Finite Group Databasebeta

← C151×#11204 #50316129

Subgroups — C151×#11204 #50316129

Order 38656.

778 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#423×C151C211yesmaximal, characteristic
2C2×#389×C151C211yesmaximal, characteristic
3C2×#343×C151C212yesmaximal
4C2×#343×C151C212yesmaximal
5#1728×C151C211yesmaximal, characteristic
6C22×M16×C151C2212yes—
7C22×M16×C151C2212yes—
8C22×C4⋊C4×C151C412yes—
9C22×C4⋊C4×C151C2211yescharacteristic
10C22×C4⋊C4×C151C2211yescharacteristic
11C22×C42×C151C2211yescharacteristic
12#423×C151—24no—
13C2×C4⋊C8×C151—21no—
14C2×C4⋊C8×C151—21no—
15#389×C151—21no—
16#389×C151—21no—
17#389×C151—21no—
18#389×C151—21no—
19C2×#95×C151C412yes—
20#343×C151—24no—
21#343×C151—24no—
22#336×C151—21no—
23#336×C151—21no—
24C23×C4×C151C2×C411yescharacteristic
25C23×C4×C151C2×C411yescharacteristic
26C23×C4×C151C2×C412yes—
27C23×C4×C151C2×C412yes—
28C23×C4×C151C2311yescharacteristic
29C2×M16×C151—22no—
30C2×M16×C151—22no—
31C2×M16×C151—22no—
32C2×M16×C151—22no—
33C2×M16×C151—22no—
34C2×M16×C151—22no—
35C2×M16×C151—22no—
36C2×M16×C151—22no—
37C2×M16×C151—22no—
38C2×M16×C151—22no—
39C2×M16×C151D414yes—
40C2×M16×C151Q814yes—
41C22×C8×C151—22no—
42C22×C8×C151—22no—
43C2×C4⋊C4×C151—21no—
44C2×C4⋊C4×C151—21no—
45C2×C4⋊C4×C151—21no—
46C2×C4⋊C4×C151—21no—
47C2×C4⋊C4×C151—22no—
48C2×C4⋊C4×C151—22no—
49C2×C4⋊C4×C151—22no—
50C2×C4⋊C4×C151—21no—
51C2×C4⋊C4×C151—21no—
52C2×C4⋊C4×C151—22no—
53C2×C4⋊C4×C151—44no—
54C2×C4⋊C4×C151D412yes—
55C2×C4⋊C4×C151Q812yes—
56C2×C42×C151—22no—
57C2×C42×C151—22no—
58C2×C42×C151D411yescharacteristic
59C2×C42×C151D411yescharacteristic
60C2×C42×C151D411yescharacteristic
61C2×C42×C151D411yescharacteristic
62C4⋊C8×C151—24no—
63C4⋊C8×C151—24no—
64#95×C151—22no—
65#95×C151—22no—
66C24×C151C22×C411yescharacteristic
67C22×C4×C151—22no—
68C22×C4×C151—22no—
69C22×C4×C151—22no—
70C22×C4×C151—22no—
71C22×C4×C151—22no—
72C22×C4×C151—22no—
73C22×C4×C151—22no—
74C22×C4×C151—24no—
75C22×C4×C151—41no—
76C22×C4×C151—41no—
77C22×C4×C151—42no—
78C22×C4×C151—42no—
79C22×C4×C151—42no—
80C22×C4×C151—42no—
81C22×C4×C151C22⋊C411yescharacteristic
82C22×C4×C151C22⋊C411yescharacteristic
83C22×C4×C151C22⋊C411yescharacteristic
84C22×C4×C151C22⋊C411yescharacteristic
85C22×C4×C151C4⋊C414yes—
86C22×C4×C151C2×D412yes—
87C22×C4×C151C2×D411yescharacteristic
88C22×C4×C151C2×D411yescharacteristic
89C22×C4×C151C2×D411yescharacteristic
90C22×C4×C151C2×Q812yes—
91C22×C4×C151C2×Q811yescharacteristic
92C22×C4×C151#4111yescharacteristic
93C22×C4×C151#4111yescharacteristic
94C22×C4×C151#4112yes—
95C22×C4×C151#4112yes—
96M16×C151—24no—
97M16×C151—24no—
98M16×C151—24no—
99M16×C151—24no—
100M16×C151—42no—
101M16×C151—42no—
102M16×C151—42no—
103M16×C151—42no—
104C2×C8×C151—24no—
105C2×C8×C151—24no—
106C2×C8×C151—42no—
107C2×C8×C151—42no—
108C2×C8×C151—42no—
109C2×C8×C151—42no—
110C4⋊C4×C151—22no—
111C4⋊C4×C151—22no—
112C4⋊C4×C151—22no—
113C4⋊C4×C151—22no—
114C4⋊C4×C151—44no—
115C4⋊C4×C151—44no—
116C4⋊C4×C151—41no—
117C4⋊C4×C151—42no—
118C4⋊C4×C151—41no—
119C42×C151—21no—
120C42×C151—21no—
121C42×C151—22no—
122C42×C151—22no—
123C42×C151—21no—
124C42×C151—21no—
125C23×C151—21no—
126C23×C151—21no—
127C23×C151—21no—
128C23×C151—21no—
129C23×C151C2×C22⋊C411yescharacteristic
130C23×C151C2×C4⋊C411yescharacteristic
131C23×C151#11711yescharacteristic
