Finite Group Databasebeta

← C151×#10003 #50314928

Subgroups — C151×#10003 #50314928

Order 38656.

500 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3104×C151C211yesmaximal, characteristic
2#3078×C151C211yesmaximal, characteristic
3#2581×C151C211yesmaximal, characteristic
4#1518×C151C211yesmaximal, characteristic
5#1487×C151C211yesmaximal, characteristic
6#1479×C151C211yesmaximal, characteristic
7#1286×C151C211yesmaximal, characteristic
8#533×C151C2211yescharacteristic
9C2×C4×Q8×C151C2211yescharacteristic
10C2×C4×Q8×C151C2211yescharacteristic
11#484×C151—21no—
12#479×C151—22no—
13#477×C151—21no—
14#477×C151—21no—
15#475×C151—21no—
16#462×C151—21no—
17#451×C151—21no—
18C4×Q16×C151—22no—
19#431×C151C2211yescharacteristic
20#431×C151C2211yescharacteristic
21#428×C151—21no—
22#423×C151C2211yescharacteristic
23#419×C151—21no—
24#400×C151—21no—
25#395×C151—21no—
26#391×C151—21no—
27#389×C151—21no—
28#387×C151—22no—
29#382×C151C2211yescharacteristic
30#328×C151—22no—
31Q8⋊C8×C151—22no—
32Q8⋊C8×C151—22no—
33C22×Q8×C151D411yescharacteristic
34C22×Q8×C151D411yescharacteristic
35C2×Q16×C151—22no—
36C2×M16×C151—21no—
37C4⋊Q8×C151D411yescharacteristic
38C4⋊Q8×C151D411yescharacteristic
39#125×C151—21no—
40C22⋊Q8×C151—21no—
41C22⋊Q8×C151—21no—
42C4×Q8×C151—21no—
43C4×Q8×C151—21no—
44C4×Q8×C151—21no—
45C4×Q8×C151—21no—
46C4×Q8×C151—21no—
47C4×Q8×C151—21no—
48C4×Q8×C151—21no—
49C4×Q8×C151—21no—
50C4×Q8×C151—21no—
51C4×Q8×C151—21no—
52#117×C151—21no—
53C2×C4⋊C4×C151—22no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151D411yescharacteristic
58C2×C4⋊C4×C151D411yescharacteristic
59C2×C42×C151—21no—
60C2×C42×C151—21no—
61C2×C42×C151C2311yescharacteristic
62#107×C151—22no—
63#107×C151—22no—
64#106×C151—22no—
65C4⋊C8×C151—21no—
66C4⋊C8×C151—21no—
67C4⋊C8×C151—21no—
68C4⋊C8×C151D412yes—
69#103×C151—22no—
70#103×C151—22no—
71#103×C151—22no—
72#103×C151—22no—
73C22⋊C8×C151—21no—
74C22⋊C8×C151—21no—
75C4×C8×C151—21no—
76C4×C8×C151D412yes—
77#95×C151—22no—
78#95×C151—22no—
79#95×C151—22no—
80#95×C151—21no—
81#95×C151D412yes—
82C2×Q8×C151—21no—
83C2×Q8×C151—21no—
84C2×Q8×C151—21no—
85C2×Q8×C151—21no—
86C2×Q8×C151—21no—
87C2×Q8×C151—21no—
88C2×Q8×C151—21no—
89C2×Q8×C151—21no—
90C2×Q8×C151—21no—
91C2×Q8×C151—42no—
92C2×Q8×C151Q1612yescomplemented
93C22×C4×C151—21no—
94C22×C4×C151—21no—
95C22×C4×C151—22no—
96C22×C4×C151—21no—
97C22×C4×C151—21no—
98C22×C4×C151C2×D411yescharacteristic
99C22×C4×C151C2×D411yescharacteristic
100C22×C4×C151C2×D411yescharacteristic
101Q16×C151—44no—
102M16×C151—41no—
103M16×C151—41no—
104C2×C8×C151—22no—
105C2×C8×C151—22no—
106C2×C8×C151—41no—
107C4⋊C4×C151—21no—
108C4⋊C4×C151—21no—
109C4⋊C4×C151—21no—
110C4⋊C4×C151—21no—
111C4⋊C4×C151—21no—
112C4⋊C4×C151—21no—
113C4⋊C4×C151—21no—
114C4⋊C4×C151—21no—
115C4⋊C4×C151—44no—
116C4⋊C4×C151—41no—
117C4⋊C4×C151—41no—
118C4⋊C4×C151—41no—
119C4⋊C4×C151—41no—
120C4⋊C4×C151—41no—
121C4⋊C4×C151—41no—
122C4⋊C4×C151—41no—
123C4⋊C4×C151—41no—
124C22⋊C4×C151—41no—
125C42×C151—41no—
126C42×C151—41no—
127C42×C151—41no—
128C42×C151—41no—
129C42×C151—41no—
130C42×C151C2×D411yescharacteristic
131C42×C151C2×D411yescharacteristic
132C42×C151C2×D411yescharacteristic
133C42×C151#4111yescharacteristic
134C23×C151#12011yescharacteristic
135Q8×C151—22no—
136Q8×C151—22no—
137Q8×C151—22no—
138Q8×C151—22no—
139Q8×C151—41no—
140Q8×C151—41no—
141Q8×C151—42no—
142Q8×C151—41no—
143Q8×C151—41no—
144Q8×C151—81no—
145C2×C4×C151—22no—
146C2×C4×C151—22no—
147C2×C4×C151—41no—
148C2×C4×C151—41no—
149C2×C4×C151—41no—
150C2×C4×C151—41no—
151C2×C4×C151—41no—
152C2×C4×C151—41no—
153C2×C4×C151—42no—
154C2×C4×C151—42no—
155C2×C4×C151—42no—
156C2×C4×C151—42no—
157C2×C4×C151—41no—
158C2×C4×C151—41no—
159C2×C4×C151—41no—
160C2×C4×C151—41no—
161C2×C4×C151—42no—
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×Q1611yescharacteristic
169C2×C4×C151#13511yescharacteristic
170C2×C4×C151#13711yescharacteristic
171C2×C4×C151#13711yescharacteristic
172C8×C151—42no—
173C8×C151—42no—
174C8×C151—81no—
175C22×C151—21no—
176C22×C151—21no—
177C22×C151#39211yescharacteristic
178C22×C151#45111yescharacteristic
179C22×C151#45211yescharacteristic
180C4×C151—21no—
181C4×C151—21no—
182C4×C151—21no—
183C4×C151—21no—
184C4×C151—42no—
185C4×C151—42no—
186C4×C151—82no—
187C4×C151—81no—
