×C42×C113C2311yescharacteristic
63C4⋊C8×C113—21no—
64C4⋊C8×C113—21no—
65C4⋊C8×C113—21no—
66C4⋊C8×C113—21no—
67C4⋊C8×C113—21no—
68#103×C113—21no—
69#103×C113—21no—
70#102×C113—21no—
71#102×C113—21no—
72C22⋊C8×C113—22no—
73C22⋊C8×C113—22no—
74C22⋊C8×C113—21no—
75C22⋊C8×C113—21no—
76C22⋊C8×C113D411yescharacteristic
77C22⋊C8×C113D411yescharacteristic
78#97×C113—21no—
79#97×C113—21no—
80#97×C113D412yes—
81C4×C8×C113—21no—
82C4×C8×C113—21no—
83C24×C113—21no—
84C24×C113—21no—
85C2×Q8×C113—21no—
86C2×Q8×C113—21no—
87C2×Q8×C113—41no—
88C2×Q8×C113—41no—
89C2×D4×C113—22no—
90C2×D4×C113—21no—
91C2×D4×C113—21no—
92C2×D4×C113—21no—
93C2×D4×C113—41no—
94C2×D4×C113—41no—
95C2×D4×C113—41no—
96C2×D4×C113C22⋊C411yescharacteristic
97C2×D4×C113C22⋊C411yescharacteristic
98C22×C4×C113—21no—
99C22×C4×C113—21no—
100C22×C4×C113—21no—
101C22×C4×C113—21no—
102C22×C4×C113—21no—
103C22×C4×C113—21no—
104C22×C4×C113—82no—
105C22×C4×C113C22×C411yescharacteristic
106C22×C4×C113C2×D411yescharacteristic
107C22×C4×C113#4111yescharacteristic
108SD16×C113—42no—
109SD16×C113—42no—
110D8×C113—42no—
111D8×C113—42no—
112M16×C113—22no—
113M16×C113—41no—
114M16×C113—82no—
115C2×C8×C113—21no—
116C2×C8×C113—21no—
117C2×C8×C113—21no—
118C2×C8×C113—21no—
119C2×C8×C113—22no—
120C2×C8×C113—41no—
121C2×C8×C113—41no—
122C2×C8×C113—41no—
123C2×C8×C113—41no—
124C2×C8×C113—82no—
125C4⋊C4×C113—21no—
126C4⋊C4×C113C22⋊C411yescharacteristic
127C4⋊C4×C113C22⋊C411yescharacteristic
128C22⋊C4×C113—21no—
129C22⋊C4×C113—21no—
130C22⋊C4×C113—21no—
131C22⋊C4×C113—21no—
132C22⋊C4×C113—41no—
133C22⋊C4×C113—41no—
134C22⋊C4×C113—41no—
135C22⋊C4×C113—41no—
136C42×C113C2×D411yescharacteristic
137C42×C113C2×D411yescharacteristic
138C42×C113C2×D411yescharacteristic
139C42×C113#4111yescharacteristic
140C23×C113—21no—
141C23×C113—21no—
142C23×C113—42no—
143C23×C113—41no—
144C23×C113—41no—
145C23×C113—41no—
146C23×C113—41no—
147C23×C113—41no—
148C23×C113—81no—
149C23×C113—81no—
150C23×C113—81no—
151C23×C113C4×D411yescharacteristic
152Q8×C113—41no—
153Q8×C113—41no—
154Q8×C113—81no—
155D4×C113—21no—
156D4×C113—21no—
157D4×C113—21no—
158D4×C113—42no—
159D4×C113—41no—
160D4×C113—41no—
161D4×C113—81no—
162D4×C113#10012yes—
163C2×C4×C113—21no—
164C2×C4×C113—21no—
165C2×C4×C113—21no—
166C2×C4×C113—21no—
167C2×C4×C113—21no—
168C2×C4×C113—21no—
169C2×C4×C113—41no—
170C2×C4×C113—42no—
171C2×C4×C113—42no—
172C2×C4×C113—41no—
173C2×C4×C113—81no—
174C2×C4×C113—81no—
175C2×C4×C113—81no—
176C2×C4×C113—81no—
177C2×C4×C113C2×C22⋊C411yescharacteristic
178C2×C4×C113C4×D411yescharacteristic
179C2×C4×C113#12011yescharacteristic
180C2×C4×C113#12111yescharacteristic
181C2×C4×C113#12111yescharacteristic
182C2×C4×C113#12311yescharacteristic
183C8×C113—41no—
184C8×C113—42no—
185C8×C113—41no—
186C8×C113—42no—
187C8×C113—41no—
188C8×C113—41no—
189C8×C113—81no—
190C22×C113—21no—
191C22×C113—21no—
192C22×C113—22no—
193C22×C113—41no—
194C22×C113—41no—
195C22×C113—41no—
196C22×C113—41no—
197C22×C113—41no—
198C22×C113—82no—
199C22×C113—82no—
200C22×C113—81no—
201C22×C113—81no—
202C22×C113—81no—
203C22×C113—161no—
204C22×C113—161no—
205C22×C113#38611yescharacteristic
206C22×C113#44311yescharacteristic
207C22×C113#44411yescharacteristic
208C4×C113—21no—
209C4×C113—21no—
210C4×C113—21no—
211C4×C113—21no—
212C4×C113—21no—
213C4×C113—41no—
214C4×C113—41no—
215C4×C113—81no—
216C4×C113C2×#10011yescharacteristic
217C4×C113#41311yescharacteristic
218#9243C11311yesmaximal, characteristic, direct product factor, Sylow
219C2×C113—21no—
220C2×C113—21no—
221C2×C113—42no—
222C2×C113—81no—
223C2×C113—161no—
224C2×C113#187611yescharacteristic
225C2×C113#190011yescharacteristic
226C2×C113#190411yescharacteristic
227C2×#463C2×C11311yescharacteristic
228#2974C2×C11311yescharacteristic, complemented
229#1527C2×C11311yescharacteristic, complemented
230#1490C2×C11311yescharacteristic, complemented
231#1469C2×C11311yescharacteristic, complemented
232#1290C2×C11311yescharacteristic, complemented
233#1283C2×C11311yescharacteristic, complemented
234C113#924311yescharacteristic, direct product factor, Sylow
235C22×SD16C4×C11311yescharacteristic
236C22×D8C4×C11311yescharacteristic
