Finite Group Databasebeta

← C113×#8377 #43276397

Subgroups — C113×#8377 #43276397

Order 28928.

1060 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C113C211yesmaximal, characteristic
2C113×#1799C211yesmaximal, characteristic, complemented
3C113×#1787C212yesmaximal, complemented
4C113×#1519C212yesmaximal, complemented
5C113×#1459C211yesmaximal, characteristic, complemented
6C22×#41×C113C411yescharacteristic, complemented
7C23×Q8×C113C2211yescharacteristic
8#548×C113—24no—
9#548×C113—24no—
10C2×#124×C113—21no—
11C2×#124×C113C411yescharacteristic, complemented
12C2×C22⋊Q8×C113—21no—
13C2×C22⋊Q8×C113C411yescharacteristic, complemented
14C2×#121×C113—21no—
15C2×#121×C113C2211yescharacteristic
16C2×C4×Q8×C113C411yescharacteristic, complemented
17C2×C4×D4×C113—21no—
18C2×C4×D4×C113C2211yescharacteristic
19C2×#103×C113—24no—
20C2×#99×C113—21no—
21C2×C22⋊C8×C113C2212yes—
22#380×C113C2212yes—
23#342×C113—21no—
24#327×C113—24no—
25#324×C113—21no—
26#323×C113—21no—
27C2×#41×C113—22no—
28C2×#41×C113—22no—
29C2×#41×C113—44no—
30C22×Q8×C113—21no—
31C22×Q8×C113—22no—
32C22×Q8×C113—44no—
33C22×Q8×C113C2×C411yescharacteristic
34C22×Q8×C113C2×C411yescharacteristic
35C22×Q8×C113D414yes—
36C22×D4×C113—21no—
37C22×D4×C113—21no—
38C22×D4×C113C2×C411yescharacteristic
39C22×D4×C113D411yescharacteristic
40C23×C4×C113—21no—
41C23×C4×C113—21no—
42C23×C4×C113C2×C411yescharacteristic
43C23×C4×C113C2311yescharacteristic
44C22×C8×C113—22no—
45#124×C113—28no—
46#124×C113—22no—
47#124×C113—22no—
48C22⋊Q8×C113—28no—
49C22⋊Q8×C113—22no—
50C22⋊Q8×C113—22no—
51#121×C113—28no—
52#121×C113—22no—
53#121×C113D414yes—
54C4×Q8×C113—22no—
55C4×Q8×C113—22no—
56C4×D4×C113—28no—
57C4×D4×C113—22no—
58C4×D4×C113—22no—
59C2×C4⋊C4×C113—21no—
60C2×C4⋊C4×C113—21no—
61C2×C4⋊C4×C113—22no—
62C2×C4⋊C4×C113C2×C411yescharacteristic
63C2×C4⋊C4×C113D411yescharacteristic
64C2×C22⋊C4×C113—21no—
65C2×C22⋊C4×C113—21no—
66C2×C22⋊C4×C113—21no—
67C2×C22⋊C4×C113—21no—
68C2×C22⋊C4×C113—22no—
69C2×C22⋊C4×C113D411yescharacteristic
70C2×C22⋊C4×C113D411yescharacteristic
71C2×C42×C113—21no—
72C2×C42×C113C2×C411yescharacteristic
73#103×C113—48no—
74#99×C113—42no—
75C22⋊C8×C113—22no—
76C22⋊C8×C113—22no—
77#95×C113—22no—
78C24×C113—21no—
79C24×C113C22⋊C411yescharacteristic
80C24×C113C2×D411yescharacteristic
81#41×C113—48no—
82#41×C113—44no—
83#41×C113—44no—
84C2×Q8×C113—24no—
85C2×Q8×C113—21no—
86C2×Q8×C113—21no—
87C2×Q8×C113—24no—
88C2×Q8×C113—28no—
89C2×Q8×C113—42no—
90C2×Q8×C113—44no—
91C2×Q8×C113—44no—
92C2×Q8×C113—48no—
93C2×Q8×C113C22⋊C412yes—
94C2×Q8×C113C22⋊C412yes—
95C2×D4×C113—24no—
96C2×D4×C113—22no—
97C2×D4×C113—24no—
98C2×D4×C113—22no—
99C2×D4×C113—21no—
100C2×D4×C113—21no—
101C2×D4×C113—21no—
102C2×D4×C113—44no—
103C2×D4×C113—42no—
104C2×D4×C113—42no—
105C2×D4×C113—41no—
106C2×D4×C113—41no—
