Finite Group Databasebeta

← C113×#9347 #43277367

Subgroups — C113×#9347 #43277367

Order 28928.

704 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3006C211yesmaximal, characteristic
2C113×#2880C211yesmaximal, characteristic, complemented
3C113×#1788C211yesmaximal, characteristic, complemented
4C113×#1519C211yesmaximal, characteristic, complemented
5C113×#1471C211yesmaximal, characteristic, complemented
6C113×#1305C211yesmaximal, characteristic, complemented
7C113×#1298C211yesmaximal, characteristic, complemented
8C22×#41×C113C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C113C411yescharacteristic, complemented
10C2×AGL(1,ℤ/8)×C113C411yescharacteristic, complemented
11C2×#131×C113—21no—
12C2×#121×C113C2211yescharacteristic
13#449×C113—21no—
14#449×C113—21no—
15#448×C113—21no—
16#447×C113—21no—
17#417×C113C411yescharacteristic, complemented
18#417×C113C411yescharacteristic, complemented
19C2×#103×C113—21no—
20C2×#102×C113—21no—
21#408×C113—21no—
22#408×C113—22no—
23#407×C113—21no—
24#407×C113C2211yescharacteristic
25#407×C113C2211yescharacteristic
26C2×C22⋊C8×C113—21no—
27C2×C22⋊C8×C113C2211yescharacteristic
28C2×C22⋊C8×C113C2211yescharacteristic
29#380×C113C2211yescharacteristic
30#327×C113—21no—
31#327×C113—21no—
32#323×C113—22no—
33C2×#41×C113—21no—
34C2×#41×C113—21no—
35C2×#41×C113—42no—
36C2×#41×C113—42no—
37C2×#41×C113C2×C411yescharacteristic
38C2×#41×C113C2×C411yescharacteristic
39C2×#41×C113D411yescharacteristic
40C2×#41×C113D411yescharacteristic
41C22×Q8×C113D411yescharacteristic
42C22×D4×C113—21no—
43C22×D4×C113—21no—
44C22×D4×C113C2×C411yescharacteristic
45C22×D4×C113D411yescharacteristic
46C23×C4×C113—21no—
47C23×C4×C113C2311yescharacteristic
48AGL(1,ℤ/8)×C113—42no—
49AGL(1,ℤ/8)×C113—42no—
50C2×SD16×C113—21no—
51C2×SD16×C113—21no—
52C2×D8×C113—21no—
53C2×D8×C113—21no—
54#131×C113—42no—
55#131×C113—42no—
56C2×M16×C113—22no—
57C2×M16×C113—21no—
58C2×M16×C113C2×C411yescharacteristic
59C2×M16×C113C2×C411yescharacteristic
60C22×C8×C113—22no—
61C22×C8×C113—21no—
62C22×C8×C113—21no—
63#121×C113—21no—
64#121×C113—21no—
65#121×C113—21no—
66#121×C113—21no—
67C2×C4⋊C4×C113—21no—
68C2×C4⋊C4×C113C2×C411yescharacteristic
69C2×C22⋊C4×C113—21no—
70C2×C22⋊C4×C113—21no—
71#103×C113—21no—
72#103×C113—21no—
73#103×C113—42no—
74#102×C113—21no—
75#102×C113—21no—
76#102×C113—42no—
77C22⋊C8×C113—22no—
78C22⋊C8×C113—22no—
79C22⋊C8×C113—21no—
80C22⋊C8×C113—21no—
81C22⋊C8×C113—21no—
82C22⋊C8×C113—21no—
83C22⋊C8×C113—21no—
84C22⋊C8×C113—21no—
85C22⋊C8×C113D412yes—
86C22⋊C8×C113D411yescharacteristic
87C22⋊C8×C113D411yescharacteristic
88#95×C113—21no—
89C24×C113—21no—
90C24×C113—21no—
91C24×C113#4111yescharacteristic
92#41×C113—22no—
93#41×C113—22no—
94#41×C113—22no—
95#41×C113—22no—
96#41×C113—41no—
97#41×C113—41no—
98#41×C113—41no—
99#41×C113—41no—
100#41×C113—44no—
101#41×C113—44no—
102C2×Q8×C113—21no—
103C2×Q8×C113—22no—
104C2×Q8×C113—41no—
105C2×Q8×C113C22⋊C411yescharacteristic
106C2×Q8×C113C22⋊C411yescharacteristic
107C2×D4×C113—21no—
108C2×D4×C113—22no—
109C2×D4×C113—21no—
110C2×D4×C113—21no—
111C2×D4×C113—21no—
112C2×D4×C113—21no—
