Finite Group Databasebeta

← C113×#8952 #43276972

Subgroups — C113×#8952 #43276972

Order 28928.

560 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#446×C113C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C113C211yesmaximal, characteristic
3C113×#1954C211yesmaximal, characteristic
4C2×Q8⋊C8×C113C211yesmaximal, characteristic, complemented
5C2×D4⋊C8×C113C211yesmaximal, characteristic
6C113×#1277C211yesmaximal, characteristic, complemented
7C113×#1273C211yesmaximal, characteristic, complemented
8C22×SD16×C113C411yescharacteristic
9C2×C4×Q8×C113C2211yescharacteristic
10C2×C4×D4×C113C2211yescharacteristic
11#446×C113—22no—
12#446×C113—22no—
13C4×SD16×C113—22no—
14C4×SD16×C113—22no—
15C2×#106×C113C411yescharacteristic
16C2×C4⋊C8×C113—21no—
17C2×C4⋊C8×C113C2211yescharacteristic
18C2×C4⋊C8×C113C2211yescharacteristic
19C2×#103×C113C411yescharacteristic
20C2×#102×C113C411yescharacteristic
21C2×C22⋊C8×C113—21no—
22C2×C22⋊C8×C113—21no—
23C2×#97×C113—21no—
24C2×C4×C8×C113C2211yescharacteristic
25C2×C4×C8×C113C2211yescharacteristic
26C2×C4×C8×C113C2211yescharacteristic
27Q8⋊C8×C113—22no—
28D4⋊C8×C113—22no—
29C22×Q8×C113C2×C411yescharacteristic
30C22×D4×C113C2×C411yescharacteristic
31C23×C4×C113—21no—
32C2×SD16×C113—22no—
33C2×SD16×C113—22no—
34C2×SD16×C113—22no—
35C22×C8×C113—21no—
36C22×C8×C113—21no—
37C22×C8×C113—21no—
38C22×C8×C113C2×C411yescharacteristic
39C22×C8×C113C2×C411yescharacteristic
40C22×C8×C113D411yescharacteristic
41C22×C8×C113D411yescharacteristic
42C4×Q8×C113—21no—
43C4×Q8×C113—21no—
44C4×Q8×C113D412yes—
45C4×Q8×C113D412yes—
46C4×D4×C113—21no—
47C4×D4×C113—21no—
48C4×D4×C113—21no—
49C4×D4×C113—21no—
50C2×C4⋊C4×C113—21no—
51C2×C4⋊C4×C113C2×C411yescharacteristic
52C2×C4⋊C4×C113C2×C411yescharacteristic
53C2×C22⋊C4×C113—21no—
54C2×C42×C113—21no—
55C2×C42×C113C2311yescharacteristic
56#106×C113—22no—
57C4⋊C8×C113—24no—
58C4⋊C8×C113—21no—
59C4⋊C8×C113—21no—
60C4⋊C8×C113—21no—
61C4⋊C8×C113D412yes—
62#103×C113—22no—
63#102×C113—22no—
64C22⋊C8×C113—42no—
65C22⋊C8×C113—42no—
66#97×C113—24no—
67C4×C8×C113—21no—
68C4×C8×C113—21no—
69C4×C8×C113—21no—
70C4×C8×C113—21no—
71C4×C8×C113—21no—
72C4×C8×C113—21no—
73C24×C113—21no—
74C2×Q8×C113—21no—
75C2×Q8×C113—21no—
76C2×Q8×C113—21no—
77C2×Q8×C113—21no—
78C2×Q8×C113—21no—
79C2×Q8×C113C22⋊C412yes—
80C2×D4×C113—21no—
81C2×D4×C113—21no—
82C2×D4×C113—21no—
83C2×D4×C113—21no—
84C2×D4×C113—21no—
85C2×D4×C113M1612yes—
86C22×C4×C113—21no—
87C22×C4×C113—21no—
88C22×C4×C113—21no—
89C22×C4×C113—41no—
90C22×C4×C113—41no—
91C22×C4×C113—41no—
92C22×C4×C113—41no—
93C22×C4×C113—41no—
94C22×C4×C113—41no—
95C22×C4×C113C22×C411yescharacteristic
96C22×C4×C113C2×D411yescharacteristic
97C22×C4×C113#4111yescharacteristic
98SD16×C113—28no—
99C2×C8×C113—21no—
100C2×C8×C113—21no—
101C2×C8×C113—21no—
102C2×C8×C113—21no—
103C2×C8×C113—22no—
104C2×C8×C113—21no—
105C2×C8×C113—21no—
106C2×C8×C113—22no—
107C2×C8×C113—21no—
108C2×C8×C113—21no—
109C2×C8×C113—21no—
110C2×C8×C113—21no—
111C2×C8×C113—41no—
112C2×C8×C113—41no—
113C2×C8×C113—41no—
114C2×C8×C113—41no—
115C2×C8×C113—41no—
116C2×C8×C113—41no—
117C2×C8×C113—41no—
118C2×C8×C113M1612yes—
119C2×C8×C113SD1612yescomplemented
120C4⋊C4×C113—21no—
121C4⋊C4×C113—22no—
122C4⋊C4×C113—22no—
123C4⋊C4×C113—21no—
124C4⋊C4×C113—21no—
125C4⋊C4×C113C22⋊C412yes—
126C22⋊C4×C113—41no—
127C22⋊C4×C113—41no—
128C42×C113—22no—
129C42×C113—22no—
130C42×C113C2×D411yescharacteristic
131C42×C113C2×D411yescharacteristic
132C42×C113C2×D411yescharacteristic
133C42×C113#4111yescharacteristic
134C23×C113—22no—
135C23×C113—41no—
136C23×C113—41no—
137C23×C113—41no—
138C23×C113—41no—
139C23×C113—41no—
140C23×C113—41no—
141C23×C113C4×D411yescharacteristic
142Q8×C113—22no—
