Finite Group Databasebeta

← C151×#10055 #50314980

Subgroups — C151×#10055 #50314980

Order 38656.

702 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#492×C151C211yesmaximal, characteristic
2C2×#477×C151C211yesmaximal, characteristic, complemented
3#2548×C151C211yesmaximal, characteristic
4#1987×C151C211yesmaximal, characteristic, complemented
5C2×#331×C151C211yesmaximal, characteristic
6C2×Q8⋊C8×C151C211yesmaximal, characteristic, complemented
7#1279×C151C211yesmaximal, characteristic, complemented
8C22×SD16×C151—22no—
9C2×C4⋊Q8×C151C2211yescharacteristic
10C2×#127×C151C2211yescharacteristic
11C2×#124×C151—21no—
12C2×C4×Q8×C151C2211yescharacteristic
13#492×C151—22no—
14#492×C151—22no—
15#477×C151—22no—
16#477×C151—22no—
17C2×#107×C151—21no—
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×C4⋊C8×C151C2211yescharacteristic
20C2×#103×C151—21no—
21C2×C4×C8×C151C2211yescharacteristic
22#394×C151—22no—
23#390×C151—21no—
24#390×C151—22no—
25C4×C4⋊C4×C151C2211yescharacteristic
26#340×C151—22no—
27#331×C151—22no—
28Q8⋊C8×C151—22no—
29C22×Q8×C151—21no—
30C22×Q8×C151D411yescharacteristic
31C22×D4×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151D412yes—
34C2×SD16×C151—28no—
35C2×SD16×C151—48no—
36C22×C8×C151—21no—
37C22×C8×C151—21no—
38C22×C8×C151—21no—
39C4⋊Q8×C151—21no—
40C4⋊Q8×C151—21no—
41C4⋊Q8×C151—21no—
42C4⋊Q8×C151D412yes—
43#127×C151—21no—
44#127×C151—21no—
45#127×C151—21no—
46#127×C151—21no—
47#124×C151—42no—
48#124×C151—42no—
49C4×Q8×C151—21no—
50C4×Q8×C151—21no—
51C4×Q8×C151—21no—
52C4×Q8×C151—21no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151D412yes—
57C2×C4⋊C4×C151D411yescharacteristic
58C2×C22⋊C4×C151—24no—
59C2×C22⋊C4×C151—24no—
60C2×C42×C151—21no—
61C2×C42×C151—21no—
62C2×C42×C151C2311yescharacteristic
63#107×C151—24no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66C4⋊C8×C151—21no—
67C4⋊C8×C151D412yes—
68#103×C151—24no—
69C4×C8×C151—21no—
70C4×C8×C151D412yes—
71#95×C151—21no—
72C24×C151—22no—
73C2×Q8×C151—21no—
74C2×Q8×C151—21no—
75C2×Q8×C151—22no—
76C2×Q8×C151—21no—
77C2×Q8×C151—21no—
78C2×Q8×C151—21no—
79C2×Q8×C151—44no—
80C2×Q8×C151—41no—
81C2×Q8×C151SD1612yescomplemented
82C2×D4×C151—22no—
83C2×D4×C151—22no—
84C2×D4×C151—44no—
85C2×D4×C151—41no—
86C2×D4×C151—41no—
87C2×D4×C151—41no—
88C2×D4×C151—41no—
89C2×D4×C151—41no—
90C2×D4×C151—41no—
91C2×D4×C151—42no—
92C2×D4×C151—41no—
93C2×D4×C151—41no—
94C2×D4×C151—42no—
95C22×C4×C151—21no—
96C22×C4×C151—22no—
97C22×C4×C151—21no—
98C22×C4×C151—41no—
99C22×C4×C151C2×D411yescharacteristic
100C22×C4×C151C2×D411yescharacteristic
101C22×C4×C151C2×D411yescharacteristic
102SD16×C151—416no—
103C2×C8×C151—24no—
104C2×C8×C151—22no—
105C2×C8×C151—22no—
106C2×C8×C151—41no—
107C2×C8×C151—41no—
108C2×C8×C151—41no—
109C2×C8×C151—42no—
110C4⋊C4×C151—22no—
111C4⋊C4×C151—21no—
112C4⋊C4×C151—22no—
113C4⋊C4×C151—21no—
114C4⋊C4×C151—22no—
115C4⋊C4×C151—22no—
116C4⋊C4×C151—41no—
117C4⋊C4×C151—41no—
118C4⋊C4×C151—41no—
119C4⋊C4×C151—41no—
120C22⋊C4×C151—48no—
121C22⋊C4×C151—84no—
122C42×C151—41no—
123C42×C151—41no—
124C42×C151—41no—
125C42×C151—41no—
126C42×C151C2×D411yescharacteristic
127C42×C151C2×D411yescharacteristic