113C2×D4×C113—21no—
114C2×D4×C113—21no—
115C2×D4×C113—41no—
116C2×D4×C113—41no—
117C2×D4×C113—41no—
118C2×D4×C113—44no—
119C2×D4×C113—41no—
120C2×D4×C113—41no—
121C2×D4×C113—81no—
122C2×D4×C113—81no—
123C2×D4×C113C22⋊C411yescharacteristic
124C2×D4×C113C22⋊C411yescharacteristic
125C22×C4×C113—21no—
126C22×C4×C113—21no—
127C22×C4×C113—21no—
128C22×C4×C113—21no—
129C22×C4×C113—21no—
130C22×C4×C113—21no—
131C22×C4×C113—41no—
132C22×C4×C113—41no—
133C22×C4×C113—44no—
134C22×C4×C113—41no—
135C22×C4×C113C22×C411yescharacteristic
136C22×C4×C113C2×D411yescharacteristic
137C22×C4×C113C2×D411yescharacteristic
138C22×C4×C113C2×D411yescharacteristic
139C22×C4×C113C2×D411yescharacteristic
140C22×C4×C113#4111yescharacteristic
141SD16×C113—42no—
142SD16×C113—42no—
143D8×C113—42no—
144D8×C113—42no—
145M16×C113—44no—
146M16×C113—41no—
147M16×C113—41no—
148M16×C113—41no—
149M16×C113—41no—
150C2×C8×C113—21no—
151C2×C8×C113—21no—
152C2×C8×C113—21no—
153C2×C8×C113—22no—
154C2×C8×C113—21no—
155C2×C8×C113—44no—
156C2×C8×C113—41no—
157C2×C8×C113—41no—
158C2×C8×C113—41no—
159C2×C8×C113—41no—
160C2×C8×C113—41no—
161C4⋊C4×C113—21no—
162C4⋊C4×C113—21no—
163C4⋊C4×C113—41no—
164C4⋊C4×C113—41no—
165C22⋊C4×C113—41no—
166C22⋊C4×C113—41no—
167C22⋊C4×C113—81no—
168C23×C113—21no—
169C23×C113—21no—
170C23×C113—21no—
171C23×C113—21no—
172C23×C113—41no—
173C23×C113—41no—
174C23×C113—42no—
175C23×C113—42no—
176C23×C113—41no—
177C23×C113—41no—
178C23×C113—41no—
179C23×C113—81no—
180C23×C113—81no—
181C23×C113—81no—
182C23×C113C4×D411yescharacteristic
183C23×C113#12111yescharacteristic
184C23×C113#12311yescharacteristic
185Q8×C113—21no—
186Q8×C113—21no—
187Q8×C113—21no—
188Q8×C113—42no—
189Q8×C113#9912yes—
190D4×C113—24no—
191D4×C113—21no—
192D4×C113—21no—
193D4×C113—21no—
194D4×C113—42no—
195D4×C113—42no—
196D4×C113—42no—
197D4×C113—42no—
198D4×C113—41no—
199D4×C113—41no—
200D4×C113—81no—
201D4×C113—82no—
202D4×C113—81no—
203D4×C113—81no—
204D4×C113#9912yes—
205C2×C4×C113—24no—
206C2×C4×C113—21no—
207C2×C4×C113—21no—
208C2×C4×C113—21no—
209C2×C4×C113—21no—
210C2×C4×C113—21no—
211C2×C4×C113—21no—
212C2×C4×C113—21no—
213C2×C4×C113—21no—
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—41no—
222C2×C4×C113—81no—
223C2×C4×C113—81no—
224C2×C4×C113—81no—
225C2×C4×C113—81no—
226C2×C4×C113C2×C22⋊C411yescharacteristic
227C2×C4×C113C4×D411yescharacteristic
228C2×C4×C113#12011yescharacteristic
229C2×C4×C113#12111yescharacteristic
230C8×C113—41no—
231C8×C113—42no—
232C8×C113—41no—
233C8×C113—41no—
234C8×C113—41no—
235C8×C113—81no—
236C22×C113—21no—
237C22×C113—21no—
238C22×C113—21no—
239C22×C113—21no—
240C22×C113—21no—
241C22×C113—22no—
242C22×C113—21no—
243C22×C113—21no—
244C22×C113—21no—
245C22×C113—41no—
246C22×C113—41no—
247C22×C113—41no—
248C22×C113—41no—
249C22×C113—41no—
250C22×C113—81no—
251C22×C113—81no—
252C22×C113—82no—
253C22×C113—82no—
254C22×C113—81no—
255C22×C113—81no—
256C22×C113—81no—
257C22×C113—162no—
258C22×C113#38611yescharacteristic
259C22×C113#47111yescharacteristic
260C22×C113#47211yescharacteristic
261C4×C113—21no—
262C4×C113—21no—
263C4×C113—22no—
264C4×C113—21no—
