Finite Group Databasebeta

← C151×#18218 #50323143

Subgroups — C151×#18218 #50323143

Order 38656.

1222 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3497×C151C211yesmaximal, characteristic, complemented
2#3100×C151C212yesmaximal, complemented
3#2536×C151C211yesmaximal, characteristic, complemented
4#1610×C151C214yesmaximal, complemented
5#1598×C151C214yesmaximal, complemented
6#1517×C151C212yesmaximal, complemented
7#1461×C151C211yesmaximal, characteristic, complemented
8C2×2−1+4×C151—21no—
9#550×C151—22no—
10D4×Q8×C151—22no—
11#548×C151—24no—
12#537×C151—21no—
13#537×C151C2214yes—
14#532×C151—22no—
15#532×C151C2212yes—
16C2×C22⋊Q8×C151—21no—
17C2×C4×Q8×C151C2211yescharacteristic
18C2×C4×D4×C151C2211yescharacteristic
19#480×C151C2214yes—
20#474×C151—22no—
21#459×C151—22no—
22#447×C151C2214yes—
23C4×D8×C151—24no—
24#431×C151C2212yes—
25#398×C151C2212yes—
26#394×C151C2212yes—
27#388×C151—22no—
28#382×C151C2211yescharacteristic
29#380×C151—21no—
30#327×C151C2218yes—
31#324×C151C2214yes—
322−1+4×C151—44no—
332−1+4×C151—44no—
34C2×#41×C151—24no—
35C2×#41×C151—24no—
36C2×#41×C151—22no—
37C22×Q8×C151—24no—
38C22×Q8×C151D411yescharacteristic
39C22×D4×C151C2311yescharacteristic
40C23×C4×C151—21no—
41C2×D8×C151—24no—
42C4⋊Q8×C151—22no—
43C4⋊Q8×C151D412yes—
44#127×C151—22no—
45#127×C151D412yes—
46#124×C151—24no—
47#124×C151—22no—
48C22⋊Q8×C151—24no—
49C22⋊Q8×C151—28no—
50C22⋊Q8×C151—44no—
51#121×C151—24no—
52#121×C151—28no—
53#121×C151—22no—
54#121×C151—24no—
55#121×C151C2314yes—
56C4×Q8×C151—22no—
57C4×Q8×C151—22no—
58C4×D4×C151—24no—
59C4×D4×C151—24no—
60C4×D4×C151—22no—
61C4×D4×C151—22no—
62C4×D4×C151—22no—
63C4×D4×C151D414yes—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151D411yescharacteristic
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2312yes—
69C2×C22⋊C4×C151—22no—
70C2×C22⋊C4×C151—21no—
71C2×C22⋊C4×C151—22no—
72C2×C42×C151D412yes—
73C2×C42×C151C2311yescharacteristic
74#107×C151—24no—
75C4⋊C8×C151—22no—
76#102×C151—24no—
77#102×C151—24no—
78C22⋊C8×C151C2314yes—
79C4×C8×C151—22no—
80#95×C151—22no—
81#95×C151—21no—
82#95×C151C2312yes—
83C24×C151—21no—
84#41×C151—48no—
85#41×C151—416no—
86#41×C151—48no—
87#41×C151—44no—
88#41×C151—44no—
89C2×Q8×C151—24no—
90C2×Q8×C151—22no—
91C2×Q8×C151—22no—
92C2×Q8×C151—22no—
93C2×Q8×C151—416no—
94C2×Q8×C151D814yescomplemented
95C2×D4×C151—24no—
96C2×D4×C151—24no—
97C2×D4×C151—24no—
98C2×D4×C151—22no—
99C2×D4×C151—22no—
100C2×D4×C151—22no—
101C2×D4×C151—42no—
102C2×D4×C151C2×D414yes—
103C22×C4×C151—28no—
104C22×C4×C151—24no—
105C22×C4×C151—22no—
106C22×C4×C151—21no—
107C22×C4×C151—42no—
108C22×C4×C151—42no—
109C22×C4×C151—42no—
110C22×C4×C151C2×D412yes—
111C22×C4×C151C2×D412yes—
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2×D411yescharacteristic
114C22×C4×C151C2411yescharacteristic
115D8×C151—48no—
116C2×C8×C151—24no—
117C4⋊C4×C151—24no—
118C4⋊C4×C151—22no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—24no—
121C4⋊C4×C151—22no—
122C4⋊C4×C151—42no—
123C4⋊C4×C151—44no—
124C4⋊C4×C151C2×D414yes—
125C22⋊C4×C151—28no—
126C22⋊C4×C151—24no—
127C22⋊C4×C151—24no—
128C22⋊C4×C151—44no—
129C22⋊C4×C151—41no—
130C22⋊C4×C151—41no—
131C22⋊C4×C151—44no—
