Finite Group Databasebeta

← C151×#22559 #50327484

Subgroups — C151×#22559 #50327484

Order 38656.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#433×C151C211yesmaximal, characteristic, complemented
2C2×#407×C151C211yesmaximal, characteristic
3#2280×C151C211yesmaximal, characteristic
4#1924×C151C211yesmaximal, characteristic, complemented
5#1924×C151C211yesmaximal, characteristic, complemented
6#1923×C151C211yesmaximal, characteristic, complemented
7#1923×C151C211yesmaximal, characteristic, complemented
8#1851×C151C211yesmaximal, characteristic, complemented
9#1851×C151C211yesmaximal, characteristic, complemented
10#1818×C151C211yesmaximal, characteristic, complemented
11#1798×C151C211yesmaximal, characteristic, complemented
12#1779×C151C211yesmaximal, characteristic
13#1753×C151C211yesmaximal, characteristic, complemented
14#1753×C151C211yesmaximal, characteristic, complemented
15#1750×C151C211yesmaximal, characteristic, complemented
16C24×C4×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C22×M16×C151C2211yescharacteristic
19C2×#117×C151C2211yescharacteristic
20C2×#117×C151C2211yescharacteristic
21#433×C151—24no—
22C2×C4⋊C8×C151C2211yescharacteristic, complemented
23C2×C4⋊C8×C151C2211yescharacteristic, complemented
24C2×C4⋊C8×C151C2211yescharacteristic, complemented
25C2×C4⋊C8×C151C2211yescharacteristic, complemented
26#407×C151—24no—
27C2×C22⋊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×#97×C151C2211yescharacteristic, complemented
38C2×#97×C151C2211yescharacteristic, complemented
39C2×C4×C8×C151C2211yescharacteristic, complemented
40C2×C4×C8×C151C2211yescharacteristic, complemented
41#381×C151C411yescharacteristic
42#381×C151C411yescharacteristic
43#380×C151C411yescharacteristic
44#380×C151C411yescharacteristic
45#380×C151C411yescharacteristic
46#380×C151C411yescharacteristic
47#379×C151C411yescharacteristic
48#379×C151C411yescharacteristic
49C4×C22⋊C4×C151C2211yescharacteristic
50C4×C22⋊C4×C151C2211yescharacteristic
51C4×C22⋊C4×C151C2211yescharacteristic
52C4×C22⋊C4×C151C2211yescharacteristic
53#336×C151C2211yescharacteristic, complemented
54#336×C151C2211yescharacteristic, complemented
55#336×C151C2211yescharacteristic, complemented
56#336×C151C2211yescharacteristic, complemented
57#336×C151C2211yescharacteristic, complemented
58#336×C151C2211yescharacteristic, complemented
59#336×C151C2211yescharacteristic, complemented
60#336×C151C2211yescharacteristic, complemented
61C25×C151C2×C411yescharacteristic
62C23×C4×C151—22no—
63C23×C4×C151—22no—
64C23×C4×C151—22no—
65C23×C4×C151—22no—
66C23×C4×C151—41no—
67C23×C4×C151—41no—
68C23×C4×C151C2×C411yescharacteristic
69C23×C4×C151C2×C411yescharacteristic
70C23×C4×C151C2×C411yescharacteristic
71C23×C4×C151C2311yescharacteristic
72C23×C4×C151C2311yescharacteristic
73C23×C4×C151C2311yescharacteristic
74C2×M16×C151—22no—
75C2×M16×C151—22no—
76C2×M16×C151—22no—
77C2×M16×C151—22no—
78C2×M16×C151—41no—
79C2×M16×C151—41no—
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88#117×C151—22no—
89#117×C151—22no—
90#117×C151—41no—
91#117×C151—41no—
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—22no—
114C4⋊C8×C151—41no—
115C4⋊C8×C151—41no—
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—41no—
124C22⋊C8×C151—41no—
125C22⋊C8×C151D414yes—
126#97×C151—22no—
127#97×C151—41no—
128C4×C8×C151—22no—
129C4×C8×C151—41no—
130#95×C151C2×C411yescharacteristic
131#95×C151C2×C411yescharacteristic
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×C151—22no—
139C24×C151—22no—
140C24×C151—22no—
141C24×C151—41no—
142C24×C151—41no—
143C24×C151—41no—
144C24×C151—41no—
145C24×C151C22×C411yescharacteristic
146C24×C151C22×C411yescharacteristic
147C24×C151C22×C411yescharacteristic
148C22×C4×C151—21no—
149C22×C4×C151—21no—
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—22no—
157C22×C4×C151—22no—
158C22×C4×C151—22no—
159C22×C4×C151—22no—
160C22×C4×C151—22no—