143Q8×C113—22no—
144Q8×C113—41no—
145Q8×C113—41no—
146D4×C113—22no—
147D4×C113—22no—
148D4×C113—41no—
149D4×C113—41no—
150C2×C4×C113—21no—
151C2×C4×C113—21no—
152C2×C4×C113—22no—
153C2×C4×C113—22no—
154C2×C4×C113—41no—
155C2×C4×C113—41no—
156C2×C4×C113—41no—
157C2×C4×C113—41no—
158C2×C4×C113—41no—
159C2×C4×C113—41no—
160C2×C4×C113—41no—
161C2×C4×C113—81no—
162C2×C4×C113—81no—
163C2×C4×C113—81no—
164C2×C4×C113—81no—
165C2×C4×C113C2×C22⋊C411yescharacteristic
166C2×C4×C113C4×D411yescharacteristic
167C2×C4×C113#12011yescharacteristic
168C2×C4×C113#12111yescharacteristic
169C2×C4×C113#12111yescharacteristic
170C2×C4×C113#12311yescharacteristic
171C2×C4×C113C2×M1611yescharacteristic
172C2×C4×C113C2×M1611yescharacteristic
173C2×C4×C113#13111yescharacteristic
174C2×C4×C113#13111yescharacteristic
175C2×C4×C113C2×SD1611yescharacteristic
176C2×C4×C113#13511yescharacteristic
177C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C113#13711yescharacteristic
179C8×C113—22no—
180C8×C113—22no—
181C8×C113—42no—
182C8×C113—41no—
183C8×C113—41no—
184C8×C113—42no—
185C8×C113—81no—
186C22×C113—42no—
187C22×C113—42no—
188C22×C113—42no—
189C22×C113—81no—
190C22×C113—81no—
191C22×C113—81no—
192C22×C113—81no—
193C22×C113#38611yescharacteristic
194C22×C113#43511yescharacteristic
195C22×C113#43611yescharacteristic
196C22×C113C4×SD1611yescharacteristic
197C22×C113#44011yescharacteristic
198C22×C113#44311yescharacteristic
199C22×C113#44411yescharacteristic
200C4×C113—21no—
201C4×C113—21no—
202C4×C113—42no—
203C4×C113—42no—
204C4×C113—81no—
205C4×C113#40711yescharacteristic
206C4×C113#40811yescharacteristic
207C4×C113#43511yescharacteristic
208C4×C113#43611yescharacteristic
209C4×C113#44811yescharacteristic
210C4×C113#44911yescharacteristic
211C4×C113#46011yescharacteristic
212C4×C113#46411yescharacteristic
213#8952C11311yesmaximal, characteristic, direct product factor, Sylow
214C2×C113—82no—
215C2×C113#158211yescharacteristic
216C2×C113#158511yescharacteristic
217C2×C113#159011yescharacteristic
218C2×C113#159211yescharacteristic
219C2×C113#187011yescharacteristic
220C2×C113#187611yescharacteristic
221C2×C113#188011yescharacteristic
222C2×#446C2×C11311yescharacteristic, complemented
223C2×C4×SD16C2×C11311yescharacteristic
224#1954C2×C11311yescharacteristic
225C2×Q8⋊C8C2×C11311yescharacteristic, complemented
226C2×D4⋊C8C2×C11311yescharacteristic
227#1277C2×C11311yescharacteristic, complemented
228#1273C2×C11311yescharacteristic, complemented
229C113#895211yescharacteristic, direct product factor, Sylow
230C22×SD16C4×C11311yescharacteristic
231C2×C4×Q8C22×C11311yescharacteristic
232C2×C4×D4C22×C11311yescharacteristic
233#446—22no—
234#446—22no—
235C4×SD16—22no—
236C4×SD16—22no—
237C2×#106C4×C11311yescharacteristic
238C2×C4⋊C8—21no—
239C2×C4⋊C8C22×C11311yescharacteristic
240C2×C4⋊C8C22×C11311yescharacteristic
241C2×#103C4×C11311yescharacteristic
242C2×#102C4×C11311yescharacteristic
243C2×C22⋊C8—21no—
244C2×C22⋊C8—21no—
245C2×#97—21no—
246C2×C4×C8C22×C11311yescharacteristic
247C2×C4×C8C22×C11311yescharacteristic
248C2×C4×C8C22×C11311yescharacteristic
249Q8⋊C8—22no—
250D4⋊C8—22no—
251C22×Q8C2×C4×C11311yescharacteristic
252C22×D4C2×C4×C11311yescharacteristic
253C23×C4—21no—
254C2×SD16—22no—
255C2×SD16—22no—
256C2×SD16—22no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8C2×C4×C11311yescharacteristic
261C22×C8C2×C4×C11311yescharacteristic
262C22×C8D4×C11311yescharacteristic
263C22×C8D4×C11311yescharacteristic
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8D4×C11312yes—
267C4×Q8D4×C11312yes—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4C2×C4×C11311yescharacteristic
274C2×C4⋊C4C2×C4×C11311yescharacteristic
275C2×C22⋊C4—21no—
