Finite Group Databasebeta

← C151×#23085 #50328010

Subgroups — C151×#23085 #50328010

Order 38656.

978 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C151C211yesmaximal, characteristic, complemented
2C2×#431×C151C211yesmaximal, characteristic, complemented
3C4×#121×C151C211yesmaximal, characteristic
4#1955×C151C211yesmaximal, characteristic, complemented
5#1955×C151C211yesmaximal, characteristic, complemented
6#1954×C151C211yesmaximal, characteristic, complemented
7#1940×C151C211yesmaximal, characteristic, complemented
8#1923×C151C211yesmaximal, characteristic, complemented
9#1923×C151C211yesmaximal, characteristic, complemented
10#1870×C151C211yesmaximal, characteristic, complemented
11#1869×C151C211yesmaximal, characteristic, complemented
12#1771×C151C211yesmaximal, characteristic, complemented
13#1753×C151C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C151C211yesmaximal, characteristic, complemented
15#1749×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C2×#121×C151C411yescharacteristic
19C2×C4×D4×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C22×C42×C151C2211yescharacteristic
23#435×C151—24no—
24#431×C151—24no—
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×C22⋊C8×C151C2211yescharacteristic
30C2×C22⋊C8×C151C2211yescharacteristic
31C2×C22⋊C8×C151C2211yescharacteristic
32C2×C22⋊C8×C151C2211yescharacteristic
33C2×C22⋊C8×C151C2211yescharacteristic
34C2×C22⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×#97×C151C2211yescharacteristic
40C2×#97×C151C2211yescharacteristic
41C2×#97×C151C2211yescharacteristic
42C2×C4×C8×C151C2211yescharacteristic
43C2×C4×C8×C151C2211yescharacteristic
44C2×C4×C8×C151C2211yescharacteristic
45#390×C151C411yescharacteristic
46#389×C151C411yescharacteristic
47#388×C151C411yescharacteristic
48#388×C151C411yescharacteristic
49#386×C151C411yescharacteristic
50#386×C151C411yescharacteristic
51#380×C151C411yescharacteristic
52C4×C4⋊C4×C151C2211yescharacteristic
53C4×C22⋊C4×C151C2211yescharacteristic
54C4×C22⋊C4×C151C2211yescharacteristic
55#336×C151C2211yescharacteristic
56#336×C151C2211yescharacteristic
57#336×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C22×D4×C151C2×C411yescharacteristic
62C22×D4×C151C2×C411yescharacteristic
63C22×D4×C151C2×C411yescharacteristic
64C23×C4×C151C2×C411yescharacteristic
65C23×C4×C151C2×C411yescharacteristic
66C23×C4×C151C2311yescharacteristic
67C23×C4×C151C2311yescharacteristic
68C23×C4×C151C2311yescharacteristic
69C2×M16×C151—22no—
70C2×M16×C151—22no—
71C2×M16×C151—41no—
72C22×C8×C151—22no—
73C22×C8×C151—22no—
74C22×C8×C151—41no—
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83#121×C151—24no—
84C4×D4×C151—22no—
85C4×D4×C151—22no—
86C4×D4×C151—41no—
87C4×D4×C151—41no—
88C4×D4×C151—41no—
89C4×D4×C151—41no—
90C2×C4⋊C4×C151C2×C411yescharacteristic
91C2×C4⋊C4×C151C2×C411yescharacteristic
92C2×C4⋊C4×C151C2×C411yescharacteristic
93C2×C4⋊C4×C151C2×C411yescharacteristic
94C2×C4⋊C4×C151C2×C411yescharacteristic
95C2×C22⋊C4×C151C2×C411yescharacteristic
96C2×C22⋊C4×C151C2×C411yescharacteristic
97C2×C22⋊C4×C151C2×C411yescharacteristic
98C2×C22⋊C4×C151C2×C411yescharacteristic
99C2×C22⋊C4×C151C2×C411yescharacteristic
100C2×C22⋊C4×C151C2×C411yescharacteristic
101C2×C22⋊C4×C151C2×C411yescharacteristic
102C2×C22⋊C4×C151C2×C411yescharacteristic
103C2×C22⋊C4×C151C2×C411yescharacteristic
