Finite Group Databasebeta

← C151×#23089 #50328014

Subgroups — C151×#23089 #50328014

Order 38656.

926 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D4×C151C211yesmaximal, characteristic, complemented
2C2×#433×C151C211yesmaximal, characteristic, complemented
3#2392×C151C211yesmaximal, characteristic
4#1955×C151C211yesmaximal, characteristic, complemented
5#1955×C151C211yesmaximal, characteristic, complemented
6#1954×C151C211yesmaximal, characteristic, complemented
7#1939×C151C211yesmaximal, characteristic, complemented
8#1924×C151C211yesmaximal, characteristic, complemented
9#1923×C151C211yesmaximal, characteristic, complemented
10#1869×C151C211yesmaximal, characteristic, complemented
11#1869×C151C211yesmaximal, characteristic, complemented
12#1771×C151C211yesmaximal, characteristic, complemented
13#1752×C151C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C151C211yesmaximal, characteristic, complemented
15#1750×C151C211yesmaximal, characteristic, complemented
16C23×C8×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C2×C4×D4×C151C2211yescharacteristic
19C2×C4×D4×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22C8×D4×C151—24no—
23#433×C151—24no—
24C2×C4⋊C8×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×C22⋊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×#97×C151C2211yescharacteristic
39C2×#97×C151C2211yescharacteristic
40C2×#97×C151C2211yescharacteristic
41C2×C4×C8×C151C2211yescharacteristic
42C2×C4×C8×C151C2211yescharacteristic
43C2×C4×C8×C151C2211yescharacteristic
44#398×C151C411yescharacteristic
45#397×C151C411yescharacteristic
46#396×C151C411yescharacteristic
47#396×C151C411yescharacteristic
48#394×C151C411yescharacteristic
49#394×C151C411yescharacteristic
50#394×C151C411yescharacteristic
51#392×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×C151C2311yescharacteristic
65C23×C4×C151C2311yescharacteristic
66C23×C4×C151C2311yescharacteristic
67C22×C8×C151—22no—
68C22×C8×C151—22no—
69C22×C8×C151—22no—
70C22×C8×C151—22no—
71C22×C8×C151—41no—
72C22×C8×C151—41no—
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C4×D4×C151—22no—
82C4×D4×C151—22no—
83C4×D4×C151—41no—
84C4×D4×C151—41no—
85C4×D4×C151—41no—
86C4×D4×C151—41no—
87#117×C151—22no—
88#117×C151—22no—
89C2×C4⋊C4×C151C2×C411yescharacteristic
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×C4⋊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×C22⋊C4×C151C2×C411yescharacteristic
106C2×C22⋊C4×C151C2×C411yescharacteristic
107C2×C22⋊C4×C151C2×C411yescharacteristic
108C2×C42×C151C2311yescharacteristic
109C2×C42×C151C2311yescharacteristic
110C2×C42×C151C2311yescharacteristic
111C2×C42×C151C2311yescharacteristic
112C4⋊C8×C151—22no—
113C4⋊C8×C151—41no—
114C4⋊C8×C151—41no—
115C4⋊C8×C151D414yescomplemented
116C22⋊C8×C151—22no—
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—41no—
125C22⋊C8×C151—41no—
126#97×C151—22no—
127#97×C151—22no—
128#97×C151—41no—
129C4×C8×C151—22no—
130C4×C8×C151—22no—
131C4×C8×C151—41no—
132#95×C151C2×C411yescharacteristic
133#95×C151C2×C411yescharacteristic
134#95×C151C2×C411yescharacteristic
135#95×C151C2×C411yescharacteristic
136#95×C151C2×C411yescharacteristic
137#95×C151C2×C411yescharacteristic
138C24×C151C22×C411yescharacteristic
139C24×C151C22×C411yescharacteristic
140C24×C151C22×C411yescharacteristic
141C2×D4×C151—22no—
142C2×D4×C151—22no—
143C2×D4×C151—22no—
144C2×D4×C151—22no—
145C2×D4×C151—22no—
146C2×D4×C151—22no—
147C2×D4×C151—41no—
148C2×D4×C151—41no—
149C2×D4×C151—41no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
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×C151C22×C411yescharacteristic
169C22×C4×C151C22×C411yescharacteristic
170C22×C4×C151C22×C411yescharacteristic