128C42×C151C2×D411yescharacteristic
129C42×C151#4111yescharacteristic
130C23×C151—42no—
131C23×C151—42no—
132C23×C151—42no—
133C23×C151—44no—
134C23×C151—44no—
135C23×C151#12011yescharacteristic
136Q8×C151—22no—
137Q8×C151—22no—
138Q8×C151—44no—
139Q8×C151—41no—
140Q8×C151—41no—
141Q8×C151—82no—
142D4×C151—44no—
143D4×C151—82no—
144D4×C151—81no—
145D4×C151—81no—
146D4×C151—82no—
147D4×C151—81no—
148D4×C151—81no—
149D4×C151—81no—
150D4×C151—81no—
151C2×C4×C151—22no—
152C2×C4×C151—22no—
153C2×C4×C151—41no—
154C2×C4×C151—41no—
155C2×C4×C151—42no—
156C2×C4×C151—41no—
157C2×C4×C151—42no—
158C2×C4×C151—42no—
159C2×C4×C151—42no—
160C2×C4×C151—42no—
161C2×C4×C151—82no—
162C2×C4×C151#12011yescharacteristic
163C2×C4×C151#12011yescharacteristic
164C2×C4×C151#12111yescharacteristic
165C2×C4×C151#12111yescharacteristic
166C2×C4×C151#12111yescharacteristic
167C2×C4×C151#12711yescharacteristic
168C2×C4×C151C2×SD1611yescharacteristic
169C2×C4×C151#13511yescharacteristic
170C2×C4×C151#13512yes—
171C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C151#13711yescharacteristic
173C2×C4×C151#13712yes—
174C8×C151—24no—
175C8×C151—42no—
176C8×C151—81no—
177C22×C151—84no—
178C22×C151—84no—
179C22×C151—82no—
180C22×C151—82no—
181C22×C151—82no—
182C22×C151#39211yescharacteristic
183C22×C151#45011yescharacteristic
184C22×C151#45211yescharacteristic
185C22×C151#45212yes—
186C22×C151#45312yes—
187C4×C151—21no—
188C4×C151—21no—
189C4×C151—42no—
190C4×C151—82no—
191C4×C151—81no—
192C4×C151—82no—
193C4×C151#44811yescharacteristic
194C4×C151#44911yescharacteristic
195C4×C151#46412yes—
196C4×C151#46511yescharacteristic
197C4×C151#46811yescharacteristic
198C4×C151#49511yescharacteristic
199C4×C151#49711yescharacteristic
200C2×C151—162no—
201C2×C151#163012yes—
202C2×C151#163112yes—
203C2×C151#200011yescharacteristic
204C2×C151#200211yescharacteristic
205C2×C151#201511yescharacteristic
206#10055C15111yesmaximal, characteristic, direct product factor, Sylow
207C151#1005511yescharacteristic, direct product factor, Sylow
208C2×#492C2×C15111yescharacteristic
209C2×#477C2×C15111yescharacteristic, complemented
210#2548C2×C15111yescharacteristic
211#1987C2×C15111yescharacteristic, complemented
212C2×#331C2×C15111yescharacteristic
213C2×Q8⋊C8C2×C15111yescharacteristic, complemented
214#1279C2×C15111yescharacteristic, complemented
215C22×SD16—22no—
216C2×C4⋊Q8C22×C15111yescharacteristic
217C2×#127C22×C15111yescharacteristic
218C2×#124—21no—
219C2×C4×Q8C22×C15111yescharacteristic
220#492—22no—
221#492—22no—
222#477—22no—
223#477—22no—
224C2×#107—21no—
225C2×C4⋊C8C22×C15111yescharacteristic
226C2×C4⋊C8C22×C15111yescharacteristic
227C2×#103—21no—
228C2×C4×C8C22×C15111yescharacteristic
229#394—22no—
230#390—22no—
231#390—21no—
232C4×C4⋊C4C22×C15111yescharacteristic
233#340—22no—
234#331—22no—
235Q8⋊C8—22no—
236C22×Q8—21no—
237C22×Q8D4×C15111yescharacteristic
238C22×D4—21no—
239C22×D4—21no—
240C22×D4D4×C15112yes—
241C2×SD16—28no—
242C2×SD16—48no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8D4×C15112yes—
250#127—21no—
251#127—21no—
252#127—21no—
253#127—21no—
254#124—42no—
255#124—42no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4D4×C15111yescharacteristic