104C2×C22⋊C4×C151C2×C411yescharacteristic
105C2×C42×C151—22no—
106C2×C42×C151—22no—
107C2×C42×C151C2×C411yescharacteristic
108C2×C42×C151C2×C411yescharacteristic
109C2×C42×C151C2311yescharacteristic
110C2×C42×C151C2311yescharacteristic
111C2×C42×C151C2311yescharacteristic
112C2×C42×C151C2311yescharacteristic
113C4⋊C8×C151—22no—
114C4⋊C8×C151—41no—
115C4⋊C8×C151—41no—
116C4⋊C8×C151D414yescomplemented
117C22⋊C8×C151—22no—
118C22⋊C8×C151—22no—
119C22⋊C8×C151—22no—
120C22⋊C8×C151—22no—
121C22⋊C8×C151—22no—
122C22⋊C8×C151—22no—
123C22⋊C8×C151—22no—
124C22⋊C8×C151—22no—
125C22⋊C8×C151—41no—
126C22⋊C8×C151—41no—
127#97×C151—22no—
128#97×C151—22no—
129#97×C151—41no—
130C4×C8×C151—22no—
131C4×C8×C151—22no—
132C4×C8×C151—41no—
133#95×C151C2×C411yescharacteristic
134#95×C151C2×C411yescharacteristic
135#95×C151C2×C411yescharacteristic
136#95×C151C2×C411yescharacteristic
137#95×C151C2×C411yescharacteristic
138#95×C151C2×C411yescharacteristic
139C24×C151C22×C411yescharacteristic
140C24×C151C22×C411yescharacteristic
141C24×C151C22×C411yescharacteristic
142C2×D4×C151—22no—
143C2×D4×C151—22no—
144C2×D4×C151—22no—
145C2×D4×C151—22no—
146C2×D4×C151—22no—
147C2×D4×C151—22no—
148C2×D4×C151—41no—
149C2×D4×C151—41no—
150C2×D4×C151—41no—
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151—22no—
154C22×C4×C151—22no—
155C22×C4×C151—22no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—41no—
175C22×C4×C151C22×C411yescharacteristic
176C22×C4×C151C22×C411yescharacteristic
177C22×C4×C151C22×C411yescharacteristic
178C22×C4×C151C22×C411yescharacteristic
179C22×C4×C151C22×C411yescharacteristic
180C22×C4×C151C22×C411yescharacteristic
181C22×C4×C151C22×C411yescharacteristic
182C22×C4×C151C22×C411yescharacteristic
183C22×C4×C151C22×C411yescharacteristic
184C22×C4×C151C22×C411yescharacteristic
185C22×C4×C151C22×C411yescharacteristic
186C22×C4×C151C2411yescharacteristic
187M16×C151—44no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—44no—
209C2×C8×C151C2×D412yes—
210C2×C8×C151C2×D412yes—
211C2×C8×C151#4112yes—
212C2×C8×C151#4112yes—
213C4⋊C4×C151—22no—
214C4⋊C4×C151—22no—
215C4⋊C4×C151—41no—
216C4⋊C4×C151—41no—
217C4⋊C4×C151—41no—
218C22⋊C4×C151—22no—
219C22⋊C4×C151—22no—
220C22⋊C4×C151—22no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—22no—
223C22⋊C4×C151—41no—
224C22⋊C4×C151—41no—
225C22⋊C4×C151—41no—
226C22⋊C4×C151—41no—
227C22⋊C4×C151M1614yescomplemented
228C42×C151—22no—
229C42×C151—22no—
230C42×C151—21no—
231C42×C151—21no—
232C42×C151—21no—
233C42×C151—21no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151C2×D412yes—
237C42×C151#4112yes—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—21no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151C2×M1612yes—
258C23×C151#13112yes—
259C23×C151C23×C411yescharacteristic
260D4×C151—44no—
261D4×C151—44no—
262D4×C151—44no—
263C2×C4×C151—28no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—21no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
284C2×C4×C151—21no—
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—44no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151C4×D412yes—
306C2×C4×C151C4×D412yes—
307C2×C4×C151C2×M1612yes—
308C2×C4×C151C2×M1612yes—
309C2×C4×C151#13112yes—
310C2×C4×C151C22×D411yescharacteristic
311C2×C4×C151C2×#4111yescharacteristic
312C2×C4×C151C2×#4111yescharacteristic
313C2×C4×C151C2×#4111yescharacteristic