132C42×C151—22no—
133C42×C151—22no—
134C42×C151C2×D412yes—
135C42×C151C2×D412yes—
136C23×C151—22no—
137C23×C151—24no—
138C23×C151—41no—
139C23×C151—41no—
140C23×C151—41no—
141C23×C151—41no—
142C23×C151—41no—
143C23×C151—41no—
144C23×C151C22×D411yescharacteristic
145Q8×C151—28no—
146Q8×C151—48no—
147Q8×C151—44no—
148D4×C151—24no—
149D4×C151—44no—
150D4×C151—48no—
151D4×C151—44no—
152D4×C151—42no—
153D4×C151—44no—
154D4×C151—44no—
155D4×C151—44no—
156D4×C151—84no—
157C2×C4×C151—22no—
158C2×C4×C151—22no—
159C2×C4×C151—24no—
160C2×C4×C151—22no—
161C2×C4×C151—41no—
162C2×C4×C151—41no—
163C2×C4×C151—416no—
164C2×C4×C151—48no—
165C2×C4×C151—42no—
166C2×C4×C151—42no—
167C2×C4×C151—42no—
168C2×C4×C151—41no—
169C2×C4×C151—42no—
170C2×C4×C151—41no—
171C2×C4×C151—41no—
172C2×C4×C151—84no—
173C2×C4×C151#12011yescharacteristic
174C2×C4×C151#12011yescharacteristic
175C2×C4×C151#12012yes—
176C2×C4×C151C2×D814yes—
177C2×C4×C151C2×D812yes—
178C2×C4×C151AGL(1,ℤ/8)12yes—
179C2×C4×C151C22×D412yes—
180C8×C151—44no—
181C22×C151—21no—
182C22×C151—21no—
183C22×C151—42no—
184C22×C151—42no—
185C22×C151—44no—
186C22×C151—44no—
187C22×C151—42no—
188C22×C151—44no—
189C22×C151—81no—
190C22×C151—81no—
191C22×C151—81no—
192C22×C151—81no—
193C22×C151C2×#12011yescharacteristic
194C22×C151C22×D811yescharacteristic
195C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
196C4×C151—24no—
197C4×C151—21no—
198C4×C151—21no—
199C4×C151—22no—
200C4×C151—44no—
201C4×C151—42no—
202C4×C151—82no—
203C4×C151—81no—
204C4×C151#44714yes—
205C2×C151—21no—
206C2×C151—21no—
207C2×C151—84no—
208C2×C151—82no—
209C2×C151C2×#44711yescharacteristic
210C2×C151#302011yescharacteristic
211C2×C151#302511yescharacteristic
212#18218C15111yesmaximal, characteristic, direct product factor, Sylow
213C151#1821811yescharacteristic, direct product factor, Sylow
214#3497C2×C15111yescharacteristic, complemented
215#3100C2×C15112yescomplemented
216#2536C2×C15111yescharacteristic, complemented
217#1610C2×C15114yescomplemented
218#1598C2×C15114yescomplemented
219#1517C2×C15112yescomplemented
220#1461C2×C15111yescharacteristic, complemented
221C2×2−1+4—21no—
222#550—22no—
223D4×Q8—22no—
224#548—24no—
225#537—21no—
226#537C22×C15114yes—
227#532—22no—
228#532C22×C15112yes—
229C2×C22⋊Q8—21no—
230C2×C4×Q8C22×C15111yescharacteristic
231C2×C4×D4C22×C15111yescharacteristic
232#480C22×C15114yes—
233#474—22no—
234#459—22no—
235#447C22×C15114yes—
236C4×D8—24no—
237#431C22×C15112yes—
238#398C22×C15112yes—
239#394C22×C15112yes—
240#388—22no—
241#382C22×C15111yescharacteristic
242#380—21no—
243#327C22×C15118yes—
244#324C22×C15114yes—
2452−1+4—44no—
2462−1+4—44no—
247C2×#41—24no—
248C2×#41—24no—
249C2×#41—22no—
250C22×Q8—24no—
251C22×Q8D4×C15111yescharacteristic
252C22×D4C23×C15111yescharacteristic
253C23×C4—21no—
254C2×D8—24no—
255C4⋊Q8—22no—
256C4⋊Q8D4×C15112yes—
257#127—22no—
258#127D4×C15112yes—
259#124—24no—
260#124—22no—
261C22⋊Q8—24no—
262C22⋊Q8—28no—
263C22⋊Q8—44no—
264#121—24no—
265#121—28no—
266#121—22no—
267#121—24no—
268#121C23×C15114yes—
269C4×Q8—22no—
270C4×Q8—22no—
271C4×D4—24no—
272C4×D4—24no—
273C4×D4—22no—
274C4×D4—22no—
275C4×D4—22no—