264C2×C4⋊C4D4×C15112yes—
265C2×C22⋊C4—24no—
266C2×C22⋊C4—24no—
267C2×C42—21no—
268C2×C42—21no—
269C2×C42C23×C15111yescharacteristic
270#107—24no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8D4×C15112yes—
275#103—24no—
276C4×C8—21no—
277C4×C8D4×C15112yes—
278#95—21no—
279C24—22no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—44no—
287C2×Q8—41no—
288C2×Q8SD16×C15112yescomplemented
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—44no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—42no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4C2×D4×C15111yescharacteristic
307C22×C4C2×D4×C15111yescharacteristic
308C22×C4C2×D4×C15111yescharacteristic
309SD16—416no—
310C2×C8—24no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—42no—
317C4⋊C4—22no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C22⋊C4—48no—
328C22⋊C4—84no—
329C42—41no—
330C42—41no—
331C42—41no—
332C42—41no—
333C42C2×D4×C15111yescharacteristic
334C42C2×D4×C15111yescharacteristic
335C42C2×D4×C15111yescharacteristic
336C42#41×C15111yescharacteristic
337C23—42no—
338C23—42no—
339C23—42no—
340C23—44no—
341C23—44no—
342C23#120×C15111yescharacteristic
343Q8—22no—
344Q8—22no—
345Q8—44no—
346Q8—41no—
347Q8—41no—
348Q8—82no—
349D4—44no—
350D4—82no—
351D4—81no—
352D4—81no—
353D4—82no—
354D4—81no—
355D4—81no—
356D4—81no—
357D4—81no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4#120×C15111yescharacteristic
370C2×C4#120×C15111yescharacteristic
371C2×C4#121×C15111yescharacteristic
372C2×C4#121×C15111yescharacteristic
373C2×C4#121×C15111yescharacteristic
374C2×C4#127×C15111yescharacteristic
375C2×C4C2×SD16×C15111yescharacteristic
376C2×C4#135×C15111yescharacteristic
377C2×C4#135×C15112yes—
378C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
379C2×C4#137×C15111yescharacteristic
380C2×C4#137×C15112yes—
381C8—24no—
382C8—42no—
383C8—81no—
384C22—84no—
385C22—84no—
386C22—82no—
387C22—82no—
388C22—82no—
389C22#392×C15111yescharacteristic
390C22#450×C15111yescharacteristic
391C22#452×C15111yescharacteristic
392C22#452×C15112yes—
393C22#453×C15112yes—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—82no—
398C4—81no—
399C4—82no—
400C4#448×C15111yescharacteristic
401C4#449×C15111yescharacteristic
402C4#464×C15112yes—
403C4#465×C15111yescharacteristic
404C4#468×C15111yescharacteristic
405C4#495×C15111yescharacteristic
406C4#497×C15111yescharacteristic
407C2—162no—
408C2#1630×C15112yes—
409C2#1631×C15112yes—
410C2#2000×C15111yescharacteristic
411C2#2002×C15111yescharacteristic
412C2#2015×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC2×#127×C151C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#477×C151C2semidirect
4. #1987×C151C2semidirect
6. C2×Q8⋊C8×C151C2semidirect
7. #1279×C151C2semidirect
81. C2×Q8×C151SD16semidirect
206. #10055C151direct (N × H)
207. C151#10055direct (N × H)
209. C2×#477C2×C151semidirect
211. #1987C2×C151semidirect
213. C2×Q8⋊C8C2×C151semidirect
214. #1279C2×C151semidirect
288. C2×Q8SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#492×C1512
C2×#477×C1512
#2548×C1512
#1987×C1512
C2×#331×C1512
C2×Q8⋊C8×C1512
#1279×C1512
#10055151