Finite Group Databasebeta

← C151×#23118 #50328043

Subgroups — C151×#23118 #50328043

Order 38656.

994 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#436×C151C211yesmaximal, characteristic, complemented
2C2×#435×C151C211yesmaximal, characteristic, complemented
3C4×#121×C151C211yesmaximal, characteristic
4#1923×C151C211yesmaximal, characteristic, complemented
5#1923×C151C211yesmaximal, characteristic, complemented
6#1917×C151C211yesmaximal, characteristic, complemented
7#1916×C151C211yesmaximal, characteristic, complemented
8#1870×C151C211yesmaximal, characteristic, complemented
9#1870×C151C211yesmaximal, characteristic, complemented
10#1870×C151C211yesmaximal, characteristic, complemented
11#1869×C151C211yesmaximal, characteristic, complemented
12#1753×C151C211yesmaximal, characteristic, complemented
13C8×C22⋊C4×C151C211yesmaximal, characteristic, complemented
14C4×C22⋊C8×C151C211yesmaximal, characteristic, complemented
15#1728×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C22×M16×C151C2211yescharacteristic
19C23×C8×C151C2211yescharacteristic
20C2×#121×C151C411yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C22×C42×C151C2211yescharacteristic
25#436×C151—24no—
26#435×C151—24no—
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×#97×C151C2211yescharacteristic
38C2×C4×C8×C151C2211yescharacteristic
39C2×C4×C8×C151C2211yescharacteristic
40C2×C4×C8×C151C2211yescharacteristic
41#390×C151C411yescharacteristic
42#389×C151C411yescharacteristic
43#388×C151C411yescharacteristic
44#388×C151C411yescharacteristic
45#386×C151C411yescharacteristic
46#386×C151C411yescharacteristic
47#380×C151C411yescharacteristic
48C4×C4⋊C4×C151C2211yescharacteristic
49C4×C22⋊C4×C151C2211yescharacteristic
50C4×C22⋊C4×C151C2211yescharacteristic
51#336×C151C2211yescharacteristic
52#336×C151C2211yescharacteristic
53#336×C151C2211yescharacteristic
54#336×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—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
89#121×C151—24no—
90C4×D4×C151—22no—
91C4×D4×C151—22no—
92C4×D4×C151—22no—
93C4×D4×C151—22no—
94C4×D4×C151—41no—
95C4×D4×C151—41no—
96C2×C4⋊C4×C151C2×C411yescharacteristic
97C2×C4⋊C4×C151C2×C411yescharacteristic
98C2×C4⋊C4×C151C2×C411yescharacteristic
99C2×C4⋊C4×C151C2×C411yescharacteristic
100C2×C4⋊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×C22⋊C4×C151C2×C411yescharacteristic
109C2×C22⋊C4×C151C2×C411yescharacteristic
110C2×C22⋊C4×C151C2×C411yescharacteristic
111C2×C42×C151—41no—
112C2×C42×C151—41no—
113C2×C42×C151C2×C411yescharacteristic
114C2×C42×C151C2×C411yescharacteristic
115C2×C42×C151C2311yescharacteristic
116C2×C42×C151C2311yescharacteristic
117C2×C42×C151C2311yescharacteristic
118C2×C42×C151C2311yescharacteristic
119C4⋊C8×C151—22no—
120C4⋊C8×C151—22no—
121C22⋊C8×C151—22no—
122C22⋊C8×C151—22no—
123C22⋊C8×C151—22no—
124C22⋊C8×C151—22no—
125C22⋊C8×C151—22no—
126C22⋊C8×C151—41no—
127C22⋊C8×C151—41no—
128C22⋊C8×C151D414yescomplemented
129#97×C151—22no—
130C4×C8×C151—22no—
131C4×C8×C151—41no—
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—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—22no—
156C22×C4×C151—22no—
157C22×C4×C151—22no—
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—41no—
171C22×C4×C151—41no—
172C22×C4×C151—41no—
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×C151C22×C411yescharacteristic
184C22×C4×C151C2×D412yes—
