Finite Group Databasebeta

← C113×#9322 #43277342

Subgroups — C113×#9322 #43277342

Order 28928.

558 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3038C211yesmaximal, characteristic
2C113×#2989C211yesmaximal, characteristic, complemented
3C113×#1982C211yesmaximal, characteristic, complemented
4C113×#1806C211yesmaximal, characteristic, complemented
5C113×#1545C211yesmaximal, characteristic, complemented
6C113×#1303C211yesmaximal, characteristic, complemented
7C113×#1292C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C113—21no—
9C2×#127×C113C2211yescharacteristic
10C4×#41×C113C2211yescharacteristic
11#460×C113—21no—
12#460×C113C412yescomplemented
13#459×C113—21no—
14#459×C113C412yescomplemented
15#446×C113—21no—
16#436×C113—21no—
17#435×C113—22no—
18#432×C113—21no—
19#431×C113C2211yescharacteristic
20#423×C113—21no—
21#423×C113C2211yescharacteristic
22#423×C113C2211yescharacteristic
23C2×C4⋊C8×C113C2211yescharacteristic
24C2×#104×C113—21no—
25#418×C113—21no—
26C2×#102×C113—22no—
27C4×C4⋊C4×C113C2211yescharacteristic
28#339×C113—21no—
29#331×C113—21no—
30#331×C113—21no—
31C2×#41×C113D411yescharacteristic
32C22×D4×C113—21no—
33C22×D4×C113—21no—
34C22×D4×C113—21no—
35AGL(1,ℤ/8)×C113—42no—
36AGL(1,ℤ/8)×C113—42no—
37C2×SD16×C113—22no—
38C2×D8×C113—22no—
39C2×M16×C113—21no—
40C2×M16×C113—22no—
41C2×M16×C113—21no—
42C22×C8×C113D412yes—
43#127×C113—21no—
44#127×C113—21no—
45#127×C113—21no—
46#127×C113C2×C412yes—
47C4×Q8×C113C2×C411yescharacteristic
48C4×Q8×C113D411yescharacteristic
49C4×D4×C113—21no—
50C4×D4×C113—21no—
51C4×D4×C113C2×C411yescharacteristic
52C4×D4×C113D411yescharacteristic
53#117×C113—21no—
54#117×C113D411yescharacteristic
55C2×C4⋊C4×C113—21no—
56C2×C42×C113—21no—
57C2×C42×C113—21no—
58C2×C42×C113C2311yescharacteristic
59C4⋊C8×C113—22no—
60C4⋊C8×C113—21no—
61C4⋊C8×C113—21no—
62C4⋊C8×C113—21no—
63C4⋊C8×C113—21no—
64C4⋊C8×C113—21no—
65C4⋊C8×C113C2×C412yes—
66C4⋊C8×C113D411yescharacteristic
67C4⋊C8×C113D411yescharacteristic
68#104×C113—42no—
69#102×C113—22no—
70#102×C113—22no—
71#102×C113—44no—
72C22⋊C8×C113—22no—
73C22⋊C8×C113—21no—
74#97×C113—22no—
75C4×C8×C113—21no—
76#95×C113—21no—
77C24×C113—41no—
78#41×C113—21no—
79#41×C113—21no—
80#41×C113—21no—
81#41×C113—21no—
82C2×Q8×C113C22⋊C411yescharacteristic
83C2×D4×C113—21no—
84C2×D4×C113—22no—
85C2×D4×C113—22no—
86C2×D4×C113—22no—
87C2×D4×C113—42no—
88C2×D4×C113—42no—
89C2×D4×C113—41no—
90C2×D4×C113—41no—
91C2×D4×C113—41no—
92C2×D4×C113—41no—
93C2×D4×C113—41no—
94C2×D4×C113—41no—
95C2×D4×C113—41no—
96C2×D4×C113—82no—
97C2×D4×C113C22⋊C411yescharacteristic
98C22×C4×C113—21no—
99C22×C4×C113—21no—
100C22×C4×C113—21no—
101C22×C4×C113—41no—
102C22×C4×C113C2×D411yescharacteristic
103C22×C4×C113C2×D411yescharacteristic
104C22×C4×C113#4111yescharacteristic
105SD16×C113—44no—
106D8×C113—44no—
107M16×C113—41no—
108M16×C113—41no—
109M16×C113—41no—
110M16×C113—41no—
111M16×C113—82no—
112C2×C8×C113—22no—
113C2×C8×C113—21no—
114C2×C8×C113—21no—
115C2×C8×C113—22no—
116C2×C8×C113—42no—
117C2×C8×C113—41no—
118C4⋊C4×C113—21no—
119C4⋊C4×C113—21no—
120C4⋊C4×C113—22no—
121C4⋊C4×C113—41no—
122C4⋊C4×C113C22⋊C411yescharacteristic
123C4⋊C4×C113C22⋊C411yescharacteristic
124C22⋊C4×C113—21no—
125C22⋊C4×C113—21no—
126C22⋊C4×C113—21no—
127C42×C113—21no—
128C42×C113—21no—
129C42×C113—21no—
130C42×C113—41no—
131C42×C113—41no—
132C42×C113C22×C411yescharacteristic
133C42×C113C2×D411yescharacteristic
134C42×C113C2×D411yescharacteristic
135C42×C113#4111yescharacteristic
136C23×C113—21no—
137C23×C113—42no—
