Finite Group Databasebeta

← C151×#22994 #50327919

Subgroups — C151×#22994 #50327919

Order 38656.

992 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#436×C151C211yesmaximal, characteristic, complemented
2C2×#436×C151C211yesmaximal, characteristic, complemented
3C2×#435×C151C211yesmaximal, characteristic, complemented
4C2×#424×C151C211yesmaximal, characteristic, complemented
5#2392×C151C211yesmaximal, characteristic
6#1955×C151C211yesmaximal, characteristic, complemented
7#1939×C151C211yesmaximal, characteristic, complemented
8#1924×C151C211yesmaximal, characteristic, complemented
9#1923×C151C211yesmaximal, characteristic, complemented
10#1870×C151C211yesmaximal, characteristic, complemented
11#1869×C151C211yesmaximal, characteristic, complemented
12#1851×C151C211yesmaximal, characteristic, complemented
13#1851×C151C211yesmaximal, characteristic, complemented
14#1771×C151C211yesmaximal, characteristic, complemented
15#1750×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C22×M16×C151C2211yescharacteristic
19C23×C8×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24#436×C151—24no—
25#436×C151—24no—
26#435×C151—24no—
27#424×C151—24no—
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×C4⋊C8×C151C2211yescharacteristic
32C2×C4⋊C8×C151C2211yescharacteristic
33C2×C4⋊C8×C151C2211yescharacteristic
34C2×C22⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×C22⋊C8×C151C2211yescharacteristic
41C2×C22⋊C8×C151C2211yescharacteristic
42C2×#97×C151C2211yescharacteristic
43C2×#97×C151C2211yescharacteristic
44C2×C4×C8×C151C2211yescharacteristic
45C2×C4×C8×C151C2211yescharacteristic
46#398×C151C411yescharacteristic
47#397×C151C411yescharacteristic
48#396×C151C411yescharacteristic
49#396×C151C411yescharacteristic
50#394×C151C411yescharacteristic
51#394×C151C411yescharacteristic
52#394×C151C411yescharacteristic
53#392×C151C411yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C22⋊C4×C151C2211yescharacteristic
56C4×C22⋊C4×C151C2211yescharacteristic
57#336×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×D4×C151C2×C411yescharacteristic
64C22×D4×C151C2×C411yescharacteristic
65C22×D4×C151C2×C411yescharacteristic
66C23×C4×C151C2311yescharacteristic
67C23×C4×C151C2311yescharacteristic
68C23×C4×C151C2311yescharacteristic
69C2×M16×C151—22no—
70C2×M16×C151—22no—
71C2×M16×C151—22no—
72C2×M16×C151—22no—
73C2×M16×C151—22no—
74C2×M16×C151—22no—
75C2×M16×C151—41no—
76C2×M16×C151—41no—
77C2×M16×C151—41no—
78C22×C8×C151—22no—
79C22×C8×C151—22no—
80C22×C8×C151—41no—
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88C22×C8×C151C2311yescharacteristic
89C4×D4×C151—22no—
90C4×D4×C151—22no—
91C4×D4×C151—22no—
92C4×D4×C151—22no—
93C4×D4×C151—22no—
94C4×D4×C151—22no—
95#117×C151—22no—
96#117×C151—22no—
97C2×C4⋊C4×C151C2×C411yescharacteristic
98C2×C4⋊C4×C151C2×C411yescharacteristic
99C2×C4⋊C4×C151C2×C411yescharacteristic
100C2×C4⋊C4×C151C2×C411yescharacteristic
101C2×C4⋊C4×C151C2×C411yescharacteristic
102C2×C4⋊C4×C151C2×C411yescharacteristic
103C2×C4⋊C4×C151C2×C411yescharacteristic
104C2×C22⋊C4×C151C2×C411yescharacteristic
105C2×C22⋊C4×C151C2×C411yescharacteristic
106C2×C22⋊C4×C151C2×C411yescharacteristic
107C2×C22⋊C4×C151C2×C411yescharacteristic
108C2×C22⋊C4×C151C2×C411yescharacteristic