161C22×C4×C151—22no—
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—41no—
169C22×C4×C151—41no—
170C22×C4×C151—41no—
171C22×C4×C151—44no—
172C22×C4×C151—44no—
173C22×C4×C151—44no—
174C22×C4×C151—44no—
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×C151C2×D412yes—
187C22×C4×C151#4112yes—
188C22×C4×C151#4112yes—
189C22×C4×C151#4112yes—
190C22×C4×C151C2411yescharacteristic
191M16×C151—44no—
192M16×C151—44no—
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—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151C2×D412yes—
216C2×C8×C151C2×D412yes—
217C4⋊C4×C151—22no—
218C4⋊C4×C151—22no—
219C4⋊C4×C151—41no—
220C4⋊C4×C151—41no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—22no—
223C22⋊C4×C151—22no—
224C22⋊C4×C151—22no—
225C22⋊C4×C151—41no—
226C22⋊C4×C151—41no—
227C22⋊C4×C151—41no—
228C22⋊C4×C151—41no—
229C22⋊C4×C151—41no—
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×C151—21no—
240C42×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×C151—44no—
260C23×C151—44no—
261C23×C151—44no—
262C23×C151—44no—
263C23×C151—44no—
264C23×C151—44no—
265C23×C151—44no—
266C23×C151#11712yes—
267C23×C151C4×D412yes—
268C23×C151#13112yes—
269C23×C151C23×C411yescharacteristic
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—22no—
279C2×C4×C151—22no—
280C2×C4×C151—22no—
281C2×C4×C151—22no—
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—21no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—44no—
310C2×C4×C151—44no—
311C2×C4×C151—44no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151#11712yes—
317C2×C4×C151C4×D412yes—
318C2×C4×C151C22×D411yescharacteristic
319C2×C4×C151C2×#4111yescharacteristic
320C2×C4×C151C2×#4111yescharacteristic
321C2×C4×C151C2×#4111yescharacteristic
322C2×C4×C151H(5,𝔽2)11yescharacteristic
323C2×C4×C151H(5,𝔽2)11yescharacteristic
324C8×C151—22no—
325C8×C151—22no—
326C8×C151—41no—
327C8×C151—41no—
328C8×C151—41no—
329C8×C151—41no—
330C8×C151—41no—
331C8×C151—41no—
332C22×C151—22no—
333C22×C151—22no—
334C22×C151—22no—
335C22×C151—22no—
336C22×C151—22no—
337C22×C151—22no—
338C22×C151—22no—
339C22×C151—22no—
340C22×C151—22no—
341C22×C151—416no—
342C22×C151—41no—
343C22×C151—41no—
344C22×C151—41no—
345C22×C151—41no—
346C22×C151—41no—
347C22×C151—41no—
348C22×C151—41no—
349C22×C151—41no—
350C22×C151—41no—
351C22×C151—41no—
352C22×C151—41no—
353C22×C151—41no—
354C22×C151C2×#11711yescharacteristic
355C22×C151C2×C4×D411yescharacteristic
356C22×C151#51811yescharacteristic
357C22×C151C2×#13111yescharacteristic
358C22×C151#56811yescharacteristic
359C22×C151#56811yescharacteristic
360C22×C151#56811yescharacteristic
361C4×C151—22no—
362C4×C151—22no—
363C4×C151—41no—
364C4×C151—41no—
365C4×C151—41no—
366C4×C151—41no—
367C4×C151—41no—
368C4×C151—41no—
369C4×C151—41no—
370C4×C151—41no—
371C4×C151—41no—
372C4×C151#54611yescharacteristic
373C4×C151#54611yescharacteristic
374C4×C151#55111yescharacteristic
375C4×C151#55111yescharacteristic
376C2×C151—42no—
377C2×C151—42no—
378C2×C151—42no—
379C2×C151#234211yescharacteristic
380C2×C151#292111yescharacteristic
381C2×C151#292411yescharacteristic
382C2×C151#293011yescharacteristic
383C2×C151#293311yescharacteristic
384C2×C151#297611yescharacteristic
385C2×C151#297811yescharacteristic
386#22559C15111yesmaximal, characteristic, direct product factor, Sylow
387C151#2255911yescharacteristic, direct product factor, Sylow
388C2×#433C2×C15111yescharacteristic, complemented
389C2×#407C2×C15111yescharacteristic
390#2280C2×C15111yescharacteristic
391#1924C2×C15111yescharacteristic, complemented
392#1924C2×C15111yescharacteristic, complemented
393#1923C2×C15111yescharacteristic, complemented
394#1923C2×C15111yescharacteristic, complemented
395#1851C2×C15111yescharacteristic, complemented
396#1851C2×C15111yescharacteristic, complemented
397#1818C2×C15111yescharacteristic, complemented
398#1798C2×C15111yescharacteristic, complemented