276C2×C42—21no—
277C2×C42C23×C11311yescharacteristic
278#106—22no—
279C4⋊C8—24no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8D4×C11312yes—
284#103—22no—
285#102—22no—
286C22⋊C8—42no—
287C22⋊C8—42no—
288#97—24no—
289C4×C8—21no—
290C4×C8—21no—
291C4×C8—21no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8—21no—
295C24—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8C22⋊C4×C11312yes—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4M16×C11312yes—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4C22×C4×C11311yescharacteristic
318C22×C4C2×D4×C11311yescharacteristic
319C22×C4#41×C11311yescharacteristic
320SD16—28no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—22no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—22no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8M16×C11312yes—
341C2×C8SD16×C11312yescomplemented
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4C22⋊C4×C11312yes—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C42—22no—
351C42—22no—
352C42C2×D4×C11311yescharacteristic
353C42C2×D4×C11311yescharacteristic
354C42C2×D4×C11311yescharacteristic
355C42#41×C11311yescharacteristic
356C23—22no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23C4×D4×C11311yescharacteristic
364Q8—22no—
365Q8—22no—
366Q8—41no—
367Q8—41no—
368D4—22no—
369D4—22no—
370D4—41no—
371D4—41no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4C2×C22⋊C4×C11311yescharacteristic
388C2×C4C4×D4×C11311yescharacteristic
389C2×C4#120×C11311yescharacteristic
390C2×C4#121×C11311yescharacteristic
391C2×C4#121×C11311yescharacteristic
392C2×C4#123×C11311yescharacteristic
393C2×C4C2×M16×C11311yescharacteristic
394C2×C4C2×M16×C11311yescharacteristic
395C2×C4#131×C11311yescharacteristic
396C2×C4#131×C11311yescharacteristic
397C2×C4C2×SD16×C11311yescharacteristic
398C2×C4#135×C11311yescharacteristic
399C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
400C2×C4#137×C11311yescharacteristic
401C8—22no—
402C8—22no—
403C8—42no—
404C8—41no—
405C8—41no—
406C8—42no—
407C8—81no—
408C22—42no—
409C22—42no—
410C22—42no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22#386×C11311yescharacteristic
416C22#435×C11311yescharacteristic
417C22#436×C11311yescharacteristic
418C22C4×SD16×C11311yescharacteristic
419C22#440×C11311yescharacteristic
420C22#443×C11311yescharacteristic
421C22#444×C11311yescharacteristic
422C4—21no—
423C4—21no—
424C4—42no—
425C4—42no—
426C4—81no—
427C4#407×C11311yescharacteristic
428C4#408×C11311yescharacteristic
429C4#435×C11311yescharacteristic
430C4#436×C11311yescharacteristic
431C4#448×C11311yescharacteristic
432C4#449×C11311yescharacteristic
433C4#460×C11311yescharacteristic
434C4#464×C11311yescharacteristic
435C2—82no—
436C2C113×#158211yescharacteristic
437C2C113×#158511yescharacteristic
438C2C113×#159011yescharacteristic
439C2C113×#159211yescharacteristic
440C2C113×#187011yescharacteristic
441C2C113×#187611yescharacteristic
442C2C113×#188011yescharacteristic
subgroupG/H
centerC22×C4×C113C2×D4
commutatorC22×C4C22×C4×C113
Frattini, cosocleC2×C42C23×C113
socleC23×C113C4×D4
prime radicalC22×D4×C113C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C113 ◁ C2×C4×C8×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#446×C113C2semidirect
4. C2×Q8⋊C8×C113C2semidirect
6. C113×#1277C2semidirect
7. C113×#1273C2semidirect
119. C2×C8×C113SD16semidirect
213. #8952C113direct (N × H)
222. C2×#446C2×C113semidirect
225. C2×Q8⋊C8C2×C113semidirect
227. #1277C2×C113semidirect
228. #1273C2×C113semidirect
229. C113#8952direct (N × H)
341. C2×C8SD16×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#446×C1132
C2×C4×SD16×C1132
C113×#19542
C2×Q8⋊C8×C1132
C2×D4⋊C8×C1132
C113×#12772
C113×#12732
#8952113