109C2×C22⋊C4×C151C2×C411yescharacteristic
110C2×C22⋊C4×C151C2×C411yescharacteristic
111C2×C22⋊C4×C151C2×C411yescharacteristic
112C2×C22⋊C4×C151C2×C411yescharacteristic
113C2×C22⋊C4×C151C2×C411yescharacteristic
114C2×C22⋊C4×C151C2×C411yescharacteristic
115C2×C22⋊C4×C151C2×C411yescharacteristic
116C2×C42×C151C2311yescharacteristic
117C2×C42×C151C2311yescharacteristic
118C2×C42×C151C2311yescharacteristic
119C2×C42×C151C2311yescharacteristic
120C4⋊C8×C151—22no—
121C4⋊C8×C151—22no—
122C4⋊C8×C151—22no—
123C4⋊C8×C151—22no—
124C4⋊C8×C151—22no—
125C4⋊C8×C151D414yescomplemented
126C22⋊C8×C151—22no—
127C22⋊C8×C151—22no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—22no—
130C22⋊C8×C151—22no—
131C22⋊C8×C151—41no—
132C22⋊C8×C151—41no—
133C22⋊C8×C151D414yescomplemented
134#97×C151—22no—
135#97×C151—22no—
136C4×C8×C151—22no—
137C4×C8×C151—22no—
138#95×C151C2×C411yescharacteristic
139#95×C151C2×C411yescharacteristic
140#95×C151C2×C411yescharacteristic
141#95×C151C2×C411yescharacteristic
142#95×C151C2×C411yescharacteristic
143#95×C151C2×C411yescharacteristic
144C24×C151C22×C411yescharacteristic
145C24×C151C22×C411yescharacteristic
146C24×C151C22×C411yescharacteristic
147C2×D4×C151—22no—
148C2×D4×C151—22no—
149C2×D4×C151—22no—
150C2×D4×C151—22no—
151C2×D4×C151—41no—
152C2×D4×C151—41no—
153C2×D4×C151—41no—
154C2×D4×C151—41no—
155C2×D4×C151—41no—
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×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×C151C22×C411yescharacteristic
180C22×C4×C151C22×C411yescharacteristic
181C22×C4×C151C22×C411yescharacteristic
182C22×C4×C151C22×C411yescharacteristic
183C22×C4×C151C2×D412yes—
184C22×C4×C151#4112yes—
185C22×C4×C151C2411yescharacteristic
186M16×C151—44no—
187M16×C151—44no—
188M16×C151—44no—
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—21no—
209C2×C8×C151—44no—
210C2×C8×C151C2×D412yes—
211C2×C8×C151C2×D412yes—
212C2×C8×C151C2×D412yes—
213C2×C8×C151C2×D412yes—
214C4⋊C4×C151—22no—
215C4⋊C4×C151—22no—
216C4⋊C4×C151—22no—
217C4⋊C4×C151—22no—
218C4⋊C4×C151—22no—
219C4⋊C4×C151—22no—
220C4⋊C4×C151—41no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—22no—
223C22⋊C4×C151—22no—
224C22⋊C4×C151—22no—
225C22⋊C4×C151—22no—
226C22⋊C4×C151—22no—
227C22⋊C4×C151—22no—
228C22⋊C4×C151—22no—
229C22⋊C4×C151—22no—
230C22⋊C4×C151—41no—
231C22⋊C4×C151—41no—
232C22⋊C4×C151—41no—
233C42×C151—21no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151—21no—
237C42×C151—21no—
238C42×C151—21no—
239C42×C151C2×D412yes—
240C42×C151#4112yes—
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×C151—21no—
258C23×C151—21no—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151C4×D412yes—
262C23×C151C23×C411yescharacteristic
263D4×C151—44no—
264D4×C151—44no—
265D4×C151—44no—
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—22no—
275C2×C4×C151—22no—
276C2×C4×C151—22no—
277C2×C4×C151—22no—
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—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
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×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151C4×D412yes—
308C2×C4×C151C4×D412yes—
309C2×C4×C151C4×D412yes—
310C2×C4×C151#13112yes—
311C2×C4×C151C22×D411yescharacteristic
