Finite Group Databasebeta

← C113×#8996 #43277016

Subgroups — C113×#8996 #43277016

Order 28928.

484 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3035C211yesmaximal, characteristic
2C113×#2925C211yesmaximal, characteristic, complemented
3C113×#1492C211yesmaximal, characteristic, complemented
4C113×#1480C211yesmaximal, characteristic, complemented
5C113×#1476C211yesmaximal, characteristic, complemented
6C113×#1301C211yesmaximal, characteristic, complemented
7C113×#1277C211yesmaximal, characteristic, complemented
8C2×#135×C113—21no—
9#532×C113C2211yescharacteristic
10C4×#41×C113C2211yescharacteristic
11#464×C113—21no—
12#463×C113—21no—
13#462×C113C411yescharacteristic
14#461×C113C411yescharacteristic
15#460×C113C411yescharacteristic
16#459×C113C411yescharacteristic
17#433×C113—22no—
18#432×C113—21no—
19#431×C113—21no—
20#431×C113C2211yescharacteristic
21#423×C113C2211yescharacteristic
22C2×C4⋊C8×C113C2211yescharacteristic
23C2×C4⋊C8×C113C2211yescharacteristic
24#416×C113—21no—
25#408×C113—21no—
26#405×C113—21no—
27C2×C4×C8×C113C2211yescharacteristic
28Q8⋊C8×C113—21no—
29D4⋊C8×C113—21no—
30D4⋊C8×C113—21no—
31D4⋊C8×C113—21no—
32D4⋊C8×C113—22no—
33C2×#41×C113—21no—
34C2×#41×C113D411yescharacteristic
35#135×C113—42no—
36#135×C113—42no—
37C2×Q16×C113—21no—
38C2×SD16×C113—21no—
39C2×SD16×C113—21no—
40C2×D8×C113—21no—
41C2×M16×C113—21no—
42C22×C8×C113—21no—
43C22×C8×C113—21no—
44C22×C8×C113—21no—
45C4⋊Q8×C113C2×C411yescharacteristic
46#127×C113C2×C411yescharacteristic
47#124×C113—21no—
48#121×C113—21no—
49#121×C113—21no—
50C4×Q8×C113C2×C411yescharacteristic
51C4×Q8×C113D411yescharacteristic
52C4×D4×C113—21no—
53C4×D4×C113—21no—
54C4×D4×C113—21no—
55C4×D4×C113—21no—
56C4×D4×C113C2×C411yescharacteristic
57C4×D4×C113D411yescharacteristic
58#117×C113—21no—
59#117×C113D411yescharacteristic
60C2×C42×C113—21no—
61C2×C42×C113C2311yescharacteristic
62C4⋊C8×C113—21no—
63C4⋊C8×C113—21no—
64C4⋊C8×C113—21no—
65C4⋊C8×C113—21no—
66C4⋊C8×C113C2×C411yescharacteristic
67C4⋊C8×C113C2×C411yescharacteristic
68C4⋊C8×C113D411yescharacteristic
69C4⋊C8×C113D411yescharacteristic
70C4⋊C8×C113D412yes—
71#103×C113—21no—
72#103×C113—21no—
73#102×C113—21no—
74#102×C113—21no—
75C22⋊C8×C113—22no—
76C22⋊C8×C113—22no—
77C22⋊C8×C113—21no—
78#97×C113—22no—
79C4×C8×C113—22no—
80C4×C8×C113—21no—
81C4×C8×C113—21no—
82C4×C8×C113—21no—
83#41×C113—21no—
84#41×C113—21no—
85#41×C113—21no—
86#41×C113—21no—
87#41×C113—41no—
88#41×C113—41no—
89#41×C113—41no—
90#41×C113—41no—
91C2×Q8×C113—21no—
92C2×Q8×C113C22⋊C411yescharacteristic
93C2×D4×C113—21no—
94C2×D4×C113—21no—
95C2×D4×C113—21no—
96C2×D4×C113—21no—
97C2×D4×C113—41no—
98C2×D4×C113C22⋊C411yescharacteristic
99C22×C4×C113—21no—
100C22×C4×C113—21no—
101C22×C4×C113—21no—
102C22×C4×C113—41no—
103C22×C4×C113C2×D411yescharacteristic
104C22×C4×C113#4111yescharacteristic
105C22×C4×C113#4111yescharacteristic
106Q16×C113—42no—
107SD16×C113—42no—
108SD16×C113—42no—
109D8×C113—42no—
110M16×C113—41no—
111M16×C113—41no—
112C2×C8×C113—22no—
113C2×C8×C113—21no—
114C2×C8×C113—21no—
115C2×C8×C113—21no—
116C2×C8×C113—22no—
117C2×C8×C113—21no—
118C2×C8×C113—41no—
119C2×C8×C113—41no—
120C2×C8×C113—41no—
121C2×C8×C113—41no—
122C2×C8×C113—41no—
123C2×C8×C113—41no—
124C2×C8×C113—41no—
125C4⋊C4×C113—21no—
126C4⋊C4×C113—21no—
127C4⋊C4×C113—21no—
128C4⋊C4×C113—21no—
129C4⋊C4×C113C22⋊C411yescharacteristic
130C4⋊C4×C113C22⋊C411yescharacteristic
131C22⋊C4×C113—21no—
132C22⋊C4×C113—21no—
133C22⋊C4×C113—21no—
134C22⋊C4×C113—41no—
135C22⋊C4×C113—41no—
