Finite Group Databasebeta

← C113×#12151 #43280171

Subgroups — C113×#12151 #43280171

Order 28928.

492 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#2712C211yesmaximal, characteristic, complemented
2C113×#2044C211yesmaximal, characteristic, complemented
3C113×#1607C211yesmaximal, characteristic, complemented
4C113×#1595C211yesmaximal, characteristic
5C113×#1344C211yesmaximal, characteristic, complemented
6C113×#1343C211yesmaximal, characteristic, complemented
7C113×#1326C211yesmaximal, characteristic, complemented
8#534×C113C2211yescharacteristic
9C2×#124×C113—21no—
10#480×C113—21no—
11#447×C113—21no—
12C2×#99×C113—21no—
13#397×C113C2211yescharacteristic
14#394×C113—21no—
15#393×C113—21no—
16#392×C113C2211yescharacteristic
17#391×C113—21no—
18#388×C113—21no—
19#386×C113—21no—
20#386×C113—21no—
21#385×C113C2211yescharacteristic
22#342×C113C2211yescharacteristic
23#327×C113—21no—
24#327×C113—21no—
25#323×C113C2211yescharacteristic
26#323×C113C2211yescharacteristic
27C22×Q8×C113—21no—
28C22×D4×C113—21no—
29C22×D4×C113—21no—
30C22×D4×C113D411yescharacteristic
31C23×C4×C113D411yescharacteristic
32C2×D8×C113—41no—
33#124×C113—42no—
34#124×C113—42no—
35#123×C113—41no—
36#121×C113—21no—
37#121×C113—21no—
38#120×C113—41no—
39C2×C4⋊C4×C113—21no—
40C2×C4⋊C4×C113D411yescharacteristic
41C2×C22⋊C4×C113—21no—
42C2×C22⋊C4×C113—21no—
43C2×C22⋊C4×C113—21no—
44C2×C22⋊C4×C113—21no—
45C2×C22⋊C4×C113—21no—
46C2×C22⋊C4×C113—21no—
47C2×C22⋊C4×C113—21no—
48C2×C22⋊C4×C113—41no—
49C2×C22⋊C4×C113D411yescharacteristic
50C2×C22⋊C4×C113C2311yescharacteristic
51C2×C42×C113—21no—
52#107×C113—41no—
53#102×C113—41no—
54#102×C113—41no—
55#99×C113—42no—
56C22⋊C8×C113—21no—
57C22⋊C8×C113—21no—
58#95×C113—21no—
59#95×C113—21no—
60#95×C113—21no—
61#95×C113—21no—
62#95×C113—41no—
63#95×C113D411yescharacteristic
64#95×C113D411yescharacteristic
65C24×C113—21no—
66C24×C113—21no—
67C24×C113C2×D411yescharacteristic
68C2×Q8×C113—42no—
69C2×Q8×C113—42no—
70C2×Q8×C113—81no—
71C2×D4×C113—21no—
72C2×D4×C113—21no—
73C2×D4×C113—41no—
74C2×D4×C113—42no—
75C2×D4×C113—41no—
76C2×D4×C113—41no—
77C2×D4×C113—41no—
78C2×D4×C113—41no—
79C2×D4×C113—41no—
80C2×D4×C113—41no—
81C2×D4×C113—41no—
82C2×D4×C113—41no—
83C2×D4×C113—81no—
84C2×D4×C113—81no—
85C22×C4×C113—21no—
86C22×C4×C113—21no—
87C22×C4×C113—21no—
88C22×C4×C113—21no—
89C22×C4×C113—21no—
90C22×C4×C113—21no—
91C22×C4×C113—41no—
92C22×C4×C113—41no—
93C22×C4×C113—81no—
94C22×C4×C113C2×D411yescharacteristic
95C22×C4×C113C2×D411yescharacteristic
96D8×C113—82no—
97C2×C8×C113—41no—
98C2×C8×C113—41no—
99C4⋊C4×C113—21no—
100C4⋊C4×C113—21no—
101C4⋊C4×C113—41no—
102C4⋊C4×C113—81no—
103C22⋊C4×C113—21no—
104C22⋊C4×C113—41no—
105C22⋊C4×C113—42no—
106C22⋊C4×C113—42no—
107C22⋊C4×C113—42no—
108C22⋊C4×C113—41no—
109C22⋊C4×C113—41no—
110C22⋊C4×C113—41no—
111C22⋊C4×C113—41no—
112C22⋊C4×C113—41no—
113C22⋊C4×C113—41no—
114C22⋊C4×C113—81no—
115C22⋊C4×C113—81no—
116C22⋊C4×C113—82no—
117C22⋊C4×C113D812yescomplemented
118C42×C113—42no—
119C23×C113—21no—
120C23×C113—21no—
121C23×C113—41no—
122C23×C113—41no—
123C23×C113—41no—
124C23×C113—41no—
125C23×C113—41no—
126C23×C113—41no—
127C23×C113—41no—
128C23×C113—41no—
129C23×C113—41no—
130C23×C113—41no—
131C23×C113—41no—
132C23×C113—41no—
133C23×C113—81no—
134C23×C113—81no—
135C23×C113#12011yescharacteristic
136C23×C113C2×D811yescharacteristic
137C23×C113AGL(1,ℤ/8)11yescharacteristic
138Q8×C113—84no—
139D4×C113—42no—
140D4×C113—82no—
141D4×C113—82no—
142D4×C113—81no—
143D4×C113—81no—
144D4×C113—81no—
145D4×C113—81no—
146D4×C113—81no—
147D4×C113—81no—
148D4×C113—81no—
149C2×C4×C113—22no—
150C2×C4×C113—22no—
151C2×C4×C113—21no—
152C2×C4×C113—21no—
153C2×C4×C113—41no—
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—41no—
162C2×C4×C113—41no—
163C2×C4×C113—41no—
164C2×C4×C113—41no—
165C2×C4×C113—42no—
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×C113—81no—
176C8×C113—81no—
177C8×C113—81no—
178C22×C113—21no—
179C22×C113—21no—
180C22×C113—21no—
181C22×C113—21no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113—81no—
187C22×C113—81no—
188C22×C113—81no—
189C22×C113—81no—
190C22×C113—81no—
191C22×C113—82no—
192C22×C113—81no—
193C22×C113—81no—
194C22×C113—81no—
195C22×C113—81no—
196C22×C113—81no—
197C22×C113—81no—
198C22×C113—161no—
