Finite Group Databasebeta

← C151×#22557 #50327482

Subgroups — C151×#22557 #50327482

Order 38656.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#432×C151C211yesmaximal, characteristic, complemented
2C2×#408×C151C211yesmaximal, characteristic
3#2297×C151C211yesmaximal, characteristic
4#1924×C151C211yesmaximal, characteristic, complemented
5#1924×C151C211yesmaximal, characteristic, complemented
6#1924×C151C211yesmaximal, characteristic, complemented
7#1923×C151C211yesmaximal, characteristic, complemented
8#1851×C151C211yesmaximal, characteristic, complemented
9#1850×C151C211yesmaximal, characteristic, complemented
10#1817×C151C211yesmaximal, characteristic, complemented
11#1798×C151C211yesmaximal, characteristic, complemented
12#1780×C151C211yesmaximal, characteristic
13#1753×C151C211yesmaximal, characteristic, complemented
14#1752×C151C211yesmaximal, characteristic, complemented
15#1750×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C23×C8×C151C2211yescharacteristic
19C2×#117×C151C2211yescharacteristic
20C22×C42×C151C2211yescharacteristic
21#432×C151—24no—
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×C4⋊C8×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2211yescharacteristic
26#408×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
38C2×#97×C151C2211yescharacteristic
39C2×#97×C151C2211yescharacteristic
40C2×C4×C8×C151C2211yescharacteristic
41#391×C151C411yescharacteristic
42#391×C151C411yescharacteristic
43#390×C151C411yescharacteristic
44#390×C151C411yescharacteristic
45#386×C151C411yescharacteristic
46#386×C151C411yescharacteristic
47#386×C151C411yescharacteristic
48#386×C151C411yescharacteristic
49C4×C22⋊C4×C151C2211yescharacteristic
50C4×C22⋊C4×C151C2211yescharacteristic
51C4×C22⋊C4×C151C2211yescharacteristic
52C4×C22⋊C4×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
61C2×#41×C151—22no—
62C2×#41×C151—22no—
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—41no—
66C2×#41×C151—41no—
67C22×Q8×C151C2×C411yescharacteristic
68C22×D4×C151C2×C411yescharacteristic
69C22×D4×C151C2×C411yescharacteristic
70C22×D4×C151C2×C411yescharacteristic
71C23×C4×C151C2×C411yescharacteristic
72C23×C4×C151C2×C411yescharacteristic
73C23×C4×C151C2311yescharacteristic
74C23×C4×C151C2311yescharacteristic
75C23×C4×C151C2311yescharacteristic
76C2×M16×C151—22no—
77C2×M16×C151—22no—
78C2×M16×C151—41no—
79C22×C8×C151—22no—
80C22×C8×C151—22no—
81C22×C8×C151—41no—
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88C22×C8×C151C2311yescharacteristic
89C22×C8×C151C2311yescharacteristic
90#117×C151—41no—
91#117×C151—41no—
92C2×C4⋊C4×C151C2×C411yescharacteristic
93C2×C4⋊C4×C151C2×C411yescharacteristic
94C2×C22⋊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×C42×C151—22no—
105C2×C42×C151—22no—
106C2×C42×C151C2×C411yescharacteristic
107C2×C42×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—22no—
128#97×C151—41no—
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×C151C22×C411yescharacteristic
139C24×C151C22×C411yescharacteristic
140C24×C151C22×C411yescharacteristic
141#41×C151—44no—
142#41×C151—44no—
143#41×C151—44no—
144#41×C151—44no—
145C2×Q8×C151—22no—
146C2×Q8×C151—22no—
147C2×Q8×C151—41no—
148C2×D4×C151—22no—
149C2×D4×C151—22no—
150C2×D4×C151—22no—
151C2×D4×C151—22no—
152C2×D4×C151—22no—
153C2×D4×C151—22no—
154C2×D4×C151—41no—
155C2×D4×C151—41no—
156C2×D4×C151—41no—
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—22no—