185C22×C4×C151#4112yes—
186C22×C4×C151C2411yescharacteristic
187M16×C151—44no—
188M16×C151—44no—
189M16×C151—44no—
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—21no—
210C2×C8×C151—44no—
211C2×C8×C151C2×D412yes—
212C2×C8×C151C2×D412yes—
213C2×C8×C151#4112yes—
214C2×C8×C151#4112yes—
215C4⋊C4×C151—22no—
216C4⋊C4×C151—22no—
217C4⋊C4×C151—22no—
218C4⋊C4×C151—22no—
219C4⋊C4×C151—41no—
220C22⋊C4×C151—22no—
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—41no—
228C22⋊C4×C151—41no—
229C22⋊C4×C151M1614yescomplemented
230C42×C151—21no—
231C42×C151—21no—
232C42×C151—21no—
233C42×C151—21no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151—21no—
237C42×C151—21no—
238C42×C151—41no—
239C42×C151—41no—
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×C151—21no—
258C23×C151—21no—
259C23×C151C4×D412yes—
260C23×C151C2×M1612yes—
261C23×C151C23×C411yescharacteristic
262D4×C151—44no—
263D4×C151—44no—
264D4×C151—44no—
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—22no—
276C2×C4×C151—22no—
277C2×C4×C151—22no—
278C2×C4×C151—22no—
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—44no—
298C2×C4×C151—44no—
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×C151C2×M1612yes—
309C2×C4×C151C2×M1612yes—
310C2×C4×C151#13112yes—
311C2×C4×C151#13112yes—
312C2×C4×C151C22×D411yescharacteristic
313C2×C4×C151C2×#4111yescharacteristic
314C2×C4×C151C2×#4111yescharacteristic
315C2×C4×C151C2×#4111yescharacteristic
316C2×C4×C151H(5,𝔽2)11yescharacteristic
317C2×C4×C151H(5,𝔽2)11yescharacteristic
318C8×C151—22no—
319C8×C151—22no—
320C8×C151—22no—
321C8×C151—22no—
322C8×C151—41no—
323C8×C151—41no—
324C8×C151—41no—
325C8×C151—41no—
326C22×C151—22no—
327C22×C151—22no—
328C22×C151—22no—
329C22×C151—22no—
330C22×C151—22no—
331C22×C151—22no—
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×C151—41no—
347C22×C151C2×C4×D411yescharacteristic
348C22×C151C4×#4111yescharacteristic
349C22×C151#51811yescharacteristic
350C22×C151C22×M1611yescharacteristic
351C22×C151C2×#13111yescharacteristic
352C22×C151C2×#13111yescharacteristic
353C22×C151#56811yescharacteristic
354C4×C151—22no—
355C4×C151—22no—
356C4×C151—22no—
357C4×C151—22no—
358C4×C151—22no—
359C4×C151—41no—
360C4×C151—41no—
361C4×C151—41no—
362C4×C151—41no—
363C4×C151—41no—
364C4×C151—41no—
365C4×C151#54611yescharacteristic
366C4×C151#54611yescharacteristic
367C4×C151#55311yescharacteristic
368C4×C151#55311yescharacteristic
369C2×C151—42no—
370C2×C151—42no—
371C2×C151—81no—
372C2×C151#236411yescharacteristic
373C2×C151#293111yescharacteristic
374C2×C151D4×M1611yescharacteristic
375C2×C151#296511yescharacteristic
376C2×C151#296911yescharacteristic
377C2×C151#297411yescharacteristic
378C2×C151#297611yescharacteristic
379#23118C15111yesmaximal, characteristic, direct product factor, Sylow
380C151#2311811yescharacteristic, direct product factor, Sylow
381C2×#436C2×C15111yescharacteristic, complemented
382C2×#435C2×C15111yescharacteristic, complemented
383C4×#121C2×C15111yescharacteristic
384#1923C2×C15111yescharacteristic, complemented
385#1923C2×C15111yescharacteristic, complemented
386#1917C2×C15111yescharacteristic, complemented
387#1916C2×C15111yescharacteristic, complemented
388#1870C2×C15111yescharacteristic, complemented
389#1870C2×C15111yescharacteristic, complemented
390#1870C2×C15111yescharacteristic, complemented
391#1869C2×C15111yescharacteristic, complemented