138C23×C113—82no—
139C23×C113—82no—
140C23×C113—81no—
141C23×C113—81no—
142C23×C113#12111yescharacteristic
143Q8×C113—21no—
144Q8×C113—21no—
145D4×C113—21no—
146D4×C113—21no—
147D4×C113—44no—
148D4×C113—41no—
149D4×C113—41no—
150D4×C113—42no—
151D4×C113—42no—
152D4×C113—82no—
153D4×C113—82no—
154D4×C113—81no—
155D4×C113—81no—
156D4×C113—81no—
157D4×C113—81no—
158C2×C4×C113—21no—
159C2×C4×C113—21no—
160C2×C4×C113—21no—
161C2×C4×C113—21no—
162C2×C4×C113—21no—
163C2×C4×C113—41no—
164C2×C4×C113—41no—
165C2×C4×C113—41no—
166C2×C4×C113—41no—
167C2×C4×C113—41no—
168C2×C4×C113—42no—
169C2×C4×C113—81no—
170C2×C4×C113—81no—
171C2×C4×C113—81no—
172C2×C4×C113C2×C22⋊C411yescharacteristic
173C2×C4×C113C4×D411yescharacteristic
174C2×C4×C113C4×D411yescharacteristic
175C2×C4×C113#12011yescharacteristic
176C2×C4×C113#12111yescharacteristic
177C2×C4×C113#12311yescharacteristic
178C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C113#13711yescharacteristic
182C8×C113—42no—
183C8×C113—42no—
184C8×C113—41no—
185C8×C113—41no—
186C8×C113—81no—
187C22×C113—21no—
188C22×C113—21no—
189C22×C113—41no—
190C22×C113—41no—
191C22×C113—41no—
192C22×C113—82no—
193C22×C113—82no—
194C22×C113—82no—
195C22×C113—162no—
196C22×C113—162no—
197C22×C113#38611yescharacteristic
198C22×C113#46811yescharacteristic
199C22×C113#46911yescharacteristic
200C4×C113—21no—
201C4×C113—21no—
202C4×C113—21no—
203C4×C113—41no—
204C4×C113—41no—
205C4×C113—41no—
206C4×C113—82no—
207C4×C113#41711yescharacteristic
208C4×C113#41811yescharacteristic
209C4×C113#45311yescharacteristic
210C4×C113#45411yescharacteristic
211C4×C113#46811yescharacteristic
212C4×C113#46911yescharacteristic
213#9322C11311yesmaximal, characteristic, direct product factor, Sylow
214C2×C113—21no—
215C2×C113—21no—
216C2×C113—81no—
217C2×C113—162no—
218C2×C113#188311yescharacteristic
219C2×C113#189511yescharacteristic
220C2×C113#190311yescharacteristic
221#3038C2×C11311yescharacteristic
222#2989C2×C11311yescharacteristic, complemented
223#1982C2×C11311yescharacteristic, complemented
224#1806C2×C11311yescharacteristic, complemented
225#1545C2×C11311yescharacteristic, complemented
226#1303C2×C11311yescharacteristic, complemented
227#1292C2×C11311yescharacteristic, complemented
228C113#932211yescharacteristic, direct product factor, Sylow
229C2×AGL(1,ℤ/8)—21no—
230C2×#127C22×C11311yescharacteristic
231C4×#41C22×C11311yescharacteristic
232#460—21no—
233#460C4×C11312yescomplemented
234#459—21no—
235#459C4×C11312yescomplemented
236#446—21no—
237#436—21no—
238#435—22no—
239#432—21no—
240#431C22×C11311yescharacteristic
241#423—21no—
242#423C22×C11311yescharacteristic
243#423C22×C11311yescharacteristic
244C2×C4⋊C8C22×C11311yescharacteristic
245C2×#104—21no—
246#418—21no—
247C2×#102—22no—
248C4×C4⋊C4C22×C11311yescharacteristic
249#339—21no—
250#331—21no—
251#331—21no—
252C2×#41D4×C11311yescharacteristic
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—21no—
256AGL(1,ℤ/8)—42no—
257AGL(1,ℤ/8)—42no—
258C2×SD16—22no—
259C2×D8—22no—
260C2×M16—21no—
261C2×M16—22no—
262C2×M16—21no—
263C22×C8D4×C11312yes—
264#127—21no—
265#127—21no—
266#127—21no—
267#127C2×C4×C11312yes—
268C4×Q8C2×C4×C11311yescharacteristic
269C4×Q8D4×C11311yescharacteristic
270C4×D4—21no—
271C4×D4—21no—
272C4×D4C2×C4×C11311yescharacteristic
273C4×D4D4×C11311yescharacteristic
274#117—21no—
275#117D4×C11311yescharacteristic
276C2×C4⋊C4—21no—
277C2×C42—21no—
278C2×C42—21no—
279C2×C42C23×C11311yescharacteristic
280C4⋊C8—22no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8C2×C4×C11312yes—