166C22×C4×C151—22no—
167C22×C4×C151—22no—
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×C151—41no—
176C22×C4×C151—41no—
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×C151C22×C411yescharacteristic
187C22×C4×C151C22×C411yescharacteristic
188C22×C4×C151C2×D412yes—
189C22×C4×C151#4112yes—
190C22×C4×C151#4112yes—
191C22×C4×C151#4112yes—
192C22×C4×C151C2411yescharacteristic
193M16×C151—44no—
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×C151—21no—
216C2×C8×C151—44no—
217C2×C8×C151C2×D412yes—
218C2×C8×C151C2×D412yes—
219C4⋊C4×C151—41no—
220C4⋊C4×C151—41no—
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×C151—41no—
228C22⋊C4×C151—41no—
229C22⋊C4×C151—41no—
230C22⋊C4×C151—41no—
231C42×C151—22no—
232C42×C151—22no—
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—21no—
260C23×C151#11712yes—
261C23×C151C4×D412yes—
262C23×C151C23×C411yescharacteristic
263Q8×C151—44no—
264D4×C151—44no—
265D4×C151—44no—
266D4×C151—44no—
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—22no—
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—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—21no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—44no—
306C2×C4×C151—44no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151#11712yes—
312C2×C4×C151C4×D412yes—
313C2×C4×C151#13112yes—
314C2×C4×C151C22×D411yescharacteristic
315C2×C4×C151C2×#4111yescharacteristic
316C2×C4×C151C2×#4111yescharacteristic
317C2×C4×C151C2×#4111yescharacteristic
318C2×C4×C151H(5,𝔽2)11yescharacteristic
319C2×C4×C151H(5,𝔽2)11yescharacteristic
320C8×C151—22no—
321C8×C151—22no—
322C8×C151—41no—
323C8×C151—41no—
324C8×C151—41no—
325C8×C151—41no—
326C8×C151—41no—
327C8×C151—41no—
328C22×C151—22no—
329C22×C151—22no—
330C22×C151—22no—
331C22×C151—22no—
332C22×C151—22no—
333C22×C151—22no—
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×C151—41no—
348C22×C151—41no—
349C22×C151C2×#11711yescharacteristic
350C22×C151C2×C4×D411yescharacteristic
351C22×C151#51811yescharacteristic
352C22×C151C2×#13111yescharacteristic
353C22×C151#56811yescharacteristic
354C22×C151#56811yescharacteristic
355C22×C151#56811yescharacteristic
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—41no—
366C4×C151—41no—
367C4×C151#54611yescharacteristic
368C4×C151#54611yescharacteristic
369C4×C151#55111yescharacteristic
370C4×C151#55111yescharacteristic
371C2×C151—42no—
372C2×C151—42no—
373C2×C151—81no—
374C2×C151#234211yescharacteristic
375C2×C151#292311yescharacteristic
376C2×C151#292511yescharacteristic
377C2×C151#293011yescharacteristic
378C2×C151#293311yescharacteristic
379C2×C151#298011yescharacteristic
380C2×C151#298111yescharacteristic
381#22557C15111yesmaximal, characteristic, direct product factor, Sylow
382C151#2255711yescharacteristic, direct product factor, Sylow
383C2×#432C2×C15111yescharacteristic, complemented
384C2×#408C2×C15111yescharacteristic
385#2297C2×C15111yescharacteristic
386#1924C2×C15111yescharacteristic, complemented
387#1924C2×C15111yescharacteristic, complemented
388#1924C2×C15111yescharacteristic, complemented
389#1923C2×C15111yescharacteristic, complemented
390#1851C2×C15111yescharacteristic, complemented
391#1850C2×C15111yescharacteristic, complemented
392#1817C2×C15111yescharacteristic, complemented
393#1798C2×C15111yescharacteristic, complemented
394#1780C2×C15111yescharacteristic
395#1753C2×C15111yescharacteristic, complemented