265C4×C113—41no—
266C4×C113—81no—
267C4×C113—161no—
268C4×C113C2×#9911yescharacteristic
269C4×C113C2×#9911yescharacteristic
270#9347C11311yesmaximal, characteristic, direct product factor, Sylow
271C2×C113—21no—
272C2×C113—21no—
273C2×C113—41no—
274C2×C113—41no—
275C2×C113—42no—
276C2×C113—81no—
277C2×C113—161no—
278C2×C113#188111yescharacteristic
279C2×C113#189811yescharacteristic
280C2×C113#190711yescharacteristic
281#3006C2×C11311yescharacteristic
282#2880C2×C11311yescharacteristic, complemented
283#1788C2×C11311yescharacteristic, complemented
284#1519C2×C11311yescharacteristic, complemented
285#1471C2×C11311yescharacteristic, complemented
286#1305C2×C11311yescharacteristic, complemented
287#1298C2×C11311yescharacteristic, complemented
288C113#934711yescharacteristic, direct product factor, Sylow
289C22×#41C22×C11311yescharacteristic
290C2×AGL(1,ℤ/8)C4×C11311yescharacteristic, complemented
291C2×AGL(1,ℤ/8)C4×C11311yescharacteristic, complemented
292C2×#131—21no—
293C2×#121C22×C11311yescharacteristic
294#449—21no—
295#449—21no—
296#448—21no—
297#447—21no—
298#417C4×C11311yescharacteristic, complemented
299#417C4×C11311yescharacteristic, complemented
300C2×#103—21no—
301C2×#102—21no—
302#408—21no—
303#408—22no—
304#407—21no—
305#407C22×C11311yescharacteristic
306#407C22×C11311yescharacteristic
307C2×C22⋊C8—21no—
308C2×C22⋊C8C22×C11311yescharacteristic
309C2×C22⋊C8C22×C11311yescharacteristic
310#380C22×C11311yescharacteristic
311#327—21no—
312#327—21no—
313#323—22no—
314C2×#41—21no—
315C2×#41—21no—
316C2×#41—42no—
317C2×#41—42no—
318C2×#41C2×C4×C11311yescharacteristic
319C2×#41C2×C4×C11311yescharacteristic
320C2×#41D4×C11311yescharacteristic
321C2×#41D4×C11311yescharacteristic
322C22×Q8D4×C11311yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C2×C4×C11311yescharacteristic
326C22×D4D4×C11311yescharacteristic
327C23×C4—21no—
328C23×C4C23×C11311yescharacteristic
329AGL(1,ℤ/8)—42no—
330AGL(1,ℤ/8)—42no—
331C2×SD16—21no—
332C2×SD16—21no—
333C2×D8—21no—
334C2×D8—21no—
335#131—42no—
336#131—42no—
337C2×M16—22no—
338C2×M16—21no—
339C2×M16C2×C4×C11311yescharacteristic
340C2×M16C2×C4×C11311yescharacteristic
341C22×C8—22no—
342C22×C8—21no—
343C22×C8—21no—
344#121—21no—
345#121—21no—
346#121—21no—
347#121—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C2×C4×C11311yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352#103—21no—
353#103—21no—
354#103—42no—
355#102—21no—
356#102—21no—
357#102—42no—
358C22⋊C8—22no—
359C22⋊C8—22no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8D4×C11312yes—
367C22⋊C8D4×C11311yescharacteristic
368C22⋊C8D4×C11311yescharacteristic
369#95—21no—
370C24—21no—
371C24—21no—
372C24#41×C11311yescharacteristic
373#41—22no—
374#41—22no—
375#41—22no—
376#41—22no—
377#41—41no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—44no—
382#41—44no—
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—41no—
386C2×Q8C22⋊C4×C11311yescharacteristic
387C2×Q8C22⋊C4×C11311yescharacteristic
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—44no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—81no—
403C2×D4—81no—