107C2×D4×C113C22⋊C412yes—
108C22×C4×C113—21no—
109C22×C4×C113—24no—
110C22×C4×C113—21no—
111C22×C4×C113—21no—
112C22×C4×C113—24no—
113C22×C4×C113—21no—
114C22×C4×C113—21no—
115C22×C4×C113—42no—
116C22×C4×C113—44no—
117C22×C4×C113—44no—
118C22×C4×C113—42no—
119C22×C4×C113—42no—
120C22×C4×C113C22⋊C411yescharacteristic
121C22×C4×C113C22⋊C411yescharacteristic
122C22×C4×C113C22⋊C411yescharacteristic
123C22×C4×C113C22×C411yescharacteristic
124C22×C4×C113C2×D412yes—
125C22×C4×C113C2×D412yes—
126C22×C4×C113C2×D411yescharacteristic
127C2×C8×C113—44no—
128C2×C8×C113—42no—
129C4⋊C4×C113—24no—
130C4⋊C4×C113—24no—
131C4⋊C4×C113—21no—
132C4⋊C4×C113—22no—
133C4⋊C4×C113—44no—
134C4⋊C4×C113C22⋊C412yes—
135C22⋊C4×C113—24no—
136C22⋊C4×C113—24no—
137C22⋊C4×C113—24no—
138C22⋊C4×C113—22no—
139C22⋊C4×C113—24no—
140C22⋊C4×C113—22no—
141C22⋊C4×C113—42no—
142C22⋊C4×C113—42no—
143C42×C113—24no—
144C42×C113—21no—
145C42×C113—21no—
146C23×C113—21no—
147C23×C113—22no—
148C23×C113—21no—
149C23×C113—21no—
150C23×C113—41no—
151C23×C113—41no—
152C23×C113—42no—
153C23×C113—42no—
154C23×C113—41no—
155C23×C113—41no—
156C23×C113—41no—
157C23×C113—41no—
158C23×C113C2×C22⋊C411yescharacteristic
159C23×C113#12012yes—
160C23×C113#13512yes—
161C23×C113AGL(1,ℤ/8)11yescharacteristic
162C23×C113#13711yescharacteristic
163Q8×C113—24no—
164Q8×C113—22no—
165Q8×C113—24no—
166Q8×C113—48no—
167Q8×C113—42no—
168Q8×C113#9914yescomplemented
169D4×C113—42no—
170D4×C113—48no—
171D4×C113—42no—
172D4×C113—44no—
173D4×C113—42no—
174D4×C113—44no—
175D4×C113—42no—
176C2×C4×C113—24no—
177C2×C4×C113—22no—
178C2×C4×C113—24no—
179C2×C4×C113—22no—
180C2×C4×C113—21no—
181C2×C4×C113—21no—
182C2×C4×C113—22no—
183C2×C4×C113—22no—
184C2×C4×C113—21no—
185C2×C4×C113—21no—
186C2×C4×C113—21no—
187C2×C4×C113—41no—
188C2×C4×C113—42no—
189C2×C4×C113—48no—
190C2×C4×C113—48no—
191C2×C4×C113—42no—
192C2×C4×C113—42no—
193C2×C4×C113—41no—
194C2×C4×C113—41no—
195C2×C4×C113—42no—
196C2×C4×C113—41no—
197C2×C4×C113—41no—
198C2×C4×C113—82no—
199C2×C4×C113—82no—
200C2×C4×C113—82no—
201C2×C4×C113C2×C22⋊C411yescharacteristic
202C2×C4×C113C2×C22⋊C411yescharacteristic
203C2×C4×C113#12012yes—
204C8×C113—82no—
205C22×C113—21no—
206C22×C113—22no—
207C22×C113—21no—
208C22×C113—22no—
209C22×C113—42no—
210C22×C113—41no—
211C22×C113—41no—
212C22×C113—41no—
213C22×C113—42no—
214C22×C113—41no—
215C22×C113—42no—
216C22×C113—41no—
217C22×C113—42no—
218C22×C113—81no—
219C22×C113—81no—
220C22×C113—82no—
221C22×C113—82no—
222C22×C113#37911yescharacteristic
223C22×C113#41611yescharacteristic
224C22×C113#41711yescharacteristic
225C22×C113#44912yes—
226C22×C113#45212yes—
227C4×C113—22no—
228C4×C113—24no—
229C4×C113—21no—
230C4×C113—41no—
231C4×C113—41no—
232C4×C113—42no—
233C4×C113—41no—
234C4×C113—42no—
235C4×C113—162no—
236C4×C113C2×#9912yes—