312C2×C4×C151C22×D411yescharacteristic
313C2×C4×C151C2×#4111yescharacteristic
314C2×C4×C151C2×#4111yescharacteristic
315C2×C4×C151H(5,𝔽2)11yescharacteristic
316C2×C4×C1512−1+411yescharacteristic
317C8×C151—22no—
318C8×C151—22no—
319C8×C151—22no—
320C8×C151—22no—
321C8×C151—41no—
322C8×C151—41no—
323C8×C151—41no—
324C8×C151—41no—
325C22×C151—22no—
326C22×C151—22no—
327C22×C151—22no—
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×C151—41no—
339C22×C151—41no—
340C22×C151—41no—
341C22×C151—41no—
342C22×C151—41no—
343C22×C151—41no—
344C22×C151—41no—
345C22×C151—41no—
346C22×C151C2×C4×D411yescharacteristic
347C22×C151C2×C4×D411yescharacteristic
348C22×C151#52011yescharacteristic
349C22×C151C2×#13111yescharacteristic
350C22×C151#56811yescharacteristic
351C22×C151#56811yescharacteristic
352C22×C151#56811yescharacteristic
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—41no—
364C4×C151D4211yescharacteristic
365C4×C151#54711yescharacteristic
366C4×C151#54811yescharacteristic
367C4×C151#55311yescharacteristic
368C2×C151—42no—
369C2×C151—81no—
370C2×C151—81no—
371C2×C151#236111yescharacteristic
372C2×C151#293011yescharacteristic
373C2×C151#293011yescharacteristic
374C2×C151#293311yescharacteristic
375C2×C151#293511yescharacteristic
376C2×C151#299311yescharacteristic
377C2×C151#299511yescharacteristic
378#22994C15111yesmaximal, characteristic, direct product factor, Sylow
379C151#2299411yescharacteristic, direct product factor, Sylow
380C2×#436C2×C15111yescharacteristic, complemented
381C2×#436C2×C15111yescharacteristic, complemented
382C2×#435C2×C15111yescharacteristic, complemented
383C2×#424C2×C15111yescharacteristic, complemented
384#2392C2×C15111yescharacteristic
385#1955C2×C15111yescharacteristic, complemented
386#1939C2×C15111yescharacteristic, complemented
387#1924C2×C15111yescharacteristic, complemented
388#1923C2×C15111yescharacteristic, complemented
389#1870C2×C15111yescharacteristic, complemented
390#1869C2×C15111yescharacteristic, complemented
391#1851C2×C15111yescharacteristic, complemented
392#1851C2×C15111yescharacteristic, complemented
393#1771C2×C15111yescharacteristic, complemented
394#1750C2×C15111yescharacteristic, complemented
395C22×M16C22×C15111yescharacteristic
396C22×M16C22×C15111yescharacteristic
397C22×M16C22×C15111yescharacteristic
398C23×C8C22×C15111yescharacteristic
399C2×C4×D4C22×C15111yescharacteristic
400C2×C4×D4C22×C15111yescharacteristic
401C2×C4×D4C22×C15111yescharacteristic
402C2×#117C22×C15111yescharacteristic
403#436—24no—
404#436—24no—
405#435—24no—
406#424—24no—
407C2×C4⋊C8C22×C15111yescharacteristic
408C2×C4⋊C8C22×C15111yescharacteristic
409C2×C4⋊C8C22×C15111yescharacteristic
410C2×C4⋊C8C22×C15111yescharacteristic
411C2×C4⋊C8C22×C15111yescharacteristic
412C2×C4⋊C8C22×C15111yescharacteristic
413C2×C22⋊C8C22×C15111yescharacteristic
414C2×C22⋊C8C22×C15111yescharacteristic
415C2×C22⋊C8C22×C15111yescharacteristic
416C2×C22⋊C8C22×C15111yescharacteristic
417C2×C22⋊C8C22×C15111yescharacteristic
418C2×C22⋊C8C22×C15111yescharacteristic
419C2×C22⋊C8C22×C15111yescharacteristic
420C2×C22⋊C8C22×C15111yescharacteristic
421C2×#97C22×C15111yescharacteristic
422C2×#97C22×C15111yescharacteristic
423C2×C4×C8C22×C15111yescharacteristic