404C2×D4C22⋊C4×C11311yescharacteristic
405C2×D4C22⋊C4×C11311yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—44no—
415C22×C4—41no—
416C22×C4C22×C4×C11311yescharacteristic
417C22×C4C2×D4×C11311yescharacteristic
418C22×C4C2×D4×C11311yescharacteristic
419C22×C4C2×D4×C11311yescharacteristic
420C22×C4C2×D4×C11311yescharacteristic
421C22×C4#41×C11311yescharacteristic
422SD16—42no—
423SD16—42no—
424D8—42no—
425D8—42no—
426M16—44no—
427M16—41no—
428M16—41no—
429M16—41no—
430M16—41no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—44no—
437C2×C8—41no—
438C2×C8—41no—
439C2×C8—41no—
440C2×C8—41no—
441C2×C8—41no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—81no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—41no—
454C23—41no—
455C23—42no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23C4×D4×C11311yescharacteristic
464C23#121×C11311yescharacteristic
465C23#123×C11311yescharacteristic
466Q8—21no—
467Q8—21no—
468Q8—21no—
469Q8—42no—
470Q8#99×C11312yes—
471D4—24no—
472D4—21no—
473D4—21no—
474D4—21no—
475D4—42no—
476D4—42no—
477D4—42no—
478D4—42no—
479D4—41no—
480D4—41no—
481D4—81no—
482D4—82no—
483D4—81no—
484D4—81no—
485D4#99×C11312yes—
486C2×C4—24no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—81no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4C2×C22⋊C4×C11311yescharacteristic
508C2×C4C4×D4×C11311yescharacteristic
509C2×C4#120×C11311yescharacteristic
510C2×C4#121×C11311yescharacteristic
511C8—41no—
512C8—42no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—81no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—22no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—81no—
532C22—81no—
533C22—82no—
534C22—82no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—162no—
539C22#386×C11311yescharacteristic
540C22#471×C11311yescharacteristic
541C22#472×C11311yescharacteristic
542C4—21no—
543C4—21no—
544C4—22no—
545C4—21no—
546C4—41no—
547C4—81no—
548C4—161no—
549C4C2×#99×C11311yescharacteristic
550C4C2×#99×C11311yescharacteristic
551C2—21no—
552C2—21no—
553C2—41no—
554C2—41no—
555C2—42no—
556C2—81no—
557C2—161no—
558C2C113×#188111yescharacteristic
559C2C113×#189811yescharacteristic
560C2C113×#190711yescharacteristic
subgroupG/H
center, socleC22×C113#386
commutatorC22×C4C22×C4×C113
Frattini, cosocleC23×C4C23×C113
prime radicalC113×#3006C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2880C2semidirect
3. C113×#1788C2semidirect
4. C113×#1519C2semidirect
5. C113×#1471C2semidirect
6. C113×#1305C2semidirect
7. C113×#1298C2semidirect
9. C2×AGL(1,ℤ/8)×C113C4semidirect
10. C2×AGL(1,ℤ/8)×C113C4semidirect
17. #417×C113C4semidirect
18. #417×C113C4semidirect
270. #9347C113direct (N × H)
282. #2880C2×C113semidirect
283. #1788C2×C113semidirect
284. #1519C2×C113semidirect
285. #1471C2×C113semidirect
286. #1305C2×C113semidirect
287. #1298C2×C113semidirect
288. C113#9347direct (N × H)
290. C2×AGL(1,ℤ/8)C4×C113semidirect
291. C2×AGL(1,ℤ/8)C4×C113semidirect
298. #417C4×C113semidirect
299. #417C4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#30062
C113×#28802
C113×#17882
C113×#15192
C113×#14712
C113×#13052
C113×#12982
#9347113