399#1779C2×C15111yescharacteristic
400#1753C2×C15111yescharacteristic, complemented
401#1753C2×C15111yescharacteristic, complemented
402#1750C2×C15111yescharacteristic, complemented
403C24×C4C22×C15111yescharacteristic
404C22×M16C22×C15111yescharacteristic
405C22×M16C22×C15111yescharacteristic
406C2×#117C22×C15111yescharacteristic
407C2×#117C22×C15111yescharacteristic
408#433—24no—
409C2×C4⋊C8C22×C15111yescharacteristic, complemented
410C2×C4⋊C8C22×C15111yescharacteristic, complemented
411C2×C4⋊C8C22×C15111yescharacteristic, complemented
412C2×C4⋊C8C22×C15111yescharacteristic, complemented
413#407—24no—
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×C22⋊C8C22×C15111yescharacteristic
422C2×C22⋊C8C22×C15111yescharacteristic
423C2×C22⋊C8C22×C15111yescharacteristic
424C2×#97C22×C15111yescharacteristic, complemented
425C2×#97C22×C15111yescharacteristic, complemented
426C2×C4×C8C22×C15111yescharacteristic, complemented
427C2×C4×C8C22×C15111yescharacteristic, complemented
428#381C4×C15111yescharacteristic
429#381C4×C15111yescharacteristic
430#380C4×C15111yescharacteristic
431#380C4×C15111yescharacteristic
432#380C4×C15111yescharacteristic
433#380C4×C15111yescharacteristic
434#379C4×C15111yescharacteristic
435#379C4×C15111yescharacteristic
436C4×C22⋊C4C22×C15111yescharacteristic
437C4×C22⋊C4C22×C15111yescharacteristic
438C4×C22⋊C4C22×C15111yescharacteristic
439C4×C22⋊C4C22×C15111yescharacteristic
440#336C22×C15111yescharacteristic, complemented
441#336C22×C15111yescharacteristic, complemented
442#336C22×C15111yescharacteristic, complemented
443#336C22×C15111yescharacteristic, complemented
444#336C22×C15111yescharacteristic, complemented
445#336C22×C15111yescharacteristic, complemented
446#336C22×C15111yescharacteristic, complemented
447#336C22×C15111yescharacteristic, complemented
448C25C2×C4×C15111yescharacteristic
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—41no—
454C23×C4—41no—
455C23×C4C2×C4×C15111yescharacteristic
456C23×C4C2×C4×C15111yescharacteristic
457C23×C4C2×C4×C15111yescharacteristic
458C23×C4C23×C15111yescharacteristic
459C23×C4C23×C15111yescharacteristic
460C23×C4C23×C15111yescharacteristic
461C2×M16—22no—
462C2×M16—22no—
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—41no—
466C2×M16—41no—
467C22×C8C23×C15111yescharacteristic
468C22×C8C23×C15111yescharacteristic
469C22×C8C23×C15111yescharacteristic
470C22×C8C23×C15111yescharacteristic
471C22×C8C23×C15111yescharacteristic
472C22×C8C23×C15111yescharacteristic
473C22×C8C23×C15111yescharacteristic
474C22×C8C23×C15111yescharacteristic
475#117—22no—
476#117—22no—
477#117—41no—
478#117—41no—
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—41no—
502C4⋊C8—41no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—41no—
511C22⋊C8—41no—
512C22⋊C8D4×C15114yes—
513#97—22no—
514#97—41no—
515C4×C8—22no—
516C4×C8—41no—
517#95C2×C4×C15111yescharacteristic
518#95C2×C4×C15111yescharacteristic
519#95C2×C4×C15111yescharacteristic
520#95C2×C4×C15111yescharacteristic
521#95C2×C4×C15111yescharacteristic
522#95C2×C4×C15111yescharacteristic
523#95C2×C4×C15111yescharacteristic
524#95C2×C4×C15111yescharacteristic
525C24—22no—
526C24—22no—
527C24—22no—
528C24—41no—
529C24—41no—
530C24—41no—
531C24—41no—
532C24C22×C4×C15111yescharacteristic
533C24C22×C4×C15111yescharacteristic
534C24C22×C4×C15111yescharacteristic
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—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4C22×C4×C15111yescharacteristic
563C22×C4C22×C4×C15111yescharacteristic
564C22×C4C22×C4×C15111yescharacteristic
565C22×C4C22×C4×C15111yescharacteristic
566C22×C4C22×C4×C15111yescharacteristic
567C22×C4C22×C4×C15111yescharacteristic
568C22×C4C22×C4×C15111yescharacteristic
569C22×C4C22×C4×C15111yescharacteristic
570C22×C4C22×C4×C15111yescharacteristic
571C22×C4C22×C4×C15111yescharacteristic
572C22×C4C22×C4×C15111yescharacteristic
573C22×C4C2×D4×C15112yes—