276C4×D4D4×C15114yes—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4D4×C15111yescharacteristic
280C2×C4⋊C4C23×C15111yescharacteristic
281C2×C4⋊C4C23×C15112yes—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C42D4×C15112yes—
286C2×C42C23×C15111yescharacteristic
287#107—24no—
288C4⋊C8—22no—
289#102—24no—
290#102—24no—
291C22⋊C8C23×C15114yes—
292C4×C8—22no—
293#95—22no—
294#95—21no—
295#95C23×C15112yes—
296C24—21no—
297#41—48no—
298#41—416no—
299#41—48no—
300#41—44no—
301#41—44no—
302C2×Q8—24no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—416no—
307C2×Q8D8×C15114yescomplemented
308C2×D4—24no—
309C2×D4—24no—
310C2×D4—24no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—42no—
315C2×D4C2×D4×C15114yes—
316C22×C4—28no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4C2×D4×C15112yes—
324C22×C4C2×D4×C15112yes—
325C22×C4C2×D4×C15111yescharacteristic
326C22×C4C2×D4×C15111yescharacteristic
327C22×C4C24×C15111yescharacteristic
328D8—48no—
329C2×C8—24no—
330C4⋊C4—24no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—24no—
334C4⋊C4—22no—
335C4⋊C4—42no—
336C4⋊C4—44no—
337C4⋊C4C2×D4×C15114yes—
338C22⋊C4—28no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—44no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—44no—
345C42—22no—
346C42—22no—
347C42C2×D4×C15112yes—
348C42C2×D4×C15112yes—
349C23—22no—
350C23—24no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23C22×D4×C15111yescharacteristic
358Q8—28no—
359Q8—48no—
360Q8—44no—
361D4—24no—
362D4—44no—
363D4—42no—
364D4—48no—
365D4—44no—
366D4—44no—
367D4—44no—
368D4—44no—
369D4—84no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—416no—
377C2×C4—48no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—84no—
386C2×C4#120×C15111yescharacteristic
387C2×C4#120×C15111yescharacteristic
388C2×C4#120×C15112yes—
389C2×C4C2×D8×C15114yes—
390C2×C4C2×D8×C15112yes—
391C2×C4AGL(1,ℤ/8)×C15112yes—
392C2×C4C22×D4×C15112yes—
393C8—44no—
394C22—21no—
395C22—21no—
396C22—42no—
397C22—42no—
398C22—44no—
399C22—44no—
400C22—42no—
401C22—44no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22C2×#120×C15111yescharacteristic
407C22C22×D8×C15111yescharacteristic
408C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
409C4—24no—
410C4—21no—
411C4—21no—
412C4—22no—
413C4—44no—
414C4—42no—
415C4—82no—
416C4—81no—
417C4#447×C15114yes—
418C2—21no—
419C2—21no—
420C2—82no—
421C2—84no—
422C2C2×#447×C15111yescharacteristic
423C2#3020×C15111yescharacteristic
424C2#3025×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3497×C151C2semidirect
2. #3100×C151C2semidirect
3. #2536×C151C2semidirect
4. #1610×C151C2semidirect
5. #1598×C151C2semidirect
6. #1517×C151C2semidirect
7. #1461×C151C2semidirect
94. C2×Q8×C151D8semidirect
212. #18218C151direct (N × H)
213. C151#18218direct (N × H)
214. #3497C2×C151semidirect
215. #3100C2×C151semidirect
216. #2536C2×C151semidirect
217. #1610C2×C151semidirect
218. #1598C2×C151semidirect
219. #1517C2×C151semidirect
220. #1461C2×C151semidirect
307. C2×Q8D8×C151semidirect

Maximal subgroups

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

subgroupindex
#3497×C1512
#3100×C1512
#2536×C1512
#1610×C1512
#1598×C1512
#1517×C1512
#1461×C1512
#18218151