171C22×C4×C151C22×C411yescharacteristic
172C22×C4×C151C22×C411yescharacteristic
173C22×C4×C151C22×C411yescharacteristic
174C22×C4×C151C22×C411yescharacteristic
175C22×C4×C151C22×C411yescharacteristic
176C22×C4×C151C22×C411yescharacteristic
177C22×C4×C151C22×C411yescharacteristic
178C22×C4×C151C22×C411yescharacteristic
179C22×C4×C151C2411yescharacteristic
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
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—44no—
201C2×C8×C151—44no—
202C2×C8×C151C2×D412yes—
203C2×C8×C151C2×D412yes—
204C2×C8×C151#4112yes—
205C2×C8×C151#4112yes—
206C4⋊C4×C151—22no—
207C4⋊C4×C151—22no—
208C4⋊C4×C151—22no—
209C4⋊C4×C151—22no—
210C4⋊C4×C151—41no—
211C4⋊C4×C151—41no—
212C4⋊C4×C151—41no—
213C22⋊C4×C151—22no—
214C22⋊C4×C151—22no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—22no—
219C22⋊C4×C151—22no—
220C22⋊C4×C151—41no—
221C22⋊C4×C151—41no—
222C22⋊C4×C151—41no—
223C22⋊C4×C151—41no—
224C22⋊C4×C151—41no—
225C42×C151—21no—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151—21no—
231C42×C151C2×D412yes—
232C42×C151#4112yes—
233C23×C151—21no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
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#13112yes—
253C23×C151#13112yes—
254C23×C151C23×C411yescharacteristic
255D4×C151—28no—
256D4×C151—44no—
257D4×C151—44no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
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—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
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×C151C4×D412yes—
301C2×C4×C151C4×D412yes—
302C2×C4×C151#13112yes—
303C2×C4×C151C22×D411yescharacteristic
304C2×C4×C151C2×#4111yescharacteristic
305C2×C4×C151C2×#4111yescharacteristic
306C2×C4×C151C2×#4111yescharacteristic
307C2×C4×C151H(5,𝔽2)11yescharacteristic
308C2×C4×C151H(5,𝔽2)11yescharacteristic
309C8×C151—22no—
310C8×C151—22no—
311C8×C151—22no—
312C8×C151—22no—
313C8×C151—41no—
314C8×C151—41no—
315C8×C151—41no—
316C8×C151—41no—
317C22×C151—22no—
318C22×C151—22no—
319C22×C151—22no—
320C22×C151—22no—
321C22×C151—22no—
322C22×C151—22no—
323C22×C151—41no—
324C22×C151—41no—
325C22×C151—41no—
326C22×C151—41no—
327C22×C151—41no—
328C22×C151—41no—
329C22×C151—41no—
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×C151C2×C4×D411yescharacteristic
339C22×C151C4×#4111yescharacteristic
340C22×C151#51811yescharacteristic
341C22×C151C2×#13111yescharacteristic
342C22×C151C2×#13111yescharacteristic
343C22×C151C2×#13111yescharacteristic
344C22×C151#56811yescharacteristic
345C4×C151—22no—
346C4×C151—22no—
347C4×C151—22no—
348C4×C151—41no—
349C4×C151—41no—
350C4×C151—41no—
351C4×C151—41no—
352C4×C151—41no—
353C4×C151—41no—
354C4×C151—41no—
355C4×C151—41no—
356C4×C151#54611yescharacteristic
357C4×C151#55011yescharacteristic
358C4×C151#55311yescharacteristic
359C4×C151#55511yescharacteristic
360C2×C151—42no—
361C2×C151—42no—
362C2×C151—81no—
363C2×C151#236311yescharacteristic
364C2×C151#292911yescharacteristic
365C2×C151#293511yescharacteristic
366C2×C151#296611yescharacteristic
367C2×C151#296811yescharacteristic
368C2×C151#297611yescharacteristic
369C2×C151#297711yescharacteristic
370#23089C15111yesmaximal, characteristic, direct product factor, Sylow
371C151#2308911yescharacteristic, direct product factor, Sylow
372C2×C8×D4C2×C15111yescharacteristic, complemented
373C2×#433C2×C15111yescharacteristic, complemented
374#2392C2×C15111yescharacteristic
375#1955C2×C15111yescharacteristic, complemented
376#1955C2×C15111yescharacteristic, complemented
377#1954C2×C15111yescharacteristic, complemented
378#1939C2×C15111yescharacteristic, complemented
379#1924C2×C15111yescharacteristic, complemented
380#1923C2×C15111yescharacteristic, complemented