396#1752C2×C15111yescharacteristic, complemented
397#1750C2×C15111yescharacteristic, complemented
398C22×#41C22×C15111yescharacteristic
399C22×M16C22×C15111yescharacteristic
400C23×C8C22×C15111yescharacteristic
401C2×#117C22×C15111yescharacteristic
402C22×C42C22×C15111yescharacteristic
403#432—24no—
404C2×C4⋊C8C22×C15111yescharacteristic
405C2×C4⋊C8C22×C15111yescharacteristic
406C2×C4⋊C8C22×C15111yescharacteristic
407C2×C4⋊C8C22×C15111yescharacteristic
408#408—24no—
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×C22⋊C8C22×C15111yescharacteristic
418C2×C22⋊C8C22×C15111yescharacteristic
419C2×#97C22×C15111yescharacteristic
420C2×#97C22×C15111yescharacteristic
421C2×#97C22×C15111yescharacteristic
422C2×C4×C8C22×C15111yescharacteristic
423#391C4×C15111yescharacteristic
424#391C4×C15111yescharacteristic
425#390C4×C15111yescharacteristic
426#390C4×C15111yescharacteristic
427#386C4×C15111yescharacteristic
428#386C4×C15111yescharacteristic
429#386C4×C15111yescharacteristic
430#386C4×C15111yescharacteristic
431C4×C22⋊C4C22×C15111yescharacteristic
432C4×C22⋊C4C22×C15111yescharacteristic
433C4×C22⋊C4C22×C15111yescharacteristic
434C4×C22⋊C4C22×C15111yescharacteristic
435#336C22×C15111yescharacteristic
436#336C22×C15111yescharacteristic
437#336C22×C15111yescharacteristic
438#336C22×C15111yescharacteristic
439#336C22×C15111yescharacteristic
440#336C22×C15111yescharacteristic
441#336C22×C15111yescharacteristic
442#336C22×C15111yescharacteristic
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C22×Q8C2×C4×C15111yescharacteristic
450C22×D4C2×C4×C15111yescharacteristic
451C22×D4C2×C4×C15111yescharacteristic
452C22×D4C2×C4×C15111yescharacteristic
453C23×C4C2×C4×C15111yescharacteristic
454C23×C4C2×C4×C15111yescharacteristic
455C23×C4C23×C15111yescharacteristic
456C23×C4C23×C15111yescharacteristic
457C23×C4C23×C15111yescharacteristic
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—41no—
461C22×C8—22no—
462C22×C8—22no—
463C22×C8—41no—
464C22×C8C23×C15111yescharacteristic
465C22×C8C23×C15111yescharacteristic
466C22×C8C23×C15111yescharacteristic
467C22×C8C23×C15111yescharacteristic
468C22×C8C23×C15111yescharacteristic
469C22×C8C23×C15111yescharacteristic
470C22×C8C23×C15111yescharacteristic
471C22×C8C23×C15111yescharacteristic
472#117—41no—
473#117—41no—
474C2×C4⋊C4C2×C4×C15111yescharacteristic
475C2×C4⋊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×C22⋊C4C2×C4×C15111yescharacteristic
484C2×C22⋊C4C2×C4×C15111yescharacteristic
485C2×C22⋊C4C2×C4×C15111yescharacteristic
486C2×C42—22no—
487C2×C42—22no—
488C2×C42C2×C4×C15111yescharacteristic
489C2×C42C2×C4×C15111yescharacteristic
490C2×C42C23×C15111yescharacteristic
491C2×C42C23×C15111yescharacteristic
492C2×C42C23×C15111yescharacteristic
493C2×C42C23×C15111yescharacteristic
494C4⋊C8—22no—
495C4⋊C8—22no—
496C4⋊C8—41no—
497C4⋊C8—41no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—41no—
506C22⋊C8—41no—
507C22⋊C8D4×C15114yes—
508#97—22no—
509#97—22no—
510#97—41no—
511C4×C8—41no—
512#95C2×C4×C15111yescharacteristic
513#95C2×C4×C15111yescharacteristic
514#95C2×C4×C15111yescharacteristic
515#95C2×C4×C15111yescharacteristic
516#95C2×C4×C15111yescharacteristic
517#95C2×C4×C15111yescharacteristic
518#95C2×C4×C15111yescharacteristic
519#95C2×C4×C15111yescharacteristic
520C24C22×C4×C15111yescharacteristic
521C24C22×C4×C15111yescharacteristic
522C24C22×C4×C15111yescharacteristic
523#41—44no—
524#41—44no—
525#41—44no—