199C22×C113#44711yescharacteristic
200C22×C113#45411yescharacteristic
201C22×C113B(4,𝔽2)11yescharacteristic
202C4×C113—42no—
203C4×C113—42no—
204C4×C113—41no—
205C4×C113—41no—
206C4×C113—81no—
207C4×C113—81no—
208C4×C113—81no—
209C4×C113—81no—
210C4×C113—161no—
211#12151C11311yesmaximal, characteristic, direct product factor, Sylow
212C2×C113—21no—
213C2×C113—21no—
214C2×C113—41no—
215C2×C113—41no—
216C2×C113—161no—
217C2×C113—161no—
218C2×C113#159811yescharacteristic
219C2×C113#219811yescharacteristic
220C2×C113#219911yescharacteristic
221#2712C2×C11311yescharacteristic, complemented
222#2044C2×C11311yescharacteristic, complemented
223#1607C2×C11311yescharacteristic, complemented
224#1595C2×C11311yescharacteristic
225#1344C2×C11311yescharacteristic, complemented
226#1343C2×C11311yescharacteristic, complemented
227#1326C2×C11311yescharacteristic, complemented
228C113#1215111yescharacteristic, direct product factor, Sylow
229#534C22×C11311yescharacteristic
230C2×#124—21no—
231#480—21no—
232#447—21no—
233C2×#99—21no—
234#397C22×C11311yescharacteristic
235#394—21no—
236#393—21no—
237#392C22×C11311yescharacteristic
238#391—21no—
239#388—21no—
240#386—21no—
241#386—21no—
242#385C22×C11311yescharacteristic
243#342C22×C11311yescharacteristic
244#327—21no—
245#327—21no—
246#323C22×C11311yescharacteristic
247#323C22×C11311yescharacteristic
248C22×Q8—21no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4D4×C11311yescharacteristic
252C23×C4D4×C11311yescharacteristic
253C2×D8—41no—
254#124—42no—
255#124—42no—
256#123—41no—
257#121—21no—
258#121—21no—
259#120—41no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4D4×C11311yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—41no—
270C2×C22⋊C4D4×C11311yescharacteristic
271C2×C22⋊C4C23×C11311yescharacteristic
272C2×C42—21no—
273#107—41no—
274#102—41no—
275#102—41no—
276#99—42no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—41no—
284#95D4×C11311yescharacteristic
285#95D4×C11311yescharacteristic
286C24—21no—
287C24—21no—
288C24C2×D4×C11311yescharacteristic
289C2×Q8—42no—
290C2×Q8—42no—
291C2×Q8—81no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—81no—
305C2×D4—81no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—81no—
315C22×C4C2×D4×C11311yescharacteristic
316C22×C4C2×D4×C11311yescharacteristic
317D8—82no—
318C2×C8—41no—
319C2×C8—41no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—81no—
324C22⋊C4—21no—
325C22⋊C4—41no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—81no—
336C22⋊C4—81no—
337C22⋊C4—82no—
338C22⋊C4D8×C11312yescomplemented
339C42—42no—
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—81no—
355C23—81no—
356C23#120×C11311yescharacteristic
357C23C2×D8×C11311yescharacteristic
358C23AGL(1,ℤ/8)×C11311yescharacteristic
359Q8—84no—
360D4—42no—
361D4—82no—
362D4—82no—
363D4—81no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4—81no—
368D4—81no—
369D4—81no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C8—81no—
398C8—81no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—82no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—161no—
420C22#447×C11311yescharacteristic
421C22#454×C11311yescharacteristic
422C22B(4,𝔽2)×C11311yescharacteristic
423C4—42no—
424C4—42no—
425C4—41no—
426C4—41no—
427C4—81no—
428C4—81no—
429C4—81no—
430C4—81no—
431C4—161no—
432C2—21no—
433C2—21no—
434C2—41no—
435C2—41no—
436C2—161no—
437C2—161no—
438C2C113×#159811yescharacteristic
439C2C113×#219811yescharacteristic
440C2C113×#219911yescharacteristic
subgroupG/H
center, socleC22×C113B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C113
prime radicalC113×#1595C2
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C113 ◁ C2×C22⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#2712C2semidirect
2. C113×#2044C2semidirect
3. C113×#1607C2semidirect
5. C113×#1344C2semidirect
6. C113×#1343C2semidirect
7. C113×#1326C2semidirect
117. C22⋊C4×C113D8semidirect
211. #12151C113direct (N × H)
221. #2712C2×C113semidirect
222. #2044C2×C113semidirect
223. #1607C2×C113semidirect
225. #1344C2×C113semidirect
226. #1343C2×C113semidirect
227. #1326C2×C113semidirect
228. C113#12151direct (N × H)
338. C22⋊C4D8×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#27122
C113×#20442
C113×#16072
C113×#15952
C113×#13442
C113×#13432
C113×#13262
#12151113