392#1753C2×C15111yescharacteristic, complemented
393C8×C22⋊C4C2×C15111yescharacteristic, complemented
394C4×C22⋊C8C2×C15111yescharacteristic, complemented
395#1728C2×C15111yescharacteristic, complemented
396C22×M16C22×C15111yescharacteristic
397C22×M16C22×C15111yescharacteristic
398C22×M16C22×C15111yescharacteristic
399C23×C8C22×C15111yescharacteristic
400C2×#121C4×C15111yescharacteristic
401C2×C4×D4C22×C15111yescharacteristic
402C2×C4×D4C22×C15111yescharacteristic
403C2×C4×D4C22×C15111yescharacteristic
404C22×C42C22×C15111yescharacteristic
405#436—24no—
406#435—24no—
407C2×C4⋊C8C22×C15111yescharacteristic
408C2×C4⋊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×C4×C8C22×C15111yescharacteristic
419C2×C4×C8C22×C15111yescharacteristic
420C2×C4×C8C22×C15111yescharacteristic
421#390C4×C15111yescharacteristic
422#389C4×C15111yescharacteristic
423#388C4×C15111yescharacteristic
424#388C4×C15111yescharacteristic
425#386C4×C15111yescharacteristic
426#386C4×C15111yescharacteristic
427#380C4×C15111yescharacteristic
428C4×C4⋊C4C22×C15111yescharacteristic
429C4×C22⋊C4C22×C15111yescharacteristic
430C4×C22⋊C4C22×C15111yescharacteristic
431#336C22×C15111yescharacteristic
432#336C22×C15111yescharacteristic
433#336C22×C15111yescharacteristic
434#336C22×C15111yescharacteristic
435#336C22×C15111yescharacteristic
436#336C22×C15111yescharacteristic
437#336C22×C15111yescharacteristic
438#336C22×C15111yescharacteristic
439#336C22×C15111yescharacteristic
440#336C22×C15111yescharacteristic
441C22×D4C2×C4×C15111yescharacteristic
442C22×D4C2×C4×C15111yescharacteristic
443C22×D4C2×C4×C15111yescharacteristic
444C23×C4C2×C4×C15111yescharacteristic
445C23×C4C2×C4×C15111yescharacteristic
446C23×C4C23×C15111yescharacteristic
447C23×C4C23×C15111yescharacteristic
448C23×C4C23×C15111yescharacteristic
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—22no—
453C2×M16—22no—
454C2×M16—22no—
455C2×M16—41no—
456C2×M16—41no—
457C2×M16—41no—
458C22×C8—22no—
459C22×C8—22no—
460C22×C8—41no—
461C22×C8C23×C15111yescharacteristic
462C22×C8C23×C15111yescharacteristic
463C22×C8C23×C15111yescharacteristic
464C22×C8C23×C15111yescharacteristic
465C22×C8C23×C15111yescharacteristic
466C22×C8C23×C15111yescharacteristic
467C22×C8C23×C15111yescharacteristic
468C22×C8C23×C15111yescharacteristic
469#121—24no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—41no—
475C4×D4—41no—
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×C22⋊C4C2×C4×C15111yescharacteristic
482C2×C22⋊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×C42—41no—
492C2×C42—41no—
493C2×C42C2×C4×C15111yescharacteristic
494C2×C42C2×C4×C15111yescharacteristic
495C2×C42C23×C15111yescharacteristic
496C2×C42C23×C15111yescharacteristic
497C2×C42C23×C15111yescharacteristic
498C2×C42C23×C15111yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—41no—
507C22⋊C8—41no—
508C22⋊C8D4×C15114yescomplemented
509#97—22no—
510C4×C8—22no—
511C4×C8—41no—
512C4×C8—41no—
513#95C2×C4×C15111yescharacteristic
514#95C2×C4×C15111yescharacteristic
515#95C2×C4×C15111yescharacteristic
516#95C2×C4×C15111yescharacteristic
517#95C2×C4×C15111yescharacteristic
518#95C2×C4×C15111yescharacteristic
519C24C22×C4×C15111yescharacteristic
520C24C22×C4×C15111yescharacteristic
521C24C22×C4×C15111yescharacteristic
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—41no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