314C2×C4×C151H(5,𝔽2)11yescharacteristic
315C2×C4×C151H(5,𝔽2)11yescharacteristic
316C8×C151—22no—
317C8×C151—22no—
318C8×C151—22no—
319C8×C151—22no—
320C8×C151—41no—
321C8×C151—41no—
322C8×C151—41no—
323C8×C151—41no—
324C22×C151—22no—
325C22×C151—22no—
326C22×C151—22no—
327C22×C151—22no—
328C22×C151—22no—
329C22×C151—22no—
330C22×C151—41no—
331C22×C151—41no—
332C22×C151—41no—
333C22×C151—41no—
334C22×C151—41no—
335C22×C151—41no—
336C22×C151—41no—
337C22×C151—41no—
338C22×C151—41no—
339C22×C151—41no—
340C22×C151—41no—
341C22×C151—41no—
342C22×C151—41no—
343C22×C151—41no—
344C22×C151—41no—
345C22×C151C2×C4×D411yescharacteristic
346C22×C151C4×#4111yescharacteristic
347C22×C151#51811yescharacteristic
348C22×C151C22×M1611yescharacteristic
349C22×C151C2×#13111yescharacteristic
350C22×C151C2×#13111yescharacteristic
351C22×C151#56811yescharacteristic
352C4×C151—22no—
353C4×C151—22no—
354C4×C151—22no—
355C4×C151—22no—
356C4×C151—22no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—41no—
360C4×C151—41no—
361C4×C151—41no—
362C4×C151—41no—
363C4×C151#54611yescharacteristic
364C4×C151#55011yescharacteristic
365C4×C151#55311yescharacteristic
366C4×C151#55511yescharacteristic
367C2×C151—42no—
368C2×C151—42no—
369C2×C151—81no—
370C2×C151#236311yescharacteristic
371C2×C151#292911yescharacteristic
372C2×C151D4×M1611yescharacteristic
373C2×C151#296511yescharacteristic
374C2×C151#296811yescharacteristic
375C2×C151#297411yescharacteristic
376C2×C151#298111yescharacteristic
377#23085C15111yesmaximal, characteristic, direct product factor, Sylow
378C151#2308511yescharacteristic, direct product factor, Sylow
379C2×#435C2×C15111yescharacteristic, complemented
380C2×#431C2×C15111yescharacteristic, complemented
381C4×#121C2×C15111yescharacteristic
382#1955C2×C15111yescharacteristic, complemented
383#1955C2×C15111yescharacteristic, complemented
384#1954C2×C15111yescharacteristic, complemented
385#1940C2×C15111yescharacteristic, complemented
386#1923C2×C15111yescharacteristic, complemented
387#1923C2×C15111yescharacteristic, complemented
388#1870C2×C15111yescharacteristic, complemented
389#1869C2×C15111yescharacteristic, complemented
390#1771C2×C15111yescharacteristic, complemented
391#1753C2×C15111yescharacteristic, complemented
392C8×C22⋊C4C2×C15111yescharacteristic, complemented
393#1749C2×C15111yescharacteristic, complemented
394C22×M16C22×C15111yescharacteristic
395C23×C8C22×C15111yescharacteristic
396C2×#121C4×C15111yescharacteristic
397C2×C4×D4C22×C15111yescharacteristic
398C2×C4×D4C22×C15111yescharacteristic
399C2×C4×D4C22×C15111yescharacteristic
400C22×C42C22×C15111yescharacteristic
401#435—24no—
402#431—24no—
403C2×C4⋊C8C22×C15111yescharacteristic
404C2×C4⋊C8C22×C15111yescharacteristic
405C2×C4⋊C8C22×C15111yescharacteristic
406C2×C4⋊C8C22×C15111yescharacteristic
407C2×C22⋊C8C22×C15111yescharacteristic
408C2×C22⋊C8C22×C15111yescharacteristic
409C2×C22⋊C8C22×C15111yescharacteristic
410C2×C22⋊C8C22×C15111yescharacteristic
411C2×C22⋊C8C22×C15111yescharacteristic
412C2×C22⋊C8C22×C15111yescharacteristic
413C2×C22⋊C8C22×C15111yescharacteristic
414C2×C22⋊C8C22×C15111yescharacteristic
415C2×C22⋊C8C22×C15111yescharacteristic
416C2×C22⋊C8C22×C15111yescharacteristic
417C2×#97C22×C15111yescharacteristic
418C2×#97C22×C15111yescharacteristic
419C2×#97C22×C15111yescharacteristic
420C2×C4×C8C22×C15111yescharacteristic