136C42×C113—21no—
137C42×C113—21no—
138C42×C113—21no—
139C42×C113C22×C411yescharacteristic
140C42×C113C2×D411yescharacteristic
141C42×C113C2×D411yescharacteristic
142C42×C113C2×D411yescharacteristic
143C23×C113—21no—
144C23×C113—41no—
145C23×C113#12311yescharacteristic
146Q8×C113—21no—
147Q8×C113—21no—
148Q8×C113—41no—
149Q8×C113—41no—
150D4×C113—21no—
151D4×C113—21no—
152D4×C113—42no—
153D4×C113—41no—
154D4×C113—41no—
155D4×C113—41no—
156D4×C113—41no—
157D4×C113—41no—
158D4×C113—41no—
159D4×C113—81no—
160D4×C113—81no—
161C2×C4×C113—21no—
162C2×C4×C113—21no—
163C2×C4×C113—21no—
164C2×C4×C113—21no—
165C2×C4×C113—21no—
166C2×C4×C113—41no—
167C2×C4×C113—41no—
168C2×C4×C113—41no—
169C2×C4×C113—41no—
170C2×C4×C113—41no—
171C2×C4×C113—41no—
172C2×C4×C113—81no—
173C2×C4×C113—81no—
174C2×C4×C113—81no—
175C2×C4×C113C2×C22⋊C411yescharacteristic
176C2×C4×C113C4×D411yescharacteristic
177C2×C4×C113C4×D411yescharacteristic
178C2×C4×C113#12011yescharacteristic
179C2×C4×C113#12111yescharacteristic
180C2×C4×C113#12111yescharacteristic
181C2×C4×C113#13511yescharacteristic
182C2×C4×C113#13511yescharacteristic
183C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
185C8×C113—42no—
186C8×C113—41no—
187C8×C113—41no—
188C8×C113—41no—
189C8×C113—41no—
190C8×C113—42no—
191C8×C113—81no—
192C22×C113—21no—
193C22×C113—21no—
194C22×C113—41no—
195C22×C113—41no—
196C22×C113—41no—
197C22×C113—81no—
198C22×C113—81no—
199C22×C113—81no—
200C22×C113#38611yescharacteristic
201C22×C113#48211yescharacteristic
202C22×C113#48211yescharacteristic
203C4×C113—21no—
204C4×C113—21no—
205C4×C113—21no—
206C4×C113—41no—
207C4×C113—41no—
208C4×C113—41no—
209C4×C113—81no—
210C4×C113#41611yescharacteristic
211C4×C113#41811yescharacteristic
212C4×C113#44311yescharacteristic
213C4×C113#44411yescharacteristic
214C4×C113#44911yescharacteristic
215C4×C113#44911yescharacteristic
216#8996C11311yesmaximal, characteristic, direct product factor, Sylow
217C2×C113—21no—
218C2×C113—21no—
219C2×C113—81no—
220C2×C113—161no—
221C2×C113#187511yescharacteristic
222C2×C113#187611yescharacteristic
223C2×C113#188111yescharacteristic
224#3035C2×C11311yescharacteristic
225#2925C2×C11311yescharacteristic, complemented
226#1492C2×C11311yescharacteristic, complemented
227#1480C2×C11311yescharacteristic, complemented
228#1476C2×C11311yescharacteristic, complemented
229#1301C2×C11311yescharacteristic, complemented
230#1277C2×C11311yescharacteristic, complemented
231C113#899611yescharacteristic, direct product factor, Sylow
232C2×#135—21no—
233#532C22×C11311yescharacteristic
234C4×#41C22×C11311yescharacteristic
235#464—21no—
236#463—21no—
237#462C4×C11311yescharacteristic
238#461C4×C11311yescharacteristic
239#460C4×C11311yescharacteristic
240#459C4×C11311yescharacteristic
241#433—22no—
242#432—21no—
243#431—21no—
244#431C22×C11311yescharacteristic
245#423C22×C11311yescharacteristic
246C2×C4⋊C8C22×C11311yescharacteristic
247C2×C4⋊C8C22×C11311yescharacteristic
248#416—21no—
249#408—21no—
250#405—21no—
251C2×C4×C8C22×C11311yescharacteristic
252Q8⋊C8—21no—
253D4⋊C8—21no—
254D4⋊C8—21no—
255D4⋊C8—21no—
256D4⋊C8—22no—
257C2×#41—21no—
258C2×#41D4×C11311yescharacteristic
259#135—42no—
260#135—42no—
261C2×Q16—21no—
262C2×SD16—21no—
263C2×SD16—21no—
264C2×D8—21no—
265C2×M16—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C4⋊Q8C2×C4×C11311yescharacteristic
270#127C2×C4×C11311yescharacteristic
271#124—21no—
272#121—21no—
273#121—21no—
274C4×Q8C2×C4×C11311yescharacteristic
275C4×Q8D4×C11311yescharacteristic