132C23×C151C4×D412yes—
133C23×C151C4×Q812yes—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—24no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—44no—
146C2×C4×C151—44no—
147C2×C4×C151—44no—
148C2×C4×C151—42no—
149C2×C4×C151—42no—
150C2×C4×C151—44no—
151C2×C4×C151—42no—
152C2×C4×C151—42no—
153C2×C4×C151—42no—
154C2×C4×C151—84no—
155C2×C4×C151#10012yes—
156C2×C4×C151#10112yes—
157C2×C4×C151#12011yescharacteristic
158C2×C4×C151#12112yes—
159C2×C4×C151#12111yescharacteristic
160C2×C4×C151#12111yescharacteristic
161C2×C4×C151#12112yes—
162C2×C4×C151C22⋊Q812yes—
163C2×C4×C151C22⋊Q811yescharacteristic
164C2×C4×C151C22⋊Q812yes—
165C2×C4×C151C22⋊Q812yes—
166C2×C4×C151C22⋊Q811yescharacteristic
167C2×C4×C151#12312yes—
168C2×C4×C151#12311yescharacteristic
169C2×C4×C151#12411yescharacteristic
170C2×C4×C151#12512yes—
171C2×C4×C151#12512yes—
172C2×C4×C151#12612yes—
173C2×C4×C151C4⋊Q812yes—
174C2×C4×C151C4⋊Q811yescharacteristic
175C8×C151—44no—
176C8×C151—44no—
177C22×C151—21no—
178C22×C151—21no—
179C22×C151—21no—
180C22×C151—21no—
181C22×C151—22no—
182C22×C151—22no—
183C22×C151—22no—
184C22×C151—22no—
185C22×C151#38011yescharacteristic
186C22×C151#38611yescharacteristic
187C22×C151#38712yes—
188C22×C151#38912yes—
189C22×C151#39111yescharacteristic
190C22×C151C2×#10011yescharacteristic
191C22×C151C2×#10111yescharacteristic
192C22×C151#41311yescharacteristic
193C22×C151#41311yescharacteristic
194C4×C151—22no—
195C4×C151—22no—
196C4×C151—44no—
197C4×C151—41no—
198C4×C151—41no—
199C4×C151—82no—
200C4×C151#39411yescharacteristic
201C4×C151#39511yescharacteristic
202C4×C151#39612yes—
203C4×C151#39811yescharacteristic
204C4×C151#39812yes—
205C4×C151#40011yescharacteristic
206C2×C151—22no—
207C2×C151—22no—
208C2×C151#144111yescharacteristic
209C2×C151#180011yescharacteristic
210C2×C151#180111yescharacteristic
211C2×C151#190011yescharacteristic
212C2×C151#190111yescharacteristic
213C2×C151#199711yescharacteristic
214C2×C151#199811yescharacteristic
215#11204C15111yesmaximal, characteristic, direct product factor, Sylow
216C151#1120411yescharacteristic, direct product factor, Sylow
217C2×#423C2×C15111yescharacteristic
218C2×#389C2×C15111yescharacteristic
219C2×#343C2×C15112yes—
220C2×#343C2×C15112yes—
221#1728C2×C15111yescharacteristic
222C22×M16C22×C15112yes—
223C22×M16C22×C15112yes—
224C22×C4⋊C4C4×C15112yes—
225C22×C4⋊C4C22×C15111yescharacteristic
226C22×C4⋊C4C22×C15111yescharacteristic
227C22×C42C22×C15111yescharacteristic
228#423—24no—
229C2×C4⋊C8—21no—
230C2×C4⋊C8—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235C2×#95C4×C15112yes—
236#343—24no—
237#343—24no—
238#336—21no—
239#336—21no—
240C23×C4C2×C4×C15111yescharacteristic
241C23×C4C2×C4×C15111yescharacteristic
242C23×C4C2×C4×C15112yes—
243C23×C4C2×C4×C15112yes—
244C23×C4C23×C15111yescharacteristic
245C2×M16—22no—
246C2×M16—22no—
247C2×M16—22no—
248C2×M16—22no—
249C2×M16—22no—
250C2×M16—22no—
251C2×M16—22no—
252C2×M16—22no—
253C2×M16—22no—
254C2×M16—22no—
255C2×M16D4×C15114yes—
256C2×M16Q8×C15114yes—
257C22×C8—22no—
258C22×C8—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—44no—
270C2×C4⋊C4D4×C15112yes—
271C2×C4⋊C4Q8×C15112yes—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42D4×C15111yescharacteristic
275C2×C42D4×C15111yescharacteristic