421C2×C4×C8C22×C15111yescharacteristic
422C2×C4×C8C22×C15111yescharacteristic
423#390C4×C15111yescharacteristic
424#389C4×C15111yescharacteristic
425#388C4×C15111yescharacteristic
426#388C4×C15111yescharacteristic
427#386C4×C15111yescharacteristic
428#386C4×C15111yescharacteristic
429#380C4×C15111yescharacteristic
430C4×C4⋊C4C22×C15111yescharacteristic
431C4×C22⋊C4C22×C15111yescharacteristic
432C4×C22⋊C4C22×C15111yescharacteristic
433#336C22×C15111yescharacteristic
434#336C22×C15111yescharacteristic
435#336C22×C15111yescharacteristic
436#336C22×C15111yescharacteristic
437#336C22×C15111yescharacteristic
438#336C22×C15111yescharacteristic
439C22×D4C2×C4×C15111yescharacteristic
440C22×D4C2×C4×C15111yescharacteristic
441C22×D4C2×C4×C15111yescharacteristic
442C23×C4C2×C4×C15111yescharacteristic
443C23×C4C2×C4×C15111yescharacteristic
444C23×C4C23×C15111yescharacteristic
445C23×C4C23×C15111yescharacteristic
446C23×C4C23×C15111yescharacteristic
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—41no—
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—41no—
453C22×C8C23×C15111yescharacteristic
454C22×C8C23×C15111yescharacteristic
455C22×C8C23×C15111yescharacteristic
456C22×C8C23×C15111yescharacteristic
457C22×C8C23×C15111yescharacteristic
458C22×C8C23×C15111yescharacteristic
459C22×C8C23×C15111yescharacteristic
460C22×C8C23×C15111yescharacteristic
461#121—24no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—41no—
465C4×D4—41no—
466C4×D4—41no—
467C4×D4—41no—
468C2×C4⋊C4C2×C4×C15111yescharacteristic
469C2×C4⋊C4C2×C4×C15111yescharacteristic
470C2×C4⋊C4C2×C4×C15111yescharacteristic
471C2×C4⋊C4C2×C4×C15111yescharacteristic
472C2×C4⋊C4C2×C4×C15111yescharacteristic
473C2×C22⋊C4C2×C4×C15111yescharacteristic
474C2×C22⋊C4C2×C4×C15111yescharacteristic
475C2×C22⋊C4C2×C4×C15111yescharacteristic
476C2×C22⋊C4C2×C4×C15111yescharacteristic
477C2×C22⋊C4C2×C4×C15111yescharacteristic
478C2×C22⋊C4C2×C4×C15111yescharacteristic
479C2×C22⋊C4C2×C4×C15111yescharacteristic
480C2×C22⋊C4C2×C4×C15111yescharacteristic
481C2×C22⋊C4C2×C4×C15111yescharacteristic
482C2×C22⋊C4C2×C4×C15111yescharacteristic
483C2×C42—22no—
484C2×C42—22no—
485C2×C42C2×C4×C15111yescharacteristic
486C2×C42C2×C4×C15111yescharacteristic
487C2×C42C23×C15111yescharacteristic
488C2×C42C23×C15111yescharacteristic
489C2×C42C23×C15111yescharacteristic
490C2×C42C23×C15111yescharacteristic
491C4⋊C8—22no—
492C4⋊C8—41no—
493C4⋊C8—41no—
494C4⋊C8D4×C15114yescomplemented
495C22⋊C8—22no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503C22⋊C8—41no—
504C22⋊C8—41no—
505#97—22no—
506#97—22no—
507#97—41no—
508C4×C8—22no—
509C4×C8—22no—
510C4×C8—41no—
511#95C2×C4×C15111yescharacteristic
512#95C2×C4×C15111yescharacteristic
513#95C2×C4×C15111yescharacteristic
514#95C2×C4×C15111yescharacteristic
515#95C2×C4×C15111yescharacteristic
516#95C2×C4×C15111yescharacteristic
517C24C22×C4×C15111yescharacteristic
518C24C22×C4×C15111yescharacteristic
519C24C22×C4×C15111yescharacteristic
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—41no—
553C22×C4C22×C4×C15111yescharacteristic
554C22×C4C22×C4×C15111yescharacteristic
555C22×C4C22×C4×C15111yescharacteristic
556C22×C4C22×C4×C15111yescharacteristic
557C22×C4C22×C4×C15111yescharacteristic
558C22×C4C22×C4×C15111yescharacteristic
559C22×C4C22×C4×C15111yescharacteristic
560C22×C4C22×C4×C15111yescharacteristic