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4C2×C4×C11311yescharacteristic
281C4×D4D4×C11311yescharacteristic
282#117—21no—
283#117D4×C11311yescharacteristic
284C2×C42—21no—
285C2×C42C23×C11311yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8C2×C4×C11311yescharacteristic
291C4⋊C8C2×C4×C11311yescharacteristic
292C4⋊C8D4×C11311yescharacteristic
293C4⋊C8D4×C11311yescharacteristic
294C4⋊C8D4×C11312yes—
295#103—21no—
296#103—21no—
297#102—21no—
298#102—21no—
299C22⋊C8—22no—
300C22⋊C8—22no—
301C22⋊C8—21no—
302#97—22no—
303C4×C8—22no—
304C4×C8—21no—
305C4×C8—21no—
306C4×C8—21no—
307#41—21no—
308#41—21no—
309#41—21no—
310#41—21no—
311#41—41no—
312#41—41no—
313#41—41no—
314#41—41no—
315C2×Q8—21no—
316C2×Q8C22⋊C4×C11311yescharacteristic
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—41no—
322C2×D4C22⋊C4×C11311yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4C2×D4×C11311yescharacteristic
328C22×C4#41×C11311yescharacteristic
329C22×C4#41×C11311yescharacteristic
330Q16—42no—
331SD16—42no—
332SD16—42no—
333D8—42no—
334M16—41no—
335M16—41no—
336C2×C8—22no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—22no—
341C2×C8—21no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4C22⋊C4×C11311yescharacteristic
354C4⋊C4C22⋊C4×C11311yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C42—21no—
361C42—21no—
362C42—21no—
363C42C22×C4×C11311yescharacteristic
364C42C2×D4×C11311yescharacteristic
365C42C2×D4×C11311yescharacteristic
366C42C2×D4×C11311yescharacteristic
367C23—21no—
368C23—41no—
369C23#123×C11311yescharacteristic
370Q8—21no—
371Q8—21no—
372Q8—41no—
373Q8—41no—
374D4—21no—
375D4—21no—
376D4—42no—
377D4—41no—
378D4—41no—
379D4—41no—
380D4—41no—
381D4—41no—
382D4—41no—
383D4—81no—
384D4—81no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4C2×C22⋊C4×C11311yescharacteristic
400C2×C4C4×D4×C11311yescharacteristic
401C2×C4C4×D4×C11311yescharacteristic
402C2×C4#120×C11311yescharacteristic
403C2×C4#121×C11311yescharacteristic
404C2×C4#121×C11311yescharacteristic
405C2×C4#135×C11311yescharacteristic
406C2×C4#135×C11311yescharacteristic
407C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
408C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
409C8—42no—
410C8—41no—
411C8—41no—
412C8—41no—
413C8—41no—
414C8—42no—
415C8—81no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22#386×C11311yescharacteristic
425C22#482×C11311yescharacteristic
426C22#482×C11311yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4#416×C11311yescharacteristic
435C4#418×C11311yescharacteristic
436C4#443×C11311yescharacteristic
437C4#444×C11311yescharacteristic
438C4#449×C11311yescharacteristic
439C4#449×C11311yescharacteristic
440C2—21no—
441C2—21no—
442C2—81no—
443C2—161no—
444C2C113×#187511yescharacteristic
445C2C113×#187611yescharacteristic
446C2C113×#188111yescharacteristic
subgroupG/H
centerC2×C4×C113#120
commutatorC42C22×C4×C113
Frattini, cosocleC2×C42C23×C113
socleC22×C113#386
prime radicalC113×#3035C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2925C2semidirect
3. C113×#1492C2semidirect
4. C113×#1480C2semidirect
5. C113×#1476C2semidirect
6. C113×#1301C2semidirect
7. C113×#1277C2semidirect
216. #8996C113direct (N × H)
225. #2925C2×C113semidirect
226. #1492C2×C113semidirect
227. #1480C2×C113semidirect
228. #1476C2×C113semidirect
229. #1301C2×C113semidirect
230. #1277C2×C113semidirect
231. C113#8996direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#30352
C113×#29252
C113×#14922
C113×#14802
C113×#14762
C113×#13012
C113×#12772
#8996113