276C2×C42D4×C15111yescharacteristic
277C2×C42D4×C15111yescharacteristic
278C4⋊C8—24no—
279C4⋊C8—24no—
280#95—22no—
281#95—22no—
282C24C22×C4×C15111yescharacteristic
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—24no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4C22⋊C4×C15111yescharacteristic
298C22×C4C22⋊C4×C15111yescharacteristic
299C22×C4C22⋊C4×C15111yescharacteristic
300C22×C4C22⋊C4×C15111yescharacteristic
301C22×C4C4⋊C4×C15114yes—
302C22×C4C2×D4×C15112yes—
303C22×C4C2×D4×C15111yescharacteristic
304C22×C4C2×D4×C15111yescharacteristic
305C22×C4C2×D4×C15111yescharacteristic
306C22×C4C2×Q8×C15112yes—
307C22×C4C2×Q8×C15111yescharacteristic
308C22×C4#41×C15111yescharacteristic
309C22×C4#41×C15111yescharacteristic
310C22×C4#41×C15112yes—
311C22×C4#41×C15112yes—
312M16—24no—
313M16—24no—
314M16—24no—
315M16—24no—
316M16—42no—
317M16—42no—
318M16—42no—
319M16—42no—
320C2×C8—24no—
321C2×C8—24no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—42no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—44no—
331C4⋊C4—44no—
332C4⋊C4—41no—
333C4⋊C4—42no—
334C4⋊C4—41no—
335C42—21no—
336C42—21no—
337C42—22no—
338C42—22no—
339C42—21no—
340C42—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23C2×C22⋊C4×C15111yescharacteristic
346C23C2×C4⋊C4×C15111yescharacteristic
347C23#117×C15111yescharacteristic
348C23C4×D4×C15112yes—
349C23C4×Q8×C15112yes—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—24no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—84no—
371C2×C4#100×C15112yes—
372C2×C4#101×C15112yes—
373C2×C4#120×C15111yescharacteristic
374C2×C4#121×C15112yes—
375C2×C4#121×C15111yescharacteristic
376C2×C4#121×C15111yescharacteristic
377C2×C4#121×C15112yes—
378C2×C4C22⋊Q8×C15112yes—
379C2×C4C22⋊Q8×C15111yescharacteristic
380C2×C4C22⋊Q8×C15112yes—
381C2×C4C22⋊Q8×C15112yes—
382C2×C4C22⋊Q8×C15111yescharacteristic
383C2×C4#123×C15112yes—
384C2×C4#123×C15111yescharacteristic
385C2×C4#124×C15111yescharacteristic
386C2×C4#125×C15112yes—
387C2×C4#125×C15112yes—
388C2×C4#126×C15112yes—
389C2×C4C4⋊Q8×C15112yes—
390C2×C4C4⋊Q8×C15111yescharacteristic
391C8—44no—
392C8—44no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22#380×C15111yescharacteristic
402C22#386×C15111yescharacteristic
403C22#387×C15112yes—
404C22#389×C15112yes—
405C22#391×C15111yescharacteristic
406C22C2×#100×C15111yescharacteristic
407C22C2×#101×C15111yescharacteristic
408C22#413×C15111yescharacteristic
409C22#413×C15111yescharacteristic
410C4—22no—
411C4—22no—
412C4—41no—
413C4—41no—
414C4—44no—
415C4—82no—
416C4#394×C15111yescharacteristic
417C4#395×C15111yescharacteristic
418C4#396×C15112yes—
419C4#398×C15111yescharacteristic
420C4#398×C15112yes—
421C4#400×C15111yescharacteristic
422C2—22no—
423C2—22no—
424C2#1441×C15111yescharacteristic
425C2#1800×C15111yescharacteristic
426C2#1801×C15111yescharacteristic
427C2#1900×C15111yescharacteristic
428C2#1901×C15111yescharacteristic
429C2#1997×C15111yescharacteristic
430C2#1998×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC24C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC24×C151C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
215. #11204C151direct (N × H)
216. C151#11204direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#423×C1512
C2×#389×C1512
C2×#343×C1512
#1728×C1512
#11204151