561C22×C4C22×C4×C15111yescharacteristic
562C22×C4C22×C4×C15111yescharacteristic
563C22×C4C22×C4×C15111yescharacteristic
564C22×C4C24×C15111yescharacteristic
565M16—44no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—44no—
587C2×C8C2×D4×C15112yes—
588C2×C8C2×D4×C15112yes—
589C2×C8#41×C15112yes—
590C2×C8#41×C15112yes—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4M16×C15114yescomplemented
606C42—22no—
607C42—22no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42C2×D4×C15112yes—
615C42#41×C15112yes—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23C2×M16×C15112yes—
636C23#131×C15112yes—
637C23C23×C4×C15111yescharacteristic
638D4—44no—
639D4—44no—
640D4—44no—
641C2×C4—28no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—44no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4C4×D4×C15112yes—
684C2×C4C4×D4×C15112yes—
685C2×C4C2×M16×C15112yes—
686C2×C4C2×M16×C15112yes—
687C2×C4#131×C15112yes—
688C2×C4C22×D4×C15111yescharacteristic
689C2×C4C2×#41×C15111yescharacteristic
690C2×C4C2×#41×C15111yescharacteristic
691C2×C4C2×#41×C15111yescharacteristic
692C2×C4H(5,𝔽2)×C15111yescharacteristic
693C2×C4H(5,𝔽2)×C15111yescharacteristic
694C8—22no—
695C8—22no—
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—41no—
701C8—41no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22C2×C4×D4×C15111yescharacteristic
724C22C4×#41×C15111yescharacteristic
725C22#518×C15111yescharacteristic
726C22C22×M16×C15111yescharacteristic
727C22C2×#131×C15111yescharacteristic
728C22C2×#131×C15111yescharacteristic
729C22#568×C15111yescharacteristic
730C4—22no—
731C4—22no—
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4#546×C15111yescharacteristic
742C4#550×C15111yescharacteristic
743C4#553×C15111yescharacteristic
744C4#555×C15111yescharacteristic
745C2—42no—
746C2—42no—
747C2—81no—
748C2#2363×C15111yescharacteristic
749C2#2929×C15111yescharacteristic
750C2D4×M16×C15111yescharacteristic
751C2#2965×C15111yescharacteristic
752C2#2968×C15111yescharacteristic
753C2#2974×C15111yescharacteristic
754C2#2981×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC23×C151C23×C4
prime radicalC2×#121×C151C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#435×C151C2semidirect
2. C2×#431×C151C2semidirect
4. #1955×C151C2semidirect
5. #1955×C151C2semidirect
6. #1954×C151C2semidirect
7. #1940×C151C2semidirect
8. #1923×C151C2semidirect
9. #1923×C151C2semidirect
10. #1870×C151C2semidirect
11. #1869×C151C2semidirect
12. #1771×C151C2semidirect
13. #1753×C151C2semidirect
14. C8×C22⋊C4×C151C2semidirect
15. #1749×C151C2semidirect
116. C4⋊C8×C151D4semidirect
227. C22⋊C4×C151M16semidirect
377. #23085C151direct (N × H)
378. C151#23085direct (N × H)
379. C2×#435C2×C151semidirect
380. C2×#431C2×C151semidirect
382. #1955C2×C151semidirect
383. #1955C2×C151semidirect
384. #1954C2×C151semidirect
385. #1940C2×C151semidirect
386. #1923C2×C151semidirect
387. #1923C2×C151semidirect
388. #1870C2×C151semidirect
389. #1869C2×C151semidirect
390. #1771C2×C151semidirect
391. #1753C2×C151semidirect
392. C8×C22⋊C4C2×C151semidirect
393. #1749C2×C151semidirect
494. C4⋊C8D4×C151semidirect
605. C22⋊C4M16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1512
C2×#431×C1512
C4×#121×C1512
#1955×C1512
#1954×C1512
#1940×C1512
#1923×C1512
#1870×C1512
#1869×C1512
#1771×C1512
#1753×C1512
C8×C22⋊C4×C1512
#1749×C1512
#23085151