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—41no—
551C22×C4—41no—
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×C4C2×D4×C15112yes—
565C22×C4#41×C15112yes—
566C22×C4C24×C15111yescharacteristic
567M16—44no—
568M16—44no—
569M16—44no—
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—21no—
589C2×C8—21no—
590C2×C8—44no—
591C2×C8C2×D4×C15112yes—
592C2×C8C2×D4×C15112yes—
593C2×C8#41×C15112yes—
594C2×C8#41×C15112yes—
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—41no—
608C22⋊C4—41no—
609C22⋊C4M16×C15114yescomplemented
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—41no—
619C42—41no—
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—
639C23C4×D4×C15112yes—
640C23C2×M16×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—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
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—44no—
678C2×C4—44no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4C4×D4×C15112yes—
688C2×C4C2×M16×C15112yes—
689C2×C4C2×M16×C15112yes—
690C2×C4#131×C15112yes—
691C2×C4#131×C15112yes—
692C2×C4C22×D4×C15111yescharacteristic
693C2×C4C2×#41×C15111yescharacteristic
694C2×C4C2×#41×C15111yescharacteristic
695C2×C4C2×#41×C15111yescharacteristic
696C2×C4H(5,𝔽2)×C15111yescharacteristic
697C2×C4H(5,𝔽2)×C15111yescharacteristic
698C8—22no—
699C8—22no—
700C8—22no—
701C8—22no—
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
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—
725C22—41no—
726C22—41no—
727C22C2×C4×D4×C15111yescharacteristic
728C22C4×#41×C15111yescharacteristic
729C22#518×C15111yescharacteristic
730C22C22×M16×C15111yescharacteristic
731C22C2×#131×C15111yescharacteristic
732C22C2×#131×C15111yescharacteristic
733C22#568×C15111yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4#546×C15111yescharacteristic
746C4#546×C15111yescharacteristic
747C4#553×C15111yescharacteristic
748C4#553×C15111yescharacteristic
749C2—42no—
750C2—42no—
751C2—81no—
752C2#2364×C15111yescharacteristic
753C2#2931×C15111yescharacteristic
754C2D4×M16×C15111yescharacteristic
755C2#2965×C15111yescharacteristic
756C2#2969×C15111yescharacteristic
757C2#2974×C15111yescharacteristic
758C2#2976×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×#436×C151C2semidirect
2. C2×#435×C151C2semidirect
4. #1923×C151C2semidirect
5. #1923×C151C2semidirect
6. #1917×C151C2semidirect
7. #1916×C151C2semidirect
8. #1870×C151C2semidirect
9. #1870×C151C2semidirect
10. #1870×C151C2semidirect
11. #1869×C151C2semidirect
12. #1753×C151C2semidirect
13. C8×C22⋊C4×C151C2semidirect
14. C4×C22⋊C8×C151C2semidirect
15. #1728×C151C2semidirect
128. C22⋊C8×C151D4semidirect
229. C22⋊C4×C151M16semidirect
379. #23118C151direct (N × H)
380. C151#23118direct (N × H)
381. C2×#436C2×C151semidirect
382. C2×#435C2×C151semidirect
384. #1923C2×C151semidirect
385. #1923C2×C151semidirect
386. #1917C2×C151semidirect
387. #1916C2×C151semidirect
388. #1870C2×C151semidirect
389. #1870C2×C151semidirect
390. #1870C2×C151semidirect
391. #1869C2×C151semidirect
392. #1753C2×C151semidirect
393. C8×C22⋊C4C2×C151semidirect
394. C4×C22⋊C8C2×C151semidirect
395. #1728C2×C151semidirect
508. C22⋊C8D4×C151semidirect
609. C22⋊C4M16×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
C4×#121×C1512
#1923×C1512
#1917×C1512
#1916×C1512
#1870×C1512
#1869×C1512
#1753×C1512
C8×C22⋊C4×C1512
C4×C22⋊C8×C1512
#1728×C1512
#23118151