381#1869C2×C15111yescharacteristic, complemented
382#1869C2×C15111yescharacteristic, complemented
383#1771C2×C15111yescharacteristic, complemented
384#1752C2×C15111yescharacteristic, complemented
385C8×C22⋊C4C2×C15111yescharacteristic, complemented
386#1750C2×C15111yescharacteristic, complemented
387C23×C8C22×C15111yescharacteristic
388C23×C8C22×C15111yescharacteristic
389C2×C4×D4C22×C15111yescharacteristic
390C2×C4×D4C22×C15111yescharacteristic
391C2×C4×D4C22×C15111yescharacteristic
392C2×#117C22×C15111yescharacteristic
393C8×D4—24no—
394#433—24no—
395C2×C4⋊C8C22×C15111yescharacteristic
396C2×C4⋊C8C22×C15111yescharacteristic
397C2×C4⋊C8C22×C15111yescharacteristic
398C2×C4⋊C8C22×C15111yescharacteristic
399C2×C22⋊C8C22×C15111yescharacteristic
400C2×C22⋊C8C22×C15111yescharacteristic
401C2×C22⋊C8C22×C15111yescharacteristic
402C2×C22⋊C8C22×C15111yescharacteristic
403C2×C22⋊C8C22×C15111yescharacteristic
404C2×C22⋊C8C22×C15111yescharacteristic
405C2×C22⋊C8C22×C15111yescharacteristic
406C2×C22⋊C8C22×C15111yescharacteristic
407C2×C22⋊C8C22×C15111yescharacteristic
408C2×C22⋊C8C22×C15111yescharacteristic
409C2×#97C22×C15111yescharacteristic
410C2×#97C22×C15111yescharacteristic
411C2×#97C22×C15111yescharacteristic
412C2×C4×C8C22×C15111yescharacteristic
413C2×C4×C8C22×C15111yescharacteristic
414C2×C4×C8C22×C15111yescharacteristic
415#398C4×C15111yescharacteristic
416#397C4×C15111yescharacteristic
417#396C4×C15111yescharacteristic
418#396C4×C15111yescharacteristic
419#394C4×C15111yescharacteristic
420#394C4×C15111yescharacteristic
421#394C4×C15111yescharacteristic
422#392C4×C15111yescharacteristic
423C4×C4⋊C4C22×C15111yescharacteristic
424C4×C22⋊C4C22×C15111yescharacteristic
425C4×C22⋊C4C22×C15111yescharacteristic
426#336C22×C15111yescharacteristic
427#336C22×C15111yescharacteristic
428#336C22×C15111yescharacteristic
429#336C22×C15111yescharacteristic
430#336C22×C15111yescharacteristic
431#336C22×C15111yescharacteristic
432C22×D4C2×C4×C15111yescharacteristic
433C22×D4C2×C4×C15111yescharacteristic
434C22×D4C2×C4×C15111yescharacteristic
435C23×C4C23×C15111yescharacteristic
436C23×C4C23×C15111yescharacteristic
437C23×C4C23×C15111yescharacteristic
438C22×C8—22no—
439C22×C8—22no—
440C22×C8—22no—
441C22×C8—22no—
442C22×C8—41no—
443C22×C8—41no—
444C22×C8C23×C15111yescharacteristic
445C22×C8C23×C15111yescharacteristic
446C22×C8C23×C15111yescharacteristic
447C22×C8C23×C15111yescharacteristic
448C22×C8C23×C15111yescharacteristic
449C22×C8C23×C15111yescharacteristic
450C22×C8C23×C15111yescharacteristic
451C22×C8C23×C15111yescharacteristic
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—41no—
458#117—22no—
459#117—22no—
460C2×C4⋊C4C2×C4×C15111yescharacteristic
461C2×C4⋊C4C2×C4×C15111yescharacteristic
462C2×C4⋊C4C2×C4×C15111yescharacteristic
463C2×C4⋊C4C2×C4×C15111yescharacteristic
464C2×C4⋊C4C2×C4×C15111yescharacteristic
465C2×C4⋊C4C2×C4×C15111yescharacteristic
466C2×C4⋊C4C2×C4×C15111yescharacteristic
467C2×C22⋊C4C2×C4×C15111yescharacteristic
468C2×C22⋊C4C2×C4×C15111yescharacteristic
469C2×C22⋊C4C2×C4×C15111yescharacteristic
470C2×C22⋊C4C2×C4×C15111yescharacteristic
471C2×C22⋊C4C2×C4×C15111yescharacteristic
472C2×C22⋊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×C42C23×C15111yescharacteristic
480C2×C42C23×C15111yescharacteristic
481C2×C42C23×C15111yescharacteristic
482C2×C42C23×C15111yescharacteristic
483C4⋊C8—22no—
484C4⋊C8—41no—
485C4⋊C8—41no—
486C4⋊C8D4×C15114yescomplemented
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8—41no—
496C22⋊C8—41no—
497#97—22no—
498#97—22no—
499#97—41no—
500C4×C8—22no—
501C4×C8—22no—
502C4×C8—41no—
503#95C2×C4×C15111yescharacteristic
504#95C2×C4×C15111yescharacteristic
