Finite Group Databasebeta

← C113×#18909 #43286929

Subgroups — C113×#18909 #43286929

Order 28928.

882 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3507C211yesmaximal, characteristic
2C113×#3230C211yesmaximal, characteristic, complemented
3C113×#3206C211yesmaximal, characteristic
4C2×#475×C113C211yesmaximal, characteristic, complemented
5C113×#1650C214yesmaximal, complemented
6C113×#1643C214yesmaximal, complemented
7C113×#1542C211yesmaximal, characteristic, complemented
8C113×#1480C211yesmaximal, characteristic
9C113×#1479C211yesmaximal, characteristic, complemented
10#559×C113—21no—
11#557×C113—21no—
12#556×C113—22no—
13#556×C113C2212yes—
14#554×C113C2212yes—
15#552×C113—22no—
16#539×C113—22no—
17#536×C113—21no—
18#533×C113C2211yescharacteristic
19#532×C113C2211yescharacteristic
20C2×C4⋊Q8×C113C2211yescharacteristic
21#529×C113—22no—
22#520×C113—21no—
23C2×C4×Q8×C113C2211yescharacteristic
24#500×C113C2212yes—
25#492×C113—21no—
26#487×C113—21no—
27#487×C113C2212yes—
28#484×C113—22no—
29#477×C113—22no—
30#475×C113—22no—
31#475×C113C2214yes—
32#461×C113C2214yes—
33#448×C113—22no—
34#431×C113C2211yescharacteristic
35#431×C113C2211yescharacteristic
36C2×#106×C113—21no—
37C2×C4⋊C8×C113C2211yescharacteristic
38C2×#103×C113—21no—
39#333×C113C2212yes—
40#332×C113C2212yes—
41Q8⋊C8×C113C2214yes—
42D4⋊C8×C113C2214yes—
43C2×#41×C113—21no—
44C22×Q8×C113—21no—
45C22×Q8×C113D411yescharacteristic
46C2×SD16×C113—24no—
47C22×C8×C113—21no—
48C4⋊Q8×C113—22no—
49C4⋊Q8×C113—21no—
50C4⋊Q8×C113—21no—
51C4⋊Q8×C113—21no—
52C4⋊Q8×C113D411yescharacteristic
53C4⋊Q8×C113C2312yes—
54C4⋊Q8×C113C2311yescharacteristic
55C4⋊Q8×C113C2311yescharacteristic
56#127×C113D411yescharacteristic
57#126×C113—24no—
58#126×C113—24no—
59#125×C113—24no—
60#125×C113—22no—
61#125×C113—21no—
62#124×C113—22no—
63#124×C113—22no—
64#124×C113—21no—
65#123×C113—24no—
66#123×C113—24no—
67C22⋊Q8×C113—22no—
68C22⋊Q8×C113—22no—
69C22⋊Q8×C113—24no—
70C22⋊Q8×C113—21no—
71C22⋊Q8×C113D412yes—
72#121×C113—21no—
73#121×C113D412yes—
74C4×Q8×C113—22no—
75C4×Q8×C113—22no—
76C4×Q8×C113—21no—
77C4×Q8×C113—21no—
78C4×Q8×C113—21no—
79C4×Q8×C113D412yes—
80C4×Q8×C113D412yes—
81C4×Q8×C113C2312yes—
82C4×D4×C113—24no—
83C4×D4×C113—22no—
84C4×D4×C113—22no—
85C4×D4×C113—21no—
86C4×D4×C113C2312yes—
87#117×C113—24no—
88#117×C113—21no—
89#117×C113—22no—
90C2×C4⋊C4×C113—21no—
91C2×C4⋊C4×C113—22no—
92C2×C4⋊C4×C113—21no—
93C2×C4⋊C4×C113—21no—
94C2×C4⋊C4×C113D411yescharacteristic
95C2×C42×C113—21no—
96C2×C42×C113C2311yescharacteristic
97#107×C113—24no—
98#106×C113—24no—
99C4⋊C8×C113—21no—
100C4⋊C8×C113—21no—
101C4⋊C8×C113C2312yes—
102C4⋊C8×C113C2312yes—
103#103×C113—24no—
104#103×C113—24no—
105#103×C113—24no—
106C22⋊C8×C113—21no—
107C22⋊C8×C113—21no—
108C4×C8×C113—21no—
109C4×C8×C113C2312yes—
110#41×C113—42no—
111#41×C113—42no—
112C2×Q8×C113—21no—
113C2×Q8×C113—21no—
114C2×Q8×C113—21no—
115C2×Q8×C113—22no—
116C2×Q8×C113—22no—
117C2×Q8×C113—22no—
118C2×Q8×C113—41no—
119C2×Q8×C113—82no—
120C2×Q8×C113C2×D412yes—
121C2×Q8×C113C2×D412yes—
122C2×D4×C113—22no—
123C2×D4×C113—21no—
124C2×D4×C113—21no—
125C2×D4×C113C2×D412yes—
126C22×C4×C113—21no—
127C22×C4×C113—24no—
128C22×C4×C113—21no—
129C22×C4×C113—22no—
130C22×C4×C113—41no—
131C22×C4×C113C2×D411yescharacteristic
132C22×C4×C113C2×D411yescharacteristic
133C22×C4×C113C2×D411yescharacteristic
134SD16×C113—84no—
135C2×C8×C113—22no—
136C2×C8×C113—22no—
137C2×C8×C113—22no—
138C2×C8×C113—42no—
139C4⋊C4×C113—24no—
140C4⋊C4×C113—24no—
141C4⋊C4×C113—24no—
142C4⋊C4×C113—22no—
143C4⋊C4×C113—21no—
144C4⋊C4×C113—22no—
145C4⋊C4×C113—21no—