574C22×C4#41×C15112yes—
575C22×C4#41×C15112yes—
576C22×C4#41×C15112yes—
577C22×C4C24×C15111yescharacteristic
578M16—44no—
579M16—44no—
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—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8C2×D4×C15112yes—
603C2×C8C2×D4×C15112yes—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C22⋊C4—41no—
617C22⋊C4—41no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—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—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23#117×C15112yes—
654C23C4×D4×C15112yes—
655C23#131×C15112yes—
656C23C23×C4×C15111yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
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—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4#117×C15112yes—
704C2×C4C4×D4×C15112yes—
705C2×C4C22×D4×C15111yescharacteristic
706C2×C4C2×#41×C15111yescharacteristic
707C2×C4C2×#41×C15111yescharacteristic
708C2×C4C2×#41×C15111yescharacteristic
709C2×C4H(5,𝔽2)×C15111yescharacteristic
710C2×C4H(5,𝔽2)×C15111yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—41no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—416no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22C2×#117×C15111yescharacteristic
742C22C2×C4×D4×C15111yescharacteristic
743C22#518×C15111yescharacteristic
744C22C2×#131×C15111yescharacteristic
745C22#568×C15111yescharacteristic
746C22#568×C15111yescharacteristic
747C22#568×C15111yescharacteristic
748C4—22no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4#546×C15111yescharacteristic
760C4#546×C15111yescharacteristic
761C4#551×C15111yescharacteristic
762C4#551×C15111yescharacteristic
763C2—42no—
764C2—42no—
765C2—42no—
766C2#2342×C15111yescharacteristic
767C2#2921×C15111yescharacteristic
768C2#2924×C15111yescharacteristic
769C2#2930×C15111yescharacteristic
770C2#2933×C15111yescharacteristic
771C2#2976×C15111yescharacteristic
772C2#2978×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC23×C151C23×C4
prime radicalC25×C151C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#433×C151C2semidirect
4. #1924×C151C2semidirect
5. #1924×C151C2semidirect
6. #1923×C151C2semidirect
7. #1923×C151C2semidirect
8. #1851×C151C2semidirect
9. #1851×C151C2semidirect
10. #1818×C151C2semidirect
11. #1798×C151C2semidirect
13. #1753×C151C2semidirect
14. #1753×C151C2semidirect
15. #1750×C151C2semidirect
22. C2×C4⋊C8×C151C22semidirect
23. C2×C4⋊C8×C151C22semidirect
24. C2×C4⋊C8×C151C22semidirect
25. C2×C4⋊C8×C151C22semidirect
37. C2×#97×C151C22semidirect
38. C2×#97×C151C22semidirect
39. C2×C4×C8×C151C22semidirect
40. C2×C4×C8×C151C22semidirect
53. #336×C151C22semidirect
54. #336×C151C22semidirect
55. #336×C151C22semidirect
56. #336×C151C22semidirect
57. #336×C151C22semidirect
58. #336×C151C22semidirect
59. #336×C151C22semidirect
60. #336×C151C22semidirect
386. #22559C151direct (N × H)
387. C151#22559direct (N × H)
388. C2×#433C2×C151semidirect
391. #1924C2×C151semidirect
392. #1924C2×C151semidirect
393. #1923C2×C151semidirect
394. #1923C2×C151semidirect
395. #1851C2×C151semidirect
396. #1851C2×C151semidirect
397. #1818C2×C151semidirect
398. #1798C2×C151semidirect
400. #1753C2×C151semidirect
401. #1753C2×C151semidirect
402. #1750C2×C151semidirect
409. C2×C4⋊C8C22×C151semidirect
410. C2×C4⋊C8C22×C151semidirect
411. C2×C4⋊C8C22×C151semidirect
412. C2×C4⋊C8C22×C151semidirect
424. C2×#97C22×C151semidirect
425. C2×#97C22×C151semidirect
426. C2×C4×C8C22×C151semidirect
427. C2×C4×C8C22×C151semidirect
440. #336C22×C151semidirect
441. #336C22×C151semidirect
442. #336C22×C151semidirect
443. #336C22×C151semidirect
444. #336C22×C151semidirect
445. #336C22×C151semidirect
446. #336C22×C151semidirect
447. #336C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#433×C1512
C2×#407×C1512
#2280×C1512
#1924×C1512
#1923×C1512
#1851×C1512
#1818×C1512
#1798×C1512
#1779×C1512
#1753×C1512
#1750×C1512
#22559151