424C2×C4×C8C22×C15111yescharacteristic
425#398C4×C15111yescharacteristic
426#397C4×C15111yescharacteristic
427#396C4×C15111yescharacteristic
428#396C4×C15111yescharacteristic
429#394C4×C15111yescharacteristic
430#394C4×C15111yescharacteristic
431#394C4×C15111yescharacteristic
432#392C4×C15111yescharacteristic
433C4×C4⋊C4C22×C15111yescharacteristic
434C4×C22⋊C4C22×C15111yescharacteristic
435C4×C22⋊C4C22×C15111yescharacteristic
436#336C22×C15111yescharacteristic
437#336C22×C15111yescharacteristic
438#336C22×C15111yescharacteristic
439#336C22×C15111yescharacteristic
440#336C22×C15111yescharacteristic
441#336C22×C15111yescharacteristic
442C22×D4C2×C4×C15111yescharacteristic
443C22×D4C2×C4×C15111yescharacteristic
444C22×D4C2×C4×C15111yescharacteristic
445C23×C4C23×C15111yescharacteristic
446C23×C4C23×C15111yescharacteristic
447C23×C4C23×C15111yescharacteristic
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—22no—
453C2×M16—22no—
454C2×M16—41no—
455C2×M16—41no—
456C2×M16—41no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8—41no—
460C22×C8C23×C15111yescharacteristic
461C22×C8C23×C15111yescharacteristic
462C22×C8C23×C15111yescharacteristic
463C22×C8C23×C15111yescharacteristic
464C22×C8C23×C15111yescharacteristic
465C22×C8C23×C15111yescharacteristic
466C22×C8C23×C15111yescharacteristic
467C22×C8C23×C15111yescharacteristic
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474#117—22no—
475#117—22no—
476C2×C4⋊C4C2×C4×C15111yescharacteristic
477C2×C4⋊C4C2×C4×C15111yescharacteristic
478C2×C4⋊C4C2×C4×C15111yescharacteristic
479C2×C4⋊C4C2×C4×C15111yescharacteristic
480C2×C4⋊C4C2×C4×C15111yescharacteristic
481C2×C4⋊C4C2×C4×C15111yescharacteristic
482C2×C4⋊C4C2×C4×C15111yescharacteristic
483C2×C22⋊C4C2×C4×C15111yescharacteristic
484C2×C22⋊C4C2×C4×C15111yescharacteristic
485C2×C22⋊C4C2×C4×C15111yescharacteristic
486C2×C22⋊C4C2×C4×C15111yescharacteristic
487C2×C22⋊C4C2×C4×C15111yescharacteristic
488C2×C22⋊C4C2×C4×C15111yescharacteristic
489C2×C22⋊C4C2×C4×C15111yescharacteristic
490C2×C22⋊C4C2×C4×C15111yescharacteristic
491C2×C22⋊C4C2×C4×C15111yescharacteristic
492C2×C22⋊C4C2×C4×C15111yescharacteristic
493C2×C22⋊C4C2×C4×C15111yescharacteristic
494C2×C22⋊C4C2×C4×C15111yescharacteristic
495C2×C42C23×C15111yescharacteristic
496C2×C42C23×C15111yescharacteristic
497C2×C42C23×C15111yescharacteristic
498C2×C42C23×C15111yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8D4×C15114yescomplemented
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—41no—
511C22⋊C8—41no—
512C22⋊C8D4×C15114yescomplemented
513#97—22no—
514#97—22no—
515C4×C8—22no—
516C4×C8—22no—
517#95C2×C4×C15111yescharacteristic
518#95C2×C4×C15111yescharacteristic
519#95C2×C4×C15111yescharacteristic
520#95C2×C4×C15111yescharacteristic
521#95C2×C4×C15111yescharacteristic
522#95C2×C4×C15111yescharacteristic
523C24C22×C4×C15111yescharacteristic
524C24C22×C4×C15111yescharacteristic
525C24C22×C4×C15111yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
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×C4C22×C4×C15111yescharacteristic
552C22×C4C22×C4×C15111yescharacteristic
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×C4C2×D4×C15112yes—
563C22×C4#41×C15112yes—
564C22×C4C24×C15111yescharacteristic
565M16—44no—