146C4⋊C4×C113—22no—
147C4⋊C4×C113—21no—
148C4⋊C4×C113—22no—
149C4⋊C4×C113—21no—
150C4⋊C4×C113—21no—
151C4⋊C4×C113—22no—
152C4⋊C4×C113—22no—
153C4⋊C4×C113—41no—
154C4⋊C4×C113—41no—
155C4⋊C4×C113C2×D412yes—
156C4⋊C4×C113C2×D412yes—
157C4⋊C4×C113C2×D412yes—
158C22⋊C4×C113—24no—
159C22⋊C4×C113—24no—
160C22⋊C4×C113—24no—
161C22⋊C4×C113—22no—
162C22⋊C4×C113—22no—
163C22⋊C4×C113—22no—
164C42×C113—24no—
165C42×C113—22no—
166C42×C113—22no—
167C42×C113—22no—
168C42×C113C2×D411yescharacteristic
169C42×C113C2×D411yescharacteristic
170C42×C113C2×D411yescharacteristic
171C42×C113C2411yescharacteristic
172C23×C113—22no—
173C23×C113#12011yescharacteristic
174Q8×C113—22no—
175Q8×C113—22no—
176Q8×C113—42no—
177Q8×C113—42no—
178Q8×C113—42no—
179Q8×C113—42no—
180Q8×C113—44no—
181Q8×C113—82no—
182D4×C113—24no—
183D4×C113—44no—
184D4×C113—42no—
185D4×C113—81no—
186C2×C4×C113—22no—
187C2×C4×C113—22no—
188C2×C4×C113—22no—
189C2×C4×C113—22no—
190C2×C4×C113—22no—
191C2×C4×C113—22no—
192C2×C4×C113—41no—
193C2×C4×C113—42no—
194C2×C4×C113—42no—
195C2×C4×C113—42no—
196C2×C4×C113—42no—
197C2×C4×C113—81no—
198C2×C4×C113—84no—
199C2×C4×C113—82no—
200C2×C4×C113#12011yescharacteristic
201C2×C4×C113#12011yescharacteristic
202C2×C4×C113#12011yescharacteristic
203C2×C4×C113#13512yes—
204C2×C4×C113#13712yes—
205C2×C4×C113C22×D411yescharacteristic
206C2×C4×C113C22×D411yescharacteristic
207C2×C4×C113C22×D411yescharacteristic
208C8×C113—42no—
209C8×C113—42no—
210C8×C113—42no—
211C22×C113—21no—
212C22×C113—21no—
213C22×C113—42no—
214C22×C113—42no—
215C22×C113—42no—
216C22×C113#45212yes—
217C22×C113C2×#12011yescharacteristic
218C4×C113—21no—
219C4×C113—21no—
220C4×C113—21no—
221C4×C113—42no—
222C4×C113—42no—
223C4×C113—42no—
224C4×C113—42no—
225C4×C113—42no—
226C4×C113—82no—
227C4×C113#45212yes—
228C4×C113C2×#13511yescharacteristic
229C4×C113C2×#13711yescharacteristic
230C4×C113#57712yes—
231#18909C11311yesmaximal, characteristic, direct product factor, Sylow
232C2×C113—22no—
233C2×C113—82no—
234C2×C113C2×#45211yescharacteristic
235C2×C113#301011yescharacteristic
236C2×C113#302211yescharacteristic
237#3507C2×C11311yescharacteristic
238#3230C2×C11311yescharacteristic, complemented
239#3206C2×C11311yescharacteristic
240C2×#475C2×C11311yescharacteristic, complemented
241#1650C2×C11314yescomplemented
242#1643C2×C11314yescomplemented
243#1542C2×C11311yescharacteristic, complemented
244#1480C2×C11311yescharacteristic
245#1479C2×C11311yescharacteristic, complemented
246C113#1890911yescharacteristic, direct product factor, Sylow
247#559—21no—
248#557—21no—
249#556—22no—
250#556C22×C11312yes—
251#554C22×C11312yes—
252#552—22no—
253#539—22no—
254#536—21no—
255#533C22×C11311yescharacteristic
256#532C22×C11311yescharacteristic
257C2×C4⋊Q8C22×C11311yescharacteristic
258#529—22no—
259#520—21no—
260C2×C4×Q8C22×C11311yescharacteristic
261#500C22×C11312yes—
262#492—21no—
263#487—21no—
264#487C22×C11312yes—
265#484—22no—
266#477—22no—
267#475—22no—
268#475C22×C11314yes—
269#461C22×C11314yes—
270#448—22no—
271#431C22×C11311yescharacteristic
272#431C22×C11311yescharacteristic
273C2×#106—21no—
274C2×C4⋊C8C22×C11311yescharacteristic
275C2×#103—21no—
276#333C22×C11312yes—
277#332C22×C11312yes—
278Q8⋊C8C22×C11314yes—
279D4⋊C8C22×C11314yes—
280C2×#41—21no—
281C22×Q8—21no—
282C22×Q8D4×C11311yescharacteristic
283C2×SD16—24no—
284C22×C8—21no—
285C4⋊Q8—22no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8D4×C11311yescharacteristic
290C4⋊Q8C23×C11312yes—
291C4⋊Q8C23×C11311yescharacteristic
292C4⋊Q8C23×C11311yescharacteristic
293#127D4×C11311yescharacteristic