188C4×C151—81no—
189C4×C151—81no—
190C4×C151—81no—
191C4×C151#45111yescharacteristic
192C4×C151#45211yescharacteristic
193C4×C151#46711yescharacteristic
194C4×C151#47011yescharacteristic
195C2×C151—21no—
196C2×C151—21no—
197C2×C151#200111yescharacteristic
198C2×C151#200911yescharacteristic
199C2×C151#201011yescharacteristic
200#10003C15111yesmaximal, characteristic, direct product factor, Sylow
201C151#1000311yescharacteristic, direct product factor, Sylow
202#3104C2×C15111yescharacteristic
203#3078C2×C15111yescharacteristic
204#2581C2×C15111yescharacteristic
205#1518C2×C15111yescharacteristic
206#1487C2×C15111yescharacteristic
207#1479C2×C15111yescharacteristic
208#1286C2×C15111yescharacteristic
209#533C22×C15111yescharacteristic
210C2×C4×Q8C22×C15111yescharacteristic
211C2×C4×Q8C22×C15111yescharacteristic
212#484—21no—
213#479—22no—
214#477—21no—
215#477—21no—
216#475—21no—
217#462—21no—
218#451—21no—
219C4×Q16—22no—
220#431C22×C15111yescharacteristic
221#431C22×C15111yescharacteristic
222#428—21no—
223#423C22×C15111yescharacteristic
224#419—21no—
225#400—21no—
226#395—21no—
227#391—21no—
228#389—21no—
229#387—22no—
230#382C22×C15111yescharacteristic
231#328—22no—
232Q8⋊C8—22no—
233Q8⋊C8—22no—
234C22×Q8D4×C15111yescharacteristic
235C22×Q8D4×C15111yescharacteristic
236C2×Q16—22no—
237C2×M16—21no—
238C4⋊Q8D4×C15111yescharacteristic
239C4⋊Q8D4×C15111yescharacteristic
240#125—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253#117—21no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4D4×C15111yescharacteristic
259C2×C4⋊C4D4×C15111yescharacteristic
260C2×C42—21no—
261C2×C42—21no—
262C2×C42C23×C15111yescharacteristic
263#107—22no—
264#107—22no—
265#106—22no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8D4×C15112yes—
270#103—22no—
271#103—22no—
272#103—22no—
273#103—22no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C4×C8—21no—
277C4×C8D4×C15112yes—
278#95—22no—
279#95—22no—
280#95—22no—
281#95—21no—
282#95D4×C15112yes—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—42no—
293C2×Q8Q16×C15112yescomplemented
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4C2×D4×C15111yescharacteristic
300C22×C4C2×D4×C15111yescharacteristic
301C22×C4C2×D4×C15111yescharacteristic
302Q16—44no—
303M16—41no—
304M16—41no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—41no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—44no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C22⋊C4—41no—
326C42—41no—
327C42—41no—
328C42—41no—
329C42—41no—
330C42—41no—
331C42C2×D4×C15111yescharacteristic
332C42C2×D4×C15111yescharacteristic
333C42C2×D4×C15111yescharacteristic
334C42#41×C15111yescharacteristic
335C23#120×C15111yescharacteristic
336Q8—22no—
337Q8—22no—
338Q8—22no—
339Q8—22no—
340Q8—41no—
341Q8—41no—
342Q8—42no—
343Q8—41no—
344Q8—41no—
345Q8—81no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4#120×C15111yescharacteristic
364C2×C4#120×C15111yescharacteristic
365C2×C4#121×C15111yescharacteristic
366C2×C4#121×C15111yescharacteristic
367C2×C4#121×C15111yescharacteristic
368C2×C4#127×C15111yescharacteristic
369C2×C4C2×Q16×C15111yescharacteristic
370C2×C4#135×C15111yescharacteristic
371C2×C4#137×C15111yescharacteristic
372C2×C4#137×C15111yescharacteristic
373C8—42no—
374C8—42no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22#392×C15111yescharacteristic
379C22#451×C15111yescharacteristic
380C22#452×C15111yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—42no—
386C4—42no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4—81no—
391C4—81no—
392C4#451×C15111yescharacteristic
393C4#452×C15111yescharacteristic
394C4#467×C15111yescharacteristic
395C4#470×C15111yescharacteristic
396C2—21no—
397C2—21no—
398C2#2001×C15111yescharacteristic
399C2#2009×C15111yescharacteristic
400C2#2010×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#392
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC23×C151#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
92. C2×Q8×C151Q16semidirect
200. #10003C151direct (N × H)
201. C151#10003direct (N × H)
293. C2×Q8Q16×C151semidirect

Maximal subgroups

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

subgroupindex
#3104×C1512
#3078×C1512
#2581×C1512
#1518×C1512
#1487×C1512
#1479×C1512
#1286×C1512
#10003151