237#8377C11311yesmaximal, characteristic, direct product factor, Sylow
238C2×C113—22no—
239C2×C113—21no—
240C2×C113—21no—
241C2×C113—22no—
242C2×C113—81no—
243C2×C113—82no—
244C2×C113#178111yescharacteristic
245C2×C113#178811yescharacteristic
246C2×C113#179611yescharacteristic
247C2×#548C2×C11311yescharacteristic
248#1799C2×C11311yescharacteristic, complemented
249#1787C2×C11312yescomplemented
250#1519C2×C11312yescomplemented
251#1459C2×C11311yescharacteristic, complemented
252C113#837711yescharacteristic, direct product factor, Sylow
253C22×#41C4×C11311yescharacteristic, complemented
254C23×Q8C22×C11311yescharacteristic
255#548—24no—
256#548—24no—
257C2×#124—21no—
258C2×#124C4×C11311yescharacteristic, complemented
259C2×C22⋊Q8—21no—
260C2×C22⋊Q8C4×C11311yescharacteristic, complemented
261C2×#121—21no—
262C2×#121C22×C11311yescharacteristic
263C2×C4×Q8C4×C11311yescharacteristic, complemented
264C2×C4×D4—21no—
265C2×C4×D4C22×C11311yescharacteristic
266C2×#103—24no—
267C2×#99—21no—
268C2×C22⋊C8C22×C11312yes—
269#380C22×C11312yes—
270#342—21no—
271#327—24no—
272#324—21no—
273#323—21no—
274C2×#41—22no—
275C2×#41—22no—
276C2×#41—44no—
277C22×Q8—21no—
278C22×Q8—22no—
279C22×Q8—44no—
280C22×Q8C2×C4×C11311yescharacteristic
281C22×Q8C2×C4×C11311yescharacteristic
282C22×Q8D4×C11314yes—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4C2×C4×C11311yescharacteristic
286C22×D4D4×C11311yescharacteristic
287C23×C4—21no—
288C23×C4—21no—
289C23×C4C2×C4×C11311yescharacteristic
290C23×C4C23×C11311yescharacteristic
291C22×C8—22no—
292#124—28no—
293#124—22no—
294#124—22no—
295C22⋊Q8—28no—
296C22⋊Q8—22no—
297C22⋊Q8—22no—
298#121—28no—
299#121—22no—
300#121D4×C11314yes—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×D4—28no—
304C4×D4—22no—
305C4×D4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4C2×C4×C11311yescharacteristic
310C2×C4⋊C4D4×C11311yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4D4×C11311yescharacteristic
317C2×C22⋊C4D4×C11311yescharacteristic
318C2×C42—21no—
319C2×C42C2×C4×C11311yescharacteristic
320#103—48no—
321#99—42no—
322C22⋊C8—22no—
323C22⋊C8—22no—
324#95—22no—
325C24—21no—
326C24C22⋊C4×C11311yescharacteristic
327C24C2×D4×C11311yescharacteristic
328#41—48no—
329#41—44no—
330#41—44no—
331C2×Q8—24no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—24no—
335C2×Q8—28no—
336C2×Q8—42no—
337C2×Q8—44no—
338C2×Q8—44no—
339C2×Q8—48no—
340C2×Q8C22⋊C4×C11312yes—
341C2×Q8C22⋊C4×C11312yes—
342C2×D4—24no—
343C2×D4—22no—
344C2×D4—24no—
345C2×D4—22no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—44no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4C22⋊C4×C11312yes—
355C22×C4—21no—
356C22×C4—24no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—24no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—42no—
363C22×C4—44no—