294#126—24no—
295#126—24no—
296#125—24no—
297#125—22no—
298#125—21no—
299#124—22no—
300#124—22no—
301#124—21no—
302#123—24no—
303#123—24no—
304C22⋊Q8—22no—
305C22⋊Q8—22no—
306C22⋊Q8—24no—
307C22⋊Q8—21no—
308C22⋊Q8D4×C11312yes—
309#121—21no—
310#121D4×C11312yes—
311C4×Q8—22no—
312C4×Q8—22no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8D4×C11312yes—
317C4×Q8D4×C11312yes—
318C4×Q8C23×C11312yes—
319C4×D4—24no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—21no—
323C4×D4C23×C11312yes—
324#117—24no—
325#117—21no—
326#117—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4D4×C11311yescharacteristic
332C2×C42—21no—
333C2×C42C23×C11311yescharacteristic
334#107—24no—
335#106—24no—
336C4⋊C8—21no—
337C4⋊C8—21no—
338C4⋊C8C23×C11312yes—
339C4⋊C8C23×C11312yes—
340#103—24no—
341#103—24no—
342#103—24no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C4×C8—21no—
346C4×C8C23×C11312yes—
347#41—42no—
348#41—42no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—41no—
356C2×Q8—82no—
357C2×Q8C2×D4×C11312yes—
358C2×Q8C2×D4×C11312yes—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4C2×D4×C11312yes—
363C22×C4—21no—
364C22×C4—24no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—41no—
368C22×C4C2×D4×C11311yescharacteristic
369C22×C4C2×D4×C11311yescharacteristic
370C22×C4C2×D4×C11311yescharacteristic
371SD16—84no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—42no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—24no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4C2×D4×C11312yes—
393C4⋊C4C2×D4×C11312yes—
394C4⋊C4C2×D4×C11312yes—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C42—24no—
402C42—22no—
403C42—22no—
404C42—22no—
405C42C2×D4×C11311yescharacteristic
406C42C2×D4×C11311yescharacteristic
407C42C2×D4×C11311yescharacteristic
408C42C24×C11311yescharacteristic
409C23—22no—
410C23#120×C11311yescharacteristic
411Q8—22no—
412Q8—22no—
413Q8—42no—
414Q8—42no—
415Q8—42no—
416Q8—42no—
417Q8—44no—
418Q8—82no—
419D4—24no—
420D4—44no—
421D4—42no—
422D4—81no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—81no—
435C2×C4—84no—
436C2×C4—82no—
437C2×C4#120×C11311yescharacteristic
438C2×C4#120×C11311yescharacteristic
439C2×C4#120×C11311yescharacteristic
440C2×C4#135×C11312yes—
441C2×C4#137×C11312yes—
442C2×C4C22×D4×C11311yescharacteristic
443C2×C4C22×D4×C11311yescharacteristic
444C2×C4C22×D4×C11311yescharacteristic
445C8—42no—
446C8—42no—
447C8—42no—
448C22—21no—
449C22—21no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22#452×C11312yes—
454C22C2×#120×C11311yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—42no—
459C4—42no—
460C4—42no—
461C4—42no—
462C4—42no—
463C4—82no—
464C4#452×C11312yes—
465C4C2×#135×C11311yescharacteristic
466C4C2×#137×C11311yescharacteristic
467C4#577×C11312yes—
468C2—22no—
469C2—82no—
470C2C2×#452×C11311yescharacteristic
471C2C113×#301011yescharacteristic
472C2C113×#302211yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radical#532×C113C22
LCSG ▷ C42 ▷ 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×#3230C2semidirect
4. C2×#475×C113C2semidirect
5. C113×#1650C2semidirect
6. C113×#1643C2semidirect
7. C113×#1542C2semidirect
9. C113×#1479C2semidirect
231. #18909C113direct (N × H)
238. #3230C2×C113semidirect
240. C2×#475C2×C113semidirect
241. #1650C2×C113semidirect
242. #1643C2×C113semidirect
243. #1542C2×C113semidirect
245. #1479C2×C113semidirect
246. C113#18909direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35072
C113×#32302
C113×#32062
C2×#475×C1132
C113×#16502
C113×#16432
C113×#15422
C113×#14802
C113×#14792
#18909113