287C4⋊C8D4×C11311yescharacteristic
288C4⋊C8D4×C11311yescharacteristic
289#104—42no—
290#102—22no—
291#102—22no—
292#102—44no—
293C22⋊C8—22no—
294C22⋊C8—21no—
295#97—22no—
296C4×C8—21no—
297#95—21no—
298C24—41no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—21no—
303C2×Q8C22⋊C4×C11311yescharacteristic
304C2×D4—21no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—42no—
309C2×D4—42no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—82no—
318C2×D4C22⋊C4×C11311yescharacteristic
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4C2×D4×C11311yescharacteristic
324C22×C4C2×D4×C11311yescharacteristic
325C22×C4#41×C11311yescharacteristic
326SD16—44no—
327D8—44no—
328M16—41no—
329M16—41no—
330M16—41no—
331M16—41no—
332M16—82no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—22no—
337C2×C8—42no—
338C2×C8—41no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—41no—
343C4⋊C4C22⋊C4×C11311yescharacteristic
344C4⋊C4C22⋊C4×C11311yescharacteristic
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C42—21no—
349C42—21no—
350C42—21no—
351C42—41no—
352C42—41no—
353C42C22×C4×C11311yescharacteristic
354C42C2×D4×C11311yescharacteristic
355C42C2×D4×C11311yescharacteristic
356C42#41×C11311yescharacteristic
357C23—21no—
358C23—42no—
359C23—82no—
360C23—82no—
361C23—81no—
362C23—81no—
363C23#121×C11311yescharacteristic
364Q8—21no—
365Q8—21no—
366D4—21no—
367D4—21no—
368D4—44no—
369D4—41no—
370D4—41no—
371D4—42no—
372D4—42no—
373D4—82no—
374D4—82no—
375D4—81no—
376D4—81no—
377D4—81no—
378D4—81no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4C2×C22⋊C4×C11311yescharacteristic
394C2×C4C4×D4×C11311yescharacteristic
395C2×C4C4×D4×C11311yescharacteristic
396C2×C4#120×C11311yescharacteristic
397C2×C4#121×C11311yescharacteristic
398C2×C4#123×C11311yescharacteristic
399C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
400C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
401C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
402C2×C4#137×C11311yescharacteristic
403C8—42no—
404C8—42no—
405C8—41no—
406C8—41no—
407C8—81no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—82no—
414C22—82no—
415C22—82no—
416C22—162no—
417C22—162no—
418C22#386×C11311yescharacteristic
419C22#468×C11311yescharacteristic
420C22#469×C11311yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—82no—
428C4#417×C11311yescharacteristic
429C4#418×C11311yescharacteristic
430C4#453×C11311yescharacteristic
431C4#454×C11311yescharacteristic
432C4#468×C11311yescharacteristic
433C4#469×C11311yescharacteristic
434C2—21no—
435C2—21no—
436C2—81no—
437C2—162no—
438C2C113×#188311yescharacteristic
439C2C113×#189511yescharacteristic
440C2C113×#190311yescharacteristic
subgroupG/H
center, socleC22×C113#386
commutatorC42C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC113×#3038C2
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×#2989C2semidirect
3. C113×#1982C2semidirect
4. C113×#1806C2semidirect
5. C113×#1545C2semidirect
6. C113×#1303C2semidirect
7. C113×#1292C2semidirect
12. #460×C113C4semidirect
14. #459×C113C4semidirect
213. #9322C113direct (N × H)
222. #2989C2×C113semidirect
223. #1982C2×C113semidirect
224. #1806C2×C113semidirect
225. #1545C2×C113semidirect
226. #1303C2×C113semidirect
227. #1292C2×C113semidirect
228. C113#9322direct (N × H)
233. #460C4×C113semidirect
235. #459C4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#30382
C113×#29892
C113×#19822
C113×#18062
C113×#15452
C113×#13032
C113×#12922
#9322113