526#41—44no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—41no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
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—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4C22×C4×C15111yescharacteristic
560C22×C4C22×C4×C15111yescharacteristic
561C22×C4C22×C4×C15111yescharacteristic
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×C4C2×D4×C15112yes—
571C22×C4#41×C15112yes—
572C22×C4#41×C15112yes—
573C22×C4#41×C15112yes—
574C22×C4C24×C15111yescharacteristic
575M16—44no—
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—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—44no—
599C2×C8C2×D4×C15112yes—
600C2×C8C2×D4×C15112yes—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C42—22no—
614C42—22no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—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—
640C23—21no—
641C23—21no—
642C23#117×C15112yes—
643C23C4×D4×C15112yes—
644C23C23×C4×C15111yescharacteristic
645Q8—44no—
646D4—44no—
647D4—44no—
648D4—44no—
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—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
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—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—44no—
688C2×C4—44no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4#117×C15112yes—
694C2×C4C4×D4×C15112yes—
695C2×C4#131×C15112yes—
696C2×C4C22×D4×C15111yescharacteristic
697C2×C4C2×#41×C15111yescharacteristic
698C2×C4C2×#41×C15111yescharacteristic
699C2×C4C2×#41×C15111yescharacteristic
700C2×C4H(5,𝔽2)×C15111yescharacteristic
701C2×C4H(5,𝔽2)×C15111yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22C2×#117×C15111yescharacteristic
732C22C2×C4×D4×C15111yescharacteristic
733C22#518×C15111yescharacteristic
734C22C2×#131×C15111yescharacteristic
735C22#568×C15111yescharacteristic
736C22#568×C15111yescharacteristic
737C22#568×C15111yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4#546×C15111yescharacteristic
750C4#546×C15111yescharacteristic
751C4#551×C15111yescharacteristic
752C4#551×C15111yescharacteristic
753C2—42no—
754C2—42no—
755C2—81no—
756C2#2342×C15111yescharacteristic
757C2#2923×C15111yescharacteristic
758C2#2925×C15111yescharacteristic
759C2#2930×C15111yescharacteristic
760C2#2933×C15111yescharacteristic
761C2#2980×C15111yescharacteristic
762C2#2981×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC23×C151C23×C4
prime radicalC22×#41×C151C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#432×C151C2semidirect
4. #1924×C151C2semidirect
5. #1924×C151C2semidirect
6. #1924×C151C2semidirect
7. #1923×C151C2semidirect
8. #1851×C151C2semidirect
9. #1850×C151C2semidirect
10. #1817×C151C2semidirect
11. #1798×C151C2semidirect
13. #1753×C151C2semidirect
14. #1752×C151C2semidirect
15. #1750×C151C2semidirect
381. #22557C151direct (N × H)
382. C151#22557direct (N × H)
383. C2×#432C2×C151semidirect
386. #1924C2×C151semidirect
387. #1924C2×C151semidirect
388. #1924C2×C151semidirect
389. #1923C2×C151semidirect
390. #1851C2×C151semidirect
391. #1850C2×C151semidirect
392. #1817C2×C151semidirect
393. #1798C2×C151semidirect
395. #1753C2×C151semidirect
396. #1752C2×C151semidirect
397. #1750C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#432×C1512
C2×#408×C1512
#2297×C1512
#1924×C1512
#1923×C1512
#1851×C1512
#1850×C1512
#1817×C1512
#1798×C1512
#1780×C1512
#1753×C1512
#1752×C1512
#1750×C1512
#22557151