566M16—44no—
567M16—44no—
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—21no—
587C2×C8—21no—
588C2×C8—44no—
589C2×C8C2×D4×C15112yes—
590C2×C8C2×D4×C15112yes—
591C2×C8C2×D4×C15112yes—
592C2×C8C2×D4×C15112yes—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—41no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42C2×D4×C15112yes—
619C42#41×C15112yes—
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—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23C4×D4×C15112yes—
641C23C23×C4×C15111yescharacteristic
642D4—44no—
643D4—44no—
644D4—44no—
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—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
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—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4C4×D4×C15112yes—
687C2×C4C4×D4×C15112yes—
688C2×C4C4×D4×C15112yes—
689C2×C4#131×C15112yes—
690C2×C4C22×D4×C15111yescharacteristic
691C2×C4C22×D4×C15111yescharacteristic
692C2×C4C2×#41×C15111yescharacteristic
693C2×C4C2×#41×C15111yescharacteristic
694C2×C4H(5,𝔽2)×C15111yescharacteristic
695C2×C42−1+4×C15111yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C8—41no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
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—
723C22—41no—
724C22—41no—
725C22C2×C4×D4×C15111yescharacteristic
726C22C2×C4×D4×C15111yescharacteristic
727C22#520×C15111yescharacteristic
728C22C2×#131×C15111yescharacteristic
729C22#568×C15111yescharacteristic
730C22#568×C15111yescharacteristic
731C22#568×C15111yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—22no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4D42×C15111yescharacteristic
744C4#547×C15111yescharacteristic
745C4#548×C15111yescharacteristic
746C4#553×C15111yescharacteristic
747C2—42no—
748C2—81no—
749C2—81no—
750C2#2361×C15111yescharacteristic
751C2#2930×C15111yescharacteristic
752C2#2930×C15111yescharacteristic
753C2#2933×C15111yescharacteristic
754C2#2935×C15111yescharacteristic
755C2#2993×C15111yescharacteristic
756C2#2995×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×#436×C151C2semidirect
2. C2×#436×C151C2semidirect
3. C2×#435×C151C2semidirect
4. C2×#424×C151C2semidirect
6. #1955×C151C2semidirect
7. #1939×C151C2semidirect
8. #1924×C151C2semidirect
9. #1923×C151C2semidirect
10. #1870×C151C2semidirect
11. #1869×C151C2semidirect
12. #1851×C151C2semidirect
13. #1851×C151C2semidirect
14. #1771×C151C2semidirect
15. #1750×C151C2semidirect
125. C4⋊C8×C151D4semidirect
133. C22⋊C8×C151D4semidirect
378. #22994C151direct (N × H)
379. C151#22994direct (N × H)
380. C2×#436C2×C151semidirect
381. C2×#436C2×C151semidirect
382. C2×#435C2×C151semidirect
383. C2×#424C2×C151semidirect
385. #1955C2×C151semidirect
386. #1939C2×C151semidirect
387. #1924C2×C151semidirect
388. #1923C2×C151semidirect
389. #1870C2×C151semidirect
390. #1869C2×C151semidirect
391. #1851C2×C151semidirect
392. #1851C2×C151semidirect
393. #1771C2×C151semidirect
394. #1750C2×C151semidirect
504. C4⋊C8D4×C151semidirect
512. C22⋊C8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#436×C1512
C2×#435×C1512
C2×#424×C1512
#2392×C1512
#1955×C1512
#1939×C1512
#1924×C1512
#1923×C1512
#1870×C1512
#1869×C1512
#1851×C1512
#1771×C1512
#1750×C1512
#22994151