237C2×#124C22×C11311yescharacteristic
238C2×C4×D4C22×C11311yescharacteristic
239#463—21no—
240#463—21no—
241#463—21no—
242#463—21no—
243#436—21no—
244#435—22no—
245C8×D4—21no—
246#432C22×C11311yescharacteristic
247#432C22×C11311yescharacteristic
248#431C22×C11311yescharacteristic
249C2×C4⋊C8C22×C11311yescharacteristic
250C2×#103C4×C11311yescharacteristic
251C2×#102C4×C11311yescharacteristic
252#407—21no—
253C2×C22⋊C8—21no—
254C4×M16C22×C11311yescharacteristic
255#329—22no—
256D4⋊C8—21no—
257D4⋊C8—21no—
258#323—21no—
259#323—21no—
260C22×Q8C2×C4×C11311yescharacteristic
261C22×D4C2×C4×C11311yescharacteristic
262C22×D4C2×C4×C11311yescharacteristic
263C23×C4—21no—
264C2×SD16—21no—
265C2×SD16—21no—
266C2×SD16—42no—
267C2×D8—21no—
268C2×D8—21no—
269C2×D8—42no—
270C2×M16—22no—
271C2×M16—21no—
272C22×C8—22no—
273C22×C8C2×C4×C11311yescharacteristic
274C22×C8C2×C4×C11311yescharacteristic
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4D4×C11311yescharacteristic
282C4×D4D4×C11311yescharacteristic
283C4×D4D4×C11311yescharacteristic
284C4×D4D4×C11311yescharacteristic
285C2×C4⋊C4C2×C4×C11311yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C42C23×C11311yescharacteristic
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—21no—
295#103—21no—
296#103—21no—
297#102—21no—
298#102—21no—
299C22⋊C8—22no—
300C22⋊C8—22no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303C22⋊C8D4×C11311yescharacteristic
304C22⋊C8D4×C11311yescharacteristic
305#97—21no—
306#97—21no—
307#97D4×C11312yes—
308C4×C8—21no—
309C4×C8—21no—
310C24—21no—
311C24—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4C22⋊C4×C11311yescharacteristic
324C2×D4C22⋊C4×C11311yescharacteristic
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—82no—
332C22×C4C22×C4×C11311yescharacteristic
333C22×C4C2×D4×C11311yescharacteristic
334C22×C4#41×C11311yescharacteristic
335SD16—42no—
336SD16—42no—
337D8—42no—
338D8—42no—
339M16—22no—
340M16—41no—
341M16—82no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—22no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—82no—
352C4⋊C4—21no—
353C4⋊C4C22⋊C4×C11311yescharacteristic
354C4⋊C4C22⋊C4×C11311yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C42C2×D4×C11311yescharacteristic
364C42C2×D4×C11311yescharacteristic
365C42C2×D4×C11311yescharacteristic
366C42#41×C11311yescharacteristic
367C23—21no—
368C23—21no—
369C23—42no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23C4×D4×C11311yescharacteristic
379Q8—41no—
380Q8—41no—
381Q8—81no—
382D4—21no—
383D4—21no—
384D4—21no—
385D4—42no—
386D4—41no—
387D4—41no—
388D4—81no—
389D4#100×C11312yes—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4C2×C22⋊C4×C11311yescharacteristic
405C2×C4C4×D4×C11311yescharacteristic
406C2×C4#120×C11311yescharacteristic
407C2×C4#121×C11311yescharacteristic
408C2×C4#121×C11311yescharacteristic
409C2×C4#123×C11311yescharacteristic
410C8—41no—
411C8—42no—
412C8—41no—
413C8—42no—
414C8—41no—
415C8—41no—
416C8—81no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—82no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—161no—
431C22—161no—
432C22#386×C11311yescharacteristic
433C22#443×C11311yescharacteristic
434C22#444×C11311yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—81no—
443C4C2×#100×C11311yescharacteristic
444C4#413×C11311yescharacteristic
445C2—21no—
446C2—21no—
447C2—42no—
448C2—81no—
449C2—161no—
450C2C113×#187611yescharacteristic
451C2C113×#190011yescharacteristic
452C2C113×#190411yescharacteristic
subgroupG/H
center, socleC22×C113#386
commutatorC22×C4C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC22×D8×C113C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2974C2semidirect
3. C113×#1527C2semidirect
4. C113×#1490C2semidirect
5. C113×#1469C2semidirect
6. C113×#1290C2semidirect
7. C113×#1283C2semidirect
218. #9243C113direct (N × H)
228. #2974C2×C113semidirect
229. #1527C2×C113semidirect
230. #1490C2×C113semidirect
231. #1469C2×C113semidirect
232. #1290C2×C113semidirect
233. #1283C2×C113semidirect
234. C113#9243direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#463×C1132
C113×#29742
C113×#15272
C113×#14902
C113×#14692
C113×#12902
C113×#12832
#9243113