364C22×C4—44no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4C22⋊C4×C11311yescharacteristic
368C22×C4C22⋊C4×C11311yescharacteristic
369C22×C4C22⋊C4×C11311yescharacteristic
370C22×C4C22×C4×C11311yescharacteristic
371C22×C4C2×D4×C11312yes—
372C22×C4C2×D4×C11312yes—
373C22×C4C2×D4×C11311yescharacteristic
374C2×C8—44no—
375C2×C8—42no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—44no—
381C4⋊C4C22⋊C4×C11312yes—
382C22⋊C4—24no—
383C22⋊C4—24no—
384C22⋊C4—24no—
385C22⋊C4—22no—
386C22⋊C4—24no—
387C22⋊C4—22no—
388C22⋊C4—42no—
389C22⋊C4—42no—
390C42—24no—
391C42—21no—
392C42—21no—
393C23—21no—
394C23—22no—
395C23—21no—
396C23—21no—
397C23—41no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23C2×C22⋊C4×C11311yescharacteristic
406C23#120×C11312yes—
407C23#135×C11312yes—
408C23AGL(1,ℤ/8)×C11311yescharacteristic
409C23#137×C11311yescharacteristic
410Q8—24no—
411Q8—22no—
412Q8—24no—
413Q8—48no—
414Q8—42no—
415Q8#99×C11314yescomplemented
416D4—42no—
417D4—48no—
418D4—42no—
419D4—44no—
420D4—42no—
421D4—44no—
422D4—42no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—48no—
437C2×C4—48no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4C2×C22⋊C4×C11311yescharacteristic
449C2×C4C2×C22⋊C4×C11311yescharacteristic
450C2×C4#120×C11312yes—
451C8—82no—
452C22—21no—
453C22—22no—
454C22—21no—
455C22—22no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—42no—
461C22—41no—
462C22—42no—
463C22—42no—
464C22—41no—
465C22—81no—
466C22—81no—
467C22—82no—
468C22—82no—
469C22#379×C11311yescharacteristic
470C22#416×C11311yescharacteristic
471C22#417×C11311yescharacteristic
472C22#449×C11312yes—
473C22#452×C11312yes—
474C4—22no—
475C4—24no—
476C4—21no—
477C4—41no—
478C4—42no—
479C4—41no—
480C4—42no—
481C4—41no—
482C4—162no—
483C4C2×#99×C11312yes—
484C2—22no—
485C2—21no—
486C2—21no—
487C2—22no—
488C2—82no—
489C2—81no—
490C2C113×#178111yescharacteristic
491C2C113×#178811yescharacteristic
492C2C113×#179611yescharacteristic
subgroupG/H
center, socleC22×C113#379
commutatorC22×C4C22×C4×C113
Frattini, cosocleC23×C4C23×C113
prime radicalC2×#548×C113C2
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×#1799C2semidirect
3. C113×#1787C2semidirect
4. C113×#1519C2semidirect
5. C113×#1459C2semidirect
6. C22×#41×C113C4semidirect
11. C2×#124×C113C4semidirect
13. C2×C22⋊Q8×C113C4semidirect
16. C2×C4×Q8×C113C4semidirect
168. Q8×C113#99semidirect
237. #8377C113direct (N × H)
248. #1799C2×C113semidirect
249. #1787C2×C113semidirect
250. #1519C2×C113semidirect
251. #1459C2×C113semidirect
252. C113#8377direct (N × H)
253. C22×#41C4×C113semidirect
258. C2×#124C4×C113semidirect
260. C2×C22⋊Q8C4×C113semidirect
263. C2×C4×Q8C4×C113semidirect
415. Q8#99×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1132
C113×#17992
C113×#17872
C113×#15192
C113×#14592
#8377113