505#95C2×C4×C15111yescharacteristic
506#95C2×C4×C15111yescharacteristic
507#95C2×C4×C15111yescharacteristic
508#95C2×C4×C15111yescharacteristic
509C24C22×C4×C15111yescharacteristic
510C24C22×C4×C15111yescharacteristic
511C24C22×C4×C15111yescharacteristic
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4C22×C4×C15111yescharacteristic
540C22×C4C22×C4×C15111yescharacteristic
541C22×C4C22×C4×C15111yescharacteristic
542C22×C4C22×C4×C15111yescharacteristic
543C22×C4C22×C4×C15111yescharacteristic
544C22×C4C22×C4×C15111yescharacteristic
545C22×C4C22×C4×C15111yescharacteristic
546C22×C4C22×C4×C15111yescharacteristic
547C22×C4C22×C4×C15111yescharacteristic
548C22×C4C22×C4×C15111yescharacteristic
549C22×C4C22×C4×C15111yescharacteristic
550C22×C4C24×C15111yescharacteristic
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—44no—
572C2×C8—44no—
573C2×C8C2×D4×C15112yes—
574C2×C8C2×D4×C15112yes—
575C2×C8#41×C15112yes—
576C2×C8#41×C15112yes—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42C2×D4×C15112yes—
603C42#41×C15112yes—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23#131×C15112yes—
624C23#131×C15112yes—
625C23C23×C4×C15111yescharacteristic
626D4—28no—
627D4—44no—
628D4—44no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
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—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4C4×D4×C15112yes—
672C2×C4C4×D4×C15112yes—
673C2×C4#131×C15112yes—
674C2×C4C22×D4×C15111yescharacteristic
675C2×C4C2×#41×C15111yescharacteristic
676C2×C4C2×#41×C15111yescharacteristic
677C2×C4C2×#41×C15111yescharacteristic
678C2×C4H(5,𝔽2)×C15111yescharacteristic
679C2×C4H(5,𝔽2)×C15111yescharacteristic
680C8—22no—
681C8—22no—
682C8—22no—
683C8—22no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22C2×C4×D4×C15111yescharacteristic
710C22C4×#41×C15111yescharacteristic
711C22#518×C15111yescharacteristic
712C22C2×#131×C15111yescharacteristic
713C22C2×#131×C15111yescharacteristic
714C22C2×#131×C15111yescharacteristic
715C22#568×C15111yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4#546×C15111yescharacteristic
728C4#550×C15111yescharacteristic
729C4#553×C15111yescharacteristic
730C4#555×C15111yescharacteristic
731C2—42no—
732C2—42no—
733C2—81no—
734C2#2363×C15111yescharacteristic
735C2#2929×C15111yescharacteristic
736C2#2935×C15111yescharacteristic
737C2#2966×C15111yescharacteristic
738C2#2968×C15111yescharacteristic
739C2#2976×C15111yescharacteristic
740C2#2977×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC23×C151C23×C4
prime radical#392×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×C8×D4×C151C2semidirect
2. C2×#433×C151C2semidirect
4. #1955×C151C2semidirect
5. #1955×C151C2semidirect
6. #1954×C151C2semidirect
7. #1939×C151C2semidirect
8. #1924×C151C2semidirect
9. #1923×C151C2semidirect
10. #1869×C151C2semidirect
11. #1869×C151C2semidirect
12. #1771×C151C2semidirect
13. #1752×C151C2semidirect
14. C8×C22⋊C4×C151C2semidirect
15. #1750×C151C2semidirect
115. C4⋊C8×C151D4semidirect
370. #23089C151direct (N × H)
371. C151#23089direct (N × H)
372. C2×C8×D4C2×C151semidirect
373. C2×#433C2×C151semidirect
375. #1955C2×C151semidirect
376. #1955C2×C151semidirect
377. #1954C2×C151semidirect
378. #1939C2×C151semidirect
379. #1924C2×C151semidirect
380. #1923C2×C151semidirect
381. #1869C2×C151semidirect
382. #1869C2×C151semidirect
383. #1771C2×C151semidirect
384. #1752C2×C151semidirect
385. C8×C22⋊C4C2×C151semidirect
386. #1750C2×C151semidirect
486. C4⋊C8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D4×C1512
C2×#433×C1512
#2392×C1512
#1955×C1512
#1954×C1512
#1939×C1512
#1924×C1512
#1923×C1512
#1869×C1512
#1771×C1512
#1752×C1512
C8×C22⋊C4×C1512
#1750×C1512
#23089151